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