tvl-depot/absl/strings/internal/charconv_bigint.cc

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-- f28d30df5769bb832dec3ff36d2fcd2bcdf494a3 by Shaindel Schwartz <shaindel@google.com>: Internal change PiperOrigin-RevId: 201046831 -- 711715a78b7e53dfaafd4d7f08a74e76db22af88 by Mark Barolak <mbar@google.com>: Internal fix PiperOrigin-RevId: 201043684 -- 64b53edd6bf1fa48f74e7f5d33f00f80d5089147 by Shaindel Schwartz <shaindel@google.com>: Remove extra whitespace PiperOrigin-RevId: 201041989 -- 0bdd2a0b33657b688e4a04aeba9ebba47e4dc6ca by Shaindel Schwartz <shaindel@google.com>: Whitespace fix. PiperOrigin-RevId: 201034413 -- 3deb0ac296ef1b74c4789e114a8a8bf53253f26b by Shaindel Schwartz <shaindel@google.com>: Scrub build tags. No functional changes. PiperOrigin-RevId: 201032927 -- da75d0f8b73baa7e8f4e9a092bba546012ed3b71 by Alex Strelnikov <strel@google.com>: Internal change. PiperOrigin-RevId: 201026131 -- 6815d80caa19870d0c441b6b9816c68db41393a5 by Tom Manshreck <shreck@google.com>: Add documentation for our LTS snapshot branches PiperOrigin-RevId: 201025191 -- 64c3b02006f39e6a8127bbabf9ec947fb45b6504 by Greg Falcon <gfalcon@google.com>: Provide absl::from_chars for double and float types. This is a forward-compatible implementation of std::from_chars from C++17. This provides exact "round_to_nearest" conversions, and has some nice properties: * Works with string_view (it can convert numbers from non-NUL-terminated buffers) * Never allocates memory * Faster than the standard library strtod() in our toolchain * Uses integer math in its calculations, so is unaffected by floating point environment * Unaffected by C locale Also change SimpleAtod/SimpleAtoi to use this new API under the hood. PiperOrigin-RevId: 201003324 -- 542869258eb100779497c899103dc96aced52749 by Greg Falcon <gfalcon@google.com>: Internal change PiperOrigin-RevId: 200999200 -- 3aba192775c7f80e2cd7f221b0a73537823c54ea by Gennadiy Rozental <rogeeff@google.com>: Internal change PiperOrigin-RevId: 200947470 -- daf9b9feedd748d5364a4c06165b7cb7604d3e1e by Mark Barolak <mbar@google.com>: Add an absl:: qualification to a usage of base_internal::SchedulingMode outside of an absl:: namespace. PiperOrigin-RevId: 200748234 -- a8d265290a22d629f3d9bf9f872c204200bfe8c8 by Mark Barolak <mbar@google.com>: Add a missing namespace closing comment to optional.h. PiperOrigin-RevId: 200739934 -- f05af8ee1c6b864dad2df7c907d424209a3e3202 by Abseil Team <absl-team@google.com>: Internal change PiperOrigin-RevId: 200719115 GitOrigin-RevId: f28d30df5769bb832dec3ff36d2fcd2bcdf494a3 Change-Id: Ie4fa601078fd4aa57286372611f1d114fdec82c0
2018-06-18 22:18:53 +02:00
// Copyright 2018 The Abseil 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
-- f28d30df5769bb832dec3ff36d2fcd2bcdf494a3 by Shaindel Schwartz <shaindel@google.com>: Internal change PiperOrigin-RevId: 201046831 -- 711715a78b7e53dfaafd4d7f08a74e76db22af88 by Mark Barolak <mbar@google.com>: Internal fix PiperOrigin-RevId: 201043684 -- 64b53edd6bf1fa48f74e7f5d33f00f80d5089147 by Shaindel Schwartz <shaindel@google.com>: Remove extra whitespace PiperOrigin-RevId: 201041989 -- 0bdd2a0b33657b688e4a04aeba9ebba47e4dc6ca by Shaindel Schwartz <shaindel@google.com>: Whitespace fix. PiperOrigin-RevId: 201034413 -- 3deb0ac296ef1b74c4789e114a8a8bf53253f26b by Shaindel Schwartz <shaindel@google.com>: Scrub build tags. No functional changes. PiperOrigin-RevId: 201032927 -- da75d0f8b73baa7e8f4e9a092bba546012ed3b71 by Alex Strelnikov <strel@google.com>: Internal change. PiperOrigin-RevId: 201026131 -- 6815d80caa19870d0c441b6b9816c68db41393a5 by Tom Manshreck <shreck@google.com>: Add documentation for our LTS snapshot branches PiperOrigin-RevId: 201025191 -- 64c3b02006f39e6a8127bbabf9ec947fb45b6504 by Greg Falcon <gfalcon@google.com>: Provide absl::from_chars for double and float types. This is a forward-compatible implementation of std::from_chars from C++17. This provides exact "round_to_nearest" conversions, and has some nice properties: * Works with string_view (it can convert numbers from non-NUL-terminated buffers) * Never allocates memory * Faster than the standard library strtod() in our toolchain * Uses integer math in its calculations, so is unaffected by floating point environment * Unaffected by C locale Also change SimpleAtod/SimpleAtoi to use this new API under the hood. PiperOrigin-RevId: 201003324 -- 542869258eb100779497c899103dc96aced52749 by Greg Falcon <gfalcon@google.com>: Internal change PiperOrigin-RevId: 200999200 -- 3aba192775c7f80e2cd7f221b0a73537823c54ea by Gennadiy Rozental <rogeeff@google.com>: Internal change PiperOrigin-RevId: 200947470 -- daf9b9feedd748d5364a4c06165b7cb7604d3e1e by Mark Barolak <mbar@google.com>: Add an absl:: qualification to a usage of base_internal::SchedulingMode outside of an absl:: namespace. PiperOrigin-RevId: 200748234 -- a8d265290a22d629f3d9bf9f872c204200bfe8c8 by Mark Barolak <mbar@google.com>: Add a missing namespace closing comment to optional.h. PiperOrigin-RevId: 200739934 -- f05af8ee1c6b864dad2df7c907d424209a3e3202 by Abseil Team <absl-team@google.com>: Internal change PiperOrigin-RevId: 200719115 GitOrigin-RevId: f28d30df5769bb832dec3ff36d2fcd2bcdf494a3 Change-Id: Ie4fa601078fd4aa57286372611f1d114fdec82c0
2018-06-18 22:18:53 +02:00
//
// 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.
#include "absl/strings/internal/charconv_bigint.h"
#include <algorithm>
#include <cassert>
#include <string>
namespace absl {
namespace strings_internal {
namespace {
// Table containing some large powers of 5, for fast computation.
// Constant step size for entries in the kLargePowersOfFive table. Each entry
// is larger than the previous entry by a factor of 5**kLargePowerOfFiveStep
// (or 5**27).
//
// In other words, the Nth entry in the table is 5**(27*N).
//
// 5**27 is the largest power of 5 that fits in 64 bits.
constexpr int kLargePowerOfFiveStep = 27;
// The largest legal index into the kLargePowersOfFive table.
//
// In other words, the largest precomputed power of 5 is 5**(27*20).
constexpr int kLargestPowerOfFiveIndex = 20;
// Table of powers of (5**27), up to (5**27)**20 == 5**540.
//
// Used to generate large powers of 5 while limiting the number of repeated
// multiplications required.
//
// clang-format off
const uint32_t kLargePowersOfFive[] = {
// 5**27 (i=1), start=0, end=2
0xfa10079dU, 0x6765c793U,
// 5**54 (i=2), start=2, end=6
0x97d9f649U, 0x6664242dU, 0x29939b14U, 0x29c30f10U,
// 5**81 (i=3), start=6, end=12
0xc4f809c5U, 0x7bf3f22aU, 0x67bdae34U, 0xad340517U, 0x369d1b5fU, 0x10de1593U,
// 5**108 (i=4), start=12, end=20
0x92b260d1U, 0x9efff7c7U, 0x81de0ec6U, 0xaeba5d56U, 0x410664a4U, 0x4f40737aU,
0x20d3846fU, 0x06d00f73U,
// 5**135 (i=5), start=20, end=30
0xff1b172dU, 0x13a1d71cU, 0xefa07617U, 0x7f682d3dU, 0xff8c90c0U, 0x3f0131e7U,
0x3fdcb9feU, 0x917b0177U, 0x16c407a7U, 0x02c06b9dU,
// 5**162 (i=6), start=30, end=42
0x960f7199U, 0x056667ecU, 0xe07aefd8U, 0x80f2b9ccU, 0x8273f5e3U, 0xeb9a214aU,
0x40b38005U, 0x0e477ad4U, 0x277d08e6U, 0xfa28b11eU, 0xd3f7d784U, 0x011c835bU,
// 5**189 (i=7), start=42, end=56
0xf723d9d5U, 0x3282d3f3U, 0xe00857d1U, 0x69659d25U, 0x2cf117cfU, 0x24da6d07U,
0x954d1417U, 0x3e5d8cedU, 0x7a8bb766U, 0xfd785ae6U, 0x645436d2U, 0x40c78b34U,
0x94151217U, 0x0072e9f7U,
// 5**216 (i=8), start=56, end=72
0x2b416aa1U, 0x7893c5a7U, 0xe37dc6d4U, 0x2bad2beaU, 0xf0fc846cU, 0x7575ae4bU,
0x62587b14U, 0x83b67a34U, 0x02110cdbU, 0xf7992f55U, 0x00deb022U, 0xa4a23becU,
0x8af5c5cdU, 0xb85b654fU, 0x818df38bU, 0x002e69d2U,
// 5**243 (i=9), start=72, end=90
0x3518cbbdU, 0x20b0c15fU, 0x38756c2fU, 0xfb5dc3ddU, 0x22ad2d94U, 0xbf35a952U,
0xa699192aU, 0x9a613326U, 0xad2a9cedU, 0xd7f48968U, 0xe87dfb54U, 0xc8f05db6U,
0x5ef67531U, 0x31c1ab49U, 0xe202ac9fU, 0x9b2957b5U, 0xa143f6d3U, 0x0012bf07U,
// 5**270 (i=10), start=90, end=110
0x8b971de9U, 0x21aba2e1U, 0x63944362U, 0x57172336U, 0xd9544225U, 0xfb534166U,
0x08c563eeU, 0x14640ee2U, 0x24e40d31U, 0x02b06537U, 0x03887f14U, 0x0285e533U,
0xb744ef26U, 0x8be3a6c4U, 0x266979b4U, 0x6761ece2U, 0xd9cb39e4U, 0xe67de319U,
0x0d39e796U, 0x00079250U,
// 5**297 (i=11), start=110, end=132
0x260eb6e5U, 0xf414a796U, 0xee1a7491U, 0xdb9368ebU, 0xf50c105bU, 0x59157750U,
0x9ed2fb5cU, 0xf6e56d8bU, 0xeaee8d23U, 0x0f319f75U, 0x2aa134d6U, 0xac2908e9U,
0xd4413298U, 0x02f02a55U, 0x989d5a7aU, 0x70dde184U, 0xba8040a7U, 0x03200981U,
0xbe03b11cU, 0x3c1c2a18U, 0xd60427a1U, 0x00030ee0U,
// 5**324 (i=12), start=132, end=156
0xce566d71U, 0xf1c4aa25U, 0x4e93ca53U, 0xa72283d0U, 0x551a73eaU, 0x3d0538e2U,
0x8da4303fU, 0x6a58de60U, 0x0e660221U, 0x49cf61a6U, 0x8d058fc1U, 0xb9d1a14cU,
0x4bab157dU, 0xc85c6932U, 0x518c8b9eU, 0x9b92b8d0U, 0x0d8a0e21U, 0xbd855df9U,
0xb3ea59a1U, 0x8da29289U, 0x4584d506U, 0x3752d80fU, 0xb72569c6U, 0x00013c33U,
// 5**351 (i=13), start=156, end=182
0x190f354dU, 0x83695cfeU, 0xe5a4d0c7U, 0xb60fb7e8U, 0xee5bbcc4U, 0xb922054cU,
0xbb4f0d85U, 0x48394028U, 0x1d8957dbU, 0x0d7edb14U, 0x4ecc7587U, 0x505e9e02U,
0x4c87f36bU, 0x99e66bd6U, 0x44b9ed35U, 0x753037d4U, 0xe5fe5f27U, 0x2742c203U,
0x13b2ed2bU, 0xdc525d2cU, 0xe6fde59aU, 0x77ffb18fU, 0x13c5752cU, 0x08a84bccU,
0x859a4940U, 0x00007fb6U,
// 5**378 (i=14), start=182, end=210
0x4f98cb39U, 0xa60edbbcU, 0x83b5872eU, 0xa501acffU, 0x9cc76f78U, 0xbadd4c73U,
0x43e989faU, 0xca7acf80U, 0x2e0c824fU, 0xb19f4ffcU, 0x092fd81cU, 0xe4eb645bU,
0xa1ff84c2U, 0x8a5a83baU, 0xa8a1fae9U, 0x1db43609U, 0xb0fed50bU, 0x0dd7d2bdU,
0x7d7accd8U, 0x91fa640fU, 0x37dcc6c5U, 0x1c417fd5U, 0xe4d462adU, 0xe8a43399U,
0x131bf9a5U, 0x8df54d29U, 0x36547dc1U, 0x00003395U,
// 5**405 (i=15), start=210, end=240
0x5bd330f5U, 0x77d21967U, 0x1ac481b7U, 0x6be2f7ceU, 0x7f4792a9U, 0xe84c2c52U,
0x84592228U, 0x9dcaf829U, 0xdab44ce1U, 0x3d0c311bU, 0x532e297dU, 0x4704e8b4U,
0x9cdc32beU, 0x41e64d9dU, 0x7717bea1U, 0xa824c00dU, 0x08f50b27U, 0x0f198d77U,
0x49bbfdf0U, 0x025c6c69U, 0xd4e55cd3U, 0xf083602bU, 0xb9f0fecdU, 0xc0864aeaU,
0x9cb98681U, 0xaaf620e9U, 0xacb6df30U, 0x4faafe66U, 0x8af13c3bU, 0x000014d5U,
// 5**432 (i=16), start=240, end=272
0x682bb941U, 0x89a9f297U, 0xcba75d7bU, 0x404217b1U, 0xb4e519e9U, 0xa1bc162bU,
0xf7f5910aU, 0x98715af5U, 0x2ff53e57U, 0xe3ef118cU, 0x490c4543U, 0xbc9b1734U,
0x2affbe4dU, 0x4cedcb4cU, 0xfb14e99eU, 0x35e34212U, 0xece39c24U, 0x07673ab3U,
0xe73115ddU, 0xd15d38e7U, 0x093eed3bU, 0xf8e7eac5U, 0x78a8cc80U, 0x25227aacU,
0x3f590551U, 0x413da1cbU, 0xdf643a55U, 0xab65ad44U, 0xd70b23d7U, 0xc672cd76U,
0x3364ea62U, 0x0000086aU,
// 5**459 (i=17), start=272, end=306
0x22f163ddU, 0x23cf07acU, 0xbe2af6c2U, 0xf412f6f6U, 0xc3ff541eU, 0x6eeaf7deU,
0xa47047e0U, 0x408cda92U, 0x0f0eeb08U, 0x56deba9dU, 0xcfc6b090U, 0x8bbbdf04U,
0x3933cdb3U, 0x9e7bb67dU, 0x9f297035U, 0x38946244U, 0xee1d37bbU, 0xde898174U,
0x63f3559dU, 0x705b72fbU, 0x138d27d9U, 0xf8603a78U, 0x735eec44U, 0xe30987d5U,
0xc6d38070U, 0x9cfe548eU, 0x9ff01422U, 0x7c564aa8U, 0x91cc60baU, 0xcbc3565dU,
0x7550a50bU, 0x6909aeadU, 0x13234c45U, 0x00000366U,
// 5**486 (i=18), start=306, end=342
0x17954989U, 0x3a7d7709U, 0x98042de5U, 0xa9011443U, 0x45e723c2U, 0x269ffd6fU,
0x58852a46U, 0xaaa1042aU, 0x2eee8153U, 0xb2b6c39eU, 0xaf845b65U, 0xf6c365d7U,
0xe4cffb2bU, 0xc840e90cU, 0xabea8abbU, 0x5c58f8d2U, 0x5c19fa3aU, 0x4670910aU,
0x4449f21cU, 0xefa645b3U, 0xcc427decU, 0x083c3d73U, 0x467cb413U, 0x6fe10ae4U,
0x3caffc72U, 0x9f8da55eU, 0x5e5c8ea7U, 0x490594bbU, 0xf0871b0bU, 0xdd89816cU,
0x8e931df8U, 0xe85ce1c9U, 0xcca090a5U, 0x575fa16bU, 0x6b9f106cU, 0x0000015fU,
// 5**513 (i=19), start=342, end=380
0xee20d805U, 0x57bc3c07U, 0xcdea624eU, 0xd3f0f52dU, 0x9924b4f4U, 0xcf968640U,
0x61d41962U, 0xe87fb464U, 0xeaaf51c7U, 0x564c8b60U, 0xccda4028U, 0x529428bbU,
0x313a1fa8U, 0x96bd0f94U, 0x7a82ebaaU, 0xad99e7e9U, 0xf2668cd4U, 0xbe33a45eU,
0xfd0db669U, 0x87ee369fU, 0xd3ec20edU, 0x9c4d7db7U, 0xdedcf0d8U, 0x7cd2ca64U,
0xe25a6577U, 0x61003fd4U, 0xe56f54ccU, 0x10b7c748U, 0x40526e5eU, 0x7300ae87U,
0x5c439261U, 0x2c0ff469U, 0xbf723f12U, 0xb2379b61U, 0xbf59b4f5U, 0xc91b1c3fU,
0xf0046d27U, 0x0000008dU,
// 5**540 (i=20), start=380, end=420
0x525c9e11U, 0xf4e0eb41U, 0xebb2895dU, 0x5da512f9U, 0x7d9b29d4U, 0x452f4edcU,
0x0b90bc37U, 0x341777cbU, 0x63d269afU, 0x1da77929U, 0x0a5c1826U, 0x77991898U,
0x5aeddf86U, 0xf853a877U, 0x538c31ccU, 0xe84896daU, 0xb7a0010bU, 0x17ef4de5U,
0xa52a2adeU, 0x029fd81cU, 0x987ce701U, 0x27fefd77U, 0xdb46c66fU, 0x5d301900U,
0x496998c0U, 0xbb6598b9U, 0x5eebb607U, 0xe547354aU, 0xdf4a2f7eU, 0xf06c4955U,
0x96242ffaU, 0x1775fb27U, 0xbecc58ceU, 0xebf2a53bU, 0x3eaad82aU, 0xf41137baU,
0x573e6fbaU, 0xfb4866b8U, 0x54002148U, 0x00000039U,
};
// clang-format on
// Returns a pointer to the big integer data for (5**27)**i. i must be
// between 1 and 20, inclusive.
const uint32_t* LargePowerOfFiveData(int i) {
return kLargePowersOfFive + i * (i - 1);
}
// Returns the size of the big integer data for (5**27)**i, in words. i must be
// between 1 and 20, inclusive.
int LargePowerOfFiveSize(int i) { return 2 * i; }
} // namespace
const uint32_t kFiveToNth[14] = {
1, 5, 25, 125, 625, 3125, 15625,
78125, 390625, 1953125, 9765625, 48828125, 244140625, 1220703125,
};
const uint32_t kTenToNth[10] = {
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000,
};
template <int max_words>
int BigUnsigned<max_words>::ReadFloatMantissa(const ParsedFloat& fp,
int significant_digits) {
SetToZero();
assert(fp.type == FloatType::kNumber);
if (fp.subrange_begin == nullptr) {
// We already exactly parsed the mantissa, so no more work is necessary.
words_[0] = fp.mantissa & 0xffffffffu;
words_[1] = fp.mantissa >> 32;
if (words_[1]) {
size_ = 2;
} else if (words_[0]) {
size_ = 1;
}
return fp.exponent;
}
int exponent_adjust =
ReadDigits(fp.subrange_begin, fp.subrange_end, significant_digits);
return fp.literal_exponent + exponent_adjust;
}
template <int max_words>
int BigUnsigned<max_words>::ReadDigits(const char* begin, const char* end,
int significant_digits) {
assert(significant_digits <= Digits10() + 1);
SetToZero();
bool after_decimal_point = false;
// Discard any leading zeroes before the decimal point
while (begin < end && *begin == '0') {
++begin;
}
int dropped_digits = 0;
// Discard any trailing zeroes. These may or may not be after the decimal
// point.
while (begin < end && *std::prev(end) == '0') {
--end;
++dropped_digits;
}
if (begin < end && *std::prev(end) == '.') {
// If the std::string ends in '.', either before or after dropping zeroes, then
// drop the decimal point and look for more digits to drop.
dropped_digits = 0;
--end;
while (begin < end && *std::prev(end) == '0') {
--end;
++dropped_digits;
}
} else if (dropped_digits) {
// We dropped digits, and aren't sure if they're before or after the decimal
// point. Figure that out now.
const char* dp = std::find(begin, end, '.');
if (dp != end) {
// The dropped trailing digits were after the decimal point, so don't
// count them.
dropped_digits = 0;
}
}
// Any non-fraction digits we dropped need to be accounted for in our exponent
// adjustment.
int exponent_adjust = dropped_digits;
uint32_t queued = 0;
int digits_queued = 0;
for (; begin != end && significant_digits > 0; ++begin) {
if (*begin == '.') {
after_decimal_point = true;
continue;
}
if (after_decimal_point) {
// For each fractional digit we emit in our parsed integer, adjust our
// decimal exponent to compensate.
--exponent_adjust;
}
int digit = (*begin - '0');
--significant_digits;
if (significant_digits == 0 && std::next(begin) != end &&
(digit == 0 || digit == 5)) {
// If this is the very last significant digit, but insignificant digits
// remain, we know that the last of those remaining significant digits is
// nonzero. (If it wasn't, we would have stripped it before we got here.)
// So if this final digit is a 0 or 5, adjust it upward by 1.
//
// This adjustment is what allows incredibly large mantissas ending in
// 500000...000000000001 to correctly round up, rather than to nearest.
++digit;
}
queued = 10 * queued + digit;
++digits_queued;
if (digits_queued == kMaxSmallPowerOfTen) {
MultiplyBy(kTenToNth[kMaxSmallPowerOfTen]);
AddWithCarry(0, queued);
queued = digits_queued = 0;
}
}
// Encode any remaining digits.
if (digits_queued) {
MultiplyBy(kTenToNth[digits_queued]);
AddWithCarry(0, queued);
}
// If any insignificant digits remain, we will drop them. But if we have not
// yet read the decimal point, then we have to adjust the exponent to account
// for the dropped digits.
if (begin < end && !after_decimal_point) {
// This call to std::find will result in a pointer either to the decimal
// point, or to the end of our buffer if there was none.
//
// Either way, [begin, decimal_point) will contain the set of dropped digits
// that require an exponent adjustment.
const char* decimal_point = std::find(begin, end, '.');
exponent_adjust += (decimal_point - begin);
}
return exponent_adjust;
}
template <int max_words>
/* static */ BigUnsigned<max_words> BigUnsigned<max_words>::FiveToTheNth(
int n) {
BigUnsigned answer(1u);
// Seed from the table of large powers, if possible.
bool first_pass = true;
while (n >= kLargePowerOfFiveStep) {
int big_power =
std::min(n / kLargePowerOfFiveStep, kLargestPowerOfFiveIndex);
if (first_pass) {
// just copy, rather than multiplying by 1
std::copy(
LargePowerOfFiveData(big_power),
LargePowerOfFiveData(big_power) + LargePowerOfFiveSize(big_power),
answer.words_);
answer.size_ = LargePowerOfFiveSize(big_power);
first_pass = false;
} else {
answer.MultiplyBy(LargePowerOfFiveSize(big_power),
LargePowerOfFiveData(big_power));
}
n -= kLargePowerOfFiveStep * big_power;
}
answer.MultiplyByFiveToTheNth(n);
return answer;
}
template <int max_words>
void BigUnsigned<max_words>::MultiplyStep(int original_size,
const uint32_t* other_words,
int other_size, int step) {
int this_i = std::min(original_size - 1, step);
int other_i = step - this_i;
uint64_t this_word = 0;
uint64_t carry = 0;
for (; this_i >= 0 && other_i < other_size; --this_i, ++other_i) {
uint64_t product = words_[this_i];
product *= other_words[other_i];
this_word += product;
carry += (this_word >> 32);
this_word &= 0xffffffff;
}
AddWithCarry(step + 1, carry);
words_[step] = this_word & 0xffffffff;
if (this_word > 0 && size_ <= step) {
size_ = step + 1;
}
}
template <int max_words>
std::string BigUnsigned<max_words>::ToString() const {
BigUnsigned<max_words> copy = *this;
std::string result;
// Build result in reverse order
while (copy.size() > 0) {
int next_digit = copy.DivMod<10>();
result.push_back('0' + next_digit);
}
if (result.empty()) {
result.push_back('0');
}
std::reverse(result.begin(), result.end());
return result;
}
template class BigUnsigned<4>;
template class BigUnsigned<84>;
} // namespace strings_internal
} // namespace absl