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skia / external / github.com / google / wuffs / 89ceb9fabc7f714eebdf9764bbc6ce44bae89f14 / . / 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, we can return early.
if (mantissa == 0) {
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 -comments
// 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__big_powers_of_10 contains approximations
// to the powers of 10, ranging from 1e-348 to 1e+340, with the exponent
// stepping by 8: -348, -340, -332, ..., -12, -4, +4, +12, ..., +340. Each step
// consists of three uint32_t elements. There are 87 triples, 87 * 3 = 261.
//
// For example, the third approximation, for 1e-332, consists of the uint32_t
// triple (0x3055AC76, 0x8B16FB20, 0xFFFFFB72). The first two of that triple
// are a little-endian uint64_t value: 0x8B16FB203055AC76. The last one is an
// int32_t value: -1166. Together, they represent the approximation:
// 1e-332 ≈ 0x8B16FB203055AC76 * (2 ** -1166)
// 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__big_powers_of_10[261] = {
0x081C0288, 0xFA8FD5A0, 0xFFFFFB3C, 0xA23EBF76, 0xBAAEE17F, 0xFFFFFB57,
0x3055AC76, 0x8B16FB20, 0xFFFFFB72, 0x5DCE35EA, 0xCF42894A, 0xFFFFFB8C,
0x55653B2D, 0x9A6BB0AA, 0xFFFFFBA7, 0x3D1A45DF, 0xE61ACF03, 0xFFFFFBC1,
0xC79AC6CA, 0xAB70FE17, 0xFFFFFBDC, 0xBEBCDC4F, 0xFF77B1FC, 0xFFFFFBF6,
0x416BD60C, 0xBE5691EF, 0xFFFFFC11, 0x907FFC3C, 0x8DD01FAD, 0xFFFFFC2C,
0x31559A83, 0xD3515C28, 0xFFFFFC46, 0xADA6C9B5, 0x9D71AC8F, 0xFFFFFC61,
0x23EE8BCB, 0xEA9C2277, 0xFFFFFC7B, 0x4078536D, 0xAECC4991, 0xFFFFFC96,
0x5DB6CE57, 0x823C1279, 0xFFFFFCB1, 0x4DFB5637, 0xC2109436, 0xFFFFFCCB,
0x3848984F, 0x9096EA6F, 0xFFFFFCE6, 0x25823AC7, 0xD77485CB, 0xFFFFFD00,
0x97BF97F4, 0xA086CFCD, 0xFFFFFD1B, 0x172AACE5, 0xEF340A98, 0xFFFFFD35,
0x2A35B28E, 0xB23867FB, 0xFFFFFD50, 0xD2C63F3B, 0x84C8D4DF, 0xFFFFFD6B,
0x1AD3CDBA, 0xC5DD4427, 0xFFFFFD85, 0xBB25C996, 0x936B9FCE, 0xFFFFFDA0,
0x7D62A584, 0xDBAC6C24, 0xFFFFFDBA, 0x0D5FDAF6, 0xA3AB6658, 0xFFFFFDD5,
0xDEC3F126, 0xF3E2F893, 0xFFFFFDEF, 0xAAFF80B8, 0xB5B5ADA8, 0xFFFFFE0A,
0x6C7C4A8B, 0x87625F05, 0xFFFFFE25, 0x34C13053, 0xC9BCFF60, 0xFFFFFE3F,
0x91BA2655, 0x964E858C, 0xFFFFFE5A, 0x70297EBD, 0xDFF97724, 0xFFFFFE74,
0xB8E5B88F, 0xA6DFBD9F, 0xFFFFFE8F, 0x88747D94, 0xF8A95FCF, 0xFFFFFEA9,
0x8FA89BCF, 0xB9447093, 0xFFFFFEC4, 0xBF0F156B, 0x8A08F0F8, 0xFFFFFEDF,
0x653131B6, 0xCDB02555, 0xFFFFFEF9, 0xD07B7FAC, 0x993FE2C6, 0xFFFFFF14,
0x2A2B3B06, 0xE45C10C4, 0xFFFFFF2E, 0x697392D3, 0xAA242499, 0xFFFFFF49,
0x8300CA0E, 0xFD87B5F2, 0xFFFFFF63, 0x92111AEB, 0xBCE50864, 0xFFFFFF7E,
0x6F5088CC, 0x8CBCCC09, 0xFFFFFF99, 0xE219652C, 0xD1B71758, 0xFFFFFFB3,
0x00000000, 0x9C400000, 0xFFFFFFCE, 0x00000000, 0xE8D4A510, 0xFFFFFFE8,
0xAC620000, 0xAD78EBC5, 0x00000003, 0xF8940984, 0x813F3978, 0x0000001E,
0xC90715B3, 0xC097CE7B, 0x00000038, 0x7BEA5C70, 0x8F7E32CE, 0x00000053,
0xABE98068, 0xD5D238A4, 0x0000006D, 0x179A2245, 0x9F4F2726, 0x00000088,
0xD4C4FB27, 0xED63A231, 0x000000A2, 0x8CC8ADA8, 0xB0DE6538, 0x000000BD,
0x1AAB65DB, 0x83C7088E, 0x000000D8, 0x42711D9A, 0xC45D1DF9, 0x000000F2,
0xA61BE758, 0x924D692C, 0x0000010D, 0x1A708DEA, 0xDA01EE64, 0x00000127,
0x9AEF774A, 0xA26DA399, 0x00000142, 0xB47D6B85, 0xF209787B, 0x0000015C,
0x79DD1877, 0xB454E4A1, 0x00000177, 0x5B9BC5C2, 0x865B8692, 0x00000192,
0xC8965D3D, 0xC83553C5, 0x000001AC, 0xFA97A0B3, 0x952AB45C, 0x000001C7,
0x99A05FE3, 0xDE469FBD, 0x000001E1, 0xDB398C25, 0xA59BC234, 0x000001FC,
0xA3989F5C, 0xF6C69A72, 0x00000216, 0x54E9BECE, 0xB7DCBF53, 0x00000231,
0xF22241E2, 0x88FCF317, 0x0000024C, 0xD35C78A5, 0xCC20CE9B, 0x00000266,
0x7B2153DF, 0x98165AF3, 0x00000281, 0x971F303A, 0xE2A0B5DC, 0x0000029B,
0x5CE3B396, 0xA8D9D153, 0x000002B6, 0xA4A7443C, 0xFB9B7CD9, 0x000002D0,
0xA7A44410, 0xBB764C4C, 0x000002EB, 0xB6409C1A, 0x8BAB8EEF, 0x00000306,
0xA657842C, 0xD01FEF10, 0x00000320, 0xE9913129, 0x9B10A4E5, 0x0000033B,
0xA19C0C9D, 0xE7109BFB, 0x00000355, 0x623BF429, 0xAC2820D9, 0x00000370,
0x7AA7CF85, 0x80444B5E, 0x0000038B, 0x03ACDD2D, 0xBF21E440, 0x000003A5,
0x5E44FF8F, 0x8E679C2F, 0x000003C0, 0x9C8CB841, 0xD433179D, 0x000003DA,
0xB4E31BA9, 0x9E19DB92, 0x000003F5, 0xBADF77D9, 0xEB96BF6E, 0x0000040F,
0x9BF0EE6B, 0xAF87023B, 0x0000042A,
};
// wuffs_base__private_implementation__small_powers_of_10 contains
// approximations to the powers of 10, ranging from 1e+0 to 1e+7, with the
// exponent stepping by 1. Each step consists of three uint32_t elements.
//
// For example, the third approximation, for 1e+2, consists of the uint32_t
// triple (0x00000000, 0xC8000000, 0xFFFFFFC7). The first two of that triple
// are a little-endian uint64_t value: 0xC800000000000000. The last one is an
// int32_t value: -57. Together, they represent the approximation:
// 1e+2 ≈ 0xC800000000000000 * (2 ** -57) // This approx'n is exact.
// Similarly, the (0x00000000, 0x9C400000, 0xFFFFFFCE) uint32_t triple means:
// 1e+4 ≈ 0x9C40000000000000 * (2 ** -50) // This approx'n is exact.
static const uint32_t
wuffs_base__private_implementation__small_powers_of_10[24] = {
0x00000000, 0x80000000, 0xFFFFFFC1, 0x00000000, 0xA0000000, 0xFFFFFFC4,
0x00000000, 0xC8000000, 0xFFFFFFC7, 0x00000000, 0xFA000000, 0xFFFFFFCA,
0x00000000, 0x9C400000, 0xFFFFFFCE, 0x00000000, 0xC3500000, 0xFFFFFFD1,
0x00000000, 0xF4240000, 0xFFFFFFD4, 0x00000000, 0x98968000, 0xFFFFFFD8,
};
// 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 (big_powers_of_10 + small_powers_of_10)
// range, -348 ..= +347, stepping big_powers_of_10 by 8 (which is 87
// triples) and small_powers_of_10 by 1 (which is 8 triples).
int32_t exp10 = h->decimal_point - ((int32_t)(i_end));
if (exp10 < -348) {
goto fail;
}
uint32_t bpo10 = ((uint32_t)(exp10 + 348)) / 8;
uint32_t spo10 = ((uint32_t)(exp10 + 348)) % 8;
if (bpo10 >= 87) {
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.
if (exp10 > 22) {
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 small_powers_of_10[etc].
wuffs_base__private_implementation__medium_prec_bin__mul_pow_10(
m, &wuffs_base__private_implementation__small_powers_of_10[3 * spo10]);
error += 2;
error <<= wuffs_base__private_implementation__medium_prec_bin__normalize(m);
// Multiply by big_powers_of_10[etc].
wuffs_base__private_implementation__medium_prec_bin__mul_pow_10(
m, &wuffs_base__private_implementation__big_powers_of_10[3 * bpo10]);
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);
}