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1 // -*- C++ -*-
2 //===----------------------------------------------------------------------===//
3 //
4 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
5 // See https://llvm.org/LICENSE.txt for license information.
6 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
7 //
8 //===----------------------------------------------------------------------===//
9 
10 #ifndef _LIBCPP___FORMAT_FORMATTER_FLOATING_POINT_H
11 #define _LIBCPP___FORMAT_FORMATTER_FLOATING_POINT_H
12 
13 #include <__algorithm/copy_n.h>
14 #include <__algorithm/find.h>
15 #include <__algorithm/max.h>
16 #include <__algorithm/min.h>
17 #include <__algorithm/rotate.h>
18 #include <__algorithm/transform.h>
19 #include <__charconv/chars_format.h>
20 #include <__charconv/to_chars_floating_point.h>
21 #include <__charconv/to_chars_result.h>
22 #include <__concepts/arithmetic.h>
23 #include <__concepts/same_as.h>
24 #include <__config>
25 #include <__format/concepts.h>
26 #include <__format/format_parse_context.h>
27 #include <__format/formatter.h>
28 #include <__format/formatter_integral.h>
29 #include <__format/formatter_output.h>
30 #include <__format/parser_std_format_spec.h>
31 #include <__memory/allocator.h>
32 #include <__system_error/errc.h>
33 #include <__type_traits/conditional.h>
34 #include <__utility/move.h>
35 #include <__utility/unreachable.h>
36 #include <cmath>
37 #include <cstddef>
38 
39 #ifndef _LIBCPP_HAS_NO_LOCALIZATION
40 #  include <locale>
41 #endif
42 
43 #if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
44 #  pragma GCC system_header
45 #endif
46 
47 _LIBCPP_PUSH_MACROS
48 #include <__undef_macros>
49 
50 _LIBCPP_BEGIN_NAMESPACE_STD
51 
52 #if _LIBCPP_STD_VER >= 20
53 
54 namespace __formatter {
55 
56 template <floating_point _Tp>
__to_buffer(char * __first,char * __last,_Tp __value)57 _LIBCPP_HIDE_FROM_ABI char* __to_buffer(char* __first, char* __last, _Tp __value) {
58   to_chars_result __r = _VSTD::to_chars(__first, __last, __value);
59   _LIBCPP_ASSERT(__r.ec == errc(0), "Internal buffer too small");
60   return __r.ptr;
61 }
62 
63 template <floating_point _Tp>
__to_buffer(char * __first,char * __last,_Tp __value,chars_format __fmt)64 _LIBCPP_HIDE_FROM_ABI char* __to_buffer(char* __first, char* __last, _Tp __value, chars_format __fmt) {
65   to_chars_result __r = _VSTD::to_chars(__first, __last, __value, __fmt);
66   _LIBCPP_ASSERT(__r.ec == errc(0), "Internal buffer too small");
67   return __r.ptr;
68 }
69 
70 template <floating_point _Tp>
__to_buffer(char * __first,char * __last,_Tp __value,chars_format __fmt,int __precision)71 _LIBCPP_HIDE_FROM_ABI char* __to_buffer(char* __first, char* __last, _Tp __value, chars_format __fmt, int __precision) {
72   to_chars_result __r = _VSTD::to_chars(__first, __last, __value, __fmt, __precision);
73   _LIBCPP_ASSERT(__r.ec == errc(0), "Internal buffer too small");
74   return __r.ptr;
75 }
76 
77 // https://en.cppreference.com/w/cpp/language/types#cite_note-1
78 // float             min subnormal: +/-0x1p-149   max: +/- 3.402,823,4 10^38
79 // double            min subnormal: +/-0x1p-1074  max  +/- 1.797,693,134,862,315,7 10^308
80 // long double (x86) min subnormal: +/-0x1p-16446 max: +/- 1.189,731,495,357,231,765,021 10^4932
81 //
82 // The maximum number of digits required for the integral part is based on the
83 // maximum's value power of 10. Every power of 10 requires one additional
84 // decimal digit.
85 // The maximum number of digits required for the fractional part is based on
86 // the minimal subnormal hexadecimal output's power of 10. Every division of a
87 // fraction's binary 1 by 2, requires one additional decimal digit.
88 //
89 // The maximum size of a formatted value depends on the selected output format.
90 // Ignoring the fact the format string can request a precision larger than the
91 // values maximum required, these values are:
92 //
93 // sign                    1 code unit
94 // __max_integral
95 // radix point             1 code unit
96 // __max_fractional
97 // exponent character      1 code unit
98 // sign                    1 code unit
99 // __max_fractional_value
100 // -----------------------------------
101 // total                   4 code units extra required.
102 //
103 // TODO FMT Optimize the storage to avoid storing digits that are known to be zero.
104 // https://www.exploringbinary.com/maximum-number-of-decimal-digits-in-binary-floating-point-numbers/
105 
106 // TODO FMT Add long double specialization when to_chars has proper long double support.
107 template <class _Tp>
108 struct __traits;
109 
110 template <floating_point _Fp>
__float_buffer_size(int __precision)111 _LIBCPP_HIDE_FROM_ABI constexpr size_t __float_buffer_size(int __precision) {
112   using _Traits = __traits<_Fp>;
113   return 4 + _Traits::__max_integral + __precision + _Traits::__max_fractional_value;
114 }
115 
116 template <>
117 struct __traits<float> {
118   static constexpr int __max_integral = 38;
119   static constexpr int __max_fractional = 149;
120   static constexpr int __max_fractional_value = 3;
121   static constexpr size_t __stack_buffer_size = 256;
122 
123   static constexpr int __hex_precision_digits = 3;
124 };
125 
126 template <>
127 struct __traits<double> {
128   static constexpr int __max_integral = 308;
129   static constexpr int __max_fractional = 1074;
130   static constexpr int __max_fractional_value = 4;
131   static constexpr size_t __stack_buffer_size = 1024;
132 
133   static constexpr int __hex_precision_digits = 4;
134 };
135 
136 /// Helper class to store the conversion buffer.
137 ///
138 /// Depending on the maxium size required for a value, the buffer is allocated
139 /// on the stack or the heap.
140 template <floating_point _Fp>
141 class _LIBCPP_TEMPLATE_VIS __float_buffer {
142   using _Traits = __traits<_Fp>;
143 
144 public:
145   // TODO FMT Improve this constructor to do a better estimate.
146   // When using a scientific formatting with a precision of 6 a stack buffer
147   // will always suffice. At the moment that isn't important since floats and
148   // doubles use a stack buffer, unless the precision used in the format string
149   // is large.
150   // When supporting long doubles the __max_integral part becomes 4932 which
151   // may be too much for some platforms. For these cases a better estimate is
152   // required.
153   explicit _LIBCPP_HIDE_FROM_ABI __float_buffer(int __precision)
154       : __precision_(__precision != -1 ? __precision : _Traits::__max_fractional) {
155 
156     // When the precision is larger than _Traits::__max_fractional the digits in
157     // the range (_Traits::__max_fractional, precision] will contain the value
158     // zero. There's no need to request to_chars to write these zeros:
159     // - When the value is large a temporary heap buffer needs to be allocated.
160     // - When to_chars writes the values they need to be "copied" to the output:
161     //   - char: std::fill on the output iterator is faster than std::copy.
162     //   - wchar_t: same argument as char, but additional std::copy won't work.
163     //     The input is always a char buffer, so every char in the buffer needs
164     //     to be converted from a char to a wchar_t.
165     if (__precision_ > _Traits::__max_fractional) {
166       __num_trailing_zeros_ = __precision_ - _Traits::__max_fractional;
167       __precision_ = _Traits::__max_fractional;
168     }
169 
170     __size_ = __formatter::__float_buffer_size<_Fp>(__precision_);
171     if (__size_ > _Traits::__stack_buffer_size)
172       // The allocated buffer's contents don't need initialization.
173       __begin_ = allocator<char>{}.allocate(__size_);
174     else
175       __begin_ = __buffer_;
176   }
177 
178   _LIBCPP_HIDE_FROM_ABI ~__float_buffer() {
179     if (__size_ > _Traits::__stack_buffer_size)
180       allocator<char>{}.deallocate(__begin_, __size_);
181   }
182   _LIBCPP_HIDE_FROM_ABI __float_buffer(const __float_buffer&) = delete;
183   _LIBCPP_HIDE_FROM_ABI __float_buffer& operator=(const __float_buffer&) = delete;
184 
185   _LIBCPP_HIDE_FROM_ABI char* begin() const { return __begin_; }
186   _LIBCPP_HIDE_FROM_ABI char* end() const { return __begin_ + __size_; }
187 
188   _LIBCPP_HIDE_FROM_ABI int __precision() const { return __precision_; }
189   _LIBCPP_HIDE_FROM_ABI int __num_trailing_zeros() const { return __num_trailing_zeros_; }
190   _LIBCPP_HIDE_FROM_ABI void __remove_trailing_zeros() { __num_trailing_zeros_ = 0; }
191   _LIBCPP_HIDE_FROM_ABI void __add_trailing_zeros(int __zeros) { __num_trailing_zeros_ += __zeros; }
192 
193 private:
194   int __precision_;
195   int __num_trailing_zeros_{0};
196   size_t __size_;
197   char* __begin_;
198   char __buffer_[_Traits::__stack_buffer_size];
199 };
200 
201 struct __float_result {
202   /// Points at the beginning of the integral part in the buffer.
203   ///
204   /// When there's no sign character this points at the start of the buffer.
205   char* __integral;
206 
207   /// Points at the radix point, when not present it's the same as \ref __last.
208   char* __radix_point;
209 
210   /// Points at the exponent character, when not present it's the same as \ref __last.
211   char* __exponent;
212 
213   /// Points beyond the last written element in the buffer.
214   char* __last;
215 };
216 
217 /// Finds the position of the exponent character 'e' at the end of the buffer.
218 ///
219 /// Assuming there is an exponent the input will terminate with
220 /// eSdd and eSdddd (S = sign, d = digit)
221 ///
222 /// \returns a pointer to the exponent or __last when not found.
223 constexpr inline _LIBCPP_HIDE_FROM_ABI char* __find_exponent(char* __first, char* __last) {
224   ptrdiff_t __size = __last - __first;
225   if (__size >= 4) {
226     __first = __last - _VSTD::min(__size, ptrdiff_t(6));
227     for (; __first != __last - 3; ++__first) {
228       if (*__first == 'e')
229         return __first;
230     }
231   }
232   return __last;
233 }
234 
235 template <class _Fp, class _Tp>
236 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_default(const __float_buffer<_Fp>& __buffer, _Tp __value,
237                                                              char* __integral) {
238   __float_result __result;
239   __result.__integral = __integral;
240   __result.__last     = __formatter::__to_buffer(__integral, __buffer.end(), __value);
241 
242   __result.__exponent = __formatter::__find_exponent(__result.__integral, __result.__last);
243 
244   // Constrains:
245   // - There's at least one decimal digit before the radix point.
246   // - The radix point, when present, is placed before the exponent.
247   __result.__radix_point = _VSTD::find(__result.__integral + 1, __result.__exponent, '.');
248 
249   // When the radix point isn't found its position is the exponent instead of
250   // __result.__last.
251   if (__result.__radix_point == __result.__exponent)
252     __result.__radix_point = __result.__last;
253 
254   // clang-format off
255   _LIBCPP_ASSERT((__result.__integral != __result.__last) &&
256                  (__result.__radix_point == __result.__last || *__result.__radix_point == '.') &&
257                  (__result.__exponent == __result.__last || *__result.__exponent == 'e'),
258                  "Post-condition failure.");
259   // clang-format on
260 
261   return __result;
262 }
263 
264 template <class _Fp, class _Tp>
265 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_hexadecimal_lower_case(const __float_buffer<_Fp>& __buffer,
266                                                                             _Tp __value, int __precision,
267                                                                             char* __integral) {
268   __float_result __result;
269   __result.__integral = __integral;
270   if (__precision == -1)
271     __result.__last = __formatter::__to_buffer(__integral, __buffer.end(), __value, chars_format::hex);
272   else
273     __result.__last = __formatter::__to_buffer(__integral, __buffer.end(), __value, chars_format::hex, __precision);
274 
275   // H = one or more hex-digits
276   // S = sign
277   // D = one or more decimal-digits
278   // When the fractional part is zero and no precision the output is 0p+0
279   // else the output is                                              0.HpSD
280   // So testing the second position can differentiate between these two cases.
281   char* __first = __integral + 1;
282   if (*__first == '.') {
283     __result.__radix_point = __first;
284     // One digit is the minimum
285     // 0.hpSd
286     //       ^-- last
287     //     ^---- integral = end of search
288     // ^-------- start of search
289     // 0123456
290     //
291     // Four digits is the maximum
292     // 0.hpSdddd
293     //          ^-- last
294     //        ^---- integral = end of search
295     //    ^-------- start of search
296     // 0123456789
297     static_assert(__traits<_Fp>::__hex_precision_digits <= 4, "Guard against possible underflow.");
298 
299     char* __last = __result.__last - 2;
300     __first = __last - __traits<_Fp>::__hex_precision_digits;
301     __result.__exponent = _VSTD::find(__first, __last, 'p');
302   } else {
303     __result.__radix_point = __result.__last;
304     __result.__exponent = __first;
305   }
306 
307   // clang-format off
308   _LIBCPP_ASSERT((__result.__integral != __result.__last) &&
309                  (__result.__radix_point == __result.__last || *__result.__radix_point == '.') &&
310                  (__result.__exponent != __result.__last && *__result.__exponent == 'p'),
311                  "Post-condition failure.");
312   // clang-format on
313 
314   return __result;
315 }
316 
317 template <class _Fp, class _Tp>
318 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_hexadecimal_upper_case(const __float_buffer<_Fp>& __buffer,
319                                                                             _Tp __value, int __precision,
320                                                                             char* __integral) {
321   __float_result __result =
322       __formatter::__format_buffer_hexadecimal_lower_case(__buffer, __value, __precision, __integral);
323   _VSTD::transform(__result.__integral, __result.__exponent, __result.__integral, __hex_to_upper);
324   *__result.__exponent = 'P';
325   return __result;
326 }
327 
328 template <class _Fp, class _Tp>
329 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_scientific_lower_case(const __float_buffer<_Fp>& __buffer,
330                                                                            _Tp __value, int __precision,
331                                                                            char* __integral) {
332   __float_result __result;
333   __result.__integral = __integral;
334   __result.__last =
335       __formatter::__to_buffer(__integral, __buffer.end(), __value, chars_format::scientific, __precision);
336 
337   char* __first = __integral + 1;
338   _LIBCPP_ASSERT(__first != __result.__last, "No exponent present");
339   if (*__first == '.') {
340     __result.__radix_point = __first;
341     __result.__exponent    = __formatter::__find_exponent(__first + 1, __result.__last);
342   } else {
343     __result.__radix_point = __result.__last;
344     __result.__exponent = __first;
345   }
346 
347   // clang-format off
348   _LIBCPP_ASSERT((__result.__integral != __result.__last) &&
349                  (__result.__radix_point == __result.__last || *__result.__radix_point == '.') &&
350                  (__result.__exponent != __result.__last && *__result.__exponent == 'e'),
351                  "Post-condition failure.");
352   // clang-format on
353   return __result;
354 }
355 
356 template <class _Fp, class _Tp>
357 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_scientific_upper_case(const __float_buffer<_Fp>& __buffer,
358                                                                            _Tp __value, int __precision,
359                                                                            char* __integral) {
360   __float_result __result =
361       __formatter::__format_buffer_scientific_lower_case(__buffer, __value, __precision, __integral);
362   *__result.__exponent = 'E';
363   return __result;
364 }
365 
366 template <class _Fp, class _Tp>
367 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_fixed(const __float_buffer<_Fp>& __buffer, _Tp __value,
368                                                            int __precision, char* __integral) {
369   __float_result __result;
370   __result.__integral = __integral;
371   __result.__last     = __formatter::__to_buffer(__integral, __buffer.end(), __value, chars_format::fixed, __precision);
372 
373   // When there's no precision there's no radix point.
374   // Else the radix point is placed at __precision + 1 from the end.
375   // By converting __precision to a bool the subtraction can be done
376   // unconditionally.
377   __result.__radix_point = __result.__last - (__precision + bool(__precision));
378   __result.__exponent = __result.__last;
379 
380   // clang-format off
381   _LIBCPP_ASSERT((__result.__integral != __result.__last) &&
382                  (__result.__radix_point == __result.__last || *__result.__radix_point == '.') &&
383                  (__result.__exponent == __result.__last),
384                  "Post-condition failure.");
385   // clang-format on
386   return __result;
387 }
388 
389 template <class _Fp, class _Tp>
390 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_general_lower_case(__float_buffer<_Fp>& __buffer, _Tp __value,
391                                                                         int __precision, char* __integral) {
392 
393   __buffer.__remove_trailing_zeros();
394 
395   __float_result __result;
396   __result.__integral = __integral;
397   __result.__last = __formatter::__to_buffer(__integral, __buffer.end(), __value, chars_format::general, __precision);
398 
399   char* __first = __integral + 1;
400   if (__first == __result.__last) {
401     __result.__radix_point = __result.__last;
402     __result.__exponent = __result.__last;
403   } else {
404     __result.__exponent = __formatter::__find_exponent(__first, __result.__last);
405     if (__result.__exponent != __result.__last)
406       // In scientific mode if there's a radix point it will always be after
407       // the first digit. (This is the position __first points at).
408       __result.__radix_point = *__first == '.' ? __first : __result.__last;
409     else {
410       // In fixed mode the algorithm truncates trailing spaces and possibly the
411       // radix point. There's no good guess for the position of the radix point
412       // therefore scan the output after the first digit.
413       __result.__radix_point = _VSTD::find(__first, __result.__last, '.');
414     }
415   }
416 
417   // clang-format off
418   _LIBCPP_ASSERT((__result.__integral != __result.__last) &&
419                  (__result.__radix_point == __result.__last || *__result.__radix_point == '.') &&
420                  (__result.__exponent == __result.__last || *__result.__exponent == 'e'),
421                  "Post-condition failure.");
422   // clang-format on
423 
424   return __result;
425 }
426 
427 template <class _Fp, class _Tp>
428 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer_general_upper_case(__float_buffer<_Fp>& __buffer, _Tp __value,
429                                                                         int __precision, char* __integral) {
430   __float_result __result = __formatter::__format_buffer_general_lower_case(__buffer, __value, __precision, __integral);
431   if (__result.__exponent != __result.__last)
432     *__result.__exponent = 'E';
433   return __result;
434 }
435 
436 /// Fills the buffer with the data based on the requested formatting.
437 ///
438 /// This function, when needed, turns the characters to upper case and
439 /// determines the "interesting" locations which are returned to the caller.
440 ///
441 /// This means the caller never has to convert the contents of the buffer to
442 /// upper case or search for radix points and the location of the exponent.
443 /// This gives a bit of overhead. The original code didn't do that, but due
444 /// to the number of possible additional work needed to turn this number to
445 /// the proper output the code was littered with tests for upper cases and
446 /// searches for radix points and exponents.
447 /// - When a precision larger than the type's precision is selected
448 ///   additional zero characters need to be written before the exponent.
449 /// - alternate form needs to add a radix point when not present.
450 /// - localization needs to do grouping in the integral part.
451 template <class _Fp, class _Tp>
452 // TODO FMT _Fp should just be _Tp when to_chars has proper long double support.
453 _LIBCPP_HIDE_FROM_ABI __float_result __format_buffer(
454     __float_buffer<_Fp>& __buffer,
455     _Tp __value,
456     bool __negative,
457     bool __has_precision,
458     __format_spec::__sign __sign,
459     __format_spec::__type __type) {
460   char* __first = __formatter::__insert_sign(__buffer.begin(), __negative, __sign);
461   switch (__type) {
462   case __format_spec::__type::__default:
463     if (__has_precision)
464       return __formatter::__format_buffer_general_lower_case(__buffer, __value, __buffer.__precision(), __first);
465     else
466       return __formatter::__format_buffer_default(__buffer, __value, __first);
467 
468   case __format_spec::__type::__hexfloat_lower_case:
469     return __formatter::__format_buffer_hexadecimal_lower_case(
470         __buffer, __value, __has_precision ? __buffer.__precision() : -1, __first);
471 
472   case __format_spec::__type::__hexfloat_upper_case:
473     return __formatter::__format_buffer_hexadecimal_upper_case(
474         __buffer, __value, __has_precision ? __buffer.__precision() : -1, __first);
475 
476   case __format_spec::__type::__scientific_lower_case:
477     return __formatter::__format_buffer_scientific_lower_case(__buffer, __value, __buffer.__precision(), __first);
478 
479   case __format_spec::__type::__scientific_upper_case:
480     return __formatter::__format_buffer_scientific_upper_case(__buffer, __value, __buffer.__precision(), __first);
481 
482   case __format_spec::__type::__fixed_lower_case:
483   case __format_spec::__type::__fixed_upper_case:
484     return __formatter::__format_buffer_fixed(__buffer, __value, __buffer.__precision(), __first);
485 
486   case __format_spec::__type::__general_lower_case:
487     return __formatter::__format_buffer_general_lower_case(__buffer, __value, __buffer.__precision(), __first);
488 
489   case __format_spec::__type::__general_upper_case:
490     return __formatter::__format_buffer_general_upper_case(__buffer, __value, __buffer.__precision(), __first);
491 
492   default:
493     _LIBCPP_ASSERT(false, "The parser should have validated the type");
494     __libcpp_unreachable();
495   }
496 }
497 
498 #  ifndef _LIBCPP_HAS_NO_LOCALIZATION
499 template <class _OutIt, class _Fp, class _CharT>
500 _LIBCPP_HIDE_FROM_ABI _OutIt __format_locale_specific_form(
501     _OutIt __out_it,
502     const __float_buffer<_Fp>& __buffer,
503     const __float_result& __result,
504     _VSTD::locale __loc,
505     __format_spec::__parsed_specifications<_CharT> __specs) {
506   const auto& __np = std::use_facet<numpunct<_CharT>>(__loc);
507   string __grouping = __np.grouping();
508   char* __first = __result.__integral;
509   // When no radix point or exponent are present __last will be __result.__last.
510   char* __last = _VSTD::min(__result.__radix_point, __result.__exponent);
511 
512   ptrdiff_t __digits = __last - __first;
513   if (!__grouping.empty()) {
514     if (__digits <= __grouping[0])
515       __grouping.clear();
516     else
517       __grouping = __formatter::__determine_grouping(__digits, __grouping);
518   }
519 
520   ptrdiff_t __size =
521       __result.__last - __buffer.begin() + // Formatted string
522       __buffer.__num_trailing_zeros() +    // Not yet rendered zeros
523       __grouping.size() -                  // Grouping contains one
524       !__grouping.empty();                 // additional character
525 
526   __formatter::__padding_size_result __padding    = {0, 0};
527   bool __zero_padding                             = __specs.__alignment_ == __format_spec::__alignment::__zero_padding;
528   if (__size < __specs.__width_) {
529     if (__zero_padding) {
530       __specs.__alignment_ = __format_spec::__alignment::__right;
531       __specs.__fill_      = _CharT('0');
532     }
533 
534     __padding = __formatter::__padding_size(__size, __specs.__width_, __specs.__alignment_);
535   }
536 
537   // sign and (zero padding or alignment)
538   if (__zero_padding && __first != __buffer.begin())
539     *__out_it++ = *__buffer.begin();
540   __out_it = __formatter::__fill(_VSTD::move(__out_it), __padding.__before_, __specs.__fill_);
541   if (!__zero_padding && __first != __buffer.begin())
542     *__out_it++ = *__buffer.begin();
543 
544   // integral part
545   if (__grouping.empty()) {
546     __out_it = __formatter::__copy(__first, __digits, _VSTD::move(__out_it));
547   } else {
548     auto __r = __grouping.rbegin();
549     auto __e = __grouping.rend() - 1;
550     _CharT __sep = __np.thousands_sep();
551     // The output is divided in small groups of numbers to write:
552     // - A group before the first separator.
553     // - A separator and a group, repeated for the number of separators.
554     // - A group after the last separator.
555     // This loop achieves that process by testing the termination condition
556     // midway in the loop.
557     while (true) {
558       __out_it = __formatter::__copy(__first, *__r, _VSTD::move(__out_it));
559       __first += *__r;
560 
561       if (__r == __e)
562         break;
563 
564       ++__r;
565       *__out_it++ = __sep;
566     }
567   }
568 
569   // fractional part
570   if (__result.__radix_point != __result.__last) {
571     *__out_it++ = __np.decimal_point();
572     __out_it    = __formatter::__copy(__result.__radix_point + 1, __result.__exponent, _VSTD::move(__out_it));
573     __out_it    = __formatter::__fill(_VSTD::move(__out_it), __buffer.__num_trailing_zeros(), _CharT('0'));
574   }
575 
576   // exponent
577   if (__result.__exponent != __result.__last)
578     __out_it = __formatter::__copy(__result.__exponent, __result.__last, _VSTD::move(__out_it));
579 
580   // alignment
581   return __formatter::__fill(_VSTD::move(__out_it), __padding.__after_, __specs.__fill_);
582 }
583 #  endif // _LIBCPP_HAS_NO_LOCALIZATION
584 
585 template <class _OutIt, class _CharT>
586 _LIBCPP_HIDE_FROM_ABI _OutIt __format_floating_point_non_finite(
587     _OutIt __out_it, __format_spec::__parsed_specifications<_CharT> __specs, bool __negative, bool __isnan) {
588   char __buffer[4];
589   char* __last = __formatter::__insert_sign(__buffer, __negative, __specs.__std_.__sign_);
590 
591   // to_chars can return inf, infinity, nan, and nan(n-char-sequence).
592   // The format library requires inf and nan.
593   // All in one expression to avoid dangling references.
594   bool __upper_case =
595       __specs.__std_.__type_ == __format_spec::__type::__hexfloat_upper_case ||
596       __specs.__std_.__type_ == __format_spec::__type::__scientific_upper_case ||
597       __specs.__std_.__type_ == __format_spec::__type::__fixed_upper_case ||
598       __specs.__std_.__type_ == __format_spec::__type::__general_upper_case;
599   __last = _VSTD::copy_n(&("infnanINFNAN"[6 * __upper_case + 3 * __isnan]), 3, __last);
600 
601   // [format.string.std]/13
602   // A zero (0) character preceding the width field pads the field with
603   // leading zeros (following any indication of sign or base) to the field
604   // width, except when applied to an infinity or NaN.
605   if (__specs.__alignment_ == __format_spec::__alignment::__zero_padding)
606     __specs.__alignment_ = __format_spec::__alignment::__right;
607 
608   return __formatter::__write(__buffer, __last, _VSTD::move(__out_it), __specs);
609 }
610 
611 template <floating_point _Tp, class _CharT>
612 _LIBCPP_HIDE_FROM_ABI auto
613 __format_floating_point(_Tp __value, auto& __ctx, __format_spec::__parsed_specifications<_CharT> __specs)
614     -> decltype(__ctx.out()) {
615   bool __negative = _VSTD::signbit(__value);
616 
617   if (!_VSTD::isfinite(__value)) [[unlikely]]
618     return __formatter::__format_floating_point_non_finite(__ctx.out(), __specs, __negative, _VSTD::isnan(__value));
619 
620   // Depending on the std-format-spec string the sign and the value
621   // might not be outputted together:
622   // - zero-padding may insert additional '0' characters.
623   // Therefore the value is processed as a non negative value.
624   // The function @ref __insert_sign will insert a '-' when the value was
625   // negative.
626 
627   if (__negative)
628     __value = -__value;
629 
630   // TODO FMT _Fp should just be _Tp when to_chars has proper long double support.
631   using _Fp = conditional_t<same_as<_Tp, long double>, double, _Tp>;
632   // Force the type of the precision to avoid -1 to become an unsigned value.
633   __float_buffer<_Fp> __buffer(__specs.__precision_);
634   __float_result __result = __formatter::__format_buffer(
635       __buffer, __value, __negative, (__specs.__has_precision()), __specs.__std_.__sign_, __specs.__std_.__type_);
636 
637   if (__specs.__std_.__alternate_form_) {
638     if (__result.__radix_point == __result.__last) {
639       *__result.__last++ = '.';
640 
641       // When there is an exponent the point needs to be moved before the
642       // exponent. When there's no exponent the rotate does nothing. Since
643       // rotate tests whether the operation is a nop, call it unconditionally.
644       _VSTD::rotate(__result.__exponent, __result.__last - 1, __result.__last);
645       __result.__radix_point = __result.__exponent;
646 
647       // The radix point is always placed before the exponent.
648       // - No exponent needs to point to the new last.
649       // - An exponent needs to move one position to the right.
650       // So it's safe to increment the value unconditionally.
651       ++__result.__exponent;
652     }
653 
654     // [format.string.std]/6
655     //   In addition, for g and G conversions, trailing zeros are not removed
656     //   from the result.
657     //
658     // If the type option for a floating-point type is none it may use the
659     // general formatting, but it's not a g or G conversion. So in that case
660     // the formatting should not append trailing zeros.
661     bool __is_general = __specs.__std_.__type_ == __format_spec::__type::__general_lower_case ||
662                         __specs.__std_.__type_ == __format_spec::__type::__general_upper_case;
663 
664     if (__is_general) {
665       // https://en.cppreference.com/w/c/io/fprintf
666       // Let P equal the precision if nonzero, 6 if the precision is not
667       // specified, or 1 if the precision is 0. Then, if a conversion with
668       // style E would have an exponent of X:
669       int __p = _VSTD::max(1, (__specs.__has_precision() ? __specs.__precision_ : 6));
670       if (__result.__exponent == __result.__last)
671         // if P > X >= -4, the conversion is with style f or F and precision P - 1 - X.
672         // By including the radix point it calculates P - (1 + X)
673         __p -= __result.__radix_point - __result.__integral;
674       else
675         // otherwise, the conversion is with style e or E and precision P - 1.
676         --__p;
677 
678       ptrdiff_t __precision = (__result.__exponent - __result.__radix_point) - 1;
679       if (__precision < __p)
680         __buffer.__add_trailing_zeros(__p - __precision);
681     }
682   }
683 
684 #  ifndef _LIBCPP_HAS_NO_LOCALIZATION
685   if (__specs.__std_.__locale_specific_form_)
686     return __formatter::__format_locale_specific_form(__ctx.out(), __buffer, __result, __ctx.locale(), __specs);
687 #  endif
688 
689   ptrdiff_t __size         = __result.__last - __buffer.begin();
690   int __num_trailing_zeros = __buffer.__num_trailing_zeros();
691   if (__size + __num_trailing_zeros >= __specs.__width_) {
692     if (__num_trailing_zeros && __result.__exponent != __result.__last)
693       // Insert trailing zeros before exponent character.
694       return __formatter::__copy(
695           __result.__exponent,
696           __result.__last,
697           __formatter::__fill(__formatter::__copy(__buffer.begin(), __result.__exponent, __ctx.out()),
698                               __num_trailing_zeros,
699                               _CharT('0')));
700 
701     return __formatter::__fill(
702         __formatter::__copy(__buffer.begin(), __result.__last, __ctx.out()), __num_trailing_zeros, _CharT('0'));
703   }
704 
705   auto __out_it = __ctx.out();
706   char* __first = __buffer.begin();
707   if (__specs.__alignment_ == __format_spec::__alignment ::__zero_padding) {
708     // When there is a sign output it before the padding. Note the __size
709     // doesn't need any adjustment, regardless whether the sign is written
710     // here or in __formatter::__write.
711     if (__first != __result.__integral)
712       *__out_it++ = *__first++;
713     // After the sign is written, zero padding is the same a right alignment
714     // with '0'.
715     __specs.__alignment_ = __format_spec::__alignment::__right;
716     __specs.__fill_      = _CharT('0');
717   }
718 
719   if (__num_trailing_zeros)
720     return __formatter::__write_using_trailing_zeros(
721         __first, __result.__last, _VSTD::move(__out_it), __specs, __size, __result.__exponent, __num_trailing_zeros);
722 
723   return __formatter::__write(__first, __result.__last, _VSTD::move(__out_it), __specs, __size);
724 }
725 
726 } // namespace __formatter
727 
728 template <__fmt_char_type _CharT>
729 struct _LIBCPP_TEMPLATE_VIS __formatter_floating_point {
730 public:
731   _LIBCPP_HIDE_FROM_ABI constexpr auto
732   parse(basic_format_parse_context<_CharT>& __parse_ctx) -> decltype(__parse_ctx.begin()) {
733     auto __result = __parser_.__parse(__parse_ctx, __format_spec::__fields_floating_point);
734     __format_spec::__process_parsed_floating_point(__parser_);
735     return __result;
736   }
737 
738   template <floating_point _Tp>
739   _LIBCPP_HIDE_FROM_ABI auto format(_Tp __value, auto& __ctx) const -> decltype(__ctx.out()) {
740     return __formatter::__format_floating_point(__value, __ctx, __parser_.__get_parsed_std_specifications(__ctx));
741   }
742 
743   __format_spec::__parser<_CharT> __parser_;
744 };
745 
746 template <__fmt_char_type _CharT>
747 struct _LIBCPP_TEMPLATE_VIS formatter<float, _CharT>
748     : public __formatter_floating_point<_CharT> {};
749 template <__fmt_char_type _CharT>
750 struct _LIBCPP_TEMPLATE_VIS formatter<double, _CharT>
751     : public __formatter_floating_point<_CharT> {};
752 template <__fmt_char_type _CharT>
753 struct _LIBCPP_TEMPLATE_VIS formatter<long double, _CharT>
754     : public __formatter_floating_point<_CharT> {};
755 
756 #endif //_LIBCPP_STD_VER >= 20
757 
758 _LIBCPP_END_NAMESPACE_STD
759 
760 _LIBCPP_POP_MACROS
761 
762 #endif // _LIBCPP___FORMAT_FORMATTER_FLOATING_POINT_H
763