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skia / external / github.com / google / wuffs / 177aa7f0c6f9813be098e27ab98c072445abcf8b / . / internal / cgen / base / f64conv-submodule.c
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// 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;
}
}
}
}
// --------
// The wuffs_base__private_implementation__etc_powers_of_10 tables were printed
// by script/print-mpb-powers-of-10.go. That script has an optional -detail
// flag, whose output is not copied here, which prints further detail.
//
// These tables are used in
// wuffs_base__private_implementation__medium_prec_bin__assign_from_hpd.
// 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.
//
// 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))
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__medium_prec_bin (abbreviated as MPB) is
// a fixed precision floating point binary number. Unlike IEEE 754 Floating
// Point, it cannot represent infinity or NaN (Not a Number).
//
// "Medium precision" means that the mantissa holds 64 binary digits, a little
// more than "double precision", and sizeof(MPB) > sizeof(double). 64 is
// obviously the number of bits in a uint64_t.
//
// An MPB isn't for general purpose arithmetic, only for conversions to and
// from IEEE 754 double-precision floating point.
//
// There is no implicit mantissa bit. The mantissa field is zero if and only if
// the overall floating point value is ±0. An MPB is normalized if the mantissa
// is zero or its high bit (the 1<<63 bit) is set.
//
// There is no negative bit. An MPB can only represent non-negative numbers.
//
// The "all fields are zero" value is valid, and represents the number +0.
//
// This is the "Do It Yourself Floating Point" data structure from Loitsch,
// "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
typedef struct {
uint64_t mantissa;
int32_t exp2;
} wuffs_base__private_implementation__medium_prec_bin;
static uint32_t //
wuffs_base__private_implementation__medium_prec_bin__normalize(
wuffs_base__private_implementation__medium_prec_bin* m) {
if (m->mantissa == 0) {
return 0;
}
uint32_t shift = wuffs_base__count_leading_zeroes_u64(m->mantissa);
m->mantissa <<= shift;
m->exp2 -= (int32_t)shift;
return shift;
}
// wuffs_base__private_implementation__medium_prec_bin__mul_pow_10 sets m to be
// (m * pow), where pow comes from an etc__powers_of_10 triple starting at p.
//
// The result is rounded, but not necessarily normalized.
//
// Preconditions:
// - m is non-NULL.
// - m->mantissa is non-zero.
// - m->mantissa's high bit is set (i.e. m is normalized).
//
// The etc__powers_of_10 triple is already normalized.
static void //
wuffs_base__private_implementation__medium_prec_bin__mul_pow_10(
wuffs_base__private_implementation__medium_prec_bin* m,
const uint32_t* p) {
uint64_t p_mantissa = ((uint64_t)p[2]) | (((uint64_t)p[3]) << 32);
int32_t p_exp2 = (int32_t)p[4];
wuffs_base__multiply_u64__output o =
wuffs_base__multiply_u64(m->mantissa, p_mantissa);
// Round the mantissa up. It cannot overflow because the maximum possible
// value of o.hi is 0xFFFFFFFFFFFFFFFE.
m->mantissa = o.hi + (o.lo >> 63);
m->exp2 = m->exp2 + p_exp2 + 128 - 1214;
}
// wuffs_base__private_implementation__medium_prec_bin__as_f64 converts m to a
// double (what C calls a double-precision float64).
//
// Preconditions:
// - m is non-NULL.
// - m->mantissa is non-zero.
// - m->mantissa's high bit is set (i.e. m is normalized).
static double //
wuffs_base__private_implementation__medium_prec_bin__as_f64(
const wuffs_base__private_implementation__medium_prec_bin* m,
bool negative) {
uint64_t mantissa64 = m->mantissa;
// An mpb's mantissa has the implicit (binary) decimal point at the right
// hand end of the mantissa's explicit digits. A double-precision's mantissa
// has that decimal point near the left hand end. There's also an explicit
// versus implicit leading 1 bit (binary digit). Together, the difference in
// semantics corresponds to adding 63.
int32_t exp2 = m->exp2 + 63;
// Ensure that exp2 is at least -1022, the minimum double-precision exponent
// for normal (as opposed to subnormal) numbers.
if (-1022 > exp2) {
uint32_t n = (uint32_t)(-1022 - exp2);
mantissa64 >>= n;
exp2 += (int32_t)n;
}
// Extract the (1 + 52) bits from the 64-bit mantissa64. 52 is the number of
// explicit mantissa bits in a double-precision f64.
//
// Before, we have 64 bits and due to normalization, the high bit 'H' is 1.
// 63 55 47 etc 15 7
// H210_9876_5432_1098_7654_etc_etc_etc_5432_1098_7654_3210
// ++++_++++_++++_++++_++++_etc_etc_etc_++++_+..._...._.... Kept bits.
// ...._...._...H_2109_8765_etc_etc_etc_6543_2109_8765_4321 After shifting.
// After, we have 53 bits (and bit #52 is this 'H' bit).
uint64_t mantissa53 = mantissa64 >> 11;
// Round up if the old bit #10 (the highest bit dropped by shifting) was set.
// We also fix any overflow from rounding up.
if (mantissa64 & 1024) {
mantissa53++;
if ((mantissa53 >> 53) != 0) {
mantissa53 >>= 1;
exp2++;
}
}
// Handle double-precision infinity (a nominal exponent of 1024) and
// subnormals (an exponent of -1023 and no implicit mantissa bit, bit #52).
if (exp2 >= 1024) {
mantissa53 = 0;
exp2 = 1024;
} else if ((mantissa53 >> 52) == 0) {
exp2 = -1023;
}
// Pack the bits and return.
const int32_t f64_bias = -1023;
uint64_t exp2_bits =
(uint64_t)((exp2 - f64_bias) & 0x07FF); // (1 << 11) - 1.
uint64_t bits = (mantissa53 & 0x000FFFFFFFFFFFFF) | // (1 << 52) - 1.
(exp2_bits << 52) | //
(negative ? 0x8000000000000000 : 0); // (1 << 63).
return wuffs_base__ieee_754_bit_representation__to_f64(bits);
}
// wuffs_base__private_implementation__medium_prec_bin__parse_number_f64
// converts from an HPD to a double, using an MPB as scratch space. It returns
// a NULL status.repr if there is no ambiguity in the truncation or rounding to
// a float64 (an IEEE 754 double-precision floating point value).
//
// It may modify m even if it returns a non-NULL status.repr.
static wuffs_base__result_f64 //
wuffs_base__private_implementation__medium_prec_bin__parse_number_f64(
wuffs_base__private_implementation__medium_prec_bin* m,
const wuffs_base__private_implementation__high_prec_dec* h,
bool skip_fast_path_for_tests) {
do {
// m->mantissa is a uint64_t, which is an integer approximation to a
// rational value - h's underlying digits after m's normalization. This
// error is an upper bound on the difference between the approximate and
// actual value.
//
// The DiyFpStrtod function in https://github.com/google/double-conversion
// uses a finer grain (1/8th of the ULP, Unit in the Last Place) when
// tracking error. This implementation is coarser (1 ULP) but simpler.
//
// It is an error in the "numerical approximation" sense, not in the
// typical programming sense (as in "bad input" or "a result type").
uint64_t error = 0;
// Convert up to 19 decimal digits (in h->digits) to 64 binary digits (in
// m->mantissa): (1e19 < (1<<64)) and ((1<<64) < 1e20). If we have more
// than 19 digits, we're truncating (with error).
uint32_t i;
uint32_t i_end = h->num_digits;
if (i_end > 19) {
i_end = 19;
error = 1;
}
uint64_t mantissa = 0;
for (i = 0; i < i_end; i++) {
mantissa = (10 * mantissa) + h->digits[i];
}
m->mantissa = mantissa;
m->exp2 = 0;
// Check that exp10 lies in the etc__powers_of_10 range (637 triples).
int32_t exp10 = h->decimal_point - ((int32_t)(i_end));
if ((exp10 < -326) || (+310 < exp10)) {
goto fail;
}
// Try a fast path, if float64 math would be exact.
//
// 15 is such that 1e15 can be losslessly represented in a float64
// mantissa: (1e15 < (1<<53)) and ((1<<53) < 1e16).
//
// 22 is the maximum valid index for the
// wuffs_base__private_implementation__f64_powers_of_10 array.
do {
if (skip_fast_path_for_tests || ((mantissa >> 52) != 0)) {
break;
}
double d = (double)mantissa;
if (exp10 == 0) {
wuffs_base__result_f64 ret;
ret.status.repr = NULL;
ret.value = h->negative ? -d : +d;
return ret;
} else if (exp10 > 0) {
if (exp10 > 22) {
if (exp10 > (15 + 22)) {
break;
}
// If exp10 is in the range 23 ..= 37, try moving a few of the zeroes
// from the exponent to the mantissa. If we're still under 1e15, we
// haven't truncated any mantissa bits.
d *= wuffs_base__private_implementation__f64_powers_of_10[exp10 - 22];
exp10 = 22;
if (d >= 1e15) {
break;
}
}
d *= wuffs_base__private_implementation__f64_powers_of_10[exp10];
wuffs_base__result_f64 ret;
ret.status.repr = NULL;
ret.value = h->negative ? -d : +d;
return ret;
} else { // "if (exp10 < 0)" is effectively "if (true)" here.
if (exp10 < -22) {
break;
}
d /= wuffs_base__private_implementation__f64_powers_of_10[-exp10];
wuffs_base__result_f64 ret;
ret.status.repr = NULL;
ret.value = h->negative ? -d : +d;
return ret;
}
} while (0);
// Normalize (and scale the error).
error <<= wuffs_base__private_implementation__medium_prec_bin__normalize(m);
// Multiplying two MPB values nominally multiplies two mantissas, call them
// A and B, which are integer approximations to the precise values (A+a)
// and (B+b) for some error terms a and b.
//
// MPB multiplication calculates (((A+a) * (B+b)) >> 64) to be ((A*B) >>
// 64). Shifting (truncating) and rounding introduces further error. The
// difference between the calculated result:
// ((A*B ) >> 64)
// and the true result:
// ((A*B + A*b + a*B + a*b) >> 64) + rounding_error
// is:
// (( A*b + a*B + a*b) >> 64) + rounding_error
// which can be re-grouped as:
// ((A*b) >> 64) + ((a*(B+b)) >> 64) + rounding_error
//
// Now, let A and a be "m->mantissa" and "error", and B and b be the
// pre-calculated power of 10. A and B are both less than (1 << 64), a is
// the "error" local variable and b is less than 1.
//
// An upper bound (in absolute value) on ((A*b) >> 64) is therefore 1.
//
// An upper bound on ((a*(B+b)) >> 64) is a, also known as error.
//
// Finally, the rounding_error is at most 1.
//
// In total, calling mpb__mul_pow_10 will raise the worst-case error by 2.
// The subsequent re-normalization can multiply that by a further factor.
// Multiply by powers_of_10[etc].
wuffs_base__private_implementation__medium_prec_bin__mul_pow_10(
m,
&wuffs_base__private_implementation__powers_of_10[5 * (exp10 + 326)]);
error += 2;
error <<= wuffs_base__private_implementation__medium_prec_bin__normalize(m);
// We have a good approximation of h, but we still have to check whether
// the error is small enough. Equivalently, whether the number of surplus
// mantissa bits (the bits dropped when going from m's 64 mantissa bits to
// the smaller number of double-precision mantissa bits) would always round
// up or down, even when perturbed by ±error. We start at 11 surplus bits
// (m has 64, double-precision has 1+52), but it can be higher for
// subnormals.
//
// In many cases, the error is small enough and we return true.
const int32_t f64_bias = -1023;
int32_t subnormal_exp2 = f64_bias - 63;
uint32_t surplus_bits = 11;
if (subnormal_exp2 >= m->exp2) {
surplus_bits += 1 + ((uint32_t)(subnormal_exp2 - m->exp2));
}
uint64_t surplus_mask =
(((uint64_t)1) << surplus_bits) - 1; // e.g. 0x07FF.
uint64_t surplus = m->mantissa & surplus_mask;
uint64_t halfway = ((uint64_t)1) << (surplus_bits - 1); // e.g. 0x0400.
// Do the final calculation in *signed* arithmetic.
int64_t i_surplus = (int64_t)surplus;
int64_t i_halfway = (int64_t)halfway;
int64_t i_error = (int64_t)error;
if ((i_surplus > (i_halfway - i_error)) &&
(i_surplus < (i_halfway + i_error))) {
goto fail;
}
wuffs_base__result_f64 ret;
ret.status.repr = NULL;
ret.value = wuffs_base__private_implementation__medium_prec_bin__as_f64(
m, h->negative);
return ret;
} while (0);
fail:
do {
wuffs_base__result_f64 ret;
ret.status.repr = "#base: mpb__parse_number_f64 failed";
ret.value = 0;
return ret;
} while (0);
}
// --------
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__parse_number_f64(wuffs_base__slice_u8 s) {
wuffs_base__private_implementation__medium_prec_bin m;
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, //
};
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);
}
// 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;
}
wuffs_base__result_f64 mpb_result =
wuffs_base__private_implementation__medium_prec_bin__parse_number_f64(
&m, &h, false);
if (mpb_result.status.repr == NULL) {
return mpb_result;
}
// 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 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);
}