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1//===----------------------------------------------------------------------===//
2//
3// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
4// See https://llvm.org/LICENSE.txt for license information.
5// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
6//
7//===----------------------------------------------------------------------===//
8
9// Copyright (c) Microsoft Corporation.
10// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
11
12// Copyright 2018 Ulf Adams
13// Copyright (c) Microsoft Corporation. All rights reserved.
14
15// Boost Software License - Version 1.0 - August 17th, 2003
16
17// Permission is hereby granted, free of charge, to any person or organization
18// obtaining a copy of the software and accompanying documentation covered by
19// this license (the "Software") to use, reproduce, display, distribute,
20// execute, and transmit the Software, and to prepare derivative works of the
21// Software, and to permit third-parties to whom the Software is furnished to
22// do so, all subject to the following:
23
24// The copyright notices in the Software and this entire statement, including
25// the above license grant, this restriction and the following disclaimer,
26// must be included in all copies of the Software, in whole or in part, and
27// all derivative works of the Software, unless such copies or derivative
28// works are solely in the form of machine-executable object code generated by
29// a source language processor.
30
31// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
32// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
33// FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
34// SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
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36// ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
37// DEALINGS IN THE SOFTWARE.
38
39// Avoid formatting to keep the changes with the original code minimal.
40// clang-format off
41
42#include <__assert>
43#include <__config>
44#include <charconv>
45#include <cstdint>
46#include <cstddef>
47
48#include "include/ryu/common.h"
49#include "include/ryu/d2fixed.h"
50#include "include/ryu/d2s_intrinsics.h"
51#include "include/ryu/digit_table.h"
52#include "include/ryu/f2s.h"
53#include "include/ryu/ryu.h"
54
55_LIBCPP_BEGIN_NAMESPACE_STD
56
57inline constexpr int __FLOAT_MANTISSA_BITS = 23;
58inline constexpr int __FLOAT_EXPONENT_BITS = 8;
59inline constexpr int __FLOAT_BIAS = 127;
60
61inline constexpr int __FLOAT_POW5_INV_BITCOUNT = 59;
62inline constexpr uint64_t __FLOAT_POW5_INV_SPLIT[31] = {
63 576460752303423489u, 461168601842738791u, 368934881474191033u, 295147905179352826u,
64 472236648286964522u, 377789318629571618u, 302231454903657294u, 483570327845851670u,
65 386856262276681336u, 309485009821345069u, 495176015714152110u, 396140812571321688u,
66 316912650057057351u, 507060240091291761u, 405648192073033409u, 324518553658426727u,
67 519229685853482763u, 415383748682786211u, 332306998946228969u, 531691198313966350u,
68 425352958651173080u, 340282366920938464u, 544451787073501542u, 435561429658801234u,
69 348449143727040987u, 557518629963265579u, 446014903970612463u, 356811923176489971u,
70 570899077082383953u, 456719261665907162u, 365375409332725730u
71};
72inline constexpr int __FLOAT_POW5_BITCOUNT = 61;
73inline constexpr uint64_t __FLOAT_POW5_SPLIT[47] = {
74 1152921504606846976u, 1441151880758558720u, 1801439850948198400u, 2251799813685248000u,
75 1407374883553280000u, 1759218604441600000u, 2199023255552000000u, 1374389534720000000u,
76 1717986918400000000u, 2147483648000000000u, 1342177280000000000u, 1677721600000000000u,
77 2097152000000000000u, 1310720000000000000u, 1638400000000000000u, 2048000000000000000u,
78 1280000000000000000u, 1600000000000000000u, 2000000000000000000u, 1250000000000000000u,
79 1562500000000000000u, 1953125000000000000u, 1220703125000000000u, 1525878906250000000u,
80 1907348632812500000u, 1192092895507812500u, 1490116119384765625u, 1862645149230957031u,
81 1164153218269348144u, 1455191522836685180u, 1818989403545856475u, 2273736754432320594u,
82 1421085471520200371u, 1776356839400250464u, 2220446049250313080u, 1387778780781445675u,
83 1734723475976807094u, 2168404344971008868u, 1355252715606880542u, 1694065894508600678u,
84 2117582368135750847u, 1323488980084844279u, 1654361225106055349u, 2067951531382569187u,
85 1292469707114105741u, 1615587133892632177u, 2019483917365790221u
86};
87
88[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __pow5Factor(uint32_t __value) {
89 uint32_t __count = 0;
90 for (;;) {
91 _LIBCPP_ASSERT_INTERNAL(__value != 0, "");
92 const uint32_t __q = __value / 5;
93 const uint32_t __r = __value % 5;
94 if (__r != 0) {
95 break;
96 }
97 __value = __q;
98 ++__count;
99 }
100 return __count;
101}
102
103// Returns true if __value is divisible by 5^__p.
104[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf5(const uint32_t __value, const uint32_t __p) {
105 return __pow5Factor(__value) >= __p;
106}
107
108// Returns true if __value is divisible by 2^__p.
109[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __multipleOfPowerOf2(const uint32_t __value, const uint32_t __p) {
110 _LIBCPP_ASSERT_INTERNAL(__value != 0, "");
111 _LIBCPP_ASSERT_INTERNAL(__p < 32, "");
112 // __builtin_ctz doesn't appear to be faster here.
113 return (__value & ((1u << __p) - 1)) == 0;
114}
115
116[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulShift(const uint32_t __m, const uint64_t __factor, const int32_t __shift) {
117 _LIBCPP_ASSERT_INTERNAL(__shift > 32, "");
118
119 // The casts here help MSVC to avoid calls to the __allmul library
120 // function.
121 const uint32_t __factorLo = static_cast<uint32_t>(__factor);
122 const uint32_t __factorHi = static_cast<uint32_t>(__factor >> 32);
123 const uint64_t __bits0 = static_cast<uint64_t>(__m) * __factorLo;
124 const uint64_t __bits1 = static_cast<uint64_t>(__m) * __factorHi;
125
126#ifndef _LIBCPP_64_BIT
127 // On 32-bit platforms we can avoid a 64-bit shift-right since we only
128 // need the upper 32 bits of the result and the shift value is > 32.
129 const uint32_t __bits0Hi = static_cast<uint32_t>(__bits0 >> 32);
130 uint32_t __bits1Lo = static_cast<uint32_t>(__bits1);
131 uint32_t __bits1Hi = static_cast<uint32_t>(__bits1 >> 32);
132 __bits1Lo += __bits0Hi;
133 __bits1Hi += (__bits1Lo < __bits0Hi);
134 const int32_t __s = __shift - 32;
135 return (__bits1Hi << (32 - __s)) | (__bits1Lo >> __s);
136#else // ^^^ 32-bit ^^^ / vvv 64-bit vvv
137 const uint64_t __sum = (__bits0 >> 32) + __bits1;
138 const uint64_t __shiftedSum = __sum >> (__shift - 32);
139 _LIBCPP_ASSERT_INTERNAL(__shiftedSum <= UINT32_MAX, "");
140 return static_cast<uint32_t>(__shiftedSum);
141#endif // ^^^ 64-bit ^^^
142}
143
144[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5InvDivPow2(const uint32_t __m, const uint32_t __q, const int32_t __j) {
145 return __mulShift(__m, __FLOAT_POW5_INV_SPLIT[__q], __j);
146}
147
148[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __mulPow5divPow2(const uint32_t __m, const uint32_t __i, const int32_t __j) {
149 return __mulShift(__m, __FLOAT_POW5_SPLIT[__i], __j);
150}
151
152// A floating decimal representing m * 10^e.
153struct __floating_decimal_32 {
154 uint32_t __mantissa;
155 int32_t __exponent;
156};
157
158[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_32 __f2d(const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
159 int32_t __e2;
160 uint32_t __m2;
161 if (__ieeeExponent == 0) {
162 // We subtract 2 so that the bounds computation has 2 additional bits.
163 __e2 = 1 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
164 __m2 = __ieeeMantissa;
165 } else {
166 __e2 = static_cast<int32_t>(__ieeeExponent) - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS - 2;
167 __m2 = (1u << __FLOAT_MANTISSA_BITS) | __ieeeMantissa;
168 }
169 const bool __even = (__m2 & 1) == 0;
170 const bool __acceptBounds = __even;
171
172 // Step 2: Determine the interval of valid decimal representations.
173 const uint32_t __mv = 4 * __m2;
174 const uint32_t __mp = 4 * __m2 + 2;
175 // Implicit bool -> int conversion. True is 1, false is 0.
176 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;
177 const uint32_t __mm = 4 * __m2 - 1 - __mmShift;
178
179 // Step 3: Convert to a decimal power base using 64-bit arithmetic.
180 uint32_t __vr, __vp, __vm;
181 int32_t __e10;
182 bool __vmIsTrailingZeros = false;
183 bool __vrIsTrailingZeros = false;
184 uint8_t __lastRemovedDigit = 0;
185 if (__e2 >= 0) {
186 const uint32_t __q = __log10Pow2(__e2);
187 __e10 = static_cast<int32_t>(__q);
188 const int32_t __k = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;
189 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;
190 __vr = __mulPow5InvDivPow2(__mv, __q, __i);
191 __vp = __mulPow5InvDivPow2(__mp, __q, __i);
192 __vm = __mulPow5InvDivPow2(__mm, __q, __i);
193 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
194 // We need to know one removed digit even if we are not going to loop below. We could use
195 // __q = X - 1 above, except that would require 33 bits for the result, and we've found that
196 // 32-bit arithmetic is faster even on 64-bit machines.
197 const int32_t __l = __FLOAT_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q - 1)) - 1;
198 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5InvDivPow2(__mv, __q - 1,
199 -__e2 + static_cast<int32_t>(__q) - 1 + __l) % 10);
200 }
201 if (__q <= 9) {
202 // The largest power of 5 that fits in 24 bits is 5^10, but __q <= 9 seems to be safe as well.
203 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any.
204 if (__mv % 5 == 0) {
205 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);
206 } else if (__acceptBounds) {
207 __vmIsTrailingZeros = __multipleOfPowerOf5(__mm, __q);
208 } else {
209 __vp -= __multipleOfPowerOf5(__mp, __q);
210 }
211 }
212 } else {
213 const uint32_t __q = __log10Pow5(-__e2);
214 __e10 = static_cast<int32_t>(__q) + __e2;
215 const int32_t __i = -__e2 - static_cast<int32_t>(__q);
216 const int32_t __k = __pow5bits(__i) - __FLOAT_POW5_BITCOUNT;
217 int32_t __j = static_cast<int32_t>(__q) - __k;
218 __vr = __mulPow5divPow2(__mv, static_cast<uint32_t>(__i), __j);
219 __vp = __mulPow5divPow2(__mp, static_cast<uint32_t>(__i), __j);
220 __vm = __mulPow5divPow2(__mm, static_cast<uint32_t>(__i), __j);
221 if (__q != 0 && (__vp - 1) / 10 <= __vm / 10) {
222 __j = static_cast<int32_t>(__q) - 1 - (__pow5bits(__i + 1) - __FLOAT_POW5_BITCOUNT);
223 __lastRemovedDigit = static_cast<uint8_t>(__mulPow5divPow2(__mv, static_cast<uint32_t>(__i + 1), __j) % 10);
224 }
225 if (__q <= 1) {
226 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.
227 // __mv = 4 * __m2, so it always has at least two trailing 0 bits.
228 __vrIsTrailingZeros = true;
229 if (__acceptBounds) {
230 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.
231 __vmIsTrailingZeros = __mmShift == 1;
232 } else {
233 // __mp = __mv + 2, so it always has at least one trailing 0 bit.
234 --__vp;
235 }
236 } else if (__q < 31) { // TRANSITION(ulfjack): Use a tighter bound here.
237 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);
238 }
239 }
240
241 // Step 4: Find the shortest decimal representation in the interval of valid representations.
242 int32_t __removed = 0;
243 uint32_t _Output;
244 if (__vmIsTrailingZeros || __vrIsTrailingZeros) {
245 // General case, which happens rarely (~4.0%).
246 while (__vp / 10 > __vm / 10) {
247#ifdef __clang__ // TRANSITION, LLVM-23106
248 __vmIsTrailingZeros &= __vm - (__vm / 10) * 10 == 0;
249#else
250 __vmIsTrailingZeros &= __vm % 10 == 0;
251#endif
252 __vrIsTrailingZeros &= __lastRemovedDigit == 0;
253 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
254 __vr /= 10;
255 __vp /= 10;
256 __vm /= 10;
257 ++__removed;
258 }
259 if (__vmIsTrailingZeros) {
260 while (__vm % 10 == 0) {
261 __vrIsTrailingZeros &= __lastRemovedDigit == 0;
262 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
263 __vr /= 10;
264 __vp /= 10;
265 __vm /= 10;
266 ++__removed;
267 }
268 }
269 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {
270 // Round even if the exact number is .....50..0.
271 __lastRemovedDigit = 4;
272 }
273 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
274 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);
275 } else {
276 // Specialized for the common case (~96.0%). Percentages below are relative to this.
277 // Loop iterations below (approximately):
278 // 0: 13.6%, 1: 70.7%, 2: 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
279 while (__vp / 10 > __vm / 10) {
280 __lastRemovedDigit = static_cast<uint8_t>(__vr % 10);
281 __vr /= 10;
282 __vp /= 10;
283 __vm /= 10;
284 ++__removed;
285 }
286 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
287 _Output = __vr + (__vr == __vm || __lastRemovedDigit >= 5);
288 }
289 const int32_t __exp = __e10 + __removed;
290
291 __floating_decimal_32 __fd;
292 __fd.__exponent = __exp;
293 __fd.__mantissa = _Output;
294 return __fd;
295}
296
297[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result _Large_integer_to_chars(char* const _First, char* const _Last,
298 const uint32_t _Mantissa2, const int32_t _Exponent2) {
299
300 // Print the integer _Mantissa2 * 2^_Exponent2 exactly.
301
302 // For nonzero integers, _Exponent2 >= -23. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.
303 // In that case, _Mantissa2 is the implicit 1 bit followed by 23 zeros, so _Exponent2 is -23 to shift away
304 // the zeros.) The dense range of exactly representable integers has negative or zero exponents
305 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:
306 // every digit is necessary to uniquely identify the value, so Ryu must print them all.
307
308 // Positive exponents are the non-dense range of exactly representable integers.
309 // This contains all of the values for which Ryu can't be used (and a few Ryu-friendly values).
310
311 // Performance note: Long division appears to be faster than losslessly widening float to double and calling
312 // __d2fixed_buffered_n(). If __f2fixed_buffered_n() is implemented, it might be faster than long division.
313
314 _LIBCPP_ASSERT_INTERNAL(_Exponent2 > 0, "");
315 _LIBCPP_ASSERT_INTERNAL(_Exponent2 <= 104, ""); // because __ieeeExponent <= 254
316
317 // Manually represent _Mantissa2 * 2^_Exponent2 as a large integer. _Mantissa2 is always 24 bits
318 // (due to the implicit bit), while _Exponent2 indicates a shift of at most 104 bits.
319 // 24 + 104 equals 128 equals 4 * 32, so we need exactly 4 32-bit elements.
320 // We use a little-endian representation, visualized like this:
321
322 // << left shift <<
323 // most significant
324 // _Data[3] _Data[2] _Data[1] _Data[0]
325 // least significant
326 // >> right shift >>
327
328 constexpr uint32_t _Data_size = 4;
329 uint32_t _Data[_Data_size]{};
330
331 // _Maxidx is the index of the most significant nonzero element.
332 uint32_t _Maxidx = ((24 + static_cast<uint32_t>(_Exponent2) + 31) / 32) - 1;
333 _LIBCPP_ASSERT_INTERNAL(_Maxidx < _Data_size, "");
334
335 const uint32_t _Bit_shift = static_cast<uint32_t>(_Exponent2) % 32;
336 if (_Bit_shift <= 8) { // _Mantissa2's 24 bits don't cross an element boundary
337 _Data[_Maxidx] = _Mantissa2 << _Bit_shift;
338 } else { // _Mantissa2's 24 bits cross an element boundary
339 _Data[_Maxidx - 1] = _Mantissa2 << _Bit_shift;
340 _Data[_Maxidx] = _Mantissa2 >> (32 - _Bit_shift);
341 }
342
343 // If Ryu hasn't determined the total output length, we need to buffer the digits generated from right to left
344 // by long division. The largest possible float is: 340'282346638'528859811'704183484'516925440
345 uint32_t _Blocks[4];
346 int32_t _Filled_blocks = 0;
347 // From left to right, we're going to print:
348 // _Data[0] will be [1, 10] digits.
349 // Then if _Filled_blocks > 0:
350 // _Blocks[_Filled_blocks - 1], ..., _Blocks[0] will be 0-filled 9-digit blocks.
351
352 if (_Maxidx != 0) { // If the integer is actually large, perform long division.
353 // Otherwise, skip to printing _Data[0].
354 for (;;) {
355 // Loop invariant: _Maxidx != 0 (i.e. the integer is actually large)
356
357 const uint32_t _Most_significant_elem = _Data[_Maxidx];
358 const uint32_t _Initial_remainder = _Most_significant_elem % 1000000000;
359 const uint32_t _Initial_quotient = _Most_significant_elem / 1000000000;
360 _Data[_Maxidx] = _Initial_quotient;
361 uint64_t _Remainder = _Initial_remainder;
362
363 // Process less significant elements.
364 uint32_t _Idx = _Maxidx;
365 do {
366 --_Idx; // Initially, _Remainder is at most 10^9 - 1.
367
368 // Now, _Remainder is at most (10^9 - 1) * 2^32 + 2^32 - 1, simplified to 10^9 * 2^32 - 1.
369 _Remainder = (_Remainder << 32) | _Data[_Idx];
370
371 // floor((10^9 * 2^32 - 1) / 10^9) == 2^32 - 1, so uint32_t _Quotient is lossless.
372 const uint32_t _Quotient = static_cast<uint32_t>(__div1e9(_Remainder));
373
374 // _Remainder is at most 10^9 - 1 again.
375 // For uint32_t truncation, see the __mod1e9() comment in d2s_intrinsics.h.
376 _Remainder = static_cast<uint32_t>(_Remainder) - 1000000000u * _Quotient;
377
378 _Data[_Idx] = _Quotient;
379 } while (_Idx != 0);
380
381 // Store a 0-filled 9-digit block.
382 _Blocks[_Filled_blocks++] = static_cast<uint32_t>(_Remainder);
383
384 if (_Initial_quotient == 0) { // Is the large integer shrinking?
385 --_Maxidx; // log2(10^9) is 29.9, so we can't shrink by more than one element.
386 if (_Maxidx == 0) {
387 break; // We've finished long division. Now we need to print _Data[0].
388 }
389 }
390 }
391 }
392
393 _LIBCPP_ASSERT_INTERNAL(_Data[0] != 0, "");
394 for (uint32_t _Idx = 1; _Idx < _Data_size; ++_Idx) {
395 _LIBCPP_ASSERT_INTERNAL(_Data[_Idx] == 0, "");
396 }
397
398 const uint32_t _Data_olength = _Data[0] >= 1000000000 ? 10 : __decimalLength9(_Data[0]);
399 const uint32_t _Total_fixed_length = _Data_olength + 9 * _Filled_blocks;
400
401 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
402 return { _Last, errc::value_too_large };
403 }
404
405 char* _Result = _First;
406
407 // Print _Data[0]. While it's up to 10 digits,
408 // which is more than Ryu generates, the code below can handle this.
409 __append_n_digits(_Data_olength, _Data[0], _Result);
410 _Result += _Data_olength;
411
412 // Print 0-filled 9-digit blocks.
413 for (int32_t _Idx = _Filled_blocks - 1; _Idx >= 0; --_Idx) {
414 __append_nine_digits(_Blocks[_Idx], _Result);
415 _Result += 9;
416 }
417
418 return { _Result, errc{} };
419}
420
421[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_32 __v,
422 chars_format _Fmt, const uint32_t __ieeeMantissa, const uint32_t __ieeeExponent) {
423 // Step 5: Print the decimal representation.
424 uint32_t _Output = __v.__mantissa;
425 int32_t _Ryu_exponent = __v.__exponent;
426 const uint32_t __olength = __decimalLength9(_Output);
427 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;
428
429 if (_Fmt == chars_format{}) {
430 int32_t _Lower;
431 int32_t _Upper;
432
433 if (__olength == 1) {
434 // Value | Fixed | Scientific
435 // 1e-3 | "0.001" | "1e-03"
436 // 1e4 | "10000" | "1e+04"
437 _Lower = -3;
438 _Upper = 4;
439 } else {
440 // Value | Fixed | Scientific
441 // 1234e-7 | "0.0001234" | "1.234e-04"
442 // 1234e5 | "123400000" | "1.234e+08"
443 _Lower = -static_cast<int32_t>(__olength + 3);
444 _Upper = 5;
445 }
446
447 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {
448 _Fmt = chars_format::fixed;
449 } else {
450 _Fmt = chars_format::scientific;
451 }
452 } else if (_Fmt == chars_format::general) {
453 // C11 7.21.6.1 "The fprintf function"/8:
454 // "Let P equal [...] 6 if the precision is omitted [...].
455 // Then, if a conversion with style E would have an exponent of X:
456 // - if P > X >= -4, the conversion is with style f [...].
457 // - otherwise, the conversion is with style e [...]."
458 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {
459 _Fmt = chars_format::fixed;
460 } else {
461 _Fmt = chars_format::scientific;
462 }
463 }
464
465 if (_Fmt == chars_format::fixed) {
466 // Example: _Output == 1729, __olength == 4
467
468 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes
469 // --------------|----------|---------------|----------------------|---------------------------------------
470 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing
471 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero.
472 // --------------|----------|---------------|----------------------|---------------------------------------
473 // 0 | 1729 | 4 | _Whole_digits | Unified length cases.
474 // --------------|----------|---------------|----------------------|---------------------------------------
475 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for
476 // -2 | 17.29 | 2 | | __olength == 1, but no additional
477 // -3 | 1.729 | 1 | | code is needed to avoid it.
478 // --------------|----------|---------------|----------------------|---------------------------------------
479 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8:
480 // -5 | 0.01729 | -1 | | "If a decimal-point character appears,
481 // -6 | 0.001729 | -2 | | at least one digit appears before it."
482
483 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;
484
485 uint32_t _Total_fixed_length;
486 if (_Ryu_exponent >= 0) { // cases "172900" and "1729"
487 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits);
488 if (_Output == 1) {
489 // Rounding can affect the number of digits.
490 // For example, 1e11f is exactly "99999997952" which is 11 digits instead of 12.
491 // We can use a lookup table to detect this and adjust the total length.
492 static constexpr uint8_t _Adjustment[39] = {
493 0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,1,0,1,1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,1,1,0,1,1,1 };
494 _Total_fixed_length -= _Adjustment[_Ryu_exponent];
495 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.
496 }
497 } else if (_Whole_digits > 0) { // case "17.29"
498 _Total_fixed_length = __olength + 1;
499 } else { // case "0.001729"
500 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);
501 }
502
503 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
504 return { _Last, errc::value_too_large };
505 }
506
507 char* _Mid;
508 if (_Ryu_exponent > 0) { // case "172900"
509 bool _Can_use_ryu;
510
511 if (_Ryu_exponent > 10) { // 10^10 is the largest power of 10 that's exactly representable as a float.
512 _Can_use_ryu = false;
513 } else {
514 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent
515 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)
516 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent
517
518 // _Trailing_zero_bits is [0, 29] (aside: because 2^29 is the largest power of 2
519 // with 9 decimal digits, which is float's round-trip limit.)
520 // _Ryu_exponent is [1, 10].
521 // Normalization adds [2, 23] (aside: at least 2 because the pre-normalized mantissa is at least 5).
522 // This adds up to [3, 62], which is well below float's maximum binary exponent 127.
523
524 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.
525
526 // If that product would exceed 24 bits, then X can't be exactly represented as a float.
527 // (That's not a problem for round-tripping, because X is close enough to the original float,
528 // but X isn't mathematically equal to the original float.) This requires a high-precision fallback.
529
530 // If the product is 24 bits or smaller, then X can be exactly represented as a float (and we don't
531 // need to re-synthesize it; the original float must have been X, because Ryu wouldn't produce the
532 // same output for two different floats X and Y). This allows Ryu's output to be used (zero-filled).
533
534 // (2^24 - 1) / 5^0 (for indexing), (2^24 - 1) / 5^1, ..., (2^24 - 1) / 5^10
535 static constexpr uint32_t _Max_shifted_mantissa[11] = {
536 16777215, 3355443, 671088, 134217, 26843, 5368, 1073, 214, 42, 8, 1 };
537
538 unsigned long _Trailing_zero_bits;
539 (void) _BitScanForward(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero
540 const uint32_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;
541 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];
542 }
543
544 if (!_Can_use_ryu) {
545 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
546 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
547 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization
548
549 // Performance note: We've already called Ryu, so this will redundantly perform buffering and bounds checking.
550 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
551 }
552
553 // _Can_use_ryu
554 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).
555 _Mid = _First + __olength;
556 } else { // cases "1729", "17.29", and "0.001729"
557 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).
558 _Mid = _First + _Total_fixed_length;
559 }
560
561 while (_Output >= 10000) {
562#ifdef __clang__ // TRANSITION, LLVM-38217
563 const uint32_t __c = _Output - 10000 * (_Output / 10000);
564#else
565 const uint32_t __c = _Output % 10000;
566#endif
567 _Output /= 10000;
568 const uint32_t __c0 = (__c % 100) << 1;
569 const uint32_t __c1 = (__c / 100) << 1;
570 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2);
571 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2);
572 }
573 if (_Output >= 100) {
574 const uint32_t __c = (_Output % 100) << 1;
575 _Output /= 100;
576 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
577 }
578 if (_Output >= 10) {
579 const uint32_t __c = _Output << 1;
580 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
581 } else {
582 *--_Mid = static_cast<char>('0' + _Output);
583 }
584
585 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu
586 // Performance note: it might be more efficient to do this immediately after setting _Mid.
587 std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent));
588 } else if (_Ryu_exponent == 0) { // case "1729"
589 // Done!
590 } else if (_Whole_digits > 0) { // case "17.29"
591 // Performance note: moving digits might not be optimal.
592 std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits));
593 _First[_Whole_digits] = '.';
594 } else { // case "0.001729"
595 // Performance note: a larger memset() followed by overwriting '.' might be more efficient.
596 _First[0] = '0';
597 _First[1] = '.';
598 std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits));
599 }
600
601 return { _First + _Total_fixed_length, errc{} };
602 }
603
604 const uint32_t _Total_scientific_length =
605 __olength + (__olength > 1) + 4; // digits + possible decimal point + scientific exponent
606 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {
607 return { _Last, errc::value_too_large };
608 }
609 char* const __result = _First;
610
611 // Print the decimal digits.
612 uint32_t __i = 0;
613 while (_Output >= 10000) {
614#ifdef __clang__ // TRANSITION, LLVM-38217
615 const uint32_t __c = _Output - 10000 * (_Output / 10000);
616#else
617 const uint32_t __c = _Output % 10000;
618#endif
619 _Output /= 10000;
620 const uint32_t __c0 = (__c % 100) << 1;
621 const uint32_t __c1 = (__c / 100) << 1;
622 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2);
623 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2);
624 __i += 4;
625 }
626 if (_Output >= 100) {
627 const uint32_t __c = (_Output % 100) << 1;
628 _Output /= 100;
629 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2);
630 __i += 2;
631 }
632 if (_Output >= 10) {
633 const uint32_t __c = _Output << 1;
634 // We can't use memcpy here: the decimal dot goes between these two digits.
635 __result[2] = __DIGIT_TABLE[__c + 1];
636 __result[0] = __DIGIT_TABLE[__c];
637 } else {
638 __result[0] = static_cast<char>('0' + _Output);
639 }
640
641 // Print decimal point if needed.
642 uint32_t __index;
643 if (__olength > 1) {
644 __result[1] = '.';
645 __index = __olength + 1;
646 } else {
647 __index = 1;
648 }
649
650 // Print the exponent.
651 __result[__index++] = 'e';
652 if (_Scientific_exponent < 0) {
653 __result[__index++] = '-';
654 _Scientific_exponent = -_Scientific_exponent;
655 } else {
656 __result[__index++] = '+';
657 }
658
659 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2);
660 __index += 2;
661
662 return { _First + _Total_scientific_length, errc{} };
663}
664
665[[nodiscard]] to_chars_result __f2s_buffered_n(char* const _First, char* const _Last, const float __f,
666 const chars_format _Fmt) {
667
668 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
669 const uint32_t __bits = __float_to_bits(__f);
670
671 // Case distinction; exit early for the easy cases.
672 if (__bits == 0) {
673 if (_Fmt == chars_format::scientific) {
674 if (_Last - _First < 5) {
675 return { _Last, errc::value_too_large };
676 }
677
678 std::memcpy(_First, "0e+00", 5);
679
680 return { _First + 5, errc{} };
681 }
682
683 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.
684 if (_First == _Last) {
685 return { _Last, errc::value_too_large };
686 }
687
688 *_First = '0';
689
690 return { _First + 1, errc{} };
691 }
692
693 // Decode __bits into mantissa and exponent.
694 const uint32_t __ieeeMantissa = __bits & ((1u << __FLOAT_MANTISSA_BITS) - 1);
695 const uint32_t __ieeeExponent = __bits >> __FLOAT_MANTISSA_BITS;
696
697 // When _Fmt == chars_format::fixed and the floating-point number is a large integer,
698 // it's faster to skip Ryu and immediately print the integer exactly.
699 if (_Fmt == chars_format::fixed) {
700 const uint32_t _Mantissa2 = __ieeeMantissa | (1u << __FLOAT_MANTISSA_BITS); // restore implicit bit
701 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
702 - __FLOAT_BIAS - __FLOAT_MANTISSA_BITS; // bias and normalization
703
704 // Normal values are equal to _Mantissa2 * 2^_Exponent2.
705 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)
706
707 if (_Exponent2 > 0) {
708 return _Large_integer_to_chars(_First, _Last, _Mantissa2, _Exponent2);
709 }
710 }
711
712 const __floating_decimal_32 __v = __f2d(__ieeeMantissa, __ieeeExponent);
713 return __to_chars(_First, _Last, __v, _Fmt, __ieeeMantissa, __ieeeExponent);
714}
715
716_LIBCPP_END_NAMESPACE_STD
717
718// clang-format on