Factor f64conv-submodule.c into code and data
diff --git a/internal/cgen/base/f64conv-submodule-code.c b/internal/cgen/base/f64conv-submodule-code.c
new file mode 100644
index 0000000..2a352ee
--- /dev/null
+++ b/internal/cgen/base/f64conv-submodule-code.c
@@ -0,0 +1,1719 @@
+// After editing this file, run "go generate" in the parent directory.
+
+// Copyright 2020 The Wuffs Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// ---------------- IEEE 754 Floating Point
+
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE 2047
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION 800
+
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL is the largest N
+// such that ((10 << N) < (1 << 64)).
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL 60
+
+// wuffs_base__private_implementation__high_prec_dec (abbreviated as HPD) is a
+// fixed precision floating point decimal number, augmented with ±infinity
+// values, but it cannot represent NaN (Not a Number).
+//
+// "High precision" means that the mantissa holds 800 decimal digits. 800 is
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION.
+//
+// An HPD isn't for general purpose arithmetic, only for conversions to and
+// from IEEE 754 double-precision floating point, where the largest and
+// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.
+// HPD exponents above +2047 mean infinity, below -2047 mean zero. The ±2047
+// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION and
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+//
+// digits[.. num_digits] are the number's digits in big-endian order. The
+// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'
+// is the ASCII value 0x37.
+//
+// decimal_point is the index (within digits) of the decimal point. It may be
+// negative or be larger than num_digits, in which case the explicit digits are
+// padded with implicit zeroes.
+//
+// For example, if num_digits is 3 and digits is "\x07\x08\x09":
+// - A decimal_point of -2 means ".00789"
+// - A decimal_point of -1 means ".0789"
+// - A decimal_point of +0 means ".789"
+// - A decimal_point of +1 means "7.89"
+// - A decimal_point of +2 means "78.9"
+// - A decimal_point of +3 means "789."
+// - A decimal_point of +4 means "7890."
+// - A decimal_point of +5 means "78900."
+//
+// As above, a decimal_point higher than +2047 means that the overall value is
+// infinity, lower than -2047 means zero.
+//
+// negative is a sign bit. An HPD can distinguish positive and negative zero.
+//
+// truncated is whether there are more than
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION digits, and at
+// least one of those extra digits are non-zero. The existence of long-tail
+// digits can affect rounding.
+//
+// The "all fields are zero" value is valid, and represents the number +0.
+typedef struct {
+ uint32_t num_digits;
+ int32_t decimal_point;
+ bool negative;
+ bool truncated;
+ uint8_t digits[WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION];
+} wuffs_base__private_implementation__high_prec_dec;
+
+// wuffs_base__private_implementation__high_prec_dec__trim trims trailing
+// zeroes from the h->digits[.. h->num_digits] slice. They have no benefit,
+// since we explicitly track h->decimal_point.
+//
+// Preconditions:
+// - h is non-NULL.
+static inline void //
+wuffs_base__private_implementation__high_prec_dec__trim(
+ wuffs_base__private_implementation__high_prec_dec* h) {
+ while ((h->num_digits > 0) && (h->digits[h->num_digits - 1] == 0)) {
+ h->num_digits--;
+ }
+}
+
+// wuffs_base__private_implementation__high_prec_dec__assign sets h to
+// represent the number x.
+//
+// Preconditions:
+// - h is non-NULL.
+static void //
+wuffs_base__private_implementation__high_prec_dec__assign(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint64_t x,
+ bool negative) {
+ uint32_t n = 0;
+
+ // Set h->digits.
+ if (x > 0) {
+ // Calculate the digits, working right-to-left. After we determine n (how
+ // many digits there are), copy from buf to h->digits.
+ //
+ // UINT64_MAX, 18446744073709551615, is 20 digits long. It can be faster to
+ // copy a constant number of bytes than a variable number (20 instead of
+ // n). Make buf large enough (and start writing to it from the middle) so
+ // that can we always copy 20 bytes: the slice buf[(20-n) .. (40-n)].
+ uint8_t buf[40] = {0};
+ uint8_t* ptr = &buf[20];
+ do {
+ uint64_t remaining = x / 10;
+ x -= remaining * 10;
+ ptr--;
+ *ptr = (uint8_t)x;
+ n++;
+ x = remaining;
+ } while (x > 0);
+ memcpy(h->digits, ptr, 20);
+ }
+
+ // Set h's other fields.
+ h->num_digits = n;
+ h->decimal_point = (int32_t)n;
+ h->negative = negative;
+ h->truncated = false;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static wuffs_base__status //
+wuffs_base__private_implementation__high_prec_dec__parse(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ wuffs_base__slice_u8 s) {
+ if (!h) {
+ return wuffs_base__make_status(wuffs_base__error__bad_receiver);
+ }
+ h->num_digits = 0;
+ h->decimal_point = 0;
+ h->negative = false;
+ h->truncated = false;
+
+ uint8_t* p = s.ptr;
+ uint8_t* q = s.ptr + s.len;
+
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+
+ // Parse sign.
+ do {
+ if (*p == '+') {
+ p++;
+ } else if (*p == '-') {
+ h->negative = true;
+ p++;
+ } else {
+ break;
+ }
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+ } while (0);
+
+ // Parse digits, up to (and including) a '.', 'E' or 'e'. Examples for each
+ // limb in this if-else chain:
+ // - "0.789"
+ // - "1002.789"
+ // - ".789"
+ // - Other (invalid input).
+ uint32_t nd = 0;
+ int32_t dp = 0;
+ bool no_digits_before_separator = false;
+ if ('0' == *p) {
+ p++;
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ goto after_sep;
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+ } else if (('0' < *p) && (*p <= '9')) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ dp = (int32_t)nd;
+ p++;
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if (('0' <= *p) && (*p <= '9')) {
+ if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ dp = (int32_t)nd;
+ } else if ('0' != *p) {
+ // Long-tail non-zeroes set the truncated bit.
+ h->truncated = true;
+ }
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ goto after_sep;
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ no_digits_before_separator = true;
+
+ } else {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+
+after_sep:
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if ('0' == *p) {
+ if (nd == 0) {
+ // Track leading zeroes implicitly.
+ dp--;
+ } else if (nd <
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ }
+ } else if (('0' < *p) && (*p <= '9')) {
+ if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ } else {
+ // Long-tail non-zeroes set the truncated bit.
+ h->truncated = true;
+ }
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+after_exp:
+ do {
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+
+ int32_t exp_sign = +1;
+ if (*p == '+') {
+ p++;
+ } else if (*p == '-') {
+ exp_sign = -1;
+ p++;
+ }
+
+ int32_t exp = 0;
+ const int32_t exp_large =
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE +
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
+ bool saw_exp_digits = false;
+ for (; p < q; p++) {
+ if (*p == '_') {
+ // No-op.
+ } else if (('0' <= *p) && (*p <= '9')) {
+ saw_exp_digits = true;
+ if (exp < exp_large) {
+ exp = (10 * exp) + ((int32_t)(*p - '0'));
+ }
+ } else {
+ break;
+ }
+ }
+ if (!saw_exp_digits) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ dp += exp_sign * exp;
+ } while (0);
+
+after_all:
+ if (p != q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ h->num_digits = nd;
+ if (nd == 0) {
+ if (no_digits_before_separator) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ h->decimal_point = 0;
+ } else if (dp <
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ h->decimal_point =
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE - 1;
+ } else if (dp >
+ +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ h->decimal_point =
+ +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE + 1;
+ } else {
+ h->decimal_point = dp;
+ }
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+ return wuffs_base__make_status(NULL);
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
+// returns the number of additional decimal digits when left-shifting by shift.
+//
+// See below for preconditions.
+static uint32_t //
+wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ // Masking with 0x3F should be unnecessary (assuming the preconditions) but
+ // it's cheap and ensures that we don't overflow the
+ // wuffs_base__private_implementation__hpd_left_shift array.
+ shift &= 63;
+
+ uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];
+ uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];
+ uint32_t num_new_digits = x_a >> 11;
+ uint32_t pow5_a = 0x7FF & x_a;
+ uint32_t pow5_b = 0x7FF & x_b;
+
+ const uint8_t* pow5 =
+ &wuffs_base__private_implementation__powers_of_5[pow5_a];
+ uint32_t i = 0;
+ uint32_t n = pow5_b - pow5_a;
+ for (; i < n; i++) {
+ if (i >= h->num_digits) {
+ return num_new_digits - 1;
+ } else if (h->digits[i] == pow5[i]) {
+ continue;
+ } else if (h->digits[i] < pow5[i]) {
+ return num_new_digits - 1;
+ } else {
+ return num_new_digits;
+ }
+ }
+ return num_new_digits;
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__rounded_integer returns
+// the integral (non-fractional) part of h, provided that it is 18 or fewer
+// decimal digits. For 19 or more digits, it returns UINT64_MAX. Note that:
+// - (1 << 53) is 9007199254740992, which has 16 decimal digits.
+// - (1 << 56) is 72057594037927936, which has 17 decimal digits.
+// - (1 << 59) is 576460752303423488, which has 18 decimal digits.
+// - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
+// and that IEEE 754 double precision has 52 mantissa bits.
+//
+// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.
+//
+// h's negative bit is ignored: rounding -8.6 returns 9.
+//
+// See below for preconditions.
+static uint64_t //
+wuffs_base__private_implementation__high_prec_dec__rounded_integer(
+ wuffs_base__private_implementation__high_prec_dec* h) {
+ if ((h->num_digits == 0) || (h->decimal_point < 0)) {
+ return 0;
+ } else if (h->decimal_point > 18) {
+ return UINT64_MAX;
+ }
+
+ uint32_t dp = (uint32_t)(h->decimal_point);
+ uint64_t n = 0;
+ uint32_t i = 0;
+ for (; i < dp; i++) {
+ n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);
+ }
+
+ bool round_up = false;
+ if (dp < h->num_digits) {
+ round_up = h->digits[dp] >= 5;
+ if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {
+ // We are exactly halfway. If we're truncated, round up, otherwise round
+ // to even.
+ round_up = h->truncated || //
+ ((dp > 0) && (1 & h->digits[dp - 1]));
+ }
+ }
+ if (round_up) {
+ n++;
+ }
+
+ return n;
+}
+
+// wuffs_base__private_implementation__high_prec_dec__small_xshift shifts h's
+// number (where 'x' is 'l' or 'r' for left or right) by a small shift value.
+//
+// Preconditions:
+// - h is non-NULL.
+// - h->decimal_point is "not extreme".
+// - shift is non-zero.
+// - shift is "a small shift".
+//
+// "Not extreme" means within
+// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+//
+// "A small shift" means not more than
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
+//
+// wuffs_base__private_implementation__high_prec_dec__rounded_integer and
+// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
+// have the same preconditions.
+//
+// wuffs_base__private_implementation__high_prec_dec__lshift keeps the first
+// two preconditions but not the last two. Its shift argument is signed and
+// does not need to be "small": zero is a no-op, positive means left shift and
+// negative means right shift.
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ if (h->num_digits == 0) {
+ return;
+ }
+ uint32_t num_new_digits =
+ wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
+ h, shift);
+ uint32_t rx = h->num_digits - 1; // Read index.
+ uint32_t wx = h->num_digits - 1 + num_new_digits; // Write index.
+ uint64_t n = 0;
+
+ // Repeat: pick up a digit, put down a digit, right to left.
+ while (((int32_t)rx) >= 0) {
+ n += ((uint64_t)(h->digits[rx])) << shift;
+ uint64_t quo = n / 10;
+ uint64_t rem = n - (10 * quo);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx] = (uint8_t)rem;
+ } else if (rem > 0) {
+ h->truncated = true;
+ }
+ n = quo;
+ wx--;
+ rx--;
+ }
+
+ // Put down leading digits, right to left.
+ while (n > 0) {
+ uint64_t quo = n / 10;
+ uint64_t rem = n - (10 * quo);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx] = (uint8_t)rem;
+ } else if (rem > 0) {
+ h->truncated = true;
+ }
+ n = quo;
+ wx--;
+ }
+
+ // Finish.
+ h->num_digits += num_new_digits;
+ if (h->num_digits >
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->num_digits = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
+ }
+ h->decimal_point += (int32_t)num_new_digits;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ uint32_t rx = 0; // Read index.
+ uint32_t wx = 0; // Write index.
+ uint64_t n = 0;
+
+ // Pick up enough leading digits to cover the first shift.
+ while ((n >> shift) == 0) {
+ if (rx < h->num_digits) {
+ // Read a digit.
+ n = (10 * n) + h->digits[rx++];
+ } else if (n == 0) {
+ // h's number used to be zero and remains zero.
+ return;
+ } else {
+ // Read sufficient implicit trailing zeroes.
+ while ((n >> shift) == 0) {
+ n = 10 * n;
+ rx++;
+ }
+ break;
+ }
+ }
+ h->decimal_point -= ((int32_t)(rx - 1));
+ if (h->decimal_point <
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ // After the shift, h's number is effectively zero.
+ h->num_digits = 0;
+ h->decimal_point = 0;
+ h->negative = false;
+ h->truncated = false;
+ return;
+ }
+
+ // Repeat: pick up a digit, put down a digit, left to right.
+ uint64_t mask = (((uint64_t)(1)) << shift) - 1;
+ while (rx < h->num_digits) {
+ uint8_t new_digit = ((uint8_t)(n >> shift));
+ n = (10 * (n & mask)) + h->digits[rx++];
+ h->digits[wx++] = new_digit;
+ }
+
+ // Put down trailing digits, left to right.
+ while (n > 0) {
+ uint8_t new_digit = ((uint8_t)(n >> shift));
+ n = 10 * (n & mask);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx++] = new_digit;
+ } else if (new_digit > 0) {
+ h->truncated = true;
+ }
+ }
+
+ // Finish.
+ h->num_digits = wx;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__lshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t shift) {
+ if (shift > 0) {
+ while (shift > +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
+ shift -= WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ h, ((uint32_t)(+shift)));
+ } else if (shift < 0) {
+ while (shift < -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
+ shift += WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ h, ((uint32_t)(-shift)));
+ }
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__round_etc rounds h's
+// number. For those functions that take an n argument, rounding produces at
+// most n digits (which is not necessarily at most n decimal places). Negative
+// n values are ignored, as well as any n greater than or equal to h's number
+// of digits. The etc__round_just_enough function implicitly chooses an n to
+// implement WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION.
+//
+// Preconditions:
+// - h is non-NULL.
+// - h->decimal_point is "not extreme".
+//
+// "Not extreme" means within
+// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_down(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+ h->num_digits = (uint32_t)(n);
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_up(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+
+ for (n--; n >= 0; n--) {
+ if (h->digits[n] < 9) {
+ h->digits[n]++;
+ h->num_digits = (uint32_t)(n + 1);
+ return;
+ }
+ }
+
+ // The number is all 9s. Change to a single 1 and adjust the decimal point.
+ h->digits[0] = 1;
+ h->num_digits = 1;
+ h->decimal_point++;
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+ bool up = h->digits[n] >= 5;
+ if ((h->digits[n] == 5) && ((n + 1) == ((int32_t)(h->num_digits)))) {
+ up = h->truncated || //
+ ((n > 0) && ((h->digits[n - 1] & 1) != 0));
+ }
+
+ if (up) {
+ wuffs_base__private_implementation__high_prec_dec__round_up(h, n);
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_down(h, n);
+ }
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_just_enough(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t exp2,
+ uint64_t mantissa) {
+ // The magic numbers 52 and 53 in this function are because IEEE 754 double
+ // precision has 52 mantissa bits.
+ //
+ // Let f be the floating point number represented by exp2 and mantissa (and
+ // also the number in h): the number (mantissa * (2 ** (exp2 - 52))).
+ //
+ // If f is zero or a small integer, we can return early.
+ if ((mantissa == 0) ||
+ ((exp2 < 53) && (h->decimal_point >= ((int32_t)(h->num_digits))))) {
+ return;
+ }
+
+ // The smallest normal f has an exp2 of -1022 and a mantissa of (1 << 52).
+ // Subnormal numbers have the same exp2 but a smaller mantissa.
+ static const int32_t min_incl_normal_exp2 = -1022;
+ static const uint64_t min_incl_normal_mantissa = 0x0010000000000000ul;
+
+ // Compute lower and upper bounds such that any number between them (possibly
+ // inclusive) will round to f. First, the lower bound. Our number f is:
+ // ((mantissa + 0) * (2 ** ( exp2 - 52)))
+ //
+ // The next lowest floating point number is:
+ // ((mantissa - 1) * (2 ** ( exp2 - 52)))
+ // unless (mantissa - 1) drops the (1 << 52) bit and exp2 is not the
+ // min_incl_normal_exp2. Either way, call it:
+ // ((l_mantissa) * (2 ** (l_exp2 - 52)))
+ //
+ // The lower bound is halfway between them (noting that 52 became 53):
+ // (((2 * l_mantissa) + 1) * (2 ** (l_exp2 - 53)))
+ int32_t l_exp2 = exp2;
+ uint64_t l_mantissa = mantissa - 1;
+ if ((exp2 > min_incl_normal_exp2) && (mantissa <= min_incl_normal_mantissa)) {
+ l_exp2 = exp2 - 1;
+ l_mantissa = (2 * mantissa) - 1;
+ }
+ wuffs_base__private_implementation__high_prec_dec lower;
+ wuffs_base__private_implementation__high_prec_dec__assign(
+ &lower, (2 * l_mantissa) + 1, false);
+ wuffs_base__private_implementation__high_prec_dec__lshift(&lower,
+ l_exp2 - 53);
+
+ // Next, the upper bound. Our number f is:
+ // ((mantissa + 0) * (2 ** (exp2 - 52)))
+ //
+ // The next highest floating point number is:
+ // ((mantissa + 1) * (2 ** (exp2 - 52)))
+ //
+ // The upper bound is halfway between them (noting that 52 became 53):
+ // (((2 * mantissa) + 1) * (2 ** (exp2 - 53)))
+ wuffs_base__private_implementation__high_prec_dec upper;
+ wuffs_base__private_implementation__high_prec_dec__assign(
+ &upper, (2 * mantissa) + 1, false);
+ wuffs_base__private_implementation__high_prec_dec__lshift(&upper, exp2 - 53);
+
+ // The lower and upper bounds are possible outputs only if the original
+ // mantissa is even, so that IEEE round-to-even would round to the original
+ // mantissa and not its neighbors.
+ bool inclusive = (mantissa & 1) == 0;
+
+ // As we walk the digits, we want to know whether rounding up would fall
+ // within the upper bound. This is tracked by upper_delta:
+ // - When -1, the digits of h and upper are the same so far.
+ // - When +0, we saw a difference of 1 between h and upper on a previous
+ // digit and subsequently only 9s for h and 0s for upper. Thus, rounding
+ // up may fall outside of the bound if !inclusive.
+ // - When +1, the difference is greater than 1 and we know that rounding up
+ // falls within the bound.
+ //
+ // This is a state machine with three states. The numerical value for each
+ // state (-1, +0 or +1) isn't important, other than their order.
+ int upper_delta = -1;
+
+ // We can now figure out the shortest number of digits required. Walk the
+ // digits until h has distinguished itself from lower or upper.
+ //
+ // The zi and zd variables are indexes and digits, for z in l (lower), h (the
+ // number) and u (upper).
+ //
+ // The lower, h and upper numbers may have their decimal points at different
+ // places. In this case, upper is the longest, so we iterate ui starting from
+ // 0 and iterate li and hi starting from either 0 or -1.
+ int32_t ui = 0;
+ for (;; ui++) {
+ // Calculate hd, the middle number's digit.
+ int32_t hi = ui - upper.decimal_point + h->decimal_point;
+ if (hi >= ((int32_t)(h->num_digits))) {
+ break;
+ }
+ uint8_t hd = (((uint32_t)hi) < h->num_digits) ? h->digits[hi] : 0;
+
+ // Calculate ld, the lower bound's digit.
+ int32_t li = ui - upper.decimal_point + lower.decimal_point;
+ uint8_t ld = (((uint32_t)li) < lower.num_digits) ? lower.digits[li] : 0;
+
+ // We can round down (truncate) if lower has a different digit than h or if
+ // lower is inclusive and is exactly the result of rounding down (i.e. we
+ // have reached the final digit of lower).
+ bool can_round_down =
+ (ld != hd) || //
+ (inclusive && ((li + 1) == ((int32_t)(lower.num_digits))));
+
+ // Calculate ud, the upper bound's digit, and update upper_delta.
+ uint8_t ud = (((uint32_t)ui) < upper.num_digits) ? upper.digits[ui] : 0;
+ if (upper_delta < 0) {
+ if ((hd + 1) < ud) {
+ // For example:
+ // h = 12345???
+ // upper = 12347???
+ upper_delta = +1;
+ } else if (hd != ud) {
+ // For example:
+ // h = 12345???
+ // upper = 12346???
+ upper_delta = +0;
+ }
+ } else if (upper_delta == 0) {
+ if ((hd != 9) || (ud != 0)) {
+ // For example:
+ // h = 1234598?
+ // upper = 1234600?
+ upper_delta = +1;
+ }
+ }
+
+ // We can round up if upper has a different digit than h and either upper
+ // is inclusive or upper is bigger than the result of rounding up.
+ bool can_round_up =
+ (upper_delta > 0) || //
+ ((upper_delta == 0) && //
+ (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));
+
+ // If we can round either way, round to nearest. If we can round only one
+ // way, do it. If we can't round, continue the loop.
+ if (can_round_down) {
+ if (can_round_up) {
+ wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ h, hi + 1);
+ return;
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_down(h,
+ hi + 1);
+ return;
+ }
+ } else {
+ if (can_round_up) {
+ wuffs_base__private_implementation__high_prec_dec__round_up(h, hi + 1);
+ return;
+ }
+ }
+ }
+}
+
+// --------
+
+// wuffs_base__private_implementation__parse_number_f64_eisel produces the IEEE
+// 754 double-precision value for an exact mantissa and base-10 exponent.
+//
+// On success, it returns a non-negative int64_t such that the low 63 bits hold
+// the 11-bit exponent and 52-bit mantissa.
+//
+// On failure, it returns a negative value.
+//
+// The algorithm is based on an original idea by Michael Eisel. See
+// https://lemire.me/blog/2020/03/10/fast-float-parsing-in-practice/
+//
+// Preconditions:
+// - man is non-zero.
+// - exp10 is in the range -326 ..= 310, the same range of the
+// wuffs_base__private_implementation__powers_of_10 array.
+static int64_t //
+wuffs_base__private_implementation__parse_number_f64_eisel(uint64_t man,
+ int32_t exp10) {
+ // Look up the (possibly truncated) base-2 representation of (10 ** exp10).
+ // The look-up table was constructed so that it is already normalized: the
+ // table entry's mantissa's MSB (most significant bit) is on.
+ const uint32_t* po10 =
+ &wuffs_base__private_implementation__powers_of_10[5 * (exp10 + 326)];
+
+ // Normalize the man argument. The (man != 0) precondition means that a
+ // non-zero bit exists.
+ uint32_t clz = wuffs_base__count_leading_zeroes_u64(man);
+ man <<= clz;
+
+ // Calculate the return value's base-2 exponent. We might tweak it by ±1
+ // later, but its initial value comes from the look-up table and clz.
+ uint64_t ret_exp2 = ((uint64_t)po10[4]) - ((uint64_t)clz);
+
+ // Multiply the two mantissas. Normalization means that both mantissas are at
+ // least (1<<63), so the 128-bit product must be at least (1<<126). The high
+ // 64 bits of the product, x.hi, must therefore be at least (1<<62).
+ //
+ // As a consequence, x.hi has either 0 or 1 leading zeroes. Shifting x.hi
+ // right by either 9 or 10 bits (depending on x.hi's MSB) will therefore
+ // leave the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on.
+ wuffs_base__multiply_u64__output x = wuffs_base__multiply_u64(
+ man, ((uint64_t)po10[2]) | (((uint64_t)po10[3]) << 32));
+
+ // Before we shift right by at least 9 bits, recall that the look-up table
+ // entry was possibly truncated. We have so far only calculated a lower bound
+ // for the product (man * e), where e is (10 ** exp10). The upper bound would
+ // add a further (man * 1) to the 128-bit product, which overflows the lower
+ // 64-bit limb if ((x.lo + man) < man).
+ //
+ // If overflow occurs, that adds 1 to x.hi. Since we're about to shift right
+ // by at least 9 bits, that carried 1 can be ignored unless the higher 64-bit
+ // limb's low 9 bits are all on.
+ if (((x.hi & 0x1FF) == 0x1FF) && ((x.lo + man) < man)) {
+ // Refine our calculation of (man * e). Before, our approximation of e used
+ // a "low resolution" 64-bit mantissa. Now use a "high resolution" 128-bit
+ // mantissa. We've already calculated x = (man * bits_0_to_63_incl_of_e).
+ // Now calculate y = (man * bits_64_to_127_incl_of_e).
+ wuffs_base__multiply_u64__output y = wuffs_base__multiply_u64(
+ man, ((uint64_t)po10[0]) | (((uint64_t)po10[1]) << 32));
+
+ // Merge the 128-bit x and 128-bit y, which overlap by 64 bits, to
+ // calculate the 192-bit product of the 64-bit man by the 128-bit e.
+ // As we exit this if-block, we only care about the high 128 bits
+ // (merged_hi and merged_lo) of that 192-bit product.
+ uint64_t merged_hi = x.hi;
+ uint64_t merged_lo = x.lo + y.hi;
+ if (merged_lo < x.lo) {
+ merged_hi++; // Carry the overflow bit.
+ }
+
+ // The "high resolution" approximation of e is still a lower bound. Once
+ // again, see if the upper bound is large enough to produce a different
+ // result. This time, if it does, give up instead of reaching for an even
+ // more precise approximation to e.
+ //
+ // This three-part check is similar to the two-part check that guarded the
+ // if block that we're now in, but it has an extra term for the middle 64
+ // bits (checking that adding 1 to merged_lo would overflow).
+ if (((merged_hi & 0x1FF) == 0x1FF) && ((merged_lo + 1) == 0) &&
+ (y.lo + man < man)) {
+ return -1;
+ }
+
+ // Replace the 128-bit x with merged.
+ x.hi = merged_hi;
+ x.lo = merged_lo;
+ }
+
+ // As mentioned above, shifting x.hi right by either 9 or 10 bits will leave
+ // the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on. If the
+ // MSB (before shifting) was on, adjust ret_exp2 for the larger shift.
+ //
+ // Having bit 53 on (and higher bits off) means that ret_mantissa is a 54-bit
+ // number.
+ uint64_t msb = x.hi >> 63;
+ uint64_t ret_mantissa = x.hi >> (msb + 9);
+ ret_exp2 -= 1 ^ msb;
+
+ // IEEE 754 rounds to-nearest with ties rounded to-even. Rounding to-even can
+ // be tricky. If we're half-way between two exactly representable numbers
+ // (x's low 73 bits are zero and the next 2 bits that matter are "01"), give
+ // up instead of trying to pick the winner.
+ //
+ // Technically, we could tighten the condition by changing "73" to "73 or 74,
+ // depending on msb", but a flat "73" is simpler.
+ if ((x.lo == 0) && ((x.hi & 0x1FF) == 0) && ((ret_mantissa & 3) == 1)) {
+ return -1;
+ }
+
+ // If we're not halfway then it's rounding to-nearest. Starting with a 54-bit
+ // number, carry the lowest bit (bit 0) up if it's on. Regardless of whether
+ // it was on or off, shifting right by one then produces a 53-bit number. If
+ // carrying up overflowed, shift again.
+ ret_mantissa += ret_mantissa & 1;
+ ret_mantissa >>= 1;
+ if ((ret_mantissa >> 53) > 0) {
+ ret_mantissa >>= 1;
+ ret_exp2++;
+ }
+
+ // Starting with a 53-bit number, IEEE 754 double-precision normal numbers
+ // have an implicit mantissa bit. Mask that away and keep the low 52 bits.
+ ret_mantissa &= 0x000FFFFFFFFFFFFF;
+
+ // IEEE 754 double-precision floating point has 11 exponent bits. All off (0)
+ // means subnormal numbers. All on (2047) means infinity or NaN.
+ if ((ret_exp2 <= 0) || (2047 <= ret_exp2)) {
+ return -1;
+ }
+
+ // Pack the bits and return.
+ return ((int64_t)(ret_mantissa | (ret_exp2 << 52)));
+}
+
+// --------
+
+static wuffs_base__result_f64 //
+wuffs_base__parse_number_f64_special(wuffs_base__slice_u8 s,
+ const char* fallback_status_repr) {
+ do {
+ uint8_t* p = s.ptr;
+ uint8_t* q = s.ptr + s.len;
+
+ for (; (p < q) && (*p == '_'); p++) {
+ }
+ if (p >= q) {
+ goto fallback;
+ }
+
+ // Parse sign.
+ bool negative = false;
+ do {
+ if (*p == '+') {
+ p++;
+ } else if (*p == '-') {
+ negative = true;
+ p++;
+ } else {
+ break;
+ }
+ for (; (p < q) && (*p == '_'); p++) {
+ }
+ } while (0);
+ if (p >= q) {
+ goto fallback;
+ }
+
+ bool nan = false;
+ switch (p[0]) {
+ case 'I':
+ case 'i':
+ if (((q - p) < 3) || //
+ ((p[1] != 'N') && (p[1] != 'n')) || //
+ ((p[2] != 'F') && (p[2] != 'f'))) {
+ goto fallback;
+ }
+ p += 3;
+
+ if ((p >= q) || (*p == '_')) {
+ break;
+ } else if (((q - p) < 5) || //
+ ((p[0] != 'I') && (p[0] != 'i')) || //
+ ((p[1] != 'N') && (p[1] != 'n')) || //
+ ((p[2] != 'I') && (p[2] != 'i')) || //
+ ((p[3] != 'T') && (p[3] != 't')) || //
+ ((p[4] != 'Y') && (p[4] != 'y'))) {
+ goto fallback;
+ }
+ p += 5;
+
+ if ((p >= q) || (*p == '_')) {
+ break;
+ }
+ goto fallback;
+
+ case 'N':
+ case 'n':
+ if (((q - p) < 3) || //
+ ((p[1] != 'A') && (p[1] != 'a')) || //
+ ((p[2] != 'N') && (p[2] != 'n'))) {
+ goto fallback;
+ }
+ p += 3;
+
+ if ((p >= q) || (*p == '_')) {
+ nan = true;
+ break;
+ }
+ goto fallback;
+
+ default:
+ goto fallback;
+ }
+
+ // Finish.
+ for (; (p < q) && (*p == '_'); p++) {
+ }
+ if (p != q) {
+ goto fallback;
+ }
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
+ (nan ? 0x7FFFFFFFFFFFFFFF : 0x7FF0000000000000) |
+ (negative ? 0x8000000000000000 : 0));
+ return ret;
+ } while (0);
+
+fallback:
+ do {
+ wuffs_base__result_f64 ret;
+ ret.status.repr = fallback_status_repr;
+ ret.value = 0;
+ return ret;
+ } while (0);
+}
+
+WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //
+wuffs_base__private_implementation__parse_number_f64__fallback(
+ wuffs_base__private_implementation__high_prec_dec* h) {
+ do {
+ // powers converts decimal powers of 10 to binary powers of 2. For example,
+ // (10000 >> 13) is 1. It stops before the elements exceed 60, also known
+ // as WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
+ static const uint32_t num_powers = 19;
+ static const uint8_t powers[19] = {
+ 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //
+ 33, 36, 39, 43, 46, 49, 53, 56, 59, //
+ };
+
+ // Handle zero and obvious extremes. The largest and smallest positive
+ // finite f64 values are approximately 1.8e+308 and 4.9e-324.
+ if ((h->num_digits == 0) || (h->decimal_point < -326)) {
+ goto zero;
+ } else if (h->decimal_point > 310) {
+ goto infinity;
+ }
+
+ // Try the fast Eisel algorithm again. Calculating the (man, exp10) pair
+ // from the high_prec_dec h is more correct but slower than the approach
+ // taken in wuffs_base__parse_number_f64. The latter is optimized for the
+ // common cases (e.g. assuming no underscores or a leading '+' sign) rather
+ // than the full set of cases allowed by the Wuffs API.
+ if (h->num_digits <= 19) {
+ uint64_t man = 0;
+ uint32_t i;
+ for (i = 0; i < h->num_digits; i++) {
+ man = (10 * man) + h->digits[i];
+ }
+ int32_t exp10 = h->decimal_point - ((int32_t)(h->num_digits));
+ if ((man != 0) && (-326 <= exp10) && (exp10 <= 310)) {
+ int64_t r = wuffs_base__private_implementation__parse_number_f64_eisel(
+ man, exp10);
+ if (r >= 0) {
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
+ ((uint64_t)r) | (((uint64_t)(h->negative)) << 63));
+ return ret;
+ }
+ }
+ }
+
+ // Scale by powers of 2 until we're in the range [½ .. 1], which gives us
+ // our exponent (in base-2). First we shift right, possibly a little too
+ // far, ending with a value certainly below 1 and possibly below ½...
+ const int32_t f64_bias = -1023;
+ int32_t exp2 = 0;
+ while (h->decimal_point > 0) {
+ uint32_t n = (uint32_t)(+h->decimal_point);
+ uint32_t shift =
+ (n < num_powers)
+ ? powers[n]
+ : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(h, shift);
+ if (h->decimal_point <
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ goto zero;
+ }
+ exp2 += (int32_t)shift;
+ }
+ // ...then we shift left, putting us in [½ .. 1].
+ while (h->decimal_point <= 0) {
+ uint32_t shift;
+ if (h->decimal_point == 0) {
+ if (h->digits[0] >= 5) {
+ break;
+ }
+ shift = (h->digits[0] <= 2) ? 2 : 1;
+ } else {
+ uint32_t n = (uint32_t)(-h->decimal_point);
+ shift = (n < num_powers)
+ ? powers[n]
+ : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(h, shift);
+ if (h->decimal_point >
+ +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ goto infinity;
+ }
+ exp2 -= (int32_t)shift;
+ }
+
+ // We're in the range [½ .. 1] but f64 uses [1 .. 2].
+ exp2--;
+
+ // The minimum normal exponent is (f64_bias + 1).
+ while ((f64_bias + 1) > exp2) {
+ uint32_t n = (uint32_t)((f64_bias + 1) - exp2);
+ if (n > WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
+ n = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(h, n);
+ exp2 += (int32_t)n;
+ }
+
+ // Check for overflow.
+ if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.
+ goto infinity;
+ }
+
+ // Extract 53 bits for the mantissa (in base-2).
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(h, 53);
+ uint64_t man2 =
+ wuffs_base__private_implementation__high_prec_dec__rounded_integer(h);
+
+ // Rounding might have added one bit. If so, shift and re-check overflow.
+ if ((man2 >> 53) != 0) {
+ man2 >>= 1;
+ exp2++;
+ if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.
+ goto infinity;
+ }
+ }
+
+ // Handle subnormal numbers.
+ if ((man2 >> 52) == 0) {
+ exp2 = f64_bias;
+ }
+
+ // Pack the bits and return.
+ uint64_t exp2_bits =
+ (uint64_t)((exp2 - f64_bias) & 0x07FF); // (1 << 11) - 1.
+ uint64_t bits = (man2 & 0x000FFFFFFFFFFFFF) | // (1 << 52) - 1.
+ (exp2_bits << 52) | //
+ (h->negative ? 0x8000000000000000 : 0); // (1 << 63).
+
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
+ return ret;
+ } while (0);
+
+zero:
+ do {
+ uint64_t bits = h->negative ? 0x8000000000000000 : 0;
+
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
+ return ret;
+ } while (0);
+
+infinity:
+ do {
+ uint64_t bits = h->negative ? 0xFFF0000000000000 : 0x7FF0000000000000;
+
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
+ return ret;
+ } while (0);
+}
+
+static inline bool //
+wuffs_base__private_implementation__is_decimal_digit(uint8_t c) {
+ return ('0' <= c) && (c <= '9');
+}
+
+WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //
+wuffs_base__parse_number_f64(wuffs_base__slice_u8 s, uint32_t options) {
+ // In practice, almost all "dd.ddddE±xxx" numbers can be represented
+ // losslessly by a uint64_t mantissa "dddddd" and an int32_t base-10
+ // exponent, adjusting "xxx" for the position (if present) of the decimal
+ // separator '.' or ','.
+ //
+ // This (u64 man, i32 exp10) data structure is superficially similar to the
+ // "Do It Yourself Floating Point" type from Loitsch (†), but the exponent
+ // here is base-10, not base-2.
+ //
+ // If s's number fits in a (man, exp10), parse that pair with the Eisel
+ // algorithm. If not, or if Eisel fails, parsing s with the fallback
+ // algorithm is slower but comprehensive.
+ //
+ // † "Printing Floating-Point Numbers Quickly and Accurately with Integers"
+ // (https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf).
+ // Florian Loitsch is also the primary contributor to
+ // https://github.com/google/double-conversion
+ do {
+ // Calculating that (man, exp10) pair needs to stay within s's bounds.
+ // Provided that s isn't extremely long, work on a NUL-terminated copy of
+ // s's contents. The NUL byte isn't a valid part of "±dd.ddddE±xxx".
+ //
+ // As the pointer p walks the contents, it's faster to repeatedly check "is
+ // *p a valid digit" than "is p within bounds and *p a valid digit".
+ if (s.len >= 256) {
+ goto fallback;
+ }
+ uint8_t z[256];
+ memcpy(&z[0], s.ptr, s.len);
+ z[s.len] = 0;
+ const uint8_t* p = &z[0];
+
+ // Look for a leading minus sign. Technically, we could also look for an
+ // optional plus sign, but the "script/process-json-numbers.c with -p"
+ // benchmark is noticably slower if we do. It's optional and, in practice,
+ // usually absent. Let the fallback catch it.
+ bool negative = (*p == '-');
+ if (negative) {
+ p++;
+ }
+
+ // After walking "dd.dddd", comparing p later with p now will produce the
+ // number of "d"s and "."s.
+ const uint8_t* const start_of_digits_ptr = p;
+
+ // Walk the "d"s before a '.', 'E', NUL byte, etc. If it starts with '0',
+ // it must be a single '0'. If it starts with a non-zero decimal digit, it
+ // can be a sequence of decimal digits.
+ //
+ // Update the man variable during the walk. It's OK if man overflows now.
+ // We'll detect that later.
+ uint64_t man;
+ if (*p == '0') {
+ man = 0;
+ p++;
+ if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ goto fallback;
+ }
+ } else if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ man = ((uint8_t)(*p - '0'));
+ p++;
+ for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {
+ man = (10 * man) + ((uint8_t)(*p - '0'));
+ }
+ } else {
+ goto fallback;
+ }
+
+ // Walk the "d"s after the optional decimal separator ('.' or ','),
+ // updating the man and exp10 variables.
+ int32_t exp10 = 0;
+ if ((*p == '.') || (*p == ',')) {
+ p++;
+ const uint8_t* first_after_separator_ptr = p;
+ if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ goto fallback;
+ }
+ man = (10 * man) + ((uint8_t)(*p - '0'));
+ p++;
+ for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {
+ man = (10 * man) + ((uint8_t)(*p - '0'));
+ }
+ exp10 = ((int32_t)(first_after_separator_ptr - p));
+ }
+
+ // Count the number of digits:
+ // - for an input of "314159", digit_count is 6.
+ // - for an input of "3.14159", digit_count is 7.
+ //
+ // This is off-by-one if there is a decimal separator. That's OK for now.
+ // We'll correct for that later. The "script/process-json-numbers.c with
+ // -p" benchmark is noticably slower if we try to correct for that now.
+ uint32_t digit_count = (uint32_t)(p - start_of_digits_ptr);
+
+ // Update exp10 for the optional exponent, starting with 'E' or 'e'.
+ if ((*p | 0x20) == 'e') {
+ p++;
+ int32_t exp_sign = +1;
+ if (*p == '-') {
+ p++;
+ exp_sign = -1;
+ } else if (*p == '+') {
+ p++;
+ }
+ if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ goto fallback;
+ }
+ int32_t exp_num = ((uint8_t)(*p - '0'));
+ p++;
+ // The rest of the exp_num walking has a peculiar control flow but, once
+ // again, the "script/process-json-numbers.c with -p" benchmark is
+ // sensitive to alternative formulations.
+ if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+ p++;
+ }
+ if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+ p++;
+ }
+ while (wuffs_base__private_implementation__is_decimal_digit(*p)) {
+ if (exp_num > 0x1000000) {
+ goto fallback;
+ }
+ exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
+ p++;
+ }
+ exp10 += exp_sign * exp_num;
+ }
+
+ // The Wuffs API is that the original slice has no trailing data. It also
+ // allows underscores, which we don't catch here but the fallback should.
+ if (p != &z[s.len]) {
+ goto fallback;
+ }
+
+ // Check that the uint64_t typed man variable has not overflowed, based on
+ // digit_count.
+ //
+ // For reference:
+ // - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
+ // - (1 << 64) is 18446744073709551616, which has 20 decimal digits.
+ // - 19 nines, 9999999999999999999, is 0x8AC7230489E7FFFF, which has 64
+ // bits and 16 hexadecimal digits.
+ // - 20 nines, 99999999999999999999, is 0x56BC75E2D630FFFFF, which has 67
+ // bits and 17 hexadecimal digits.
+ if (digit_count > 19) {
+ // Even if we have more than 19 pseudo-digits, it's not yet definitely an
+ // overflow. Recall that digit_count might be off-by-one (too large) if
+ // there's a decimal separator. It will also over-report the number of
+ // meaningful digits if the input looks something like "0.000dddExxx".
+ //
+ // We adjust by the number of leading '0's and '.'s and re-compare to 19.
+ // Once again, technically, we could skip ','s too, but that perturbs the
+ // "script/process-json-numbers.c with -p" benchmark.
+ const uint8_t* q = start_of_digits_ptr;
+ for (; (*q == '0') || (*q == '.'); q++) {
+ }
+ digit_count -= (uint32_t)(q - start_of_digits_ptr);
+ if (digit_count > 19) {
+ goto fallback;
+ }
+ }
+
+ // The wuffs_base__private_implementation__parse_number_f64_eisel
+ // preconditions include that exp10 is in the range -326 ..= 310.
+ if ((exp10 < -326) || (310 < exp10)) {
+ goto fallback;
+ }
+
+ // If man and exp10 are small enough, all three of (man), (10 ** exp10) and
+ // (man ** (10 ** exp10)) are exactly representable by a double. We don't
+ // need to run the Eisel algorithm.
+ if ((-22 <= exp10) && (exp10 <= 22) && ((man >> 53) == 0)) {
+ double d = (double)man;
+ if (exp10 >= 0) {
+ d *= wuffs_base__private_implementation__f64_powers_of_10[+exp10];
+ } else {
+ d /= wuffs_base__private_implementation__f64_powers_of_10[-exp10];
+ }
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = negative ? -d : +d;
+ return ret;
+ }
+
+ // The wuffs_base__private_implementation__parse_number_f64_eisel
+ // preconditions include that man is non-zero. Parsing "0" should be caught
+ // by the "If man and exp10 are small enough" above, but "0e99" might not.
+ if (man == 0) {
+ goto fallback;
+ }
+
+ // Our man and exp10 are in range. Run the Eisel algorithm.
+ int64_t r =
+ wuffs_base__private_implementation__parse_number_f64_eisel(man, exp10);
+ if (r < 0) {
+ goto fallback;
+ }
+ wuffs_base__result_f64 ret;
+ ret.status.repr = NULL;
+ ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
+ ((uint64_t)r) | (((uint64_t)negative) << 63));
+ return ret;
+ } while (0);
+
+fallback:
+ do {
+ wuffs_base__private_implementation__high_prec_dec h;
+ wuffs_base__status status =
+ wuffs_base__private_implementation__high_prec_dec__parse(&h, s);
+ if (status.repr) {
+ return wuffs_base__parse_number_f64_special(s, status.repr);
+ }
+ return wuffs_base__private_implementation__parse_number_f64__fallback(&h);
+ } while (0);
+}
+
+// --------
+
+static inline size_t //
+wuffs_base__private_implementation__render_inf(wuffs_base__slice_u8 dst,
+ bool neg,
+ uint32_t options) {
+ if (neg) {
+ if (dst.len < 4) {
+ return 0;
+ }
+ wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492D); // '-Inf'le.
+ return 4;
+ }
+
+ if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+ if (dst.len < 4) {
+ return 0;
+ }
+ wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492B); // '+Inf'le.
+ return 4;
+ }
+
+ if (dst.len < 3) {
+ return 0;
+ }
+ wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x666E49); // 'Inf'le.
+ return 3;
+}
+
+static inline size_t //
+wuffs_base__private_implementation__render_nan(wuffs_base__slice_u8 dst) {
+ if (dst.len < 3) {
+ return 0;
+ }
+ wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x4E614E); // 'NaN'le.
+ return 3;
+}
+
+static size_t //
+wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
+ wuffs_base__slice_u8 dst,
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t precision,
+ uint32_t options) {
+ size_t n = (h->negative ||
+ (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
+ ? 1
+ : 0;
+ if (h->decimal_point <= 0) {
+ n += 1;
+ } else {
+ n += (size_t)(h->decimal_point);
+ }
+ if (precision > 0) {
+ n += precision + 1; // +1 for the '.'.
+ }
+
+ // Don't modify dst if the formatted number won't fit.
+ if (n > dst.len) {
+ return 0;
+ }
+
+ // Align-left or align-right.
+ uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
+ ? &dst.ptr[dst.len - n]
+ : &dst.ptr[0];
+
+ // Leading "±".
+ if (h->negative) {
+ *ptr++ = '-';
+ } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+ *ptr++ = '+';
+ }
+
+ // Integral digits.
+ if (h->decimal_point <= 0) {
+ *ptr++ = '0';
+ } else {
+ uint32_t m =
+ wuffs_base__u32__min(h->num_digits, (uint32_t)(h->decimal_point));
+ uint32_t i = 0;
+ for (; i < m; i++) {
+ *ptr++ = (uint8_t)('0' | h->digits[i]);
+ }
+ for (; i < (uint32_t)(h->decimal_point); i++) {
+ *ptr++ = '0';
+ }
+ }
+
+ // Separator and then fractional digits.
+ if (precision > 0) {
+ *ptr++ =
+ (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+ ? ','
+ : '.';
+ uint32_t i = 0;
+ for (; i < precision; i++) {
+ uint32_t j = ((uint32_t)(h->decimal_point)) + i;
+ *ptr++ = (uint8_t)('0' | ((j < h->num_digits) ? h->digits[j] : 0));
+ }
+ }
+
+ return n;
+}
+
+static size_t //
+wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
+ wuffs_base__slice_u8 dst,
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t precision,
+ uint32_t options) {
+ int32_t exp = 0;
+ if (h->num_digits > 0) {
+ exp = h->decimal_point - 1;
+ }
+ bool negative_exp = exp < 0;
+ if (negative_exp) {
+ exp = -exp;
+ }
+
+ size_t n = (h->negative ||
+ (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
+ ? 4
+ : 3; // Mininum 3 bytes: first digit and then "e±".
+ if (precision > 0) {
+ n += precision + 1; // +1 for the '.'.
+ }
+ n += (exp < 100) ? 2 : 3;
+
+ // Don't modify dst if the formatted number won't fit.
+ if (n > dst.len) {
+ return 0;
+ }
+
+ // Align-left or align-right.
+ uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
+ ? &dst.ptr[dst.len - n]
+ : &dst.ptr[0];
+
+ // Leading "±".
+ if (h->negative) {
+ *ptr++ = '-';
+ } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
+ *ptr++ = '+';
+ }
+
+ // Integral digit.
+ if (h->num_digits > 0) {
+ *ptr++ = (uint8_t)('0' | h->digits[0]);
+ } else {
+ *ptr++ = '0';
+ }
+
+ // Separator and then fractional digits.
+ if (precision > 0) {
+ *ptr++ =
+ (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
+ ? ','
+ : '.';
+ uint32_t i = 1;
+ uint32_t j = wuffs_base__u32__min(h->num_digits, precision + 1);
+ for (; i < j; i++) {
+ *ptr++ = (uint8_t)('0' | h->digits[i]);
+ }
+ for (; i <= precision; i++) {
+ *ptr++ = '0';
+ }
+ }
+
+ // Exponent: "e±" and then 2 or 3 digits.
+ *ptr++ = 'e';
+ *ptr++ = negative_exp ? '-' : '+';
+ if (exp < 10) {
+ *ptr++ = '0';
+ *ptr++ = (uint8_t)('0' | exp);
+ } else if (exp < 100) {
+ *ptr++ = (uint8_t)('0' | (exp / 10));
+ *ptr++ = (uint8_t)('0' | (exp % 10));
+ } else {
+ int32_t e = exp / 100;
+ exp -= e * 100;
+ *ptr++ = (uint8_t)('0' | e);
+ *ptr++ = (uint8_t)('0' | (exp / 10));
+ *ptr++ = (uint8_t)('0' | (exp % 10));
+ }
+
+ return n;
+}
+
+WUFFS_BASE__MAYBE_STATIC size_t //
+wuffs_base__render_number_f64(wuffs_base__slice_u8 dst,
+ double x,
+ uint32_t precision,
+ uint32_t options) {
+ // Decompose x (64 bits) into negativity (1 bit), base-2 exponent (11 bits
+ // with a -1023 bias) and mantissa (52 bits).
+ uint64_t bits = wuffs_base__ieee_754_bit_representation__from_f64(x);
+ bool neg = (bits >> 63) != 0;
+ int32_t exp2 = ((int32_t)(bits >> 52)) & 0x7FF;
+ uint64_t man = bits & 0x000FFFFFFFFFFFFFul;
+
+ // Apply the exponent bias and set the implicit top bit of the mantissa,
+ // unless x is subnormal. Also take care of Inf and NaN.
+ if (exp2 == 0x7FF) {
+ if (man != 0) {
+ return wuffs_base__private_implementation__render_nan(dst);
+ }
+ return wuffs_base__private_implementation__render_inf(dst, neg, options);
+ } else if (exp2 == 0) {
+ exp2 = -1022;
+ } else {
+ exp2 -= 1023;
+ man |= 0x0010000000000000ul;
+ }
+
+ // Ensure that precision isn't too large.
+ if (precision > 4095) {
+ precision = 4095;
+ }
+
+ // Convert from the (neg, exp2, man) tuple to an HPD.
+ wuffs_base__private_implementation__high_prec_dec h;
+ wuffs_base__private_implementation__high_prec_dec__assign(&h, man, neg);
+ if (h.num_digits > 0) {
+ wuffs_base__private_implementation__high_prec_dec__lshift(
+ &h, exp2 - 52); // 52 mantissa bits.
+ }
+
+ // Handle the "%e" and "%f" formats.
+ switch (options & (WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT |
+ WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT)) {
+ case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT: // The "%"f" format.
+ if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+ wuffs_base__private_implementation__high_prec_dec__round_just_enough(
+ &h, exp2, man);
+ int32_t p = ((int32_t)(h.num_digits)) - h.decimal_point;
+ precision = ((uint32_t)(wuffs_base__i32__max(0, p)));
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ &h, ((int32_t)precision) + h.decimal_point);
+ }
+ return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
+ dst, &h, precision, options);
+
+ case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT: // The "%e" format.
+ if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+ wuffs_base__private_implementation__high_prec_dec__round_just_enough(
+ &h, exp2, man);
+ precision = (h.num_digits > 0) ? (h.num_digits - 1) : 0;
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ &h, ((int32_t)precision) + 1);
+ }
+ return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
+ dst, &h, precision, options);
+ }
+
+ // We have the "%g" format and so precision means the number of significant
+ // digits, not the number of digits after the decimal separator. Perform
+ // rounding and determine whether to use "%e" or "%f".
+ int32_t e_threshold = 0;
+ if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
+ wuffs_base__private_implementation__high_prec_dec__round_just_enough(
+ &h, exp2, man);
+ precision = h.num_digits;
+ e_threshold = 6;
+ } else {
+ if (precision == 0) {
+ precision = 1;
+ }
+ wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ &h, ((int32_t)precision));
+ e_threshold = ((int32_t)precision);
+ int32_t nd = ((int32_t)(h.num_digits));
+ if ((e_threshold > nd) && (nd >= h.decimal_point)) {
+ e_threshold = nd;
+ }
+ }
+
+ // Use the "%e" format if the exponent is large.
+ int32_t e = h.decimal_point - 1;
+ if ((e < -4) || (e_threshold <= e)) {
+ uint32_t p = wuffs_base__u32__min(precision, h.num_digits);
+ return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
+ dst, &h, (p > 0) ? (p - 1) : 0, options);
+ }
+
+ // Use the "%f" format otherwise.
+ int32_t p = ((int32_t)precision);
+ if (p > h.decimal_point) {
+ p = ((int32_t)(h.num_digits));
+ }
+ precision = ((uint32_t)(wuffs_base__i32__max(0, p - h.decimal_point)));
+ return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
+ dst, &h, precision, options);
+}
diff --git a/internal/cgen/base/f64conv-submodule-data.c b/internal/cgen/base/f64conv-submodule-data.c
new file mode 100644
index 0000000..865fc99
--- /dev/null
+++ b/internal/cgen/base/f64conv-submodule-data.c
@@ -0,0 +1,802 @@
+// After editing this file, run "go generate" in the parent directory.
+
+// Copyright 2020 The Wuffs Authors.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+// https://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+// ---------------- IEEE 754 Floating Point
+
+// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by
+// script/print-hpd-left-shift.go. That script has an optional -comments flag,
+// whose output is not copied here, which prints further detail.
+//
+// These tables are used in
+// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits.
+
+// wuffs_base__private_implementation__hpd_left_shift[i] encodes the number of
+// new digits created after multiplying a positive integer by (1 << i): the
+// additional length in the decimal representation. For example, shifting "234"
+// by 3 (equivalent to multiplying by 8) will produce "1872". Going from a
+// 3-length string to a 4-length string means that 1 new digit was added (and
+// existing digits may have changed).
+//
+// Shifting by i can add either N or N-1 new digits, depending on whether the
+// original positive integer compares >= or < to the i'th power of 5 (as 10
+// equals 2 * 5). Comparison is lexicographic, not numerical.
+//
+// For example, shifting by 4 (i.e. multiplying by 16) can add 1 or 2 new
+// digits, depending on a lexicographic comparison to (5 ** 4), i.e. "625":
+// - ("1" << 4) is "16", which adds 1 new digit.
+// - ("5678" << 4) is "90848", which adds 1 new digit.
+// - ("624" << 4) is "9984", which adds 1 new digit.
+// - ("62498" << 4) is "999968", which adds 1 new digit.
+// - ("625" << 4) is "10000", which adds 2 new digits.
+// - ("625001" << 4) is "10000016", which adds 2 new digits.
+// - ("7008" << 4) is "112128", which adds 2 new digits.
+// - ("99" << 4) is "1584", which adds 2 new digits.
+//
+// Thus, when i is 4, N is 2 and (5 ** i) is "625". This etc__hpd_left_shift
+// array encodes this as:
+// - etc__hpd_left_shift[4] is 0x1006 = (2 << 11) | 0x0006.
+// - etc__hpd_left_shift[5] is 0x1009 = (? << 11) | 0x0009.
+// where the ? isn't relevant for i == 4.
+//
+// The high 5 bits of etc__hpd_left_shift[i] is N, the higher of the two
+// possible number of new digits. The low 11 bits are an offset into the
+// etc__powers_of_5 array (of length 0x051C, so offsets fit in 11 bits). When i
+// is 4, its offset and the next one is 6 and 9, and etc__powers_of_5[6 .. 9]
+// is the string "\x06\x02\x05", so the relevant power of 5 is "625".
+//
+// Thanks to Ken Thompson for the original idea.
+static const uint16_t wuffs_base__private_implementation__hpd_left_shift[65] = {
+ 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
+ 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
+ 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
+ 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
+ 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
+ 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
+ 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
+ 0x051C, 0x051C,
+};
+
+// wuffs_base__private_implementation__powers_of_5 contains the powers of 5,
+// concatenated together: "5", "25", "125", "625", "3125", etc.
+static const uint8_t wuffs_base__private_implementation__powers_of_5[0x051C] = {
+ 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9,
+ 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2,
+ 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5,
+ 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8, 9, 0,
+ 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, 9, 7, 2, 6, 5,
+ 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,
+ 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4,
+ 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7,
+ 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0,
+ 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3,
+ 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1,
+ 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,
+ 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5,
+ 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0,
+ 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6,
+ 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8,
+ 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7,
+ 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,
+ 1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8,
+ 0, 6, 6, 4, 0, 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9,
+ 0, 3, 3, 2, 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2,
+ 9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8,
+ 5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,
+ 2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
+ 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3,
+ 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2,
+ 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9,
+ 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, 0, 1, 4, 8,
+ 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4,
+ 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,
+ 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5,
+ 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1,
+ 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5,
+ 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3,
+ 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4,
+ 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,
+ 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8,
+ 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2,
+ 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6,
+ 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2,
+ 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2,
+ 5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,
+ 8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5,
+ 6, 2, 8, 9, 1, 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8,
+ 1, 2, 5, 1, 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9,
+ 5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,
+ 9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6,
+ 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
+ 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1,
+ 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4,
+ 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7,
+ 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3,
+ 6, 9, 1, 4, 0, 6, 2, 5,
+};
+
+// --------
+
+// wuffs_base__private_implementation__powers_of_10 contains truncated
+// approximations to the powers of 10, ranging from 1e-326 to 1e+310 inclusive,
+// as 637 uint32_t quintuples (128-bit mantissa, 32-bit base-2 exponent biased
+// by 0x04BE (which is 1214)). The array size is 637 * 5 = 3185.
+//
+// The 1214 bias in this look-up table equals 1023 + 191. 1023 is the bias for
+// IEEE 754 double-precision floating point. 191 is ((3 * 64) - 1) and
+// wuffs_base__private_implementation__parse_number_f64_eisel works with
+// multiples-of-64-bit mantissas.
+//
+// For example, the third approximation, for 1e-324, consists of the uint32_t
+// quintuple (0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A). The
+// first four form a little-endian uint128_t value. The last one is an int32_t
+// value: -1140. Together, they represent the approximation to 1e-324:
+// 0xCF42894A_5DCE35EA_52064CAC_828675B9 * (2 ** (0x000A - 0x04BE))
+//
+// Similarly, 1e+4 is approximated by the uint64_t quintuple
+// (0x00000000, 0x00000000, 0x00000000, 0x9C400000, 0x044C) which means:
+// 0x9C400000_00000000_00000000_00000000 * (2 ** (0x044C - 0x04BE))
+//
+// Similarly, 1e+68 is approximated by the uint64_t quintuple
+// (0x63EE4BDD, 0x4CA7AAA8, 0xD4C4FB27, 0xED63A231, 0x0520) which means:
+// 0xED63A231_D4C4FB27.4CA7AAA8_63EE4BDD * (2 ** (0x0520 - 0x04BE))
+//
+// This table was generated by by script/print-mpb-powers-of-10.go
+static const uint32_t wuffs_base__private_implementation__powers_of_10[3185] = {
+ 0xF7604B57, 0x014BB630, 0xFE98746D, 0x84A57695, 0x0004, // 1e-326
+ 0x35385E2D, 0x419EA3BD, 0x7E3E9188, 0xA5CED43B, 0x0007, // 1e-325
+ 0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A, // 1e-324
+ 0xD1940993, 0x7343EFEB, 0x7AA0E1B2, 0x818995CE, 0x000E, // 1e-323
+ 0xC5F90BF8, 0x1014EBE6, 0x19491A1F, 0xA1EBFB42, 0x0011, // 1e-322
+ 0x77774EF6, 0xD41A26E0, 0x9F9B60A6, 0xCA66FA12, 0x0014, // 1e-321
+ 0x955522B4, 0x8920B098, 0x478238D0, 0xFD00B897, 0x0017, // 1e-320
+ 0x5D5535B0, 0x55B46E5F, 0x8CB16382, 0x9E20735E, 0x001B, // 1e-319
+ 0x34AA831D, 0xEB2189F7, 0x2FDDBC62, 0xC5A89036, 0x001E, // 1e-318
+ 0x01D523E4, 0xA5E9EC75, 0xBBD52B7B, 0xF712B443, 0x0021, // 1e-317
+ 0x2125366E, 0x47B233C9, 0x55653B2D, 0x9A6BB0AA, 0x0025, // 1e-316
+ 0x696E840A, 0x999EC0BB, 0xEABE89F8, 0xC1069CD4, 0x0028, // 1e-315
+ 0x43CA250D, 0xC00670EA, 0x256E2C76, 0xF148440A, 0x002B, // 1e-314
+ 0x6A5E5728, 0x38040692, 0x5764DBCA, 0x96CD2A86, 0x002F, // 1e-313
+ 0x04F5ECF2, 0xC6050837, 0xED3E12BC, 0xBC807527, 0x0032, // 1e-312
+ 0xC633682E, 0xF7864A44, 0xE88D976B, 0xEBA09271, 0x0035, // 1e-311
+ 0xFBE0211D, 0x7AB3EE6A, 0x31587EA3, 0x93445B87, 0x0039, // 1e-310
+ 0xBAD82964, 0x5960EA05, 0xFDAE9E4C, 0xB8157268, 0x003C, // 1e-309
+ 0x298E33BD, 0x6FB92487, 0x3D1A45DF, 0xE61ACF03, 0x003F, // 1e-308
+ 0x79F8E056, 0xA5D3B6D4, 0x06306BAB, 0x8FD0C162, 0x0043, // 1e-307
+ 0x9877186C, 0x8F48A489, 0x87BC8696, 0xB3C4F1BA, 0x0046, // 1e-306
+ 0xFE94DE87, 0x331ACDAB, 0x29ABA83C, 0xE0B62E29, 0x0049, // 1e-305
+ 0x7F1D0B14, 0x9FF0C08B, 0xBA0B4925, 0x8C71DCD9, 0x004D, // 1e-304
+ 0x5EE44DD9, 0x07ECF0AE, 0x288E1B6F, 0xAF8E5410, 0x0050, // 1e-303
+ 0xF69D6150, 0xC9E82CD9, 0x32B1A24A, 0xDB71E914, 0x0053, // 1e-302
+ 0x3A225CD2, 0xBE311C08, 0x9FAF056E, 0x892731AC, 0x0057, // 1e-301
+ 0x48AAF406, 0x6DBD630A, 0xC79AC6CA, 0xAB70FE17, 0x005A, // 1e-300
+ 0xDAD5B108, 0x092CBBCC, 0xB981787D, 0xD64D3D9D, 0x005D, // 1e-299
+ 0x08C58EA5, 0x25BBF560, 0x93F0EB4E, 0x85F04682, 0x0061, // 1e-298
+ 0x0AF6F24E, 0xAF2AF2B8, 0x38ED2621, 0xA76C5823, 0x0064, // 1e-297
+ 0x0DB4AEE1, 0x1AF5AF66, 0x07286FAA, 0xD1476E2C, 0x0067, // 1e-296
+ 0xC890ED4D, 0x50D98D9F, 0x847945CA, 0x82CCA4DB, 0x006B, // 1e-295
+ 0xBAB528A0, 0xE50FF107, 0x6597973C, 0xA37FCE12, 0x006E, // 1e-294
+ 0xA96272C8, 0x1E53ED49, 0xFEFD7D0C, 0xCC5FC196, 0x0071, // 1e-293
+ 0x13BB0F7A, 0x25E8E89C, 0xBEBCDC4F, 0xFF77B1FC, 0x0074, // 1e-292
+ 0x8C54E9AC, 0x77B19161, 0xF73609B1, 0x9FAACF3D, 0x0078, // 1e-291
+ 0xEF6A2417, 0xD59DF5B9, 0x75038C1D, 0xC795830D, 0x007B, // 1e-290
+ 0x6B44AD1D, 0x4B057328, 0xD2446F25, 0xF97AE3D0, 0x007E, // 1e-289
+ 0x430AEC32, 0x4EE367F9, 0x836AC577, 0x9BECCE62, 0x0082, // 1e-288
+ 0x93CDA73F, 0x229C41F7, 0x244576D5, 0xC2E801FB, 0x0085, // 1e-287
+ 0x78C1110F, 0x6B435275, 0xED56D48A, 0xF3A20279, 0x0088, // 1e-286
+ 0x6B78AAA9, 0x830A1389, 0x345644D6, 0x9845418C, 0x008C, // 1e-285
+ 0xC656D553, 0x23CC986B, 0x416BD60C, 0xBE5691EF, 0x008F, // 1e-284
+ 0xB7EC8AA8, 0x2CBFBE86, 0x11C6CB8F, 0xEDEC366B, 0x0092, // 1e-283
+ 0x32F3D6A9, 0x7BF7D714, 0xEB1C3F39, 0x94B3A202, 0x0096, // 1e-282
+ 0x3FB0CC53, 0xDAF5CCD9, 0xA5E34F07, 0xB9E08A83, 0x0099, // 1e-281
+ 0x8F9CFF68, 0xD1B3400F, 0x8F5C22C9, 0xE858AD24, 0x009C, // 1e-280
+ 0xB9C21FA1, 0x23100809, 0xD99995BE, 0x91376C36, 0x00A0, // 1e-279
+ 0x2832A78A, 0xABD40A0C, 0x8FFFFB2D, 0xB5854744, 0x00A3, // 1e-278
+ 0x323F516C, 0x16C90C8F, 0xB3FFF9F9, 0xE2E69915, 0x00A6, // 1e-277
+ 0x7F6792E3, 0xAE3DA7D9, 0x907FFC3B, 0x8DD01FAD, 0x00AA, // 1e-276
+ 0xDF41779C, 0x99CD11CF, 0xF49FFB4A, 0xB1442798, 0x00AD, // 1e-275
+ 0xD711D583, 0x40405643, 0x31C7FA1D, 0xDD95317F, 0x00B0, // 1e-274
+ 0x666B2572, 0x482835EA, 0x7F1CFC52, 0x8A7D3EEF, 0x00B4, // 1e-273
+ 0x0005EECF, 0xDA324365, 0x5EE43B66, 0xAD1C8EAB, 0x00B7, // 1e-272
+ 0x40076A82, 0x90BED43E, 0x369D4A40, 0xD863B256, 0x00BA, // 1e-271
+ 0xE804A291, 0x5A7744A6, 0xE2224E68, 0x873E4F75, 0x00BE, // 1e-270
+ 0xA205CB36, 0x711515D0, 0x5AAAE202, 0xA90DE353, 0x00C1, // 1e-269
+ 0xCA873E03, 0x0D5A5B44, 0x31559A83, 0xD3515C28, 0x00C4, // 1e-268
+ 0xFE9486C2, 0xE858790A, 0x1ED58091, 0x8412D999, 0x00C8, // 1e-267
+ 0xBE39A872, 0x626E974D, 0x668AE0B6, 0xA5178FFF, 0x00CB, // 1e-266
+ 0x2DC8128F, 0xFB0A3D21, 0x402D98E3, 0xCE5D73FF, 0x00CE, // 1e-265
+ 0xBC9D0B99, 0x7CE66634, 0x881C7F8E, 0x80FA687F, 0x00D2, // 1e-264
+ 0xEBC44E80, 0x1C1FFFC1, 0x6A239F72, 0xA139029F, 0x00D5, // 1e-263
+ 0x66B56220, 0xA327FFB2, 0x44AC874E, 0xC9874347, 0x00D8, // 1e-262
+ 0x0062BAA8, 0x4BF1FF9F, 0x15D7A922, 0xFBE91419, 0x00DB, // 1e-261
+ 0x603DB4A9, 0x6F773FC3, 0xADA6C9B5, 0x9D71AC8F, 0x00DF, // 1e-260
+ 0x384D21D3, 0xCB550FB4, 0x99107C22, 0xC4CE17B3, 0x00E2, // 1e-259
+ 0x46606A48, 0x7E2A53A1, 0x7F549B2B, 0xF6019DA0, 0x00E5, // 1e-258
+ 0xCBFC426D, 0x2EDA7444, 0x4F94E0FB, 0x99C10284, 0x00E9, // 1e-257
+ 0xFEFB5308, 0xFA911155, 0x637A1939, 0xC0314325, 0x00EC, // 1e-256
+ 0x7EBA27CA, 0x793555AB, 0xBC589F88, 0xF03D93EE, 0x00EF, // 1e-255
+ 0x2F3458DE, 0x4BC1558B, 0x35B763B5, 0x96267C75, 0x00F3, // 1e-254
+ 0xFB016F16, 0x9EB1AAED, 0x83253CA2, 0xBBB01B92, 0x00F6, // 1e-253
+ 0x79C1CADC, 0x465E15A9, 0x23EE8BCB, 0xEA9C2277, 0x00F9, // 1e-252
+ 0xEC191EC9, 0x0BFACD89, 0x7675175F, 0x92A1958A, 0x00FD, // 1e-251
+ 0x671F667B, 0xCEF980EC, 0x14125D36, 0xB749FAED, 0x0100, // 1e-250
+ 0x80E7401A, 0x82B7E127, 0x5916F484, 0xE51C79A8, 0x0103, // 1e-249
+ 0xB0908810, 0xD1B2ECB8, 0x37AE58D2, 0x8F31CC09, 0x0107, // 1e-248
+ 0xDCB4AA15, 0x861FA7E6, 0x8599EF07, 0xB2FE3F0B, 0x010A, // 1e-247
+ 0x93E1D49A, 0x67A791E0, 0x67006AC9, 0xDFBDCECE, 0x010D, // 1e-246
+ 0x5C6D24E0, 0xE0C8BB2C, 0x006042BD, 0x8BD6A141, 0x0111, // 1e-245
+ 0x73886E18, 0x58FAE9F7, 0x4078536D, 0xAECC4991, 0x0114, // 1e-244
+ 0x506A899E, 0xAF39A475, 0x90966848, 0xDA7F5BF5, 0x0117, // 1e-243
+ 0x52429603, 0x6D8406C9, 0x7A5E012D, 0x888F9979, 0x011B, // 1e-242
+ 0xA6D33B83, 0xC8E5087B, 0xD8F58178, 0xAAB37FD7, 0x011E, // 1e-241
+ 0x90880A64, 0xFB1E4A9A, 0xCF32E1D6, 0xD5605FCD, 0x0121, // 1e-240
+ 0x9A55067F, 0x5CF2EEA0, 0xA17FCD26, 0x855C3BE0, 0x0125, // 1e-239
+ 0xC0EA481E, 0xF42FAA48, 0xC9DFC06F, 0xA6B34AD8, 0x0128, // 1e-238
+ 0xF124DA26, 0xF13B94DA, 0xFC57B08B, 0xD0601D8E, 0x012B, // 1e-237
+ 0xD6B70858, 0x76C53D08, 0x5DB6CE57, 0x823C1279, 0x012F, // 1e-236
+ 0x0C64CA6E, 0x54768C4B, 0xB52481ED, 0xA2CB1717, 0x0132, // 1e-235
+ 0xCF7DFD09, 0xA9942F5D, 0xA26DA268, 0xCB7DDCDD, 0x0135, // 1e-234
+ 0x435D7C4C, 0xD3F93B35, 0x0B090B02, 0xFE5D5415, 0x0138, // 1e-233
+ 0x4A1A6DAF, 0xC47BC501, 0x26E5A6E1, 0x9EFA548D, 0x013C, // 1e-232
+ 0x9CA1091B, 0x359AB641, 0x709F109A, 0xC6B8E9B0, 0x013F, // 1e-231
+ 0x03C94B62, 0xC30163D2, 0x8CC6D4C0, 0xF867241C, 0x0142, // 1e-230
+ 0x425DCF1D, 0x79E0DE63, 0xD7FC44F8, 0x9B407691, 0x0146, // 1e-229
+ 0x12F542E4, 0x985915FC, 0x4DFB5636, 0xC2109436, 0x0149, // 1e-228
+ 0x17B2939D, 0x3E6F5B7B, 0xE17A2BC4, 0xF294B943, 0x014C, // 1e-227
+ 0xEECF9C42, 0xA705992C, 0x6CEC5B5A, 0x979CF3CA, 0x0150, // 1e-226
+ 0x2A838353, 0x50C6FF78, 0x08277231, 0xBD8430BD, 0x0153, // 1e-225
+ 0x35246428, 0xA4F8BF56, 0x4A314EBD, 0xECE53CEC, 0x0156, // 1e-224
+ 0xE136BE99, 0x871B7795, 0xAE5ED136, 0x940F4613, 0x015A, // 1e-223
+ 0x59846E3F, 0x28E2557B, 0x99F68584, 0xB9131798, 0x015D, // 1e-222
+ 0x2FE589CF, 0x331AEADA, 0xC07426E5, 0xE757DD7E, 0x0160, // 1e-221
+ 0x5DEF7621, 0x3FF0D2C8, 0x3848984F, 0x9096EA6F, 0x0164, // 1e-220
+ 0x756B53A9, 0x0FED077A, 0x065ABE63, 0xB4BCA50B, 0x0167, // 1e-219
+ 0x12C62894, 0xD3E84959, 0xC7F16DFB, 0xE1EBCE4D, 0x016A, // 1e-218
+ 0xABBBD95C, 0x64712DD7, 0x9CF6E4BD, 0x8D3360F0, 0x016E, // 1e-217
+ 0x96AACFB3, 0xBD8D794D, 0xC4349DEC, 0xB080392C, 0x0171, // 1e-216
+ 0xFC5583A0, 0xECF0D7A0, 0xF541C567, 0xDCA04777, 0x0174, // 1e-215
+ 0x9DB57244, 0xF41686C4, 0xF9491B60, 0x89E42CAA, 0x0178, // 1e-214
+ 0xC522CED5, 0x311C2875, 0xB79B6239, 0xAC5D37D5, 0x017B, // 1e-213
+ 0x366B828B, 0x7D633293, 0x25823AC7, 0xD77485CB, 0x017E, // 1e-212
+ 0x02033197, 0xAE5DFF9C, 0xF77164BC, 0x86A8D39E, 0x0182, // 1e-211
+ 0x0283FDFC, 0xD9F57F83, 0xB54DBDEB, 0xA8530886, 0x0185, // 1e-210
+ 0xC324FD7B, 0xD072DF63, 0x62A12D66, 0xD267CAA8, 0x0188, // 1e-209
+ 0x59F71E6D, 0x4247CB9E, 0x3DA4BC60, 0x8380DEA9, 0x018C, // 1e-208
+ 0xF074E608, 0x52D9BE85, 0x8D0DEB78, 0xA4611653, 0x018F, // 1e-207
+ 0x6C921F8B, 0x67902E27, 0x70516656, 0xCD795BE8, 0x0192, // 1e-206
+ 0xA3DB53B6, 0x00BA1CD8, 0x4632DFF6, 0x806BD971, 0x0196, // 1e-205
+ 0xCCD228A4, 0x80E8A40E, 0x97BF97F3, 0xA086CFCD, 0x0199, // 1e-204
+ 0x8006B2CD, 0x6122CD12, 0xFDAF7DF0, 0xC8A883C0, 0x019C, // 1e-203
+ 0x20085F81, 0x796B8057, 0x3D1B5D6C, 0xFAD2A4B1, 0x019F, // 1e-202
+ 0x74053BB0, 0xCBE33036, 0xC6311A63, 0x9CC3A6EE, 0x01A3, // 1e-201
+ 0x11068A9C, 0xBEDBFC44, 0x77BD60FC, 0xC3F490AA, 0x01A6, // 1e-200
+ 0x15482D44, 0xEE92FB55, 0x15ACB93B, 0xF4F1B4D5, 0x01A9, // 1e-199
+ 0x2D4D1C4A, 0x751BDD15, 0x2D8BF3C5, 0x99171105, 0x01AD, // 1e-198
+ 0x78A0635D, 0xD262D45A, 0x78EEF0B6, 0xBF5CD546, 0x01B0, // 1e-197
+ 0x16C87C34, 0x86FB8971, 0x172AACE4, 0xEF340A98, 0x01B3, // 1e-196
+ 0xAE3D4DA0, 0xD45D35E6, 0x0E7AAC0E, 0x9580869F, 0x01B7, // 1e-195
+ 0x59CCA109, 0x89748360, 0xD2195712, 0xBAE0A846, 0x01BA, // 1e-194
+ 0x703FC94B, 0x2BD1A438, 0x869FACD7, 0xE998D258, 0x01BD, // 1e-193
+ 0x4627DDCF, 0x7B6306A3, 0x5423CC06, 0x91FF8377, 0x01C1, // 1e-192
+ 0x17B1D542, 0x1A3BC84C, 0x292CBF08, 0xB67F6455, 0x01C4, // 1e-191
+ 0x1D9E4A93, 0x20CABA5F, 0x7377EECA, 0xE41F3D6A, 0x01C7, // 1e-190
+ 0x7282EE9C, 0x547EB47B, 0x882AF53E, 0x8E938662, 0x01CB, // 1e-189
+ 0x4F23AA43, 0xE99E619A, 0x2A35B28D, 0xB23867FB, 0x01CE, // 1e-188
+ 0xE2EC94D4, 0x6405FA00, 0xF4C31F31, 0xDEC681F9, 0x01D1, // 1e-187
+ 0x8DD3DD04, 0xDE83BC40, 0x38F9F37E, 0x8B3C113C, 0x01D5, // 1e-186
+ 0xB148D445, 0x9624AB50, 0x4738705E, 0xAE0B158B, 0x01D8, // 1e-185
+ 0xDD9B0957, 0x3BADD624, 0x19068C76, 0xD98DDAEE, 0x01DB, // 1e-184
+ 0x0A80E5D6, 0xE54CA5D7, 0xCFA417C9, 0x87F8A8D4, 0x01DF, // 1e-183
+ 0xCD211F4C, 0x5E9FCF4C, 0x038D1DBC, 0xA9F6D30A, 0x01E2, // 1e-182
+ 0x0069671F, 0x7647C320, 0x8470652B, 0xD47487CC, 0x01E5, // 1e-181
+ 0x0041E073, 0x29ECD9F4, 0xD2C63F3B, 0x84C8D4DF, 0x01E9, // 1e-180
+ 0x00525890, 0xF4681071, 0xC777CF09, 0xA5FB0A17, 0x01EC, // 1e-179
+ 0x4066EEB4, 0x7182148D, 0xB955C2CC, 0xCF79CC9D, 0x01EF, // 1e-178
+ 0x48405530, 0xC6F14CD8, 0x93D599BF, 0x81AC1FE2, 0x01F3, // 1e-177
+ 0x5A506A7C, 0xB8ADA00E, 0x38CB002F, 0xA21727DB, 0x01F6, // 1e-176
+ 0xF0E4851C, 0xA6D90811, 0x06FDC03B, 0xCA9CF1D2, 0x01F9, // 1e-175
+ 0x6D1DA663, 0x908F4A16, 0x88BD304A, 0xFD442E46, 0x01FC, // 1e-174
+ 0x043287FE, 0x9A598E4E, 0x15763E2E, 0x9E4A9CEC, 0x0200, // 1e-173
+ 0x853F29FD, 0x40EFF1E1, 0x1AD3CDBA, 0xC5DD4427, 0x0203, // 1e-172
+ 0xE68EF47C, 0xD12BEE59, 0xE188C128, 0xF7549530, 0x0206, // 1e-171
+ 0x301958CE, 0x82BB74F8, 0x8CF578B9, 0x9A94DD3E, 0x020A, // 1e-170
+ 0x3C1FAF01, 0xE36A5236, 0x3032D6E7, 0xC13A148E, 0x020D, // 1e-169
+ 0xCB279AC1, 0xDC44E6C3, 0xBC3F8CA1, 0xF18899B1, 0x0210, // 1e-168
+ 0x5EF8C0B9, 0x29AB103A, 0x15A7B7E5, 0x96F5600F, 0x0214, // 1e-167
+ 0xF6B6F0E7, 0x7415D448, 0xDB11A5DE, 0xBCB2B812, 0x0217, // 1e-166
+ 0x3464AD21, 0x111B495B, 0x91D60F56, 0xEBDF6617, 0x021A, // 1e-165
+ 0x00BEEC34, 0xCAB10DD9, 0xBB25C995, 0x936B9FCE, 0x021E, // 1e-164
+ 0x40EEA742, 0x3D5D514F, 0x69EF3BFB, 0xB84687C2, 0x0221, // 1e-163
+ 0x112A5112, 0x0CB4A5A3, 0x046B0AFA, 0xE65829B3, 0x0224, // 1e-162
+ 0xEABA72AB, 0x47F0E785, 0xE2C2E6DC, 0x8FF71A0F, 0x0228, // 1e-161
+ 0x65690F56, 0x59ED2167, 0xDB73A093, 0xB3F4E093, 0x022B, // 1e-160
+ 0x3EC3532C, 0x306869C1, 0xD25088B8, 0xE0F218B8, 0x022E, // 1e-159
+ 0xC73A13FB, 0x1E414218, 0x83725573, 0x8C974F73, 0x0232, // 1e-158
+ 0xF90898FA, 0xE5D1929E, 0x644EEACF, 0xAFBD2350, 0x0235, // 1e-157
+ 0xB74ABF39, 0xDF45F746, 0x7D62A583, 0xDBAC6C24, 0x0238, // 1e-156
+ 0x328EB783, 0x6B8BBA8C, 0xCE5DA772, 0x894BC396, 0x023C, // 1e-155
+ 0x3F326564, 0x066EA92F, 0x81F5114F, 0xAB9EB47C, 0x023F, // 1e-154
+ 0x0EFEFEBD, 0xC80A537B, 0xA27255A2, 0xD686619B, 0x0242, // 1e-153
+ 0xE95F5F36, 0xBD06742C, 0x45877585, 0x8613FD01, 0x0246, // 1e-152
+ 0x23B73704, 0x2C481138, 0x96E952E7, 0xA798FC41, 0x0249, // 1e-151
+ 0x2CA504C5, 0xF75A1586, 0xFCA3A7A0, 0xD17F3B51, 0x024C, // 1e-150
+ 0xDBE722FB, 0x9A984D73, 0x3DE648C4, 0x82EF8513, 0x0250, // 1e-149
+ 0xD2E0EBBA, 0xC13E60D0, 0x0D5FDAF5, 0xA3AB6658, 0x0253, // 1e-148
+ 0x079926A8, 0x318DF905, 0x10B7D1B3, 0xCC963FEE, 0x0256, // 1e-147
+ 0x497F7052, 0xFDF17746, 0x94E5C61F, 0xFFBBCFE9, 0x0259, // 1e-146
+ 0xEDEFA633, 0xFEB6EA8B, 0xFD0F9BD3, 0x9FD561F1, 0x025D, // 1e-145
+ 0xE96B8FC0, 0xFE64A52E, 0x7C5382C8, 0xC7CABA6E, 0x0260, // 1e-144
+ 0xA3C673B0, 0x3DFDCE7A, 0x1B68637B, 0xF9BD690A, 0x0263, // 1e-143
+ 0xA65C084E, 0x06BEA10C, 0x51213E2D, 0x9C1661A6, 0x0267, // 1e-142
+ 0xCFF30A62, 0x486E494F, 0xE5698DB8, 0xC31BFA0F, 0x026A, // 1e-141
+ 0xC3EFCCFA, 0x5A89DBA3, 0xDEC3F126, 0xF3E2F893, 0x026D, // 1e-140
+ 0x5A75E01C, 0xF8962946, 0x6B3A76B7, 0x986DDB5C, 0x0271, // 1e-139
+ 0xF1135823, 0xF6BBB397, 0x86091465, 0xBE895233, 0x0274, // 1e-138
+ 0xED582E2C, 0x746AA07D, 0x678B597F, 0xEE2BA6C0, 0x0277, // 1e-137
+ 0xB4571CDC, 0xA8C2A44E, 0x40B717EF, 0x94DB4838, 0x027B, // 1e-136
+ 0x616CE413, 0x92F34D62, 0x50E4DDEB, 0xBA121A46, 0x027E, // 1e-135
+ 0xF9C81D17, 0x77B020BA, 0xE51E1566, 0xE896A0D7, 0x0281, // 1e-134
+ 0xDC1D122E, 0x0ACE1474, 0xEF32CD60, 0x915E2486, 0x0285, // 1e-133
+ 0x132456BA, 0x0D819992, 0xAAFF80B8, 0xB5B5ADA8, 0x0288, // 1e-132
+ 0x97ED6C69, 0x10E1FFF6, 0xD5BF60E6, 0xE3231912, 0x028B, // 1e-131
+ 0x1EF463C1, 0xCA8D3FFA, 0xC5979C8F, 0x8DF5EFAB, 0x028F, // 1e-130
+ 0xA6B17CB2, 0xBD308FF8, 0xB6FD83B3, 0xB1736B96, 0x0292, // 1e-129
+ 0xD05DDBDE, 0xAC7CB3F6, 0x64BCE4A0, 0xDDD0467C, 0x0295, // 1e-128
+ 0x423AA96B, 0x6BCDF07A, 0xBEF60EE4, 0x8AA22C0D, 0x0299, // 1e-127
+ 0xD2C953C6, 0x86C16C98, 0x2EB3929D, 0xAD4AB711, 0x029C, // 1e-126
+ 0x077BA8B7, 0xE871C7BF, 0x7A607744, 0xD89D64D5, 0x029F, // 1e-125
+ 0x64AD4972, 0x11471CD7, 0x6C7C4A8B, 0x87625F05, 0x02A3, // 1e-124
+ 0x3DD89BCF, 0xD598E40D, 0xC79B5D2D, 0xA93AF6C6, 0x02A6, // 1e-123
+ 0x8D4EC2C3, 0x4AFF1D10, 0x79823479, 0xD389B478, 0x02A9, // 1e-122
+ 0x585139BA, 0xCEDF722A, 0x4BF160CB, 0x843610CB, 0x02AD, // 1e-121
+ 0xEE658828, 0xC2974EB4, 0x1EEDB8FE, 0xA54394FE, 0x02B0, // 1e-120
+ 0x29FEEA32, 0x733D2262, 0xA6A9273E, 0xCE947A3D, 0x02B3, // 1e-119
+ 0x5A3F525F, 0x0806357D, 0x8829B887, 0x811CCC66, 0x02B7, // 1e-118
+ 0xB0CF26F7, 0xCA07C2DC, 0x2A3426A8, 0xA163FF80, 0x02BA, // 1e-117
+ 0xDD02F0B5, 0xFC89B393, 0x34C13052, 0xC9BCFF60, 0x02BD, // 1e-116
+ 0xD443ACE2, 0xBBAC2078, 0x41F17C67, 0xFC2C3F38, 0x02C0, // 1e-115
+ 0x84AA4C0D, 0xD54B944B, 0x2936EDC0, 0x9D9BA783, 0x02C4, // 1e-114
+ 0x65D4DF11, 0x0A9E795E, 0xF384A931, 0xC5029163, 0x02C7, // 1e-113
+ 0xFF4A16D5, 0x4D4617B5, 0xF065D37D, 0xF64335BC, 0x02CA, // 1e-112
+ 0xBF8E4E45, 0x504BCED1, 0x163FA42E, 0x99EA0196, 0x02CE, // 1e-111
+ 0x2F71E1D6, 0xE45EC286, 0x9BCF8D39, 0xC06481FB, 0x02D1, // 1e-110
+ 0xBB4E5A4C, 0x5D767327, 0x82C37088, 0xF07DA27A, 0x02D4, // 1e-109
+ 0xD510F86F, 0x3A6A07F8, 0x91BA2655, 0x964E858C, 0x02D8, // 1e-108
+ 0x0A55368B, 0x890489F7, 0xB628AFEA, 0xBBE226EF, 0x02DB, // 1e-107
+ 0xCCEA842E, 0x2B45AC74, 0xA3B2DBE5, 0xEADAB0AB, 0x02DE, // 1e-106
+ 0x0012929D, 0x3B0B8BC9, 0x464FC96F, 0x92C8AE6B, 0x02E2, // 1e-105
+ 0x40173744, 0x09CE6EBB, 0x17E3BBCB, 0xB77ADA06, 0x02E5, // 1e-104
+ 0x101D0515, 0xCC420A6A, 0x9DDCAABD, 0xE5599087, 0x02E8, // 1e-103
+ 0x4A12232D, 0x9FA94682, 0xC2A9EAB6, 0x8F57FA54, 0x02EC, // 1e-102
+ 0xDC96ABF9, 0x47939822, 0xF3546564, 0xB32DF8E9, 0x02EF, // 1e-101
+ 0x93BC56F7, 0x59787E2B, 0x70297EBD, 0xDFF97724, 0x02F2, // 1e-100
+ 0x3C55B65A, 0x57EB4EDB, 0xC619EF36, 0x8BFBEA76, 0x02F6, // 1e-99
+ 0x0B6B23F1, 0xEDE62292, 0x77A06B03, 0xAEFAE514, 0x02F9, // 1e-98
+ 0x8E45ECED, 0xE95FAB36, 0x958885C4, 0xDAB99E59, 0x02FC, // 1e-97
+ 0x18EBB414, 0x11DBCB02, 0xFD75539B, 0x88B402F7, 0x0300, // 1e-96
+ 0x9F26A119, 0xD652BDC2, 0xFCD2A881, 0xAAE103B5, 0x0303, // 1e-95
+ 0x46F0495F, 0x4BE76D33, 0x7C0752A2, 0xD59944A3, 0x0306, // 1e-94
+ 0x0C562DDB, 0x6F70A440, 0x2D8493A5, 0x857FCAE6, 0x030A, // 1e-93
+ 0x0F6BB952, 0xCB4CCD50, 0xB8E5B88E, 0xA6DFBD9F, 0x030D, // 1e-92
+ 0x1346A7A7, 0x7E2000A4, 0xA71F26B2, 0xD097AD07, 0x0310, // 1e-91
+ 0x8C0C28C8, 0x8ED40066, 0xC873782F, 0x825ECC24, 0x0314, // 1e-90
+ 0x2F0F32FA, 0x72890080, 0xFA90563B, 0xA2F67F2D, 0x0317, // 1e-89
+ 0x3AD2FFB9, 0x4F2B40A0, 0x79346BCA, 0xCBB41EF9, 0x031A, // 1e-88
+ 0x4987BFA8, 0xE2F610C8, 0xD78186BC, 0xFEA126B7, 0x031D, // 1e-87
+ 0x2DF4D7C9, 0x0DD9CA7D, 0xE6B0F436, 0x9F24B832, 0x0321, // 1e-86
+ 0x79720DBB, 0x91503D1C, 0xA05D3143, 0xC6EDE63F, 0x0324, // 1e-85
+ 0x97CE912A, 0x75A44C63, 0x88747D94, 0xF8A95FCF, 0x0327, // 1e-84
+ 0x3EE11ABA, 0xC986AFBE, 0xB548CE7C, 0x9B69DBE1, 0x032B, // 1e-83
+ 0xCE996168, 0xFBE85BAD, 0x229B021B, 0xC24452DA, 0x032E, // 1e-82
+ 0x423FB9C3, 0xFAE27299, 0xAB41C2A2, 0xF2D56790, 0x0331, // 1e-81
+ 0xC967D41A, 0xDCCD879F, 0x6B0919A5, 0x97C560BA, 0x0335, // 1e-80
+ 0xBBC1C920, 0x5400E987, 0x05CB600F, 0xBDB6B8E9, 0x0338, // 1e-79
+ 0xAAB23B68, 0x290123E9, 0x473E3813, 0xED246723, 0x033B, // 1e-78
+ 0x0AAF6521, 0xF9A0B672, 0x0C86E30B, 0x9436C076, 0x033F, // 1e-77
+ 0x8D5B3E69, 0xF808E40E, 0x8FA89BCE, 0xB9447093, 0x0342, // 1e-76
+ 0x30B20E04, 0xB60B1D12, 0x7392C2C2, 0xE7958CB8, 0x0345, // 1e-75
+ 0x5E6F48C2, 0xB1C6F22B, 0x483BB9B9, 0x90BD77F3, 0x0349, // 1e-74
+ 0x360B1AF3, 0x1E38AEB6, 0x1A4AA828, 0xB4ECD5F0, 0x034C, // 1e-73
+ 0xC38DE1B0, 0x25C6DA63, 0x20DD5232, 0xE2280B6C, 0x034F, // 1e-72
+ 0x5A38AD0E, 0x579C487E, 0x948A535F, 0x8D590723, 0x0353, // 1e-71
+ 0xF0C6D851, 0x2D835A9D, 0x79ACE837, 0xB0AF48EC, 0x0356, // 1e-70
+ 0x6CF88E65, 0xF8E43145, 0x98182244, 0xDCDB1B27, 0x0359, // 1e-69
+ 0x641B58FF, 0x1B8E9ECB, 0xBF0F156B, 0x8A08F0F8, 0x035D, // 1e-68
+ 0x3D222F3F, 0xE272467E, 0xEED2DAC5, 0xAC8B2D36, 0x0360, // 1e-67
+ 0xCC6ABB0F, 0x5B0ED81D, 0xAA879177, 0xD7ADF884, 0x0363, // 1e-66
+ 0x9FC2B4E9, 0x98E94712, 0xEA94BAEA, 0x86CCBB52, 0x0367, // 1e-65
+ 0x47B36224, 0x3F2398D7, 0xA539E9A5, 0xA87FEA27, 0x036A, // 1e-64
+ 0x19A03AAD, 0x8EEC7F0D, 0x8E88640E, 0xD29FE4B1, 0x036D, // 1e-63
+ 0x300424AC, 0x1953CF68, 0xF9153E89, 0x83A3EEEE, 0x0371, // 1e-62
+ 0x3C052DD7, 0x5FA8C342, 0xB75A8E2B, 0xA48CEAAA, 0x0374, // 1e-61
+ 0xCB06794D, 0x3792F412, 0x653131B6, 0xCDB02555, 0x0377, // 1e-60
+ 0xBEE40BD0, 0xE2BBD88B, 0x5F3EBF11, 0x808E1755, 0x037B, // 1e-59
+ 0xAE9D0EC4, 0x5B6ACEAE, 0xB70E6ED6, 0xA0B19D2A, 0x037E, // 1e-58
+ 0x5A445275, 0xF245825A, 0x64D20A8B, 0xC8DE0475, 0x0381, // 1e-57
+ 0xF0D56712, 0xEED6E2F0, 0xBE068D2E, 0xFB158592, 0x0384, // 1e-56
+ 0x9685606B, 0x55464DD6, 0xB6C4183D, 0x9CED737B, 0x0388, // 1e-55
+ 0x3C26B886, 0xAA97E14C, 0xA4751E4C, 0xC428D05A, 0x038B, // 1e-54
+ 0x4B3066A8, 0xD53DD99F, 0x4D9265DF, 0xF5330471, 0x038E, // 1e-53
+ 0x8EFE4029, 0xE546A803, 0xD07B7FAB, 0x993FE2C6, 0x0392, // 1e-52
+ 0x72BDD033, 0xDE985204, 0x849A5F96, 0xBF8FDB78, 0x0395, // 1e-51
+ 0x8F6D4440, 0x963E6685, 0xA5C0F77C, 0xEF73D256, 0x0398, // 1e-50
+ 0x79A44AA8, 0xDDE70013, 0x27989AAD, 0x95A86376, 0x039C, // 1e-49
+ 0x580D5D52, 0x5560C018, 0xB17EC159, 0xBB127C53, 0x039F, // 1e-48
+ 0x6E10B4A6, 0xAAB8F01E, 0x9DDE71AF, 0xE9D71B68, 0x03A2, // 1e-47
+ 0x04CA70E8, 0xCAB39613, 0x62AB070D, 0x92267121, 0x03A6, // 1e-46
+ 0xC5FD0D22, 0x3D607B97, 0xBB55C8D1, 0xB6B00D69, 0x03A9, // 1e-45
+ 0xB77C506A, 0x8CB89A7D, 0x2A2B3B05, 0xE45C10C4, 0x03AC, // 1e-44
+ 0x92ADB242, 0x77F3608E, 0x9A5B04E3, 0x8EB98A7A, 0x03B0, // 1e-43
+ 0x37591ED3, 0x55F038B2, 0x40F1C61C, 0xB267ED19, 0x03B3, // 1e-42
+ 0xC52F6688, 0x6B6C46DE, 0x912E37A3, 0xDF01E85F, 0x03B6, // 1e-41
+ 0x3B3DA015, 0x2323AC4B, 0xBABCE2C6, 0x8B61313B, 0x03BA, // 1e-40
+ 0x0A0D081A, 0xABEC975E, 0xA96C1B77, 0xAE397D8A, 0x03BD, // 1e-39
+ 0x8C904A21, 0x96E7BD35, 0x53C72255, 0xD9C7DCED, 0x03C0, // 1e-38
+ 0x77DA2E54, 0x7E50D641, 0x545C7575, 0x881CEA14, 0x03C4, // 1e-37
+ 0xD5D0B9E9, 0xDDE50BD1, 0x697392D2, 0xAA242499, 0x03C7, // 1e-36
+ 0x4B44E864, 0x955E4EC6, 0xC3D07787, 0xD4AD2DBF, 0x03CA, // 1e-35
+ 0xEF0B113E, 0xBD5AF13B, 0xDA624AB4, 0x84EC3C97, 0x03CE, // 1e-34
+ 0xEACDD58E, 0xECB1AD8A, 0xD0FADD61, 0xA6274BBD, 0x03D1, // 1e-33
+ 0xA5814AF2, 0x67DE18ED, 0x453994BA, 0xCFB11EAD, 0x03D4, // 1e-32
+ 0x8770CED7, 0x80EACF94, 0x4B43FCF4, 0x81CEB32C, 0x03D8, // 1e-31
+ 0xA94D028D, 0xA1258379, 0x5E14FC31, 0xA2425FF7, 0x03DB, // 1e-30
+ 0x13A04330, 0x096EE458, 0x359A3B3E, 0xCAD2F7F5, 0x03DE, // 1e-29
+ 0x188853FC, 0x8BCA9D6E, 0x8300CA0D, 0xFD87B5F2, 0x03E1, // 1e-28
+ 0xCF55347D, 0x775EA264, 0x91E07E48, 0x9E74D1B7, 0x03E5, // 1e-27
+ 0x032A819D, 0x95364AFE, 0x76589DDA, 0xC6120625, 0x03E8, // 1e-26
+ 0x83F52204, 0x3A83DDBD, 0xD3EEC551, 0xF79687AE, 0x03EB, // 1e-25
+ 0x72793542, 0xC4926A96, 0x44753B52, 0x9ABE14CD, 0x03EF, // 1e-24
+ 0x0F178293, 0x75B7053C, 0x95928A27, 0xC16D9A00, 0x03F2, // 1e-23
+ 0x12DD6338, 0x5324C68B, 0xBAF72CB1, 0xF1C90080, 0x03F5, // 1e-22
+ 0xEBCA5E03, 0xD3F6FC16, 0x74DA7BEE, 0x971DA050, 0x03F9, // 1e-21
+ 0xA6BCF584, 0x88F4BB1C, 0x92111AEA, 0xBCE50864, 0x03FC, // 1e-20
+ 0xD06C32E5, 0x2B31E9E3, 0xB69561A5, 0xEC1E4A7D, 0x03FF, // 1e-19
+ 0x62439FCF, 0x3AFF322E, 0x921D5D07, 0x9392EE8E, 0x0403, // 1e-18
+ 0xFAD487C2, 0x09BEFEB9, 0x36A4B449, 0xB877AA32, 0x0406, // 1e-17
+ 0x7989A9B3, 0x4C2EBE68, 0xC44DE15B, 0xE69594BE, 0x0409, // 1e-16
+ 0x4BF60A10, 0x0F9D3701, 0x3AB0ACD9, 0x901D7CF7, 0x040D, // 1e-15
+ 0x9EF38C94, 0x538484C1, 0x095CD80F, 0xB424DC35, 0x0410, // 1e-14
+ 0x06B06FB9, 0x2865A5F2, 0x4BB40E13, 0xE12E1342, 0x0413, // 1e-13
+ 0x442E45D3, 0xF93F87B7, 0x6F5088CB, 0x8CBCCC09, 0x0417, // 1e-12
+ 0x1539D748, 0xF78F69A5, 0xCB24AAFE, 0xAFEBFF0B, 0x041A, // 1e-11
+ 0x5A884D1B, 0xB573440E, 0xBDEDD5BE, 0xDBE6FECE, 0x041D, // 1e-10
+ 0xF8953030, 0x31680A88, 0x36B4A597, 0x89705F41, 0x0421, // 1e-9
+ 0x36BA7C3D, 0xFDC20D2B, 0x8461CEFC, 0xABCC7711, 0x0424, // 1e-8
+ 0x04691B4C, 0x3D329076, 0xE57A42BC, 0xD6BF94D5, 0x0427, // 1e-7
+ 0xC2C1B10F, 0xA63F9A49, 0xAF6C69B5, 0x8637BD05, 0x042B, // 1e-6
+ 0x33721D53, 0x0FCF80DC, 0x1B478423, 0xA7C5AC47, 0x042E, // 1e-5
+ 0x404EA4A8, 0xD3C36113, 0xE219652B, 0xD1B71758, 0x0431, // 1e-4
+ 0x083126E9, 0x645A1CAC, 0x8D4FDF3B, 0x83126E97, 0x0435, // 1e-3
+ 0x0A3D70A3, 0x3D70A3D7, 0x70A3D70A, 0xA3D70A3D, 0x0438, // 1e-2
+ 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0x043B, // 1e-1
+ 0x00000000, 0x00000000, 0x00000000, 0x80000000, 0x043F, // 1e0
+ 0x00000000, 0x00000000, 0x00000000, 0xA0000000, 0x0442, // 1e1
+ 0x00000000, 0x00000000, 0x00000000, 0xC8000000, 0x0445, // 1e2
+ 0x00000000, 0x00000000, 0x00000000, 0xFA000000, 0x0448, // 1e3
+ 0x00000000, 0x00000000, 0x00000000, 0x9C400000, 0x044C, // 1e4
+ 0x00000000, 0x00000000, 0x00000000, 0xC3500000, 0x044F, // 1e5
+ 0x00000000, 0x00000000, 0x00000000, 0xF4240000, 0x0452, // 1e6
+ 0x00000000, 0x00000000, 0x00000000, 0x98968000, 0x0456, // 1e7
+ 0x00000000, 0x00000000, 0x00000000, 0xBEBC2000, 0x0459, // 1e8
+ 0x00000000, 0x00000000, 0x00000000, 0xEE6B2800, 0x045C, // 1e9
+ 0x00000000, 0x00000000, 0x00000000, 0x9502F900, 0x0460, // 1e10
+ 0x00000000, 0x00000000, 0x00000000, 0xBA43B740, 0x0463, // 1e11
+ 0x00000000, 0x00000000, 0x00000000, 0xE8D4A510, 0x0466, // 1e12
+ 0x00000000, 0x00000000, 0x00000000, 0x9184E72A, 0x046A, // 1e13
+ 0x00000000, 0x00000000, 0x80000000, 0xB5E620F4, 0x046D, // 1e14
+ 0x00000000, 0x00000000, 0xA0000000, 0xE35FA931, 0x0470, // 1e15
+ 0x00000000, 0x00000000, 0x04000000, 0x8E1BC9BF, 0x0474, // 1e16
+ 0x00000000, 0x00000000, 0xC5000000, 0xB1A2BC2E, 0x0477, // 1e17
+ 0x00000000, 0x00000000, 0x76400000, 0xDE0B6B3A, 0x047A, // 1e18
+ 0x00000000, 0x00000000, 0x89E80000, 0x8AC72304, 0x047E, // 1e19
+ 0x00000000, 0x00000000, 0xAC620000, 0xAD78EBC5, 0x0481, // 1e20
+ 0x00000000, 0x00000000, 0x177A8000, 0xD8D726B7, 0x0484, // 1e21
+ 0x00000000, 0x00000000, 0x6EAC9000, 0x87867832, 0x0488, // 1e22
+ 0x00000000, 0x00000000, 0x0A57B400, 0xA968163F, 0x048B, // 1e23
+ 0x00000000, 0x00000000, 0xCCEDA100, 0xD3C21BCE, 0x048E, // 1e24
+ 0x00000000, 0x00000000, 0x401484A0, 0x84595161, 0x0492, // 1e25
+ 0x00000000, 0x00000000, 0x9019A5C8, 0xA56FA5B9, 0x0495, // 1e26
+ 0x00000000, 0x00000000, 0xF4200F3A, 0xCECB8F27, 0x0498, // 1e27
+ 0x00000000, 0x40000000, 0xF8940984, 0x813F3978, 0x049C, // 1e28
+ 0x00000000, 0x50000000, 0x36B90BE5, 0xA18F07D7, 0x049F, // 1e29
+ 0x00000000, 0xA4000000, 0x04674EDE, 0xC9F2C9CD, 0x04A2, // 1e30
+ 0x00000000, 0x4D000000, 0x45812296, 0xFC6F7C40, 0x04A5, // 1e31
+ 0x00000000, 0xF0200000, 0x2B70B59D, 0x9DC5ADA8, 0x04A9, // 1e32
+ 0x00000000, 0x6C280000, 0x364CE305, 0xC5371912, 0x04AC, // 1e33
+ 0x00000000, 0xC7320000, 0xC3E01BC6, 0xF684DF56, 0x04AF, // 1e34
+ 0x00000000, 0x3C7F4000, 0x3A6C115C, 0x9A130B96, 0x04B3, // 1e35
+ 0x00000000, 0x4B9F1000, 0xC90715B3, 0xC097CE7B, 0x04B6, // 1e36
+ 0x00000000, 0x1E86D400, 0xBB48DB20, 0xF0BDC21A, 0x04B9, // 1e37
+ 0x00000000, 0x13144480, 0xB50D88F4, 0x96769950, 0x04BD, // 1e38
+ 0x00000000, 0x17D955A0, 0xE250EB31, 0xBC143FA4, 0x04C0, // 1e39
+ 0x00000000, 0x5DCFAB08, 0x1AE525FD, 0xEB194F8E, 0x04C3, // 1e40
+ 0x00000000, 0x5AA1CAE5, 0xD0CF37BE, 0x92EFD1B8, 0x04C7, // 1e41
+ 0x40000000, 0xF14A3D9E, 0x050305AD, 0xB7ABC627, 0x04CA, // 1e42
+ 0xD0000000, 0x6D9CCD05, 0xC643C719, 0xE596B7B0, 0x04CD, // 1e43
+ 0xA2000000, 0xE4820023, 0x7BEA5C6F, 0x8F7E32CE, 0x04D1, // 1e44
+ 0x8A800000, 0xDDA2802C, 0x1AE4F38B, 0xB35DBF82, 0x04D4, // 1e45
+ 0xAD200000, 0xD50B2037, 0xA19E306E, 0xE0352F62, 0x04D7, // 1e46
+ 0xCC340000, 0x4526F422, 0xA502DE45, 0x8C213D9D, 0x04DB, // 1e47
+ 0x7F410000, 0x9670B12B, 0x0E4395D6, 0xAF298D05, 0x04DE, // 1e48
+ 0x5F114000, 0x3C0CDD76, 0x51D47B4C, 0xDAF3F046, 0x04E1, // 1e49
+ 0xFB6AC800, 0xA5880A69, 0xF324CD0F, 0x88D8762B, 0x04E5, // 1e50
+ 0x7A457A00, 0x8EEA0D04, 0xEFEE0053, 0xAB0E93B6, 0x04E8, // 1e51
+ 0x98D6D880, 0x72A49045, 0xABE98068, 0xD5D238A4, 0x04EB, // 1e52
+ 0x7F864750, 0x47A6DA2B, 0xEB71F041, 0x85A36366, 0x04EF, // 1e53
+ 0x5F67D924, 0x999090B6, 0xA64E6C51, 0xA70C3C40, 0x04F2, // 1e54
+ 0xF741CF6D, 0xFFF4B4E3, 0xCFE20765, 0xD0CF4B50, 0x04F5, // 1e55
+ 0x7A8921A4, 0xBFF8F10E, 0x81ED449F, 0x82818F12, 0x04F9, // 1e56
+ 0x192B6A0D, 0xAFF72D52, 0x226895C7, 0xA321F2D7, 0x04FC, // 1e57
+ 0x9F764490, 0x9BF4F8A6, 0xEB02BB39, 0xCBEA6F8C, 0x04FF, // 1e58
+ 0x4753D5B4, 0x02F236D0, 0x25C36A08, 0xFEE50B70, 0x0502, // 1e59
+ 0x2C946590, 0x01D76242, 0x179A2245, 0x9F4F2726, 0x0506, // 1e60
+ 0xB7B97EF5, 0x424D3AD2, 0x9D80AAD6, 0xC722F0EF, 0x0509, // 1e61
+ 0x65A7DEB2, 0xD2E08987, 0x84E0D58B, 0xF8EBAD2B, 0x050C, // 1e62
+ 0x9F88EB2F, 0x63CC55F4, 0x330C8577, 0x9B934C3B, 0x0510, // 1e63
+ 0xC76B25FB, 0x3CBF6B71, 0xFFCFA6D5, 0xC2781F49, 0x0513, // 1e64
+ 0x3945EF7A, 0x8BEF464E, 0x7FC3908A, 0xF316271C, 0x0516, // 1e65
+ 0xE3CBB5AC, 0x97758BF0, 0xCFDA3A56, 0x97EDD871, 0x051A, // 1e66
+ 0x1CBEA317, 0x3D52EEED, 0x43D0C8EC, 0xBDE94E8E, 0x051D, // 1e67
+ 0x63EE4BDD, 0x4CA7AAA8, 0xD4C4FB27, 0xED63A231, 0x0520, // 1e68
+ 0x3E74EF6A, 0x8FE8CAA9, 0x24FB1CF8, 0x945E455F, 0x0524, // 1e69
+ 0x8E122B44, 0xB3E2FD53, 0xEE39E436, 0xB975D6B6, 0x0527, // 1e70
+ 0x7196B616, 0x60DBBCA8, 0xA9C85D44, 0xE7D34C64, 0x052A, // 1e71
+ 0x46FE31CD, 0xBC8955E9, 0xEA1D3A4A, 0x90E40FBE, 0x052E, // 1e72
+ 0x98BDBE41, 0x6BABAB63, 0xA4A488DD, 0xB51D13AE, 0x0531, // 1e73
+ 0x7EED2DD1, 0xC696963C, 0x4DCDAB14, 0xE264589A, 0x0534, // 1e74
+ 0xCF543CA2, 0xFC1E1DE5, 0x70A08AEC, 0x8D7EB760, 0x0538, // 1e75
+ 0x43294BCB, 0x3B25A55F, 0x8CC8ADA8, 0xB0DE6538, 0x053B, // 1e76
+ 0x13F39EBE, 0x49EF0EB7, 0xAFFAD912, 0xDD15FE86, 0x053E, // 1e77
+ 0x6C784337, 0x6E356932, 0x2DFCC7AB, 0x8A2DBF14, 0x0542, // 1e78
+ 0x07965404, 0x49C2C37F, 0x397BF996, 0xACB92ED9, 0x0545, // 1e79
+ 0xC97BE906, 0xDC33745E, 0x87DAF7FB, 0xD7E77A8F, 0x0548, // 1e80
+ 0x3DED71A3, 0x69A028BB, 0xB4E8DAFD, 0x86F0AC99, 0x054C, // 1e81
+ 0x0D68CE0C, 0xC40832EA, 0x222311BC, 0xA8ACD7C0, 0x054F, // 1e82
+ 0x90C30190, 0xF50A3FA4, 0x2AABD62B, 0xD2D80DB0, 0x0552, // 1e83
+ 0xDA79E0FA, 0x792667C6, 0x1AAB65DB, 0x83C7088E, 0x0556, // 1e84
+ 0x91185938, 0x577001B8, 0xA1563F52, 0xA4B8CAB1, 0x0559, // 1e85
+ 0xB55E6F86, 0xED4C0226, 0x09ABCF26, 0xCDE6FD5E, 0x055C, // 1e86
+ 0x315B05B4, 0x544F8158, 0xC60B6178, 0x80B05E5A, 0x0560, // 1e87
+ 0x3DB1C721, 0x696361AE, 0x778E39D6, 0xA0DC75F1, 0x0563, // 1e88
+ 0xCD1E38E9, 0x03BC3A19, 0xD571C84C, 0xC913936D, 0x0566, // 1e89
+ 0x4065C723, 0x04AB48A0, 0x4ACE3A5F, 0xFB587849, 0x0569, // 1e90
+ 0x283F9C76, 0x62EB0D64, 0xCEC0E47B, 0x9D174B2D, 0x056D, // 1e91
+ 0x324F8394, 0x3BA5D0BD, 0x42711D9A, 0xC45D1DF9, 0x0570, // 1e92
+ 0x7EE36479, 0xCA8F44EC, 0x930D6500, 0xF5746577, 0x0573, // 1e93
+ 0xCF4E1ECB, 0x7E998B13, 0xBBE85F20, 0x9968BF6A, 0x0577, // 1e94
+ 0xC321A67E, 0x9E3FEDD8, 0x6AE276E8, 0xBFC2EF45, 0x057A, // 1e95
+ 0xF3EA101E, 0xC5CFE94E, 0xC59B14A2, 0xEFB3AB16, 0x057D, // 1e96
+ 0x58724A12, 0xBBA1F1D1, 0x3B80ECE5, 0x95D04AEE, 0x0581, // 1e97
+ 0xAE8EDC97, 0x2A8A6E45, 0xCA61281F, 0xBB445DA9, 0x0584, // 1e98
+ 0x1A3293BD, 0xF52D09D7, 0x3CF97226, 0xEA157514, 0x0587, // 1e99
+ 0x705F9C56, 0x593C2626, 0xA61BE758, 0x924D692C, 0x058B, // 1e100
+ 0x0C77836C, 0x6F8B2FB0, 0xCFA2E12E, 0xB6E0C377, 0x058E, // 1e101
+ 0x0F956447, 0x0B6DFB9C, 0xC38B997A, 0xE498F455, 0x0591, // 1e102
+ 0x89BD5EAC, 0x4724BD41, 0x9A373FEC, 0x8EDF98B5, 0x0595, // 1e103
+ 0xEC2CB657, 0x58EDEC91, 0x00C50FE7, 0xB2977EE3, 0x0598, // 1e104
+ 0x6737E3ED, 0x2F2967B6, 0xC0F653E1, 0xDF3D5E9B, 0x059B, // 1e105
+ 0x0082EE74, 0xBD79E0D2, 0x5899F46C, 0x8B865B21, 0x059F, // 1e106
+ 0x80A3AA11, 0xECD85906, 0xAEC07187, 0xAE67F1E9, 0x05A2, // 1e107
+ 0x20CC9495, 0xE80E6F48, 0x1A708DE9, 0xDA01EE64, 0x05A5, // 1e108
+ 0x147FDCDD, 0x3109058D, 0x908658B2, 0x884134FE, 0x05A9, // 1e109
+ 0x599FD415, 0xBD4B46F0, 0x34A7EEDE, 0xAA51823E, 0x05AC, // 1e110
+ 0x7007C91A, 0x6C9E18AC, 0xC1D1EA96, 0xD4E5E2CD, 0x05AF, // 1e111
+ 0xC604DDB0, 0x03E2CF6B, 0x9923329E, 0x850FADC0, 0x05B3, // 1e112
+ 0xB786151C, 0x84DB8346, 0xBF6BFF45, 0xA6539930, 0x05B6, // 1e113
+ 0x65679A63, 0xE6126418, 0xEF46FF16, 0xCFE87F7C, 0x05B9, // 1e114
+ 0x3F60C07E, 0x4FCB7E8F, 0x158C5F6E, 0x81F14FAE, 0x05BD, // 1e115
+ 0x0F38F09D, 0xE3BE5E33, 0x9AEF7749, 0xA26DA399, 0x05C0, // 1e116
+ 0xD3072CC5, 0x5CADF5BF, 0x01AB551C, 0xCB090C80, 0x05C3, // 1e117
+ 0xC7C8F7F6, 0x73D9732F, 0x02162A63, 0xFDCB4FA0, 0x05C6, // 1e118
+ 0xDCDD9AFA, 0x2867E7FD, 0x014DDA7E, 0x9E9F11C4, 0x05CA, // 1e119
+ 0x541501B8, 0xB281E1FD, 0x01A1511D, 0xC646D635, 0x05CD, // 1e120
+ 0xA91A4226, 0x1F225A7C, 0x4209A565, 0xF7D88BC2, 0x05D0, // 1e121
+ 0xE9B06958, 0x3375788D, 0x6946075F, 0x9AE75759, 0x05D4, // 1e122
+ 0x641C83AE, 0x0052D6B1, 0xC3978937, 0xC1A12D2F, 0x05D7, // 1e123
+ 0xBD23A49A, 0xC0678C5D, 0xB47D6B84, 0xF209787B, 0x05DA, // 1e124
+ 0x963646E0, 0xF840B7BA, 0x50CE6332, 0x9745EB4D, 0x05DE, // 1e125
+ 0x3BC3D898, 0xB650E5A9, 0xA501FBFF, 0xBD176620, 0x05E1, // 1e126
+ 0x8AB4CEBE, 0xA3E51F13, 0xCE427AFF, 0xEC5D3FA8, 0x05E4, // 1e127
+ 0x36B10137, 0xC66F336C, 0x80E98CDF, 0x93BA47C9, 0x05E8, // 1e128
+ 0x445D4184, 0xB80B0047, 0xE123F017, 0xB8A8D9BB, 0x05EB, // 1e129
+ 0x157491E5, 0xA60DC059, 0xD96CEC1D, 0xE6D3102A, 0x05EE, // 1e130
+ 0xAD68DB2F, 0x87C89837, 0xC7E41392, 0x9043EA1A, 0x05F2, // 1e131
+ 0x98C311FB, 0x29BABE45, 0x79DD1877, 0xB454E4A1, 0x05F5, // 1e132
+ 0xFEF3D67A, 0xF4296DD6, 0xD8545E94, 0xE16A1DC9, 0x05F8, // 1e133
+ 0x5F58660C, 0x1899E4A6, 0x2734BB1D, 0x8CE2529E, 0x05FC, // 1e134
+ 0xF72E7F8F, 0x5EC05DCF, 0xB101E9E4, 0xB01AE745, 0x05FF, // 1e135
+ 0xF4FA1F73, 0x76707543, 0x1D42645D, 0xDC21A117, 0x0602, // 1e136
+ 0x791C53A8, 0x6A06494A, 0x72497EBA, 0x899504AE, 0x0606, // 1e137
+ 0x17636892, 0x0487DB9D, 0x0EDBDE69, 0xABFA45DA, 0x0609, // 1e138
+ 0x5D3C42B6, 0x45A9D284, 0x9292D603, 0xD6F8D750, 0x060C, // 1e139
+ 0xBA45A9B2, 0x0B8A2392, 0x5B9BC5C2, 0x865B8692, 0x0610, // 1e140
+ 0x68D7141E, 0x8E6CAC77, 0xF282B732, 0xA7F26836, 0x0613, // 1e141
+ 0x430CD926, 0x3207D795, 0xAF2364FF, 0xD1EF0244, 0x0616, // 1e142
+ 0x49E807B8, 0x7F44E6BD, 0xED761F1F, 0x8335616A, 0x061A, // 1e143
+ 0x9C6209A6, 0x5F16206C, 0xA8D3A6E7, 0xA402B9C5, 0x061D, // 1e144
+ 0xC37A8C0F, 0x36DBA887, 0x130890A1, 0xCD036837, 0x0620, // 1e145
+ 0xDA2C9789, 0xC2494954, 0x6BE55A64, 0x80222122, 0x0624, // 1e146
+ 0x10B7BD6C, 0xF2DB9BAA, 0x06DEB0FD, 0xA02AA96B, 0x0627, // 1e147
+ 0x94E5ACC7, 0x6F928294, 0xC8965D3D, 0xC83553C5, 0x062A, // 1e148
+ 0xBA1F17F9, 0xCB772339, 0x3ABBF48C, 0xFA42A8B7, 0x062D, // 1e149
+ 0x14536EFB, 0xFF2A7604, 0x84B578D7, 0x9C69A972, 0x0631, // 1e150
+ 0x19684ABA, 0xFEF51385, 0x25E2D70D, 0xC38413CF, 0x0634, // 1e151
+ 0x5FC25D69, 0x7EB25866, 0xEF5B8CD1, 0xF46518C2, 0x0637, // 1e152
+ 0xFBD97A61, 0xEF2F773F, 0xD5993802, 0x98BF2F79, 0x063B, // 1e153
+ 0xFACFD8FA, 0xAAFB550F, 0x4AFF8603, 0xBEEEFB58, 0x063E, // 1e154
+ 0xF983CF38, 0x95BA2A53, 0x5DBF6784, 0xEEAABA2E, 0x0641, // 1e155
+ 0x7BF26183, 0xDD945A74, 0xFA97A0B2, 0x952AB45C, 0x0645, // 1e156
+ 0x9AEEF9E4, 0x94F97111, 0x393D88DF, 0xBA756174, 0x0648, // 1e157
+ 0x01AAB85D, 0x7A37CD56, 0x478CEB17, 0xE912B9D1, 0x064B, // 1e158
+ 0xC10AB33A, 0xAC62E055, 0xCCB812EE, 0x91ABB422, 0x064F, // 1e159
+ 0x314D6009, 0x577B986B, 0x7FE617AA, 0xB616A12B, 0x0652, // 1e160
+ 0xFDA0B80B, 0xED5A7E85, 0x5FDF9D94, 0xE39C4976, 0x0655, // 1e161
+ 0xBE847307, 0x14588F13, 0xFBEBC27D, 0x8E41ADE9, 0x0659, // 1e162
+ 0xAE258FC8, 0x596EB2D8, 0x7AE6B31C, 0xB1D21964, 0x065C, // 1e163
+ 0xD9AEF3BB, 0x6FCA5F8E, 0x99A05FE3, 0xDE469FBD, 0x065F, // 1e164
+ 0x480D5854, 0x25DE7BB9, 0x80043BEE, 0x8AEC23D6, 0x0663, // 1e165
+ 0x9A10AE6A, 0xAF561AA7, 0x20054AE9, 0xADA72CCC, 0x0666, // 1e166
+ 0x8094DA04, 0x1B2BA151, 0x28069DA4, 0xD910F7FF, 0x0669, // 1e167
+ 0xF05D0842, 0x90FB44D2, 0x79042286, 0x87AA9AFF, 0x066D, // 1e168
+ 0xAC744A53, 0x353A1607, 0x57452B28, 0xA99541BF, 0x0670, // 1e169
+ 0x97915CE8, 0x42889B89, 0x2D1675F2, 0xD3FA922F, 0x0673, // 1e170
+ 0xFEBADA11, 0x69956135, 0x7C2E09B7, 0x847C9B5D, 0x0677, // 1e171
+ 0x7E699095, 0x43FAB983, 0xDB398C25, 0xA59BC234, 0x067A, // 1e172
+ 0x5E03F4BB, 0x94F967E4, 0x1207EF2E, 0xCF02B2C2, 0x067D, // 1e173
+ 0xBAC278F5, 0x1D1BE0EE, 0x4B44F57D, 0x8161AFB9, 0x0681, // 1e174
+ 0x69731732, 0x6462D92A, 0x9E1632DC, 0xA1BA1BA7, 0x0684, // 1e175
+ 0x03CFDCFE, 0x7D7B8F75, 0x859BBF93, 0xCA28A291, 0x0687, // 1e176
+ 0x44C3D43E, 0x5CDA7352, 0xE702AF78, 0xFCB2CB35, 0x068A, // 1e177
+ 0x6AFA64A7, 0x3A088813, 0xB061ADAB, 0x9DEFBF01, 0x068E, // 1e178
+ 0x45B8FDD0, 0x088AAA18, 0x1C7A1916, 0xC56BAEC2, 0x0691, // 1e179
+ 0x57273D45, 0x8AAD549E, 0xA3989F5B, 0xF6C69A72, 0x0694, // 1e180
+ 0xF678864B, 0x36AC54E2, 0xA63F6399, 0x9A3C2087, 0x0698, // 1e181
+ 0xB416A7DD, 0x84576A1B, 0x8FCF3C7F, 0xC0CB28A9, 0x069B, // 1e182
+ 0xA11C51D5, 0x656D44A2, 0xF3C30B9F, 0xF0FDF2D3, 0x069E, // 1e183
+ 0xA4B1B325, 0x9F644AE5, 0x7859E743, 0x969EB7C4, 0x06A2, // 1e184
+ 0x0DDE1FEE, 0x873D5D9F, 0x96706114, 0xBC4665B5, 0x06A5, // 1e185
+ 0xD155A7EA, 0xA90CB506, 0xFC0C7959, 0xEB57FF22, 0x06A8, // 1e186
+ 0x42D588F2, 0x09A7F124, 0xDD87CBD8, 0x9316FF75, 0x06AC, // 1e187
+ 0x538AEB2F, 0x0C11ED6D, 0x54E9BECE, 0xB7DCBF53, 0x06AF, // 1e188
+ 0xA86DA5FA, 0x8F1668C8, 0x2A242E81, 0xE5D3EF28, 0x06B2, // 1e189
+ 0x694487BC, 0xF96E017D, 0x1A569D10, 0x8FA47579, 0x06B6, // 1e190
+ 0xC395A9AC, 0x37C981DC, 0x60EC4455, 0xB38D92D7, 0x06B9, // 1e191
+ 0xF47B1417, 0x85BBE253, 0x3927556A, 0xE070F78D, 0x06BC, // 1e192
+ 0x78CCEC8E, 0x93956D74, 0x43B89562, 0x8C469AB8, 0x06C0, // 1e193
+ 0x970027B2, 0x387AC8D1, 0x54A6BABB, 0xAF584166, 0x06C3, // 1e194
+ 0xFCC0319E, 0x06997B05, 0xE9D0696A, 0xDB2E51BF, 0x06C6, // 1e195
+ 0xBDF81F03, 0x441FECE3, 0xF22241E2, 0x88FCF317, 0x06CA, // 1e196
+ 0xAD7626C3, 0xD527E81C, 0xEEAAD25A, 0xAB3C2FDD, 0x06CD, // 1e197
+ 0xD8D3B074, 0x8A71E223, 0x6A5586F1, 0xD60B3BD5, 0x06D0, // 1e198
+ 0x67844E49, 0xF6872D56, 0x62757456, 0x85C70565, 0x06D4, // 1e199
+ 0x016561DB, 0xB428F8AC, 0xBB12D16C, 0xA738C6BE, 0x06D7, // 1e200
+ 0x01BEBA52, 0xE13336D7, 0x69D785C7, 0xD106F86E, 0x06DA, // 1e201
+ 0x61173473, 0xECC00246, 0x0226B39C, 0x82A45B45, 0x06DE, // 1e202
+ 0xF95D0190, 0x27F002D7, 0x42B06084, 0xA34D7216, 0x06E1, // 1e203
+ 0xF7B441F4, 0x31EC038D, 0xD35C78A5, 0xCC20CE9B, 0x06E4, // 1e204
+ 0x75A15271, 0x7E670471, 0xC83396CE, 0xFF290242, 0x06E7, // 1e205
+ 0xE984D386, 0x0F0062C6, 0xBD203E41, 0x9F79A169, 0x06EB, // 1e206
+ 0xA3E60868, 0x52C07B78, 0x2C684DD1, 0xC75809C4, 0x06EE, // 1e207
+ 0xCCDF8A82, 0xA7709A56, 0x37826145, 0xF92E0C35, 0x06F1, // 1e208
+ 0x400BB691, 0x88A66076, 0x42B17CCB, 0x9BBCC7A1, 0x06F5, // 1e209
+ 0xD00EA435, 0x6ACFF893, 0x935DDBFE, 0xC2ABF989, 0x06F8, // 1e210
+ 0xC4124D43, 0x0583F6B8, 0xF83552FE, 0xF356F7EB, 0x06FB, // 1e211
+ 0x7A8B704A, 0xC3727A33, 0x7B2153DE, 0x98165AF3, 0x06FF, // 1e212
+ 0x592E4C5C, 0x744F18C0, 0x59E9A8D6, 0xBE1BF1B0, 0x0702, // 1e213
+ 0x6F79DF73, 0x1162DEF0, 0x7064130C, 0xEDA2EE1C, 0x0705, // 1e214
+ 0x45AC2BA8, 0x8ADDCB56, 0xC63E8BE7, 0x9485D4D1, 0x0709, // 1e215
+ 0xD7173692, 0x6D953E2B, 0x37CE2EE1, 0xB9A74A06, 0x070C, // 1e216
+ 0xCCDD0437, 0xC8FA8DB6, 0xC5C1BA99, 0xE8111C87, 0x070F, // 1e217
+ 0x400A22A2, 0x1D9C9892, 0xDB9914A0, 0x910AB1D4, 0x0713, // 1e218
+ 0xD00CAB4B, 0x2503BEB6, 0x127F59C8, 0xB54D5E4A, 0x0716, // 1e219
+ 0x840FD61D, 0x2E44AE64, 0x971F303A, 0xE2A0B5DC, 0x0719, // 1e220
+ 0xD289E5D2, 0x5CEAECFE, 0xDE737E24, 0x8DA471A9, 0x071D, // 1e221
+ 0x872C5F47, 0x7425A83E, 0x56105DAD, 0xB10D8E14, 0x0720, // 1e222
+ 0x28F77719, 0xD12F124E, 0x6B947518, 0xDD50F199, 0x0723, // 1e223
+ 0xD99AAA6F, 0x82BD6B70, 0xE33CC92F, 0x8A5296FF, 0x0727, // 1e224
+ 0x1001550B, 0x636CC64D, 0xDC0BFB7B, 0xACE73CBF, 0x072A, // 1e225
+ 0x5401AA4E, 0x3C47F7E0, 0xD30EFA5A, 0xD8210BEF, 0x072D, // 1e226
+ 0x34810A71, 0x65ACFAEC, 0xE3E95C78, 0x8714A775, 0x0731, // 1e227
+ 0x41A14D0D, 0x7F1839A7, 0x5CE3B396, 0xA8D9D153, 0x0734, // 1e228
+ 0x1209A050, 0x1EDE4811, 0x341CA07C, 0xD31045A8, 0x0737, // 1e229
+ 0xAB460432, 0x934AED0A, 0x2091E44D, 0x83EA2B89, 0x073B, // 1e230
+ 0x5617853F, 0xF81DA84D, 0x68B65D60, 0xA4E4B66B, 0x073E, // 1e231
+ 0xAB9D668E, 0x36251260, 0x42E3F4B9, 0xCE1DE406, 0x0741, // 1e232
+ 0x6B426019, 0xC1D72B7C, 0xE9CE78F3, 0x80D2AE83, 0x0745, // 1e233
+ 0x8612F81F, 0xB24CF65B, 0xE4421730, 0xA1075A24, 0x0748, // 1e234
+ 0x6797B627, 0xDEE033F2, 0x1D529CFC, 0xC94930AE, 0x074B, // 1e235
+ 0x017DA3B1, 0x169840EF, 0xA4A7443C, 0xFB9B7CD9, 0x074E, // 1e236
+ 0x60EE864E, 0x8E1F2895, 0x06E88AA5, 0x9D412E08, 0x0752, // 1e237
+ 0xB92A27E2, 0xF1A6F2BA, 0x08A2AD4E, 0xC491798A, 0x0755, // 1e238
+ 0x6774B1DB, 0xAE10AF69, 0x8ACB58A2, 0xF5B5D7EC, 0x0758, // 1e239
+ 0xE0A8EF29, 0xACCA6DA1, 0xD6BF1765, 0x9991A6F3, 0x075C, // 1e240
+ 0x58D32AF3, 0x17FD090A, 0xCC6EDD3F, 0xBFF610B0, 0x075F, // 1e241
+ 0xEF07F5B0, 0xDDFC4B4C, 0xFF8A948E, 0xEFF394DC, 0x0762, // 1e242
+ 0x1564F98E, 0x4ABDAF10, 0x1FB69CD9, 0x95F83D0A, 0x0766, // 1e243
+ 0x1ABE37F1, 0x9D6D1AD4, 0xA7A4440F, 0xBB764C4C, 0x0769, // 1e244
+ 0x216DC5ED, 0x84C86189, 0xD18D5513, 0xEA53DF5F, 0x076C, // 1e245
+ 0xB4E49BB4, 0x32FD3CF5, 0xE2F8552C, 0x92746B9B, 0x0770, // 1e246
+ 0x221DC2A1, 0x3FBC8C33, 0xDBB66A77, 0xB7118682, 0x0773, // 1e247
+ 0xEAA5334A, 0x0FABAF3F, 0x92A40515, 0xE4D5E823, 0x0776, // 1e248
+ 0xF2A7400E, 0x29CB4D87, 0x3BA6832D, 0x8F05B116, 0x077A, // 1e249
+ 0xEF511012, 0x743E20E9, 0xCA9023F8, 0xB2C71D5B, 0x077D, // 1e250
+ 0x6B255416, 0x914DA924, 0xBD342CF6, 0xDF78E4B2, 0x0780, // 1e251
+ 0xC2F7548E, 0x1AD089B6, 0xB6409C1A, 0x8BAB8EEF, 0x0784, // 1e252
+ 0x73B529B1, 0xA184AC24, 0xA3D0C320, 0xAE9672AB, 0x0787, // 1e253
+ 0x90A2741E, 0xC9E5D72D, 0x8CC4F3E8, 0xDA3C0F56, 0x078A, // 1e254
+ 0x7A658892, 0x7E2FA67C, 0x17FB1871, 0x88658996, 0x078E, // 1e255
+ 0x98FEEAB7, 0xDDBB901B, 0x9DF9DE8D, 0xAA7EEBFB, 0x0791, // 1e256
+ 0x7F3EA565, 0x552A7422, 0x85785631, 0xD51EA6FA, 0x0794, // 1e257
+ 0x8F87275F, 0xD53A8895, 0x936B35DE, 0x8533285C, 0x0798, // 1e258
+ 0xF368F137, 0x8A892ABA, 0xB8460356, 0xA67FF273, 0x079B, // 1e259
+ 0xB0432D85, 0x2D2B7569, 0xA657842C, 0xD01FEF10, 0x079E, // 1e260
+ 0x0E29FC73, 0x9C3B2962, 0x67F6B29B, 0x8213F56A, 0x07A2, // 1e261
+ 0x91B47B8F, 0x8349F3BA, 0x01F45F42, 0xA298F2C5, 0x07A5, // 1e262
+ 0x36219A73, 0x241C70A9, 0x42717713, 0xCB3F2F76, 0x07A8, // 1e263
+ 0x83AA0110, 0xED238CD3, 0xD30DD4D7, 0xFE0EFB53, 0x07AB, // 1e264
+ 0x324A40AA, 0xF4363804, 0x63E8A506, 0x9EC95D14, 0x07AF, // 1e265
+ 0x3EDCD0D5, 0xB143C605, 0x7CE2CE48, 0xC67BB459, 0x07B2, // 1e266
+ 0x8E94050A, 0xDD94B786, 0xDC1B81DA, 0xF81AA16F, 0x07B5, // 1e267
+ 0x191C8326, 0xCA7CF2B4, 0xE9913128, 0x9B10A4E5, 0x07B9, // 1e268
+ 0x1F63A3F0, 0xFD1C2F61, 0x63F57D72, 0xC1D4CE1F, 0x07BC, // 1e269
+ 0x673C8CEC, 0xBC633B39, 0x3CF2DCCF, 0xF24A01A7, 0x07BF, // 1e270
+ 0xE085D813, 0xD5BE0503, 0x8617CA01, 0x976E4108, 0x07C3, // 1e271
+ 0xD8A74E18, 0x4B2D8644, 0xA79DBC82, 0xBD49D14A, 0x07C6, // 1e272
+ 0x0ED1219E, 0xDDF8E7D6, 0x51852BA2, 0xEC9C459D, 0x07C9, // 1e273
+ 0xC942B503, 0xCABB90E5, 0x52F33B45, 0x93E1AB82, 0x07CD, // 1e274
+ 0x3B936243, 0x3D6A751F, 0xE7B00A17, 0xB8DA1662, 0x07D0, // 1e275
+ 0x0A783AD4, 0x0CC51267, 0xA19C0C9D, 0xE7109BFB, 0x07D3, // 1e276
+ 0x668B24C5, 0x27FB2B80, 0x450187E2, 0x906A617D, 0x07D7, // 1e277
+ 0x802DEDF6, 0xB1F9F660, 0x9641E9DA, 0xB484F9DC, 0x07DA, // 1e278
+ 0xA0396973, 0x5E7873F8, 0xBBD26451, 0xE1A63853, 0x07DD, // 1e279
+ 0x6423E1E8, 0xDB0B487B, 0x55637EB2, 0x8D07E334, 0x07E1, // 1e280
+ 0x3D2CDA62, 0x91CE1A9A, 0x6ABC5E5F, 0xB049DC01, 0x07E4, // 1e281
+ 0xCC7810FB, 0x7641A140, 0xC56B75F7, 0xDC5C5301, 0x07E7, // 1e282
+ 0x7FCB0A9D, 0xA9E904C8, 0x1B6329BA, 0x89B9B3E1, 0x07EB, // 1e283
+ 0x9FBDCD44, 0x546345FA, 0x623BF429, 0xAC2820D9, 0x07EE, // 1e284
+ 0x47AD4095, 0xA97C1779, 0xBACAF133, 0xD732290F, 0x07F1, // 1e285
+ 0xCCCC485D, 0x49ED8EAB, 0xD4BED6C0, 0x867F59A9, 0x07F5, // 1e286
+ 0xBFFF5A74, 0x5C68F256, 0x49EE8C70, 0xA81F3014, 0x07F8, // 1e287
+ 0x6FFF3111, 0x73832EEC, 0x5C6A2F8C, 0xD226FC19, 0x07FB, // 1e288
+ 0xC5FF7EAB, 0xC831FD53, 0xD9C25DB7, 0x83585D8F, 0x07FF, // 1e289
+ 0xB77F5E55, 0xBA3E7CA8, 0xD032F525, 0xA42E74F3, 0x0802, // 1e290
+ 0xE55F35EB, 0x28CE1BD2, 0xC43FB26F, 0xCD3A1230, 0x0805, // 1e291
+ 0xCF5B81B3, 0x7980D163, 0x7AA7CF85, 0x80444B5E, 0x0809, // 1e292
+ 0xC332621F, 0xD7E105BC, 0x1951C366, 0xA0555E36, 0x080C, // 1e293
+ 0xF3FEFAA7, 0x8DD9472B, 0x9FA63440, 0xC86AB5C3, 0x080F, // 1e294
+ 0xF0FEB951, 0xB14F98F6, 0x878FC150, 0xFA856334, 0x0812, // 1e295
+ 0x569F33D3, 0x6ED1BF9A, 0xD4B9D8D2, 0x9C935E00, 0x0816, // 1e296
+ 0xEC4700C8, 0x0A862F80, 0x09E84F07, 0xC3B83581, 0x0819, // 1e297
+ 0x2758C0FA, 0xCD27BB61, 0x4C6262C8, 0xF4A642E1, 0x081C, // 1e298
+ 0xB897789C, 0x8038D51C, 0xCFBD7DBD, 0x98E7E9CC, 0x0820, // 1e299
+ 0xE6BD56C3, 0xE0470A63, 0x03ACDD2C, 0xBF21E440, 0x0823, // 1e300
+ 0xE06CAC74, 0x1858CCFC, 0x04981478, 0xEEEA5D50, 0x0826, // 1e301
+ 0x0C43EBC8, 0x0F37801E, 0x02DF0CCB, 0x95527A52, 0x082A, // 1e302
+ 0x8F54E6BA, 0xD3056025, 0x8396CFFD, 0xBAA718E6, 0x082D, // 1e303
+ 0xF32A2069, 0x47C6B82E, 0x247C83FD, 0xE950DF20, 0x0830, // 1e304
+ 0x57FA5441, 0x4CDC331D, 0x16CDD27E, 0x91D28B74, 0x0834, // 1e305
+ 0xADF8E952, 0xE0133FE4, 0x1C81471D, 0xB6472E51, 0x0837, // 1e306
+ 0xD97723A6, 0x58180FDD, 0x63A198E5, 0xE3D8F9E5, 0x083A, // 1e307
+ 0xA7EA7648, 0x570F09EA, 0x5E44FF8F, 0x8E679C2F, 0x083E, // 1e308
+ 0x51E513DA, 0x2CD2CC65, 0x35D63F73, 0xB201833B, 0x0841, // 1e309
+ 0xA65E58D1, 0xF8077F7E, 0x034BCF4F, 0xDE81E40A, 0x0844, // 1e310
+};
+
+// wuffs_base__private_implementation__f64_powers_of_10 holds powers of 10 that
+// can be exactly represented by a float64 (what C calls a double).
+static const double wuffs_base__private_implementation__f64_powers_of_10[23] = {
+ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
+ 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,
+};
diff --git a/internal/cgen/base/f64conv-submodule.c b/internal/cgen/base/f64conv-submodule.c
deleted file mode 100644
index e7e6b29..0000000
--- a/internal/cgen/base/f64conv-submodule.c
+++ /dev/null
@@ -1,2504 +0,0 @@
-// After editing this file, run "go generate" in the parent directory.
-
-// Copyright 2020 The Wuffs Authors.
-//
-// Licensed under the Apache License, Version 2.0 (the "License");
-// you may not use this file except in compliance with the License.
-// You may obtain a copy of the License at
-//
-// https://www.apache.org/licenses/LICENSE-2.0
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-
-// ---------------- IEEE 754 Floating Point
-
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE 2047
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION 800
-
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL is the largest N
-// such that ((10 << N) < (1 << 64)).
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL 60
-
-// wuffs_base__private_implementation__high_prec_dec (abbreviated as HPD) is a
-// fixed precision floating point decimal number, augmented with ±infinity
-// values, but it cannot represent NaN (Not a Number).
-//
-// "High precision" means that the mantissa holds 800 decimal digits. 800 is
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION.
-//
-// An HPD isn't for general purpose arithmetic, only for conversions to and
-// from IEEE 754 double-precision floating point, where the largest and
-// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.
-// HPD exponents above +2047 mean infinity, below -2047 mean zero. The ±2047
-// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION and
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-//
-// digits[.. num_digits] are the number's digits in big-endian order. The
-// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'
-// is the ASCII value 0x37.
-//
-// decimal_point is the index (within digits) of the decimal point. It may be
-// negative or be larger than num_digits, in which case the explicit digits are
-// padded with implicit zeroes.
-//
-// For example, if num_digits is 3 and digits is "\x07\x08\x09":
-// - A decimal_point of -2 means ".00789"
-// - A decimal_point of -1 means ".0789"
-// - A decimal_point of +0 means ".789"
-// - A decimal_point of +1 means "7.89"
-// - A decimal_point of +2 means "78.9"
-// - A decimal_point of +3 means "789."
-// - A decimal_point of +4 means "7890."
-// - A decimal_point of +5 means "78900."
-//
-// As above, a decimal_point higher than +2047 means that the overall value is
-// infinity, lower than -2047 means zero.
-//
-// negative is a sign bit. An HPD can distinguish positive and negative zero.
-//
-// truncated is whether there are more than
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION digits, and at
-// least one of those extra digits are non-zero. The existence of long-tail
-// digits can affect rounding.
-//
-// The "all fields are zero" value is valid, and represents the number +0.
-typedef struct {
- uint32_t num_digits;
- int32_t decimal_point;
- bool negative;
- bool truncated;
- uint8_t digits[WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION];
-} wuffs_base__private_implementation__high_prec_dec;
-
-// wuffs_base__private_implementation__high_prec_dec__trim trims trailing
-// zeroes from the h->digits[.. h->num_digits] slice. They have no benefit,
-// since we explicitly track h->decimal_point.
-//
-// Preconditions:
-// - h is non-NULL.
-static inline void //
-wuffs_base__private_implementation__high_prec_dec__trim(
- wuffs_base__private_implementation__high_prec_dec* h) {
- while ((h->num_digits > 0) && (h->digits[h->num_digits - 1] == 0)) {
- h->num_digits--;
- }
-}
-
-// wuffs_base__private_implementation__high_prec_dec__assign sets h to
-// represent the number x.
-//
-// Preconditions:
-// - h is non-NULL.
-static void //
-wuffs_base__private_implementation__high_prec_dec__assign(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint64_t x,
- bool negative) {
- uint32_t n = 0;
-
- // Set h->digits.
- if (x > 0) {
- // Calculate the digits, working right-to-left. After we determine n (how
- // many digits there are), copy from buf to h->digits.
- //
- // UINT64_MAX, 18446744073709551615, is 20 digits long. It can be faster to
- // copy a constant number of bytes than a variable number (20 instead of
- // n). Make buf large enough (and start writing to it from the middle) so
- // that can we always copy 20 bytes: the slice buf[(20-n) .. (40-n)].
- uint8_t buf[40] = {0};
- uint8_t* ptr = &buf[20];
- do {
- uint64_t remaining = x / 10;
- x -= remaining * 10;
- ptr--;
- *ptr = (uint8_t)x;
- n++;
- x = remaining;
- } while (x > 0);
- memcpy(h->digits, ptr, 20);
- }
-
- // Set h's other fields.
- h->num_digits = n;
- h->decimal_point = (int32_t)n;
- h->negative = negative;
- h->truncated = false;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static wuffs_base__status //
-wuffs_base__private_implementation__high_prec_dec__parse(
- wuffs_base__private_implementation__high_prec_dec* h,
- wuffs_base__slice_u8 s) {
- if (!h) {
- return wuffs_base__make_status(wuffs_base__error__bad_receiver);
- }
- h->num_digits = 0;
- h->decimal_point = 0;
- h->negative = false;
- h->truncated = false;
-
- uint8_t* p = s.ptr;
- uint8_t* q = s.ptr + s.len;
-
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
-
- // Parse sign.
- do {
- if (*p == '+') {
- p++;
- } else if (*p == '-') {
- h->negative = true;
- p++;
- } else {
- break;
- }
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
- } while (0);
-
- // Parse digits, up to (and including) a '.', 'E' or 'e'. Examples for each
- // limb in this if-else chain:
- // - "0.789"
- // - "1002.789"
- // - ".789"
- // - Other (invalid input).
- uint32_t nd = 0;
- int32_t dp = 0;
- bool no_digits_before_separator = false;
- if ('0' == *p) {
- p++;
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- goto after_sep;
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
- } else if (('0' < *p) && (*p <= '9')) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- dp = (int32_t)nd;
- p++;
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if (('0' <= *p) && (*p <= '9')) {
- if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- dp = (int32_t)nd;
- } else if ('0' != *p) {
- // Long-tail non-zeroes set the truncated bit.
- h->truncated = true;
- }
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- goto after_sep;
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- no_digits_before_separator = true;
-
- } else {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
-
-after_sep:
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if ('0' == *p) {
- if (nd == 0) {
- // Track leading zeroes implicitly.
- dp--;
- } else if (nd <
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- }
- } else if (('0' < *p) && (*p <= '9')) {
- if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- } else {
- // Long-tail non-zeroes set the truncated bit.
- h->truncated = true;
- }
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
-after_exp:
- do {
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
-
- int32_t exp_sign = +1;
- if (*p == '+') {
- p++;
- } else if (*p == '-') {
- exp_sign = -1;
- p++;
- }
-
- int32_t exp = 0;
- const int32_t exp_large =
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE +
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
- bool saw_exp_digits = false;
- for (; p < q; p++) {
- if (*p == '_') {
- // No-op.
- } else if (('0' <= *p) && (*p <= '9')) {
- saw_exp_digits = true;
- if (exp < exp_large) {
- exp = (10 * exp) + ((int32_t)(*p - '0'));
- }
- } else {
- break;
- }
- }
- if (!saw_exp_digits) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- dp += exp_sign * exp;
- } while (0);
-
-after_all:
- if (p != q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- h->num_digits = nd;
- if (nd == 0) {
- if (no_digits_before_separator) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- h->decimal_point = 0;
- } else if (dp <
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- h->decimal_point =
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE - 1;
- } else if (dp >
- +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- h->decimal_point =
- +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE + 1;
- } else {
- h->decimal_point = dp;
- }
- wuffs_base__private_implementation__high_prec_dec__trim(h);
- return wuffs_base__make_status(NULL);
-}
-
-// --------
-
-// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by
-// script/print-hpd-left-shift.go. That script has an optional -comments flag,
-// whose output is not copied here, which prints further detail.
-//
-// These tables are used in
-// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits.
-
-// wuffs_base__private_implementation__hpd_left_shift[i] encodes the number of
-// new digits created after multiplying a positive integer by (1 << i): the
-// additional length in the decimal representation. For example, shifting "234"
-// by 3 (equivalent to multiplying by 8) will produce "1872". Going from a
-// 3-length string to a 4-length string means that 1 new digit was added (and
-// existing digits may have changed).
-//
-// Shifting by i can add either N or N-1 new digits, depending on whether the
-// original positive integer compares >= or < to the i'th power of 5 (as 10
-// equals 2 * 5). Comparison is lexicographic, not numerical.
-//
-// For example, shifting by 4 (i.e. multiplying by 16) can add 1 or 2 new
-// digits, depending on a lexicographic comparison to (5 ** 4), i.e. "625":
-// - ("1" << 4) is "16", which adds 1 new digit.
-// - ("5678" << 4) is "90848", which adds 1 new digit.
-// - ("624" << 4) is "9984", which adds 1 new digit.
-// - ("62498" << 4) is "999968", which adds 1 new digit.
-// - ("625" << 4) is "10000", which adds 2 new digits.
-// - ("625001" << 4) is "10000016", which adds 2 new digits.
-// - ("7008" << 4) is "112128", which adds 2 new digits.
-// - ("99" << 4) is "1584", which adds 2 new digits.
-//
-// Thus, when i is 4, N is 2 and (5 ** i) is "625". This etc__hpd_left_shift
-// array encodes this as:
-// - etc__hpd_left_shift[4] is 0x1006 = (2 << 11) | 0x0006.
-// - etc__hpd_left_shift[5] is 0x1009 = (? << 11) | 0x0009.
-// where the ? isn't relevant for i == 4.
-//
-// The high 5 bits of etc__hpd_left_shift[i] is N, the higher of the two
-// possible number of new digits. The low 11 bits are an offset into the
-// etc__powers_of_5 array (of length 0x051C, so offsets fit in 11 bits). When i
-// is 4, its offset and the next one is 6 and 9, and etc__powers_of_5[6 .. 9]
-// is the string "\x06\x02\x05", so the relevant power of 5 is "625".
-//
-// Thanks to Ken Thompson for the original idea.
-static const uint16_t wuffs_base__private_implementation__hpd_left_shift[65] = {
- 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,
- 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,
- 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,
- 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,
- 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,
- 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,
- 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,
- 0x051C, 0x051C,
-};
-
-// wuffs_base__private_implementation__powers_of_5 contains the powers of 5,
-// concatenated together: "5", "25", "125", "625", "3125", etc.
-static const uint8_t wuffs_base__private_implementation__powers_of_5[0x051C] = {
- 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9,
- 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2,
- 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5,
- 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8, 9, 0,
- 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, 9, 7, 2, 6, 5,
- 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,
- 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4,
- 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7,
- 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0,
- 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3,
- 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1,
- 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,
- 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5,
- 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0,
- 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6,
- 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8,
- 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7,
- 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,
- 1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8,
- 0, 6, 6, 4, 0, 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9,
- 0, 3, 3, 2, 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2,
- 9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8,
- 5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,
- 2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,
- 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3,
- 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2,
- 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9,
- 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, 0, 1, 4, 8,
- 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4,
- 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,
- 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5,
- 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1,
- 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5,
- 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3,
- 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4,
- 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,
- 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8,
- 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2,
- 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6,
- 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2,
- 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2,
- 5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,
- 8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5,
- 6, 2, 8, 9, 1, 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8,
- 1, 2, 5, 1, 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9,
- 5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,
- 9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6,
- 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,
- 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1,
- 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4,
- 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7,
- 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3,
- 6, 9, 1, 4, 0, 6, 2, 5,
-};
-
-// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
-// returns the number of additional decimal digits when left-shifting by shift.
-//
-// See below for preconditions.
-static uint32_t //
-wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- // Masking with 0x3F should be unnecessary (assuming the preconditions) but
- // it's cheap and ensures that we don't overflow the
- // wuffs_base__private_implementation__hpd_left_shift array.
- shift &= 63;
-
- uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];
- uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];
- uint32_t num_new_digits = x_a >> 11;
- uint32_t pow5_a = 0x7FF & x_a;
- uint32_t pow5_b = 0x7FF & x_b;
-
- const uint8_t* pow5 =
- &wuffs_base__private_implementation__powers_of_5[pow5_a];
- uint32_t i = 0;
- uint32_t n = pow5_b - pow5_a;
- for (; i < n; i++) {
- if (i >= h->num_digits) {
- return num_new_digits - 1;
- } else if (h->digits[i] == pow5[i]) {
- continue;
- } else if (h->digits[i] < pow5[i]) {
- return num_new_digits - 1;
- } else {
- return num_new_digits;
- }
- }
- return num_new_digits;
-}
-
-// --------
-
-// wuffs_base__private_implementation__high_prec_dec__rounded_integer returns
-// the integral (non-fractional) part of h, provided that it is 18 or fewer
-// decimal digits. For 19 or more digits, it returns UINT64_MAX. Note that:
-// - (1 << 53) is 9007199254740992, which has 16 decimal digits.
-// - (1 << 56) is 72057594037927936, which has 17 decimal digits.
-// - (1 << 59) is 576460752303423488, which has 18 decimal digits.
-// - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
-// and that IEEE 754 double precision has 52 mantissa bits.
-//
-// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.
-//
-// h's negative bit is ignored: rounding -8.6 returns 9.
-//
-// See below for preconditions.
-static uint64_t //
-wuffs_base__private_implementation__high_prec_dec__rounded_integer(
- wuffs_base__private_implementation__high_prec_dec* h) {
- if ((h->num_digits == 0) || (h->decimal_point < 0)) {
- return 0;
- } else if (h->decimal_point > 18) {
- return UINT64_MAX;
- }
-
- uint32_t dp = (uint32_t)(h->decimal_point);
- uint64_t n = 0;
- uint32_t i = 0;
- for (; i < dp; i++) {
- n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);
- }
-
- bool round_up = false;
- if (dp < h->num_digits) {
- round_up = h->digits[dp] >= 5;
- if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {
- // We are exactly halfway. If we're truncated, round up, otherwise round
- // to even.
- round_up = h->truncated || //
- ((dp > 0) && (1 & h->digits[dp - 1]));
- }
- }
- if (round_up) {
- n++;
- }
-
- return n;
-}
-
-// wuffs_base__private_implementation__high_prec_dec__small_xshift shifts h's
-// number (where 'x' is 'l' or 'r' for left or right) by a small shift value.
-//
-// Preconditions:
-// - h is non-NULL.
-// - h->decimal_point is "not extreme".
-// - shift is non-zero.
-// - shift is "a small shift".
-//
-// "Not extreme" means within
-// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-//
-// "A small shift" means not more than
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
-//
-// wuffs_base__private_implementation__high_prec_dec__rounded_integer and
-// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
-// have the same preconditions.
-//
-// wuffs_base__private_implementation__high_prec_dec__lshift keeps the first
-// two preconditions but not the last two. Its shift argument is signed and
-// does not need to be "small": zero is a no-op, positive means left shift and
-// negative means right shift.
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__small_lshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- if (h->num_digits == 0) {
- return;
- }
- uint32_t num_new_digits =
- wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
- h, shift);
- uint32_t rx = h->num_digits - 1; // Read index.
- uint32_t wx = h->num_digits - 1 + num_new_digits; // Write index.
- uint64_t n = 0;
-
- // Repeat: pick up a digit, put down a digit, right to left.
- while (((int32_t)rx) >= 0) {
- n += ((uint64_t)(h->digits[rx])) << shift;
- uint64_t quo = n / 10;
- uint64_t rem = n - (10 * quo);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx] = (uint8_t)rem;
- } else if (rem > 0) {
- h->truncated = true;
- }
- n = quo;
- wx--;
- rx--;
- }
-
- // Put down leading digits, right to left.
- while (n > 0) {
- uint64_t quo = n / 10;
- uint64_t rem = n - (10 * quo);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx] = (uint8_t)rem;
- } else if (rem > 0) {
- h->truncated = true;
- }
- n = quo;
- wx--;
- }
-
- // Finish.
- h->num_digits += num_new_digits;
- if (h->num_digits >
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->num_digits = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
- }
- h->decimal_point += (int32_t)num_new_digits;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__small_rshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- uint32_t rx = 0; // Read index.
- uint32_t wx = 0; // Write index.
- uint64_t n = 0;
-
- // Pick up enough leading digits to cover the first shift.
- while ((n >> shift) == 0) {
- if (rx < h->num_digits) {
- // Read a digit.
- n = (10 * n) + h->digits[rx++];
- } else if (n == 0) {
- // h's number used to be zero and remains zero.
- return;
- } else {
- // Read sufficient implicit trailing zeroes.
- while ((n >> shift) == 0) {
- n = 10 * n;
- rx++;
- }
- break;
- }
- }
- h->decimal_point -= ((int32_t)(rx - 1));
- if (h->decimal_point <
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- // After the shift, h's number is effectively zero.
- h->num_digits = 0;
- h->decimal_point = 0;
- h->negative = false;
- h->truncated = false;
- return;
- }
-
- // Repeat: pick up a digit, put down a digit, left to right.
- uint64_t mask = (((uint64_t)(1)) << shift) - 1;
- while (rx < h->num_digits) {
- uint8_t new_digit = ((uint8_t)(n >> shift));
- n = (10 * (n & mask)) + h->digits[rx++];
- h->digits[wx++] = new_digit;
- }
-
- // Put down trailing digits, left to right.
- while (n > 0) {
- uint8_t new_digit = ((uint8_t)(n >> shift));
- n = 10 * (n & mask);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx++] = new_digit;
- } else if (new_digit > 0) {
- h->truncated = true;
- }
- }
-
- // Finish.
- h->num_digits = wx;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__lshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t shift) {
- if (shift > 0) {
- while (shift > +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
- wuffs_base__private_implementation__high_prec_dec__small_lshift(
- h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
- shift -= WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
- wuffs_base__private_implementation__high_prec_dec__small_lshift(
- h, ((uint32_t)(+shift)));
- } else if (shift < 0) {
- while (shift < -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
- wuffs_base__private_implementation__high_prec_dec__small_rshift(
- h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
- shift += WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
- wuffs_base__private_implementation__high_prec_dec__small_rshift(
- h, ((uint32_t)(-shift)));
- }
-}
-
-// --------
-
-// wuffs_base__private_implementation__high_prec_dec__round_etc rounds h's
-// number. For those functions that take an n argument, rounding produces at
-// most n digits (which is not necessarily at most n decimal places). Negative
-// n values are ignored, as well as any n greater than or equal to h's number
-// of digits. The etc__round_just_enough function implicitly chooses an n to
-// implement WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION.
-//
-// Preconditions:
-// - h is non-NULL.
-// - h->decimal_point is "not extreme".
-//
-// "Not extreme" means within
-// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_down(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
- h->num_digits = (uint32_t)(n);
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_up(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
-
- for (n--; n >= 0; n--) {
- if (h->digits[n] < 9) {
- h->digits[n]++;
- h->num_digits = (uint32_t)(n + 1);
- return;
- }
- }
-
- // The number is all 9s. Change to a single 1 and adjust the decimal point.
- h->digits[0] = 1;
- h->num_digits = 1;
- h->decimal_point++;
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_nearest(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
- bool up = h->digits[n] >= 5;
- if ((h->digits[n] == 5) && ((n + 1) == ((int32_t)(h->num_digits)))) {
- up = h->truncated || //
- ((n > 0) && ((h->digits[n - 1] & 1) != 0));
- }
-
- if (up) {
- wuffs_base__private_implementation__high_prec_dec__round_up(h, n);
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_down(h, n);
- }
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_just_enough(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t exp2,
- uint64_t mantissa) {
- // The magic numbers 52 and 53 in this function are because IEEE 754 double
- // precision has 52 mantissa bits.
- //
- // Let f be the floating point number represented by exp2 and mantissa (and
- // also the number in h): the number (mantissa * (2 ** (exp2 - 52))).
- //
- // If f is zero or a small integer, we can return early.
- if ((mantissa == 0) ||
- ((exp2 < 53) && (h->decimal_point >= ((int32_t)(h->num_digits))))) {
- return;
- }
-
- // The smallest normal f has an exp2 of -1022 and a mantissa of (1 << 52).
- // Subnormal numbers have the same exp2 but a smaller mantissa.
- static const int32_t min_incl_normal_exp2 = -1022;
- static const uint64_t min_incl_normal_mantissa = 0x0010000000000000ul;
-
- // Compute lower and upper bounds such that any number between them (possibly
- // inclusive) will round to f. First, the lower bound. Our number f is:
- // ((mantissa + 0) * (2 ** ( exp2 - 52)))
- //
- // The next lowest floating point number is:
- // ((mantissa - 1) * (2 ** ( exp2 - 52)))
- // unless (mantissa - 1) drops the (1 << 52) bit and exp2 is not the
- // min_incl_normal_exp2. Either way, call it:
- // ((l_mantissa) * (2 ** (l_exp2 - 52)))
- //
- // The lower bound is halfway between them (noting that 52 became 53):
- // (((2 * l_mantissa) + 1) * (2 ** (l_exp2 - 53)))
- int32_t l_exp2 = exp2;
- uint64_t l_mantissa = mantissa - 1;
- if ((exp2 > min_incl_normal_exp2) && (mantissa <= min_incl_normal_mantissa)) {
- l_exp2 = exp2 - 1;
- l_mantissa = (2 * mantissa) - 1;
- }
- wuffs_base__private_implementation__high_prec_dec lower;
- wuffs_base__private_implementation__high_prec_dec__assign(
- &lower, (2 * l_mantissa) + 1, false);
- wuffs_base__private_implementation__high_prec_dec__lshift(&lower,
- l_exp2 - 53);
-
- // Next, the upper bound. Our number f is:
- // ((mantissa + 0) * (2 ** (exp2 - 52)))
- //
- // The next highest floating point number is:
- // ((mantissa + 1) * (2 ** (exp2 - 52)))
- //
- // The upper bound is halfway between them (noting that 52 became 53):
- // (((2 * mantissa) + 1) * (2 ** (exp2 - 53)))
- wuffs_base__private_implementation__high_prec_dec upper;
- wuffs_base__private_implementation__high_prec_dec__assign(
- &upper, (2 * mantissa) + 1, false);
- wuffs_base__private_implementation__high_prec_dec__lshift(&upper, exp2 - 53);
-
- // The lower and upper bounds are possible outputs only if the original
- // mantissa is even, so that IEEE round-to-even would round to the original
- // mantissa and not its neighbors.
- bool inclusive = (mantissa & 1) == 0;
-
- // As we walk the digits, we want to know whether rounding up would fall
- // within the upper bound. This is tracked by upper_delta:
- // - When -1, the digits of h and upper are the same so far.
- // - When +0, we saw a difference of 1 between h and upper on a previous
- // digit and subsequently only 9s for h and 0s for upper. Thus, rounding
- // up may fall outside of the bound if !inclusive.
- // - When +1, the difference is greater than 1 and we know that rounding up
- // falls within the bound.
- //
- // This is a state machine with three states. The numerical value for each
- // state (-1, +0 or +1) isn't important, other than their order.
- int upper_delta = -1;
-
- // We can now figure out the shortest number of digits required. Walk the
- // digits until h has distinguished itself from lower or upper.
- //
- // The zi and zd variables are indexes and digits, for z in l (lower), h (the
- // number) and u (upper).
- //
- // The lower, h and upper numbers may have their decimal points at different
- // places. In this case, upper is the longest, so we iterate ui starting from
- // 0 and iterate li and hi starting from either 0 or -1.
- int32_t ui = 0;
- for (;; ui++) {
- // Calculate hd, the middle number's digit.
- int32_t hi = ui - upper.decimal_point + h->decimal_point;
- if (hi >= ((int32_t)(h->num_digits))) {
- break;
- }
- uint8_t hd = (((uint32_t)hi) < h->num_digits) ? h->digits[hi] : 0;
-
- // Calculate ld, the lower bound's digit.
- int32_t li = ui - upper.decimal_point + lower.decimal_point;
- uint8_t ld = (((uint32_t)li) < lower.num_digits) ? lower.digits[li] : 0;
-
- // We can round down (truncate) if lower has a different digit than h or if
- // lower is inclusive and is exactly the result of rounding down (i.e. we
- // have reached the final digit of lower).
- bool can_round_down =
- (ld != hd) || //
- (inclusive && ((li + 1) == ((int32_t)(lower.num_digits))));
-
- // Calculate ud, the upper bound's digit, and update upper_delta.
- uint8_t ud = (((uint32_t)ui) < upper.num_digits) ? upper.digits[ui] : 0;
- if (upper_delta < 0) {
- if ((hd + 1) < ud) {
- // For example:
- // h = 12345???
- // upper = 12347???
- upper_delta = +1;
- } else if (hd != ud) {
- // For example:
- // h = 12345???
- // upper = 12346???
- upper_delta = +0;
- }
- } else if (upper_delta == 0) {
- if ((hd != 9) || (ud != 0)) {
- // For example:
- // h = 1234598?
- // upper = 1234600?
- upper_delta = +1;
- }
- }
-
- // We can round up if upper has a different digit than h and either upper
- // is inclusive or upper is bigger than the result of rounding up.
- bool can_round_up =
- (upper_delta > 0) || //
- ((upper_delta == 0) && //
- (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));
-
- // If we can round either way, round to nearest. If we can round only one
- // way, do it. If we can't round, continue the loop.
- if (can_round_down) {
- if (can_round_up) {
- wuffs_base__private_implementation__high_prec_dec__round_nearest(
- h, hi + 1);
- return;
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_down(h,
- hi + 1);
- return;
- }
- } else {
- if (can_round_up) {
- wuffs_base__private_implementation__high_prec_dec__round_up(h, hi + 1);
- return;
- }
- }
- }
-}
-
-// --------
-
-// wuffs_base__private_implementation__powers_of_10 contains truncated
-// approximations to the powers of 10, ranging from 1e-326 to 1e+310 inclusive,
-// as 637 uint32_t quintuples (128-bit mantissa, 32-bit base-2 exponent biased
-// by 0x04BE (which is 1214)). The array size is 637 * 5 = 3185.
-//
-// The 1214 bias in this look-up table equals 1023 + 191. 1023 is the bias for
-// IEEE 754 double-precision floating point. 191 is ((3 * 64) - 1) and
-// wuffs_base__private_implementation__parse_number_f64_eisel works with
-// multiples-of-64-bit mantissas.
-//
-// For example, the third approximation, for 1e-324, consists of the uint32_t
-// quintuple (0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A). The
-// first four form a little-endian uint128_t value. The last one is an int32_t
-// value: -1140. Together, they represent the approximation to 1e-324:
-// 0xCF42894A_5DCE35EA_52064CAC_828675B9 * (2 ** (0x000A - 0x04BE))
-//
-// Similarly, 1e+4 is approximated by the uint64_t quintuple
-// (0x00000000, 0x00000000, 0x00000000, 0x9C400000, 0x044C) which means:
-// 0x9C400000_00000000_00000000_00000000 * (2 ** (0x044C - 0x04BE))
-//
-// Similarly, 1e+68 is approximated by the uint64_t quintuple
-// (0x63EE4BDD, 0x4CA7AAA8, 0xD4C4FB27, 0xED63A231, 0x0520) which means:
-// 0xED63A231_D4C4FB27.4CA7AAA8_63EE4BDD * (2 ** (0x0520 - 0x04BE))
-//
-// This table was generated by by script/print-mpb-powers-of-10.go
-static const uint32_t wuffs_base__private_implementation__powers_of_10[3185] = {
- 0xF7604B57, 0x014BB630, 0xFE98746D, 0x84A57695, 0x0004, // 1e-326
- 0x35385E2D, 0x419EA3BD, 0x7E3E9188, 0xA5CED43B, 0x0007, // 1e-325
- 0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A, // 1e-324
- 0xD1940993, 0x7343EFEB, 0x7AA0E1B2, 0x818995CE, 0x000E, // 1e-323
- 0xC5F90BF8, 0x1014EBE6, 0x19491A1F, 0xA1EBFB42, 0x0011, // 1e-322
- 0x77774EF6, 0xD41A26E0, 0x9F9B60A6, 0xCA66FA12, 0x0014, // 1e-321
- 0x955522B4, 0x8920B098, 0x478238D0, 0xFD00B897, 0x0017, // 1e-320
- 0x5D5535B0, 0x55B46E5F, 0x8CB16382, 0x9E20735E, 0x001B, // 1e-319
- 0x34AA831D, 0xEB2189F7, 0x2FDDBC62, 0xC5A89036, 0x001E, // 1e-318
- 0x01D523E4, 0xA5E9EC75, 0xBBD52B7B, 0xF712B443, 0x0021, // 1e-317
- 0x2125366E, 0x47B233C9, 0x55653B2D, 0x9A6BB0AA, 0x0025, // 1e-316
- 0x696E840A, 0x999EC0BB, 0xEABE89F8, 0xC1069CD4, 0x0028, // 1e-315
- 0x43CA250D, 0xC00670EA, 0x256E2C76, 0xF148440A, 0x002B, // 1e-314
- 0x6A5E5728, 0x38040692, 0x5764DBCA, 0x96CD2A86, 0x002F, // 1e-313
- 0x04F5ECF2, 0xC6050837, 0xED3E12BC, 0xBC807527, 0x0032, // 1e-312
- 0xC633682E, 0xF7864A44, 0xE88D976B, 0xEBA09271, 0x0035, // 1e-311
- 0xFBE0211D, 0x7AB3EE6A, 0x31587EA3, 0x93445B87, 0x0039, // 1e-310
- 0xBAD82964, 0x5960EA05, 0xFDAE9E4C, 0xB8157268, 0x003C, // 1e-309
- 0x298E33BD, 0x6FB92487, 0x3D1A45DF, 0xE61ACF03, 0x003F, // 1e-308
- 0x79F8E056, 0xA5D3B6D4, 0x06306BAB, 0x8FD0C162, 0x0043, // 1e-307
- 0x9877186C, 0x8F48A489, 0x87BC8696, 0xB3C4F1BA, 0x0046, // 1e-306
- 0xFE94DE87, 0x331ACDAB, 0x29ABA83C, 0xE0B62E29, 0x0049, // 1e-305
- 0x7F1D0B14, 0x9FF0C08B, 0xBA0B4925, 0x8C71DCD9, 0x004D, // 1e-304
- 0x5EE44DD9, 0x07ECF0AE, 0x288E1B6F, 0xAF8E5410, 0x0050, // 1e-303
- 0xF69D6150, 0xC9E82CD9, 0x32B1A24A, 0xDB71E914, 0x0053, // 1e-302
- 0x3A225CD2, 0xBE311C08, 0x9FAF056E, 0x892731AC, 0x0057, // 1e-301
- 0x48AAF406, 0x6DBD630A, 0xC79AC6CA, 0xAB70FE17, 0x005A, // 1e-300
- 0xDAD5B108, 0x092CBBCC, 0xB981787D, 0xD64D3D9D, 0x005D, // 1e-299
- 0x08C58EA5, 0x25BBF560, 0x93F0EB4E, 0x85F04682, 0x0061, // 1e-298
- 0x0AF6F24E, 0xAF2AF2B8, 0x38ED2621, 0xA76C5823, 0x0064, // 1e-297
- 0x0DB4AEE1, 0x1AF5AF66, 0x07286FAA, 0xD1476E2C, 0x0067, // 1e-296
- 0xC890ED4D, 0x50D98D9F, 0x847945CA, 0x82CCA4DB, 0x006B, // 1e-295
- 0xBAB528A0, 0xE50FF107, 0x6597973C, 0xA37FCE12, 0x006E, // 1e-294
- 0xA96272C8, 0x1E53ED49, 0xFEFD7D0C, 0xCC5FC196, 0x0071, // 1e-293
- 0x13BB0F7A, 0x25E8E89C, 0xBEBCDC4F, 0xFF77B1FC, 0x0074, // 1e-292
- 0x8C54E9AC, 0x77B19161, 0xF73609B1, 0x9FAACF3D, 0x0078, // 1e-291
- 0xEF6A2417, 0xD59DF5B9, 0x75038C1D, 0xC795830D, 0x007B, // 1e-290
- 0x6B44AD1D, 0x4B057328, 0xD2446F25, 0xF97AE3D0, 0x007E, // 1e-289
- 0x430AEC32, 0x4EE367F9, 0x836AC577, 0x9BECCE62, 0x0082, // 1e-288
- 0x93CDA73F, 0x229C41F7, 0x244576D5, 0xC2E801FB, 0x0085, // 1e-287
- 0x78C1110F, 0x6B435275, 0xED56D48A, 0xF3A20279, 0x0088, // 1e-286
- 0x6B78AAA9, 0x830A1389, 0x345644D6, 0x9845418C, 0x008C, // 1e-285
- 0xC656D553, 0x23CC986B, 0x416BD60C, 0xBE5691EF, 0x008F, // 1e-284
- 0xB7EC8AA8, 0x2CBFBE86, 0x11C6CB8F, 0xEDEC366B, 0x0092, // 1e-283
- 0x32F3D6A9, 0x7BF7D714, 0xEB1C3F39, 0x94B3A202, 0x0096, // 1e-282
- 0x3FB0CC53, 0xDAF5CCD9, 0xA5E34F07, 0xB9E08A83, 0x0099, // 1e-281
- 0x8F9CFF68, 0xD1B3400F, 0x8F5C22C9, 0xE858AD24, 0x009C, // 1e-280
- 0xB9C21FA1, 0x23100809, 0xD99995BE, 0x91376C36, 0x00A0, // 1e-279
- 0x2832A78A, 0xABD40A0C, 0x8FFFFB2D, 0xB5854744, 0x00A3, // 1e-278
- 0x323F516C, 0x16C90C8F, 0xB3FFF9F9, 0xE2E69915, 0x00A6, // 1e-277
- 0x7F6792E3, 0xAE3DA7D9, 0x907FFC3B, 0x8DD01FAD, 0x00AA, // 1e-276
- 0xDF41779C, 0x99CD11CF, 0xF49FFB4A, 0xB1442798, 0x00AD, // 1e-275
- 0xD711D583, 0x40405643, 0x31C7FA1D, 0xDD95317F, 0x00B0, // 1e-274
- 0x666B2572, 0x482835EA, 0x7F1CFC52, 0x8A7D3EEF, 0x00B4, // 1e-273
- 0x0005EECF, 0xDA324365, 0x5EE43B66, 0xAD1C8EAB, 0x00B7, // 1e-272
- 0x40076A82, 0x90BED43E, 0x369D4A40, 0xD863B256, 0x00BA, // 1e-271
- 0xE804A291, 0x5A7744A6, 0xE2224E68, 0x873E4F75, 0x00BE, // 1e-270
- 0xA205CB36, 0x711515D0, 0x5AAAE202, 0xA90DE353, 0x00C1, // 1e-269
- 0xCA873E03, 0x0D5A5B44, 0x31559A83, 0xD3515C28, 0x00C4, // 1e-268
- 0xFE9486C2, 0xE858790A, 0x1ED58091, 0x8412D999, 0x00C8, // 1e-267
- 0xBE39A872, 0x626E974D, 0x668AE0B6, 0xA5178FFF, 0x00CB, // 1e-266
- 0x2DC8128F, 0xFB0A3D21, 0x402D98E3, 0xCE5D73FF, 0x00CE, // 1e-265
- 0xBC9D0B99, 0x7CE66634, 0x881C7F8E, 0x80FA687F, 0x00D2, // 1e-264
- 0xEBC44E80, 0x1C1FFFC1, 0x6A239F72, 0xA139029F, 0x00D5, // 1e-263
- 0x66B56220, 0xA327FFB2, 0x44AC874E, 0xC9874347, 0x00D8, // 1e-262
- 0x0062BAA8, 0x4BF1FF9F, 0x15D7A922, 0xFBE91419, 0x00DB, // 1e-261
- 0x603DB4A9, 0x6F773FC3, 0xADA6C9B5, 0x9D71AC8F, 0x00DF, // 1e-260
- 0x384D21D3, 0xCB550FB4, 0x99107C22, 0xC4CE17B3, 0x00E2, // 1e-259
- 0x46606A48, 0x7E2A53A1, 0x7F549B2B, 0xF6019DA0, 0x00E5, // 1e-258
- 0xCBFC426D, 0x2EDA7444, 0x4F94E0FB, 0x99C10284, 0x00E9, // 1e-257
- 0xFEFB5308, 0xFA911155, 0x637A1939, 0xC0314325, 0x00EC, // 1e-256
- 0x7EBA27CA, 0x793555AB, 0xBC589F88, 0xF03D93EE, 0x00EF, // 1e-255
- 0x2F3458DE, 0x4BC1558B, 0x35B763B5, 0x96267C75, 0x00F3, // 1e-254
- 0xFB016F16, 0x9EB1AAED, 0x83253CA2, 0xBBB01B92, 0x00F6, // 1e-253
- 0x79C1CADC, 0x465E15A9, 0x23EE8BCB, 0xEA9C2277, 0x00F9, // 1e-252
- 0xEC191EC9, 0x0BFACD89, 0x7675175F, 0x92A1958A, 0x00FD, // 1e-251
- 0x671F667B, 0xCEF980EC, 0x14125D36, 0xB749FAED, 0x0100, // 1e-250
- 0x80E7401A, 0x82B7E127, 0x5916F484, 0xE51C79A8, 0x0103, // 1e-249
- 0xB0908810, 0xD1B2ECB8, 0x37AE58D2, 0x8F31CC09, 0x0107, // 1e-248
- 0xDCB4AA15, 0x861FA7E6, 0x8599EF07, 0xB2FE3F0B, 0x010A, // 1e-247
- 0x93E1D49A, 0x67A791E0, 0x67006AC9, 0xDFBDCECE, 0x010D, // 1e-246
- 0x5C6D24E0, 0xE0C8BB2C, 0x006042BD, 0x8BD6A141, 0x0111, // 1e-245
- 0x73886E18, 0x58FAE9F7, 0x4078536D, 0xAECC4991, 0x0114, // 1e-244
- 0x506A899E, 0xAF39A475, 0x90966848, 0xDA7F5BF5, 0x0117, // 1e-243
- 0x52429603, 0x6D8406C9, 0x7A5E012D, 0x888F9979, 0x011B, // 1e-242
- 0xA6D33B83, 0xC8E5087B, 0xD8F58178, 0xAAB37FD7, 0x011E, // 1e-241
- 0x90880A64, 0xFB1E4A9A, 0xCF32E1D6, 0xD5605FCD, 0x0121, // 1e-240
- 0x9A55067F, 0x5CF2EEA0, 0xA17FCD26, 0x855C3BE0, 0x0125, // 1e-239
- 0xC0EA481E, 0xF42FAA48, 0xC9DFC06F, 0xA6B34AD8, 0x0128, // 1e-238
- 0xF124DA26, 0xF13B94DA, 0xFC57B08B, 0xD0601D8E, 0x012B, // 1e-237
- 0xD6B70858, 0x76C53D08, 0x5DB6CE57, 0x823C1279, 0x012F, // 1e-236
- 0x0C64CA6E, 0x54768C4B, 0xB52481ED, 0xA2CB1717, 0x0132, // 1e-235
- 0xCF7DFD09, 0xA9942F5D, 0xA26DA268, 0xCB7DDCDD, 0x0135, // 1e-234
- 0x435D7C4C, 0xD3F93B35, 0x0B090B02, 0xFE5D5415, 0x0138, // 1e-233
- 0x4A1A6DAF, 0xC47BC501, 0x26E5A6E1, 0x9EFA548D, 0x013C, // 1e-232
- 0x9CA1091B, 0x359AB641, 0x709F109A, 0xC6B8E9B0, 0x013F, // 1e-231
- 0x03C94B62, 0xC30163D2, 0x8CC6D4C0, 0xF867241C, 0x0142, // 1e-230
- 0x425DCF1D, 0x79E0DE63, 0xD7FC44F8, 0x9B407691, 0x0146, // 1e-229
- 0x12F542E4, 0x985915FC, 0x4DFB5636, 0xC2109436, 0x0149, // 1e-228
- 0x17B2939D, 0x3E6F5B7B, 0xE17A2BC4, 0xF294B943, 0x014C, // 1e-227
- 0xEECF9C42, 0xA705992C, 0x6CEC5B5A, 0x979CF3CA, 0x0150, // 1e-226
- 0x2A838353, 0x50C6FF78, 0x08277231, 0xBD8430BD, 0x0153, // 1e-225
- 0x35246428, 0xA4F8BF56, 0x4A314EBD, 0xECE53CEC, 0x0156, // 1e-224
- 0xE136BE99, 0x871B7795, 0xAE5ED136, 0x940F4613, 0x015A, // 1e-223
- 0x59846E3F, 0x28E2557B, 0x99F68584, 0xB9131798, 0x015D, // 1e-222
- 0x2FE589CF, 0x331AEADA, 0xC07426E5, 0xE757DD7E, 0x0160, // 1e-221
- 0x5DEF7621, 0x3FF0D2C8, 0x3848984F, 0x9096EA6F, 0x0164, // 1e-220
- 0x756B53A9, 0x0FED077A, 0x065ABE63, 0xB4BCA50B, 0x0167, // 1e-219
- 0x12C62894, 0xD3E84959, 0xC7F16DFB, 0xE1EBCE4D, 0x016A, // 1e-218
- 0xABBBD95C, 0x64712DD7, 0x9CF6E4BD, 0x8D3360F0, 0x016E, // 1e-217
- 0x96AACFB3, 0xBD8D794D, 0xC4349DEC, 0xB080392C, 0x0171, // 1e-216
- 0xFC5583A0, 0xECF0D7A0, 0xF541C567, 0xDCA04777, 0x0174, // 1e-215
- 0x9DB57244, 0xF41686C4, 0xF9491B60, 0x89E42CAA, 0x0178, // 1e-214
- 0xC522CED5, 0x311C2875, 0xB79B6239, 0xAC5D37D5, 0x017B, // 1e-213
- 0x366B828B, 0x7D633293, 0x25823AC7, 0xD77485CB, 0x017E, // 1e-212
- 0x02033197, 0xAE5DFF9C, 0xF77164BC, 0x86A8D39E, 0x0182, // 1e-211
- 0x0283FDFC, 0xD9F57F83, 0xB54DBDEB, 0xA8530886, 0x0185, // 1e-210
- 0xC324FD7B, 0xD072DF63, 0x62A12D66, 0xD267CAA8, 0x0188, // 1e-209
- 0x59F71E6D, 0x4247CB9E, 0x3DA4BC60, 0x8380DEA9, 0x018C, // 1e-208
- 0xF074E608, 0x52D9BE85, 0x8D0DEB78, 0xA4611653, 0x018F, // 1e-207
- 0x6C921F8B, 0x67902E27, 0x70516656, 0xCD795BE8, 0x0192, // 1e-206
- 0xA3DB53B6, 0x00BA1CD8, 0x4632DFF6, 0x806BD971, 0x0196, // 1e-205
- 0xCCD228A4, 0x80E8A40E, 0x97BF97F3, 0xA086CFCD, 0x0199, // 1e-204
- 0x8006B2CD, 0x6122CD12, 0xFDAF7DF0, 0xC8A883C0, 0x019C, // 1e-203
- 0x20085F81, 0x796B8057, 0x3D1B5D6C, 0xFAD2A4B1, 0x019F, // 1e-202
- 0x74053BB0, 0xCBE33036, 0xC6311A63, 0x9CC3A6EE, 0x01A3, // 1e-201
- 0x11068A9C, 0xBEDBFC44, 0x77BD60FC, 0xC3F490AA, 0x01A6, // 1e-200
- 0x15482D44, 0xEE92FB55, 0x15ACB93B, 0xF4F1B4D5, 0x01A9, // 1e-199
- 0x2D4D1C4A, 0x751BDD15, 0x2D8BF3C5, 0x99171105, 0x01AD, // 1e-198
- 0x78A0635D, 0xD262D45A, 0x78EEF0B6, 0xBF5CD546, 0x01B0, // 1e-197
- 0x16C87C34, 0x86FB8971, 0x172AACE4, 0xEF340A98, 0x01B3, // 1e-196
- 0xAE3D4DA0, 0xD45D35E6, 0x0E7AAC0E, 0x9580869F, 0x01B7, // 1e-195
- 0x59CCA109, 0x89748360, 0xD2195712, 0xBAE0A846, 0x01BA, // 1e-194
- 0x703FC94B, 0x2BD1A438, 0x869FACD7, 0xE998D258, 0x01BD, // 1e-193
- 0x4627DDCF, 0x7B6306A3, 0x5423CC06, 0x91FF8377, 0x01C1, // 1e-192
- 0x17B1D542, 0x1A3BC84C, 0x292CBF08, 0xB67F6455, 0x01C4, // 1e-191
- 0x1D9E4A93, 0x20CABA5F, 0x7377EECA, 0xE41F3D6A, 0x01C7, // 1e-190
- 0x7282EE9C, 0x547EB47B, 0x882AF53E, 0x8E938662, 0x01CB, // 1e-189
- 0x4F23AA43, 0xE99E619A, 0x2A35B28D, 0xB23867FB, 0x01CE, // 1e-188
- 0xE2EC94D4, 0x6405FA00, 0xF4C31F31, 0xDEC681F9, 0x01D1, // 1e-187
- 0x8DD3DD04, 0xDE83BC40, 0x38F9F37E, 0x8B3C113C, 0x01D5, // 1e-186
- 0xB148D445, 0x9624AB50, 0x4738705E, 0xAE0B158B, 0x01D8, // 1e-185
- 0xDD9B0957, 0x3BADD624, 0x19068C76, 0xD98DDAEE, 0x01DB, // 1e-184
- 0x0A80E5D6, 0xE54CA5D7, 0xCFA417C9, 0x87F8A8D4, 0x01DF, // 1e-183
- 0xCD211F4C, 0x5E9FCF4C, 0x038D1DBC, 0xA9F6D30A, 0x01E2, // 1e-182
- 0x0069671F, 0x7647C320, 0x8470652B, 0xD47487CC, 0x01E5, // 1e-181
- 0x0041E073, 0x29ECD9F4, 0xD2C63F3B, 0x84C8D4DF, 0x01E9, // 1e-180
- 0x00525890, 0xF4681071, 0xC777CF09, 0xA5FB0A17, 0x01EC, // 1e-179
- 0x4066EEB4, 0x7182148D, 0xB955C2CC, 0xCF79CC9D, 0x01EF, // 1e-178
- 0x48405530, 0xC6F14CD8, 0x93D599BF, 0x81AC1FE2, 0x01F3, // 1e-177
- 0x5A506A7C, 0xB8ADA00E, 0x38CB002F, 0xA21727DB, 0x01F6, // 1e-176
- 0xF0E4851C, 0xA6D90811, 0x06FDC03B, 0xCA9CF1D2, 0x01F9, // 1e-175
- 0x6D1DA663, 0x908F4A16, 0x88BD304A, 0xFD442E46, 0x01FC, // 1e-174
- 0x043287FE, 0x9A598E4E, 0x15763E2E, 0x9E4A9CEC, 0x0200, // 1e-173
- 0x853F29FD, 0x40EFF1E1, 0x1AD3CDBA, 0xC5DD4427, 0x0203, // 1e-172
- 0xE68EF47C, 0xD12BEE59, 0xE188C128, 0xF7549530, 0x0206, // 1e-171
- 0x301958CE, 0x82BB74F8, 0x8CF578B9, 0x9A94DD3E, 0x020A, // 1e-170
- 0x3C1FAF01, 0xE36A5236, 0x3032D6E7, 0xC13A148E, 0x020D, // 1e-169
- 0xCB279AC1, 0xDC44E6C3, 0xBC3F8CA1, 0xF18899B1, 0x0210, // 1e-168
- 0x5EF8C0B9, 0x29AB103A, 0x15A7B7E5, 0x96F5600F, 0x0214, // 1e-167
- 0xF6B6F0E7, 0x7415D448, 0xDB11A5DE, 0xBCB2B812, 0x0217, // 1e-166
- 0x3464AD21, 0x111B495B, 0x91D60F56, 0xEBDF6617, 0x021A, // 1e-165
- 0x00BEEC34, 0xCAB10DD9, 0xBB25C995, 0x936B9FCE, 0x021E, // 1e-164
- 0x40EEA742, 0x3D5D514F, 0x69EF3BFB, 0xB84687C2, 0x0221, // 1e-163
- 0x112A5112, 0x0CB4A5A3, 0x046B0AFA, 0xE65829B3, 0x0224, // 1e-162
- 0xEABA72AB, 0x47F0E785, 0xE2C2E6DC, 0x8FF71A0F, 0x0228, // 1e-161
- 0x65690F56, 0x59ED2167, 0xDB73A093, 0xB3F4E093, 0x022B, // 1e-160
- 0x3EC3532C, 0x306869C1, 0xD25088B8, 0xE0F218B8, 0x022E, // 1e-159
- 0xC73A13FB, 0x1E414218, 0x83725573, 0x8C974F73, 0x0232, // 1e-158
- 0xF90898FA, 0xE5D1929E, 0x644EEACF, 0xAFBD2350, 0x0235, // 1e-157
- 0xB74ABF39, 0xDF45F746, 0x7D62A583, 0xDBAC6C24, 0x0238, // 1e-156
- 0x328EB783, 0x6B8BBA8C, 0xCE5DA772, 0x894BC396, 0x023C, // 1e-155
- 0x3F326564, 0x066EA92F, 0x81F5114F, 0xAB9EB47C, 0x023F, // 1e-154
- 0x0EFEFEBD, 0xC80A537B, 0xA27255A2, 0xD686619B, 0x0242, // 1e-153
- 0xE95F5F36, 0xBD06742C, 0x45877585, 0x8613FD01, 0x0246, // 1e-152
- 0x23B73704, 0x2C481138, 0x96E952E7, 0xA798FC41, 0x0249, // 1e-151
- 0x2CA504C5, 0xF75A1586, 0xFCA3A7A0, 0xD17F3B51, 0x024C, // 1e-150
- 0xDBE722FB, 0x9A984D73, 0x3DE648C4, 0x82EF8513, 0x0250, // 1e-149
- 0xD2E0EBBA, 0xC13E60D0, 0x0D5FDAF5, 0xA3AB6658, 0x0253, // 1e-148
- 0x079926A8, 0x318DF905, 0x10B7D1B3, 0xCC963FEE, 0x0256, // 1e-147
- 0x497F7052, 0xFDF17746, 0x94E5C61F, 0xFFBBCFE9, 0x0259, // 1e-146
- 0xEDEFA633, 0xFEB6EA8B, 0xFD0F9BD3, 0x9FD561F1, 0x025D, // 1e-145
- 0xE96B8FC0, 0xFE64A52E, 0x7C5382C8, 0xC7CABA6E, 0x0260, // 1e-144
- 0xA3C673B0, 0x3DFDCE7A, 0x1B68637B, 0xF9BD690A, 0x0263, // 1e-143
- 0xA65C084E, 0x06BEA10C, 0x51213E2D, 0x9C1661A6, 0x0267, // 1e-142
- 0xCFF30A62, 0x486E494F, 0xE5698DB8, 0xC31BFA0F, 0x026A, // 1e-141
- 0xC3EFCCFA, 0x5A89DBA3, 0xDEC3F126, 0xF3E2F893, 0x026D, // 1e-140
- 0x5A75E01C, 0xF8962946, 0x6B3A76B7, 0x986DDB5C, 0x0271, // 1e-139
- 0xF1135823, 0xF6BBB397, 0x86091465, 0xBE895233, 0x0274, // 1e-138
- 0xED582E2C, 0x746AA07D, 0x678B597F, 0xEE2BA6C0, 0x0277, // 1e-137
- 0xB4571CDC, 0xA8C2A44E, 0x40B717EF, 0x94DB4838, 0x027B, // 1e-136
- 0x616CE413, 0x92F34D62, 0x50E4DDEB, 0xBA121A46, 0x027E, // 1e-135
- 0xF9C81D17, 0x77B020BA, 0xE51E1566, 0xE896A0D7, 0x0281, // 1e-134
- 0xDC1D122E, 0x0ACE1474, 0xEF32CD60, 0x915E2486, 0x0285, // 1e-133
- 0x132456BA, 0x0D819992, 0xAAFF80B8, 0xB5B5ADA8, 0x0288, // 1e-132
- 0x97ED6C69, 0x10E1FFF6, 0xD5BF60E6, 0xE3231912, 0x028B, // 1e-131
- 0x1EF463C1, 0xCA8D3FFA, 0xC5979C8F, 0x8DF5EFAB, 0x028F, // 1e-130
- 0xA6B17CB2, 0xBD308FF8, 0xB6FD83B3, 0xB1736B96, 0x0292, // 1e-129
- 0xD05DDBDE, 0xAC7CB3F6, 0x64BCE4A0, 0xDDD0467C, 0x0295, // 1e-128
- 0x423AA96B, 0x6BCDF07A, 0xBEF60EE4, 0x8AA22C0D, 0x0299, // 1e-127
- 0xD2C953C6, 0x86C16C98, 0x2EB3929D, 0xAD4AB711, 0x029C, // 1e-126
- 0x077BA8B7, 0xE871C7BF, 0x7A607744, 0xD89D64D5, 0x029F, // 1e-125
- 0x64AD4972, 0x11471CD7, 0x6C7C4A8B, 0x87625F05, 0x02A3, // 1e-124
- 0x3DD89BCF, 0xD598E40D, 0xC79B5D2D, 0xA93AF6C6, 0x02A6, // 1e-123
- 0x8D4EC2C3, 0x4AFF1D10, 0x79823479, 0xD389B478, 0x02A9, // 1e-122
- 0x585139BA, 0xCEDF722A, 0x4BF160CB, 0x843610CB, 0x02AD, // 1e-121
- 0xEE658828, 0xC2974EB4, 0x1EEDB8FE, 0xA54394FE, 0x02B0, // 1e-120
- 0x29FEEA32, 0x733D2262, 0xA6A9273E, 0xCE947A3D, 0x02B3, // 1e-119
- 0x5A3F525F, 0x0806357D, 0x8829B887, 0x811CCC66, 0x02B7, // 1e-118
- 0xB0CF26F7, 0xCA07C2DC, 0x2A3426A8, 0xA163FF80, 0x02BA, // 1e-117
- 0xDD02F0B5, 0xFC89B393, 0x34C13052, 0xC9BCFF60, 0x02BD, // 1e-116
- 0xD443ACE2, 0xBBAC2078, 0x41F17C67, 0xFC2C3F38, 0x02C0, // 1e-115
- 0x84AA4C0D, 0xD54B944B, 0x2936EDC0, 0x9D9BA783, 0x02C4, // 1e-114
- 0x65D4DF11, 0x0A9E795E, 0xF384A931, 0xC5029163, 0x02C7, // 1e-113
- 0xFF4A16D5, 0x4D4617B5, 0xF065D37D, 0xF64335BC, 0x02CA, // 1e-112
- 0xBF8E4E45, 0x504BCED1, 0x163FA42E, 0x99EA0196, 0x02CE, // 1e-111
- 0x2F71E1D6, 0xE45EC286, 0x9BCF8D39, 0xC06481FB, 0x02D1, // 1e-110
- 0xBB4E5A4C, 0x5D767327, 0x82C37088, 0xF07DA27A, 0x02D4, // 1e-109
- 0xD510F86F, 0x3A6A07F8, 0x91BA2655, 0x964E858C, 0x02D8, // 1e-108
- 0x0A55368B, 0x890489F7, 0xB628AFEA, 0xBBE226EF, 0x02DB, // 1e-107
- 0xCCEA842E, 0x2B45AC74, 0xA3B2DBE5, 0xEADAB0AB, 0x02DE, // 1e-106
- 0x0012929D, 0x3B0B8BC9, 0x464FC96F, 0x92C8AE6B, 0x02E2, // 1e-105
- 0x40173744, 0x09CE6EBB, 0x17E3BBCB, 0xB77ADA06, 0x02E5, // 1e-104
- 0x101D0515, 0xCC420A6A, 0x9DDCAABD, 0xE5599087, 0x02E8, // 1e-103
- 0x4A12232D, 0x9FA94682, 0xC2A9EAB6, 0x8F57FA54, 0x02EC, // 1e-102
- 0xDC96ABF9, 0x47939822, 0xF3546564, 0xB32DF8E9, 0x02EF, // 1e-101
- 0x93BC56F7, 0x59787E2B, 0x70297EBD, 0xDFF97724, 0x02F2, // 1e-100
- 0x3C55B65A, 0x57EB4EDB, 0xC619EF36, 0x8BFBEA76, 0x02F6, // 1e-99
- 0x0B6B23F1, 0xEDE62292, 0x77A06B03, 0xAEFAE514, 0x02F9, // 1e-98
- 0x8E45ECED, 0xE95FAB36, 0x958885C4, 0xDAB99E59, 0x02FC, // 1e-97
- 0x18EBB414, 0x11DBCB02, 0xFD75539B, 0x88B402F7, 0x0300, // 1e-96
- 0x9F26A119, 0xD652BDC2, 0xFCD2A881, 0xAAE103B5, 0x0303, // 1e-95
- 0x46F0495F, 0x4BE76D33, 0x7C0752A2, 0xD59944A3, 0x0306, // 1e-94
- 0x0C562DDB, 0x6F70A440, 0x2D8493A5, 0x857FCAE6, 0x030A, // 1e-93
- 0x0F6BB952, 0xCB4CCD50, 0xB8E5B88E, 0xA6DFBD9F, 0x030D, // 1e-92
- 0x1346A7A7, 0x7E2000A4, 0xA71F26B2, 0xD097AD07, 0x0310, // 1e-91
- 0x8C0C28C8, 0x8ED40066, 0xC873782F, 0x825ECC24, 0x0314, // 1e-90
- 0x2F0F32FA, 0x72890080, 0xFA90563B, 0xA2F67F2D, 0x0317, // 1e-89
- 0x3AD2FFB9, 0x4F2B40A0, 0x79346BCA, 0xCBB41EF9, 0x031A, // 1e-88
- 0x4987BFA8, 0xE2F610C8, 0xD78186BC, 0xFEA126B7, 0x031D, // 1e-87
- 0x2DF4D7C9, 0x0DD9CA7D, 0xE6B0F436, 0x9F24B832, 0x0321, // 1e-86
- 0x79720DBB, 0x91503D1C, 0xA05D3143, 0xC6EDE63F, 0x0324, // 1e-85
- 0x97CE912A, 0x75A44C63, 0x88747D94, 0xF8A95FCF, 0x0327, // 1e-84
- 0x3EE11ABA, 0xC986AFBE, 0xB548CE7C, 0x9B69DBE1, 0x032B, // 1e-83
- 0xCE996168, 0xFBE85BAD, 0x229B021B, 0xC24452DA, 0x032E, // 1e-82
- 0x423FB9C3, 0xFAE27299, 0xAB41C2A2, 0xF2D56790, 0x0331, // 1e-81
- 0xC967D41A, 0xDCCD879F, 0x6B0919A5, 0x97C560BA, 0x0335, // 1e-80
- 0xBBC1C920, 0x5400E987, 0x05CB600F, 0xBDB6B8E9, 0x0338, // 1e-79
- 0xAAB23B68, 0x290123E9, 0x473E3813, 0xED246723, 0x033B, // 1e-78
- 0x0AAF6521, 0xF9A0B672, 0x0C86E30B, 0x9436C076, 0x033F, // 1e-77
- 0x8D5B3E69, 0xF808E40E, 0x8FA89BCE, 0xB9447093, 0x0342, // 1e-76
- 0x30B20E04, 0xB60B1D12, 0x7392C2C2, 0xE7958CB8, 0x0345, // 1e-75
- 0x5E6F48C2, 0xB1C6F22B, 0x483BB9B9, 0x90BD77F3, 0x0349, // 1e-74
- 0x360B1AF3, 0x1E38AEB6, 0x1A4AA828, 0xB4ECD5F0, 0x034C, // 1e-73
- 0xC38DE1B0, 0x25C6DA63, 0x20DD5232, 0xE2280B6C, 0x034F, // 1e-72
- 0x5A38AD0E, 0x579C487E, 0x948A535F, 0x8D590723, 0x0353, // 1e-71
- 0xF0C6D851, 0x2D835A9D, 0x79ACE837, 0xB0AF48EC, 0x0356, // 1e-70
- 0x6CF88E65, 0xF8E43145, 0x98182244, 0xDCDB1B27, 0x0359, // 1e-69
- 0x641B58FF, 0x1B8E9ECB, 0xBF0F156B, 0x8A08F0F8, 0x035D, // 1e-68
- 0x3D222F3F, 0xE272467E, 0xEED2DAC5, 0xAC8B2D36, 0x0360, // 1e-67
- 0xCC6ABB0F, 0x5B0ED81D, 0xAA879177, 0xD7ADF884, 0x0363, // 1e-66
- 0x9FC2B4E9, 0x98E94712, 0xEA94BAEA, 0x86CCBB52, 0x0367, // 1e-65
- 0x47B36224, 0x3F2398D7, 0xA539E9A5, 0xA87FEA27, 0x036A, // 1e-64
- 0x19A03AAD, 0x8EEC7F0D, 0x8E88640E, 0xD29FE4B1, 0x036D, // 1e-63
- 0x300424AC, 0x1953CF68, 0xF9153E89, 0x83A3EEEE, 0x0371, // 1e-62
- 0x3C052DD7, 0x5FA8C342, 0xB75A8E2B, 0xA48CEAAA, 0x0374, // 1e-61
- 0xCB06794D, 0x3792F412, 0x653131B6, 0xCDB02555, 0x0377, // 1e-60
- 0xBEE40BD0, 0xE2BBD88B, 0x5F3EBF11, 0x808E1755, 0x037B, // 1e-59
- 0xAE9D0EC4, 0x5B6ACEAE, 0xB70E6ED6, 0xA0B19D2A, 0x037E, // 1e-58
- 0x5A445275, 0xF245825A, 0x64D20A8B, 0xC8DE0475, 0x0381, // 1e-57
- 0xF0D56712, 0xEED6E2F0, 0xBE068D2E, 0xFB158592, 0x0384, // 1e-56
- 0x9685606B, 0x55464DD6, 0xB6C4183D, 0x9CED737B, 0x0388, // 1e-55
- 0x3C26B886, 0xAA97E14C, 0xA4751E4C, 0xC428D05A, 0x038B, // 1e-54
- 0x4B3066A8, 0xD53DD99F, 0x4D9265DF, 0xF5330471, 0x038E, // 1e-53
- 0x8EFE4029, 0xE546A803, 0xD07B7FAB, 0x993FE2C6, 0x0392, // 1e-52
- 0x72BDD033, 0xDE985204, 0x849A5F96, 0xBF8FDB78, 0x0395, // 1e-51
- 0x8F6D4440, 0x963E6685, 0xA5C0F77C, 0xEF73D256, 0x0398, // 1e-50
- 0x79A44AA8, 0xDDE70013, 0x27989AAD, 0x95A86376, 0x039C, // 1e-49
- 0x580D5D52, 0x5560C018, 0xB17EC159, 0xBB127C53, 0x039F, // 1e-48
- 0x6E10B4A6, 0xAAB8F01E, 0x9DDE71AF, 0xE9D71B68, 0x03A2, // 1e-47
- 0x04CA70E8, 0xCAB39613, 0x62AB070D, 0x92267121, 0x03A6, // 1e-46
- 0xC5FD0D22, 0x3D607B97, 0xBB55C8D1, 0xB6B00D69, 0x03A9, // 1e-45
- 0xB77C506A, 0x8CB89A7D, 0x2A2B3B05, 0xE45C10C4, 0x03AC, // 1e-44
- 0x92ADB242, 0x77F3608E, 0x9A5B04E3, 0x8EB98A7A, 0x03B0, // 1e-43
- 0x37591ED3, 0x55F038B2, 0x40F1C61C, 0xB267ED19, 0x03B3, // 1e-42
- 0xC52F6688, 0x6B6C46DE, 0x912E37A3, 0xDF01E85F, 0x03B6, // 1e-41
- 0x3B3DA015, 0x2323AC4B, 0xBABCE2C6, 0x8B61313B, 0x03BA, // 1e-40
- 0x0A0D081A, 0xABEC975E, 0xA96C1B77, 0xAE397D8A, 0x03BD, // 1e-39
- 0x8C904A21, 0x96E7BD35, 0x53C72255, 0xD9C7DCED, 0x03C0, // 1e-38
- 0x77DA2E54, 0x7E50D641, 0x545C7575, 0x881CEA14, 0x03C4, // 1e-37
- 0xD5D0B9E9, 0xDDE50BD1, 0x697392D2, 0xAA242499, 0x03C7, // 1e-36
- 0x4B44E864, 0x955E4EC6, 0xC3D07787, 0xD4AD2DBF, 0x03CA, // 1e-35
- 0xEF0B113E, 0xBD5AF13B, 0xDA624AB4, 0x84EC3C97, 0x03CE, // 1e-34
- 0xEACDD58E, 0xECB1AD8A, 0xD0FADD61, 0xA6274BBD, 0x03D1, // 1e-33
- 0xA5814AF2, 0x67DE18ED, 0x453994BA, 0xCFB11EAD, 0x03D4, // 1e-32
- 0x8770CED7, 0x80EACF94, 0x4B43FCF4, 0x81CEB32C, 0x03D8, // 1e-31
- 0xA94D028D, 0xA1258379, 0x5E14FC31, 0xA2425FF7, 0x03DB, // 1e-30
- 0x13A04330, 0x096EE458, 0x359A3B3E, 0xCAD2F7F5, 0x03DE, // 1e-29
- 0x188853FC, 0x8BCA9D6E, 0x8300CA0D, 0xFD87B5F2, 0x03E1, // 1e-28
- 0xCF55347D, 0x775EA264, 0x91E07E48, 0x9E74D1B7, 0x03E5, // 1e-27
- 0x032A819D, 0x95364AFE, 0x76589DDA, 0xC6120625, 0x03E8, // 1e-26
- 0x83F52204, 0x3A83DDBD, 0xD3EEC551, 0xF79687AE, 0x03EB, // 1e-25
- 0x72793542, 0xC4926A96, 0x44753B52, 0x9ABE14CD, 0x03EF, // 1e-24
- 0x0F178293, 0x75B7053C, 0x95928A27, 0xC16D9A00, 0x03F2, // 1e-23
- 0x12DD6338, 0x5324C68B, 0xBAF72CB1, 0xF1C90080, 0x03F5, // 1e-22
- 0xEBCA5E03, 0xD3F6FC16, 0x74DA7BEE, 0x971DA050, 0x03F9, // 1e-21
- 0xA6BCF584, 0x88F4BB1C, 0x92111AEA, 0xBCE50864, 0x03FC, // 1e-20
- 0xD06C32E5, 0x2B31E9E3, 0xB69561A5, 0xEC1E4A7D, 0x03FF, // 1e-19
- 0x62439FCF, 0x3AFF322E, 0x921D5D07, 0x9392EE8E, 0x0403, // 1e-18
- 0xFAD487C2, 0x09BEFEB9, 0x36A4B449, 0xB877AA32, 0x0406, // 1e-17
- 0x7989A9B3, 0x4C2EBE68, 0xC44DE15B, 0xE69594BE, 0x0409, // 1e-16
- 0x4BF60A10, 0x0F9D3701, 0x3AB0ACD9, 0x901D7CF7, 0x040D, // 1e-15
- 0x9EF38C94, 0x538484C1, 0x095CD80F, 0xB424DC35, 0x0410, // 1e-14
- 0x06B06FB9, 0x2865A5F2, 0x4BB40E13, 0xE12E1342, 0x0413, // 1e-13
- 0x442E45D3, 0xF93F87B7, 0x6F5088CB, 0x8CBCCC09, 0x0417, // 1e-12
- 0x1539D748, 0xF78F69A5, 0xCB24AAFE, 0xAFEBFF0B, 0x041A, // 1e-11
- 0x5A884D1B, 0xB573440E, 0xBDEDD5BE, 0xDBE6FECE, 0x041D, // 1e-10
- 0xF8953030, 0x31680A88, 0x36B4A597, 0x89705F41, 0x0421, // 1e-9
- 0x36BA7C3D, 0xFDC20D2B, 0x8461CEFC, 0xABCC7711, 0x0424, // 1e-8
- 0x04691B4C, 0x3D329076, 0xE57A42BC, 0xD6BF94D5, 0x0427, // 1e-7
- 0xC2C1B10F, 0xA63F9A49, 0xAF6C69B5, 0x8637BD05, 0x042B, // 1e-6
- 0x33721D53, 0x0FCF80DC, 0x1B478423, 0xA7C5AC47, 0x042E, // 1e-5
- 0x404EA4A8, 0xD3C36113, 0xE219652B, 0xD1B71758, 0x0431, // 1e-4
- 0x083126E9, 0x645A1CAC, 0x8D4FDF3B, 0x83126E97, 0x0435, // 1e-3
- 0x0A3D70A3, 0x3D70A3D7, 0x70A3D70A, 0xA3D70A3D, 0x0438, // 1e-2
- 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0xCCCCCCCC, 0x043B, // 1e-1
- 0x00000000, 0x00000000, 0x00000000, 0x80000000, 0x043F, // 1e0
- 0x00000000, 0x00000000, 0x00000000, 0xA0000000, 0x0442, // 1e1
- 0x00000000, 0x00000000, 0x00000000, 0xC8000000, 0x0445, // 1e2
- 0x00000000, 0x00000000, 0x00000000, 0xFA000000, 0x0448, // 1e3
- 0x00000000, 0x00000000, 0x00000000, 0x9C400000, 0x044C, // 1e4
- 0x00000000, 0x00000000, 0x00000000, 0xC3500000, 0x044F, // 1e5
- 0x00000000, 0x00000000, 0x00000000, 0xF4240000, 0x0452, // 1e6
- 0x00000000, 0x00000000, 0x00000000, 0x98968000, 0x0456, // 1e7
- 0x00000000, 0x00000000, 0x00000000, 0xBEBC2000, 0x0459, // 1e8
- 0x00000000, 0x00000000, 0x00000000, 0xEE6B2800, 0x045C, // 1e9
- 0x00000000, 0x00000000, 0x00000000, 0x9502F900, 0x0460, // 1e10
- 0x00000000, 0x00000000, 0x00000000, 0xBA43B740, 0x0463, // 1e11
- 0x00000000, 0x00000000, 0x00000000, 0xE8D4A510, 0x0466, // 1e12
- 0x00000000, 0x00000000, 0x00000000, 0x9184E72A, 0x046A, // 1e13
- 0x00000000, 0x00000000, 0x80000000, 0xB5E620F4, 0x046D, // 1e14
- 0x00000000, 0x00000000, 0xA0000000, 0xE35FA931, 0x0470, // 1e15
- 0x00000000, 0x00000000, 0x04000000, 0x8E1BC9BF, 0x0474, // 1e16
- 0x00000000, 0x00000000, 0xC5000000, 0xB1A2BC2E, 0x0477, // 1e17
- 0x00000000, 0x00000000, 0x76400000, 0xDE0B6B3A, 0x047A, // 1e18
- 0x00000000, 0x00000000, 0x89E80000, 0x8AC72304, 0x047E, // 1e19
- 0x00000000, 0x00000000, 0xAC620000, 0xAD78EBC5, 0x0481, // 1e20
- 0x00000000, 0x00000000, 0x177A8000, 0xD8D726B7, 0x0484, // 1e21
- 0x00000000, 0x00000000, 0x6EAC9000, 0x87867832, 0x0488, // 1e22
- 0x00000000, 0x00000000, 0x0A57B400, 0xA968163F, 0x048B, // 1e23
- 0x00000000, 0x00000000, 0xCCEDA100, 0xD3C21BCE, 0x048E, // 1e24
- 0x00000000, 0x00000000, 0x401484A0, 0x84595161, 0x0492, // 1e25
- 0x00000000, 0x00000000, 0x9019A5C8, 0xA56FA5B9, 0x0495, // 1e26
- 0x00000000, 0x00000000, 0xF4200F3A, 0xCECB8F27, 0x0498, // 1e27
- 0x00000000, 0x40000000, 0xF8940984, 0x813F3978, 0x049C, // 1e28
- 0x00000000, 0x50000000, 0x36B90BE5, 0xA18F07D7, 0x049F, // 1e29
- 0x00000000, 0xA4000000, 0x04674EDE, 0xC9F2C9CD, 0x04A2, // 1e30
- 0x00000000, 0x4D000000, 0x45812296, 0xFC6F7C40, 0x04A5, // 1e31
- 0x00000000, 0xF0200000, 0x2B70B59D, 0x9DC5ADA8, 0x04A9, // 1e32
- 0x00000000, 0x6C280000, 0x364CE305, 0xC5371912, 0x04AC, // 1e33
- 0x00000000, 0xC7320000, 0xC3E01BC6, 0xF684DF56, 0x04AF, // 1e34
- 0x00000000, 0x3C7F4000, 0x3A6C115C, 0x9A130B96, 0x04B3, // 1e35
- 0x00000000, 0x4B9F1000, 0xC90715B3, 0xC097CE7B, 0x04B6, // 1e36
- 0x00000000, 0x1E86D400, 0xBB48DB20, 0xF0BDC21A, 0x04B9, // 1e37
- 0x00000000, 0x13144480, 0xB50D88F4, 0x96769950, 0x04BD, // 1e38
- 0x00000000, 0x17D955A0, 0xE250EB31, 0xBC143FA4, 0x04C0, // 1e39
- 0x00000000, 0x5DCFAB08, 0x1AE525FD, 0xEB194F8E, 0x04C3, // 1e40
- 0x00000000, 0x5AA1CAE5, 0xD0CF37BE, 0x92EFD1B8, 0x04C7, // 1e41
- 0x40000000, 0xF14A3D9E, 0x050305AD, 0xB7ABC627, 0x04CA, // 1e42
- 0xD0000000, 0x6D9CCD05, 0xC643C719, 0xE596B7B0, 0x04CD, // 1e43
- 0xA2000000, 0xE4820023, 0x7BEA5C6F, 0x8F7E32CE, 0x04D1, // 1e44
- 0x8A800000, 0xDDA2802C, 0x1AE4F38B, 0xB35DBF82, 0x04D4, // 1e45
- 0xAD200000, 0xD50B2037, 0xA19E306E, 0xE0352F62, 0x04D7, // 1e46
- 0xCC340000, 0x4526F422, 0xA502DE45, 0x8C213D9D, 0x04DB, // 1e47
- 0x7F410000, 0x9670B12B, 0x0E4395D6, 0xAF298D05, 0x04DE, // 1e48
- 0x5F114000, 0x3C0CDD76, 0x51D47B4C, 0xDAF3F046, 0x04E1, // 1e49
- 0xFB6AC800, 0xA5880A69, 0xF324CD0F, 0x88D8762B, 0x04E5, // 1e50
- 0x7A457A00, 0x8EEA0D04, 0xEFEE0053, 0xAB0E93B6, 0x04E8, // 1e51
- 0x98D6D880, 0x72A49045, 0xABE98068, 0xD5D238A4, 0x04EB, // 1e52
- 0x7F864750, 0x47A6DA2B, 0xEB71F041, 0x85A36366, 0x04EF, // 1e53
- 0x5F67D924, 0x999090B6, 0xA64E6C51, 0xA70C3C40, 0x04F2, // 1e54
- 0xF741CF6D, 0xFFF4B4E3, 0xCFE20765, 0xD0CF4B50, 0x04F5, // 1e55
- 0x7A8921A4, 0xBFF8F10E, 0x81ED449F, 0x82818F12, 0x04F9, // 1e56
- 0x192B6A0D, 0xAFF72D52, 0x226895C7, 0xA321F2D7, 0x04FC, // 1e57
- 0x9F764490, 0x9BF4F8A6, 0xEB02BB39, 0xCBEA6F8C, 0x04FF, // 1e58
- 0x4753D5B4, 0x02F236D0, 0x25C36A08, 0xFEE50B70, 0x0502, // 1e59
- 0x2C946590, 0x01D76242, 0x179A2245, 0x9F4F2726, 0x0506, // 1e60
- 0xB7B97EF5, 0x424D3AD2, 0x9D80AAD6, 0xC722F0EF, 0x0509, // 1e61
- 0x65A7DEB2, 0xD2E08987, 0x84E0D58B, 0xF8EBAD2B, 0x050C, // 1e62
- 0x9F88EB2F, 0x63CC55F4, 0x330C8577, 0x9B934C3B, 0x0510, // 1e63
- 0xC76B25FB, 0x3CBF6B71, 0xFFCFA6D5, 0xC2781F49, 0x0513, // 1e64
- 0x3945EF7A, 0x8BEF464E, 0x7FC3908A, 0xF316271C, 0x0516, // 1e65
- 0xE3CBB5AC, 0x97758BF0, 0xCFDA3A56, 0x97EDD871, 0x051A, // 1e66
- 0x1CBEA317, 0x3D52EEED, 0x43D0C8EC, 0xBDE94E8E, 0x051D, // 1e67
- 0x63EE4BDD, 0x4CA7AAA8, 0xD4C4FB27, 0xED63A231, 0x0520, // 1e68
- 0x3E74EF6A, 0x8FE8CAA9, 0x24FB1CF8, 0x945E455F, 0x0524, // 1e69
- 0x8E122B44, 0xB3E2FD53, 0xEE39E436, 0xB975D6B6, 0x0527, // 1e70
- 0x7196B616, 0x60DBBCA8, 0xA9C85D44, 0xE7D34C64, 0x052A, // 1e71
- 0x46FE31CD, 0xBC8955E9, 0xEA1D3A4A, 0x90E40FBE, 0x052E, // 1e72
- 0x98BDBE41, 0x6BABAB63, 0xA4A488DD, 0xB51D13AE, 0x0531, // 1e73
- 0x7EED2DD1, 0xC696963C, 0x4DCDAB14, 0xE264589A, 0x0534, // 1e74
- 0xCF543CA2, 0xFC1E1DE5, 0x70A08AEC, 0x8D7EB760, 0x0538, // 1e75
- 0x43294BCB, 0x3B25A55F, 0x8CC8ADA8, 0xB0DE6538, 0x053B, // 1e76
- 0x13F39EBE, 0x49EF0EB7, 0xAFFAD912, 0xDD15FE86, 0x053E, // 1e77
- 0x6C784337, 0x6E356932, 0x2DFCC7AB, 0x8A2DBF14, 0x0542, // 1e78
- 0x07965404, 0x49C2C37F, 0x397BF996, 0xACB92ED9, 0x0545, // 1e79
- 0xC97BE906, 0xDC33745E, 0x87DAF7FB, 0xD7E77A8F, 0x0548, // 1e80
- 0x3DED71A3, 0x69A028BB, 0xB4E8DAFD, 0x86F0AC99, 0x054C, // 1e81
- 0x0D68CE0C, 0xC40832EA, 0x222311BC, 0xA8ACD7C0, 0x054F, // 1e82
- 0x90C30190, 0xF50A3FA4, 0x2AABD62B, 0xD2D80DB0, 0x0552, // 1e83
- 0xDA79E0FA, 0x792667C6, 0x1AAB65DB, 0x83C7088E, 0x0556, // 1e84
- 0x91185938, 0x577001B8, 0xA1563F52, 0xA4B8CAB1, 0x0559, // 1e85
- 0xB55E6F86, 0xED4C0226, 0x09ABCF26, 0xCDE6FD5E, 0x055C, // 1e86
- 0x315B05B4, 0x544F8158, 0xC60B6178, 0x80B05E5A, 0x0560, // 1e87
- 0x3DB1C721, 0x696361AE, 0x778E39D6, 0xA0DC75F1, 0x0563, // 1e88
- 0xCD1E38E9, 0x03BC3A19, 0xD571C84C, 0xC913936D, 0x0566, // 1e89
- 0x4065C723, 0x04AB48A0, 0x4ACE3A5F, 0xFB587849, 0x0569, // 1e90
- 0x283F9C76, 0x62EB0D64, 0xCEC0E47B, 0x9D174B2D, 0x056D, // 1e91
- 0x324F8394, 0x3BA5D0BD, 0x42711D9A, 0xC45D1DF9, 0x0570, // 1e92
- 0x7EE36479, 0xCA8F44EC, 0x930D6500, 0xF5746577, 0x0573, // 1e93
- 0xCF4E1ECB, 0x7E998B13, 0xBBE85F20, 0x9968BF6A, 0x0577, // 1e94
- 0xC321A67E, 0x9E3FEDD8, 0x6AE276E8, 0xBFC2EF45, 0x057A, // 1e95
- 0xF3EA101E, 0xC5CFE94E, 0xC59B14A2, 0xEFB3AB16, 0x057D, // 1e96
- 0x58724A12, 0xBBA1F1D1, 0x3B80ECE5, 0x95D04AEE, 0x0581, // 1e97
- 0xAE8EDC97, 0x2A8A6E45, 0xCA61281F, 0xBB445DA9, 0x0584, // 1e98
- 0x1A3293BD, 0xF52D09D7, 0x3CF97226, 0xEA157514, 0x0587, // 1e99
- 0x705F9C56, 0x593C2626, 0xA61BE758, 0x924D692C, 0x058B, // 1e100
- 0x0C77836C, 0x6F8B2FB0, 0xCFA2E12E, 0xB6E0C377, 0x058E, // 1e101
- 0x0F956447, 0x0B6DFB9C, 0xC38B997A, 0xE498F455, 0x0591, // 1e102
- 0x89BD5EAC, 0x4724BD41, 0x9A373FEC, 0x8EDF98B5, 0x0595, // 1e103
- 0xEC2CB657, 0x58EDEC91, 0x00C50FE7, 0xB2977EE3, 0x0598, // 1e104
- 0x6737E3ED, 0x2F2967B6, 0xC0F653E1, 0xDF3D5E9B, 0x059B, // 1e105
- 0x0082EE74, 0xBD79E0D2, 0x5899F46C, 0x8B865B21, 0x059F, // 1e106
- 0x80A3AA11, 0xECD85906, 0xAEC07187, 0xAE67F1E9, 0x05A2, // 1e107
- 0x20CC9495, 0xE80E6F48, 0x1A708DE9, 0xDA01EE64, 0x05A5, // 1e108
- 0x147FDCDD, 0x3109058D, 0x908658B2, 0x884134FE, 0x05A9, // 1e109
- 0x599FD415, 0xBD4B46F0, 0x34A7EEDE, 0xAA51823E, 0x05AC, // 1e110
- 0x7007C91A, 0x6C9E18AC, 0xC1D1EA96, 0xD4E5E2CD, 0x05AF, // 1e111
- 0xC604DDB0, 0x03E2CF6B, 0x9923329E, 0x850FADC0, 0x05B3, // 1e112
- 0xB786151C, 0x84DB8346, 0xBF6BFF45, 0xA6539930, 0x05B6, // 1e113
- 0x65679A63, 0xE6126418, 0xEF46FF16, 0xCFE87F7C, 0x05B9, // 1e114
- 0x3F60C07E, 0x4FCB7E8F, 0x158C5F6E, 0x81F14FAE, 0x05BD, // 1e115
- 0x0F38F09D, 0xE3BE5E33, 0x9AEF7749, 0xA26DA399, 0x05C0, // 1e116
- 0xD3072CC5, 0x5CADF5BF, 0x01AB551C, 0xCB090C80, 0x05C3, // 1e117
- 0xC7C8F7F6, 0x73D9732F, 0x02162A63, 0xFDCB4FA0, 0x05C6, // 1e118
- 0xDCDD9AFA, 0x2867E7FD, 0x014DDA7E, 0x9E9F11C4, 0x05CA, // 1e119
- 0x541501B8, 0xB281E1FD, 0x01A1511D, 0xC646D635, 0x05CD, // 1e120
- 0xA91A4226, 0x1F225A7C, 0x4209A565, 0xF7D88BC2, 0x05D0, // 1e121
- 0xE9B06958, 0x3375788D, 0x6946075F, 0x9AE75759, 0x05D4, // 1e122
- 0x641C83AE, 0x0052D6B1, 0xC3978937, 0xC1A12D2F, 0x05D7, // 1e123
- 0xBD23A49A, 0xC0678C5D, 0xB47D6B84, 0xF209787B, 0x05DA, // 1e124
- 0x963646E0, 0xF840B7BA, 0x50CE6332, 0x9745EB4D, 0x05DE, // 1e125
- 0x3BC3D898, 0xB650E5A9, 0xA501FBFF, 0xBD176620, 0x05E1, // 1e126
- 0x8AB4CEBE, 0xA3E51F13, 0xCE427AFF, 0xEC5D3FA8, 0x05E4, // 1e127
- 0x36B10137, 0xC66F336C, 0x80E98CDF, 0x93BA47C9, 0x05E8, // 1e128
- 0x445D4184, 0xB80B0047, 0xE123F017, 0xB8A8D9BB, 0x05EB, // 1e129
- 0x157491E5, 0xA60DC059, 0xD96CEC1D, 0xE6D3102A, 0x05EE, // 1e130
- 0xAD68DB2F, 0x87C89837, 0xC7E41392, 0x9043EA1A, 0x05F2, // 1e131
- 0x98C311FB, 0x29BABE45, 0x79DD1877, 0xB454E4A1, 0x05F5, // 1e132
- 0xFEF3D67A, 0xF4296DD6, 0xD8545E94, 0xE16A1DC9, 0x05F8, // 1e133
- 0x5F58660C, 0x1899E4A6, 0x2734BB1D, 0x8CE2529E, 0x05FC, // 1e134
- 0xF72E7F8F, 0x5EC05DCF, 0xB101E9E4, 0xB01AE745, 0x05FF, // 1e135
- 0xF4FA1F73, 0x76707543, 0x1D42645D, 0xDC21A117, 0x0602, // 1e136
- 0x791C53A8, 0x6A06494A, 0x72497EBA, 0x899504AE, 0x0606, // 1e137
- 0x17636892, 0x0487DB9D, 0x0EDBDE69, 0xABFA45DA, 0x0609, // 1e138
- 0x5D3C42B6, 0x45A9D284, 0x9292D603, 0xD6F8D750, 0x060C, // 1e139
- 0xBA45A9B2, 0x0B8A2392, 0x5B9BC5C2, 0x865B8692, 0x0610, // 1e140
- 0x68D7141E, 0x8E6CAC77, 0xF282B732, 0xA7F26836, 0x0613, // 1e141
- 0x430CD926, 0x3207D795, 0xAF2364FF, 0xD1EF0244, 0x0616, // 1e142
- 0x49E807B8, 0x7F44E6BD, 0xED761F1F, 0x8335616A, 0x061A, // 1e143
- 0x9C6209A6, 0x5F16206C, 0xA8D3A6E7, 0xA402B9C5, 0x061D, // 1e144
- 0xC37A8C0F, 0x36DBA887, 0x130890A1, 0xCD036837, 0x0620, // 1e145
- 0xDA2C9789, 0xC2494954, 0x6BE55A64, 0x80222122, 0x0624, // 1e146
- 0x10B7BD6C, 0xF2DB9BAA, 0x06DEB0FD, 0xA02AA96B, 0x0627, // 1e147
- 0x94E5ACC7, 0x6F928294, 0xC8965D3D, 0xC83553C5, 0x062A, // 1e148
- 0xBA1F17F9, 0xCB772339, 0x3ABBF48C, 0xFA42A8B7, 0x062D, // 1e149
- 0x14536EFB, 0xFF2A7604, 0x84B578D7, 0x9C69A972, 0x0631, // 1e150
- 0x19684ABA, 0xFEF51385, 0x25E2D70D, 0xC38413CF, 0x0634, // 1e151
- 0x5FC25D69, 0x7EB25866, 0xEF5B8CD1, 0xF46518C2, 0x0637, // 1e152
- 0xFBD97A61, 0xEF2F773F, 0xD5993802, 0x98BF2F79, 0x063B, // 1e153
- 0xFACFD8FA, 0xAAFB550F, 0x4AFF8603, 0xBEEEFB58, 0x063E, // 1e154
- 0xF983CF38, 0x95BA2A53, 0x5DBF6784, 0xEEAABA2E, 0x0641, // 1e155
- 0x7BF26183, 0xDD945A74, 0xFA97A0B2, 0x952AB45C, 0x0645, // 1e156
- 0x9AEEF9E4, 0x94F97111, 0x393D88DF, 0xBA756174, 0x0648, // 1e157
- 0x01AAB85D, 0x7A37CD56, 0x478CEB17, 0xE912B9D1, 0x064B, // 1e158
- 0xC10AB33A, 0xAC62E055, 0xCCB812EE, 0x91ABB422, 0x064F, // 1e159
- 0x314D6009, 0x577B986B, 0x7FE617AA, 0xB616A12B, 0x0652, // 1e160
- 0xFDA0B80B, 0xED5A7E85, 0x5FDF9D94, 0xE39C4976, 0x0655, // 1e161
- 0xBE847307, 0x14588F13, 0xFBEBC27D, 0x8E41ADE9, 0x0659, // 1e162
- 0xAE258FC8, 0x596EB2D8, 0x7AE6B31C, 0xB1D21964, 0x065C, // 1e163
- 0xD9AEF3BB, 0x6FCA5F8E, 0x99A05FE3, 0xDE469FBD, 0x065F, // 1e164
- 0x480D5854, 0x25DE7BB9, 0x80043BEE, 0x8AEC23D6, 0x0663, // 1e165
- 0x9A10AE6A, 0xAF561AA7, 0x20054AE9, 0xADA72CCC, 0x0666, // 1e166
- 0x8094DA04, 0x1B2BA151, 0x28069DA4, 0xD910F7FF, 0x0669, // 1e167
- 0xF05D0842, 0x90FB44D2, 0x79042286, 0x87AA9AFF, 0x066D, // 1e168
- 0xAC744A53, 0x353A1607, 0x57452B28, 0xA99541BF, 0x0670, // 1e169
- 0x97915CE8, 0x42889B89, 0x2D1675F2, 0xD3FA922F, 0x0673, // 1e170
- 0xFEBADA11, 0x69956135, 0x7C2E09B7, 0x847C9B5D, 0x0677, // 1e171
- 0x7E699095, 0x43FAB983, 0xDB398C25, 0xA59BC234, 0x067A, // 1e172
- 0x5E03F4BB, 0x94F967E4, 0x1207EF2E, 0xCF02B2C2, 0x067D, // 1e173
- 0xBAC278F5, 0x1D1BE0EE, 0x4B44F57D, 0x8161AFB9, 0x0681, // 1e174
- 0x69731732, 0x6462D92A, 0x9E1632DC, 0xA1BA1BA7, 0x0684, // 1e175
- 0x03CFDCFE, 0x7D7B8F75, 0x859BBF93, 0xCA28A291, 0x0687, // 1e176
- 0x44C3D43E, 0x5CDA7352, 0xE702AF78, 0xFCB2CB35, 0x068A, // 1e177
- 0x6AFA64A7, 0x3A088813, 0xB061ADAB, 0x9DEFBF01, 0x068E, // 1e178
- 0x45B8FDD0, 0x088AAA18, 0x1C7A1916, 0xC56BAEC2, 0x0691, // 1e179
- 0x57273D45, 0x8AAD549E, 0xA3989F5B, 0xF6C69A72, 0x0694, // 1e180
- 0xF678864B, 0x36AC54E2, 0xA63F6399, 0x9A3C2087, 0x0698, // 1e181
- 0xB416A7DD, 0x84576A1B, 0x8FCF3C7F, 0xC0CB28A9, 0x069B, // 1e182
- 0xA11C51D5, 0x656D44A2, 0xF3C30B9F, 0xF0FDF2D3, 0x069E, // 1e183
- 0xA4B1B325, 0x9F644AE5, 0x7859E743, 0x969EB7C4, 0x06A2, // 1e184
- 0x0DDE1FEE, 0x873D5D9F, 0x96706114, 0xBC4665B5, 0x06A5, // 1e185
- 0xD155A7EA, 0xA90CB506, 0xFC0C7959, 0xEB57FF22, 0x06A8, // 1e186
- 0x42D588F2, 0x09A7F124, 0xDD87CBD8, 0x9316FF75, 0x06AC, // 1e187
- 0x538AEB2F, 0x0C11ED6D, 0x54E9BECE, 0xB7DCBF53, 0x06AF, // 1e188
- 0xA86DA5FA, 0x8F1668C8, 0x2A242E81, 0xE5D3EF28, 0x06B2, // 1e189
- 0x694487BC, 0xF96E017D, 0x1A569D10, 0x8FA47579, 0x06B6, // 1e190
- 0xC395A9AC, 0x37C981DC, 0x60EC4455, 0xB38D92D7, 0x06B9, // 1e191
- 0xF47B1417, 0x85BBE253, 0x3927556A, 0xE070F78D, 0x06BC, // 1e192
- 0x78CCEC8E, 0x93956D74, 0x43B89562, 0x8C469AB8, 0x06C0, // 1e193
- 0x970027B2, 0x387AC8D1, 0x54A6BABB, 0xAF584166, 0x06C3, // 1e194
- 0xFCC0319E, 0x06997B05, 0xE9D0696A, 0xDB2E51BF, 0x06C6, // 1e195
- 0xBDF81F03, 0x441FECE3, 0xF22241E2, 0x88FCF317, 0x06CA, // 1e196
- 0xAD7626C3, 0xD527E81C, 0xEEAAD25A, 0xAB3C2FDD, 0x06CD, // 1e197
- 0xD8D3B074, 0x8A71E223, 0x6A5586F1, 0xD60B3BD5, 0x06D0, // 1e198
- 0x67844E49, 0xF6872D56, 0x62757456, 0x85C70565, 0x06D4, // 1e199
- 0x016561DB, 0xB428F8AC, 0xBB12D16C, 0xA738C6BE, 0x06D7, // 1e200
- 0x01BEBA52, 0xE13336D7, 0x69D785C7, 0xD106F86E, 0x06DA, // 1e201
- 0x61173473, 0xECC00246, 0x0226B39C, 0x82A45B45, 0x06DE, // 1e202
- 0xF95D0190, 0x27F002D7, 0x42B06084, 0xA34D7216, 0x06E1, // 1e203
- 0xF7B441F4, 0x31EC038D, 0xD35C78A5, 0xCC20CE9B, 0x06E4, // 1e204
- 0x75A15271, 0x7E670471, 0xC83396CE, 0xFF290242, 0x06E7, // 1e205
- 0xE984D386, 0x0F0062C6, 0xBD203E41, 0x9F79A169, 0x06EB, // 1e206
- 0xA3E60868, 0x52C07B78, 0x2C684DD1, 0xC75809C4, 0x06EE, // 1e207
- 0xCCDF8A82, 0xA7709A56, 0x37826145, 0xF92E0C35, 0x06F1, // 1e208
- 0x400BB691, 0x88A66076, 0x42B17CCB, 0x9BBCC7A1, 0x06F5, // 1e209
- 0xD00EA435, 0x6ACFF893, 0x935DDBFE, 0xC2ABF989, 0x06F8, // 1e210
- 0xC4124D43, 0x0583F6B8, 0xF83552FE, 0xF356F7EB, 0x06FB, // 1e211
- 0x7A8B704A, 0xC3727A33, 0x7B2153DE, 0x98165AF3, 0x06FF, // 1e212
- 0x592E4C5C, 0x744F18C0, 0x59E9A8D6, 0xBE1BF1B0, 0x0702, // 1e213
- 0x6F79DF73, 0x1162DEF0, 0x7064130C, 0xEDA2EE1C, 0x0705, // 1e214
- 0x45AC2BA8, 0x8ADDCB56, 0xC63E8BE7, 0x9485D4D1, 0x0709, // 1e215
- 0xD7173692, 0x6D953E2B, 0x37CE2EE1, 0xB9A74A06, 0x070C, // 1e216
- 0xCCDD0437, 0xC8FA8DB6, 0xC5C1BA99, 0xE8111C87, 0x070F, // 1e217
- 0x400A22A2, 0x1D9C9892, 0xDB9914A0, 0x910AB1D4, 0x0713, // 1e218
- 0xD00CAB4B, 0x2503BEB6, 0x127F59C8, 0xB54D5E4A, 0x0716, // 1e219
- 0x840FD61D, 0x2E44AE64, 0x971F303A, 0xE2A0B5DC, 0x0719, // 1e220
- 0xD289E5D2, 0x5CEAECFE, 0xDE737E24, 0x8DA471A9, 0x071D, // 1e221
- 0x872C5F47, 0x7425A83E, 0x56105DAD, 0xB10D8E14, 0x0720, // 1e222
- 0x28F77719, 0xD12F124E, 0x6B947518, 0xDD50F199, 0x0723, // 1e223
- 0xD99AAA6F, 0x82BD6B70, 0xE33CC92F, 0x8A5296FF, 0x0727, // 1e224
- 0x1001550B, 0x636CC64D, 0xDC0BFB7B, 0xACE73CBF, 0x072A, // 1e225
- 0x5401AA4E, 0x3C47F7E0, 0xD30EFA5A, 0xD8210BEF, 0x072D, // 1e226
- 0x34810A71, 0x65ACFAEC, 0xE3E95C78, 0x8714A775, 0x0731, // 1e227
- 0x41A14D0D, 0x7F1839A7, 0x5CE3B396, 0xA8D9D153, 0x0734, // 1e228
- 0x1209A050, 0x1EDE4811, 0x341CA07C, 0xD31045A8, 0x0737, // 1e229
- 0xAB460432, 0x934AED0A, 0x2091E44D, 0x83EA2B89, 0x073B, // 1e230
- 0x5617853F, 0xF81DA84D, 0x68B65D60, 0xA4E4B66B, 0x073E, // 1e231
- 0xAB9D668E, 0x36251260, 0x42E3F4B9, 0xCE1DE406, 0x0741, // 1e232
- 0x6B426019, 0xC1D72B7C, 0xE9CE78F3, 0x80D2AE83, 0x0745, // 1e233
- 0x8612F81F, 0xB24CF65B, 0xE4421730, 0xA1075A24, 0x0748, // 1e234
- 0x6797B627, 0xDEE033F2, 0x1D529CFC, 0xC94930AE, 0x074B, // 1e235
- 0x017DA3B1, 0x169840EF, 0xA4A7443C, 0xFB9B7CD9, 0x074E, // 1e236
- 0x60EE864E, 0x8E1F2895, 0x06E88AA5, 0x9D412E08, 0x0752, // 1e237
- 0xB92A27E2, 0xF1A6F2BA, 0x08A2AD4E, 0xC491798A, 0x0755, // 1e238
- 0x6774B1DB, 0xAE10AF69, 0x8ACB58A2, 0xF5B5D7EC, 0x0758, // 1e239
- 0xE0A8EF29, 0xACCA6DA1, 0xD6BF1765, 0x9991A6F3, 0x075C, // 1e240
- 0x58D32AF3, 0x17FD090A, 0xCC6EDD3F, 0xBFF610B0, 0x075F, // 1e241
- 0xEF07F5B0, 0xDDFC4B4C, 0xFF8A948E, 0xEFF394DC, 0x0762, // 1e242
- 0x1564F98E, 0x4ABDAF10, 0x1FB69CD9, 0x95F83D0A, 0x0766, // 1e243
- 0x1ABE37F1, 0x9D6D1AD4, 0xA7A4440F, 0xBB764C4C, 0x0769, // 1e244
- 0x216DC5ED, 0x84C86189, 0xD18D5513, 0xEA53DF5F, 0x076C, // 1e245
- 0xB4E49BB4, 0x32FD3CF5, 0xE2F8552C, 0x92746B9B, 0x0770, // 1e246
- 0x221DC2A1, 0x3FBC8C33, 0xDBB66A77, 0xB7118682, 0x0773, // 1e247
- 0xEAA5334A, 0x0FABAF3F, 0x92A40515, 0xE4D5E823, 0x0776, // 1e248
- 0xF2A7400E, 0x29CB4D87, 0x3BA6832D, 0x8F05B116, 0x077A, // 1e249
- 0xEF511012, 0x743E20E9, 0xCA9023F8, 0xB2C71D5B, 0x077D, // 1e250
- 0x6B255416, 0x914DA924, 0xBD342CF6, 0xDF78E4B2, 0x0780, // 1e251
- 0xC2F7548E, 0x1AD089B6, 0xB6409C1A, 0x8BAB8EEF, 0x0784, // 1e252
- 0x73B529B1, 0xA184AC24, 0xA3D0C320, 0xAE9672AB, 0x0787, // 1e253
- 0x90A2741E, 0xC9E5D72D, 0x8CC4F3E8, 0xDA3C0F56, 0x078A, // 1e254
- 0x7A658892, 0x7E2FA67C, 0x17FB1871, 0x88658996, 0x078E, // 1e255
- 0x98FEEAB7, 0xDDBB901B, 0x9DF9DE8D, 0xAA7EEBFB, 0x0791, // 1e256
- 0x7F3EA565, 0x552A7422, 0x85785631, 0xD51EA6FA, 0x0794, // 1e257
- 0x8F87275F, 0xD53A8895, 0x936B35DE, 0x8533285C, 0x0798, // 1e258
- 0xF368F137, 0x8A892ABA, 0xB8460356, 0xA67FF273, 0x079B, // 1e259
- 0xB0432D85, 0x2D2B7569, 0xA657842C, 0xD01FEF10, 0x079E, // 1e260
- 0x0E29FC73, 0x9C3B2962, 0x67F6B29B, 0x8213F56A, 0x07A2, // 1e261
- 0x91B47B8F, 0x8349F3BA, 0x01F45F42, 0xA298F2C5, 0x07A5, // 1e262
- 0x36219A73, 0x241C70A9, 0x42717713, 0xCB3F2F76, 0x07A8, // 1e263
- 0x83AA0110, 0xED238CD3, 0xD30DD4D7, 0xFE0EFB53, 0x07AB, // 1e264
- 0x324A40AA, 0xF4363804, 0x63E8A506, 0x9EC95D14, 0x07AF, // 1e265
- 0x3EDCD0D5, 0xB143C605, 0x7CE2CE48, 0xC67BB459, 0x07B2, // 1e266
- 0x8E94050A, 0xDD94B786, 0xDC1B81DA, 0xF81AA16F, 0x07B5, // 1e267
- 0x191C8326, 0xCA7CF2B4, 0xE9913128, 0x9B10A4E5, 0x07B9, // 1e268
- 0x1F63A3F0, 0xFD1C2F61, 0x63F57D72, 0xC1D4CE1F, 0x07BC, // 1e269
- 0x673C8CEC, 0xBC633B39, 0x3CF2DCCF, 0xF24A01A7, 0x07BF, // 1e270
- 0xE085D813, 0xD5BE0503, 0x8617CA01, 0x976E4108, 0x07C3, // 1e271
- 0xD8A74E18, 0x4B2D8644, 0xA79DBC82, 0xBD49D14A, 0x07C6, // 1e272
- 0x0ED1219E, 0xDDF8E7D6, 0x51852BA2, 0xEC9C459D, 0x07C9, // 1e273
- 0xC942B503, 0xCABB90E5, 0x52F33B45, 0x93E1AB82, 0x07CD, // 1e274
- 0x3B936243, 0x3D6A751F, 0xE7B00A17, 0xB8DA1662, 0x07D0, // 1e275
- 0x0A783AD4, 0x0CC51267, 0xA19C0C9D, 0xE7109BFB, 0x07D3, // 1e276
- 0x668B24C5, 0x27FB2B80, 0x450187E2, 0x906A617D, 0x07D7, // 1e277
- 0x802DEDF6, 0xB1F9F660, 0x9641E9DA, 0xB484F9DC, 0x07DA, // 1e278
- 0xA0396973, 0x5E7873F8, 0xBBD26451, 0xE1A63853, 0x07DD, // 1e279
- 0x6423E1E8, 0xDB0B487B, 0x55637EB2, 0x8D07E334, 0x07E1, // 1e280
- 0x3D2CDA62, 0x91CE1A9A, 0x6ABC5E5F, 0xB049DC01, 0x07E4, // 1e281
- 0xCC7810FB, 0x7641A140, 0xC56B75F7, 0xDC5C5301, 0x07E7, // 1e282
- 0x7FCB0A9D, 0xA9E904C8, 0x1B6329BA, 0x89B9B3E1, 0x07EB, // 1e283
- 0x9FBDCD44, 0x546345FA, 0x623BF429, 0xAC2820D9, 0x07EE, // 1e284
- 0x47AD4095, 0xA97C1779, 0xBACAF133, 0xD732290F, 0x07F1, // 1e285
- 0xCCCC485D, 0x49ED8EAB, 0xD4BED6C0, 0x867F59A9, 0x07F5, // 1e286
- 0xBFFF5A74, 0x5C68F256, 0x49EE8C70, 0xA81F3014, 0x07F8, // 1e287
- 0x6FFF3111, 0x73832EEC, 0x5C6A2F8C, 0xD226FC19, 0x07FB, // 1e288
- 0xC5FF7EAB, 0xC831FD53, 0xD9C25DB7, 0x83585D8F, 0x07FF, // 1e289
- 0xB77F5E55, 0xBA3E7CA8, 0xD032F525, 0xA42E74F3, 0x0802, // 1e290
- 0xE55F35EB, 0x28CE1BD2, 0xC43FB26F, 0xCD3A1230, 0x0805, // 1e291
- 0xCF5B81B3, 0x7980D163, 0x7AA7CF85, 0x80444B5E, 0x0809, // 1e292
- 0xC332621F, 0xD7E105BC, 0x1951C366, 0xA0555E36, 0x080C, // 1e293
- 0xF3FEFAA7, 0x8DD9472B, 0x9FA63440, 0xC86AB5C3, 0x080F, // 1e294
- 0xF0FEB951, 0xB14F98F6, 0x878FC150, 0xFA856334, 0x0812, // 1e295
- 0x569F33D3, 0x6ED1BF9A, 0xD4B9D8D2, 0x9C935E00, 0x0816, // 1e296
- 0xEC4700C8, 0x0A862F80, 0x09E84F07, 0xC3B83581, 0x0819, // 1e297
- 0x2758C0FA, 0xCD27BB61, 0x4C6262C8, 0xF4A642E1, 0x081C, // 1e298
- 0xB897789C, 0x8038D51C, 0xCFBD7DBD, 0x98E7E9CC, 0x0820, // 1e299
- 0xE6BD56C3, 0xE0470A63, 0x03ACDD2C, 0xBF21E440, 0x0823, // 1e300
- 0xE06CAC74, 0x1858CCFC, 0x04981478, 0xEEEA5D50, 0x0826, // 1e301
- 0x0C43EBC8, 0x0F37801E, 0x02DF0CCB, 0x95527A52, 0x082A, // 1e302
- 0x8F54E6BA, 0xD3056025, 0x8396CFFD, 0xBAA718E6, 0x082D, // 1e303
- 0xF32A2069, 0x47C6B82E, 0x247C83FD, 0xE950DF20, 0x0830, // 1e304
- 0x57FA5441, 0x4CDC331D, 0x16CDD27E, 0x91D28B74, 0x0834, // 1e305
- 0xADF8E952, 0xE0133FE4, 0x1C81471D, 0xB6472E51, 0x0837, // 1e306
- 0xD97723A6, 0x58180FDD, 0x63A198E5, 0xE3D8F9E5, 0x083A, // 1e307
- 0xA7EA7648, 0x570F09EA, 0x5E44FF8F, 0x8E679C2F, 0x083E, // 1e308
- 0x51E513DA, 0x2CD2CC65, 0x35D63F73, 0xB201833B, 0x0841, // 1e309
- 0xA65E58D1, 0xF8077F7E, 0x034BCF4F, 0xDE81E40A, 0x0844, // 1e310
-};
-
-// wuffs_base__private_implementation__f64_powers_of_10 holds powers of 10 that
-// can be exactly represented by a float64 (what C calls a double).
-static const double wuffs_base__private_implementation__f64_powers_of_10[23] = {
- 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,
- 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,
-};
-
-// --------
-
-// wuffs_base__private_implementation__parse_number_f64_eisel produces the IEEE
-// 754 double-precision value for an exact mantissa and base-10 exponent.
-//
-// On success, it returns a non-negative int64_t such that the low 63 bits hold
-// the 11-bit exponent and 52-bit mantissa.
-//
-// On failure, it returns a negative value.
-//
-// The algorithm is based on an original idea by Michael Eisel. See
-// https://lemire.me/blog/2020/03/10/fast-float-parsing-in-practice/
-//
-// Preconditions:
-// - man is non-zero.
-// - exp10 is in the range -326 ..= 310, the same range of the
-// wuffs_base__private_implementation__powers_of_10 array.
-static int64_t //
-wuffs_base__private_implementation__parse_number_f64_eisel(uint64_t man,
- int32_t exp10) {
- // Look up the (possibly truncated) base-2 representation of (10 ** exp10).
- // The look-up table was constructed so that it is already normalized: the
- // table entry's mantissa's MSB (most significant bit) is on.
- const uint32_t* po10 =
- &wuffs_base__private_implementation__powers_of_10[5 * (exp10 + 326)];
-
- // Normalize the man argument. The (man != 0) precondition means that a
- // non-zero bit exists.
- uint32_t clz = wuffs_base__count_leading_zeroes_u64(man);
- man <<= clz;
-
- // Calculate the return value's base-2 exponent. We might tweak it by ±1
- // later, but its initial value comes from the look-up table and clz.
- uint64_t ret_exp2 = ((uint64_t)po10[4]) - ((uint64_t)clz);
-
- // Multiply the two mantissas. Normalization means that both mantissas are at
- // least (1<<63), so the 128-bit product must be at least (1<<126). The high
- // 64 bits of the product, x.hi, must therefore be at least (1<<62).
- //
- // As a consequence, x.hi has either 0 or 1 leading zeroes. Shifting x.hi
- // right by either 9 or 10 bits (depending on x.hi's MSB) will therefore
- // leave the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on.
- wuffs_base__multiply_u64__output x = wuffs_base__multiply_u64(
- man, ((uint64_t)po10[2]) | (((uint64_t)po10[3]) << 32));
-
- // Before we shift right by at least 9 bits, recall that the look-up table
- // entry was possibly truncated. We have so far only calculated a lower bound
- // for the product (man * e), where e is (10 ** exp10). The upper bound would
- // add a further (man * 1) to the 128-bit product, which overflows the lower
- // 64-bit limb if ((x.lo + man) < man).
- //
- // If overflow occurs, that adds 1 to x.hi. Since we're about to shift right
- // by at least 9 bits, that carried 1 can be ignored unless the higher 64-bit
- // limb's low 9 bits are all on.
- if (((x.hi & 0x1FF) == 0x1FF) && ((x.lo + man) < man)) {
- // Refine our calculation of (man * e). Before, our approximation of e used
- // a "low resolution" 64-bit mantissa. Now use a "high resolution" 128-bit
- // mantissa. We've already calculated x = (man * bits_0_to_63_incl_of_e).
- // Now calculate y = (man * bits_64_to_127_incl_of_e).
- wuffs_base__multiply_u64__output y = wuffs_base__multiply_u64(
- man, ((uint64_t)po10[0]) | (((uint64_t)po10[1]) << 32));
-
- // Merge the 128-bit x and 128-bit y, which overlap by 64 bits, to
- // calculate the 192-bit product of the 64-bit man by the 128-bit e.
- // As we exit this if-block, we only care about the high 128 bits
- // (merged_hi and merged_lo) of that 192-bit product.
- uint64_t merged_hi = x.hi;
- uint64_t merged_lo = x.lo + y.hi;
- if (merged_lo < x.lo) {
- merged_hi++; // Carry the overflow bit.
- }
-
- // The "high resolution" approximation of e is still a lower bound. Once
- // again, see if the upper bound is large enough to produce a different
- // result. This time, if it does, give up instead of reaching for an even
- // more precise approximation to e.
- //
- // This three-part check is similar to the two-part check that guarded the
- // if block that we're now in, but it has an extra term for the middle 64
- // bits (checking that adding 1 to merged_lo would overflow).
- if (((merged_hi & 0x1FF) == 0x1FF) && ((merged_lo + 1) == 0) &&
- (y.lo + man < man)) {
- return -1;
- }
-
- // Replace the 128-bit x with merged.
- x.hi = merged_hi;
- x.lo = merged_lo;
- }
-
- // As mentioned above, shifting x.hi right by either 9 or 10 bits will leave
- // the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on. If the
- // MSB (before shifting) was on, adjust ret_exp2 for the larger shift.
- //
- // Having bit 53 on (and higher bits off) means that ret_mantissa is a 54-bit
- // number.
- uint64_t msb = x.hi >> 63;
- uint64_t ret_mantissa = x.hi >> (msb + 9);
- ret_exp2 -= 1 ^ msb;
-
- // IEEE 754 rounds to-nearest with ties rounded to-even. Rounding to-even can
- // be tricky. If we're half-way between two exactly representable numbers
- // (x's low 73 bits are zero and the next 2 bits that matter are "01"), give
- // up instead of trying to pick the winner.
- //
- // Technically, we could tighten the condition by changing "73" to "73 or 74,
- // depending on msb", but a flat "73" is simpler.
- if ((x.lo == 0) && ((x.hi & 0x1FF) == 0) && ((ret_mantissa & 3) == 1)) {
- return -1;
- }
-
- // If we're not halfway then it's rounding to-nearest. Starting with a 54-bit
- // number, carry the lowest bit (bit 0) up if it's on. Regardless of whether
- // it was on or off, shifting right by one then produces a 53-bit number. If
- // carrying up overflowed, shift again.
- ret_mantissa += ret_mantissa & 1;
- ret_mantissa >>= 1;
- if ((ret_mantissa >> 53) > 0) {
- ret_mantissa >>= 1;
- ret_exp2++;
- }
-
- // Starting with a 53-bit number, IEEE 754 double-precision normal numbers
- // have an implicit mantissa bit. Mask that away and keep the low 52 bits.
- ret_mantissa &= 0x000FFFFFFFFFFFFF;
-
- // IEEE 754 double-precision floating point has 11 exponent bits. All off (0)
- // means subnormal numbers. All on (2047) means infinity or NaN.
- if ((ret_exp2 <= 0) || (2047 <= ret_exp2)) {
- return -1;
- }
-
- // Pack the bits and return.
- return ((int64_t)(ret_mantissa | (ret_exp2 << 52)));
-}
-
-// --------
-
-static wuffs_base__result_f64 //
-wuffs_base__parse_number_f64_special(wuffs_base__slice_u8 s,
- const char* fallback_status_repr) {
- do {
- uint8_t* p = s.ptr;
- uint8_t* q = s.ptr + s.len;
-
- for (; (p < q) && (*p == '_'); p++) {
- }
- if (p >= q) {
- goto fallback;
- }
-
- // Parse sign.
- bool negative = false;
- do {
- if (*p == '+') {
- p++;
- } else if (*p == '-') {
- negative = true;
- p++;
- } else {
- break;
- }
- for (; (p < q) && (*p == '_'); p++) {
- }
- } while (0);
- if (p >= q) {
- goto fallback;
- }
-
- bool nan = false;
- switch (p[0]) {
- case 'I':
- case 'i':
- if (((q - p) < 3) || //
- ((p[1] != 'N') && (p[1] != 'n')) || //
- ((p[2] != 'F') && (p[2] != 'f'))) {
- goto fallback;
- }
- p += 3;
-
- if ((p >= q) || (*p == '_')) {
- break;
- } else if (((q - p) < 5) || //
- ((p[0] != 'I') && (p[0] != 'i')) || //
- ((p[1] != 'N') && (p[1] != 'n')) || //
- ((p[2] != 'I') && (p[2] != 'i')) || //
- ((p[3] != 'T') && (p[3] != 't')) || //
- ((p[4] != 'Y') && (p[4] != 'y'))) {
- goto fallback;
- }
- p += 5;
-
- if ((p >= q) || (*p == '_')) {
- break;
- }
- goto fallback;
-
- case 'N':
- case 'n':
- if (((q - p) < 3) || //
- ((p[1] != 'A') && (p[1] != 'a')) || //
- ((p[2] != 'N') && (p[2] != 'n'))) {
- goto fallback;
- }
- p += 3;
-
- if ((p >= q) || (*p == '_')) {
- nan = true;
- break;
- }
- goto fallback;
-
- default:
- goto fallback;
- }
-
- // Finish.
- for (; (p < q) && (*p == '_'); p++) {
- }
- if (p != q) {
- goto fallback;
- }
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
- (nan ? 0x7FFFFFFFFFFFFFFF : 0x7FF0000000000000) |
- (negative ? 0x8000000000000000 : 0));
- return ret;
- } while (0);
-
-fallback:
- do {
- wuffs_base__result_f64 ret;
- ret.status.repr = fallback_status_repr;
- ret.value = 0;
- return ret;
- } while (0);
-}
-
-WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //
-wuffs_base__private_implementation__parse_number_f64__fallback(
- wuffs_base__private_implementation__high_prec_dec* h) {
- do {
- // powers converts decimal powers of 10 to binary powers of 2. For example,
- // (10000 >> 13) is 1. It stops before the elements exceed 60, also known
- // as WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
- static const uint32_t num_powers = 19;
- static const uint8_t powers[19] = {
- 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //
- 33, 36, 39, 43, 46, 49, 53, 56, 59, //
- };
-
- // Handle zero and obvious extremes. The largest and smallest positive
- // finite f64 values are approximately 1.8e+308 and 4.9e-324.
- if ((h->num_digits == 0) || (h->decimal_point < -326)) {
- goto zero;
- } else if (h->decimal_point > 310) {
- goto infinity;
- }
-
- // Try the fast Eisel algorithm again. Calculating the (man, exp10) pair
- // from the high_prec_dec h is more correct but slower than the approach
- // taken in wuffs_base__parse_number_f64. The latter is optimized for the
- // common cases (e.g. assuming no underscores or a leading '+' sign) rather
- // than the full set of cases allowed by the Wuffs API.
- if (h->num_digits <= 19) {
- uint64_t man = 0;
- uint32_t i;
- for (i = 0; i < h->num_digits; i++) {
- man = (10 * man) + h->digits[i];
- }
- int32_t exp10 = h->decimal_point - ((int32_t)(h->num_digits));
- if ((man != 0) && (-326 <= exp10) && (exp10 <= 310)) {
- int64_t r = wuffs_base__private_implementation__parse_number_f64_eisel(
- man, exp10);
- if (r >= 0) {
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
- ((uint64_t)r) | (((uint64_t)(h->negative)) << 63));
- return ret;
- }
- }
- }
-
- // Scale by powers of 2 until we're in the range [½ .. 1], which gives us
- // our exponent (in base-2). First we shift right, possibly a little too
- // far, ending with a value certainly below 1 and possibly below ½...
- const int32_t f64_bias = -1023;
- int32_t exp2 = 0;
- while (h->decimal_point > 0) {
- uint32_t n = (uint32_t)(+h->decimal_point);
- uint32_t shift =
- (n < num_powers)
- ? powers[n]
- : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
-
- wuffs_base__private_implementation__high_prec_dec__small_rshift(h, shift);
- if (h->decimal_point <
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- goto zero;
- }
- exp2 += (int32_t)shift;
- }
- // ...then we shift left, putting us in [½ .. 1].
- while (h->decimal_point <= 0) {
- uint32_t shift;
- if (h->decimal_point == 0) {
- if (h->digits[0] >= 5) {
- break;
- }
- shift = (h->digits[0] <= 2) ? 2 : 1;
- } else {
- uint32_t n = (uint32_t)(-h->decimal_point);
- shift = (n < num_powers)
- ? powers[n]
- : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
-
- wuffs_base__private_implementation__high_prec_dec__small_lshift(h, shift);
- if (h->decimal_point >
- +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- goto infinity;
- }
- exp2 -= (int32_t)shift;
- }
-
- // We're in the range [½ .. 1] but f64 uses [1 .. 2].
- exp2--;
-
- // The minimum normal exponent is (f64_bias + 1).
- while ((f64_bias + 1) > exp2) {
- uint32_t n = (uint32_t)((f64_bias + 1) - exp2);
- if (n > WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
- n = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
- wuffs_base__private_implementation__high_prec_dec__small_rshift(h, n);
- exp2 += (int32_t)n;
- }
-
- // Check for overflow.
- if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.
- goto infinity;
- }
-
- // Extract 53 bits for the mantissa (in base-2).
- wuffs_base__private_implementation__high_prec_dec__small_lshift(h, 53);
- uint64_t man2 =
- wuffs_base__private_implementation__high_prec_dec__rounded_integer(h);
-
- // Rounding might have added one bit. If so, shift and re-check overflow.
- if ((man2 >> 53) != 0) {
- man2 >>= 1;
- exp2++;
- if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.
- goto infinity;
- }
- }
-
- // Handle subnormal numbers.
- if ((man2 >> 52) == 0) {
- exp2 = f64_bias;
- }
-
- // Pack the bits and return.
- uint64_t exp2_bits =
- (uint64_t)((exp2 - f64_bias) & 0x07FF); // (1 << 11) - 1.
- uint64_t bits = (man2 & 0x000FFFFFFFFFFFFF) | // (1 << 52) - 1.
- (exp2_bits << 52) | //
- (h->negative ? 0x8000000000000000 : 0); // (1 << 63).
-
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
- return ret;
- } while (0);
-
-zero:
- do {
- uint64_t bits = h->negative ? 0x8000000000000000 : 0;
-
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
- return ret;
- } while (0);
-
-infinity:
- do {
- uint64_t bits = h->negative ? 0xFFF0000000000000 : 0x7FF0000000000000;
-
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);
- return ret;
- } while (0);
-}
-
-static inline bool //
-wuffs_base__private_implementation__is_decimal_digit(uint8_t c) {
- return ('0' <= c) && (c <= '9');
-}
-
-WUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //
-wuffs_base__parse_number_f64(wuffs_base__slice_u8 s, uint32_t options) {
- // In practice, almost all "dd.ddddE±xxx" numbers can be represented
- // losslessly by a uint64_t mantissa "dddddd" and an int32_t base-10
- // exponent, adjusting "xxx" for the position (if present) of the decimal
- // separator '.' or ','.
- //
- // This (u64 man, i32 exp10) data structure is superficially similar to the
- // "Do It Yourself Floating Point" type from Loitsch (†), but the exponent
- // here is base-10, not base-2.
- //
- // If s's number fits in a (man, exp10), parse that pair with the Eisel
- // algorithm. If not, or if Eisel fails, parsing s with the fallback
- // algorithm is slower but comprehensive.
- //
- // † "Printing Floating-Point Numbers Quickly and Accurately with Integers"
- // (https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf).
- // Florian Loitsch is also the primary contributor to
- // https://github.com/google/double-conversion
- do {
- // Calculating that (man, exp10) pair needs to stay within s's bounds.
- // Provided that s isn't extremely long, work on a NUL-terminated copy of
- // s's contents. The NUL byte isn't a valid part of "±dd.ddddE±xxx".
- //
- // As the pointer p walks the contents, it's faster to repeatedly check "is
- // *p a valid digit" than "is p within bounds and *p a valid digit".
- if (s.len >= 256) {
- goto fallback;
- }
- uint8_t z[256];
- memcpy(&z[0], s.ptr, s.len);
- z[s.len] = 0;
- const uint8_t* p = &z[0];
-
- // Look for a leading minus sign. Technically, we could also look for an
- // optional plus sign, but the "script/process-json-numbers.c with -p"
- // benchmark is noticably slower if we do. It's optional and, in practice,
- // usually absent. Let the fallback catch it.
- bool negative = (*p == '-');
- if (negative) {
- p++;
- }
-
- // After walking "dd.dddd", comparing p later with p now will produce the
- // number of "d"s and "."s.
- const uint8_t* const start_of_digits_ptr = p;
-
- // Walk the "d"s before a '.', 'E', NUL byte, etc. If it starts with '0',
- // it must be a single '0'. If it starts with a non-zero decimal digit, it
- // can be a sequence of decimal digits.
- //
- // Update the man variable during the walk. It's OK if man overflows now.
- // We'll detect that later.
- uint64_t man;
- if (*p == '0') {
- man = 0;
- p++;
- if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
- goto fallback;
- }
- } else if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
- man = ((uint8_t)(*p - '0'));
- p++;
- for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {
- man = (10 * man) + ((uint8_t)(*p - '0'));
- }
- } else {
- goto fallback;
- }
-
- // Walk the "d"s after the optional decimal separator ('.' or ','),
- // updating the man and exp10 variables.
- int32_t exp10 = 0;
- if ((*p == '.') || (*p == ',')) {
- p++;
- const uint8_t* first_after_separator_ptr = p;
- if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {
- goto fallback;
- }
- man = (10 * man) + ((uint8_t)(*p - '0'));
- p++;
- for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {
- man = (10 * man) + ((uint8_t)(*p - '0'));
- }
- exp10 = ((int32_t)(first_after_separator_ptr - p));
- }
-
- // Count the number of digits:
- // - for an input of "314159", digit_count is 6.
- // - for an input of "3.14159", digit_count is 7.
- //
- // This is off-by-one if there is a decimal separator. That's OK for now.
- // We'll correct for that later. The "script/process-json-numbers.c with
- // -p" benchmark is noticably slower if we try to correct for that now.
- uint32_t digit_count = (uint32_t)(p - start_of_digits_ptr);
-
- // Update exp10 for the optional exponent, starting with 'E' or 'e'.
- if ((*p | 0x20) == 'e') {
- p++;
- int32_t exp_sign = +1;
- if (*p == '-') {
- p++;
- exp_sign = -1;
- } else if (*p == '+') {
- p++;
- }
- if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {
- goto fallback;
- }
- int32_t exp_num = ((uint8_t)(*p - '0'));
- p++;
- // The rest of the exp_num walking has a peculiar control flow but, once
- // again, the "script/process-json-numbers.c with -p" benchmark is
- // sensitive to alternative formulations.
- if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
- exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
- p++;
- }
- if (wuffs_base__private_implementation__is_decimal_digit(*p)) {
- exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
- p++;
- }
- while (wuffs_base__private_implementation__is_decimal_digit(*p)) {
- if (exp_num > 0x1000000) {
- goto fallback;
- }
- exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));
- p++;
- }
- exp10 += exp_sign * exp_num;
- }
-
- // The Wuffs API is that the original slice has no trailing data. It also
- // allows underscores, which we don't catch here but the fallback should.
- if (p != &z[s.len]) {
- goto fallback;
- }
-
- // Check that the uint64_t typed man variable has not overflowed, based on
- // digit_count.
- //
- // For reference:
- // - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
- // - (1 << 64) is 18446744073709551616, which has 20 decimal digits.
- // - 19 nines, 9999999999999999999, is 0x8AC7230489E7FFFF, which has 64
- // bits and 16 hexadecimal digits.
- // - 20 nines, 99999999999999999999, is 0x56BC75E2D630FFFFF, which has 67
- // bits and 17 hexadecimal digits.
- if (digit_count > 19) {
- // Even if we have more than 19 pseudo-digits, it's not yet definitely an
- // overflow. Recall that digit_count might be off-by-one (too large) if
- // there's a decimal separator. It will also over-report the number of
- // meaningful digits if the input looks something like "0.000dddExxx".
- //
- // We adjust by the number of leading '0's and '.'s and re-compare to 19.
- // Once again, technically, we could skip ','s too, but that perturbs the
- // "script/process-json-numbers.c with -p" benchmark.
- const uint8_t* q = start_of_digits_ptr;
- for (; (*q == '0') || (*q == '.'); q++) {
- }
- digit_count -= (uint32_t)(q - start_of_digits_ptr);
- if (digit_count > 19) {
- goto fallback;
- }
- }
-
- // The wuffs_base__private_implementation__parse_number_f64_eisel
- // preconditions include that exp10 is in the range -326 ..= 310.
- if ((exp10 < -326) || (310 < exp10)) {
- goto fallback;
- }
-
- // If man and exp10 are small enough, all three of (man), (10 ** exp10) and
- // (man ** (10 ** exp10)) are exactly representable by a double. We don't
- // need to run the Eisel algorithm.
- if ((-22 <= exp10) && (exp10 <= 22) && ((man >> 53) == 0)) {
- double d = (double)man;
- if (exp10 >= 0) {
- d *= wuffs_base__private_implementation__f64_powers_of_10[+exp10];
- } else {
- d /= wuffs_base__private_implementation__f64_powers_of_10[-exp10];
- }
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = negative ? -d : +d;
- return ret;
- }
-
- // The wuffs_base__private_implementation__parse_number_f64_eisel
- // preconditions include that man is non-zero. Parsing "0" should be caught
- // by the "If man and exp10 are small enough" above, but "0e99" might not.
- if (man == 0) {
- goto fallback;
- }
-
- // Our man and exp10 are in range. Run the Eisel algorithm.
- int64_t r =
- wuffs_base__private_implementation__parse_number_f64_eisel(man, exp10);
- if (r < 0) {
- goto fallback;
- }
- wuffs_base__result_f64 ret;
- ret.status.repr = NULL;
- ret.value = wuffs_base__ieee_754_bit_representation__to_f64(
- ((uint64_t)r) | (((uint64_t)negative) << 63));
- return ret;
- } while (0);
-
-fallback:
- do {
- wuffs_base__private_implementation__high_prec_dec h;
- wuffs_base__status status =
- wuffs_base__private_implementation__high_prec_dec__parse(&h, s);
- if (status.repr) {
- return wuffs_base__parse_number_f64_special(s, status.repr);
- }
- return wuffs_base__private_implementation__parse_number_f64__fallback(&h);
- } while (0);
-}
-
-// --------
-
-static inline size_t //
-wuffs_base__private_implementation__render_inf(wuffs_base__slice_u8 dst,
- bool neg,
- uint32_t options) {
- if (neg) {
- if (dst.len < 4) {
- return 0;
- }
- wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492D); // '-Inf'le.
- return 4;
- }
-
- if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
- if (dst.len < 4) {
- return 0;
- }
- wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492B); // '+Inf'le.
- return 4;
- }
-
- if (dst.len < 3) {
- return 0;
- }
- wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x666E49); // 'Inf'le.
- return 3;
-}
-
-static inline size_t //
-wuffs_base__private_implementation__render_nan(wuffs_base__slice_u8 dst) {
- if (dst.len < 3) {
- return 0;
- }
- wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x4E614E); // 'NaN'le.
- return 3;
-}
-
-static size_t //
-wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
- wuffs_base__slice_u8 dst,
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t precision,
- uint32_t options) {
- size_t n = (h->negative ||
- (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
- ? 1
- : 0;
- if (h->decimal_point <= 0) {
- n += 1;
- } else {
- n += (size_t)(h->decimal_point);
- }
- if (precision > 0) {
- n += precision + 1; // +1 for the '.'.
- }
-
- // Don't modify dst if the formatted number won't fit.
- if (n > dst.len) {
- return 0;
- }
-
- // Align-left or align-right.
- uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
- ? &dst.ptr[dst.len - n]
- : &dst.ptr[0];
-
- // Leading "±".
- if (h->negative) {
- *ptr++ = '-';
- } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
- *ptr++ = '+';
- }
-
- // Integral digits.
- if (h->decimal_point <= 0) {
- *ptr++ = '0';
- } else {
- uint32_t m =
- wuffs_base__u32__min(h->num_digits, (uint32_t)(h->decimal_point));
- uint32_t i = 0;
- for (; i < m; i++) {
- *ptr++ = (uint8_t)('0' | h->digits[i]);
- }
- for (; i < (uint32_t)(h->decimal_point); i++) {
- *ptr++ = '0';
- }
- }
-
- // Separator and then fractional digits.
- if (precision > 0) {
- *ptr++ =
- (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
- ? ','
- : '.';
- uint32_t i = 0;
- for (; i < precision; i++) {
- uint32_t j = ((uint32_t)(h->decimal_point)) + i;
- *ptr++ = (uint8_t)('0' | ((j < h->num_digits) ? h->digits[j] : 0));
- }
- }
-
- return n;
-}
-
-static size_t //
-wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
- wuffs_base__slice_u8 dst,
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t precision,
- uint32_t options) {
- int32_t exp = 0;
- if (h->num_digits > 0) {
- exp = h->decimal_point - 1;
- }
- bool negative_exp = exp < 0;
- if (negative_exp) {
- exp = -exp;
- }
-
- size_t n = (h->negative ||
- (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))
- ? 4
- : 3; // Mininum 3 bytes: first digit and then "e±".
- if (precision > 0) {
- n += precision + 1; // +1 for the '.'.
- }
- n += (exp < 100) ? 2 : 3;
-
- // Don't modify dst if the formatted number won't fit.
- if (n > dst.len) {
- return 0;
- }
-
- // Align-left or align-right.
- uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)
- ? &dst.ptr[dst.len - n]
- : &dst.ptr[0];
-
- // Leading "±".
- if (h->negative) {
- *ptr++ = '-';
- } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {
- *ptr++ = '+';
- }
-
- // Integral digit.
- if (h->num_digits > 0) {
- *ptr++ = (uint8_t)('0' | h->digits[0]);
- } else {
- *ptr++ = '0';
- }
-
- // Separator and then fractional digits.
- if (precision > 0) {
- *ptr++ =
- (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)
- ? ','
- : '.';
- uint32_t i = 1;
- uint32_t j = wuffs_base__u32__min(h->num_digits, precision + 1);
- for (; i < j; i++) {
- *ptr++ = (uint8_t)('0' | h->digits[i]);
- }
- for (; i <= precision; i++) {
- *ptr++ = '0';
- }
- }
-
- // Exponent: "e±" and then 2 or 3 digits.
- *ptr++ = 'e';
- *ptr++ = negative_exp ? '-' : '+';
- if (exp < 10) {
- *ptr++ = '0';
- *ptr++ = (uint8_t)('0' | exp);
- } else if (exp < 100) {
- *ptr++ = (uint8_t)('0' | (exp / 10));
- *ptr++ = (uint8_t)('0' | (exp % 10));
- } else {
- int32_t e = exp / 100;
- exp -= e * 100;
- *ptr++ = (uint8_t)('0' | e);
- *ptr++ = (uint8_t)('0' | (exp / 10));
- *ptr++ = (uint8_t)('0' | (exp % 10));
- }
-
- return n;
-}
-
-WUFFS_BASE__MAYBE_STATIC size_t //
-wuffs_base__render_number_f64(wuffs_base__slice_u8 dst,
- double x,
- uint32_t precision,
- uint32_t options) {
- // Decompose x (64 bits) into negativity (1 bit), base-2 exponent (11 bits
- // with a -1023 bias) and mantissa (52 bits).
- uint64_t bits = wuffs_base__ieee_754_bit_representation__from_f64(x);
- bool neg = (bits >> 63) != 0;
- int32_t exp2 = ((int32_t)(bits >> 52)) & 0x7FF;
- uint64_t man = bits & 0x000FFFFFFFFFFFFFul;
-
- // Apply the exponent bias and set the implicit top bit of the mantissa,
- // unless x is subnormal. Also take care of Inf and NaN.
- if (exp2 == 0x7FF) {
- if (man != 0) {
- return wuffs_base__private_implementation__render_nan(dst);
- }
- return wuffs_base__private_implementation__render_inf(dst, neg, options);
- } else if (exp2 == 0) {
- exp2 = -1022;
- } else {
- exp2 -= 1023;
- man |= 0x0010000000000000ul;
- }
-
- // Ensure that precision isn't too large.
- if (precision > 4095) {
- precision = 4095;
- }
-
- // Convert from the (neg, exp2, man) tuple to an HPD.
- wuffs_base__private_implementation__high_prec_dec h;
- wuffs_base__private_implementation__high_prec_dec__assign(&h, man, neg);
- if (h.num_digits > 0) {
- wuffs_base__private_implementation__high_prec_dec__lshift(
- &h, exp2 - 52); // 52 mantissa bits.
- }
-
- // Handle the "%e" and "%f" formats.
- switch (options & (WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT |
- WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT)) {
- case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT: // The "%"f" format.
- if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
- wuffs_base__private_implementation__high_prec_dec__round_just_enough(
- &h, exp2, man);
- int32_t p = ((int32_t)(h.num_digits)) - h.decimal_point;
- precision = ((uint32_t)(wuffs_base__i32__max(0, p)));
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_nearest(
- &h, ((int32_t)precision) + h.decimal_point);
- }
- return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
- dst, &h, precision, options);
-
- case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT: // The "%e" format.
- if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
- wuffs_base__private_implementation__high_prec_dec__round_just_enough(
- &h, exp2, man);
- precision = (h.num_digits > 0) ? (h.num_digits - 1) : 0;
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_nearest(
- &h, ((int32_t)precision) + 1);
- }
- return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
- dst, &h, precision, options);
- }
-
- // We have the "%g" format and so precision means the number of significant
- // digits, not the number of digits after the decimal separator. Perform
- // rounding and determine whether to use "%e" or "%f".
- int32_t e_threshold = 0;
- if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {
- wuffs_base__private_implementation__high_prec_dec__round_just_enough(
- &h, exp2, man);
- precision = h.num_digits;
- e_threshold = 6;
- } else {
- if (precision == 0) {
- precision = 1;
- }
- wuffs_base__private_implementation__high_prec_dec__round_nearest(
- &h, ((int32_t)precision));
- e_threshold = ((int32_t)precision);
- int32_t nd = ((int32_t)(h.num_digits));
- if ((e_threshold > nd) && (nd >= h.decimal_point)) {
- e_threshold = nd;
- }
- }
-
- // Use the "%e" format if the exponent is large.
- int32_t e = h.decimal_point - 1;
- if ((e < -4) || (e_threshold <= e)) {
- uint32_t p = wuffs_base__u32__min(precision, h.num_digits);
- return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(
- dst, &h, (p > 0) ? (p - 1) : 0, options);
- }
-
- // Use the "%f" format otherwise.
- int32_t p = ((int32_t)precision);
- if (p > h.decimal_point) {
- p = ((int32_t)(h.num_digits));
- }
- precision = ((uint32_t)(wuffs_base__i32__max(0, p - h.decimal_point)));
- return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(
- dst, &h, precision, options);
-}
diff --git a/internal/cgen/cgen.go b/internal/cgen/cgen.go
index 4e3009b..b039b17 100644
--- a/internal/cgen/cgen.go
+++ b/internal/cgen/cgen.go
@@ -342,7 +342,9 @@
}
func insertBaseF64ConvSubmoduleC(buf *buffer) error {
- buf.writes(data.BaseF64ConvSubmoduleC)
+ buf.writes(data.BaseF64ConvSubmoduleDataC)
+ buf.writeb('\n')
+ buf.writes(data.BaseF64ConvSubmoduleCodeC)
return nil
}
diff --git a/internal/cgen/data/data.go b/internal/cgen/data/data.go
index 801f8f7..176150b 100644
--- a/internal/cgen/data/data.go
+++ b/internal/cgen/data/data.go
@@ -28,7 +28,7 @@
"ONFIG__MODULES) || defined(WUFFS_CONFIG__MODULE__BASE) || \\\n defined(WUFFS_CONFIG__MODULE__BASE__UTF8)\n\n// !! INSERT base/utf8-submodule.c.\n\n#endif // !defined(WUFFS_CONFIG__MODULES) ||\n // defined(WUFFS_CONFIG__MODULE__BASE) ||\n // defined(WUFFS_CONFIG__MODULE__BASE__UTF8)\n\n#ifdef __cplusplus\n} // extern \"C\"\n#endif\n\n#endif // WUFFS_IMPLEMENTATION\n\n// !! WUFFS MONOLITHIC RELEASE DISCARDS EVERYTHING BELOW.\n\n#endif // WUFFS_INCLUDE_GUARD__BASE\n" +
""
-const BaseF64ConvSubmoduleC = "" +
+const BaseF64ConvSubmoduleCodeC = "" +
"// ---------------- IEEE 754 Floating Point\n\n#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE 2047\n#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION 800\n\n// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL is the largest N\n// such that ((10 << N) < (1 << 64)).\n#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL 60\n\n// wuffs_base__private_implementation__high_prec_dec (abbreviated as HPD) is a\n// fixed precision floating point decimal number, augmented with ±infinity\n// values, but it cannot represent NaN (Not a Number).\n//\n// \"High precision\" means that the mantissa holds 800 decimal digits. 800 is\n// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION.\n//\n// An HPD isn't for general purpose arithmetic, only for conversions to and\n// from IEEE 754 double-precision floating point, where the largest and\n// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.\n// HPD exponents above +2047 mean infinity, below -2047 mean zero. Th" +
"e ±2047\n// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is\n// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION and\n// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.\n//\n// digits[.. num_digits] are the number's digits in big-endian order. The\n// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'\n// is the ASCII value 0x37.\n//\n// decimal_point is the index (within digits) of the decimal point. It may be\n// negative or be larger than num_digits, in which case the explicit digits are\n// padded with implicit zeroes.\n//\n// For example, if num_digits is 3 and digits is \"\\x07\\x08\\x09\":\n// - A decimal_point of -2 means \".00789\"\n// - A decimal_point of -1 means \".0789\"\n// - A decimal_point of +0 means \".789\"\n// - A decimal_point of +1 means \"7.89\"\n// - A decimal_point of +2 means \"78.9\"\n// - A decimal_point of +3 means \"789.\"\n// - A decimal_point of +4 means \"7890.\"\n// - A decimal_point of +5 means \"78900.\"\n//\n// As above, a" +
" decimal_point higher than +2047 means that the overall value is\n// infinity, lower than -2047 means zero.\n//\n// negative is a sign bit. An HPD can distinguish positive and negative zero.\n//\n// truncated is whether there are more than\n// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION digits, and at\n// least one of those extra digits are non-zero. The existence of long-tail\n// digits can affect rounding.\n//\n// The \"all fields are zero\" value is valid, and represents the number +0.\ntypedef struct {\n uint32_t num_digits;\n int32_t decimal_point;\n bool negative;\n bool truncated;\n uint8_t digits[WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION];\n} wuffs_base__private_implementation__high_prec_dec;\n\n// wuffs_base__private_implementation__high_prec_dec__trim trims trailing\n// zeroes from the h->digits[.. h->num_digits] slice. They have no benefit,\n// since we explicitly track h->decimal_point.\n//\n// Preconditions:\n// - h is non-NULL.\nstatic inline void //\nwuffs_base__private_implementation_" +
@@ -40,15 +40,8 @@
"2_t exp_large =\n WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE +\n WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;\n bool saw_exp_digits = false;\n for (; p < q; p++) {\n if (*p == '_') {\n // No-op.\n } else if (('0' <= *p) && (*p <= '9')) {\n saw_exp_digits = true;\n if (exp < exp_large) {\n exp = (10 * exp) + ((int32_t)(*p - '0'));\n }\n } else {\n break;\n }\n }\n if (!saw_exp_digits) {\n return wuffs_base__make_status(wuffs_base__error__bad_argument);\n }\n dp += exp_sign * exp;\n } while (0);\n\nafter_all:\n if (p != q) {\n return wuffs_base__make_status(wuffs_base__error__bad_argument);\n }\n h->num_digits = nd;\n if (nd == 0) {\n if (no_digits_before_separator) {\n return wuffs_base__make_status(wuffs_base__error__bad_argument);\n }\n h->decimal_point = 0;\n } else if (dp <\n -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n h->decimal_point =\n -" +
"WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE - 1;\n } else if (dp >\n +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n h->decimal_point =\n +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE + 1;\n } else {\n h->decimal_point = dp;\n }\n wuffs_base__private_implementation__high_prec_dec__trim(h);\n return wuffs_base__make_status(NULL);\n}\n\n" +
"" +
- "// --------\n\n// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by\n// script/print-hpd-left-shift.go. That script has an optional -comments flag,\n// whose output is not copied here, which prints further detail.\n//\n// These tables are used in\n// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits.\n\n// wuffs_base__private_implementation__hpd_left_shift[i] encodes the number of\n// new digits created after multiplying a positive integer by (1 << i): the\n// additional length in the decimal representation. For example, shifting \"234\"\n// by 3 (equivalent to multiplying by 8) will produce \"1872\". Going from a\n// 3-length string to a 4-length string means that 1 new digit was added (and\n// existing digits may have changed).\n//\n// Shifting by i can add either N or N-1 new digits, depending on whether the\n// original positive integer compares >= or < to the i'th power of 5 (as 10\n// equals 2 * 5). Comparison is lexicographic, not numerical.\n//\n// For example, shifting by 4 (i.e. mul" +
- "tiplying by 16) can add 1 or 2 new\n// digits, depending on a lexicographic comparison to (5 ** 4), i.e. \"625\":\n// - (\"1\" << 4) is \"16\", which adds 1 new digit.\n// - (\"5678\" << 4) is \"90848\", which adds 1 new digit.\n// - (\"624\" << 4) is \"9984\", which adds 1 new digit.\n// - (\"62498\" << 4) is \"999968\", which adds 1 new digit.\n// - (\"625\" << 4) is \"10000\", which adds 2 new digits.\n// - (\"625001\" << 4) is \"10000016\", which adds 2 new digits.\n// - (\"7008\" << 4) is \"112128\", which adds 2 new digits.\n// - (\"99\" << 4) is \"1584\", which adds 2 new digits.\n//\n// Thus, when i is 4, N is 2 and (5 ** i) is \"625\". This etc__hpd_left_shift\n// array encodes this as:\n// - etc__hpd_left_shift[4] is 0x1006 = (2 << 11) | 0x0006.\n// - etc__hpd_left_shift[5] is 0x1009 = (? << 11) | 0x0009.\n// where the ? isn't relevant for i == 4.\n//\n// The high 5 bits of etc__hpd_left_shift[i] is N, the higher of the two\n// possible number of new digits. The low 11 bits are an offset into the\n//" +
- " etc__powers_of_5 array (of length 0x051C, so offsets fit in 11 bits). When i\n// is 4, its offset and the next one is 6 and 9, and etc__powers_of_5[6 .. 9]\n// is the string \"\\x06\\x02\\x05\", so the relevant power of 5 is \"625\".\n//\n// Thanks to Ken Thompson for the original idea.\nstatic const uint16_t wuffs_base__private_implementation__hpd_left_shift[65] = {\n 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,\n 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,\n 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,\n 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,\n 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,\n 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,\n 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,\n 0x051C, 0x051C,\n};\n\n// wuffs_base__private_implementation__powers_of_5 contains the powers of 5,\n// concatenated together: \"5\", \"" +
- "25\", \"125\", \"625\", \"3125\", etc.\nstatic const uint8_t wuffs_base__private_implementation__powers_of_5[0x051C] = {\n 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9,\n 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2,\n 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5,\n 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8, 9, 0,\n 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, 9, 7, 2, 6, 5,\n 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,\n 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4,\n 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7,\n 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0,\n 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3,\n 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1,\n 2, 5, 3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4," +
- " 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,\n 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5,\n 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0,\n 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6,\n 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8,\n 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7,\n 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,\n 1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8,\n 0, 6, 6, 4, 0, 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9,\n 0, 3, 3, 2, 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2,\n 9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8,\n 5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,\n 2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,\n 0, 8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5," +
- " 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3,\n 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2,\n 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9,\n 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, 0, 1, 4, 8,\n 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4,\n 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,\n 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5,\n 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1,\n 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5,\n 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3,\n 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4,\n 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,\n 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8,\n 5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9," +
- " 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2,\n 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6,\n 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2,\n 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2,\n 5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,\n 8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5,\n 6, 2, 8, 9, 1, 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8,\n 1, 2, 5, 1, 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9,\n 5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,\n 9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6,\n 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,\n 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1,\n 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4,\n 8, 1, 3, 9, 1, 9, 0, 6, 7, 3," +
- " 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7,\n 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3,\n 6, 9, 1, 4, 0, 6, 2, 5,\n};\n\n// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits\n// returns the number of additional decimal digits when left-shifting by shift.\n//\n// See below for preconditions.\nstatic uint32_t //\nwuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t shift) {\n // Masking with 0x3F should be unnecessary (assuming the preconditions) but\n // it's cheap and ensures that we don't overflow the\n // wuffs_base__private_implementation__hpd_left_shift array.\n shift &= 63;\n\n uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];\n uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];\n uint32_t num_new_digits = x_a >> 11;\n uint32_t pow5_a = 0x7FF & x_a;\n uint32_t pow5_b = 0x7FF & x_b;\n\n const uint8_t* pow5 =\n " +
- " &wuffs_base__private_implementation__powers_of_5[pow5_a];\n uint32_t i = 0;\n uint32_t n = pow5_b - pow5_a;\n for (; i < n; i++) {\n if (i >= h->num_digits) {\n return num_new_digits - 1;\n } else if (h->digits[i] == pow5[i]) {\n continue;\n } else if (h->digits[i] < pow5[i]) {\n return num_new_digits - 1;\n } else {\n return num_new_digits;\n }\n }\n return num_new_digits;\n}\n\n" +
+ "// --------\n\n// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits\n// returns the number of additional decimal digits when left-shifting by shift.\n//\n// See below for preconditions.\nstatic uint32_t //\nwuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t shift) {\n // Masking with 0x3F should be unnecessary (assuming the preconditions) but\n // it's cheap and ensures that we don't overflow the\n // wuffs_base__private_implementation__hpd_left_shift array.\n shift &= 63;\n\n uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];\n uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];\n uint32_t num_new_digits = x_a >> 11;\n uint32_t pow5_a = 0x7FF & x_a;\n uint32_t pow5_b = 0x7FF & x_b;\n\n const uint8_t* pow5 =\n &wuffs_base__private_implementation__powers_of_5[pow5_a];\n uint32_t i = 0;\n uint32_t n = pow5_b - pow5_a;\n for (; i < n; i++) {\n if (i >" +
+ "= h->num_digits) {\n return num_new_digits - 1;\n } else if (h->digits[i] == pow5[i]) {\n continue;\n } else if (h->digits[i] < pow5[i]) {\n return num_new_digits - 1;\n } else {\n return num_new_digits;\n }\n }\n return num_new_digits;\n}\n\n" +
"" +
"// --------\n\n// wuffs_base__private_implementation__high_prec_dec__rounded_integer returns\n// the integral (non-fractional) part of h, provided that it is 18 or fewer\n// decimal digits. For 19 or more digits, it returns UINT64_MAX. Note that:\n// - (1 << 53) is 9007199254740992, which has 16 decimal digits.\n// - (1 << 56) is 72057594037927936, which has 17 decimal digits.\n// - (1 << 59) is 576460752303423488, which has 18 decimal digits.\n// - (1 << 63) is 9223372036854775808, which has 19 decimal digits.\n// and that IEEE 754 double precision has 52 mantissa bits.\n//\n// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.\n//\n// h's negative bit is ignored: rounding -8.6 returns 9.\n//\n// See below for preconditions.\nstatic uint64_t //\nwuffs_base__private_implementation__high_prec_dec__rounded_integer(\n wuffs_base__private_implementation__high_prec_dec* h) {\n if ((h->num_digits == 0) || (h->decimal_point < 0)) {\n return 0;\n } else if (h->decimal_point > 18) {\n return U" +
"INT64_MAX;\n }\n\n uint32_t dp = (uint32_t)(h->decimal_point);\n uint64_t n = 0;\n uint32_t i = 0;\n for (; i < dp; i++) {\n n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);\n }\n\n bool round_up = false;\n if (dp < h->num_digits) {\n round_up = h->digits[dp] >= 5;\n if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {\n // We are exactly halfway. If we're truncated, round up, otherwise round\n // to even.\n round_up = h->truncated || //\n ((dp > 0) && (1 & h->digits[dp - 1]));\n }\n }\n if (round_up) {\n n++;\n }\n\n return n;\n}\n\n// wuffs_base__private_implementation__high_prec_dec__small_xshift shifts h's\n// number (where 'x' is 'l' or 'r' for left or right) by a small shift value.\n//\n// Preconditions:\n// - h is non-NULL.\n// - h->decimal_point is \"not extreme\".\n// - shift is non-zero.\n// - shift is \"a small shift\".\n//\n// \"Not extreme\" means within\n// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.\n//\n// \"A small shift\" means not more than\n/" +
@@ -68,6 +61,53 @@
" upper_delta = +1;\n } else if (hd != ud) {\n // For example:\n // h = 12345???\n // upper = 12346???\n upper_delta = +0;\n }\n } else if (upper_delta == 0) {\n if ((hd != 9) || (ud != 0)) {\n // For example:\n // h = 1234598?\n // upper = 1234600?\n upper_delta = +1;\n }\n }\n\n // We can round up if upper has a different digit than h and either upper\n // is inclusive or upper is bigger than the result of rounding up.\n bool can_round_up =\n (upper_delta > 0) || //\n ((upper_delta == 0) && //\n (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));\n\n // If we can round either way, round to nearest. If we can round only one\n // way, do it. If we can't round, continue the loop.\n if (can_round_down) {\n if (can_round_up) {\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n h, hi + 1);\n return;\n } else {\n wuffs_base__private_implementat" +
"ion__high_prec_dec__round_down(h,\n hi + 1);\n return;\n }\n } else {\n if (can_round_up) {\n wuffs_base__private_implementation__high_prec_dec__round_up(h, hi + 1);\n return;\n }\n }\n }\n}\n\n" +
"" +
+ "// --------\n\n// wuffs_base__private_implementation__parse_number_f64_eisel produces the IEEE\n// 754 double-precision value for an exact mantissa and base-10 exponent.\n//\n// On success, it returns a non-negative int64_t such that the low 63 bits hold\n// the 11-bit exponent and 52-bit mantissa.\n//\n// On failure, it returns a negative value.\n//\n// The algorithm is based on an original idea by Michael Eisel. See\n// https://lemire.me/blog/2020/03/10/fast-float-parsing-in-practice/\n//\n// Preconditions:\n// - man is non-zero.\n// - exp10 is in the range -326 ..= 310, the same range of the\n// wuffs_base__private_implementation__powers_of_10 array.\nstatic int64_t //\nwuffs_base__private_implementation__parse_number_f64_eisel(uint64_t man,\n int32_t exp10) {\n // Look up the (possibly truncated) base-2 representation of (10 ** exp10).\n // The look-up table was constructed so that it is already normalized: the\n // table entry's mantissa's MSB (most significan" +
+ "t bit) is on.\n const uint32_t* po10 =\n &wuffs_base__private_implementation__powers_of_10[5 * (exp10 + 326)];\n\n // Normalize the man argument. The (man != 0) precondition means that a\n // non-zero bit exists.\n uint32_t clz = wuffs_base__count_leading_zeroes_u64(man);\n man <<= clz;\n\n // Calculate the return value's base-2 exponent. We might tweak it by ±1\n // later, but its initial value comes from the look-up table and clz.\n uint64_t ret_exp2 = ((uint64_t)po10[4]) - ((uint64_t)clz);\n\n // Multiply the two mantissas. Normalization means that both mantissas are at\n // least (1<<63), so the 128-bit product must be at least (1<<126). The high\n // 64 bits of the product, x.hi, must therefore be at least (1<<62).\n //\n // As a consequence, x.hi has either 0 or 1 leading zeroes. Shifting x.hi\n // right by either 9 or 10 bits (depending on x.hi's MSB) will therefore\n // leave the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on.\n wuffs_base__multiply_u64__output x = wuffs_base__multipl" +
+ "y_u64(\n man, ((uint64_t)po10[2]) | (((uint64_t)po10[3]) << 32));\n\n // Before we shift right by at least 9 bits, recall that the look-up table\n // entry was possibly truncated. We have so far only calculated a lower bound\n // for the product (man * e), where e is (10 ** exp10). The upper bound would\n // add a further (man * 1) to the 128-bit product, which overflows the lower\n // 64-bit limb if ((x.lo + man) < man).\n //\n // If overflow occurs, that adds 1 to x.hi. Since we're about to shift right\n // by at least 9 bits, that carried 1 can be ignored unless the higher 64-bit\n // limb's low 9 bits are all on.\n if (((x.hi & 0x1FF) == 0x1FF) && ((x.lo + man) < man)) {\n // Refine our calculation of (man * e). Before, our approximation of e used\n // a \"low resolution\" 64-bit mantissa. Now use a \"high resolution\" 128-bit\n // mantissa. We've already calculated x = (man * bits_0_to_63_incl_of_e).\n // Now calculate y = (man * bits_64_to_127_incl_of_e).\n wuffs_base__multiply_u64__output y = " +
+ "wuffs_base__multiply_u64(\n man, ((uint64_t)po10[0]) | (((uint64_t)po10[1]) << 32));\n\n // Merge the 128-bit x and 128-bit y, which overlap by 64 bits, to\n // calculate the 192-bit product of the 64-bit man by the 128-bit e.\n // As we exit this if-block, we only care about the high 128 bits\n // (merged_hi and merged_lo) of that 192-bit product.\n uint64_t merged_hi = x.hi;\n uint64_t merged_lo = x.lo + y.hi;\n if (merged_lo < x.lo) {\n merged_hi++; // Carry the overflow bit.\n }\n\n // The \"high resolution\" approximation of e is still a lower bound. Once\n // again, see if the upper bound is large enough to produce a different\n // result. This time, if it does, give up instead of reaching for an even\n // more precise approximation to e.\n //\n // This three-part check is similar to the two-part check that guarded the\n // if block that we're now in, but it has an extra term for the middle 64\n // bits (checking that adding 1 to merged_lo would overflow).\n if (" +
+ "((merged_hi & 0x1FF) == 0x1FF) && ((merged_lo + 1) == 0) &&\n (y.lo + man < man)) {\n return -1;\n }\n\n // Replace the 128-bit x with merged.\n x.hi = merged_hi;\n x.lo = merged_lo;\n }\n\n // As mentioned above, shifting x.hi right by either 9 or 10 bits will leave\n // the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on. If the\n // MSB (before shifting) was on, adjust ret_exp2 for the larger shift.\n //\n // Having bit 53 on (and higher bits off) means that ret_mantissa is a 54-bit\n // number.\n uint64_t msb = x.hi >> 63;\n uint64_t ret_mantissa = x.hi >> (msb + 9);\n ret_exp2 -= 1 ^ msb;\n\n // IEEE 754 rounds to-nearest with ties rounded to-even. Rounding to-even can\n // be tricky. If we're half-way between two exactly representable numbers\n // (x's low 73 bits are zero and the next 2 bits that matter are \"01\"), give\n // up instead of trying to pick the winner.\n //\n // Technically, we could tighten the condition by changing \"73\" to \"73 or 74,\n // depending on msb\", bu" +
+ "t a flat \"73\" is simpler.\n if ((x.lo == 0) && ((x.hi & 0x1FF) == 0) && ((ret_mantissa & 3) == 1)) {\n return -1;\n }\n\n // If we're not halfway then it's rounding to-nearest. Starting with a 54-bit\n // number, carry the lowest bit (bit 0) up if it's on. Regardless of whether\n // it was on or off, shifting right by one then produces a 53-bit number. If\n // carrying up overflowed, shift again.\n ret_mantissa += ret_mantissa & 1;\n ret_mantissa >>= 1;\n if ((ret_mantissa >> 53) > 0) {\n ret_mantissa >>= 1;\n ret_exp2++;\n }\n\n // Starting with a 53-bit number, IEEE 754 double-precision normal numbers\n // have an implicit mantissa bit. Mask that away and keep the low 52 bits.\n ret_mantissa &= 0x000FFFFFFFFFFFFF;\n\n // IEEE 754 double-precision floating point has 11 exponent bits. All off (0)\n // means subnormal numbers. All on (2047) means infinity or NaN.\n if ((ret_exp2 <= 0) || (2047 <= ret_exp2)) {\n return -1;\n }\n\n // Pack the bits and return.\n return ((int64_t)(ret_mantissa | (ret_exp2 << " +
+ "52)));\n}\n\n" +
+ "" +
+ "// --------\n\nstatic wuffs_base__result_f64 //\nwuffs_base__parse_number_f64_special(wuffs_base__slice_u8 s,\n const char* fallback_status_repr) {\n do {\n uint8_t* p = s.ptr;\n uint8_t* q = s.ptr + s.len;\n\n for (; (p < q) && (*p == '_'); p++) {\n }\n if (p >= q) {\n goto fallback;\n }\n\n // Parse sign.\n bool negative = false;\n do {\n if (*p == '+') {\n p++;\n } else if (*p == '-') {\n negative = true;\n p++;\n } else {\n break;\n }\n for (; (p < q) && (*p == '_'); p++) {\n }\n } while (0);\n if (p >= q) {\n goto fallback;\n }\n\n bool nan = false;\n switch (p[0]) {\n case 'I':\n case 'i':\n if (((q - p) < 3) || //\n ((p[1] != 'N') && (p[1] != 'n')) || //\n ((p[2] != 'F') && (p[2] != 'f'))) {\n goto fallback;\n }\n p += 3;\n\n if ((p >= q) || (*p == '_')) {\n break;\n } else if (((q - p) < 5) || " +
+ " //\n ((p[0] != 'I') && (p[0] != 'i')) || //\n ((p[1] != 'N') && (p[1] != 'n')) || //\n ((p[2] != 'I') && (p[2] != 'i')) || //\n ((p[3] != 'T') && (p[3] != 't')) || //\n ((p[4] != 'Y') && (p[4] != 'y'))) {\n goto fallback;\n }\n p += 5;\n\n if ((p >= q) || (*p == '_')) {\n break;\n }\n goto fallback;\n\n case 'N':\n case 'n':\n if (((q - p) < 3) || //\n ((p[1] != 'A') && (p[1] != 'a')) || //\n ((p[2] != 'N') && (p[2] != 'n'))) {\n goto fallback;\n }\n p += 3;\n\n if ((p >= q) || (*p == '_')) {\n nan = true;\n break;\n }\n goto fallback;\n\n default:\n goto fallback;\n }\n\n // Finish.\n for (; (p < q) && (*p == '_'); p++) {\n }\n if (p != q) {\n goto fallback;\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.va" +
+ "lue = wuffs_base__ieee_754_bit_representation__to_f64(\n (nan ? 0x7FFFFFFFFFFFFFFF : 0x7FF0000000000000) |\n (negative ? 0x8000000000000000 : 0));\n return ret;\n } while (0);\n\nfallback:\n do {\n wuffs_base__result_f64 ret;\n ret.status.repr = fallback_status_repr;\n ret.value = 0;\n return ret;\n } while (0);\n}\n\nWUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //\nwuffs_base__private_implementation__parse_number_f64__fallback(\n wuffs_base__private_implementation__high_prec_dec* h) {\n do {\n // powers converts decimal powers of 10 to binary powers of 2. For example,\n // (10000 >> 13) is 1. It stops before the elements exceed 60, also known\n // as WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.\n static const uint32_t num_powers = 19;\n static const uint8_t powers[19] = {\n 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //\n 33, 36, 39, 43, 46, 49, 53, 56, 59, //\n };\n\n // Handle zero and obvious extremes. The largest and smallest positive\n // f" +
+ "inite f64 values are approximately 1.8e+308 and 4.9e-324.\n if ((h->num_digits == 0) || (h->decimal_point < -326)) {\n goto zero;\n } else if (h->decimal_point > 310) {\n goto infinity;\n }\n\n // Try the fast Eisel algorithm again. Calculating the (man, exp10) pair\n // from the high_prec_dec h is more correct but slower than the approach\n // taken in wuffs_base__parse_number_f64. The latter is optimized for the\n // common cases (e.g. assuming no underscores or a leading '+' sign) rather\n // than the full set of cases allowed by the Wuffs API.\n if (h->num_digits <= 19) {\n uint64_t man = 0;\n uint32_t i;\n for (i = 0; i < h->num_digits; i++) {\n man = (10 * man) + h->digits[i];\n }\n int32_t exp10 = h->decimal_point - ((int32_t)(h->num_digits));\n if ((man != 0) && (-326 <= exp10) && (exp10 <= 310)) {\n int64_t r = wuffs_base__private_implementation__parse_number_f64_eisel(\n man, exp10);\n if (r >= 0) {\n wuffs_base__re" +
+ "sult_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(\n ((uint64_t)r) | (((uint64_t)(h->negative)) << 63));\n return ret;\n }\n }\n }\n\n // Scale by powers of 2 until we're in the range [½ .. 1], which gives us\n // our exponent (in base-2). First we shift right, possibly a little too\n // far, ending with a value certainly below 1 and possibly below ½...\n const int32_t f64_bias = -1023;\n int32_t exp2 = 0;\n while (h->decimal_point > 0) {\n uint32_t n = (uint32_t)(+h->decimal_point);\n uint32_t shift =\n (n < num_powers)\n ? powers[n]\n : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n\n wuffs_base__private_implementation__high_prec_dec__small_rshift(h, shift);\n if (h->decimal_point <\n -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n goto zero;\n }\n exp2 += (int32_t)shift;\n }\n // ...then we " +
+ "shift left, putting us in [½ .. 1].\n while (h->decimal_point <= 0) {\n uint32_t shift;\n if (h->decimal_point == 0) {\n if (h->digits[0] >= 5) {\n break;\n }\n shift = (h->digits[0] <= 2) ? 2 : 1;\n } else {\n uint32_t n = (uint32_t)(-h->decimal_point);\n shift = (n < num_powers)\n ? powers[n]\n : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n }\n\n wuffs_base__private_implementation__high_prec_dec__small_lshift(h, shift);\n if (h->decimal_point >\n +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n goto infinity;\n }\n exp2 -= (int32_t)shift;\n }\n\n // We're in the range [½ .. 1] but f64 uses [1 .. 2].\n exp2--;\n\n // The minimum normal exponent is (f64_bias + 1).\n while ((f64_bias + 1) > exp2) {\n uint32_t n = (uint32_t)((f64_bias + 1) - exp2);\n if (n > WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {\n n = WUFFS_BASE__" +
+ "PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n }\n wuffs_base__private_implementation__high_prec_dec__small_rshift(h, n);\n exp2 += (int32_t)n;\n }\n\n // Check for overflow.\n if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.\n goto infinity;\n }\n\n // Extract 53 bits for the mantissa (in base-2).\n wuffs_base__private_implementation__high_prec_dec__small_lshift(h, 53);\n uint64_t man2 =\n wuffs_base__private_implementation__high_prec_dec__rounded_integer(h);\n\n // Rounding might have added one bit. If so, shift and re-check overflow.\n if ((man2 >> 53) != 0) {\n man2 >>= 1;\n exp2++;\n if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.\n goto infinity;\n }\n }\n\n // Handle subnormal numbers.\n if ((man2 >> 52) == 0) {\n exp2 = f64_bias;\n }\n\n // Pack the bits and return.\n uint64_t exp2_bits =\n (uint64_t)((exp2 - f64_bias) & 0x07FF); // (1 << 11) - 1.\n uint64_t bits = (man2 & 0x000FFFFFFFFFFFFF) | " +
+ " // (1 << 52) - 1.\n (exp2_bits << 52) | //\n (h->negative ? 0x8000000000000000 : 0); // (1 << 63).\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n\nzero:\n do {\n uint64_t bits = h->negative ? 0x8000000000000000 : 0;\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n\ninfinity:\n do {\n uint64_t bits = h->negative ? 0xFFF0000000000000 : 0x7FF0000000000000;\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n}\n\nstatic inline bool //\nwuffs_base__private_implementation__is_decimal_digit(uint8_t c) {\n return ('0' <= c) && (c <= '9');\n}\n\nWUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //\nwuffs_base__parse_numb" +
+ "er_f64(wuffs_base__slice_u8 s, uint32_t options) {\n // In practice, almost all \"dd.ddddE±xxx\" numbers can be represented\n // losslessly by a uint64_t mantissa \"dddddd\" and an int32_t base-10\n // exponent, adjusting \"xxx\" for the position (if present) of the decimal\n // separator '.' or ','.\n //\n // This (u64 man, i32 exp10) data structure is superficially similar to the\n // \"Do It Yourself Floating Point\" type from Loitsch (†), but the exponent\n // here is base-10, not base-2.\n //\n // If s's number fits in a (man, exp10), parse that pair with the Eisel\n // algorithm. If not, or if Eisel fails, parsing s with the fallback\n // algorithm is slower but comprehensive.\n //\n // † \"Printing Floating-Point Numbers Quickly and Accurately with Integers\"\n // (https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf).\n // Florian Loitsch is also the primary contributor to\n // https://github.com/google/double-conversion\n do {\n // Calculating that (man, exp10) pair needs to stay within" +
+ " s's bounds.\n // Provided that s isn't extremely long, work on a NUL-terminated copy of\n // s's contents. The NUL byte isn't a valid part of \"±dd.ddddE±xxx\".\n //\n // As the pointer p walks the contents, it's faster to repeatedly check \"is\n // *p a valid digit\" than \"is p within bounds and *p a valid digit\".\n if (s.len >= 256) {\n goto fallback;\n }\n uint8_t z[256];\n memcpy(&z[0], s.ptr, s.len);\n z[s.len] = 0;\n const uint8_t* p = &z[0];\n\n // Look for a leading minus sign. Technically, we could also look for an\n // optional plus sign, but the \"script/process-json-numbers.c with -p\"\n // benchmark is noticably slower if we do. It's optional and, in practice,\n // usually absent. Let the fallback catch it.\n bool negative = (*p == '-');\n if (negative) {\n p++;\n }\n\n // After walking \"dd.dddd\", comparing p later with p now will produce the\n // number of \"d\"s and \".\"s.\n const uint8_t* const start_of_digits_ptr = p;\n\n // Walk the \"d\"s before a '." +
+ "', 'E', NUL byte, etc. If it starts with '0',\n // it must be a single '0'. If it starts with a non-zero decimal digit, it\n // can be a sequence of decimal digits.\n //\n // Update the man variable during the walk. It's OK if man overflows now.\n // We'll detect that later.\n uint64_t man;\n if (*p == '0') {\n man = 0;\n p++;\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n } else if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n man = ((uint8_t)(*p - '0'));\n p++;\n for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {\n man = (10 * man) + ((uint8_t)(*p - '0'));\n }\n } else {\n goto fallback;\n }\n\n // Walk the \"d\"s after the optional decimal separator ('.' or ','),\n // updating the man and exp10 variables.\n int32_t exp10 = 0;\n if ((*p == '.') || (*p == ',')) {\n p++;\n const uint8_t* first_after_separator_ptr = p;\n if (!wuffs_base__private_im" +
+ "plementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n man = (10 * man) + ((uint8_t)(*p - '0'));\n p++;\n for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {\n man = (10 * man) + ((uint8_t)(*p - '0'));\n }\n exp10 = ((int32_t)(first_after_separator_ptr - p));\n }\n\n // Count the number of digits:\n // - for an input of \"314159\", digit_count is 6.\n // - for an input of \"3.14159\", digit_count is 7.\n //\n // This is off-by-one if there is a decimal separator. That's OK for now.\n // We'll correct for that later. The \"script/process-json-numbers.c with\n // -p\" benchmark is noticably slower if we try to correct for that now.\n uint32_t digit_count = (uint32_t)(p - start_of_digits_ptr);\n\n // Update exp10 for the optional exponent, starting with 'E' or 'e'.\n if ((*p | 0x20) == 'e') {\n p++;\n int32_t exp_sign = +1;\n if (*p == '-') {\n p++;\n exp_sign = -1;\n } else if (*p == '+') {\n p++;\n " +
+ " }\n if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n int32_t exp_num = ((uint8_t)(*p - '0'));\n p++;\n // The rest of the exp_num walking has a peculiar control flow but, once\n // again, the \"script/process-json-numbers.c with -p\" benchmark is\n // sensitive to alternative formulations.\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n while (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n if (exp_num > 0x1000000) {\n goto fallback;\n }\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n exp10 += exp_sign * exp_num;\n }\n\n // The Wuffs API is that the original slice has no trailing data. It also\n // allows unde" +
+ "rscores, which we don't catch here but the fallback should.\n if (p != &z[s.len]) {\n goto fallback;\n }\n\n // Check that the uint64_t typed man variable has not overflowed, based on\n // digit_count.\n //\n // For reference:\n // - (1 << 63) is 9223372036854775808, which has 19 decimal digits.\n // - (1 << 64) is 18446744073709551616, which has 20 decimal digits.\n // - 19 nines, 9999999999999999999, is 0x8AC7230489E7FFFF, which has 64\n // bits and 16 hexadecimal digits.\n // - 20 nines, 99999999999999999999, is 0x56BC75E2D630FFFFF, which has 67\n // bits and 17 hexadecimal digits.\n if (digit_count > 19) {\n // Even if we have more than 19 pseudo-digits, it's not yet definitely an\n // overflow. Recall that digit_count might be off-by-one (too large) if\n // there's a decimal separator. It will also over-report the number of\n // meaningful digits if the input looks something like \"0.000dddExxx\".\n //\n // We adjust by the number of l" +
+ "eading '0's and '.'s and re-compare to 19.\n // Once again, technically, we could skip ','s too, but that perturbs the\n // \"script/process-json-numbers.c with -p\" benchmark.\n const uint8_t* q = start_of_digits_ptr;\n for (; (*q == '0') || (*q == '.'); q++) {\n }\n digit_count -= (uint32_t)(q - start_of_digits_ptr);\n if (digit_count > 19) {\n goto fallback;\n }\n }\n\n // The wuffs_base__private_implementation__parse_number_f64_eisel\n // preconditions include that exp10 is in the range -326 ..= 310.\n if ((exp10 < -326) || (310 < exp10)) {\n goto fallback;\n }\n\n // If man and exp10 are small enough, all three of (man), (10 ** exp10) and\n // (man ** (10 ** exp10)) are exactly representable by a double. We don't\n // need to run the Eisel algorithm.\n if ((-22 <= exp10) && (exp10 <= 22) && ((man >> 53) == 0)) {\n double d = (double)man;\n if (exp10 >= 0) {\n d *= wuffs_base__private_implementation__f64_powers_of_10[+exp10];\n } el" +
+ "se {\n d /= wuffs_base__private_implementation__f64_powers_of_10[-exp10];\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = negative ? -d : +d;\n return ret;\n }\n\n // The wuffs_base__private_implementation__parse_number_f64_eisel\n // preconditions include that man is non-zero. Parsing \"0\" should be caught\n // by the \"If man and exp10 are small enough\" above, but \"0e99\" might not.\n if (man == 0) {\n goto fallback;\n }\n\n // Our man and exp10 are in range. Run the Eisel algorithm.\n int64_t r =\n wuffs_base__private_implementation__parse_number_f64_eisel(man, exp10);\n if (r < 0) {\n goto fallback;\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(\n ((uint64_t)r) | (((uint64_t)negative) << 63));\n return ret;\n } while (0);\n\nfallback:\n do {\n wuffs_base__private_implementation__high_prec_dec h;\n wuffs_base__status status =\n wu" +
+ "ffs_base__private_implementation__high_prec_dec__parse(&h, s);\n if (status.repr) {\n return wuffs_base__parse_number_f64_special(s, status.repr);\n }\n return wuffs_base__private_implementation__parse_number_f64__fallback(&h);\n } while (0);\n}\n\n" +
+ "" +
+ "// --------\n\nstatic inline size_t //\nwuffs_base__private_implementation__render_inf(wuffs_base__slice_u8 dst,\n bool neg,\n uint32_t options) {\n if (neg) {\n if (dst.len < 4) {\n return 0;\n }\n wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492D); // '-Inf'le.\n return 4;\n }\n\n if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n if (dst.len < 4) {\n return 0;\n }\n wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492B); // '+Inf'le.\n return 4;\n }\n\n if (dst.len < 3) {\n return 0;\n }\n wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x666E49); // 'Inf'le.\n return 3;\n}\n\nstatic inline size_t //\nwuffs_base__private_implementation__render_nan(wuffs_base__slice_u8 dst) {\n if (dst.len < 3) {\n return 0;\n }\n wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x4E614E); // 'NaN'le.\n return 3;\n}\n\nstatic size_t //\nwuffs_base__private_implementation__high" +
+ "_prec_dec__render_exponent_absent(\n wuffs_base__slice_u8 dst,\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t precision,\n uint32_t options) {\n size_t n = (h->negative ||\n (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))\n ? 1\n : 0;\n if (h->decimal_point <= 0) {\n n += 1;\n } else {\n n += (size_t)(h->decimal_point);\n }\n if (precision > 0) {\n n += precision + 1; // +1 for the '.'.\n }\n\n // Don't modify dst if the formatted number won't fit.\n if (n > dst.len) {\n return 0;\n }\n\n // Align-left or align-right.\n uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)\n ? &dst.ptr[dst.len - n]\n : &dst.ptr[0];\n\n // Leading \"±\".\n if (h->negative) {\n *ptr++ = '-';\n } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n *ptr++ = '+';\n }\n\n // Integral digits.\n if (h->decimal_point <= 0) {\n *ptr++ = '0';\n } else {\n uint32_t m =\n" +
+ " wuffs_base__u32__min(h->num_digits, (uint32_t)(h->decimal_point));\n uint32_t i = 0;\n for (; i < m; i++) {\n *ptr++ = (uint8_t)('0' | h->digits[i]);\n }\n for (; i < (uint32_t)(h->decimal_point); i++) {\n *ptr++ = '0';\n }\n }\n\n // Separator and then fractional digits.\n if (precision > 0) {\n *ptr++ =\n (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)\n ? ','\n : '.';\n uint32_t i = 0;\n for (; i < precision; i++) {\n uint32_t j = ((uint32_t)(h->decimal_point)) + i;\n *ptr++ = (uint8_t)('0' | ((j < h->num_digits) ? h->digits[j] : 0));\n }\n }\n\n return n;\n}\n\nstatic size_t //\nwuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n wuffs_base__slice_u8 dst,\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t precision,\n uint32_t options) {\n int32_t exp = 0;\n if (h->num_digits > 0) {\n exp = h->decimal_point - 1;\n }\n bool negative_exp = exp < 0;\n if (negative_exp) {\n" +
+ " exp = -exp;\n }\n\n size_t n = (h->negative ||\n (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))\n ? 4\n : 3; // Mininum 3 bytes: first digit and then \"e±\".\n if (precision > 0) {\n n += precision + 1; // +1 for the '.'.\n }\n n += (exp < 100) ? 2 : 3;\n\n // Don't modify dst if the formatted number won't fit.\n if (n > dst.len) {\n return 0;\n }\n\n // Align-left or align-right.\n uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)\n ? &dst.ptr[dst.len - n]\n : &dst.ptr[0];\n\n // Leading \"±\".\n if (h->negative) {\n *ptr++ = '-';\n } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n *ptr++ = '+';\n }\n\n // Integral digit.\n if (h->num_digits > 0) {\n *ptr++ = (uint8_t)('0' | h->digits[0]);\n } else {\n *ptr++ = '0';\n }\n\n // Separator and then fractional digits.\n if (precision > 0) {\n *ptr++ =\n (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPA" +
+ "RATOR_IS_A_COMMA)\n ? ','\n : '.';\n uint32_t i = 1;\n uint32_t j = wuffs_base__u32__min(h->num_digits, precision + 1);\n for (; i < j; i++) {\n *ptr++ = (uint8_t)('0' | h->digits[i]);\n }\n for (; i <= precision; i++) {\n *ptr++ = '0';\n }\n }\n\n // Exponent: \"e±\" and then 2 or 3 digits.\n *ptr++ = 'e';\n *ptr++ = negative_exp ? '-' : '+';\n if (exp < 10) {\n *ptr++ = '0';\n *ptr++ = (uint8_t)('0' | exp);\n } else if (exp < 100) {\n *ptr++ = (uint8_t)('0' | (exp / 10));\n *ptr++ = (uint8_t)('0' | (exp % 10));\n } else {\n int32_t e = exp / 100;\n exp -= e * 100;\n *ptr++ = (uint8_t)('0' | e);\n *ptr++ = (uint8_t)('0' | (exp / 10));\n *ptr++ = (uint8_t)('0' | (exp % 10));\n }\n\n return n;\n}\n\nWUFFS_BASE__MAYBE_STATIC size_t //\nwuffs_base__render_number_f64(wuffs_base__slice_u8 dst,\n double x,\n uint32_t precision,\n uint32_t options) {\n // Decompose x (64 bits) into " +
+ "negativity (1 bit), base-2 exponent (11 bits\n // with a -1023 bias) and mantissa (52 bits).\n uint64_t bits = wuffs_base__ieee_754_bit_representation__from_f64(x);\n bool neg = (bits >> 63) != 0;\n int32_t exp2 = ((int32_t)(bits >> 52)) & 0x7FF;\n uint64_t man = bits & 0x000FFFFFFFFFFFFFul;\n\n // Apply the exponent bias and set the implicit top bit of the mantissa,\n // unless x is subnormal. Also take care of Inf and NaN.\n if (exp2 == 0x7FF) {\n if (man != 0) {\n return wuffs_base__private_implementation__render_nan(dst);\n }\n return wuffs_base__private_implementation__render_inf(dst, neg, options);\n } else if (exp2 == 0) {\n exp2 = -1022;\n } else {\n exp2 -= 1023;\n man |= 0x0010000000000000ul;\n }\n\n // Ensure that precision isn't too large.\n if (precision > 4095) {\n precision = 4095;\n }\n\n // Convert from the (neg, exp2, man) tuple to an HPD.\n wuffs_base__private_implementation__high_prec_dec h;\n wuffs_base__private_implementation__high_prec_dec__assign(&h, man, neg);\n if (h.n" +
+ "um_digits > 0) {\n wuffs_base__private_implementation__high_prec_dec__lshift(\n &h, exp2 - 52); // 52 mantissa bits.\n }\n\n // Handle the \"%e\" and \"%f\" formats.\n switch (options & (WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT |\n WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT)) {\n case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT: // The \"%\"f\" format.\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n int32_t p = ((int32_t)(h.num_digits)) - h.decimal_point;\n precision = ((uint32_t)(wuffs_base__i32__max(0, p)));\n } else {\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision) + h.decimal_point);\n }\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(\n dst, &h, precision, options);\n\n case WUFFS_BASE__RENDER_NUMBER_FXX__" +
+ "EXPONENT_PRESENT: // The \"%e\" format.\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n precision = (h.num_digits > 0) ? (h.num_digits - 1) : 0;\n } else {\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision) + 1);\n }\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n dst, &h, precision, options);\n }\n\n // We have the \"%g\" format and so precision means the number of significant\n // digits, not the number of digits after the decimal separator. Perform\n // rounding and determine whether to use \"%e\" or \"%f\".\n int32_t e_threshold = 0;\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n precision = h.num_digits;\n e_threshold = 6;\n } el" +
+ "se {\n if (precision == 0) {\n precision = 1;\n }\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision));\n e_threshold = ((int32_t)precision);\n int32_t nd = ((int32_t)(h.num_digits));\n if ((e_threshold > nd) && (nd >= h.decimal_point)) {\n e_threshold = nd;\n }\n }\n\n // Use the \"%e\" format if the exponent is large.\n int32_t e = h.decimal_point - 1;\n if ((e < -4) || (e_threshold <= e)) {\n uint32_t p = wuffs_base__u32__min(precision, h.num_digits);\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n dst, &h, (p > 0) ? (p - 1) : 0, options);\n }\n\n // Use the \"%f\" format otherwise.\n int32_t p = ((int32_t)precision);\n if (p > h.decimal_point) {\n p = ((int32_t)(h.num_digits));\n }\n precision = ((uint32_t)(wuffs_base__i32__max(0, p - h.decimal_point)));\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(\n dst, &h, precision, options);\n}\n" +
+ ""
+
+const BaseF64ConvSubmoduleDataC = "" +
+ "// ---------------- IEEE 754 Floating Point\n\n// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by\n// script/print-hpd-left-shift.go. That script has an optional -comments flag,\n// whose output is not copied here, which prints further detail.\n//\n// These tables are used in\n// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits.\n\n// wuffs_base__private_implementation__hpd_left_shift[i] encodes the number of\n// new digits created after multiplying a positive integer by (1 << i): the\n// additional length in the decimal representation. For example, shifting \"234\"\n// by 3 (equivalent to multiplying by 8) will produce \"1872\". Going from a\n// 3-length string to a 4-length string means that 1 new digit was added (and\n// existing digits may have changed).\n//\n// Shifting by i can add either N or N-1 new digits, depending on whether the\n// original positive integer compares >= or < to the i'th power of 5 (as 10\n// equals 2 * 5). Comparison is lexicographic, not numerical.\n//\n// For " +
+ "example, shifting by 4 (i.e. multiplying by 16) can add 1 or 2 new\n// digits, depending on a lexicographic comparison to (5 ** 4), i.e. \"625\":\n// - (\"1\" << 4) is \"16\", which adds 1 new digit.\n// - (\"5678\" << 4) is \"90848\", which adds 1 new digit.\n// - (\"624\" << 4) is \"9984\", which adds 1 new digit.\n// - (\"62498\" << 4) is \"999968\", which adds 1 new digit.\n// - (\"625\" << 4) is \"10000\", which adds 2 new digits.\n// - (\"625001\" << 4) is \"10000016\", which adds 2 new digits.\n// - (\"7008\" << 4) is \"112128\", which adds 2 new digits.\n// - (\"99\" << 4) is \"1584\", which adds 2 new digits.\n//\n// Thus, when i is 4, N is 2 and (5 ** i) is \"625\". This etc__hpd_left_shift\n// array encodes this as:\n// - etc__hpd_left_shift[4] is 0x1006 = (2 << 11) | 0x0006.\n// - etc__hpd_left_shift[5] is 0x1009 = (? << 11) | 0x0009.\n// where the ? isn't relevant for i == 4.\n//\n// The high 5 bits of etc__hpd_left_shift[i] is N, the higher of the two\n// possible number of new digits. The low 1" +
+ "1 bits are an offset into the\n// etc__powers_of_5 array (of length 0x051C, so offsets fit in 11 bits). When i\n// is 4, its offset and the next one is 6 and 9, and etc__powers_of_5[6 .. 9]\n// is the string \"\\x06\\x02\\x05\", so the relevant power of 5 is \"625\".\n//\n// Thanks to Ken Thompson for the original idea.\nstatic const uint16_t wuffs_base__private_implementation__hpd_left_shift[65] = {\n 0x0000, 0x0800, 0x0801, 0x0803, 0x1006, 0x1009, 0x100D, 0x1812, 0x1817,\n 0x181D, 0x2024, 0x202B, 0x2033, 0x203C, 0x2846, 0x2850, 0x285B, 0x3067,\n 0x3073, 0x3080, 0x388E, 0x389C, 0x38AB, 0x38BB, 0x40CC, 0x40DD, 0x40EF,\n 0x4902, 0x4915, 0x4929, 0x513E, 0x5153, 0x5169, 0x5180, 0x5998, 0x59B0,\n 0x59C9, 0x61E3, 0x61FD, 0x6218, 0x6A34, 0x6A50, 0x6A6D, 0x6A8B, 0x72AA,\n 0x72C9, 0x72E9, 0x7B0A, 0x7B2B, 0x7B4D, 0x8370, 0x8393, 0x83B7, 0x83DC,\n 0x8C02, 0x8C28, 0x8C4F, 0x9477, 0x949F, 0x94C8, 0x9CF2, 0x051C, 0x051C,\n 0x051C, 0x051C,\n};\n\n// wuffs_base__private_implementation__powers_of_5 contains the powers of 5,\n" +
+ "// concatenated together: \"5\", \"25\", \"125\", \"625\", \"3125\", etc.\nstatic const uint8_t wuffs_base__private_implementation__powers_of_5[0x051C] = {\n 5, 2, 5, 1, 2, 5, 6, 2, 5, 3, 1, 2, 5, 1, 5, 6, 2, 5, 7, 8, 1, 2, 5, 3, 9,\n 0, 6, 2, 5, 1, 9, 5, 3, 1, 2, 5, 9, 7, 6, 5, 6, 2, 5, 4, 8, 8, 2, 8, 1, 2,\n 5, 2, 4, 4, 1, 4, 0, 6, 2, 5, 1, 2, 2, 0, 7, 0, 3, 1, 2, 5, 6, 1, 0, 3, 5,\n 1, 5, 6, 2, 5, 3, 0, 5, 1, 7, 5, 7, 8, 1, 2, 5, 1, 5, 2, 5, 8, 7, 8, 9, 0,\n 6, 2, 5, 7, 6, 2, 9, 3, 9, 4, 5, 3, 1, 2, 5, 3, 8, 1, 4, 6, 9, 7, 2, 6, 5,\n 6, 2, 5, 1, 9, 0, 7, 3, 4, 8, 6, 3, 2, 8, 1, 2, 5, 9, 5, 3, 6, 7, 4, 3, 1,\n 6, 4, 0, 6, 2, 5, 4, 7, 6, 8, 3, 7, 1, 5, 8, 2, 0, 3, 1, 2, 5, 2, 3, 8, 4,\n 1, 8, 5, 7, 9, 1, 0, 1, 5, 6, 2, 5, 1, 1, 9, 2, 0, 9, 2, 8, 9, 5, 5, 0, 7,\n 8, 1, 2, 5, 5, 9, 6, 0, 4, 6, 4, 4, 7, 7, 5, 3, 9, 0, 6, 2, 5, 2, 9, 8, 0,\n 2, 3, 2, 2, 3, 8, 7, 6, 9, 5, 3, 1, 2, 5, 1, 4, 9, 0, 1, 1, 6, 1, 1, 9, 3,\n 8, 4, 7, 6, 5, 6, 2, 5, 7, 4, 5, 0, 5, 8, 0, 5, 9, 6, 9, 2, 3, 8, 2, 8, 1,\n 2, 5, " +
+ "3, 7, 2, 5, 2, 9, 0, 2, 9, 8, 4, 6, 1, 9, 1, 4, 0, 6, 2, 5, 1, 8, 6,\n 2, 6, 4, 5, 1, 4, 9, 2, 3, 0, 9, 5, 7, 0, 3, 1, 2, 5, 9, 3, 1, 3, 2, 2, 5,\n 7, 4, 6, 1, 5, 4, 7, 8, 5, 1, 5, 6, 2, 5, 4, 6, 5, 6, 6, 1, 2, 8, 7, 3, 0,\n 7, 7, 3, 9, 2, 5, 7, 8, 1, 2, 5, 2, 3, 2, 8, 3, 0, 6, 4, 3, 6, 5, 3, 8, 6,\n 9, 6, 2, 8, 9, 0, 6, 2, 5, 1, 1, 6, 4, 1, 5, 3, 2, 1, 8, 2, 6, 9, 3, 4, 8,\n 1, 4, 4, 5, 3, 1, 2, 5, 5, 8, 2, 0, 7, 6, 6, 0, 9, 1, 3, 4, 6, 7, 4, 0, 7,\n 2, 2, 6, 5, 6, 2, 5, 2, 9, 1, 0, 3, 8, 3, 0, 4, 5, 6, 7, 3, 3, 7, 0, 3, 6,\n 1, 3, 2, 8, 1, 2, 5, 1, 4, 5, 5, 1, 9, 1, 5, 2, 2, 8, 3, 6, 6, 8, 5, 1, 8,\n 0, 6, 6, 4, 0, 6, 2, 5, 7, 2, 7, 5, 9, 5, 7, 6, 1, 4, 1, 8, 3, 4, 2, 5, 9,\n 0, 3, 3, 2, 0, 3, 1, 2, 5, 3, 6, 3, 7, 9, 7, 8, 8, 0, 7, 0, 9, 1, 7, 1, 2,\n 9, 5, 1, 6, 6, 0, 1, 5, 6, 2, 5, 1, 8, 1, 8, 9, 8, 9, 4, 0, 3, 5, 4, 5, 8,\n 5, 6, 4, 7, 5, 8, 3, 0, 0, 7, 8, 1, 2, 5, 9, 0, 9, 4, 9, 4, 7, 0, 1, 7, 7,\n 2, 9, 2, 8, 2, 3, 7, 9, 1, 5, 0, 3, 9, 0, 6, 2, 5, 4, 5, 4, 7, 4, 7, 3, 5,\n 0, " +
+ "8, 8, 6, 4, 6, 4, 1, 1, 8, 9, 5, 7, 5, 1, 9, 5, 3, 1, 2, 5, 2, 2, 7, 3,\n 7, 3, 6, 7, 5, 4, 4, 3, 2, 3, 2, 0, 5, 9, 4, 7, 8, 7, 5, 9, 7, 6, 5, 6, 2,\n 5, 1, 1, 3, 6, 8, 6, 8, 3, 7, 7, 2, 1, 6, 1, 6, 0, 2, 9, 7, 3, 9, 3, 7, 9,\n 8, 8, 2, 8, 1, 2, 5, 5, 6, 8, 4, 3, 4, 1, 8, 8, 6, 0, 8, 0, 8, 0, 1, 4, 8,\n 6, 9, 6, 8, 9, 9, 4, 1, 4, 0, 6, 2, 5, 2, 8, 4, 2, 1, 7, 0, 9, 4, 3, 0, 4,\n 0, 4, 0, 0, 7, 4, 3, 4, 8, 4, 4, 9, 7, 0, 7, 0, 3, 1, 2, 5, 1, 4, 2, 1, 0,\n 8, 5, 4, 7, 1, 5, 2, 0, 2, 0, 0, 3, 7, 1, 7, 4, 2, 2, 4, 8, 5, 3, 5, 1, 5,\n 6, 2, 5, 7, 1, 0, 5, 4, 2, 7, 3, 5, 7, 6, 0, 1, 0, 0, 1, 8, 5, 8, 7, 1, 1,\n 2, 4, 2, 6, 7, 5, 7, 8, 1, 2, 5, 3, 5, 5, 2, 7, 1, 3, 6, 7, 8, 8, 0, 0, 5,\n 0, 0, 9, 2, 9, 3, 5, 5, 6, 2, 1, 3, 3, 7, 8, 9, 0, 6, 2, 5, 1, 7, 7, 6, 3,\n 5, 6, 8, 3, 9, 4, 0, 0, 2, 5, 0, 4, 6, 4, 6, 7, 7, 8, 1, 0, 6, 6, 8, 9, 4,\n 5, 3, 1, 2, 5, 8, 8, 8, 1, 7, 8, 4, 1, 9, 7, 0, 0, 1, 2, 5, 2, 3, 2, 3, 3,\n 8, 9, 0, 5, 3, 3, 4, 4, 7, 2, 6, 5, 6, 2, 5, 4, 4, 4, 0, 8, 9, 2, 0, 9, 8,\n " +
+ "5, 0, 0, 6, 2, 6, 1, 6, 1, 6, 9, 4, 5, 2, 6, 6, 7, 2, 3, 6, 3, 2, 8, 1, 2,\n 5, 2, 2, 2, 0, 4, 4, 6, 0, 4, 9, 2, 5, 0, 3, 1, 3, 0, 8, 0, 8, 4, 7, 2, 6,\n 3, 3, 3, 6, 1, 8, 1, 6, 4, 0, 6, 2, 5, 1, 1, 1, 0, 2, 2, 3, 0, 2, 4, 6, 2,\n 5, 1, 5, 6, 5, 4, 0, 4, 2, 3, 6, 3, 1, 6, 6, 8, 0, 9, 0, 8, 2, 0, 3, 1, 2,\n 5, 5, 5, 5, 1, 1, 1, 5, 1, 2, 3, 1, 2, 5, 7, 8, 2, 7, 0, 2, 1, 1, 8, 1, 5,\n 8, 3, 4, 0, 4, 5, 4, 1, 0, 1, 5, 6, 2, 5, 2, 7, 7, 5, 5, 5, 7, 5, 6, 1, 5,\n 6, 2, 8, 9, 1, 3, 5, 1, 0, 5, 9, 0, 7, 9, 1, 7, 0, 2, 2, 7, 0, 5, 0, 7, 8,\n 1, 2, 5, 1, 3, 8, 7, 7, 7, 8, 7, 8, 0, 7, 8, 1, 4, 4, 5, 6, 7, 5, 5, 2, 9,\n 5, 3, 9, 5, 8, 5, 1, 1, 3, 5, 2, 5, 3, 9, 0, 6, 2, 5, 6, 9, 3, 8, 8, 9, 3,\n 9, 0, 3, 9, 0, 7, 2, 2, 8, 3, 7, 7, 6, 4, 7, 6, 9, 7, 9, 2, 5, 5, 6, 7, 6,\n 2, 6, 9, 5, 3, 1, 2, 5, 3, 4, 6, 9, 4, 4, 6, 9, 5, 1, 9, 5, 3, 6, 1, 4, 1,\n 8, 8, 8, 2, 3, 8, 4, 8, 9, 6, 2, 7, 8, 3, 8, 1, 3, 4, 7, 6, 5, 6, 2, 5, 1,\n 7, 3, 4, 7, 2, 3, 4, 7, 5, 9, 7, 6, 8, 0, 7, 0, 9, 4, 4, 1, 1, 9, 2, 4, 4,\n " +
+ " 8, 1, 3, 9, 1, 9, 0, 6, 7, 3, 8, 2, 8, 1, 2, 5, 8, 6, 7, 3, 6, 1, 7, 3, 7,\n 9, 8, 8, 4, 0, 3, 5, 4, 7, 2, 0, 5, 9, 6, 2, 2, 4, 0, 6, 9, 5, 9, 5, 3, 3,\n 6, 9, 1, 4, 0, 6, 2, 5,\n};\n\n" +
+ "" +
"// --------\n\n// wuffs_base__private_implementation__powers_of_10 contains truncated\n// approximations to the powers of 10, ranging from 1e-326 to 1e+310 inclusive,\n// as 637 uint32_t quintuples (128-bit mantissa, 32-bit base-2 exponent biased\n// by 0x04BE (which is 1214)). The array size is 637 * 5 = 3185.\n//\n// The 1214 bias in this look-up table equals 1023 + 191. 1023 is the bias for\n// IEEE 754 double-precision floating point. 191 is ((3 * 64) - 1) and\n// wuffs_base__private_implementation__parse_number_f64_eisel works with\n// multiples-of-64-bit mantissas.\n//\n// For example, the third approximation, for 1e-324, consists of the uint32_t\n// quintuple (0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A). The\n// first four form a little-endian uint128_t value. The last one is an int32_t\n// value: -1140. Together, they represent the approximation to 1e-324:\n// 0xCF42894A_5DCE35EA_52064CAC_828675B9 * (2 ** (0x000A - 0x04BE))\n//\n// Similarly, 1e+4 is approximated by the uint64_t quintuple\n// (0x00000000, " +
"0x00000000, 0x00000000, 0x9C400000, 0x044C) which means:\n// 0x9C400000_00000000_00000000_00000000 * (2 ** (0x044C - 0x04BE))\n//\n// Similarly, 1e+68 is approximated by the uint64_t quintuple\n// (0x63EE4BDD, 0x4CA7AAA8, 0xD4C4FB27, 0xED63A231, 0x0520) which means:\n// 0xED63A231_D4C4FB27.4CA7AAA8_63EE4BDD * (2 ** (0x0520 - 0x04BE))\n//\n// This table was generated by by script/print-mpb-powers-of-10.go\nstatic const uint32_t wuffs_base__private_implementation__powers_of_10[3185] = {\n 0xF7604B57, 0x014BB630, 0xFE98746D, 0x84A57695, 0x0004, // 1e-326\n 0x35385E2D, 0x419EA3BD, 0x7E3E9188, 0xA5CED43B, 0x0007, // 1e-325\n 0x828675B9, 0x52064CAC, 0x5DCE35EA, 0xCF42894A, 0x000A, // 1e-324\n 0xD1940993, 0x7343EFEB, 0x7AA0E1B2, 0x818995CE, 0x000E, // 1e-323\n 0xC5F90BF8, 0x1014EBE6, 0x19491A1F, 0xA1EBFB42, 0x0011, // 1e-322\n 0x77774EF6, 0xD41A26E0, 0x9F9B60A6, 0xCA66FA12, 0x0014, // 1e-321\n 0x955522B4, 0x8920B098, 0x478238D0, 0xFD00B897, 0x0017, // 1e-320\n 0x5D5535B0, 0x55B46E5F, 0x8CB16382, 0" +
"x9E20735E, 0x001B, // 1e-319\n 0x34AA831D, 0xEB2189F7, 0x2FDDBC62, 0xC5A89036, 0x001E, // 1e-318\n 0x01D523E4, 0xA5E9EC75, 0xBBD52B7B, 0xF712B443, 0x0021, // 1e-317\n 0x2125366E, 0x47B233C9, 0x55653B2D, 0x9A6BB0AA, 0x0025, // 1e-316\n 0x696E840A, 0x999EC0BB, 0xEABE89F8, 0xC1069CD4, 0x0028, // 1e-315\n 0x43CA250D, 0xC00670EA, 0x256E2C76, 0xF148440A, 0x002B, // 1e-314\n 0x6A5E5728, 0x38040692, 0x5764DBCA, 0x96CD2A86, 0x002F, // 1e-313\n 0x04F5ECF2, 0xC6050837, 0xED3E12BC, 0xBC807527, 0x0032, // 1e-312\n 0xC633682E, 0xF7864A44, 0xE88D976B, 0xEBA09271, 0x0035, // 1e-311\n 0xFBE0211D, 0x7AB3EE6A, 0x31587EA3, 0x93445B87, 0x0039, // 1e-310\n 0xBAD82964, 0x5960EA05, 0xFDAE9E4C, 0xB8157268, 0x003C, // 1e-309\n 0x298E33BD, 0x6FB92487, 0x3D1A45DF, 0xE61ACF03, 0x003F, // 1e-308\n 0x79F8E056, 0xA5D3B6D4, 0x06306BAB, 0x8FD0C162, 0x0043, // 1e-307\n 0x9877186C, 0x8F48A489, 0x87BC8696, 0xB3C4F1BA, 0x0046, // 1e-306\n 0xFE94DE87, 0x331ACDAB, 0x29ABA83C, 0xE0B62E29, 0x0049, // 1e-305\n" +
@@ -113,43 +153,7 @@
"363804, 0x63E8A506, 0x9EC95D14, 0x07AF, // 1e265\n 0x3EDCD0D5, 0xB143C605, 0x7CE2CE48, 0xC67BB459, 0x07B2, // 1e266\n 0x8E94050A, 0xDD94B786, 0xDC1B81DA, 0xF81AA16F, 0x07B5, // 1e267\n 0x191C8326, 0xCA7CF2B4, 0xE9913128, 0x9B10A4E5, 0x07B9, // 1e268\n 0x1F63A3F0, 0xFD1C2F61, 0x63F57D72, 0xC1D4CE1F, 0x07BC, // 1e269\n 0x673C8CEC, 0xBC633B39, 0x3CF2DCCF, 0xF24A01A7, 0x07BF, // 1e270\n 0xE085D813, 0xD5BE0503, 0x8617CA01, 0x976E4108, 0x07C3, // 1e271\n 0xD8A74E18, 0x4B2D8644, 0xA79DBC82, 0xBD49D14A, 0x07C6, // 1e272\n 0x0ED1219E, 0xDDF8E7D6, 0x51852BA2, 0xEC9C459D, 0x07C9, // 1e273\n 0xC942B503, 0xCABB90E5, 0x52F33B45, 0x93E1AB82, 0x07CD, // 1e274\n 0x3B936243, 0x3D6A751F, 0xE7B00A17, 0xB8DA1662, 0x07D0, // 1e275\n 0x0A783AD4, 0x0CC51267, 0xA19C0C9D, 0xE7109BFB, 0x07D3, // 1e276\n 0x668B24C5, 0x27FB2B80, 0x450187E2, 0x906A617D, 0x07D7, // 1e277\n 0x802DEDF6, 0xB1F9F660, 0x9641E9DA, 0xB484F9DC, 0x07DA, // 1e278\n 0xA0396973, 0x5E7873F8, 0xBBD26451, 0xE1A63853, 0x07DD, // " +
"1e279\n 0x6423E1E8, 0xDB0B487B, 0x55637EB2, 0x8D07E334, 0x07E1, // 1e280\n 0x3D2CDA62, 0x91CE1A9A, 0x6ABC5E5F, 0xB049DC01, 0x07E4, // 1e281\n 0xCC7810FB, 0x7641A140, 0xC56B75F7, 0xDC5C5301, 0x07E7, // 1e282\n 0x7FCB0A9D, 0xA9E904C8, 0x1B6329BA, 0x89B9B3E1, 0x07EB, // 1e283\n 0x9FBDCD44, 0x546345FA, 0x623BF429, 0xAC2820D9, 0x07EE, // 1e284\n 0x47AD4095, 0xA97C1779, 0xBACAF133, 0xD732290F, 0x07F1, // 1e285\n 0xCCCC485D, 0x49ED8EAB, 0xD4BED6C0, 0x867F59A9, 0x07F5, // 1e286\n 0xBFFF5A74, 0x5C68F256, 0x49EE8C70, 0xA81F3014, 0x07F8, // 1e287\n 0x6FFF3111, 0x73832EEC, 0x5C6A2F8C, 0xD226FC19, 0x07FB, // 1e288\n 0xC5FF7EAB, 0xC831FD53, 0xD9C25DB7, 0x83585D8F, 0x07FF, // 1e289\n 0xB77F5E55, 0xBA3E7CA8, 0xD032F525, 0xA42E74F3, 0x0802, // 1e290\n 0xE55F35EB, 0x28CE1BD2, 0xC43FB26F, 0xCD3A1230, 0x0805, // 1e291\n 0xCF5B81B3, 0x7980D163, 0x7AA7CF85, 0x80444B5E, 0x0809, // 1e292\n 0xC332621F, 0xD7E105BC, 0x1951C366, 0xA0555E36, 0x080C, // 1e293\n 0xF3FEFAA7, 0x8DD9472B, 0x9FA63440" +
", 0xC86AB5C3, 0x080F, // 1e294\n 0xF0FEB951, 0xB14F98F6, 0x878FC150, 0xFA856334, 0x0812, // 1e295\n 0x569F33D3, 0x6ED1BF9A, 0xD4B9D8D2, 0x9C935E00, 0x0816, // 1e296\n 0xEC4700C8, 0x0A862F80, 0x09E84F07, 0xC3B83581, 0x0819, // 1e297\n 0x2758C0FA, 0xCD27BB61, 0x4C6262C8, 0xF4A642E1, 0x081C, // 1e298\n 0xB897789C, 0x8038D51C, 0xCFBD7DBD, 0x98E7E9CC, 0x0820, // 1e299\n 0xE6BD56C3, 0xE0470A63, 0x03ACDD2C, 0xBF21E440, 0x0823, // 1e300\n 0xE06CAC74, 0x1858CCFC, 0x04981478, 0xEEEA5D50, 0x0826, // 1e301\n 0x0C43EBC8, 0x0F37801E, 0x02DF0CCB, 0x95527A52, 0x082A, // 1e302\n 0x8F54E6BA, 0xD3056025, 0x8396CFFD, 0xBAA718E6, 0x082D, // 1e303\n 0xF32A2069, 0x47C6B82E, 0x247C83FD, 0xE950DF20, 0x0830, // 1e304\n 0x57FA5441, 0x4CDC331D, 0x16CDD27E, 0x91D28B74, 0x0834, // 1e305\n 0xADF8E952, 0xE0133FE4, 0x1C81471D, 0xB6472E51, 0x0837, // 1e306\n 0xD97723A6, 0x58180FDD, 0x63A198E5, 0xE3D8F9E5, 0x083A, // 1e307\n 0xA7EA7648, 0x570F09EA, 0x5E44FF8F, 0x8E679C2F, 0x083E, // 1e308\n 0x51E513" +
- "DA, 0x2CD2CC65, 0x35D63F73, 0xB201833B, 0x0841, // 1e309\n 0xA65E58D1, 0xF8077F7E, 0x034BCF4F, 0xDE81E40A, 0x0844, // 1e310\n};\n\n// wuffs_base__private_implementation__f64_powers_of_10 holds powers of 10 that\n// can be exactly represented by a float64 (what C calls a double).\nstatic const double wuffs_base__private_implementation__f64_powers_of_10[23] = {\n 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,\n 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,\n};\n\n" +
- "" +
- "// --------\n\n// wuffs_base__private_implementation__parse_number_f64_eisel produces the IEEE\n// 754 double-precision value for an exact mantissa and base-10 exponent.\n//\n// On success, it returns a non-negative int64_t such that the low 63 bits hold\n// the 11-bit exponent and 52-bit mantissa.\n//\n// On failure, it returns a negative value.\n//\n// The algorithm is based on an original idea by Michael Eisel. See\n// https://lemire.me/blog/2020/03/10/fast-float-parsing-in-practice/\n//\n// Preconditions:\n// - man is non-zero.\n// - exp10 is in the range -326 ..= 310, the same range of the\n// wuffs_base__private_implementation__powers_of_10 array.\nstatic int64_t //\nwuffs_base__private_implementation__parse_number_f64_eisel(uint64_t man,\n int32_t exp10) {\n // Look up the (possibly truncated) base-2 representation of (10 ** exp10).\n // The look-up table was constructed so that it is already normalized: the\n // table entry's mantissa's MSB (most significan" +
- "t bit) is on.\n const uint32_t* po10 =\n &wuffs_base__private_implementation__powers_of_10[5 * (exp10 + 326)];\n\n // Normalize the man argument. The (man != 0) precondition means that a\n // non-zero bit exists.\n uint32_t clz = wuffs_base__count_leading_zeroes_u64(man);\n man <<= clz;\n\n // Calculate the return value's base-2 exponent. We might tweak it by ±1\n // later, but its initial value comes from the look-up table and clz.\n uint64_t ret_exp2 = ((uint64_t)po10[4]) - ((uint64_t)clz);\n\n // Multiply the two mantissas. Normalization means that both mantissas are at\n // least (1<<63), so the 128-bit product must be at least (1<<126). The high\n // 64 bits of the product, x.hi, must therefore be at least (1<<62).\n //\n // As a consequence, x.hi has either 0 or 1 leading zeroes. Shifting x.hi\n // right by either 9 or 10 bits (depending on x.hi's MSB) will therefore\n // leave the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on.\n wuffs_base__multiply_u64__output x = wuffs_base__multipl" +
- "y_u64(\n man, ((uint64_t)po10[2]) | (((uint64_t)po10[3]) << 32));\n\n // Before we shift right by at least 9 bits, recall that the look-up table\n // entry was possibly truncated. We have so far only calculated a lower bound\n // for the product (man * e), where e is (10 ** exp10). The upper bound would\n // add a further (man * 1) to the 128-bit product, which overflows the lower\n // 64-bit limb if ((x.lo + man) < man).\n //\n // If overflow occurs, that adds 1 to x.hi. Since we're about to shift right\n // by at least 9 bits, that carried 1 can be ignored unless the higher 64-bit\n // limb's low 9 bits are all on.\n if (((x.hi & 0x1FF) == 0x1FF) && ((x.lo + man) < man)) {\n // Refine our calculation of (man * e). Before, our approximation of e used\n // a \"low resolution\" 64-bit mantissa. Now use a \"high resolution\" 128-bit\n // mantissa. We've already calculated x = (man * bits_0_to_63_incl_of_e).\n // Now calculate y = (man * bits_64_to_127_incl_of_e).\n wuffs_base__multiply_u64__output y = " +
- "wuffs_base__multiply_u64(\n man, ((uint64_t)po10[0]) | (((uint64_t)po10[1]) << 32));\n\n // Merge the 128-bit x and 128-bit y, which overlap by 64 bits, to\n // calculate the 192-bit product of the 64-bit man by the 128-bit e.\n // As we exit this if-block, we only care about the high 128 bits\n // (merged_hi and merged_lo) of that 192-bit product.\n uint64_t merged_hi = x.hi;\n uint64_t merged_lo = x.lo + y.hi;\n if (merged_lo < x.lo) {\n merged_hi++; // Carry the overflow bit.\n }\n\n // The \"high resolution\" approximation of e is still a lower bound. Once\n // again, see if the upper bound is large enough to produce a different\n // result. This time, if it does, give up instead of reaching for an even\n // more precise approximation to e.\n //\n // This three-part check is similar to the two-part check that guarded the\n // if block that we're now in, but it has an extra term for the middle 64\n // bits (checking that adding 1 to merged_lo would overflow).\n if (" +
- "((merged_hi & 0x1FF) == 0x1FF) && ((merged_lo + 1) == 0) &&\n (y.lo + man < man)) {\n return -1;\n }\n\n // Replace the 128-bit x with merged.\n x.hi = merged_hi;\n x.lo = merged_lo;\n }\n\n // As mentioned above, shifting x.hi right by either 9 or 10 bits will leave\n // the top 10 MSBs (bits 54 ..= 63) off and the 11th MSB (bit 53) on. If the\n // MSB (before shifting) was on, adjust ret_exp2 for the larger shift.\n //\n // Having bit 53 on (and higher bits off) means that ret_mantissa is a 54-bit\n // number.\n uint64_t msb = x.hi >> 63;\n uint64_t ret_mantissa = x.hi >> (msb + 9);\n ret_exp2 -= 1 ^ msb;\n\n // IEEE 754 rounds to-nearest with ties rounded to-even. Rounding to-even can\n // be tricky. If we're half-way between two exactly representable numbers\n // (x's low 73 bits are zero and the next 2 bits that matter are \"01\"), give\n // up instead of trying to pick the winner.\n //\n // Technically, we could tighten the condition by changing \"73\" to \"73 or 74,\n // depending on msb\", bu" +
- "t a flat \"73\" is simpler.\n if ((x.lo == 0) && ((x.hi & 0x1FF) == 0) && ((ret_mantissa & 3) == 1)) {\n return -1;\n }\n\n // If we're not halfway then it's rounding to-nearest. Starting with a 54-bit\n // number, carry the lowest bit (bit 0) up if it's on. Regardless of whether\n // it was on or off, shifting right by one then produces a 53-bit number. If\n // carrying up overflowed, shift again.\n ret_mantissa += ret_mantissa & 1;\n ret_mantissa >>= 1;\n if ((ret_mantissa >> 53) > 0) {\n ret_mantissa >>= 1;\n ret_exp2++;\n }\n\n // Starting with a 53-bit number, IEEE 754 double-precision normal numbers\n // have an implicit mantissa bit. Mask that away and keep the low 52 bits.\n ret_mantissa &= 0x000FFFFFFFFFFFFF;\n\n // IEEE 754 double-precision floating point has 11 exponent bits. All off (0)\n // means subnormal numbers. All on (2047) means infinity or NaN.\n if ((ret_exp2 <= 0) || (2047 <= ret_exp2)) {\n return -1;\n }\n\n // Pack the bits and return.\n return ((int64_t)(ret_mantissa | (ret_exp2 << " +
- "52)));\n}\n\n" +
- "" +
- "// --------\n\nstatic wuffs_base__result_f64 //\nwuffs_base__parse_number_f64_special(wuffs_base__slice_u8 s,\n const char* fallback_status_repr) {\n do {\n uint8_t* p = s.ptr;\n uint8_t* q = s.ptr + s.len;\n\n for (; (p < q) && (*p == '_'); p++) {\n }\n if (p >= q) {\n goto fallback;\n }\n\n // Parse sign.\n bool negative = false;\n do {\n if (*p == '+') {\n p++;\n } else if (*p == '-') {\n negative = true;\n p++;\n } else {\n break;\n }\n for (; (p < q) && (*p == '_'); p++) {\n }\n } while (0);\n if (p >= q) {\n goto fallback;\n }\n\n bool nan = false;\n switch (p[0]) {\n case 'I':\n case 'i':\n if (((q - p) < 3) || //\n ((p[1] != 'N') && (p[1] != 'n')) || //\n ((p[2] != 'F') && (p[2] != 'f'))) {\n goto fallback;\n }\n p += 3;\n\n if ((p >= q) || (*p == '_')) {\n break;\n } else if (((q - p) < 5) || " +
- " //\n ((p[0] != 'I') && (p[0] != 'i')) || //\n ((p[1] != 'N') && (p[1] != 'n')) || //\n ((p[2] != 'I') && (p[2] != 'i')) || //\n ((p[3] != 'T') && (p[3] != 't')) || //\n ((p[4] != 'Y') && (p[4] != 'y'))) {\n goto fallback;\n }\n p += 5;\n\n if ((p >= q) || (*p == '_')) {\n break;\n }\n goto fallback;\n\n case 'N':\n case 'n':\n if (((q - p) < 3) || //\n ((p[1] != 'A') && (p[1] != 'a')) || //\n ((p[2] != 'N') && (p[2] != 'n'))) {\n goto fallback;\n }\n p += 3;\n\n if ((p >= q) || (*p == '_')) {\n nan = true;\n break;\n }\n goto fallback;\n\n default:\n goto fallback;\n }\n\n // Finish.\n for (; (p < q) && (*p == '_'); p++) {\n }\n if (p != q) {\n goto fallback;\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.va" +
- "lue = wuffs_base__ieee_754_bit_representation__to_f64(\n (nan ? 0x7FFFFFFFFFFFFFFF : 0x7FF0000000000000) |\n (negative ? 0x8000000000000000 : 0));\n return ret;\n } while (0);\n\nfallback:\n do {\n wuffs_base__result_f64 ret;\n ret.status.repr = fallback_status_repr;\n ret.value = 0;\n return ret;\n } while (0);\n}\n\nWUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //\nwuffs_base__private_implementation__parse_number_f64__fallback(\n wuffs_base__private_implementation__high_prec_dec* h) {\n do {\n // powers converts decimal powers of 10 to binary powers of 2. For example,\n // (10000 >> 13) is 1. It stops before the elements exceed 60, also known\n // as WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.\n static const uint32_t num_powers = 19;\n static const uint8_t powers[19] = {\n 0, 3, 6, 9, 13, 16, 19, 23, 26, 29, //\n 33, 36, 39, 43, 46, 49, 53, 56, 59, //\n };\n\n // Handle zero and obvious extremes. The largest and smallest positive\n // f" +
- "inite f64 values are approximately 1.8e+308 and 4.9e-324.\n if ((h->num_digits == 0) || (h->decimal_point < -326)) {\n goto zero;\n } else if (h->decimal_point > 310) {\n goto infinity;\n }\n\n // Try the fast Eisel algorithm again. Calculating the (man, exp10) pair\n // from the high_prec_dec h is more correct but slower than the approach\n // taken in wuffs_base__parse_number_f64. The latter is optimized for the\n // common cases (e.g. assuming no underscores or a leading '+' sign) rather\n // than the full set of cases allowed by the Wuffs API.\n if (h->num_digits <= 19) {\n uint64_t man = 0;\n uint32_t i;\n for (i = 0; i < h->num_digits; i++) {\n man = (10 * man) + h->digits[i];\n }\n int32_t exp10 = h->decimal_point - ((int32_t)(h->num_digits));\n if ((man != 0) && (-326 <= exp10) && (exp10 <= 310)) {\n int64_t r = wuffs_base__private_implementation__parse_number_f64_eisel(\n man, exp10);\n if (r >= 0) {\n wuffs_base__re" +
- "sult_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(\n ((uint64_t)r) | (((uint64_t)(h->negative)) << 63));\n return ret;\n }\n }\n }\n\n // Scale by powers of 2 until we're in the range [½ .. 1], which gives us\n // our exponent (in base-2). First we shift right, possibly a little too\n // far, ending with a value certainly below 1 and possibly below ½...\n const int32_t f64_bias = -1023;\n int32_t exp2 = 0;\n while (h->decimal_point > 0) {\n uint32_t n = (uint32_t)(+h->decimal_point);\n uint32_t shift =\n (n < num_powers)\n ? powers[n]\n : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n\n wuffs_base__private_implementation__high_prec_dec__small_rshift(h, shift);\n if (h->decimal_point <\n -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n goto zero;\n }\n exp2 += (int32_t)shift;\n }\n // ...then we " +
- "shift left, putting us in [½ .. 1].\n while (h->decimal_point <= 0) {\n uint32_t shift;\n if (h->decimal_point == 0) {\n if (h->digits[0] >= 5) {\n break;\n }\n shift = (h->digits[0] <= 2) ? 2 : 1;\n } else {\n uint32_t n = (uint32_t)(-h->decimal_point);\n shift = (n < num_powers)\n ? powers[n]\n : WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n }\n\n wuffs_base__private_implementation__high_prec_dec__small_lshift(h, shift);\n if (h->decimal_point >\n +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {\n goto infinity;\n }\n exp2 -= (int32_t)shift;\n }\n\n // We're in the range [½ .. 1] but f64 uses [1 .. 2].\n exp2--;\n\n // The minimum normal exponent is (f64_bias + 1).\n while ((f64_bias + 1) > exp2) {\n uint32_t n = (uint32_t)((f64_bias + 1) - exp2);\n if (n > WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {\n n = WUFFS_BASE__" +
- "PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;\n }\n wuffs_base__private_implementation__high_prec_dec__small_rshift(h, n);\n exp2 += (int32_t)n;\n }\n\n // Check for overflow.\n if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.\n goto infinity;\n }\n\n // Extract 53 bits for the mantissa (in base-2).\n wuffs_base__private_implementation__high_prec_dec__small_lshift(h, 53);\n uint64_t man2 =\n wuffs_base__private_implementation__high_prec_dec__rounded_integer(h);\n\n // Rounding might have added one bit. If so, shift and re-check overflow.\n if ((man2 >> 53) != 0) {\n man2 >>= 1;\n exp2++;\n if ((exp2 - f64_bias) >= 0x07FF) { // (1 << 11) - 1.\n goto infinity;\n }\n }\n\n // Handle subnormal numbers.\n if ((man2 >> 52) == 0) {\n exp2 = f64_bias;\n }\n\n // Pack the bits and return.\n uint64_t exp2_bits =\n (uint64_t)((exp2 - f64_bias) & 0x07FF); // (1 << 11) - 1.\n uint64_t bits = (man2 & 0x000FFFFFFFFFFFFF) | " +
- " // (1 << 52) - 1.\n (exp2_bits << 52) | //\n (h->negative ? 0x8000000000000000 : 0); // (1 << 63).\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n\nzero:\n do {\n uint64_t bits = h->negative ? 0x8000000000000000 : 0;\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n\ninfinity:\n do {\n uint64_t bits = h->negative ? 0xFFF0000000000000 : 0x7FF0000000000000;\n\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(bits);\n return ret;\n } while (0);\n}\n\nstatic inline bool //\nwuffs_base__private_implementation__is_decimal_digit(uint8_t c) {\n return ('0' <= c) && (c <= '9');\n}\n\nWUFFS_BASE__MAYBE_STATIC wuffs_base__result_f64 //\nwuffs_base__parse_numb" +
- "er_f64(wuffs_base__slice_u8 s, uint32_t options) {\n // In practice, almost all \"dd.ddddE±xxx\" numbers can be represented\n // losslessly by a uint64_t mantissa \"dddddd\" and an int32_t base-10\n // exponent, adjusting \"xxx\" for the position (if present) of the decimal\n // separator '.' or ','.\n //\n // This (u64 man, i32 exp10) data structure is superficially similar to the\n // \"Do It Yourself Floating Point\" type from Loitsch (†), but the exponent\n // here is base-10, not base-2.\n //\n // If s's number fits in a (man, exp10), parse that pair with the Eisel\n // algorithm. If not, or if Eisel fails, parsing s with the fallback\n // algorithm is slower but comprehensive.\n //\n // † \"Printing Floating-Point Numbers Quickly and Accurately with Integers\"\n // (https://www.cs.tufts.edu/~nr/cs257/archive/florian-loitsch/printf.pdf).\n // Florian Loitsch is also the primary contributor to\n // https://github.com/google/double-conversion\n do {\n // Calculating that (man, exp10) pair needs to stay within" +
- " s's bounds.\n // Provided that s isn't extremely long, work on a NUL-terminated copy of\n // s's contents. The NUL byte isn't a valid part of \"±dd.ddddE±xxx\".\n //\n // As the pointer p walks the contents, it's faster to repeatedly check \"is\n // *p a valid digit\" than \"is p within bounds and *p a valid digit\".\n if (s.len >= 256) {\n goto fallback;\n }\n uint8_t z[256];\n memcpy(&z[0], s.ptr, s.len);\n z[s.len] = 0;\n const uint8_t* p = &z[0];\n\n // Look for a leading minus sign. Technically, we could also look for an\n // optional plus sign, but the \"script/process-json-numbers.c with -p\"\n // benchmark is noticably slower if we do. It's optional and, in practice,\n // usually absent. Let the fallback catch it.\n bool negative = (*p == '-');\n if (negative) {\n p++;\n }\n\n // After walking \"dd.dddd\", comparing p later with p now will produce the\n // number of \"d\"s and \".\"s.\n const uint8_t* const start_of_digits_ptr = p;\n\n // Walk the \"d\"s before a '." +
- "', 'E', NUL byte, etc. If it starts with '0',\n // it must be a single '0'. If it starts with a non-zero decimal digit, it\n // can be a sequence of decimal digits.\n //\n // Update the man variable during the walk. It's OK if man overflows now.\n // We'll detect that later.\n uint64_t man;\n if (*p == '0') {\n man = 0;\n p++;\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n } else if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n man = ((uint8_t)(*p - '0'));\n p++;\n for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {\n man = (10 * man) + ((uint8_t)(*p - '0'));\n }\n } else {\n goto fallback;\n }\n\n // Walk the \"d\"s after the optional decimal separator ('.' or ','),\n // updating the man and exp10 variables.\n int32_t exp10 = 0;\n if ((*p == '.') || (*p == ',')) {\n p++;\n const uint8_t* first_after_separator_ptr = p;\n if (!wuffs_base__private_im" +
- "plementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n man = (10 * man) + ((uint8_t)(*p - '0'));\n p++;\n for (; wuffs_base__private_implementation__is_decimal_digit(*p); p++) {\n man = (10 * man) + ((uint8_t)(*p - '0'));\n }\n exp10 = ((int32_t)(first_after_separator_ptr - p));\n }\n\n // Count the number of digits:\n // - for an input of \"314159\", digit_count is 6.\n // - for an input of \"3.14159\", digit_count is 7.\n //\n // This is off-by-one if there is a decimal separator. That's OK for now.\n // We'll correct for that later. The \"script/process-json-numbers.c with\n // -p\" benchmark is noticably slower if we try to correct for that now.\n uint32_t digit_count = (uint32_t)(p - start_of_digits_ptr);\n\n // Update exp10 for the optional exponent, starting with 'E' or 'e'.\n if ((*p | 0x20) == 'e') {\n p++;\n int32_t exp_sign = +1;\n if (*p == '-') {\n p++;\n exp_sign = -1;\n } else if (*p == '+') {\n p++;\n " +
- " }\n if (!wuffs_base__private_implementation__is_decimal_digit(*p)) {\n goto fallback;\n }\n int32_t exp_num = ((uint8_t)(*p - '0'));\n p++;\n // The rest of the exp_num walking has a peculiar control flow but, once\n // again, the \"script/process-json-numbers.c with -p\" benchmark is\n // sensitive to alternative formulations.\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n if (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n while (wuffs_base__private_implementation__is_decimal_digit(*p)) {\n if (exp_num > 0x1000000) {\n goto fallback;\n }\n exp_num = (10 * exp_num) + ((uint8_t)(*p - '0'));\n p++;\n }\n exp10 += exp_sign * exp_num;\n }\n\n // The Wuffs API is that the original slice has no trailing data. It also\n // allows unde" +
- "rscores, which we don't catch here but the fallback should.\n if (p != &z[s.len]) {\n goto fallback;\n }\n\n // Check that the uint64_t typed man variable has not overflowed, based on\n // digit_count.\n //\n // For reference:\n // - (1 << 63) is 9223372036854775808, which has 19 decimal digits.\n // - (1 << 64) is 18446744073709551616, which has 20 decimal digits.\n // - 19 nines, 9999999999999999999, is 0x8AC7230489E7FFFF, which has 64\n // bits and 16 hexadecimal digits.\n // - 20 nines, 99999999999999999999, is 0x56BC75E2D630FFFFF, which has 67\n // bits and 17 hexadecimal digits.\n if (digit_count > 19) {\n // Even if we have more than 19 pseudo-digits, it's not yet definitely an\n // overflow. Recall that digit_count might be off-by-one (too large) if\n // there's a decimal separator. It will also over-report the number of\n // meaningful digits if the input looks something like \"0.000dddExxx\".\n //\n // We adjust by the number of l" +
- "eading '0's and '.'s and re-compare to 19.\n // Once again, technically, we could skip ','s too, but that perturbs the\n // \"script/process-json-numbers.c with -p\" benchmark.\n const uint8_t* q = start_of_digits_ptr;\n for (; (*q == '0') || (*q == '.'); q++) {\n }\n digit_count -= (uint32_t)(q - start_of_digits_ptr);\n if (digit_count > 19) {\n goto fallback;\n }\n }\n\n // The wuffs_base__private_implementation__parse_number_f64_eisel\n // preconditions include that exp10 is in the range -326 ..= 310.\n if ((exp10 < -326) || (310 < exp10)) {\n goto fallback;\n }\n\n // If man and exp10 are small enough, all three of (man), (10 ** exp10) and\n // (man ** (10 ** exp10)) are exactly representable by a double. We don't\n // need to run the Eisel algorithm.\n if ((-22 <= exp10) && (exp10 <= 22) && ((man >> 53) == 0)) {\n double d = (double)man;\n if (exp10 >= 0) {\n d *= wuffs_base__private_implementation__f64_powers_of_10[+exp10];\n } el" +
- "se {\n d /= wuffs_base__private_implementation__f64_powers_of_10[-exp10];\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = negative ? -d : +d;\n return ret;\n }\n\n // The wuffs_base__private_implementation__parse_number_f64_eisel\n // preconditions include that man is non-zero. Parsing \"0\" should be caught\n // by the \"If man and exp10 are small enough\" above, but \"0e99\" might not.\n if (man == 0) {\n goto fallback;\n }\n\n // Our man and exp10 are in range. Run the Eisel algorithm.\n int64_t r =\n wuffs_base__private_implementation__parse_number_f64_eisel(man, exp10);\n if (r < 0) {\n goto fallback;\n }\n wuffs_base__result_f64 ret;\n ret.status.repr = NULL;\n ret.value = wuffs_base__ieee_754_bit_representation__to_f64(\n ((uint64_t)r) | (((uint64_t)negative) << 63));\n return ret;\n } while (0);\n\nfallback:\n do {\n wuffs_base__private_implementation__high_prec_dec h;\n wuffs_base__status status =\n wu" +
- "ffs_base__private_implementation__high_prec_dec__parse(&h, s);\n if (status.repr) {\n return wuffs_base__parse_number_f64_special(s, status.repr);\n }\n return wuffs_base__private_implementation__parse_number_f64__fallback(&h);\n } while (0);\n}\n\n" +
- "" +
- "// --------\n\nstatic inline size_t //\nwuffs_base__private_implementation__render_inf(wuffs_base__slice_u8 dst,\n bool neg,\n uint32_t options) {\n if (neg) {\n if (dst.len < 4) {\n return 0;\n }\n wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492D); // '-Inf'le.\n return 4;\n }\n\n if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n if (dst.len < 4) {\n return 0;\n }\n wuffs_base__store_u32le__no_bounds_check(dst.ptr, 0x666E492B); // '+Inf'le.\n return 4;\n }\n\n if (dst.len < 3) {\n return 0;\n }\n wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x666E49); // 'Inf'le.\n return 3;\n}\n\nstatic inline size_t //\nwuffs_base__private_implementation__render_nan(wuffs_base__slice_u8 dst) {\n if (dst.len < 3) {\n return 0;\n }\n wuffs_base__store_u24le__no_bounds_check(dst.ptr, 0x4E614E); // 'NaN'le.\n return 3;\n}\n\nstatic size_t //\nwuffs_base__private_implementation__high" +
- "_prec_dec__render_exponent_absent(\n wuffs_base__slice_u8 dst,\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t precision,\n uint32_t options) {\n size_t n = (h->negative ||\n (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))\n ? 1\n : 0;\n if (h->decimal_point <= 0) {\n n += 1;\n } else {\n n += (size_t)(h->decimal_point);\n }\n if (precision > 0) {\n n += precision + 1; // +1 for the '.'.\n }\n\n // Don't modify dst if the formatted number won't fit.\n if (n > dst.len) {\n return 0;\n }\n\n // Align-left or align-right.\n uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)\n ? &dst.ptr[dst.len - n]\n : &dst.ptr[0];\n\n // Leading \"±\".\n if (h->negative) {\n *ptr++ = '-';\n } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n *ptr++ = '+';\n }\n\n // Integral digits.\n if (h->decimal_point <= 0) {\n *ptr++ = '0';\n } else {\n uint32_t m =\n" +
- " wuffs_base__u32__min(h->num_digits, (uint32_t)(h->decimal_point));\n uint32_t i = 0;\n for (; i < m; i++) {\n *ptr++ = (uint8_t)('0' | h->digits[i]);\n }\n for (; i < (uint32_t)(h->decimal_point); i++) {\n *ptr++ = '0';\n }\n }\n\n // Separator and then fractional digits.\n if (precision > 0) {\n *ptr++ =\n (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPARATOR_IS_A_COMMA)\n ? ','\n : '.';\n uint32_t i = 0;\n for (; i < precision; i++) {\n uint32_t j = ((uint32_t)(h->decimal_point)) + i;\n *ptr++ = (uint8_t)('0' | ((j < h->num_digits) ? h->digits[j] : 0));\n }\n }\n\n return n;\n}\n\nstatic size_t //\nwuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n wuffs_base__slice_u8 dst,\n wuffs_base__private_implementation__high_prec_dec* h,\n uint32_t precision,\n uint32_t options) {\n int32_t exp = 0;\n if (h->num_digits > 0) {\n exp = h->decimal_point - 1;\n }\n bool negative_exp = exp < 0;\n if (negative_exp) {\n" +
- " exp = -exp;\n }\n\n size_t n = (h->negative ||\n (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN))\n ? 4\n : 3; // Mininum 3 bytes: first digit and then \"e±\".\n if (precision > 0) {\n n += precision + 1; // +1 for the '.'.\n }\n n += (exp < 100) ? 2 : 3;\n\n // Don't modify dst if the formatted number won't fit.\n if (n > dst.len) {\n return 0;\n }\n\n // Align-left or align-right.\n uint8_t* ptr = (options & WUFFS_BASE__RENDER_NUMBER_XXX__ALIGN_RIGHT)\n ? &dst.ptr[dst.len - n]\n : &dst.ptr[0];\n\n // Leading \"±\".\n if (h->negative) {\n *ptr++ = '-';\n } else if (options & WUFFS_BASE__RENDER_NUMBER_XXX__LEADING_PLUS_SIGN) {\n *ptr++ = '+';\n }\n\n // Integral digit.\n if (h->num_digits > 0) {\n *ptr++ = (uint8_t)('0' | h->digits[0]);\n } else {\n *ptr++ = '0';\n }\n\n // Separator and then fractional digits.\n if (precision > 0) {\n *ptr++ =\n (options & WUFFS_BASE__RENDER_NUMBER_FXX__DECIMAL_SEPA" +
- "RATOR_IS_A_COMMA)\n ? ','\n : '.';\n uint32_t i = 1;\n uint32_t j = wuffs_base__u32__min(h->num_digits, precision + 1);\n for (; i < j; i++) {\n *ptr++ = (uint8_t)('0' | h->digits[i]);\n }\n for (; i <= precision; i++) {\n *ptr++ = '0';\n }\n }\n\n // Exponent: \"e±\" and then 2 or 3 digits.\n *ptr++ = 'e';\n *ptr++ = negative_exp ? '-' : '+';\n if (exp < 10) {\n *ptr++ = '0';\n *ptr++ = (uint8_t)('0' | exp);\n } else if (exp < 100) {\n *ptr++ = (uint8_t)('0' | (exp / 10));\n *ptr++ = (uint8_t)('0' | (exp % 10));\n } else {\n int32_t e = exp / 100;\n exp -= e * 100;\n *ptr++ = (uint8_t)('0' | e);\n *ptr++ = (uint8_t)('0' | (exp / 10));\n *ptr++ = (uint8_t)('0' | (exp % 10));\n }\n\n return n;\n}\n\nWUFFS_BASE__MAYBE_STATIC size_t //\nwuffs_base__render_number_f64(wuffs_base__slice_u8 dst,\n double x,\n uint32_t precision,\n uint32_t options) {\n // Decompose x (64 bits) into " +
- "negativity (1 bit), base-2 exponent (11 bits\n // with a -1023 bias) and mantissa (52 bits).\n uint64_t bits = wuffs_base__ieee_754_bit_representation__from_f64(x);\n bool neg = (bits >> 63) != 0;\n int32_t exp2 = ((int32_t)(bits >> 52)) & 0x7FF;\n uint64_t man = bits & 0x000FFFFFFFFFFFFFul;\n\n // Apply the exponent bias and set the implicit top bit of the mantissa,\n // unless x is subnormal. Also take care of Inf and NaN.\n if (exp2 == 0x7FF) {\n if (man != 0) {\n return wuffs_base__private_implementation__render_nan(dst);\n }\n return wuffs_base__private_implementation__render_inf(dst, neg, options);\n } else if (exp2 == 0) {\n exp2 = -1022;\n } else {\n exp2 -= 1023;\n man |= 0x0010000000000000ul;\n }\n\n // Ensure that precision isn't too large.\n if (precision > 4095) {\n precision = 4095;\n }\n\n // Convert from the (neg, exp2, man) tuple to an HPD.\n wuffs_base__private_implementation__high_prec_dec h;\n wuffs_base__private_implementation__high_prec_dec__assign(&h, man, neg);\n if (h.n" +
- "um_digits > 0) {\n wuffs_base__private_implementation__high_prec_dec__lshift(\n &h, exp2 - 52); // 52 mantissa bits.\n }\n\n // Handle the \"%e\" and \"%f\" formats.\n switch (options & (WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT |\n WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_PRESENT)) {\n case WUFFS_BASE__RENDER_NUMBER_FXX__EXPONENT_ABSENT: // The \"%\"f\" format.\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n int32_t p = ((int32_t)(h.num_digits)) - h.decimal_point;\n precision = ((uint32_t)(wuffs_base__i32__max(0, p)));\n } else {\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision) + h.decimal_point);\n }\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(\n dst, &h, precision, options);\n\n case WUFFS_BASE__RENDER_NUMBER_FXX__" +
- "EXPONENT_PRESENT: // The \"%e\" format.\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n precision = (h.num_digits > 0) ? (h.num_digits - 1) : 0;\n } else {\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision) + 1);\n }\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n dst, &h, precision, options);\n }\n\n // We have the \"%g\" format and so precision means the number of significant\n // digits, not the number of digits after the decimal separator. Perform\n // rounding and determine whether to use \"%e\" or \"%f\".\n int32_t e_threshold = 0;\n if (options & WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION) {\n wuffs_base__private_implementation__high_prec_dec__round_just_enough(\n &h, exp2, man);\n precision = h.num_digits;\n e_threshold = 6;\n } el" +
- "se {\n if (precision == 0) {\n precision = 1;\n }\n wuffs_base__private_implementation__high_prec_dec__round_nearest(\n &h, ((int32_t)precision));\n e_threshold = ((int32_t)precision);\n int32_t nd = ((int32_t)(h.num_digits));\n if ((e_threshold > nd) && (nd >= h.decimal_point)) {\n e_threshold = nd;\n }\n }\n\n // Use the \"%e\" format if the exponent is large.\n int32_t e = h.decimal_point - 1;\n if ((e < -4) || (e_threshold <= e)) {\n uint32_t p = wuffs_base__u32__min(precision, h.num_digits);\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_present(\n dst, &h, (p > 0) ? (p - 1) : 0, options);\n }\n\n // Use the \"%f\" format otherwise.\n int32_t p = ((int32_t)precision);\n if (p > h.decimal_point) {\n p = ((int32_t)(h.num_digits));\n }\n precision = ((uint32_t)(wuffs_base__i32__max(0, p - h.decimal_point)));\n return wuffs_base__private_implementation__high_prec_dec__render_exponent_absent(\n dst, &h, precision, options);\n}\n" +
+ "DA, 0x2CD2CC65, 0x35D63F73, 0xB201833B, 0x0841, // 1e309\n 0xA65E58D1, 0xF8077F7E, 0x034BCF4F, 0xDE81E40A, 0x0844, // 1e310\n};\n\n// wuffs_base__private_implementation__f64_powers_of_10 holds powers of 10 that\n// can be exactly represented by a float64 (what C calls a double).\nstatic const double wuffs_base__private_implementation__f64_powers_of_10[23] = {\n 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11,\n 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,\n};\n" +
""
const BaseI64ConvSubmoduleC = "" +
diff --git a/internal/cgen/data/gen.go b/internal/cgen/data/gen.go
index 5463149..34fb705 100644
--- a/internal/cgen/data/gen.go
+++ b/internal/cgen/data/gen.go
@@ -75,7 +75,8 @@
}{
{"../base/all-impl.c", "BaseAllImplC"},
- {"../base/f64conv-submodule.c", "BaseF64ConvSubmoduleC"},
+ {"../base/f64conv-submodule-code.c", "BaseF64ConvSubmoduleCodeC"},
+ {"../base/f64conv-submodule-data.c", "BaseF64ConvSubmoduleDataC"},
{"../base/i64conv-submodule.c", "BaseI64ConvSubmoduleC"},
{"../base/pixconv-submodule.c", "BasePixConvSubmoduleC"},
{"../base/utf8-submodule.c", "BaseUTF8SubmoduleC"},
diff --git a/release/c/wuffs-unsupported-snapshot.c b/release/c/wuffs-unsupported-snapshot.c
index 7313597..7c75d22 100644
--- a/release/c/wuffs-unsupported-snapshot.c
+++ b/release/c/wuffs-unsupported-snapshot.c
@@ -9018,317 +9018,6 @@
// ---------------- IEEE 754 Floating Point
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE 2047
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION 800
-
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL is the largest N
-// such that ((10 << N) < (1 << 64)).
-#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL 60
-
-// wuffs_base__private_implementation__high_prec_dec (abbreviated as HPD) is a
-// fixed precision floating point decimal number, augmented with ±infinity
-// values, but it cannot represent NaN (Not a Number).
-//
-// "High precision" means that the mantissa holds 800 decimal digits. 800 is
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION.
-//
-// An HPD isn't for general purpose arithmetic, only for conversions to and
-// from IEEE 754 double-precision floating point, where the largest and
-// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.
-// HPD exponents above +2047 mean infinity, below -2047 mean zero. The ±2047
-// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION and
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-//
-// digits[.. num_digits] are the number's digits in big-endian order. The
-// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'
-// is the ASCII value 0x37.
-//
-// decimal_point is the index (within digits) of the decimal point. It may be
-// negative or be larger than num_digits, in which case the explicit digits are
-// padded with implicit zeroes.
-//
-// For example, if num_digits is 3 and digits is "\x07\x08\x09":
-// - A decimal_point of -2 means ".00789"
-// - A decimal_point of -1 means ".0789"
-// - A decimal_point of +0 means ".789"
-// - A decimal_point of +1 means "7.89"
-// - A decimal_point of +2 means "78.9"
-// - A decimal_point of +3 means "789."
-// - A decimal_point of +4 means "7890."
-// - A decimal_point of +5 means "78900."
-//
-// As above, a decimal_point higher than +2047 means that the overall value is
-// infinity, lower than -2047 means zero.
-//
-// negative is a sign bit. An HPD can distinguish positive and negative zero.
-//
-// truncated is whether there are more than
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION digits, and at
-// least one of those extra digits are non-zero. The existence of long-tail
-// digits can affect rounding.
-//
-// The "all fields are zero" value is valid, and represents the number +0.
-typedef struct {
- uint32_t num_digits;
- int32_t decimal_point;
- bool negative;
- bool truncated;
- uint8_t digits[WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION];
-} wuffs_base__private_implementation__high_prec_dec;
-
-// wuffs_base__private_implementation__high_prec_dec__trim trims trailing
-// zeroes from the h->digits[.. h->num_digits] slice. They have no benefit,
-// since we explicitly track h->decimal_point.
-//
-// Preconditions:
-// - h is non-NULL.
-static inline void //
-wuffs_base__private_implementation__high_prec_dec__trim(
- wuffs_base__private_implementation__high_prec_dec* h) {
- while ((h->num_digits > 0) && (h->digits[h->num_digits - 1] == 0)) {
- h->num_digits--;
- }
-}
-
-// wuffs_base__private_implementation__high_prec_dec__assign sets h to
-// represent the number x.
-//
-// Preconditions:
-// - h is non-NULL.
-static void //
-wuffs_base__private_implementation__high_prec_dec__assign(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint64_t x,
- bool negative) {
- uint32_t n = 0;
-
- // Set h->digits.
- if (x > 0) {
- // Calculate the digits, working right-to-left. After we determine n (how
- // many digits there are), copy from buf to h->digits.
- //
- // UINT64_MAX, 18446744073709551615, is 20 digits long. It can be faster to
- // copy a constant number of bytes than a variable number (20 instead of
- // n). Make buf large enough (and start writing to it from the middle) so
- // that can we always copy 20 bytes: the slice buf[(20-n) .. (40-n)].
- uint8_t buf[40] = {0};
- uint8_t* ptr = &buf[20];
- do {
- uint64_t remaining = x / 10;
- x -= remaining * 10;
- ptr--;
- *ptr = (uint8_t)x;
- n++;
- x = remaining;
- } while (x > 0);
- memcpy(h->digits, ptr, 20);
- }
-
- // Set h's other fields.
- h->num_digits = n;
- h->decimal_point = (int32_t)n;
- h->negative = negative;
- h->truncated = false;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static wuffs_base__status //
-wuffs_base__private_implementation__high_prec_dec__parse(
- wuffs_base__private_implementation__high_prec_dec* h,
- wuffs_base__slice_u8 s) {
- if (!h) {
- return wuffs_base__make_status(wuffs_base__error__bad_receiver);
- }
- h->num_digits = 0;
- h->decimal_point = 0;
- h->negative = false;
- h->truncated = false;
-
- uint8_t* p = s.ptr;
- uint8_t* q = s.ptr + s.len;
-
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
-
- // Parse sign.
- do {
- if (*p == '+') {
- p++;
- } else if (*p == '-') {
- h->negative = true;
- p++;
- } else {
- break;
- }
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
- } while (0);
-
- // Parse digits, up to (and including) a '.', 'E' or 'e'. Examples for each
- // limb in this if-else chain:
- // - "0.789"
- // - "1002.789"
- // - ".789"
- // - Other (invalid input).
- uint32_t nd = 0;
- int32_t dp = 0;
- bool no_digits_before_separator = false;
- if ('0' == *p) {
- p++;
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- goto after_sep;
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
- } else if (('0' < *p) && (*p <= '9')) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- dp = (int32_t)nd;
- p++;
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if (('0' <= *p) && (*p <= '9')) {
- if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- dp = (int32_t)nd;
- } else if ('0' != *p) {
- // Long-tail non-zeroes set the truncated bit.
- h->truncated = true;
- }
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- goto after_sep;
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
- } else if ((*p == '.') || (*p == ',')) {
- p++;
- no_digits_before_separator = true;
-
- } else {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
-
-after_sep:
- for (;; p++) {
- if (p >= q) {
- goto after_all;
- } else if ('0' == *p) {
- if (nd == 0) {
- // Track leading zeroes implicitly.
- dp--;
- } else if (nd <
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- }
- } else if (('0' < *p) && (*p <= '9')) {
- if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[nd++] = (uint8_t)(*p - '0');
- } else {
- // Long-tail non-zeroes set the truncated bit.
- h->truncated = true;
- }
- } else if ((*p == 'E') || (*p == 'e')) {
- p++;
- goto after_exp;
- } else if (*p != '_') {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- }
-
-after_exp:
- do {
- for (;; p++) {
- if (p >= q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- } else if (*p != '_') {
- break;
- }
- }
-
- int32_t exp_sign = +1;
- if (*p == '+') {
- p++;
- } else if (*p == '-') {
- exp_sign = -1;
- p++;
- }
-
- int32_t exp = 0;
- const int32_t exp_large =
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE +
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
- bool saw_exp_digits = false;
- for (; p < q; p++) {
- if (*p == '_') {
- // No-op.
- } else if (('0' <= *p) && (*p <= '9')) {
- saw_exp_digits = true;
- if (exp < exp_large) {
- exp = (10 * exp) + ((int32_t)(*p - '0'));
- }
- } else {
- break;
- }
- }
- if (!saw_exp_digits) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- dp += exp_sign * exp;
- } while (0);
-
-after_all:
- if (p != q) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- h->num_digits = nd;
- if (nd == 0) {
- if (no_digits_before_separator) {
- return wuffs_base__make_status(wuffs_base__error__bad_argument);
- }
- h->decimal_point = 0;
- } else if (dp <
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- h->decimal_point =
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE - 1;
- } else if (dp >
- +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- h->decimal_point =
- +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE + 1;
- } else {
- h->decimal_point = dp;
- }
- wuffs_base__private_implementation__high_prec_dec__trim(h);
- return wuffs_base__make_status(NULL);
-}
-
-// --------
-
// The etc__hpd_left_shift and etc__powers_of_5 tables were printed by
// script/print-hpd-left-shift.go. That script has an optional -comments flag,
// whose output is not copied here, which prints further detail.
@@ -9440,477 +9129,6 @@
6, 9, 1, 4, 0, 6, 2, 5,
};
-// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
-// returns the number of additional decimal digits when left-shifting by shift.
-//
-// See below for preconditions.
-static uint32_t //
-wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- // Masking with 0x3F should be unnecessary (assuming the preconditions) but
- // it's cheap and ensures that we don't overflow the
- // wuffs_base__private_implementation__hpd_left_shift array.
- shift &= 63;
-
- uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];
- uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];
- uint32_t num_new_digits = x_a >> 11;
- uint32_t pow5_a = 0x7FF & x_a;
- uint32_t pow5_b = 0x7FF & x_b;
-
- const uint8_t* pow5 =
- &wuffs_base__private_implementation__powers_of_5[pow5_a];
- uint32_t i = 0;
- uint32_t n = pow5_b - pow5_a;
- for (; i < n; i++) {
- if (i >= h->num_digits) {
- return num_new_digits - 1;
- } else if (h->digits[i] == pow5[i]) {
- continue;
- } else if (h->digits[i] < pow5[i]) {
- return num_new_digits - 1;
- } else {
- return num_new_digits;
- }
- }
- return num_new_digits;
-}
-
-// --------
-
-// wuffs_base__private_implementation__high_prec_dec__rounded_integer returns
-// the integral (non-fractional) part of h, provided that it is 18 or fewer
-// decimal digits. For 19 or more digits, it returns UINT64_MAX. Note that:
-// - (1 << 53) is 9007199254740992, which has 16 decimal digits.
-// - (1 << 56) is 72057594037927936, which has 17 decimal digits.
-// - (1 << 59) is 576460752303423488, which has 18 decimal digits.
-// - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
-// and that IEEE 754 double precision has 52 mantissa bits.
-//
-// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.
-//
-// h's negative bit is ignored: rounding -8.6 returns 9.
-//
-// See below for preconditions.
-static uint64_t //
-wuffs_base__private_implementation__high_prec_dec__rounded_integer(
- wuffs_base__private_implementation__high_prec_dec* h) {
- if ((h->num_digits == 0) || (h->decimal_point < 0)) {
- return 0;
- } else if (h->decimal_point > 18) {
- return UINT64_MAX;
- }
-
- uint32_t dp = (uint32_t)(h->decimal_point);
- uint64_t n = 0;
- uint32_t i = 0;
- for (; i < dp; i++) {
- n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);
- }
-
- bool round_up = false;
- if (dp < h->num_digits) {
- round_up = h->digits[dp] >= 5;
- if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {
- // We are exactly halfway. If we're truncated, round up, otherwise round
- // to even.
- round_up = h->truncated || //
- ((dp > 0) && (1 & h->digits[dp - 1]));
- }
- }
- if (round_up) {
- n++;
- }
-
- return n;
-}
-
-// wuffs_base__private_implementation__high_prec_dec__small_xshift shifts h's
-// number (where 'x' is 'l' or 'r' for left or right) by a small shift value.
-//
-// Preconditions:
-// - h is non-NULL.
-// - h->decimal_point is "not extreme".
-// - shift is non-zero.
-// - shift is "a small shift".
-//
-// "Not extreme" means within
-// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-//
-// "A small shift" means not more than
-// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
-//
-// wuffs_base__private_implementation__high_prec_dec__rounded_integer and
-// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
-// have the same preconditions.
-//
-// wuffs_base__private_implementation__high_prec_dec__lshift keeps the first
-// two preconditions but not the last two. Its shift argument is signed and
-// does not need to be "small": zero is a no-op, positive means left shift and
-// negative means right shift.
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__small_lshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- if (h->num_digits == 0) {
- return;
- }
- uint32_t num_new_digits =
- wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
- h, shift);
- uint32_t rx = h->num_digits - 1; // Read index.
- uint32_t wx = h->num_digits - 1 + num_new_digits; // Write index.
- uint64_t n = 0;
-
- // Repeat: pick up a digit, put down a digit, right to left.
- while (((int32_t)rx) >= 0) {
- n += ((uint64_t)(h->digits[rx])) << shift;
- uint64_t quo = n / 10;
- uint64_t rem = n - (10 * quo);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx] = (uint8_t)rem;
- } else if (rem > 0) {
- h->truncated = true;
- }
- n = quo;
- wx--;
- rx--;
- }
-
- // Put down leading digits, right to left.
- while (n > 0) {
- uint64_t quo = n / 10;
- uint64_t rem = n - (10 * quo);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx] = (uint8_t)rem;
- } else if (rem > 0) {
- h->truncated = true;
- }
- n = quo;
- wx--;
- }
-
- // Finish.
- h->num_digits += num_new_digits;
- if (h->num_digits >
- WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->num_digits = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
- }
- h->decimal_point += (int32_t)num_new_digits;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__small_rshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- uint32_t shift) {
- uint32_t rx = 0; // Read index.
- uint32_t wx = 0; // Write index.
- uint64_t n = 0;
-
- // Pick up enough leading digits to cover the first shift.
- while ((n >> shift) == 0) {
- if (rx < h->num_digits) {
- // Read a digit.
- n = (10 * n) + h->digits[rx++];
- } else if (n == 0) {
- // h's number used to be zero and remains zero.
- return;
- } else {
- // Read sufficient implicit trailing zeroes.
- while ((n >> shift) == 0) {
- n = 10 * n;
- rx++;
- }
- break;
- }
- }
- h->decimal_point -= ((int32_t)(rx - 1));
- if (h->decimal_point <
- -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
- // After the shift, h's number is effectively zero.
- h->num_digits = 0;
- h->decimal_point = 0;
- h->negative = false;
- h->truncated = false;
- return;
- }
-
- // Repeat: pick up a digit, put down a digit, left to right.
- uint64_t mask = (((uint64_t)(1)) << shift) - 1;
- while (rx < h->num_digits) {
- uint8_t new_digit = ((uint8_t)(n >> shift));
- n = (10 * (n & mask)) + h->digits[rx++];
- h->digits[wx++] = new_digit;
- }
-
- // Put down trailing digits, left to right.
- while (n > 0) {
- uint8_t new_digit = ((uint8_t)(n >> shift));
- n = 10 * (n & mask);
- if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
- h->digits[wx++] = new_digit;
- } else if (new_digit > 0) {
- h->truncated = true;
- }
- }
-
- // Finish.
- h->num_digits = wx;
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__lshift(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t shift) {
- if (shift > 0) {
- while (shift > +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
- wuffs_base__private_implementation__high_prec_dec__small_lshift(
- h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
- shift -= WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
- wuffs_base__private_implementation__high_prec_dec__small_lshift(
- h, ((uint32_t)(+shift)));
- } else if (shift < 0) {
- while (shift < -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
- wuffs_base__private_implementation__high_prec_dec__small_rshift(
- h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
- shift += WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
- }
- wuffs_base__private_implementation__high_prec_dec__small_rshift(
- h, ((uint32_t)(-shift)));
- }
-}
-
-// --------
-
-// wuffs_base__private_implementation__high_prec_dec__round_etc rounds h's
-// number. For those functions that take an n argument, rounding produces at
-// most n digits (which is not necessarily at most n decimal places). Negative
-// n values are ignored, as well as any n greater than or equal to h's number
-// of digits. The etc__round_just_enough function implicitly chooses an n to
-// implement WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION.
-//
-// Preconditions:
-// - h is non-NULL.
-// - h->decimal_point is "not extreme".
-//
-// "Not extreme" means within
-// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_down(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
- h->num_digits = (uint32_t)(n);
- wuffs_base__private_implementation__high_prec_dec__trim(h);
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_up(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
-
- for (n--; n >= 0; n--) {
- if (h->digits[n] < 9) {
- h->digits[n]++;
- h->num_digits = (uint32_t)(n + 1);
- return;
- }
- }
-
- // The number is all 9s. Change to a single 1 and adjust the decimal point.
- h->digits[0] = 1;
- h->num_digits = 1;
- h->decimal_point++;
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_nearest(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t n) {
- if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
- return;
- }
- bool up = h->digits[n] >= 5;
- if ((h->digits[n] == 5) && ((n + 1) == ((int32_t)(h->num_digits)))) {
- up = h->truncated || //
- ((n > 0) && ((h->digits[n - 1] & 1) != 0));
- }
-
- if (up) {
- wuffs_base__private_implementation__high_prec_dec__round_up(h, n);
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_down(h, n);
- }
-}
-
-static void //
-wuffs_base__private_implementation__high_prec_dec__round_just_enough(
- wuffs_base__private_implementation__high_prec_dec* h,
- int32_t exp2,
- uint64_t mantissa) {
- // The magic numbers 52 and 53 in this function are because IEEE 754 double
- // precision has 52 mantissa bits.
- //
- // Let f be the floating point number represented by exp2 and mantissa (and
- // also the number in h): the number (mantissa * (2 ** (exp2 - 52))).
- //
- // If f is zero or a small integer, we can return early.
- if ((mantissa == 0) ||
- ((exp2 < 53) && (h->decimal_point >= ((int32_t)(h->num_digits))))) {
- return;
- }
-
- // The smallest normal f has an exp2 of -1022 and a mantissa of (1 << 52).
- // Subnormal numbers have the same exp2 but a smaller mantissa.
- static const int32_t min_incl_normal_exp2 = -1022;
- static const uint64_t min_incl_normal_mantissa = 0x0010000000000000ul;
-
- // Compute lower and upper bounds such that any number between them (possibly
- // inclusive) will round to f. First, the lower bound. Our number f is:
- // ((mantissa + 0) * (2 ** ( exp2 - 52)))
- //
- // The next lowest floating point number is:
- // ((mantissa - 1) * (2 ** ( exp2 - 52)))
- // unless (mantissa - 1) drops the (1 << 52) bit and exp2 is not the
- // min_incl_normal_exp2. Either way, call it:
- // ((l_mantissa) * (2 ** (l_exp2 - 52)))
- //
- // The lower bound is halfway between them (noting that 52 became 53):
- // (((2 * l_mantissa) + 1) * (2 ** (l_exp2 - 53)))
- int32_t l_exp2 = exp2;
- uint64_t l_mantissa = mantissa - 1;
- if ((exp2 > min_incl_normal_exp2) && (mantissa <= min_incl_normal_mantissa)) {
- l_exp2 = exp2 - 1;
- l_mantissa = (2 * mantissa) - 1;
- }
- wuffs_base__private_implementation__high_prec_dec lower;
- wuffs_base__private_implementation__high_prec_dec__assign(
- &lower, (2 * l_mantissa) + 1, false);
- wuffs_base__private_implementation__high_prec_dec__lshift(&lower,
- l_exp2 - 53);
-
- // Next, the upper bound. Our number f is:
- // ((mantissa + 0) * (2 ** (exp2 - 52)))
- //
- // The next highest floating point number is:
- // ((mantissa + 1) * (2 ** (exp2 - 52)))
- //
- // The upper bound is halfway between them (noting that 52 became 53):
- // (((2 * mantissa) + 1) * (2 ** (exp2 - 53)))
- wuffs_base__private_implementation__high_prec_dec upper;
- wuffs_base__private_implementation__high_prec_dec__assign(
- &upper, (2 * mantissa) + 1, false);
- wuffs_base__private_implementation__high_prec_dec__lshift(&upper, exp2 - 53);
-
- // The lower and upper bounds are possible outputs only if the original
- // mantissa is even, so that IEEE round-to-even would round to the original
- // mantissa and not its neighbors.
- bool inclusive = (mantissa & 1) == 0;
-
- // As we walk the digits, we want to know whether rounding up would fall
- // within the upper bound. This is tracked by upper_delta:
- // - When -1, the digits of h and upper are the same so far.
- // - When +0, we saw a difference of 1 between h and upper on a previous
- // digit and subsequently only 9s for h and 0s for upper. Thus, rounding
- // up may fall outside of the bound if !inclusive.
- // - When +1, the difference is greater than 1 and we know that rounding up
- // falls within the bound.
- //
- // This is a state machine with three states. The numerical value for each
- // state (-1, +0 or +1) isn't important, other than their order.
- int upper_delta = -1;
-
- // We can now figure out the shortest number of digits required. Walk the
- // digits until h has distinguished itself from lower or upper.
- //
- // The zi and zd variables are indexes and digits, for z in l (lower), h (the
- // number) and u (upper).
- //
- // The lower, h and upper numbers may have their decimal points at different
- // places. In this case, upper is the longest, so we iterate ui starting from
- // 0 and iterate li and hi starting from either 0 or -1.
- int32_t ui = 0;
- for (;; ui++) {
- // Calculate hd, the middle number's digit.
- int32_t hi = ui - upper.decimal_point + h->decimal_point;
- if (hi >= ((int32_t)(h->num_digits))) {
- break;
- }
- uint8_t hd = (((uint32_t)hi) < h->num_digits) ? h->digits[hi] : 0;
-
- // Calculate ld, the lower bound's digit.
- int32_t li = ui - upper.decimal_point + lower.decimal_point;
- uint8_t ld = (((uint32_t)li) < lower.num_digits) ? lower.digits[li] : 0;
-
- // We can round down (truncate) if lower has a different digit than h or if
- // lower is inclusive and is exactly the result of rounding down (i.e. we
- // have reached the final digit of lower).
- bool can_round_down =
- (ld != hd) || //
- (inclusive && ((li + 1) == ((int32_t)(lower.num_digits))));
-
- // Calculate ud, the upper bound's digit, and update upper_delta.
- uint8_t ud = (((uint32_t)ui) < upper.num_digits) ? upper.digits[ui] : 0;
- if (upper_delta < 0) {
- if ((hd + 1) < ud) {
- // For example:
- // h = 12345???
- // upper = 12347???
- upper_delta = +1;
- } else if (hd != ud) {
- // For example:
- // h = 12345???
- // upper = 12346???
- upper_delta = +0;
- }
- } else if (upper_delta == 0) {
- if ((hd != 9) || (ud != 0)) {
- // For example:
- // h = 1234598?
- // upper = 1234600?
- upper_delta = +1;
- }
- }
-
- // We can round up if upper has a different digit than h and either upper
- // is inclusive or upper is bigger than the result of rounding up.
- bool can_round_up =
- (upper_delta > 0) || //
- ((upper_delta == 0) && //
- (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));
-
- // If we can round either way, round to nearest. If we can round only one
- // way, do it. If we can't round, continue the loop.
- if (can_round_down) {
- if (can_round_up) {
- wuffs_base__private_implementation__high_prec_dec__round_nearest(
- h, hi + 1);
- return;
- } else {
- wuffs_base__private_implementation__high_prec_dec__round_down(h,
- hi + 1);
- return;
- }
- } else {
- if (can_round_up) {
- wuffs_base__private_implementation__high_prec_dec__round_up(h, hi + 1);
- return;
- }
- }
- }
-}
-
// --------
// wuffs_base__private_implementation__powers_of_10 contains truncated
@@ -10585,6 +9803,790 @@
1e12, 1e13, 1e14, 1e15, 1e16, 1e17, 1e18, 1e19, 1e20, 1e21, 1e22,
};
+// ---------------- IEEE 754 Floating Point
+
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE 2047
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION 800
+
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL is the largest N
+// such that ((10 << N) < (1 << 64)).
+#define WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL 60
+
+// wuffs_base__private_implementation__high_prec_dec (abbreviated as HPD) is a
+// fixed precision floating point decimal number, augmented with ±infinity
+// values, but it cannot represent NaN (Not a Number).
+//
+// "High precision" means that the mantissa holds 800 decimal digits. 800 is
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION.
+//
+// An HPD isn't for general purpose arithmetic, only for conversions to and
+// from IEEE 754 double-precision floating point, where the largest and
+// smallest positive, finite values are approximately 1.8e+308 and 4.9e-324.
+// HPD exponents above +2047 mean infinity, below -2047 mean zero. The ±2047
+// bounds are further away from zero than ±(324 + 800), where 800 and 2047 is
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION and
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+//
+// digits[.. num_digits] are the number's digits in big-endian order. The
+// uint8_t values are in the range [0 ..= 9], not ['0' ..= '9'], where e.g. '7'
+// is the ASCII value 0x37.
+//
+// decimal_point is the index (within digits) of the decimal point. It may be
+// negative or be larger than num_digits, in which case the explicit digits are
+// padded with implicit zeroes.
+//
+// For example, if num_digits is 3 and digits is "\x07\x08\x09":
+// - A decimal_point of -2 means ".00789"
+// - A decimal_point of -1 means ".0789"
+// - A decimal_point of +0 means ".789"
+// - A decimal_point of +1 means "7.89"
+// - A decimal_point of +2 means "78.9"
+// - A decimal_point of +3 means "789."
+// - A decimal_point of +4 means "7890."
+// - A decimal_point of +5 means "78900."
+//
+// As above, a decimal_point higher than +2047 means that the overall value is
+// infinity, lower than -2047 means zero.
+//
+// negative is a sign bit. An HPD can distinguish positive and negative zero.
+//
+// truncated is whether there are more than
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION digits, and at
+// least one of those extra digits are non-zero. The existence of long-tail
+// digits can affect rounding.
+//
+// The "all fields are zero" value is valid, and represents the number +0.
+typedef struct {
+ uint32_t num_digits;
+ int32_t decimal_point;
+ bool negative;
+ bool truncated;
+ uint8_t digits[WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION];
+} wuffs_base__private_implementation__high_prec_dec;
+
+// wuffs_base__private_implementation__high_prec_dec__trim trims trailing
+// zeroes from the h->digits[.. h->num_digits] slice. They have no benefit,
+// since we explicitly track h->decimal_point.
+//
+// Preconditions:
+// - h is non-NULL.
+static inline void //
+wuffs_base__private_implementation__high_prec_dec__trim(
+ wuffs_base__private_implementation__high_prec_dec* h) {
+ while ((h->num_digits > 0) && (h->digits[h->num_digits - 1] == 0)) {
+ h->num_digits--;
+ }
+}
+
+// wuffs_base__private_implementation__high_prec_dec__assign sets h to
+// represent the number x.
+//
+// Preconditions:
+// - h is non-NULL.
+static void //
+wuffs_base__private_implementation__high_prec_dec__assign(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint64_t x,
+ bool negative) {
+ uint32_t n = 0;
+
+ // Set h->digits.
+ if (x > 0) {
+ // Calculate the digits, working right-to-left. After we determine n (how
+ // many digits there are), copy from buf to h->digits.
+ //
+ // UINT64_MAX, 18446744073709551615, is 20 digits long. It can be faster to
+ // copy a constant number of bytes than a variable number (20 instead of
+ // n). Make buf large enough (and start writing to it from the middle) so
+ // that can we always copy 20 bytes: the slice buf[(20-n) .. (40-n)].
+ uint8_t buf[40] = {0};
+ uint8_t* ptr = &buf[20];
+ do {
+ uint64_t remaining = x / 10;
+ x -= remaining * 10;
+ ptr--;
+ *ptr = (uint8_t)x;
+ n++;
+ x = remaining;
+ } while (x > 0);
+ memcpy(h->digits, ptr, 20);
+ }
+
+ // Set h's other fields.
+ h->num_digits = n;
+ h->decimal_point = (int32_t)n;
+ h->negative = negative;
+ h->truncated = false;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static wuffs_base__status //
+wuffs_base__private_implementation__high_prec_dec__parse(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ wuffs_base__slice_u8 s) {
+ if (!h) {
+ return wuffs_base__make_status(wuffs_base__error__bad_receiver);
+ }
+ h->num_digits = 0;
+ h->decimal_point = 0;
+ h->negative = false;
+ h->truncated = false;
+
+ uint8_t* p = s.ptr;
+ uint8_t* q = s.ptr + s.len;
+
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+
+ // Parse sign.
+ do {
+ if (*p == '+') {
+ p++;
+ } else if (*p == '-') {
+ h->negative = true;
+ p++;
+ } else {
+ break;
+ }
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+ } while (0);
+
+ // Parse digits, up to (and including) a '.', 'E' or 'e'. Examples for each
+ // limb in this if-else chain:
+ // - "0.789"
+ // - "1002.789"
+ // - ".789"
+ // - Other (invalid input).
+ uint32_t nd = 0;
+ int32_t dp = 0;
+ bool no_digits_before_separator = false;
+ if ('0' == *p) {
+ p++;
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ goto after_sep;
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+ } else if (('0' < *p) && (*p <= '9')) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ dp = (int32_t)nd;
+ p++;
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if (('0' <= *p) && (*p <= '9')) {
+ if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ dp = (int32_t)nd;
+ } else if ('0' != *p) {
+ // Long-tail non-zeroes set the truncated bit.
+ h->truncated = true;
+ }
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ goto after_sep;
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+ } else if ((*p == '.') || (*p == ',')) {
+ p++;
+ no_digits_before_separator = true;
+
+ } else {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+
+after_sep:
+ for (;; p++) {
+ if (p >= q) {
+ goto after_all;
+ } else if ('0' == *p) {
+ if (nd == 0) {
+ // Track leading zeroes implicitly.
+ dp--;
+ } else if (nd <
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ }
+ } else if (('0' < *p) && (*p <= '9')) {
+ if (nd < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[nd++] = (uint8_t)(*p - '0');
+ } else {
+ // Long-tail non-zeroes set the truncated bit.
+ h->truncated = true;
+ }
+ } else if ((*p == 'E') || (*p == 'e')) {
+ p++;
+ goto after_exp;
+ } else if (*p != '_') {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ }
+
+after_exp:
+ do {
+ for (;; p++) {
+ if (p >= q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ } else if (*p != '_') {
+ break;
+ }
+ }
+
+ int32_t exp_sign = +1;
+ if (*p == '+') {
+ p++;
+ } else if (*p == '-') {
+ exp_sign = -1;
+ p++;
+ }
+
+ int32_t exp = 0;
+ const int32_t exp_large =
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE +
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
+ bool saw_exp_digits = false;
+ for (; p < q; p++) {
+ if (*p == '_') {
+ // No-op.
+ } else if (('0' <= *p) && (*p <= '9')) {
+ saw_exp_digits = true;
+ if (exp < exp_large) {
+ exp = (10 * exp) + ((int32_t)(*p - '0'));
+ }
+ } else {
+ break;
+ }
+ }
+ if (!saw_exp_digits) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ dp += exp_sign * exp;
+ } while (0);
+
+after_all:
+ if (p != q) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ h->num_digits = nd;
+ if (nd == 0) {
+ if (no_digits_before_separator) {
+ return wuffs_base__make_status(wuffs_base__error__bad_argument);
+ }
+ h->decimal_point = 0;
+ } else if (dp <
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ h->decimal_point =
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE - 1;
+ } else if (dp >
+ +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ h->decimal_point =
+ +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE + 1;
+ } else {
+ h->decimal_point = dp;
+ }
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+ return wuffs_base__make_status(NULL);
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
+// returns the number of additional decimal digits when left-shifting by shift.
+//
+// See below for preconditions.
+static uint32_t //
+wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ // Masking with 0x3F should be unnecessary (assuming the preconditions) but
+ // it's cheap and ensures that we don't overflow the
+ // wuffs_base__private_implementation__hpd_left_shift array.
+ shift &= 63;
+
+ uint32_t x_a = wuffs_base__private_implementation__hpd_left_shift[shift];
+ uint32_t x_b = wuffs_base__private_implementation__hpd_left_shift[shift + 1];
+ uint32_t num_new_digits = x_a >> 11;
+ uint32_t pow5_a = 0x7FF & x_a;
+ uint32_t pow5_b = 0x7FF & x_b;
+
+ const uint8_t* pow5 =
+ &wuffs_base__private_implementation__powers_of_5[pow5_a];
+ uint32_t i = 0;
+ uint32_t n = pow5_b - pow5_a;
+ for (; i < n; i++) {
+ if (i >= h->num_digits) {
+ return num_new_digits - 1;
+ } else if (h->digits[i] == pow5[i]) {
+ continue;
+ } else if (h->digits[i] < pow5[i]) {
+ return num_new_digits - 1;
+ } else {
+ return num_new_digits;
+ }
+ }
+ return num_new_digits;
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__rounded_integer returns
+// the integral (non-fractional) part of h, provided that it is 18 or fewer
+// decimal digits. For 19 or more digits, it returns UINT64_MAX. Note that:
+// - (1 << 53) is 9007199254740992, which has 16 decimal digits.
+// - (1 << 56) is 72057594037927936, which has 17 decimal digits.
+// - (1 << 59) is 576460752303423488, which has 18 decimal digits.
+// - (1 << 63) is 9223372036854775808, which has 19 decimal digits.
+// and that IEEE 754 double precision has 52 mantissa bits.
+//
+// That integral part is rounded-to-even: rounding 7.5 or 8.5 both give 8.
+//
+// h's negative bit is ignored: rounding -8.6 returns 9.
+//
+// See below for preconditions.
+static uint64_t //
+wuffs_base__private_implementation__high_prec_dec__rounded_integer(
+ wuffs_base__private_implementation__high_prec_dec* h) {
+ if ((h->num_digits == 0) || (h->decimal_point < 0)) {
+ return 0;
+ } else if (h->decimal_point > 18) {
+ return UINT64_MAX;
+ }
+
+ uint32_t dp = (uint32_t)(h->decimal_point);
+ uint64_t n = 0;
+ uint32_t i = 0;
+ for (; i < dp; i++) {
+ n = (10 * n) + ((i < h->num_digits) ? h->digits[i] : 0);
+ }
+
+ bool round_up = false;
+ if (dp < h->num_digits) {
+ round_up = h->digits[dp] >= 5;
+ if ((h->digits[dp] == 5) && (dp + 1 == h->num_digits)) {
+ // We are exactly halfway. If we're truncated, round up, otherwise round
+ // to even.
+ round_up = h->truncated || //
+ ((dp > 0) && (1 & h->digits[dp - 1]));
+ }
+ }
+ if (round_up) {
+ n++;
+ }
+
+ return n;
+}
+
+// wuffs_base__private_implementation__high_prec_dec__small_xshift shifts h's
+// number (where 'x' is 'l' or 'r' for left or right) by a small shift value.
+//
+// Preconditions:
+// - h is non-NULL.
+// - h->decimal_point is "not extreme".
+// - shift is non-zero.
+// - shift is "a small shift".
+//
+// "Not extreme" means within
+// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+//
+// "A small shift" means not more than
+// WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL.
+//
+// wuffs_base__private_implementation__high_prec_dec__rounded_integer and
+// wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits
+// have the same preconditions.
+//
+// wuffs_base__private_implementation__high_prec_dec__lshift keeps the first
+// two preconditions but not the last two. Its shift argument is signed and
+// does not need to be "small": zero is a no-op, positive means left shift and
+// negative means right shift.
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ if (h->num_digits == 0) {
+ return;
+ }
+ uint32_t num_new_digits =
+ wuffs_base__private_implementation__high_prec_dec__lshift_num_new_digits(
+ h, shift);
+ uint32_t rx = h->num_digits - 1; // Read index.
+ uint32_t wx = h->num_digits - 1 + num_new_digits; // Write index.
+ uint64_t n = 0;
+
+ // Repeat: pick up a digit, put down a digit, right to left.
+ while (((int32_t)rx) >= 0) {
+ n += ((uint64_t)(h->digits[rx])) << shift;
+ uint64_t quo = n / 10;
+ uint64_t rem = n - (10 * quo);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx] = (uint8_t)rem;
+ } else if (rem > 0) {
+ h->truncated = true;
+ }
+ n = quo;
+ wx--;
+ rx--;
+ }
+
+ // Put down leading digits, right to left.
+ while (n > 0) {
+ uint64_t quo = n / 10;
+ uint64_t rem = n - (10 * quo);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx] = (uint8_t)rem;
+ } else if (rem > 0) {
+ h->truncated = true;
+ }
+ n = quo;
+ wx--;
+ }
+
+ // Finish.
+ h->num_digits += num_new_digits;
+ if (h->num_digits >
+ WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->num_digits = WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION;
+ }
+ h->decimal_point += (int32_t)num_new_digits;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ uint32_t shift) {
+ uint32_t rx = 0; // Read index.
+ uint32_t wx = 0; // Write index.
+ uint64_t n = 0;
+
+ // Pick up enough leading digits to cover the first shift.
+ while ((n >> shift) == 0) {
+ if (rx < h->num_digits) {
+ // Read a digit.
+ n = (10 * n) + h->digits[rx++];
+ } else if (n == 0) {
+ // h's number used to be zero and remains zero.
+ return;
+ } else {
+ // Read sufficient implicit trailing zeroes.
+ while ((n >> shift) == 0) {
+ n = 10 * n;
+ rx++;
+ }
+ break;
+ }
+ }
+ h->decimal_point -= ((int32_t)(rx - 1));
+ if (h->decimal_point <
+ -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE) {
+ // After the shift, h's number is effectively zero.
+ h->num_digits = 0;
+ h->decimal_point = 0;
+ h->negative = false;
+ h->truncated = false;
+ return;
+ }
+
+ // Repeat: pick up a digit, put down a digit, left to right.
+ uint64_t mask = (((uint64_t)(1)) << shift) - 1;
+ while (rx < h->num_digits) {
+ uint8_t new_digit = ((uint8_t)(n >> shift));
+ n = (10 * (n & mask)) + h->digits[rx++];
+ h->digits[wx++] = new_digit;
+ }
+
+ // Put down trailing digits, left to right.
+ while (n > 0) {
+ uint8_t new_digit = ((uint8_t)(n >> shift));
+ n = 10 * (n & mask);
+ if (wx < WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
+ h->digits[wx++] = new_digit;
+ } else if (new_digit > 0) {
+ h->truncated = true;
+ }
+ }
+
+ // Finish.
+ h->num_digits = wx;
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__lshift(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t shift) {
+ if (shift > 0) {
+ while (shift > +WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
+ shift -= WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+ wuffs_base__private_implementation__high_prec_dec__small_lshift(
+ h, ((uint32_t)(+shift)));
+ } else if (shift < 0) {
+ while (shift < -WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL) {
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ h, WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL);
+ shift += WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__SHIFT__MAX_INCL;
+ }
+ wuffs_base__private_implementation__high_prec_dec__small_rshift(
+ h, ((uint32_t)(-shift)));
+ }
+}
+
+// --------
+
+// wuffs_base__private_implementation__high_prec_dec__round_etc rounds h's
+// number. For those functions that take an n argument, rounding produces at
+// most n digits (which is not necessarily at most n decimal places). Negative
+// n values are ignored, as well as any n greater than or equal to h's number
+// of digits. The etc__round_just_enough function implicitly chooses an n to
+// implement WUFFS_BASE__RENDER_NUMBER_FXX__JUST_ENOUGH_PRECISION.
+//
+// Preconditions:
+// - h is non-NULL.
+// - h->decimal_point is "not extreme".
+//
+// "Not extreme" means within
+// ±WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DECIMAL_POINT__RANGE.
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_down(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+ h->num_digits = (uint32_t)(n);
+ wuffs_base__private_implementation__high_prec_dec__trim(h);
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_up(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+
+ for (n--; n >= 0; n--) {
+ if (h->digits[n] < 9) {
+ h->digits[n]++;
+ h->num_digits = (uint32_t)(n + 1);
+ return;
+ }
+ }
+
+ // The number is all 9s. Change to a single 1 and adjust the decimal point.
+ h->digits[0] = 1;
+ h->num_digits = 1;
+ h->decimal_point++;
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t n) {
+ if ((n < 0) || (h->num_digits <= (uint32_t)n)) {
+ return;
+ }
+ bool up = h->digits[n] >= 5;
+ if ((h->digits[n] == 5) && ((n + 1) == ((int32_t)(h->num_digits)))) {
+ up = h->truncated || //
+ ((n > 0) && ((h->digits[n - 1] & 1) != 0));
+ }
+
+ if (up) {
+ wuffs_base__private_implementation__high_prec_dec__round_up(h, n);
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_down(h, n);
+ }
+}
+
+static void //
+wuffs_base__private_implementation__high_prec_dec__round_just_enough(
+ wuffs_base__private_implementation__high_prec_dec* h,
+ int32_t exp2,
+ uint64_t mantissa) {
+ // The magic numbers 52 and 53 in this function are because IEEE 754 double
+ // precision has 52 mantissa bits.
+ //
+ // Let f be the floating point number represented by exp2 and mantissa (and
+ // also the number in h): the number (mantissa * (2 ** (exp2 - 52))).
+ //
+ // If f is zero or a small integer, we can return early.
+ if ((mantissa == 0) ||
+ ((exp2 < 53) && (h->decimal_point >= ((int32_t)(h->num_digits))))) {
+ return;
+ }
+
+ // The smallest normal f has an exp2 of -1022 and a mantissa of (1 << 52).
+ // Subnormal numbers have the same exp2 but a smaller mantissa.
+ static const int32_t min_incl_normal_exp2 = -1022;
+ static const uint64_t min_incl_normal_mantissa = 0x0010000000000000ul;
+
+ // Compute lower and upper bounds such that any number between them (possibly
+ // inclusive) will round to f. First, the lower bound. Our number f is:
+ // ((mantissa + 0) * (2 ** ( exp2 - 52)))
+ //
+ // The next lowest floating point number is:
+ // ((mantissa - 1) * (2 ** ( exp2 - 52)))
+ // unless (mantissa - 1) drops the (1 << 52) bit and exp2 is not the
+ // min_incl_normal_exp2. Either way, call it:
+ // ((l_mantissa) * (2 ** (l_exp2 - 52)))
+ //
+ // The lower bound is halfway between them (noting that 52 became 53):
+ // (((2 * l_mantissa) + 1) * (2 ** (l_exp2 - 53)))
+ int32_t l_exp2 = exp2;
+ uint64_t l_mantissa = mantissa - 1;
+ if ((exp2 > min_incl_normal_exp2) && (mantissa <= min_incl_normal_mantissa)) {
+ l_exp2 = exp2 - 1;
+ l_mantissa = (2 * mantissa) - 1;
+ }
+ wuffs_base__private_implementation__high_prec_dec lower;
+ wuffs_base__private_implementation__high_prec_dec__assign(
+ &lower, (2 * l_mantissa) + 1, false);
+ wuffs_base__private_implementation__high_prec_dec__lshift(&lower,
+ l_exp2 - 53);
+
+ // Next, the upper bound. Our number f is:
+ // ((mantissa + 0) * (2 ** (exp2 - 52)))
+ //
+ // The next highest floating point number is:
+ // ((mantissa + 1) * (2 ** (exp2 - 52)))
+ //
+ // The upper bound is halfway between them (noting that 52 became 53):
+ // (((2 * mantissa) + 1) * (2 ** (exp2 - 53)))
+ wuffs_base__private_implementation__high_prec_dec upper;
+ wuffs_base__private_implementation__high_prec_dec__assign(
+ &upper, (2 * mantissa) + 1, false);
+ wuffs_base__private_implementation__high_prec_dec__lshift(&upper, exp2 - 53);
+
+ // The lower and upper bounds are possible outputs only if the original
+ // mantissa is even, so that IEEE round-to-even would round to the original
+ // mantissa and not its neighbors.
+ bool inclusive = (mantissa & 1) == 0;
+
+ // As we walk the digits, we want to know whether rounding up would fall
+ // within the upper bound. This is tracked by upper_delta:
+ // - When -1, the digits of h and upper are the same so far.
+ // - When +0, we saw a difference of 1 between h and upper on a previous
+ // digit and subsequently only 9s for h and 0s for upper. Thus, rounding
+ // up may fall outside of the bound if !inclusive.
+ // - When +1, the difference is greater than 1 and we know that rounding up
+ // falls within the bound.
+ //
+ // This is a state machine with three states. The numerical value for each
+ // state (-1, +0 or +1) isn't important, other than their order.
+ int upper_delta = -1;
+
+ // We can now figure out the shortest number of digits required. Walk the
+ // digits until h has distinguished itself from lower or upper.
+ //
+ // The zi and zd variables are indexes and digits, for z in l (lower), h (the
+ // number) and u (upper).
+ //
+ // The lower, h and upper numbers may have their decimal points at different
+ // places. In this case, upper is the longest, so we iterate ui starting from
+ // 0 and iterate li and hi starting from either 0 or -1.
+ int32_t ui = 0;
+ for (;; ui++) {
+ // Calculate hd, the middle number's digit.
+ int32_t hi = ui - upper.decimal_point + h->decimal_point;
+ if (hi >= ((int32_t)(h->num_digits))) {
+ break;
+ }
+ uint8_t hd = (((uint32_t)hi) < h->num_digits) ? h->digits[hi] : 0;
+
+ // Calculate ld, the lower bound's digit.
+ int32_t li = ui - upper.decimal_point + lower.decimal_point;
+ uint8_t ld = (((uint32_t)li) < lower.num_digits) ? lower.digits[li] : 0;
+
+ // We can round down (truncate) if lower has a different digit than h or if
+ // lower is inclusive and is exactly the result of rounding down (i.e. we
+ // have reached the final digit of lower).
+ bool can_round_down =
+ (ld != hd) || //
+ (inclusive && ((li + 1) == ((int32_t)(lower.num_digits))));
+
+ // Calculate ud, the upper bound's digit, and update upper_delta.
+ uint8_t ud = (((uint32_t)ui) < upper.num_digits) ? upper.digits[ui] : 0;
+ if (upper_delta < 0) {
+ if ((hd + 1) < ud) {
+ // For example:
+ // h = 12345???
+ // upper = 12347???
+ upper_delta = +1;
+ } else if (hd != ud) {
+ // For example:
+ // h = 12345???
+ // upper = 12346???
+ upper_delta = +0;
+ }
+ } else if (upper_delta == 0) {
+ if ((hd != 9) || (ud != 0)) {
+ // For example:
+ // h = 1234598?
+ // upper = 1234600?
+ upper_delta = +1;
+ }
+ }
+
+ // We can round up if upper has a different digit than h and either upper
+ // is inclusive or upper is bigger than the result of rounding up.
+ bool can_round_up =
+ (upper_delta > 0) || //
+ ((upper_delta == 0) && //
+ (inclusive || ((ui + 1) < ((int32_t)(upper.num_digits)))));
+
+ // If we can round either way, round to nearest. If we can round only one
+ // way, do it. If we can't round, continue the loop.
+ if (can_round_down) {
+ if (can_round_up) {
+ wuffs_base__private_implementation__high_prec_dec__round_nearest(
+ h, hi + 1);
+ return;
+ } else {
+ wuffs_base__private_implementation__high_prec_dec__round_down(h,
+ hi + 1);
+ return;
+ }
+ } else {
+ if (can_round_up) {
+ wuffs_base__private_implementation__high_prec_dec__round_up(h, hi + 1);
+ return;
+ }
+ }
+ }
+}
+
// --------
// wuffs_base__private_implementation__parse_number_f64_eisel produces the IEEE
