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
35// FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
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
46#include "include/ryu/common.h"
47#include "include/ryu/d2fixed.h"
48#include "include/ryu/d2s.h"
49#include "include/ryu/d2s_full_table.h"
50#include "include/ryu/d2s_intrinsics.h"
51#include "include/ryu/digit_table.h"
52#include "include/ryu/ryu.h"
53
54_LIBCPP_BEGIN_NAMESPACE_STD
55
56// We need a 64x128-bit multiplication and a subsequent 128-bit shift.
57// Multiplication:
58// The 64-bit factor is variable and passed in, the 128-bit factor comes
59// from a lookup table. We know that the 64-bit factor only has 55
60// significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
61// factor only has 124 significant bits (i.e., the 4 topmost bits are
62// zeros).
63// Shift:
64// In principle, the multiplication result requires 55 + 124 = 179 bits to
65// represent. However, we then shift this value to the right by __j, which is
66// at least __j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
67// bits. This means that we only need the topmost 64 significant bits of
68// the 64x128-bit multiplication.
69//
70// There are several ways to do this:
71// 1. Best case: the compiler exposes a 128-bit type.
72// We perform two 64x64-bit multiplications, add the higher 64 bits of the
73// lower result to the higher result, and shift by __j - 64 bits.
74//
75// We explicitly cast from 64-bit to 128-bit, so the compiler can tell
76// that these are only 64-bit inputs, and can map these to the best
77// possible sequence of assembly instructions.
78// x64 machines happen to have matching assembly instructions for
79// 64x64-bit multiplications and 128-bit shifts.
80//
81// 2. Second best case: the compiler exposes intrinsics for the x64 assembly
82// instructions mentioned in 1.
83//
84// 3. We only have 64x64 bit instructions that return the lower 64 bits of
85// the result, i.e., we have to use plain C.
86// Our inputs are less than the full width, so we have three options:
87// a. Ignore this fact and just implement the intrinsics manually.
88// b. Split both into 31-bit pieces, which guarantees no internal overflow,
89// but requires extra work upfront (unless we change the lookup table).
90// c. Split only the first factor into 31-bit pieces, which also guarantees
91// no internal overflow, but requires extra work since the intermediate
92// results are not perfectly aligned.
93#ifdef _LIBCPP_INTRINSIC128
94
95[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShift(const uint64_t __m, const uint64_t* const __mul, const int32_t __j) {
96 // __m is maximum 55 bits
97 uint64_t __high1; // 128
98 const uint64_t __low1 = __ryu_umul128(__m, __mul[1], &__high1); // 64
99 uint64_t __high0; // 64
100 (void) __ryu_umul128(__m, __mul[0], &__high0); // 0
101 const uint64_t __sum = __high0 + __low1;
102 if (__sum < __high0) {
103 ++__high1; // overflow into __high1
104 }
105 return __ryu_shiftright128(__sum, __high1, static_cast<uint32_t>(__j - 64));
106}
107
108[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint64_t __mulShiftAll(const uint64_t __m, const uint64_t* const __mul, const int32_t __j,
109 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) {
110 *__vp = __mulShift(4 * __m + 2, __mul, __j);
111 *__vm = __mulShift(4 * __m - 1 - __mmShift, __mul, __j);
112 return __mulShift(4 * __m, __mul, __j);
113}
114
115#else // ^^^ intrinsics available ^^^ / vvv intrinsics unavailable vvv
116
117[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline _LIBCPP_ALWAYS_INLINE uint64_t __mulShiftAll(uint64_t __m, const uint64_t* const __mul, const int32_t __j,
118 uint64_t* const __vp, uint64_t* const __vm, const uint32_t __mmShift) { // TRANSITION, VSO-634761
119 __m <<= 1;
120 // __m is maximum 55 bits
121 uint64_t __tmp;
122 const uint64_t __lo = __ryu_umul128(__m, __mul[0], &__tmp);
123 uint64_t __hi;
124 const uint64_t __mid = __tmp + __ryu_umul128(__m, __mul[1], &__hi);
125 __hi += __mid < __tmp; // overflow into __hi
126
127 const uint64_t __lo2 = __lo + __mul[0];
128 const uint64_t __mid2 = __mid + __mul[1] + (__lo2 < __lo);
129 const uint64_t __hi2 = __hi + (__mid2 < __mid);
130 *__vp = __ryu_shiftright128(__mid2, __hi2, static_cast<uint32_t>(__j - 64 - 1));
131
132 if (__mmShift == 1) {
133 const uint64_t __lo3 = __lo - __mul[0];
134 const uint64_t __mid3 = __mid - __mul[1] - (__lo3 > __lo);
135 const uint64_t __hi3 = __hi - (__mid3 > __mid);
136 *__vm = __ryu_shiftright128(__mid3, __hi3, static_cast<uint32_t>(__j - 64 - 1));
137 } else {
138 const uint64_t __lo3 = __lo + __lo;
139 const uint64_t __mid3 = __mid + __mid + (__lo3 < __lo);
140 const uint64_t __hi3 = __hi + __hi + (__mid3 < __mid);
141 const uint64_t __lo4 = __lo3 - __mul[0];
142 const uint64_t __mid4 = __mid3 - __mul[1] - (__lo4 > __lo3);
143 const uint64_t __hi4 = __hi3 - (__mid4 > __mid3);
144 *__vm = __ryu_shiftright128(__mid4, __hi4, static_cast<uint32_t>(__j - 64));
145 }
146
147 return __ryu_shiftright128(__mid, __hi, static_cast<uint32_t>(__j - 64 - 1));
148}
149
150#endif // ^^^ intrinsics unavailable ^^^
151
152[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline uint32_t __decimalLength17(const uint64_t __v) {
153 // This is slightly faster than a loop.
154 // The average output length is 16.38 digits, so we check high-to-low.
155 // Function precondition: __v is not an 18, 19, or 20-digit number.
156 // (17 digits are sufficient for round-tripping.)
157 _LIBCPP_ASSERT_INTERNAL(__v < 100000000000000000u, "");
158 if (__v >= 10000000000000000u) { return 17; }
159 if (__v >= 1000000000000000u) { return 16; }
160 if (__v >= 100000000000000u) { return 15; }
161 if (__v >= 10000000000000u) { return 14; }
162 if (__v >= 1000000000000u) { return 13; }
163 if (__v >= 100000000000u) { return 12; }
164 if (__v >= 10000000000u) { return 11; }
165 if (__v >= 1000000000u) { return 10; }
166 if (__v >= 100000000u) { return 9; }
167 if (__v >= 10000000u) { return 8; }
168 if (__v >= 1000000u) { return 7; }
169 if (__v >= 100000u) { return 6; }
170 if (__v >= 10000u) { return 5; }
171 if (__v >= 1000u) { return 4; }
172 if (__v >= 100u) { return 3; }
173 if (__v >= 10u) { return 2; }
174 return 1;
175}
176
177// A floating decimal representing m * 10^e.
178struct __floating_decimal_64 {
179 uint64_t __mantissa;
180 int32_t __exponent;
181};
182
183[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline __floating_decimal_64 __d2d(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent) {
184 int32_t __e2;
185 uint64_t __m2;
186 if (__ieeeExponent == 0) {
187 // We subtract 2 so that the bounds computation has 2 additional bits.
188 __e2 = 1 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2;
189 __m2 = __ieeeMantissa;
190 } else {
191 __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS - 2;
192 __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
193 }
194 const bool __even = (__m2 & 1) == 0;
195 const bool __acceptBounds = __even;
196
197 // Step 2: Determine the interval of valid decimal representations.
198 const uint64_t __mv = 4 * __m2;
199 // Implicit bool -> int conversion. True is 1, false is 0.
200 const uint32_t __mmShift = __ieeeMantissa != 0 || __ieeeExponent <= 1;
201 // We would compute __mp and __mm like this:
202 // uint64_t __mp = 4 * __m2 + 2;
203 // uint64_t __mm = __mv - 1 - __mmShift;
204
205 // Step 3: Convert to a decimal power base using 128-bit arithmetic.
206 uint64_t __vr, __vp, __vm;
207 int32_t __e10;
208 bool __vmIsTrailingZeros = false;
209 bool __vrIsTrailingZeros = false;
210 if (__e2 >= 0) {
211 // I tried special-casing __q == 0, but there was no effect on performance.
212 // This expression is slightly faster than max(0, __log10Pow2(__e2) - 1).
213 const uint32_t __q = __log10Pow2(__e2) - (__e2 > 3);
214 __e10 = static_cast<int32_t>(__q);
215 const int32_t __k = __DOUBLE_POW5_INV_BITCOUNT + __pow5bits(static_cast<int32_t>(__q)) - 1;
216 const int32_t __i = -__e2 + static_cast<int32_t>(__q) + __k;
217 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_INV_SPLIT[__q], __i, &__vp, &__vm, __mmShift);
218 if (__q <= 21) {
219 // This should use __q <= 22, but I think 21 is also safe. Smaller values
220 // may still be safe, but it's more difficult to reason about them.
221 // Only one of __mp, __mv, and __mm can be a multiple of 5, if any.
222 const uint32_t __mvMod5 = static_cast<uint32_t>(__mv) - 5 * static_cast<uint32_t>(__div5(__mv));
223 if (__mvMod5 == 0) {
224 __vrIsTrailingZeros = __multipleOfPowerOf5(__mv, __q);
225 } else if (__acceptBounds) {
226 // Same as min(__e2 + (~__mm & 1), __pow5Factor(__mm)) >= __q
227 // <=> __e2 + (~__mm & 1) >= __q && __pow5Factor(__mm) >= __q
228 // <=> true && __pow5Factor(__mm) >= __q, since __e2 >= __q.
229 __vmIsTrailingZeros = __multipleOfPowerOf5(__mv - 1 - __mmShift, __q);
230 } else {
231 // Same as min(__e2 + 1, __pow5Factor(__mp)) >= __q.
232 __vp -= __multipleOfPowerOf5(__mv + 2, __q);
233 }
234 }
235 } else {
236 // This expression is slightly faster than max(0, __log10Pow5(-__e2) - 1).
237 const uint32_t __q = __log10Pow5(-__e2) - (-__e2 > 1);
238 __e10 = static_cast<int32_t>(__q) + __e2;
239 const int32_t __i = -__e2 - static_cast<int32_t>(__q);
240 const int32_t __k = __pow5bits(__i) - __DOUBLE_POW5_BITCOUNT;
241 const int32_t __j = static_cast<int32_t>(__q) - __k;
242 __vr = __mulShiftAll(__m2, __DOUBLE_POW5_SPLIT[__i], __j, &__vp, &__vm, __mmShift);
243 if (__q <= 1) {
244 // {__vr,__vp,__vm} is trailing zeros if {__mv,__mp,__mm} has at least __q trailing 0 bits.
245 // __mv = 4 * __m2, so it always has at least two trailing 0 bits.
246 __vrIsTrailingZeros = true;
247 if (__acceptBounds) {
248 // __mm = __mv - 1 - __mmShift, so it has 1 trailing 0 bit iff __mmShift == 1.
249 __vmIsTrailingZeros = __mmShift == 1;
250 } else {
251 // __mp = __mv + 2, so it always has at least one trailing 0 bit.
252 --__vp;
253 }
254 } else if (__q < 63) { // TRANSITION(ulfjack): Use a tighter bound here.
255 // We need to compute min(ntz(__mv), __pow5Factor(__mv) - __e2) >= __q - 1
256 // <=> ntz(__mv) >= __q - 1 && __pow5Factor(__mv) - __e2 >= __q - 1
257 // <=> ntz(__mv) >= __q - 1 (__e2 is negative and -__e2 >= __q)
258 // <=> (__mv & ((1 << (__q - 1)) - 1)) == 0
259 // We also need to make sure that the left shift does not overflow.
260 __vrIsTrailingZeros = __multipleOfPowerOf2(__mv, __q - 1);
261 }
262 }
263
264 // Step 4: Find the shortest decimal representation in the interval of valid representations.
265 int32_t __removed = 0;
266 uint8_t __lastRemovedDigit = 0;
267 uint64_t _Output;
268 // On average, we remove ~2 digits.
269 if (__vmIsTrailingZeros || __vrIsTrailingZeros) {
270 // General case, which happens rarely (~0.7%).
271 for (;;) {
272 const uint64_t __vpDiv10 = __div10(__vp);
273 const uint64_t __vmDiv10 = __div10(__vm);
274 if (__vpDiv10 <= __vmDiv10) {
275 break;
276 }
277 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10);
278 const uint64_t __vrDiv10 = __div10(__vr);
279 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
280 __vmIsTrailingZeros &= __vmMod10 == 0;
281 __vrIsTrailingZeros &= __lastRemovedDigit == 0;
282 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10);
283 __vr = __vrDiv10;
284 __vp = __vpDiv10;
285 __vm = __vmDiv10;
286 ++__removed;
287 }
288 if (__vmIsTrailingZeros) {
289 for (;;) {
290 const uint64_t __vmDiv10 = __div10(__vm);
291 const uint32_t __vmMod10 = static_cast<uint32_t>(__vm) - 10 * static_cast<uint32_t>(__vmDiv10);
292 if (__vmMod10 != 0) {
293 break;
294 }
295 const uint64_t __vpDiv10 = __div10(__vp);
296 const uint64_t __vrDiv10 = __div10(__vr);
297 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
298 __vrIsTrailingZeros &= __lastRemovedDigit == 0;
299 __lastRemovedDigit = static_cast<uint8_t>(__vrMod10);
300 __vr = __vrDiv10;
301 __vp = __vpDiv10;
302 __vm = __vmDiv10;
303 ++__removed;
304 }
305 }
306 if (__vrIsTrailingZeros && __lastRemovedDigit == 5 && __vr % 2 == 0) {
307 // Round even if the exact number is .....50..0.
308 __lastRemovedDigit = 4;
309 }
310 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
311 _Output = __vr + ((__vr == __vm && (!__acceptBounds || !__vmIsTrailingZeros)) || __lastRemovedDigit >= 5);
312 } else {
313 // Specialized for the common case (~99.3%). Percentages below are relative to this.
314 bool __roundUp = false;
315 const uint64_t __vpDiv100 = __div100(__vp);
316 const uint64_t __vmDiv100 = __div100(__vm);
317 if (__vpDiv100 > __vmDiv100) { // Optimization: remove two digits at a time (~86.2%).
318 const uint64_t __vrDiv100 = __div100(__vr);
319 const uint32_t __vrMod100 = static_cast<uint32_t>(__vr) - 100 * static_cast<uint32_t>(__vrDiv100);
320 __roundUp = __vrMod100 >= 50;
321 __vr = __vrDiv100;
322 __vp = __vpDiv100;
323 __vm = __vmDiv100;
324 __removed += 2;
325 }
326 // Loop iterations below (approximately), without optimization above:
327 // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
328 // Loop iterations below (approximately), with optimization above:
329 // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
330 for (;;) {
331 const uint64_t __vpDiv10 = __div10(__vp);
332 const uint64_t __vmDiv10 = __div10(__vm);
333 if (__vpDiv10 <= __vmDiv10) {
334 break;
335 }
336 const uint64_t __vrDiv10 = __div10(__vr);
337 const uint32_t __vrMod10 = static_cast<uint32_t>(__vr) - 10 * static_cast<uint32_t>(__vrDiv10);
338 __roundUp = __vrMod10 >= 5;
339 __vr = __vrDiv10;
340 __vp = __vpDiv10;
341 __vm = __vmDiv10;
342 ++__removed;
343 }
344 // We need to take __vr + 1 if __vr is outside bounds or we need to round up.
345 _Output = __vr + (__vr == __vm || __roundUp);
346 }
347 const int32_t __exp = __e10 + __removed;
348
349 __floating_decimal_64 __fd;
350 __fd.__exponent = __exp;
351 __fd.__mantissa = _Output;
352 return __fd;
353}
354
355[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline to_chars_result __to_chars(char* const _First, char* const _Last, const __floating_decimal_64 __v,
356 chars_format _Fmt, const double __f) {
357 // Step 5: Print the decimal representation.
358 uint64_t _Output = __v.__mantissa;
359 int32_t _Ryu_exponent = __v.__exponent;
360 const uint32_t __olength = __decimalLength17(_Output);
361 int32_t _Scientific_exponent = _Ryu_exponent + static_cast<int32_t>(__olength) - 1;
362
363 if (_Fmt == chars_format{}) {
364 int32_t _Lower;
365 int32_t _Upper;
366
367 if (__olength == 1) {
368 // Value | Fixed | Scientific
369 // 1e-3 | "0.001" | "1e-03"
370 // 1e4 | "10000" | "1e+04"
371 _Lower = -3;
372 _Upper = 4;
373 } else {
374 // Value | Fixed | Scientific
375 // 1234e-7 | "0.0001234" | "1.234e-04"
376 // 1234e5 | "123400000" | "1.234e+08"
377 _Lower = -static_cast<int32_t>(__olength + 3);
378 _Upper = 5;
379 }
380
381 if (_Lower <= _Ryu_exponent && _Ryu_exponent <= _Upper) {
382 _Fmt = chars_format::fixed;
383 } else {
384 _Fmt = chars_format::scientific;
385 }
386 } else if (_Fmt == chars_format::general) {
387 // C11 7.21.6.1 "The fprintf function"/8:
388 // "Let P equal [...] 6 if the precision is omitted [...].
389 // Then, if a conversion with style E would have an exponent of X:
390 // - if P > X >= -4, the conversion is with style f [...].
391 // - otherwise, the conversion is with style e [...]."
392 if (-4 <= _Scientific_exponent && _Scientific_exponent < 6) {
393 _Fmt = chars_format::fixed;
394 } else {
395 _Fmt = chars_format::scientific;
396 }
397 }
398
399 if (_Fmt == chars_format::fixed) {
400 // Example: _Output == 1729, __olength == 4
401
402 // _Ryu_exponent | Printed | _Whole_digits | _Total_fixed_length | Notes
403 // --------------|----------|---------------|----------------------|---------------------------------------
404 // 2 | 172900 | 6 | _Whole_digits | Ryu can't be used for printing
405 // 1 | 17290 | 5 | (sometimes adjusted) | when the trimmed digits are nonzero.
406 // --------------|----------|---------------|----------------------|---------------------------------------
407 // 0 | 1729 | 4 | _Whole_digits | Unified length cases.
408 // --------------|----------|---------------|----------------------|---------------------------------------
409 // -1 | 172.9 | 3 | __olength + 1 | This case can't happen for
410 // -2 | 17.29 | 2 | | __olength == 1, but no additional
411 // -3 | 1.729 | 1 | | code is needed to avoid it.
412 // --------------|----------|---------------|----------------------|---------------------------------------
413 // -4 | 0.1729 | 0 | 2 - _Ryu_exponent | C11 7.21.6.1 "The fprintf function"/8:
414 // -5 | 0.01729 | -1 | | "If a decimal-point character appears,
415 // -6 | 0.001729 | -2 | | at least one digit appears before it."
416
417 const int32_t _Whole_digits = static_cast<int32_t>(__olength) + _Ryu_exponent;
418
419 uint32_t _Total_fixed_length;
420 if (_Ryu_exponent >= 0) { // cases "172900" and "1729"
421 _Total_fixed_length = static_cast<uint32_t>(_Whole_digits);
422 if (_Output == 1) {
423 // Rounding can affect the number of digits.
424 // For example, 1e23 is exactly "99999999999999991611392" which is 23 digits instead of 24.
425 // We can use a lookup table to detect this and adjust the total length.
426 static constexpr uint8_t _Adjustment[309] = {
427 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,1,1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0,
428 1,1,0,0,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,1,1,
429 1,0,0,0,0,0,0,0,1,1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,1,1,0,0,1,1,1,1,1,0,1,0,1,1,0,1,
430 1,0,0,0,0,0,0,0,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,
431 0,1,0,1,0,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,1,1,1,1,0,1,0,1,1,0,0,0,1,
432 1,1,0,1,1,0,0,0,1,0,0,0,1,0,1,0,0,0,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0,0,0,0,1,1,0,
433 0,1,0,1,1,1,0,0,1,0,0,0,0,1,0,1,0,0,0,0,0,1,0,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0 };
434 _Total_fixed_length -= _Adjustment[_Ryu_exponent];
435 // _Whole_digits doesn't need to be adjusted because these cases won't refer to it later.
436 }
437 } else if (_Whole_digits > 0) { // case "17.29"
438 _Total_fixed_length = __olength + 1;
439 } else { // case "0.001729"
440 _Total_fixed_length = static_cast<uint32_t>(2 - _Ryu_exponent);
441 }
442
443 if (_Last - _First < static_cast<ptrdiff_t>(_Total_fixed_length)) {
444 return { _Last, errc::value_too_large };
445 }
446
447 char* _Mid;
448 if (_Ryu_exponent > 0) { // case "172900"
449 bool _Can_use_ryu;
450
451 if (_Ryu_exponent > 22) { // 10^22 is the largest power of 10 that's exactly representable as a double.
452 _Can_use_ryu = false;
453 } else {
454 // Ryu generated X: __v.__mantissa * 10^_Ryu_exponent
455 // __v.__mantissa == 2^_Trailing_zero_bits * (__v.__mantissa >> _Trailing_zero_bits)
456 // 10^_Ryu_exponent == 2^_Ryu_exponent * 5^_Ryu_exponent
457
458 // _Trailing_zero_bits is [0, 56] (aside: because 2^56 is the largest power of 2
459 // with 17 decimal digits, which is double's round-trip limit.)
460 // _Ryu_exponent is [1, 22].
461 // Normalization adds [2, 52] (aside: at least 2 because the pre-normalized mantissa is at least 5).
462 // This adds up to [3, 130], which is well below double's maximum binary exponent 1023.
463
464 // Therefore, we just need to consider (__v.__mantissa >> _Trailing_zero_bits) * 5^_Ryu_exponent.
465
466 // If that product would exceed 53 bits, then X can't be exactly represented as a double.
467 // (That's not a problem for round-tripping, because X is close enough to the original double,
468 // but X isn't mathematically equal to the original double.) This requires a high-precision fallback.
469
470 // If the product is 53 bits or smaller, then X can be exactly represented as a double (and we don't
471 // need to re-synthesize it; the original double must have been X, because Ryu wouldn't produce the
472 // same output for two different doubles X and Y). This allows Ryu's output to be used (zero-filled).
473
474 // (2^53 - 1) / 5^0 (for indexing), (2^53 - 1) / 5^1, ..., (2^53 - 1) / 5^22
475 static constexpr uint64_t _Max_shifted_mantissa[23] = {
476 9007199254740991u, 1801439850948198u, 360287970189639u, 72057594037927u, 14411518807585u,
477 2882303761517u, 576460752303u, 115292150460u, 23058430092u, 4611686018u, 922337203u, 184467440u,
478 36893488u, 7378697u, 1475739u, 295147u, 59029u, 11805u, 2361u, 472u, 94u, 18u, 3u };
479
480 unsigned long _Trailing_zero_bits;
481#ifdef _LIBCPP_HAS_BITSCAN64
482 (void) _BitScanForward64(&_Trailing_zero_bits, __v.__mantissa); // __v.__mantissa is guaranteed nonzero
483#else // ^^^ 64-bit ^^^ / vvv 32-bit vvv
484 const uint32_t _Low_mantissa = static_cast<uint32_t>(__v.__mantissa);
485 if (_Low_mantissa != 0) {
486 (void) _BitScanForward(&_Trailing_zero_bits, _Low_mantissa);
487 } else {
488 const uint32_t _High_mantissa = static_cast<uint32_t>(__v.__mantissa >> 32); // nonzero here
489 (void) _BitScanForward(&_Trailing_zero_bits, _High_mantissa);
490 _Trailing_zero_bits += 32;
491 }
492#endif // ^^^ 32-bit ^^^
493 const uint64_t _Shifted_mantissa = __v.__mantissa >> _Trailing_zero_bits;
494 _Can_use_ryu = _Shifted_mantissa <= _Max_shifted_mantissa[_Ryu_exponent];
495 }
496
497 if (!_Can_use_ryu) {
498 // Print the integer exactly.
499 // Performance note: This will redundantly perform bounds checking.
500 // Performance note: This will redundantly decompose the IEEE representation.
501 return __d2fixed_buffered_n(_First, _Last, __f, 0);
502 }
503
504 // _Can_use_ryu
505 // Print the decimal digits, left-aligned within [_First, _First + _Total_fixed_length).
506 _Mid = _First + __olength;
507 } else { // cases "1729", "17.29", and "0.001729"
508 // Print the decimal digits, right-aligned within [_First, _First + _Total_fixed_length).
509 _Mid = _First + _Total_fixed_length;
510 }
511
512 // We prefer 32-bit operations, even on 64-bit platforms.
513 // We have at most 17 digits, and uint32_t can store 9 digits.
514 // If _Output doesn't fit into uint32_t, we cut off 8 digits,
515 // so the rest will fit into uint32_t.
516 if ((_Output >> 32) != 0) {
517 // Expensive 64-bit division.
518 const uint64_t __q = __div1e8(_Output);
519 uint32_t __output2 = static_cast<uint32_t>(_Output - 100000000 * __q);
520 _Output = __q;
521
522 const uint32_t __c = __output2 % 10000;
523 __output2 /= 10000;
524 const uint32_t __d = __output2 % 10000;
525 const uint32_t __c0 = (__c % 100) << 1;
526 const uint32_t __c1 = (__c / 100) << 1;
527 const uint32_t __d0 = (__d % 100) << 1;
528 const uint32_t __d1 = (__d / 100) << 1;
529
530 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2);
531 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2);
532 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d0, 2);
533 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __d1, 2);
534 }
535 uint32_t __output2 = static_cast<uint32_t>(_Output);
536 while (__output2 >= 10000) {
537#ifdef __clang__ // TRANSITION, LLVM-38217
538 const uint32_t __c = __output2 - 10000 * (__output2 / 10000);
539#else
540 const uint32_t __c = __output2 % 10000;
541#endif
542 __output2 /= 10000;
543 const uint32_t __c0 = (__c % 100) << 1;
544 const uint32_t __c1 = (__c / 100) << 1;
545 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c0, 2);
546 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c1, 2);
547 }
548 if (__output2 >= 100) {
549 const uint32_t __c = (__output2 % 100) << 1;
550 __output2 /= 100;
551 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
552 }
553 if (__output2 >= 10) {
554 const uint32_t __c = __output2 << 1;
555 std::memcpy(_Mid -= 2, __DIGIT_TABLE + __c, 2);
556 } else {
557 *--_Mid = static_cast<char>('0' + __output2);
558 }
559
560 if (_Ryu_exponent > 0) { // case "172900" with _Can_use_ryu
561 // Performance note: it might be more efficient to do this immediately after setting _Mid.
562 std::memset(_First + __olength, '0', static_cast<size_t>(_Ryu_exponent));
563 } else if (_Ryu_exponent == 0) { // case "1729"
564 // Done!
565 } else if (_Whole_digits > 0) { // case "17.29"
566 // Performance note: moving digits might not be optimal.
567 std::memmove(_First, _First + 1, static_cast<size_t>(_Whole_digits));
568 _First[_Whole_digits] = '.';
569 } else { // case "0.001729"
570 // Performance note: a larger memset() followed by overwriting '.' might be more efficient.
571 _First[0] = '0';
572 _First[1] = '.';
573 std::memset(_First + 2, '0', static_cast<size_t>(-_Whole_digits));
574 }
575
576 return { _First + _Total_fixed_length, errc{} };
577 }
578
579 const uint32_t _Total_scientific_length = __olength + (__olength > 1) // digits + possible decimal point
580 + (-100 < _Scientific_exponent && _Scientific_exponent < 100 ? 4 : 5); // + scientific exponent
581 if (_Last - _First < static_cast<ptrdiff_t>(_Total_scientific_length)) {
582 return { _Last, errc::value_too_large };
583 }
584 char* const __result = _First;
585
586 // Print the decimal digits.
587 uint32_t __i = 0;
588 // We prefer 32-bit operations, even on 64-bit platforms.
589 // We have at most 17 digits, and uint32_t can store 9 digits.
590 // If _Output doesn't fit into uint32_t, we cut off 8 digits,
591 // so the rest will fit into uint32_t.
592 if ((_Output >> 32) != 0) {
593 // Expensive 64-bit division.
594 const uint64_t __q = __div1e8(_Output);
595 uint32_t __output2 = static_cast<uint32_t>(_Output) - 100000000 * static_cast<uint32_t>(__q);
596 _Output = __q;
597
598 const uint32_t __c = __output2 % 10000;
599 __output2 /= 10000;
600 const uint32_t __d = __output2 % 10000;
601 const uint32_t __c0 = (__c % 100) << 1;
602 const uint32_t __c1 = (__c / 100) << 1;
603 const uint32_t __d0 = (__d % 100) << 1;
604 const uint32_t __d1 = (__d / 100) << 1;
605 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2);
606 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2);
607 std::memcpy(__result + __olength - __i - 5, __DIGIT_TABLE + __d0, 2);
608 std::memcpy(__result + __olength - __i - 7, __DIGIT_TABLE + __d1, 2);
609 __i += 8;
610 }
611 uint32_t __output2 = static_cast<uint32_t>(_Output);
612 while (__output2 >= 10000) {
613#ifdef __clang__ // TRANSITION, LLVM-38217
614 const uint32_t __c = __output2 - 10000 * (__output2 / 10000);
615#else
616 const uint32_t __c = __output2 % 10000;
617#endif
618 __output2 /= 10000;
619 const uint32_t __c0 = (__c % 100) << 1;
620 const uint32_t __c1 = (__c / 100) << 1;
621 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c0, 2);
622 std::memcpy(__result + __olength - __i - 3, __DIGIT_TABLE + __c1, 2);
623 __i += 4;
624 }
625 if (__output2 >= 100) {
626 const uint32_t __c = (__output2 % 100) << 1;
627 __output2 /= 100;
628 std::memcpy(__result + __olength - __i - 1, __DIGIT_TABLE + __c, 2);
629 __i += 2;
630 }
631 if (__output2 >= 10) {
632 const uint32_t __c = __output2 << 1;
633 // We can't use memcpy here: the decimal dot goes between these two digits.
634 __result[2] = __DIGIT_TABLE[__c + 1];
635 __result[0] = __DIGIT_TABLE[__c];
636 } else {
637 __result[0] = static_cast<char>('0' + __output2);
638 }
639
640 // Print decimal point if needed.
641 uint32_t __index;
642 if (__olength > 1) {
643 __result[1] = '.';
644 __index = __olength + 1;
645 } else {
646 __index = 1;
647 }
648
649 // Print the exponent.
650 __result[__index++] = 'e';
651 if (_Scientific_exponent < 0) {
652 __result[__index++] = '-';
653 _Scientific_exponent = -_Scientific_exponent;
654 } else {
655 __result[__index++] = '+';
656 }
657
658 if (_Scientific_exponent >= 100) {
659 const int32_t __c = _Scientific_exponent % 10;
660 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * (_Scientific_exponent / 10), 2);
661 __result[__index + 2] = static_cast<char>('0' + __c);
662 __index += 3;
663 } else {
664 std::memcpy(__result + __index, __DIGIT_TABLE + 2 * _Scientific_exponent, 2);
665 __index += 2;
666 }
667
668 return { _First + _Total_scientific_length, errc{} };
669}
670
671[[nodiscard]] _LIBCPP_HIDE_FROM_ABI inline bool __d2d_small_int(const uint64_t __ieeeMantissa, const uint32_t __ieeeExponent,
672 __floating_decimal_64* const __v) {
673 const uint64_t __m2 = (1ull << __DOUBLE_MANTISSA_BITS) | __ieeeMantissa;
674 const int32_t __e2 = static_cast<int32_t>(__ieeeExponent) - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS;
675
676 if (__e2 > 0) {
677 // f = __m2 * 2^__e2 >= 2^53 is an integer.
678 // Ignore this case for now.
679 return false;
680 }
681
682 if (__e2 < -52) {
683 // f < 1.
684 return false;
685 }
686
687 // Since 2^52 <= __m2 < 2^53 and 0 <= -__e2 <= 52: 1 <= f = __m2 / 2^-__e2 < 2^53.
688 // Test if the lower -__e2 bits of the significand are 0, i.e. whether the fraction is 0.
689 const uint64_t __mask = (1ull << -__e2) - 1;
690 const uint64_t __fraction = __m2 & __mask;
691 if (__fraction != 0) {
692 return false;
693 }
694
695 // f is an integer in the range [1, 2^53).
696 // Note: __mantissa might contain trailing (decimal) 0's.
697 // Note: since 2^53 < 10^16, there is no need to adjust __decimalLength17().
698 __v->__mantissa = __m2 >> -__e2;
699 __v->__exponent = 0;
700 return true;
701}
702
703[[nodiscard]] to_chars_result __d2s_buffered_n(char* const _First, char* const _Last, const double __f,
704 const chars_format _Fmt) {
705
706 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
707 const uint64_t __bits = __double_to_bits(__f);
708
709 // Case distinction; exit early for the easy cases.
710 if (__bits == 0) {
711 if (_Fmt == chars_format::scientific) {
712 if (_Last - _First < 5) {
713 return { _Last, errc::value_too_large };
714 }
715
716 std::memcpy(_First, "0e+00", 5);
717
718 return { _First + 5, errc{} };
719 }
720
721 // Print "0" for chars_format::fixed, chars_format::general, and chars_format{}.
722 if (_First == _Last) {
723 return { _Last, errc::value_too_large };
724 }
725
726 *_First = '0';
727
728 return { _First + 1, errc{} };
729 }
730
731 // Decode __bits into mantissa and exponent.
732 const uint64_t __ieeeMantissa = __bits & ((1ull << __DOUBLE_MANTISSA_BITS) - 1);
733 const uint32_t __ieeeExponent = static_cast<uint32_t>(__bits >> __DOUBLE_MANTISSA_BITS);
734
735 if (_Fmt == chars_format::fixed) {
736 // const uint64_t _Mantissa2 = __ieeeMantissa | (1ull << __DOUBLE_MANTISSA_BITS); // restore implicit bit
737 const int32_t _Exponent2 = static_cast<int32_t>(__ieeeExponent)
738 - __DOUBLE_BIAS - __DOUBLE_MANTISSA_BITS; // bias and normalization
739
740 // Normal values are equal to _Mantissa2 * 2^_Exponent2.
741 // (Subnormals are different, but they'll be rejected by the _Exponent2 test here, so they can be ignored.)
742
743 // For nonzero integers, _Exponent2 >= -52. (The minimum value occurs when _Mantissa2 * 2^_Exponent2 is 1.
744 // In that case, _Mantissa2 is the implicit 1 bit followed by 52 zeros, so _Exponent2 is -52 to shift away
745 // the zeros.) The dense range of exactly representable integers has negative or zero exponents
746 // (as positive exponents make the range non-dense). For that dense range, Ryu will always be used:
747 // every digit is necessary to uniquely identify the value, so Ryu must print them all.
748
749 // Positive exponents are the non-dense range of exactly representable integers. This contains all of the values
750 // for which Ryu can't be used (and a few Ryu-friendly values). We can save time by detecting positive
751 // exponents here and skipping Ryu. Calling __d2fixed_buffered_n() with precision 0 is valid for all integers
752 // (so it's okay if we call it with a Ryu-friendly value).
753 if (_Exponent2 > 0) {
754 return __d2fixed_buffered_n(_First, _Last, __f, 0);
755 }
756 }
757
758 __floating_decimal_64 __v;
759 const bool __isSmallInt = __d2d_small_int(__ieeeMantissa, __ieeeExponent, &__v);
760 if (__isSmallInt) {
761 // For small integers in the range [1, 2^53), __v.__mantissa might contain trailing (decimal) zeros.
762 // For scientific notation we need to move these zeros into the exponent.
763 // (This is not needed for fixed-point notation, so it might be beneficial to trim
764 // trailing zeros in __to_chars only if needed - once fixed-point notation output is implemented.)
765 for (;;) {
766 const uint64_t __q = __div10(__v.__mantissa);
767 const uint32_t __r = static_cast<uint32_t>(__v.__mantissa) - 10 * static_cast<uint32_t>(__q);
768 if (__r != 0) {
769 break;
770 }
771 __v.__mantissa = __q;
772 ++__v.__exponent;
773 }
774 } else {
775 __v = __d2d(__ieeeMantissa, __ieeeExponent);
776 }
777
778 return __to_chars(_First, _Last, __v, _Fmt, __f);
779}
780
781_LIBCPP_END_NAMESPACE_STD
782
783// clang-format on
784