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skia / external / github.com / google / wuffs / 53da68fe4b9a0ec618410754ea2efc577cace526 / . / 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 < q) && (*p == '_'); p++) {
}
if (p >= q) {
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
// Parse sign.
do {
if (*p == '+') {
p++;
} else if (*p == '-') {
h->negative = true;
p++;
} else {
break;
}
for (; (p < q) && (*p == '_'); p++) {
}
} while (0);
// Parse digits.
uint32_t nd = 0;
int32_t dp = 0;
bool saw_digits = false;
bool saw_non_zero_digits = false;
bool saw_dot = false;
for (; p < q; p++) {
if (*p == '_') {
// No-op.
} else if ((*p == '.') || (*p == ',')) {
// As per https://en.wikipedia.org/wiki/Decimal_separator, both '.' or
// ',' are commonly used. We just parse either, regardless of LOCALE.
if (saw_dot) {
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
saw_dot = true;
dp = (int32_t)nd;
} else if ('0' == *p) {
if (!saw_dot && !saw_non_zero_digits && saw_digits) {
// We don't allow unnecessary leading zeroes: "000123" or "0644".
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
saw_digits = true;
if (nd == 0) {
// Track leading zeroes implicitly.
dp--;
} else if (nd <
WUFFS_BASE__PRIVATE_IMPLEMENTATION__HPD__DIGITS_PRECISION) {
h->digits[nd++] = 0;
} else {
// Long-tail zeroes are ignored.
}
} else if (('0' < *p) && (*p <= '9')) {
if (!saw_dot && !saw_non_zero_digits && saw_digits) {
// We don't allow unnecessary leading zeroes: "000123" or "0644".
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
saw_digits = true;
saw_non_zero_digits = true;
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 {
break;
}
}
if (!saw_digits) {
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
if (!saw_dot) {
dp = (int32_t)nd;
}
// Parse exponent.
if ((p < q) && ((*p == 'E') || (*p == 'e'))) {
p++;
for (; (p < q) && (*p == '_'); p++) {
}
if (p >= q) {
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
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;
}
// Finish.
if (p != q) {
return wuffs_base__make_status(wuffs_base__error__bad_argument);
}
h->num_digits = nd;
if (nd == 0) {
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 approximations to
// the powers of 10, ranging from 1e-326 to 1e+310 inclusive, as 637 uint32_t
// triples (64-bit mantissa, 32-bit base-2 exponent), 637 * 3 = 1911.
//
// For example, the third approximation, for 1e-324, consists of the uint32_t
// triple (0x5DCE35EA, 0xCF42894A, 0xFFFFFB8C). The first two of that triple
// are a little-endian uint64_t value: 0xCF42894A5DCE35EA. The last one is an
// int32_t value: -1140. Together, they represent the approximation:
// 1e-324 ≈ 0xCF42894A5DCE35EA * (2 ** -1140)
// Similarly, the (0x00000000, 0x9C400000, 0xFFFFFFCE) uint32_t triple means:
// 1e+4 ≈ 0x9C40000000000000 * (2 ** -50) // This approx'n is exact.
// Similarly, the (0xD4C4FB27, 0xED63A231, 0x000000A2) uint32_t triple means:
// 1e+68 ≈ 0xED63A231D4C4FB27 * (2 ** 162)
static const uint32_t wuffs_base__private_implementation__powers_of_10[1911] = {
0xFE98746D, 0x84A57695, 0xFFFFFB86, // 1e-326
0x7E3E9188, 0xA5CED43B, 0xFFFFFB89, // 1e-325
0x5DCE35EA, 0xCF42894A, 0xFFFFFB8C, // 1e-324
0x7AA0E1B2, 0x818995CE, 0xFFFFFB90, // 1e-323
0x19491A1F, 0xA1EBFB42, 0xFFFFFB93, // 1e-322
0x9F9B60A7, 0xCA66FA12, 0xFFFFFB96, // 1e-321
0x478238D1, 0xFD00B897, 0xFFFFFB99, // 1e-320
0x8CB16382, 0x9E20735E, 0xFFFFFB9D, // 1e-319
0x2FDDBC63, 0xC5A89036, 0xFFFFFBA0, // 1e-318
0xBBD52B7C, 0xF712B443, 0xFFFFFBA3, // 1e-317
0x55653B2D, 0x9A6BB0AA, 0xFFFFFBA7, // 1e-316
0xEABE89F9, 0xC1069CD4, 0xFFFFFBAA, // 1e-315
0x256E2C77, 0xF148440A, 0xFFFFFBAD, // 1e-314
0x5764DBCA, 0x96CD2A86, 0xFFFFFBB1, // 1e-313
0xED3E12BD, 0xBC807527, 0xFFFFFBB4, // 1e-312
0xE88D976C, 0xEBA09271, 0xFFFFFBB7, // 1e-311
0x31587EA3, 0x93445B87, 0xFFFFFBBB, // 1e-310
0xFDAE9E4C, 0xB8157268, 0xFFFFFBBE, // 1e-309
0x3D1A45DF, 0xE61ACF03, 0xFFFFFBC1, // 1e-308
0x06306BAC, 0x8FD0C162, 0xFFFFFBC5, // 1e-307
0x87BC8697, 0xB3C4F1BA, 0xFFFFFBC8, // 1e-306
0x29ABA83C, 0xE0B62E29, 0xFFFFFBCB, // 1e-305
0xBA0B4926, 0x8C71DCD9, 0xFFFFFBCF, // 1e-304
0x288E1B6F, 0xAF8E5410, 0xFFFFFBD2, // 1e-303
0x32B1A24B, 0xDB71E914, 0xFFFFFBD5, // 1e-302
0x9FAF056F, 0x892731AC, 0xFFFFFBD9, // 1e-301
0xC79AC6CA, 0xAB70FE17, 0xFFFFFBDC, // 1e-300
0xB981787D, 0xD64D3D9D, 0xFFFFFBDF, // 1e-299
0x93F0EB4E, 0x85F04682, 0xFFFFFBE3, // 1e-298
0x38ED2622, 0xA76C5823, 0xFFFFFBE6, // 1e-297
0x07286FAA, 0xD1476E2C, 0xFFFFFBE9, // 1e-296
0x847945CA, 0x82CCA4DB, 0xFFFFFBED, // 1e-295
0x6597973D, 0xA37FCE12, 0xFFFFFBF0, // 1e-294
0xFEFD7D0C, 0xCC5FC196, 0xFFFFFBF3, // 1e-293
0xBEBCDC4F, 0xFF77B1FC, 0xFFFFFBF6, // 1e-292
0xF73609B1, 0x9FAACF3D, 0xFFFFFBFA, // 1e-291
0x75038C1E, 0xC795830D, 0xFFFFFBFD, // 1e-290
0xD2446F25, 0xF97AE3D0, 0xFFFFFC00, // 1e-289
0x836AC577, 0x9BECCE62, 0xFFFFFC04, // 1e-288
0x244576D5, 0xC2E801FB, 0xFFFFFC07, // 1e-287
0xED56D48A, 0xF3A20279, 0xFFFFFC0A, // 1e-286
0x345644D7, 0x9845418C, 0xFFFFFC0E, // 1e-285
0x416BD60C, 0xBE5691EF, 0xFFFFFC11, // 1e-284
0x11C6CB8F, 0xEDEC366B, 0xFFFFFC14, // 1e-283
0xEB1C3F39, 0x94B3A202, 0xFFFFFC18, // 1e-282
0xA5E34F08, 0xB9E08A83, 0xFFFFFC1B, // 1e-281
0x8F5C22CA, 0xE858AD24, 0xFFFFFC1E, // 1e-280
0xD99995BE, 0x91376C36, 0xFFFFFC22, // 1e-279
0x8FFFFB2E, 0xB5854744, 0xFFFFFC25, // 1e-278
0xB3FFF9F9, 0xE2E69915, 0xFFFFFC28, // 1e-277
0x907FFC3C, 0x8DD01FAD, 0xFFFFFC2C, // 1e-276
0xF49FFB4B, 0xB1442798, 0xFFFFFC2F, // 1e-275
0x31C7FA1D, 0xDD95317F, 0xFFFFFC32, // 1e-274
0x7F1CFC52, 0x8A7D3EEF, 0xFFFFFC36, // 1e-273
0x5EE43B67, 0xAD1C8EAB, 0xFFFFFC39, // 1e-272
0x369D4A41, 0xD863B256, 0xFFFFFC3C, // 1e-271
0xE2224E68, 0x873E4F75, 0xFFFFFC40, // 1e-270
0x5AAAE202, 0xA90DE353, 0xFFFFFC43, // 1e-269
0x31559A83, 0xD3515C28, 0xFFFFFC46, // 1e-268
0x1ED58092, 0x8412D999, 0xFFFFFC4A, // 1e-267
0x668AE0B6, 0xA5178FFF, 0xFFFFFC4D, // 1e-266
0x402D98E4, 0xCE5D73FF, 0xFFFFFC50, // 1e-265
0x881C7F8E, 0x80FA687F, 0xFFFFFC54, // 1e-264
0x6A239F72, 0xA139029F, 0xFFFFFC57, // 1e-263
0x44AC874F, 0xC9874347, 0xFFFFFC5A, // 1e-262
0x15D7A922, 0xFBE91419, 0xFFFFFC5D, // 1e-261
0xADA6C9B5, 0x9D71AC8F, 0xFFFFFC61, // 1e-260
0x99107C23, 0xC4CE17B3, 0xFFFFFC64, // 1e-259
0x7F549B2B, 0xF6019DA0, 0xFFFFFC67, // 1e-258
0x4F94E0FB, 0x99C10284, 0xFFFFFC6B, // 1e-257
0x637A193A, 0xC0314325, 0xFFFFFC6E, // 1e-256
0xBC589F88, 0xF03D93EE, 0xFFFFFC71, // 1e-255
0x35B763B5, 0x96267C75, 0xFFFFFC75, // 1e-254
0x83253CA3, 0xBBB01B92, 0xFFFFFC78, // 1e-253
0x23EE8BCB, 0xEA9C2277, 0xFFFFFC7B, // 1e-252
0x7675175F, 0x92A1958A, 0xFFFFFC7F, // 1e-251
0x14125D37, 0xB749FAED, 0xFFFFFC82, // 1e-250
0x5916F485, 0xE51C79A8, 0xFFFFFC85, // 1e-249
0x37AE58D3, 0x8F31CC09, 0xFFFFFC89, // 1e-248
0x8599EF08, 0xB2FE3F0B, 0xFFFFFC8C, // 1e-247
0x67006AC9, 0xDFBDCECE, 0xFFFFFC8F, // 1e-246
0x006042BE, 0x8BD6A141, 0xFFFFFC93, // 1e-245
0x4078536D, 0xAECC4991, 0xFFFFFC96, // 1e-244
0x90966849, 0xDA7F5BF5, 0xFFFFFC99, // 1e-243
0x7A5E012D, 0x888F9979, 0xFFFFFC9D, // 1e-242
0xD8F58179, 0xAAB37FD7, 0xFFFFFCA0, // 1e-241
0xCF32E1D7, 0xD5605FCD, 0xFFFFFCA3, // 1e-240
0xA17FCD26, 0x855C3BE0, 0xFFFFFCA7, // 1e-239
0xC9DFC070, 0xA6B34AD8, 0xFFFFFCAA, // 1e-238
0xFC57B08C, 0xD0601D8E, 0xFFFFFCAD, // 1e-237
0x5DB6CE57, 0x823C1279, 0xFFFFFCB1, // 1e-236
0xB52481ED, 0xA2CB1717, 0xFFFFFCB4, // 1e-235
0xA26DA269, 0xCB7DDCDD, 0xFFFFFCB7, // 1e-234
0x0B090B03, 0xFE5D5415, 0xFFFFFCBA, // 1e-233
0x26E5A6E2, 0x9EFA548D, 0xFFFFFCBE, // 1e-232
0x709F109A, 0xC6B8E9B0, 0xFFFFFCC1, // 1e-231
0x8CC6D4C1, 0xF867241C, 0xFFFFFCC4, // 1e-230
0xD7FC44F8, 0x9B407691, 0xFFFFFCC8, // 1e-229
0x4DFB5637, 0xC2109436, 0xFFFFFCCB, // 1e-228
0xE17A2BC4, 0xF294B943, 0xFFFFFCCE, // 1e-227
0x6CEC5B5B, 0x979CF3CA, 0xFFFFFCD2, // 1e-226
0x08277231, 0xBD8430BD, 0xFFFFFCD5, // 1e-225
0x4A314EBE, 0xECE53CEC, 0xFFFFFCD8, // 1e-224
0xAE5ED137, 0x940F4613, 0xFFFFFCDC, // 1e-223
0x99F68584, 0xB9131798, 0xFFFFFCDF, // 1e-222
0xC07426E5, 0xE757DD7E, 0xFFFFFCE2, // 1e-221
0x3848984F, 0x9096EA6F, 0xFFFFFCE6, // 1e-220
0x065ABE63, 0xB4BCA50B, 0xFFFFFCE9, // 1e-219
0xC7F16DFC, 0xE1EBCE4D, 0xFFFFFCEC, // 1e-218
0x9CF6E4BD, 0x8D3360F0, 0xFFFFFCF0, // 1e-217
0xC4349DED, 0xB080392C, 0xFFFFFCF3, // 1e-216
0xF541C568, 0xDCA04777, 0xFFFFFCF6, // 1e-215
0xF9491B61, 0x89E42CAA, 0xFFFFFCFA, // 1e-214
0xB79B6239, 0xAC5D37D5, 0xFFFFFCFD, // 1e-213
0x25823AC7, 0xD77485CB, 0xFFFFFD00, // 1e-212
0xF77164BD, 0x86A8D39E, 0xFFFFFD04, // 1e-211
0xB54DBDEC, 0xA8530886, 0xFFFFFD07, // 1e-210
0x62A12D67, 0xD267CAA8, 0xFFFFFD0A, // 1e-209
0x3DA4BC60, 0x8380DEA9, 0xFFFFFD0E, // 1e-208
0x8D0DEB78, 0xA4611653, 0xFFFFFD11, // 1e-207
0x70516656, 0xCD795BE8, 0xFFFFFD14, // 1e-206
0x4632DFF6, 0x806BD971, 0xFFFFFD18, // 1e-205
0x97BF97F4, 0xA086CFCD, 0xFFFFFD1B, // 1e-204
0xFDAF7DF0, 0xC8A883C0, 0xFFFFFD1E, // 1e-203
0x3D1B5D6C, 0xFAD2A4B1, 0xFFFFFD21, // 1e-202
0xC6311A64, 0x9CC3A6EE, 0xFFFFFD25, // 1e-201
0x77BD60FD, 0xC3F490AA, 0xFFFFFD28, // 1e-200
0x15ACB93C, 0xF4F1B4D5, 0xFFFFFD2B, // 1e-199
0x2D8BF3C5, 0x99171105, 0xFFFFFD2F, // 1e-198
0x78EEF0B7, 0xBF5CD546, 0xFFFFFD32, // 1e-197
0x172AACE5, 0xEF340A98, 0xFFFFFD35, // 1e-196
0x0E7AAC0F, 0x9580869F, 0xFFFFFD39, // 1e-195
0xD2195713, 0xBAE0A846, 0xFFFFFD3C, // 1e-194
0x869FACD7, 0xE998D258, 0xFFFFFD3F, // 1e-193
0x5423CC06, 0x91FF8377, 0xFFFFFD43, // 1e-192
0x292CBF08, 0xB67F6455, 0xFFFFFD46, // 1e-191
0x7377EECA, 0xE41F3D6A, 0xFFFFFD49, // 1e-190
0x882AF53E, 0x8E938662, 0xFFFFFD4D, // 1e-189
0x2A35B28E, 0xB23867FB, 0xFFFFFD50, // 1e-188
0xF4C31F31, 0xDEC681F9, 0xFFFFFD53, // 1e-187
0x38F9F37F, 0x8B3C113C, 0xFFFFFD57, // 1e-186
0x4738705F, 0xAE0B158B, 0xFFFFFD5A, // 1e-185
0x19068C76, 0xD98DDAEE, 0xFFFFFD5D, // 1e-184
0xCFA417CA, 0x87F8A8D4, 0xFFFFFD61, // 1e-183
0x038D1DBC, 0xA9F6D30A, 0xFFFFFD64, // 1e-182
0x8470652B, 0xD47487CC, 0xFFFFFD67, // 1e-181
0xD2C63F3B, 0x84C8D4DF, 0xFFFFFD6B, // 1e-180
0xC777CF0A, 0xA5FB0A17, 0xFFFFFD6E, // 1e-179
0xB955C2CC, 0xCF79CC9D, 0xFFFFFD71, // 1e-178
0x93D599C0, 0x81AC1FE2, 0xFFFFFD75, // 1e-177
0x38CB0030, 0xA21727DB, 0xFFFFFD78, // 1e-176
0x06FDC03C, 0xCA9CF1D2, 0xFFFFFD7B, // 1e-175
0x88BD304B, 0xFD442E46, 0xFFFFFD7E, // 1e-174
0x15763E2F, 0x9E4A9CEC, 0xFFFFFD82, // 1e-173
0x1AD3CDBA, 0xC5DD4427, 0xFFFFFD85, // 1e-172
0xE188C129, 0xF7549530, 0xFFFFFD88, // 1e-171
0x8CF578BA, 0x9A94DD3E, 0xFFFFFD8C, // 1e-170
0x3032D6E8, 0xC13A148E, 0xFFFFFD8F, // 1e-169
0xBC3F8CA2, 0xF18899B1, 0xFFFFFD92, // 1e-168
0x15A7B7E5, 0x96F5600F, 0xFFFFFD96, // 1e-167
0xDB11A5DE, 0xBCB2B812, 0xFFFFFD99, // 1e-166
0x91D60F56, 0xEBDF6617, 0xFFFFFD9C, // 1e-165
0xBB25C996, 0x936B9FCE, 0xFFFFFDA0, // 1e-164
0x69EF3BFB, 0xB84687C2, 0xFFFFFDA3, // 1e-163
0x046B0AFA, 0xE65829B3, 0xFFFFFDA6, // 1e-162
0xE2C2E6DC, 0x8FF71A0F, 0xFFFFFDAA, // 1e-161
0xDB73A093, 0xB3F4E093, 0xFFFFFDAD, // 1e-160
0xD25088B8, 0xE0F218B8, 0xFFFFFDB0, // 1e-159
0x83725573, 0x8C974F73, 0xFFFFFDB4, // 1e-158
0x644EEAD0, 0xAFBD2350, 0xFFFFFDB7, // 1e-157
0x7D62A584, 0xDBAC6C24, 0xFFFFFDBA, // 1e-156
0xCE5DA772, 0x894BC396, 0xFFFFFDBE, // 1e-155
0x81F5114F, 0xAB9EB47C, 0xFFFFFDC1, // 1e-154
0xA27255A3, 0xD686619B, 0xFFFFFDC4, // 1e-153
0x45877586, 0x8613FD01, 0xFFFFFDC8, // 1e-152
0x96E952E7, 0xA798FC41, 0xFFFFFDCB, // 1e-151
0xFCA3A7A1, 0xD17F3B51, 0xFFFFFDCE, // 1e-150
0x3DE648C5, 0x82EF8513, 0xFFFFFDD2, // 1e-149
0x0D5FDAF6, 0xA3AB6658, 0xFFFFFDD5, // 1e-148
0x10B7D1B3, 0xCC963FEE, 0xFFFFFDD8, // 1e-147
0x94E5C620, 0xFFBBCFE9, 0xFFFFFDDB, // 1e-146
0xFD0F9BD4, 0x9FD561F1, 0xFFFFFDDF, // 1e-145
0x7C5382C9, 0xC7CABA6E, 0xFFFFFDE2, // 1e-144
0x1B68637B, 0xF9BD690A, 0xFFFFFDE5, // 1e-143
0x51213E2D, 0x9C1661A6, 0xFFFFFDE9, // 1e-142
0xE5698DB8, 0xC31BFA0F, 0xFFFFFDEC, // 1e-141
0xDEC3F126, 0xF3E2F893, 0xFFFFFDEF, // 1e-140
0x6B3A76B8, 0x986DDB5C, 0xFFFFFDF3, // 1e-139
0x86091466, 0xBE895233, 0xFFFFFDF6, // 1e-138
0x678B597F, 0xEE2BA6C0, 0xFFFFFDF9, // 1e-137
0x40B717F0, 0x94DB4838, 0xFFFFFDFD, // 1e-136
0x50E4DDEC, 0xBA121A46, 0xFFFFFE00, // 1e-135
0xE51E1566, 0xE896A0D7, 0xFFFFFE03, // 1e-134
0xEF32CD60, 0x915E2486, 0xFFFFFE07, // 1e-133
0xAAFF80B8, 0xB5B5ADA8, 0xFFFFFE0A, // 1e-132
0xD5BF60E6, 0xE3231912, 0xFFFFFE0D, // 1e-131
0xC5979C90, 0x8DF5EFAB, 0xFFFFFE11, // 1e-130
0xB6FD83B4, 0xB1736B96, 0xFFFFFE14, // 1e-129
0x64BCE4A1, 0xDDD0467C, 0xFFFFFE17, // 1e-128
0xBEF60EE4, 0x8AA22C0D, 0xFFFFFE1B, // 1e-127
0x2EB3929E, 0xAD4AB711, 0xFFFFFE1E, // 1e-126
0x7A607745, 0xD89D64D5, 0xFFFFFE21, // 1e-125
0x6C7C4A8B, 0x87625F05, 0xFFFFFE25, // 1e-124
0xC79B5D2E, 0xA93AF6C6, 0xFFFFFE28, // 1e-123
0x79823479, 0xD389B478, 0xFFFFFE2B, // 1e-122
0x4BF160CC, 0x843610CB, 0xFFFFFE2F, // 1e-121
0x1EEDB8FF, 0xA54394FE, 0xFFFFFE32, // 1e-120
0xA6A9273E, 0xCE947A3D, 0xFFFFFE35, // 1e-119
0x8829B887, 0x811CCC66, 0xFFFFFE39, // 1e-118
0x2A3426A9, 0xA163FF80, 0xFFFFFE3C, // 1e-117
0x34C13053, 0xC9BCFF60, 0xFFFFFE3F, // 1e-116
0x41F17C68, 0xFC2C3F38, 0xFFFFFE42, // 1e-115
0x2936EDC1, 0x9D9BA783, 0xFFFFFE46, // 1e-114
0xF384A931, 0xC5029163, 0xFFFFFE49, // 1e-113
0xF065D37D, 0xF64335BC, 0xFFFFFE4C, // 1e-112
0x163FA42E, 0x99EA0196, 0xFFFFFE50, // 1e-111
0x9BCF8D3A, 0xC06481FB, 0xFFFFFE53, // 1e-110
0x82C37088, 0xF07DA27A, 0xFFFFFE56, // 1e-109
0x91BA2655, 0x964E858C, 0xFFFFFE5A, // 1e-108
0xB628AFEB, 0xBBE226EF, 0xFFFFFE5D, // 1e-107
0xA3B2DBE5, 0xEADAB0AB, 0xFFFFFE60, // 1e-106
0x464FC96F, 0x92C8AE6B, 0xFFFFFE64, // 1e-105
0x17E3BBCB, 0xB77ADA06, 0xFFFFFE67, // 1e-104
0x9DDCAABE, 0xE5599087, 0xFFFFFE6A, // 1e-103
0xC2A9EAB7, 0x8F57FA54, 0xFFFFFE6E, // 1e-102
0xF3546564, 0xB32DF8E9, 0xFFFFFE71, // 1e-101
0x70297EBD, 0xDFF97724, 0xFFFFFE74, // 1e-100
0xC619EF36, 0x8BFBEA76, 0xFFFFFE78, // 1e-99
0x77A06B04, 0xAEFAE514, 0xFFFFFE7B, // 1e-98
0x958885C5, 0xDAB99E59, 0xFFFFFE7E, // 1e-97
0xFD75539B, 0x88B402F7, 0xFFFFFE82, // 1e-96
0xFCD2A882, 0xAAE103B5, 0xFFFFFE85, // 1e-95
0x7C0752A2, 0xD59944A3, 0xFFFFFE88, // 1e-94
0x2D8493A5, 0x857FCAE6, 0xFFFFFE8C, // 1e-93
0xB8E5B88F, 0xA6DFBD9F, 0xFFFFFE8F, // 1e-92
0xA71F26B2, 0xD097AD07, 0xFFFFFE92, // 1e-91
0xC8737830, 0x825ECC24, 0xFFFFFE96, // 1e-90
0xFA90563B, 0xA2F67F2D, 0xFFFFFE99, // 1e-89
0x79346BCA, 0xCBB41EF9, 0xFFFFFE9C, // 1e-88
0xD78186BD, 0xFEA126B7, 0xFFFFFE9F, // 1e-87
0xE6B0F436, 0x9F24B832, 0xFFFFFEA3, // 1e-86
0xA05D3144, 0xC6EDE63F, 0xFFFFFEA6, // 1e-85
0x88747D94, 0xF8A95FCF, 0xFFFFFEA9, // 1e-84
0xB548CE7D, 0x9B69DBE1, 0xFFFFFEAD, // 1e-83
0x229B021C, 0xC24452DA, 0xFFFFFEB0, // 1e-82
0xAB41C2A3, 0xF2D56790, 0xFFFFFEB3, // 1e-81
0x6B0919A6, 0x97C560BA, 0xFFFFFEB7, // 1e-80
0x05CB600F, 0xBDB6B8E9, 0xFFFFFEBA, // 1e-79
0x473E3813, 0xED246723, 0xFFFFFEBD, // 1e-78
0x0C86E30C, 0x9436C076, 0xFFFFFEC1, // 1e-77
0x8FA89BCF, 0xB9447093, 0xFFFFFEC4, // 1e-76
0x7392C2C3, 0xE7958CB8, 0xFFFFFEC7, // 1e-75
0x483BB9BA, 0x90BD77F3, 0xFFFFFECB, // 1e-74
0x1A4AA828, 0xB4ECD5F0, 0xFFFFFECE, // 1e-73
0x20DD5232, 0xE2280B6C, 0xFFFFFED1, // 1e-72
0x948A535F, 0x8D590723, 0xFFFFFED5, // 1e-71
0x79ACE837, 0xB0AF48EC, 0xFFFFFED8, // 1e-70
0x98182245, 0xDCDB1B27, 0xFFFFFEDB, // 1e-69
0xBF0F156B, 0x8A08F0F8, 0xFFFFFEDF, // 1e-68
0xEED2DAC6, 0xAC8B2D36, 0xFFFFFEE2, // 1e-67
0xAA879177, 0xD7ADF884, 0xFFFFFEE5, // 1e-66
0xEA94BAEB, 0x86CCBB52, 0xFFFFFEE9, // 1e-65
0xA539E9A5, 0xA87FEA27, 0xFFFFFEEC, // 1e-64
0x8E88640F, 0xD29FE4B1, 0xFFFFFEEF, // 1e-63
0xF9153E89, 0x83A3EEEE, 0xFFFFFEF3, // 1e-62
0xB75A8E2B, 0xA48CEAAA, 0xFFFFFEF6, // 1e-61
0x653131B6, 0xCDB02555, 0xFFFFFEF9, // 1e-60
0x5F3EBF12, 0x808E1755, 0xFFFFFEFD, // 1e-59
0xB70E6ED6, 0xA0B19D2A, 0xFFFFFF00, // 1e-58
0x64D20A8C, 0xC8DE0475, 0xFFFFFF03, // 1e-57
0xBE068D2F, 0xFB158592, 0xFFFFFF06, // 1e-56
0xB6C4183D, 0x9CED737B, 0xFFFFFF0A, // 1e-55
0xA4751E4D, 0xC428D05A, 0xFFFFFF0D, // 1e-54
0x4D9265E0, 0xF5330471, 0xFFFFFF10, // 1e-53
0xD07B7FAC, 0x993FE2C6, 0xFFFFFF14, // 1e-52
0x849A5F97, 0xBF8FDB78, 0xFFFFFF17, // 1e-51
0xA5C0F77D, 0xEF73D256, 0xFFFFFF1A, // 1e-50
0x27989AAE, 0x95A86376, 0xFFFFFF1E, // 1e-49
0xB17EC159, 0xBB127C53, 0xFFFFFF21, // 1e-48
0x9DDE71B0, 0xE9D71B68, 0xFFFFFF24, // 1e-47
0x62AB070E, 0x92267121, 0xFFFFFF28, // 1e-46
0xBB55C8D1, 0xB6B00D69, 0xFFFFFF2B, // 1e-45
0x2A2B3B06, 0xE45C10C4, 0xFFFFFF2E, // 1e-44
0x9A5B04E3, 0x8EB98A7A, 0xFFFFFF32, // 1e-43
0x40F1C61C, 0xB267ED19, 0xFFFFFF35, // 1e-42
0x912E37A3, 0xDF01E85F, 0xFFFFFF38, // 1e-41
0xBABCE2C6, 0x8B61313B, 0xFFFFFF3C, // 1e-40
0xA96C1B78, 0xAE397D8A, 0xFFFFFF3F, // 1e-39
0x53C72256, 0xD9C7DCED, 0xFFFFFF42, // 1e-38
0x545C7575, 0x881CEA14, 0xFFFFFF46, // 1e-37
0x697392D3, 0xAA242499, 0xFFFFFF49, // 1e-36
0xC3D07788, 0xD4AD2DBF, 0xFFFFFF4C, // 1e-35
0xDA624AB5, 0x84EC3C97, 0xFFFFFF50, // 1e-34
0xD0FADD62, 0xA6274BBD, 0xFFFFFF53, // 1e-33
0x453994BA, 0xCFB11EAD, 0xFFFFFF56, // 1e-32
0x4B43FCF5, 0x81CEB32C, 0xFFFFFF5A, // 1e-31
0x5E14FC32, 0xA2425FF7, 0xFFFFFF5D, // 1e-30
0x359A3B3E, 0xCAD2F7F5, 0xFFFFFF60, // 1e-29
0x8300CA0E, 0xFD87B5F2, 0xFFFFFF63, // 1e-28
0x91E07E48, 0x9E74D1B7, 0xFFFFFF67, // 1e-27
0x76589DDB, 0xC6120625, 0xFFFFFF6A, // 1e-26
0xD3EEC551, 0xF79687AE, 0xFFFFFF6D, // 1e-25
0x44753B53, 0x9ABE14CD, 0xFFFFFF71, // 1e-24
0x95928A27, 0xC16D9A00, 0xFFFFFF74, // 1e-23
0xBAF72CB1, 0xF1C90080, 0xFFFFFF77, // 1e-22
0x74DA7BEF, 0x971DA050, 0xFFFFFF7B, // 1e-21
0x92111AEB, 0xBCE50864, 0xFFFFFF7E, // 1e-20
0xB69561A5, 0xEC1E4A7D, 0xFFFFFF81, // 1e-19
0x921D5D07, 0x9392EE8E, 0xFFFFFF85, // 1e-18
0x36A4B449, 0xB877AA32, 0xFFFFFF88, // 1e-17
0xC44DE15B, 0xE69594BE, 0xFFFFFF8B, // 1e-16
0x3AB0ACD9, 0x901D7CF7, 0xFFFFFF8F, // 1e-15
0x095CD80F, 0xB424DC35, 0xFFFFFF92, // 1e-14
0x4BB40E13, 0xE12E1342, 0xFFFFFF95, // 1e-13
0x6F5088CC, 0x8CBCCC09, 0xFFFFFF99, // 1e-12
0xCB24AAFF, 0xAFEBFF0B, 0xFFFFFF9C, // 1e-11
0xBDEDD5BF, 0xDBE6FECE, 0xFFFFFF9F, // 1e-10
0x36B4A597, 0x89705F41, 0xFFFFFFA3, // 1e-9
0x8461CEFD, 0xABCC7711, 0xFFFFFFA6, // 1e-8
0xE57A42BC, 0xD6BF94D5, 0xFFFFFFA9, // 1e-7
0xAF6C69B6, 0x8637BD05, 0xFFFFFFAD, // 1e-6
0x1B478423, 0xA7C5AC47, 0xFFFFFFB0, // 1e-5
0xE219652C, 0xD1B71758, 0xFFFFFFB3, // 1e-4
0x8D4FDF3B, 0x83126E97, 0xFFFFFFB7, // 1e-3
0x70A3D70A, 0xA3D70A3D, 0xFFFFFFBA, // 1e-2
0xCCCCCCCD, 0xCCCCCCCC, 0xFFFFFFBD, // 1e-1
0x00000000, 0x80000000, 0xFFFFFFC1, // 1e0
0x00000000, 0xA0000000, 0xFFFFFFC4, // 1e1
0x00000000, 0xC8000000, 0xFFFFFFC7, // 1e2
0x00000000, 0xFA000000, 0xFFFFFFCA, // 1e3
0x00000000, 0x9C400000, 0xFFFFFFCE, // 1e4
0x00000000, 0xC3500000, 0xFFFFFFD1, // 1e5
0x00000000, 0xF4240000, 0xFFFFFFD4, // 1e6
0x00000000, 0x98968000, 0xFFFFFFD8, // 1e7
0x00000000, 0xBEBC2000, 0xFFFFFFDB, // 1e8
0x00000000, 0xEE6B2800, 0xFFFFFFDE, // 1e9
0x00000000, 0x9502F900, 0xFFFFFFE2, // 1e10
0x00000000, 0xBA43B740, 0xFFFFFFE5, // 1e11
0x00000000, 0xE8D4A510, 0xFFFFFFE8, // 1e12
0x00000000, 0x9184E72A, 0xFFFFFFEC, // 1e13
0x80000000, 0xB5E620F4, 0xFFFFFFEF, // 1e14
0xA0000000, 0xE35FA931, 0xFFFFFFF2, // 1e15
0x04000000, 0x8E1BC9BF, 0xFFFFFFF6, // 1e16
0xC5000000, 0xB1A2BC2E, 0xFFFFFFF9, // 1e17
0x76400000, 0xDE0B6B3A, 0xFFFFFFFC, // 1e18
0x89E80000, 0x8AC72304, 0x00000000, // 1e19
0xAC620000, 0xAD78EBC5, 0x00000003, // 1e20
0x177A8000, 0xD8D726B7, 0x00000006, // 1e21
0x6EAC9000, 0x87867832, 0x0000000A, // 1e22
0x0A57B400, 0xA968163F, 0x0000000D, // 1e23
0xCCEDA100, 0xD3C21BCE, 0x00000010, // 1e24
0x401484A0, 0x84595161, 0x00000014, // 1e25
0x9019A5C8, 0xA56FA5B9, 0x00000017, // 1e26
0xF4200F3A, 0xCECB8F27, 0x0000001A, // 1e27
0xF8940984, 0x813F3978, 0x0000001E, // 1e28
0x36B90BE5, 0xA18F07D7, 0x00000021, // 1e29
0x04674EDF, 0xC9F2C9CD, 0x00000024, // 1e30
0x45812296, 0xFC6F7C40, 0x00000027, // 1e31
0x2B70B59E, 0x9DC5ADA8, 0x0000002B, // 1e32
0x364CE305, 0xC5371912, 0x0000002E, // 1e33
0xC3E01BC7, 0xF684DF56, 0x00000031, // 1e34
0x3A6C115C, 0x9A130B96, 0x00000035, // 1e35
0xC90715B3, 0xC097CE7B, 0x00000038, // 1e36
0xBB48DB20, 0xF0BDC21A, 0x0000003B, // 1e37
0xB50D88F4, 0x96769950, 0x0000003F, // 1e38
0xE250EB31, 0xBC143FA4, 0x00000042, // 1e39
0x1AE525FD, 0xEB194F8E, 0x00000045, // 1e40
0xD0CF37BE, 0x92EFD1B8, 0x00000049, // 1e41
0x050305AE, 0xB7ABC627, 0x0000004C, // 1e42
0xC643C719, 0xE596B7B0, 0x0000004F, // 1e43
0x7BEA5C70, 0x8F7E32CE, 0x00000053, // 1e44
0x1AE4F38C, 0xB35DBF82, 0x00000056, // 1e45
0xA19E306F, 0xE0352F62, 0x00000059, // 1e46
0xA502DE45, 0x8C213D9D, 0x0000005D, // 1e47
0x0E4395D7, 0xAF298D05, 0x00000060, // 1e48
0x51D47B4C, 0xDAF3F046, 0x00000063, // 1e49
0xF324CD10, 0x88D8762B, 0x00000067, // 1e50
0xEFEE0054, 0xAB0E93B6, 0x0000006A, // 1e51
0xABE98068, 0xD5D238A4, 0x0000006D, // 1e52
0xEB71F041, 0x85A36366, 0x00000071, // 1e53
0xA64E6C52, 0xA70C3C40, 0x00000074, // 1e54
0xCFE20766, 0xD0CF4B50, 0x00000077, // 1e55
0x81ED44A0, 0x82818F12, 0x0000007B, // 1e56
0x226895C8, 0xA321F2D7, 0x0000007E, // 1e57
0xEB02BB3A, 0xCBEA6F8C, 0x00000081, // 1e58
0x25C36A08, 0xFEE50B70, 0x00000084, // 1e59
0x179A2245, 0x9F4F2726, 0x00000088, // 1e60
0x9D80AAD6, 0xC722F0EF, 0x0000008B, // 1e61
0x84E0D58C, 0xF8EBAD2B, 0x0000008E, // 1e62
0x330C8577, 0x9B934C3B, 0x00000092, // 1e63
0xFFCFA6D5, 0xC2781F49, 0x00000095, // 1e64
0x7FC3908B, 0xF316271C, 0x00000098, // 1e65
0xCFDA3A57, 0x97EDD871, 0x0000009C, // 1e66
0x43D0C8EC, 0xBDE94E8E, 0x0000009F, // 1e67
0xD4C4FB27, 0xED63A231, 0x000000A2, // 1e68
0x24FB1CF9, 0x945E455F, 0x000000A6, // 1e69
0xEE39E437, 0xB975D6B6, 0x000000A9, // 1e70
0xA9C85D44, 0xE7D34C64, 0x000000AC, // 1e71
0xEA1D3A4B, 0x90E40FBE, 0x000000B0, // 1e72
0xA4A488DD, 0xB51D13AE, 0x000000B3, // 1e73
0x4DCDAB15, 0xE264589A, 0x000000B6, // 1e74
0x70A08AED, 0x8D7EB760, 0x000000BA, // 1e75
0x8CC8ADA8, 0xB0DE6538, 0x000000BD, // 1e76
0xAFFAD912, 0xDD15FE86, 0x000000C0, // 1e77
0x2DFCC7AB, 0x8A2DBF14, 0x000000C4, // 1e78
0x397BF996, 0xACB92ED9, 0x000000C7, // 1e79
0x87DAF7FC, 0xD7E77A8F, 0x000000CA, // 1e80
0xB4E8DAFD, 0x86F0AC99, 0x000000CE, // 1e81
0x222311BD, 0xA8ACD7C0, 0x000000D1, // 1e82
0x2AABD62C, 0xD2D80DB0, 0x000000D4, // 1e83
0x1AAB65DB, 0x83C7088E, 0x000000D8, // 1e84
0xA1563F52, 0xA4B8CAB1, 0x000000DB, // 1e85
0x09ABCF27, 0xCDE6FD5E, 0x000000DE, // 1e86
0xC60B6178, 0x80B05E5A, 0x000000E2, // 1e87
0x778E39D6, 0xA0DC75F1, 0x000000E5, // 1e88
0xD571C84C, 0xC913936D, 0x000000E8, // 1e89
0x4ACE3A5F, 0xFB587849, 0x000000EB, // 1e90
0xCEC0E47B, 0x9D174B2D, 0x000000EF, // 1e91
0x42711D9A, 0xC45D1DF9, 0x000000F2, // 1e92
0x930D6501, 0xF5746577, 0x000000F5, // 1e93
0xBBE85F20, 0x9968BF6A, 0x000000F9, // 1e94
0x6AE276E9, 0xBFC2EF45, 0x000000FC, // 1e95
0xC59B14A3, 0xEFB3AB16, 0x000000FF, // 1e96
0x3B80ECE6, 0x95D04AEE, 0x00000103, // 1e97
0xCA61281F, 0xBB445DA9, 0x00000106, // 1e98
0x3CF97227, 0xEA157514, 0x00000109, // 1e99
0xA61BE758, 0x924D692C, 0x0000010D, // 1e100
0xCFA2E12E, 0xB6E0C377, 0x00000110, // 1e101
0xC38B997A, 0xE498F455, 0x00000113, // 1e102
0x9A373FEC, 0x8EDF98B5, 0x00000117, // 1e103
0x00C50FE7, 0xB2977EE3, 0x0000011A, // 1e104
0xC0F653E1, 0xDF3D5E9B, 0x0000011D, // 1e105
0x5899F46D, 0x8B865B21, 0x00000121, // 1e106
0xAEC07188, 0xAE67F1E9, 0x00000124, // 1e107
0x1A708DEA, 0xDA01EE64, 0x00000127, // 1e108
0x908658B2, 0x884134FE, 0x0000012B, // 1e109
0x34A7EEDF, 0xAA51823E, 0x0000012E, // 1e110
0xC1D1EA96, 0xD4E5E2CD, 0x00000131, // 1e111
0x9923329E, 0x850FADC0, 0x00000135, // 1e112
0xBF6BFF46, 0xA6539930, 0x00000138, // 1e113
0xEF46FF17, 0xCFE87F7C, 0x0000013B, // 1e114
0x158C5F6E, 0x81F14FAE, 0x0000013F, // 1e115
0x9AEF774A, 0xA26DA399, 0x00000142, // 1e116
0x01AB551C, 0xCB090C80, 0x00000145, // 1e117
0x02162A63, 0xFDCB4FA0, 0x00000148, // 1e118
0x014DDA7E, 0x9E9F11C4, 0x0000014C, // 1e119
0x01A1511E, 0xC646D635, 0x0000014F, // 1e120
0x4209A565, 0xF7D88BC2, 0x00000152, // 1e121
0x6946075F, 0x9AE75759, 0x00000156, // 1e122
0xC3978937, 0xC1A12D2F, 0x00000159, // 1e123
0xB47D6B85, 0xF209787B, 0x0000015C, // 1e124
0x50CE6333, 0x9745EB4D, 0x00000160, // 1e125
0xA501FC00, 0xBD176620, 0x00000163, // 1e126
0xCE427B00, 0xEC5D3FA8, 0x00000166, // 1e127
0x80E98CE0, 0x93BA47C9, 0x0000016A, // 1e128
0xE123F018, 0xB8A8D9BB, 0x0000016D, // 1e129
0xD96CEC1E, 0xE6D3102A, 0x00000170, // 1e130
0xC7E41393, 0x9043EA1A, 0x00000174, // 1e131
0x79DD1877, 0xB454E4A1, 0x00000177, // 1e132
0xD8545E95, 0xE16A1DC9, 0x0000017A, // 1e133
0x2734BB1D, 0x8CE2529E, 0x0000017E, // 1e134
0xB101E9E4, 0xB01AE745, 0x00000181, // 1e135
0x1D42645D, 0xDC21A117, 0x00000184, // 1e136
0x72497EBA, 0x899504AE, 0x00000188, // 1e137
0x0EDBDE69, 0xABFA45DA, 0x0000018B, // 1e138
0x9292D603, 0xD6F8D750, 0x0000018E, // 1e139
0x5B9BC5C2, 0x865B8692, 0x00000192, // 1e140
0xF282B733, 0xA7F26836, 0x00000195, // 1e141
0xAF2364FF, 0xD1EF0244, 0x00000198, // 1e142
0xED761F1F, 0x8335616A, 0x0000019C, // 1e143
0xA8D3A6E7, 0xA402B9C5, 0x0000019F, // 1e144
0x130890A1, 0xCD036837, 0x000001A2, // 1e145
0x6BE55A65, 0x80222122, 0x000001A6, // 1e146
0x06DEB0FE, 0xA02AA96B, 0x000001A9, // 1e147
0xC8965D3D, 0xC83553C5, 0x000001AC, // 1e148
0x3ABBF48D, 0xFA42A8B7, 0x000001AF, // 1e149
0x84B578D8, 0x9C69A972, 0x000001B3, // 1e150
0x25E2D70E, 0xC38413CF, 0x000001B6, // 1e151
0xEF5B8CD1, 0xF46518C2, 0x000001B9, // 1e152
0xD5993803, 0x98BF2F79, 0x000001BD, // 1e153
0x4AFF8604, 0xBEEEFB58, 0x000001C0, // 1e154
0x5DBF6785, 0xEEAABA2E, 0x000001C3, // 1e155
0xFA97A0B3, 0x952AB45C, 0x000001C7, // 1e156
0x393D88E0, 0xBA756174, 0x000001CA, // 1e157
0x478CEB17, 0xE912B9D1, 0x000001CD, // 1e158
0xCCB812EF, 0x91ABB422, 0x000001D1, // 1e159
0x7FE617AA, 0xB616A12B, 0x000001D4, // 1e160
0x5FDF9D95, 0xE39C4976, 0x000001D7, // 1e161
0xFBEBC27D, 0x8E41ADE9, 0x000001DB, // 1e162
0x7AE6B31C, 0xB1D21964, 0x000001DE, // 1e163
0x99A05FE3, 0xDE469FBD, 0x000001E1, // 1e164
0x80043BEE, 0x8AEC23D6, 0x000001E5, // 1e165
0x20054AEA, 0xADA72CCC, 0x000001E8, // 1e166
0x28069DA4, 0xD910F7FF, 0x000001EB, // 1e167
0x79042287, 0x87AA9AFF, 0x000001EF, // 1e168
0x57452B28, 0xA99541BF, 0x000001F2, // 1e169
0x2D1675F2, 0xD3FA922F, 0x000001F5, // 1e170
0x7C2E09B7, 0x847C9B5D, 0x000001F9, // 1e171
0xDB398C25, 0xA59BC234, 0x000001FC, // 1e172
0x1207EF2F, 0xCF02B2C2, 0x000001FF, // 1e173
0x4B44F57D, 0x8161AFB9, 0x00000203, // 1e174
0x9E1632DC, 0xA1BA1BA7, 0x00000206, // 1e175
0x859BBF93, 0xCA28A291, 0x00000209, // 1e176
0xE702AF78, 0xFCB2CB35, 0x0000020C, // 1e177
0xB061ADAB, 0x9DEFBF01, 0x00000210, // 1e178
0x1C7A1916, 0xC56BAEC2, 0x00000213, // 1e179
0xA3989F5C, 0xF6C69A72, 0x00000216, // 1e180
0xA63F6399, 0x9A3C2087, 0x0000021A, // 1e181
0x8FCF3C80, 0xC0CB28A9, 0x0000021D, // 1e182
0xF3C30B9F, 0xF0FDF2D3, 0x00000220, // 1e183
0x7859E744, 0x969EB7C4, 0x00000224, // 1e184
0x96706115, 0xBC4665B5, 0x00000227, // 1e185
0xFC0C795A, 0xEB57FF22, 0x0000022A, // 1e186
0xDD87CBD8, 0x9316FF75, 0x0000022E, // 1e187
0x54E9BECE, 0xB7DCBF53, 0x00000231, // 1e188
0x2A242E82, 0xE5D3EF28, 0x00000234, // 1e189
0x1A569D11, 0x8FA47579, 0x00000238, // 1e190
0x60EC4455, 0xB38D92D7, 0x0000023B, // 1e191
0x3927556B, 0xE070F78D, 0x0000023E, // 1e192
0x43B89563, 0x8C469AB8, 0x00000242, // 1e193
0x54A6BABB, 0xAF584166, 0x00000245, // 1e194
0xE9D0696A, 0xDB2E51BF, 0x00000248, // 1e195
0xF22241E2, 0x88FCF317, 0x0000024C, // 1e196
0xEEAAD25B, 0xAB3C2FDD, 0x0000024F, // 1e197
0x6A5586F2, 0xD60B3BD5, 0x00000252, // 1e198
0x62757457, 0x85C70565, 0x00000256, // 1e199
0xBB12D16D, 0xA738C6BE, 0x00000259, // 1e200
0x69D785C8, 0xD106F86E, 0x0000025C, // 1e201
0x0226B39D, 0x82A45B45, 0x00000260, // 1e202
0x42B06084, 0xA34D7216, 0x00000263, // 1e203
0xD35C78A5, 0xCC20CE9B, 0x00000266, // 1e204
0xC83396CE, 0xFF290242, 0x00000269, // 1e205
0xBD203E41, 0x9F79A169, 0x0000026D, // 1e206
0x2C684DD1, 0xC75809C4, 0x00000270, // 1e207
0x37826146, 0xF92E0C35, 0x00000273, // 1e208
0x42B17CCC, 0x9BBCC7A1, 0x00000277, // 1e209
0x935DDBFE, 0xC2ABF989, 0x0000027A, // 1e210
0xF83552FE, 0xF356F7EB, 0x0000027D, // 1e211
0x7B2153DF, 0x98165AF3, 0x00000281, // 1e212
0x59E9A8D6, 0xBE1BF1B0, 0x00000284, // 1e213
0x7064130C, 0xEDA2EE1C, 0x00000287, // 1e214
0xC63E8BE8, 0x9485D4D1, 0x0000028B, // 1e215
0x37CE2EE1, 0xB9A74A06, 0x0000028E, // 1e216
0xC5C1BA9A, 0xE8111C87, 0x00000291, // 1e217
0xDB9914A0, 0x910AB1D4, 0x00000295, // 1e218
0x127F59C8, 0xB54D5E4A, 0x00000298, // 1e219
0x971F303A, 0xE2A0B5DC, 0x0000029B, // 1e220
0xDE737E24, 0x8DA471A9, 0x0000029F, // 1e221
0x56105DAD, 0xB10D8E14, 0x000002A2, // 1e222
0x6B947519, 0xDD50F199, 0x000002A5, // 1e223
0xE33CC930, 0x8A5296FF, 0x000002A9, // 1e224
0xDC0BFB7B, 0xACE73CBF, 0x000002AC, // 1e225
0xD30EFA5A, 0xD8210BEF, 0x000002AF, // 1e226
0xE3E95C78, 0x8714A775, 0x000002B3, // 1e227
0x5CE3B396, 0xA8D9D153, 0x000002B6, // 1e228
0x341CA07C, 0xD31045A8, 0x000002B9, // 1e229
0x2091E44E, 0x83EA2B89, 0x000002BD, // 1e230
0x68B65D61, 0xA4E4B66B, 0x000002C0, // 1e231
0x42E3F4B9, 0xCE1DE406, 0x000002C3, // 1e232
0xE9CE78F4, 0x80D2AE83, 0x000002C7, // 1e233
0xE4421731, 0xA1075A24, 0x000002CA, // 1e234
0x1D529CFD, 0xC94930AE, 0x000002CD, // 1e235
0xA4A7443C, 0xFB9B7CD9, 0x000002D0, // 1e236
0x06E88AA6, 0x9D412E08, 0x000002D4, // 1e237
0x08A2AD4F, 0xC491798A, 0x000002D7, // 1e238
0x8ACB58A3, 0xF5B5D7EC, 0x000002DA, // 1e239
0xD6BF1766, 0x9991A6F3, 0x000002DE, // 1e240
0xCC6EDD3F, 0xBFF610B0, 0x000002E1, // 1e241
0xFF8A948F, 0xEFF394DC, 0x000002E4, // 1e242
0x1FB69CD9, 0x95F83D0A, 0x000002E8, // 1e243
0xA7A44410, 0xBB764C4C, 0x000002EB, // 1e244
0xD18D5514, 0xEA53DF5F, 0x000002EE, // 1e245
0xE2F8552C, 0x92746B9B, 0x000002F2, // 1e246
0xDBB66A77, 0xB7118682, 0x000002F5, // 1e247
0x92A40515, 0xE4D5E823, 0x000002F8, // 1e248
0x3BA6832D, 0x8F05B116, 0x000002FC, // 1e249
0xCA9023F8, 0xB2C71D5B, 0x000002FF, // 1e250
0xBD342CF7, 0xDF78E4B2, 0x00000302, // 1e251
0xB6409C1A, 0x8BAB8EEF, 0x00000306, // 1e252
0xA3D0C321, 0xAE9672AB, 0x00000309, // 1e253
0x8CC4F3E9, 0xDA3C0F56, 0x0000030C, // 1e254
0x17FB1871, 0x88658996, 0x00000310, // 1e255
0x9DF9DE8E, 0xAA7EEBFB, 0x00000313, // 1e256
0x85785631, 0xD51EA6FA, 0x00000316, // 1e257
0x936B35DF, 0x8533285C, 0x0000031A, // 1e258
0xB8460357, 0xA67FF273, 0x0000031D, // 1e259
0xA657842C, 0xD01FEF10, 0x00000320, // 1e260
0x67F6B29C, 0x8213F56A, 0x00000324, // 1e261
0x01F45F43, 0xA298F2C5, 0x00000327, // 1e262
0x42717713, 0xCB3F2F76, 0x0000032A, // 1e263
0xD30DD4D8, 0xFE0EFB53, 0x0000032D, // 1e264
0x63E8A507, 0x9EC95D14, 0x00000331, // 1e265
0x7CE2CE49, 0xC67BB459, 0x00000334, // 1e266
0xDC1B81DB, 0xF81AA16F, 0x00000337, // 1e267
0xE9913129, 0x9B10A4E5, 0x0000033B, // 1e268
0x63F57D73, 0xC1D4CE1F, 0x0000033E, // 1e269
0x3CF2DCD0, 0xF24A01A7, 0x00000341, // 1e270
0x8617CA02, 0x976E4108, 0x00000345, // 1e271
0xA79DBC82, 0xBD49D14A, 0x00000348, // 1e272
0x51852BA3, 0xEC9C459D, 0x0000034B, // 1e273
0x52F33B46, 0x93E1AB82, 0x0000034F, // 1e274
0xE7B00A17, 0xB8DA1662, 0x00000352, // 1e275
0xA19C0C9D, 0xE7109BFB, 0x00000355, // 1e276
0x450187E2, 0x906A617D, 0x00000359, // 1e277
0x9641E9DB, 0xB484F9DC, 0x0000035C, // 1e278
0xBBD26451, 0xE1A63853, 0x0000035F, // 1e279
0x55637EB3, 0x8D07E334, 0x00000363, // 1e280
0x6ABC5E60, 0xB049DC01, 0x00000366, // 1e281
0xC56B75F7, 0xDC5C5301, 0x00000369, // 1e282
0x1B6329BB, 0x89B9B3E1, 0x0000036D, // 1e283
0x623BF429, 0xAC2820D9, 0x00000370, // 1e284
0xBACAF134, 0xD732290F, 0x00000373, // 1e285
0xD4BED6C0, 0x867F59A9, 0x00000377, // 1e286
0x49EE8C70, 0xA81F3014, 0x0000037A, // 1e287
0x5C6A2F8C, 0xD226FC19, 0x0000037D, // 1e288
0xD9C25DB8, 0x83585D8F, 0x00000381, // 1e289
0xD032F526, 0xA42E74F3, 0x00000384, // 1e290
0xC43FB26F, 0xCD3A1230, 0x00000387, // 1e291
0x7AA7CF85, 0x80444B5E, 0x0000038B, // 1e292
0x1951C367, 0xA0555E36, 0x0000038E, // 1e293
0x9FA63441, 0xC86AB5C3, 0x00000391, // 1e294
0x878FC151, 0xFA856334, 0x00000394, // 1e295
0xD4B9D8D2, 0x9C935E00, 0x00000398, // 1e296
0x09E84F07, 0xC3B83581, 0x0000039B, // 1e297
0x4C6262C9, 0xF4A642E1, 0x0000039E, // 1e298
0xCFBD7DBE, 0x98E7E9CC, 0x000003A2, // 1e299
0x03ACDD2D, 0xBF21E440, 0x000003A5, // 1e300
0x04981478, 0xEEEA5D50, 0x000003A8, // 1e301
0x02DF0CCB, 0x95527A52, 0x000003AC, // 1e302
0x8396CFFE, 0xBAA718E6, 0x000003AF, // 1e303
0x247C83FD, 0xE950DF20, 0x000003B2, // 1e304
0x16CDD27E, 0x91D28B74, 0x000003B6, // 1e305
0x1C81471E, 0xB6472E51, 0x000003B9, // 1e306
0x63A198E5, 0xE3D8F9E5, 0x000003BC, // 1e307
0x5E44FF8F, 0x8E679C2F, 0x000003C0, // 1e308
0x35D63F73, 0xB201833B, 0x000003C3, // 1e309
0x034BCF50, 0xDE81E40A, 0x000003C6, // 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[0]) | (((uint64_t)p[1]) << 32);
int32_t p_exp2 = (int32_t)p[2];
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 + 64;
}
// 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[3 * (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);
}