Line data Source code
1 : // Copyright 2020-2022 Junekey Jeon
2 : //
3 : // The contents of this file may be used under the terms of
4 : // the Apache License v2.0 with LLVM Exceptions.
5 : //
6 : // (See accompanying file LICENSE-Apache or copy at
7 : // https://llvm.org/foundation/relicensing/LICENSE.txt)
8 : //
9 : // Alternatively, the contents of this file may be used under the terms of
10 : // the Boost Software License, Version 1.0.
11 : // (See accompanying file LICENSE-Boost or copy at
12 : // https://www.boost.org/LICENSE_1_0.txt)
13 : //
14 : // Unless required by applicable law or agreed to in writing, this software
15 : // is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
16 : // KIND, either express or implied.
17 : //
18 : // Copyright 2023 Matt Borland
19 : // Distributed under the Boost Software License, Version 1.0.
20 : // https://www.boost.org/LICENSE_1_0.txt
21 :
22 : #ifndef BOOST_JSON_DETAIL_DRAGONBOX_DRAGONBOX_HPP
23 : #define BOOST_JSON_DETAIL_DRAGONBOX_DRAGONBOX_HPP
24 :
25 : #include <boost/json/detail/charconv/detail/config.hpp>
26 : #include <boost/json/detail/dragonbox/dragonbox_common.hpp>
27 : #include <boost/core/bit.hpp>
28 : #include <type_traits>
29 : #include <limits>
30 : #include <cstdint>
31 : #include <cstring>
32 :
33 : #ifdef BOOST_MSVC
34 : # pragma warning(push)
35 : # pragma warning(disable: 4127) // Conditional expression is constant (e.g. BOOST_IF_CONSTEXPR statements)
36 : # pragma warning(disable: 4307) // Integral constant overflow (Only MSVC-14.1 issued this warning)
37 : #endif
38 :
39 : namespace boost {
40 : namespace json {
41 : namespace detail {
42 :
43 : // A floating-point traits class defines ways to interpret a bit pattern of given size as an
44 : // encoding of floating-point number. This is a default implementation of such a traits class,
45 : // supporting ways to interpret 32-bits into a binary32-encoded floating-point number and to
46 : // interpret 64-bits into a binary64-encoded floating-point number. Users might specialize this
47 : // class to change the default behavior for certain types.
48 :
49 : template <typename T>
50 : struct dragonbox_float_traits
51 : {
52 : // I don't know if there is a truly reliable way of detecting
53 : // IEEE-754 binary32/binary64 formats; I just did my best here.
54 : static_assert(std::numeric_limits<T>::is_iec559 && std::numeric_limits<T>::radix == 2 &&
55 : (physical_bits<T>::value == 32 || physical_bits<T>::value == 64),
56 : "default_ieee754_traits only works for 32-bits or 64-bits types "
57 : "supporting binary32 or binary64 formats!");
58 :
59 : // The type that is being viewed.
60 : using type = T;
61 :
62 : // Refers to the format specification class.
63 : using format = typename std::conditional<physical_bits<T>::value == 32, ieee754_binary32, ieee754_binary64>::type;
64 :
65 : // Defines an unsigned integer type that is large enough to carry a variable of type T.
66 : // Most of the operations will be done on this integer type.
67 : using carrier_uint =
68 : typename std::conditional<physical_bits<T>::value == 32, std::uint32_t, std::uint64_t>::type;
69 :
70 : static_assert(sizeof(carrier_uint) == sizeof(T), "Type T must have a unsigned type with the same number of bits");
71 :
72 : // Number of bits in the above unsigned integer type.
73 : static constexpr int carrier_bits = static_cast<int>(physical_bits<carrier_uint>::value);
74 :
75 : // Convert from carrier_uint into the original type.
76 : // Depending on the floating-point encoding format, this operation might not be possible for
77 : // some specific bit patterns. However, the contract is that u always denotes a
78 : // valid bit pattern, so this function must be assumed to be noexcept.
79 : static T carrier_to_float(carrier_uint u) noexcept
80 : {
81 : T x;
82 : std::memcpy(&x, &u, sizeof(carrier_uint));
83 : return x;
84 : }
85 :
86 : // Same as above.
87 510 : static carrier_uint float_to_carrier(T x) noexcept
88 : {
89 : carrier_uint u;
90 510 : std::memcpy(&u, &x, sizeof(carrier_uint));
91 510 : return u;
92 : }
93 :
94 : // Extract exponent bits from a bit pattern.
95 : // The result must be aligned to the LSB so that there is no additional zero paddings
96 : // on the right. This function does not do bias adjustment.
97 510 : static constexpr unsigned extract_exponent_bits(carrier_uint u) noexcept
98 : {
99 510 : return static_cast<unsigned>(u >> format::significand_bits) & ((static_cast<unsigned int>(1) << format::exponent_bits) - 1);
100 : }
101 :
102 : // Extract significand bits from a bit pattern.
103 : // The result must be aligned to the LSB so that there is no additional zero paddings
104 : // on the right. The result does not contain the implicit bit.
105 : static constexpr carrier_uint extract_significand_bits(carrier_uint u) noexcept
106 : {
107 : return carrier_uint(u & carrier_uint((carrier_uint(1) << format::significand_bits) - 1));
108 : }
109 :
110 : // Remove the exponent bits and extract significand bits together with the sign bit.
111 510 : static constexpr carrier_uint remove_exponent_bits(carrier_uint u, unsigned int exponent_bits) noexcept
112 : {
113 510 : return u ^ (carrier_uint(exponent_bits) << format::significand_bits);
114 : }
115 :
116 : // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
117 444 : static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept {
118 444 : return carrier_uint(carrier_uint(u) << 1);
119 : }
120 :
121 : // The actual value of exponent is obtained by adding this value to the extracted exponent
122 : // bits.
123 : static constexpr int exponent_bias = 1 - (1 << (carrier_bits - format::significand_bits - 2));
124 :
125 : // Obtain the actual value of the binary exponent from the extracted exponent bits.
126 : static constexpr int binary_exponent(unsigned exponent_bits) noexcept
127 : {
128 : return static_cast<int>(exponent_bits == 0 ? format::min_exponent : int(exponent_bits) + format::exponent_bias);
129 : }
130 :
131 : // Obtain the actual value of the binary exponent from the extracted significand bits and
132 : // exponent bits.
133 : static constexpr carrier_uint binary_significand(carrier_uint significand_bits, unsigned exponent_bits) noexcept
134 : {
135 : return exponent_bits == 0 ? significand_bits : significand_bits | (carrier_uint(1) << format::significand_bits);
136 : }
137 :
138 : /* Various boolean observer functions */
139 :
140 495 : static constexpr bool is_nonzero(carrier_uint u) noexcept
141 : {
142 495 : return (u << 1) != 0;
143 : }
144 :
145 949 : static constexpr bool is_positive(carrier_uint u) noexcept
146 : {
147 949 : return u < (carrier_uint(1) << (format::significand_bits + format::exponent_bits));
148 : }
149 :
150 949 : static constexpr bool is_negative(carrier_uint u) noexcept
151 : {
152 949 : return !is_positive(u);
153 : }
154 :
155 510 : static constexpr bool is_finite(unsigned exponent_bits) noexcept
156 : {
157 510 : return exponent_bits != ((1u << format::exponent_bits) - 1);
158 : }
159 :
160 15 : static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept
161 : {
162 15 : return (u << 1) == 0;
163 : }
164 :
165 306 : static constexpr bool has_even_significand_bits(carrier_uint u) noexcept
166 : {
167 306 : return u % 2 == 0;
168 : }
169 : };
170 :
171 : // Convenient wrappers for floating-point traits classes.
172 : // In order to reduce the argument passing overhead, these classes should be as simple as
173 : // possible (e.g., no inheritance, no private non-static data member, etc.; this is an
174 : // unfortunate fact about common ABI convention).
175 :
176 : template <typename T, typename Traits = dragonbox_float_traits<T>>
177 : struct dragonbox_float_bits;
178 :
179 : template <typename T, typename Traits = dragonbox_float_traits<T>>
180 : struct dragonbox_signed_significand_bits;
181 :
182 : template <typename T, typename Traits>
183 : struct dragonbox_float_bits
184 : {
185 : using type = T;
186 : using traits_type = Traits;
187 : using carrier_uint = typename traits_type::carrier_uint;
188 :
189 : carrier_uint u;
190 :
191 : dragonbox_float_bits() = default;
192 : constexpr explicit dragonbox_float_bits(carrier_uint bit_pattern) noexcept : u{bit_pattern} {}
193 510 : constexpr explicit dragonbox_float_bits(T float_value) noexcept
194 510 : : u{traits_type::float_to_carrier(float_value)} {}
195 :
196 : T to_float() const noexcept
197 : {
198 : return traits_type::carrier_to_float(u);
199 : }
200 :
201 : // Extract exponent bits from a bit pattern.
202 : // The result must be aligned to the LSB so that there is no additional zero paddings
203 : // on the right. This function does not do bias adjustment.
204 510 : constexpr unsigned int extract_exponent_bits() const noexcept
205 : {
206 510 : return traits_type::extract_exponent_bits(u);
207 : }
208 :
209 : // Extract significand bits from a bit pattern.
210 : // The result must be aligned to the LSB so that there is no additional zero paddings
211 : // on the right. The result does not contain the implicit bit.
212 : constexpr carrier_uint extract_significand_bits() const noexcept
213 : {
214 : return traits_type::extract_significand_bits(u);
215 : }
216 :
217 : // Remove the exponent bits and extract significand bits together with the sign bit.
218 510 : constexpr auto remove_exponent_bits(unsigned int exponent_bits) const noexcept -> dragonbox_signed_significand_bits<type, traits_type>
219 : {
220 510 : return dragonbox_signed_significand_bits<type, traits_type>(traits_type::remove_exponent_bits(u, exponent_bits));
221 : }
222 :
223 : // Obtain the actual value of the binary exponent from the extracted exponent bits.
224 : static constexpr int binary_exponent(unsigned exponent_bits) noexcept
225 : {
226 : return traits_type::binary_exponent(exponent_bits);
227 : }
228 :
229 : constexpr int binary_exponent() const noexcept
230 : {
231 : return binary_exponent(extract_exponent_bits());
232 : }
233 :
234 : // Obtain the actual value of the binary exponent from the extracted significand bits and
235 : // exponent bits.
236 : static constexpr carrier_uint binary_significand(carrier_uint significand_bits, unsigned exponent_bits) noexcept
237 : {
238 : return traits_type::binary_significand(significand_bits, exponent_bits);
239 : }
240 :
241 : constexpr carrier_uint binary_significand() const noexcept
242 : {
243 : return binary_significand(extract_significand_bits(), extract_exponent_bits());
244 : }
245 :
246 495 : constexpr bool is_nonzero() const noexcept
247 : {
248 495 : return traits_type::is_nonzero(u);
249 : }
250 :
251 : constexpr bool is_positive() const noexcept
252 : {
253 : return traits_type::is_positive(u);
254 : }
255 :
256 : constexpr bool is_negative() const noexcept
257 : {
258 : return traits_type::is_negative(u);
259 : }
260 :
261 510 : constexpr bool is_finite(unsigned exponent_bits) const noexcept
262 : {
263 510 : return traits_type::is_finite(exponent_bits);
264 : }
265 :
266 : constexpr bool is_finite() const noexcept
267 : {
268 : return traits_type::is_finite(extract_exponent_bits());
269 : }
270 :
271 : constexpr bool has_even_significand_bits() const noexcept
272 : {
273 : return traits_type::has_even_significand_bits(u);
274 : }
275 : };
276 :
277 : template <typename T, typename Traits>
278 : struct dragonbox_signed_significand_bits
279 : {
280 : using type = T;
281 : using traits_type = Traits;
282 : using carrier_uint = typename traits_type::carrier_uint;
283 :
284 : carrier_uint u;
285 :
286 : dragonbox_signed_significand_bits() = default;
287 510 : constexpr explicit dragonbox_signed_significand_bits(carrier_uint bit_pattern) noexcept
288 510 : : u{bit_pattern} {}
289 :
290 : // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
291 444 : constexpr carrier_uint remove_sign_bit_and_shift() const noexcept
292 : {
293 444 : return traits_type::remove_sign_bit_and_shift(u);
294 : }
295 :
296 : constexpr bool is_positive() const noexcept
297 : {
298 : return traits_type::is_positive(u);
299 : }
300 :
301 949 : constexpr bool is_negative() const noexcept
302 : {
303 949 : return traits_type::is_negative(u);
304 : }
305 :
306 15 : constexpr bool has_all_zero_significand_bits() const noexcept
307 : {
308 15 : return traits_type::has_all_zero_significand_bits(u);
309 : }
310 :
311 306 : constexpr bool has_even_significand_bits() const noexcept
312 : {
313 306 : return traits_type::has_even_significand_bits(u);
314 : }
315 : };
316 :
317 : ////////////////////////////////////////////////////////////////////////////////////////
318 : // Utilities for fast divisibility tests.
319 : ////////////////////////////////////////////////////////////////////////////////////////
320 :
321 : namespace div {
322 : // Replace n by floor(n / 10^N).
323 : // Returns true if and only if n is divisible by 10^N.
324 : // Precondition: n <= 10^(N+1)
325 : // !!It takes an in-out parameter!!
326 : template <int N>
327 : struct divide_by_pow10_info;
328 :
329 : template <>
330 : struct divide_by_pow10_info<1>
331 : {
332 : static constexpr std::uint32_t magic_number = 6554;
333 : static constexpr int shift_amount = 16;
334 : };
335 :
336 : template <>
337 : struct divide_by_pow10_info<2>
338 : {
339 : static constexpr std::uint32_t magic_number = 656;
340 : static constexpr int shift_amount = 16;
341 : };
342 :
343 : template <int N>
344 1 : BOOST_CXX14_CONSTEXPR bool check_divisibility_and_divide_by_pow10(std::uint32_t& n) noexcept
345 : {
346 : // Make sure the computation for max_n does not overflow.
347 : // static_assert(N + 1 <= log::floor_log10_pow2(31));
348 1 : BOOST_ASSERT(n <= compute_power(UINT32_C(10), N + 1));
349 :
350 : using info = divide_by_pow10_info<N>;
351 1 : n *= info::magic_number;
352 :
353 1 : constexpr auto mask = std::uint32_t(std::uint32_t(1) << info::shift_amount) - 1;
354 1 : bool result = ((n & mask) < info::magic_number);
355 :
356 1 : n >>= info::shift_amount;
357 1 : return result;
358 : }
359 :
360 : // Compute floor(n / 10^N) for small n and N.
361 : // Precondition: n <= 10^(N+1)
362 : template <int N>
363 : BOOST_CXX14_CONSTEXPR std::uint32_t small_division_by_pow10(std::uint32_t n) noexcept
364 : {
365 : // Make sure the computation for max_n does not overflow.
366 : // static_assert(N + 1 <= log::floor_log10_pow2(31));
367 : BOOST_ASSERT(n <= compute_power(UINT32_C(10), N + 1));
368 :
369 : return (n * divide_by_pow10_info<N>::magic_number) >> divide_by_pow10_info<N>::shift_amount;
370 : }
371 :
372 : // Compute floor(n / 10^N) for small N.
373 : // Precondition: n <= n_max
374 : template <unsigned N, typename UInt, UInt n_max>
375 : BOOST_CXX14_CONSTEXPR UInt divide_by_pow10(UInt n) noexcept
376 : {
377 :
378 : // Specialize for 32-bit division by 100.
379 : // Compiler is supposed to generate the identical code for just writing
380 : // "n / 100", but for some reason MSVC generates an inefficient code
381 : // (mul + mov for no apparent reason, instead of single imul),
382 : // so we does this manually.
383 : BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint32_t>::value && N == 2)
384 : {
385 : return static_cast<UInt>(umul64(static_cast<std::uint32_t>(n), UINT32_C(1374389535)) >> 37);
386 : }
387 : // Specialize for 64-bit division by 1000.
388 : // Ensure that the correctness condition is met.
389 : else BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint64_t>::value && N == 3 && n_max <= UINT64_C(15534100272597517998))
390 : {
391 : return static_cast<UInt>(umul128_upper64(n, UINT64_C(2361183241434822607)) >> 7);
392 : }
393 : else
394 : {
395 : BOOST_CXX14_CONSTEXPR auto divisor = compute_power(static_cast<UInt>(10), N);
396 : return n / divisor;
397 : }
398 : }
399 :
400 : #ifdef BOOST_MSVC
401 : # pragma warning(push)
402 : # pragma warning(disable: 4100) // MSVC 14.0 does not have BOOST_ATTRIBUTE_UNUSED so we disable the warning
403 : #endif
404 :
405 : template <typename UInt>
406 306 : BOOST_CXX14_CONSTEXPR UInt divide_by_pow10(unsigned N, BOOST_ATTRIBUTE_UNUSED UInt n_max, UInt n) noexcept
407 : {
408 : BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint32_t>::value && N == 2)
409 : {
410 : return static_cast<UInt>(umul64(static_cast<std::uint32_t>(n), static_cast<std::uint32_t>(1374389535)) >> UINT32_C(37));
411 : }
412 : // Specialize for 64-bit division by 1000.
413 : // Ensure that the correctness condition is met.
414 306 : else BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint64_t>::value && N == 3 && n_max <= UINT64_C(15534100272597517998))
415 : {
416 306 : return static_cast<UInt>(umul128_upper64(n, UINT64_C(2361183241434822607)) >> 7);
417 : }
418 : else
419 : {
420 0 : auto divisor = compute_power(static_cast<UInt>(10), N);
421 0 : return n / divisor;
422 : }
423 : }
424 :
425 : #ifdef BOOST_MSVC
426 : # pragma warning(pop)
427 : #endif
428 : }
429 :
430 : ////////////////////////////////////////////////////////////////////////////////////////
431 : // Return types for the main interface function.
432 : ////////////////////////////////////////////////////////////////////////////////////////
433 :
434 : template <typename UInt, bool is_signed, bool trailing_zero_flag>
435 : struct decimal_fp;
436 :
437 : template <typename UInt>
438 : struct decimal_fp<UInt, false, false>
439 : {
440 : using carrier_uint = UInt;
441 :
442 : carrier_uint significand;
443 : int exponent;
444 : };
445 :
446 : template <typename UInt>
447 : struct decimal_fp<UInt, true, false>
448 : {
449 : using carrier_uint = UInt;
450 :
451 : carrier_uint significand;
452 : int exponent;
453 : bool is_negative;
454 : };
455 :
456 : template <typename UInt>
457 : struct decimal_fp<UInt, false, true>
458 : {
459 : using carrier_uint = UInt;
460 :
461 : carrier_uint significand;
462 : int exponent;
463 : bool may_have_trailing_zeros;
464 : };
465 :
466 : template <typename UInt>
467 : struct decimal_fp<UInt, true, true>
468 : {
469 : using carrier_uint = UInt;
470 :
471 : carrier_uint significand;
472 : int exponent;
473 : bool is_negative;
474 : bool may_have_trailing_zeros;
475 : };
476 :
477 : template <typename UInt>
478 : using unsigned_decimal_fp = decimal_fp<UInt, false, false>;
479 :
480 : template <typename UInt>
481 : using signed_decimal_fp = decimal_fp<UInt, true, false>;
482 :
483 : ////////////////////////////////////////////////////////////////////////////////////////
484 : // Computed cache entries.
485 : ////////////////////////////////////////////////////////////////////////////////////////
486 :
487 : #if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
488 : template <bool b>
489 : struct cache_holder_ieee754_binary32_impl
490 : #else
491 : struct cache_holder_ieee754_binary32
492 : #endif
493 : {
494 : using cache_entry_type = std::uint64_t;
495 : static constexpr int cache_bits = 64;
496 : static constexpr int min_k = -31;
497 : static constexpr int max_k = 46;
498 : static constexpr cache_entry_type cache[] = {
499 : 0x81ceb32c4b43fcf5, 0xa2425ff75e14fc32, 0xcad2f7f5359a3b3f, 0xfd87b5f28300ca0e,
500 : 0x9e74d1b791e07e49, 0xc612062576589ddb, 0xf79687aed3eec552, 0x9abe14cd44753b53,
501 : 0xc16d9a0095928a28, 0xf1c90080baf72cb2, 0x971da05074da7bef, 0xbce5086492111aeb,
502 : 0xec1e4a7db69561a6, 0x9392ee8e921d5d08, 0xb877aa3236a4b44a, 0xe69594bec44de15c,
503 : 0x901d7cf73ab0acda, 0xb424dc35095cd810, 0xe12e13424bb40e14, 0x8cbccc096f5088cc,
504 : 0xafebff0bcb24aaff, 0xdbe6fecebdedd5bf, 0x89705f4136b4a598, 0xabcc77118461cefd,
505 : 0xd6bf94d5e57a42bd, 0x8637bd05af6c69b6, 0xa7c5ac471b478424, 0xd1b71758e219652c,
506 : 0x83126e978d4fdf3c, 0xa3d70a3d70a3d70b, 0xcccccccccccccccd, 0x8000000000000000,
507 : 0xa000000000000000, 0xc800000000000000, 0xfa00000000000000, 0x9c40000000000000,
508 : 0xc350000000000000, 0xf424000000000000, 0x9896800000000000, 0xbebc200000000000,
509 : 0xee6b280000000000, 0x9502f90000000000, 0xba43b74000000000, 0xe8d4a51000000000,
510 : 0x9184e72a00000000, 0xb5e620f480000000, 0xe35fa931a0000000, 0x8e1bc9bf04000000,
511 : 0xb1a2bc2ec5000000, 0xde0b6b3a76400000, 0x8ac7230489e80000, 0xad78ebc5ac620000,
512 : 0xd8d726b7177a8000, 0x878678326eac9000, 0xa968163f0a57b400, 0xd3c21bcecceda100,
513 : 0x84595161401484a0, 0xa56fa5b99019a5c8, 0xcecb8f27f4200f3a, 0x813f3978f8940985,
514 : 0xa18f07d736b90be6, 0xc9f2c9cd04674edf, 0xfc6f7c4045812297, 0x9dc5ada82b70b59e,
515 : 0xc5371912364ce306, 0xf684df56c3e01bc7, 0x9a130b963a6c115d, 0xc097ce7bc90715b4,
516 : 0xf0bdc21abb48db21, 0x96769950b50d88f5, 0xbc143fa4e250eb32, 0xeb194f8e1ae525fe,
517 : 0x92efd1b8d0cf37bf, 0xb7abc627050305ae, 0xe596b7b0c643c71a, 0x8f7e32ce7bea5c70,
518 : 0xb35dbf821ae4f38c, 0xe0352f62a19e306f};
519 : };
520 :
521 : #if defined(BOOST_NO_CXX17_INLINE_VARIABLES) && (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
522 :
523 : template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::cache_bits;
524 : template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::min_k;
525 : template <bool b> constexpr int cache_holder_ieee754_binary32_impl<b>::max_k;
526 : template <bool b> constexpr typename cache_holder_ieee754_binary32_impl<b>::cache_entry_type cache_holder_ieee754_binary32_impl<b>::cache[];
527 :
528 : #endif
529 :
530 : #if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
531 : using cache_holder_ieee754_binary32 = cache_holder_ieee754_binary32_impl<true>;
532 : #endif
533 :
534 : #if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
535 : template <bool b>
536 : struct cache_holder_ieee754_binary64_impl
537 : #else
538 : struct cache_holder_ieee754_binary64
539 : #endif
540 : {
541 : using cache_entry_type = uint128;
542 : static constexpr int cache_bits = 128;
543 : static constexpr int min_k = -292;
544 : static constexpr int max_k = 326;
545 : static constexpr cache_entry_type cache[] = {
546 : {0xff77b1fcbebcdc4f, 0x25e8e89c13bb0f7b}, {0x9faacf3df73609b1, 0x77b191618c54e9ad},
547 : {0xc795830d75038c1d, 0xd59df5b9ef6a2418}, {0xf97ae3d0d2446f25, 0x4b0573286b44ad1e},
548 : {0x9becce62836ac577, 0x4ee367f9430aec33}, {0xc2e801fb244576d5, 0x229c41f793cda740},
549 : {0xf3a20279ed56d48a, 0x6b43527578c11110}, {0x9845418c345644d6, 0x830a13896b78aaaa},
550 : {0xbe5691ef416bd60c, 0x23cc986bc656d554}, {0xedec366b11c6cb8f, 0x2cbfbe86b7ec8aa9},
551 : {0x94b3a202eb1c3f39, 0x7bf7d71432f3d6aa}, {0xb9e08a83a5e34f07, 0xdaf5ccd93fb0cc54},
552 : {0xe858ad248f5c22c9, 0xd1b3400f8f9cff69}, {0x91376c36d99995be, 0x23100809b9c21fa2},
553 : {0xb58547448ffffb2d, 0xabd40a0c2832a78b}, {0xe2e69915b3fff9f9, 0x16c90c8f323f516d},
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703 : {0x878678326eac9000, 0x0000000000000000}, {0xa968163f0a57b400, 0x0000000000000000},
704 : {0xd3c21bcecceda100, 0x0000000000000000}, {0x84595161401484a0, 0x0000000000000000},
705 : {0xa56fa5b99019a5c8, 0x0000000000000000}, {0xcecb8f27f4200f3a, 0x0000000000000000},
706 : {0x813f3978f8940984, 0x4000000000000000}, {0xa18f07d736b90be5, 0x5000000000000000},
707 : {0xc9f2c9cd04674ede, 0xa400000000000000}, {0xfc6f7c4045812296, 0x4d00000000000000},
708 : {0x9dc5ada82b70b59d, 0xf020000000000000}, {0xc5371912364ce305, 0x6c28000000000000},
709 : {0xf684df56c3e01bc6, 0xc732000000000000}, {0x9a130b963a6c115c, 0x3c7f400000000000},
710 : {0xc097ce7bc90715b3, 0x4b9f100000000000}, {0xf0bdc21abb48db20, 0x1e86d40000000000},
711 : {0x96769950b50d88f4, 0x1314448000000000}, {0xbc143fa4e250eb31, 0x17d955a000000000},
712 : {0xeb194f8e1ae525fd, 0x5dcfab0800000000}, {0x92efd1b8d0cf37be, 0x5aa1cae500000000},
713 : {0xb7abc627050305ad, 0xf14a3d9e40000000}, {0xe596b7b0c643c719, 0x6d9ccd05d0000000},
714 : {0x8f7e32ce7bea5c6f, 0xe4820023a2000000}, {0xb35dbf821ae4f38b, 0xdda2802c8a800000},
715 : {0xe0352f62a19e306e, 0xd50b2037ad200000}, {0x8c213d9da502de45, 0x4526f422cc340000},
716 : {0xaf298d050e4395d6, 0x9670b12b7f410000}, {0xdaf3f04651d47b4c, 0x3c0cdd765f114000},
717 : {0x88d8762bf324cd0f, 0xa5880a69fb6ac800}, {0xab0e93b6efee0053, 0x8eea0d047a457a00},
718 : {0xd5d238a4abe98068, 0x72a4904598d6d880}, {0x85a36366eb71f041, 0x47a6da2b7f864750},
719 : {0xa70c3c40a64e6c51, 0x999090b65f67d924}, {0xd0cf4b50cfe20765, 0xfff4b4e3f741cf6d},
720 : {0x82818f1281ed449f, 0xbff8f10e7a8921a5}, {0xa321f2d7226895c7, 0xaff72d52192b6a0e},
721 : {0xcbea6f8ceb02bb39, 0x9bf4f8a69f764491}, {0xfee50b7025c36a08, 0x02f236d04753d5b5},
722 : {0x9f4f2726179a2245, 0x01d762422c946591}, {0xc722f0ef9d80aad6, 0x424d3ad2b7b97ef6},
723 : {0xf8ebad2b84e0d58b, 0xd2e0898765a7deb3}, {0x9b934c3b330c8577, 0x63cc55f49f88eb30},
724 : {0xc2781f49ffcfa6d5, 0x3cbf6b71c76b25fc}, {0xf316271c7fc3908a, 0x8bef464e3945ef7b},
725 : {0x97edd871cfda3a56, 0x97758bf0e3cbb5ad}, {0xbde94e8e43d0c8ec, 0x3d52eeed1cbea318},
726 : {0xed63a231d4c4fb27, 0x4ca7aaa863ee4bde}, {0x945e455f24fb1cf8, 0x8fe8caa93e74ef6b},
727 : {0xb975d6b6ee39e436, 0xb3e2fd538e122b45}, {0xe7d34c64a9c85d44, 0x60dbbca87196b617},
728 : {0x90e40fbeea1d3a4a, 0xbc8955e946fe31ce}, {0xb51d13aea4a488dd, 0x6babab6398bdbe42},
729 : {0xe264589a4dcdab14, 0xc696963c7eed2dd2}, {0x8d7eb76070a08aec, 0xfc1e1de5cf543ca3},
730 : {0xb0de65388cc8ada8, 0x3b25a55f43294bcc}, {0xdd15fe86affad912, 0x49ef0eb713f39ebf},
731 : {0x8a2dbf142dfcc7ab, 0x6e3569326c784338}, {0xacb92ed9397bf996, 0x49c2c37f07965405},
732 : {0xd7e77a8f87daf7fb, 0xdc33745ec97be907}, {0x86f0ac99b4e8dafd, 0x69a028bb3ded71a4},
733 : {0xa8acd7c0222311bc, 0xc40832ea0d68ce0d}, {0xd2d80db02aabd62b, 0xf50a3fa490c30191},
734 : {0x83c7088e1aab65db, 0x792667c6da79e0fb}, {0xa4b8cab1a1563f52, 0x577001b891185939},
735 : {0xcde6fd5e09abcf26, 0xed4c0226b55e6f87}, {0x80b05e5ac60b6178, 0x544f8158315b05b5},
736 : {0xa0dc75f1778e39d6, 0x696361ae3db1c722}, {0xc913936dd571c84c, 0x03bc3a19cd1e38ea},
737 : {0xfb5878494ace3a5f, 0x04ab48a04065c724}, {0x9d174b2dcec0e47b, 0x62eb0d64283f9c77},
738 : {0xc45d1df942711d9a, 0x3ba5d0bd324f8395}, {0xf5746577930d6500, 0xca8f44ec7ee3647a},
739 : {0x9968bf6abbe85f20, 0x7e998b13cf4e1ecc}, {0xbfc2ef456ae276e8, 0x9e3fedd8c321a67f},
740 : {0xefb3ab16c59b14a2, 0xc5cfe94ef3ea101f}, {0x95d04aee3b80ece5, 0xbba1f1d158724a13},
741 : {0xbb445da9ca61281f, 0x2a8a6e45ae8edc98}, {0xea1575143cf97226, 0xf52d09d71a3293be},
742 : {0x924d692ca61be758, 0x593c2626705f9c57}, {0xb6e0c377cfa2e12e, 0x6f8b2fb00c77836d},
743 : {0xe498f455c38b997a, 0x0b6dfb9c0f956448}, {0x8edf98b59a373fec, 0x4724bd4189bd5ead},
744 : {0xb2977ee300c50fe7, 0x58edec91ec2cb658}, {0xdf3d5e9bc0f653e1, 0x2f2967b66737e3ee},
745 : {0x8b865b215899f46c, 0xbd79e0d20082ee75}, {0xae67f1e9aec07187, 0xecd8590680a3aa12},
746 : {0xda01ee641a708de9, 0xe80e6f4820cc9496}, {0x884134fe908658b2, 0x3109058d147fdcde},
747 : {0xaa51823e34a7eede, 0xbd4b46f0599fd416}, {0xd4e5e2cdc1d1ea96, 0x6c9e18ac7007c91b},
748 : {0x850fadc09923329e, 0x03e2cf6bc604ddb1}, {0xa6539930bf6bff45, 0x84db8346b786151d},
749 : {0xcfe87f7cef46ff16, 0xe612641865679a64}, {0x81f14fae158c5f6e, 0x4fcb7e8f3f60c07f},
750 : {0xa26da3999aef7749, 0xe3be5e330f38f09e}, {0xcb090c8001ab551c, 0x5cadf5bfd3072cc6},
751 : {0xfdcb4fa002162a63, 0x73d9732fc7c8f7f7}, {0x9e9f11c4014dda7e, 0x2867e7fddcdd9afb},
752 : {0xc646d63501a1511d, 0xb281e1fd541501b9}, {0xf7d88bc24209a565, 0x1f225a7ca91a4227},
753 : {0x9ae757596946075f, 0x3375788de9b06959}, {0xc1a12d2fc3978937, 0x0052d6b1641c83af},
754 : {0xf209787bb47d6b84, 0xc0678c5dbd23a49b}, {0x9745eb4d50ce6332, 0xf840b7ba963646e1},
755 : {0xbd176620a501fbff, 0xb650e5a93bc3d899}, {0xec5d3fa8ce427aff, 0xa3e51f138ab4cebf},
756 : {0x93ba47c980e98cdf, 0xc66f336c36b10138}, {0xb8a8d9bbe123f017, 0xb80b0047445d4185},
757 : {0xe6d3102ad96cec1d, 0xa60dc059157491e6}, {0x9043ea1ac7e41392, 0x87c89837ad68db30},
758 : {0xb454e4a179dd1877, 0x29babe4598c311fc}, {0xe16a1dc9d8545e94, 0xf4296dd6fef3d67b},
759 : {0x8ce2529e2734bb1d, 0x1899e4a65f58660d}, {0xb01ae745b101e9e4, 0x5ec05dcff72e7f90},
760 : {0xdc21a1171d42645d, 0x76707543f4fa1f74}, {0x899504ae72497eba, 0x6a06494a791c53a9},
761 : {0xabfa45da0edbde69, 0x0487db9d17636893}, {0xd6f8d7509292d603, 0x45a9d2845d3c42b7},
762 : {0x865b86925b9bc5c2, 0x0b8a2392ba45a9b3}, {0xa7f26836f282b732, 0x8e6cac7768d7141f},
763 : {0xd1ef0244af2364ff, 0x3207d795430cd927}, {0x8335616aed761f1f, 0x7f44e6bd49e807b9},
764 : {0xa402b9c5a8d3a6e7, 0x5f16206c9c6209a7}, {0xcd036837130890a1, 0x36dba887c37a8c10},
765 : {0x802221226be55a64, 0xc2494954da2c978a}, {0xa02aa96b06deb0fd, 0xf2db9baa10b7bd6d},
766 : {0xc83553c5c8965d3d, 0x6f92829494e5acc8}, {0xfa42a8b73abbf48c, 0xcb772339ba1f17fa},
767 : {0x9c69a97284b578d7, 0xff2a760414536efc}, {0xc38413cf25e2d70d, 0xfef5138519684abb},
768 : {0xf46518c2ef5b8cd1, 0x7eb258665fc25d6a}, {0x98bf2f79d5993802, 0xef2f773ffbd97a62},
769 : {0xbeeefb584aff8603, 0xaafb550ffacfd8fb}, {0xeeaaba2e5dbf6784, 0x95ba2a53f983cf39},
770 : {0x952ab45cfa97a0b2, 0xdd945a747bf26184}, {0xba756174393d88df, 0x94f971119aeef9e5},
771 : {0xe912b9d1478ceb17, 0x7a37cd5601aab85e}, {0x91abb422ccb812ee, 0xac62e055c10ab33b},
772 : {0xb616a12b7fe617aa, 0x577b986b314d600a}, {0xe39c49765fdf9d94, 0xed5a7e85fda0b80c},
773 : {0x8e41ade9fbebc27d, 0x14588f13be847308}, {0xb1d219647ae6b31c, 0x596eb2d8ae258fc9},
774 : {0xde469fbd99a05fe3, 0x6fca5f8ed9aef3bc}, {0x8aec23d680043bee, 0x25de7bb9480d5855},
775 : {0xada72ccc20054ae9, 0xaf561aa79a10ae6b}, {0xd910f7ff28069da4, 0x1b2ba1518094da05},
776 : {0x87aa9aff79042286, 0x90fb44d2f05d0843}, {0xa99541bf57452b28, 0x353a1607ac744a54},
777 : {0xd3fa922f2d1675f2, 0x42889b8997915ce9}, {0x847c9b5d7c2e09b7, 0x69956135febada12},
778 : {0xa59bc234db398c25, 0x43fab9837e699096}, {0xcf02b2c21207ef2e, 0x94f967e45e03f4bc},
779 : {0x8161afb94b44f57d, 0x1d1be0eebac278f6}, {0xa1ba1ba79e1632dc, 0x6462d92a69731733},
780 : {0xca28a291859bbf93, 0x7d7b8f7503cfdcff}, {0xfcb2cb35e702af78, 0x5cda735244c3d43f},
781 : {0x9defbf01b061adab, 0x3a0888136afa64a8}, {0xc56baec21c7a1916, 0x088aaa1845b8fdd1},
782 : {0xf6c69a72a3989f5b, 0x8aad549e57273d46}, {0x9a3c2087a63f6399, 0x36ac54e2f678864c},
783 : {0xc0cb28a98fcf3c7f, 0x84576a1bb416a7de}, {0xf0fdf2d3f3c30b9f, 0x656d44a2a11c51d6},
784 : {0x969eb7c47859e743, 0x9f644ae5a4b1b326}, {0xbc4665b596706114, 0x873d5d9f0dde1fef},
785 : {0xeb57ff22fc0c7959, 0xa90cb506d155a7eb}, {0x9316ff75dd87cbd8, 0x09a7f12442d588f3},
786 : {0xb7dcbf5354e9bece, 0x0c11ed6d538aeb30}, {0xe5d3ef282a242e81, 0x8f1668c8a86da5fb},
787 : {0x8fa475791a569d10, 0xf96e017d694487bd}, {0xb38d92d760ec4455, 0x37c981dcc395a9ad},
788 : {0xe070f78d3927556a, 0x85bbe253f47b1418}, {0x8c469ab843b89562, 0x93956d7478ccec8f},
789 : {0xaf58416654a6babb, 0x387ac8d1970027b3}, {0xdb2e51bfe9d0696a, 0x06997b05fcc0319f},
790 : {0x88fcf317f22241e2, 0x441fece3bdf81f04}, {0xab3c2fddeeaad25a, 0xd527e81cad7626c4},
791 : {0xd60b3bd56a5586f1, 0x8a71e223d8d3b075}, {0x85c7056562757456, 0xf6872d5667844e4a},
792 : {0xa738c6bebb12d16c, 0xb428f8ac016561dc}, {0xd106f86e69d785c7, 0xe13336d701beba53},
793 : {0x82a45b450226b39c, 0xecc0024661173474}, {0xa34d721642b06084, 0x27f002d7f95d0191},
794 : {0xcc20ce9bd35c78a5, 0x31ec038df7b441f5}, {0xff290242c83396ce, 0x7e67047175a15272},
795 : {0x9f79a169bd203e41, 0x0f0062c6e984d387}, {0xc75809c42c684dd1, 0x52c07b78a3e60869},
796 : {0xf92e0c3537826145, 0xa7709a56ccdf8a83}, {0x9bbcc7a142b17ccb, 0x88a66076400bb692},
797 : {0xc2abf989935ddbfe, 0x6acff893d00ea436}, {0xf356f7ebf83552fe, 0x0583f6b8c4124d44},
798 : {0x98165af37b2153de, 0xc3727a337a8b704b}, {0xbe1bf1b059e9a8d6, 0x744f18c0592e4c5d},
799 : {0xeda2ee1c7064130c, 0x1162def06f79df74}, {0x9485d4d1c63e8be7, 0x8addcb5645ac2ba9},
800 : {0xb9a74a0637ce2ee1, 0x6d953e2bd7173693}, {0xe8111c87c5c1ba99, 0xc8fa8db6ccdd0438},
801 : {0x910ab1d4db9914a0, 0x1d9c9892400a22a3}, {0xb54d5e4a127f59c8, 0x2503beb6d00cab4c},
802 : {0xe2a0b5dc971f303a, 0x2e44ae64840fd61e}, {0x8da471a9de737e24, 0x5ceaecfed289e5d3},
803 : {0xb10d8e1456105dad, 0x7425a83e872c5f48}, {0xdd50f1996b947518, 0xd12f124e28f7771a},
804 : {0x8a5296ffe33cc92f, 0x82bd6b70d99aaa70}, {0xace73cbfdc0bfb7b, 0x636cc64d1001550c},
805 : {0xd8210befd30efa5a, 0x3c47f7e05401aa4f}, {0x8714a775e3e95c78, 0x65acfaec34810a72},
806 : {0xa8d9d1535ce3b396, 0x7f1839a741a14d0e}, {0xd31045a8341ca07c, 0x1ede48111209a051},
807 : {0x83ea2b892091e44d, 0x934aed0aab460433}, {0xa4e4b66b68b65d60, 0xf81da84d56178540},
808 : {0xce1de40642e3f4b9, 0x36251260ab9d668f}, {0x80d2ae83e9ce78f3, 0xc1d72b7c6b42601a},
809 : {0xa1075a24e4421730, 0xb24cf65b8612f820}, {0xc94930ae1d529cfc, 0xdee033f26797b628},
810 : {0xfb9b7cd9a4a7443c, 0x169840ef017da3b2}, {0x9d412e0806e88aa5, 0x8e1f289560ee864f},
811 : {0xc491798a08a2ad4e, 0xf1a6f2bab92a27e3}, {0xf5b5d7ec8acb58a2, 0xae10af696774b1dc},
812 : {0x9991a6f3d6bf1765, 0xacca6da1e0a8ef2a}, {0xbff610b0cc6edd3f, 0x17fd090a58d32af4},
813 : {0xeff394dcff8a948e, 0xddfc4b4cef07f5b1}, {0x95f83d0a1fb69cd9, 0x4abdaf101564f98f},
814 : {0xbb764c4ca7a4440f, 0x9d6d1ad41abe37f2}, {0xea53df5fd18d5513, 0x84c86189216dc5ee},
815 : {0x92746b9be2f8552c, 0x32fd3cf5b4e49bb5}, {0xb7118682dbb66a77, 0x3fbc8c33221dc2a2},
816 : {0xe4d5e82392a40515, 0x0fabaf3feaa5334b}, {0x8f05b1163ba6832d, 0x29cb4d87f2a7400f},
817 : {0xb2c71d5bca9023f8, 0x743e20e9ef511013}, {0xdf78e4b2bd342cf6, 0x914da9246b255417},
818 : {0x8bab8eefb6409c1a, 0x1ad089b6c2f7548f}, {0xae9672aba3d0c320, 0xa184ac2473b529b2},
819 : {0xda3c0f568cc4f3e8, 0xc9e5d72d90a2741f}, {0x8865899617fb1871, 0x7e2fa67c7a658893},
820 : {0xaa7eebfb9df9de8d, 0xddbb901b98feeab8}, {0xd51ea6fa85785631, 0x552a74227f3ea566},
821 : {0x8533285c936b35de, 0xd53a88958f872760}, {0xa67ff273b8460356, 0x8a892abaf368f138},
822 : {0xd01fef10a657842c, 0x2d2b7569b0432d86}, {0x8213f56a67f6b29b, 0x9c3b29620e29fc74},
823 : {0xa298f2c501f45f42, 0x8349f3ba91b47b90}, {0xcb3f2f7642717713, 0x241c70a936219a74},
824 : {0xfe0efb53d30dd4d7, 0xed238cd383aa0111}, {0x9ec95d1463e8a506, 0xf4363804324a40ab},
825 : {0xc67bb4597ce2ce48, 0xb143c6053edcd0d6}, {0xf81aa16fdc1b81da, 0xdd94b7868e94050b},
826 : {0x9b10a4e5e9913128, 0xca7cf2b4191c8327}, {0xc1d4ce1f63f57d72, 0xfd1c2f611f63a3f1},
827 : {0xf24a01a73cf2dccf, 0xbc633b39673c8ced}, {0x976e41088617ca01, 0xd5be0503e085d814},
828 : {0xbd49d14aa79dbc82, 0x4b2d8644d8a74e19}, {0xec9c459d51852ba2, 0xddf8e7d60ed1219f},
829 : {0x93e1ab8252f33b45, 0xcabb90e5c942b504}, {0xb8da1662e7b00a17, 0x3d6a751f3b936244},
830 : {0xe7109bfba19c0c9d, 0x0cc512670a783ad5}, {0x906a617d450187e2, 0x27fb2b80668b24c6},
831 : {0xb484f9dc9641e9da, 0xb1f9f660802dedf7}, {0xe1a63853bbd26451, 0x5e7873f8a0396974},
832 : {0x8d07e33455637eb2, 0xdb0b487b6423e1e9}, {0xb049dc016abc5e5f, 0x91ce1a9a3d2cda63},
833 : {0xdc5c5301c56b75f7, 0x7641a140cc7810fc}, {0x89b9b3e11b6329ba, 0xa9e904c87fcb0a9e},
834 : {0xac2820d9623bf429, 0x546345fa9fbdcd45}, {0xd732290fbacaf133, 0xa97c177947ad4096},
835 : {0x867f59a9d4bed6c0, 0x49ed8eabcccc485e}, {0xa81f301449ee8c70, 0x5c68f256bfff5a75},
836 : {0xd226fc195c6a2f8c, 0x73832eec6fff3112}, {0x83585d8fd9c25db7, 0xc831fd53c5ff7eac},
837 : {0xa42e74f3d032f525, 0xba3e7ca8b77f5e56}, {0xcd3a1230c43fb26f, 0x28ce1bd2e55f35ec},
838 : {0x80444b5e7aa7cf85, 0x7980d163cf5b81b4}, {0xa0555e361951c366, 0xd7e105bcc3326220},
839 : {0xc86ab5c39fa63440, 0x8dd9472bf3fefaa8}, {0xfa856334878fc150, 0xb14f98f6f0feb952},
840 : {0x9c935e00d4b9d8d2, 0x6ed1bf9a569f33d4}, {0xc3b8358109e84f07, 0x0a862f80ec4700c9},
841 : {0xf4a642e14c6262c8, 0xcd27bb612758c0fb}, {0x98e7e9cccfbd7dbd, 0x8038d51cb897789d},
842 : {0xbf21e44003acdd2c, 0xe0470a63e6bd56c4}, {0xeeea5d5004981478, 0x1858ccfce06cac75},
843 : {0x95527a5202df0ccb, 0x0f37801e0c43ebc9}, {0xbaa718e68396cffd, 0xd30560258f54e6bb},
844 : {0xe950df20247c83fd, 0x47c6b82ef32a206a}, {0x91d28b7416cdd27e, 0x4cdc331d57fa5442},
845 : {0xb6472e511c81471d, 0xe0133fe4adf8e953}, {0xe3d8f9e563a198e5, 0x58180fddd97723a7},
846 : {0x8e679c2f5e44ff8f, 0x570f09eaa7ea7649}, {0xb201833b35d63f73, 0x2cd2cc6551e513db},
847 : {0xde81e40a034bcf4f, 0xf8077f7ea65e58d2}, {0x8b112e86420f6191, 0xfb04afaf27faf783},
848 : {0xadd57a27d29339f6, 0x79c5db9af1f9b564}, {0xd94ad8b1c7380874, 0x18375281ae7822bd},
849 : {0x87cec76f1c830548, 0x8f2293910d0b15b6}, {0xa9c2794ae3a3c69a, 0xb2eb3875504ddb23},
850 : {0xd433179d9c8cb841, 0x5fa60692a46151ec}, {0x849feec281d7f328, 0xdbc7c41ba6bcd334},
851 : {0xa5c7ea73224deff3, 0x12b9b522906c0801}, {0xcf39e50feae16bef, 0xd768226b34870a01},
852 : {0x81842f29f2cce375, 0xe6a1158300d46641}, {0xa1e53af46f801c53, 0x60495ae3c1097fd1},
853 : {0xca5e89b18b602368, 0x385bb19cb14bdfc5}, {0xfcf62c1dee382c42, 0x46729e03dd9ed7b6},
854 : {0x9e19db92b4e31ba9, 0x6c07a2c26a8346d2}, {0xc5a05277621be293, 0xc7098b7305241886},
855 : {0xf70867153aa2db38, 0xb8cbee4fc66d1ea8}};
856 : };
857 :
858 : #if defined(BOOST_NO_CXX17_INLINE_VARIABLES) && (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
859 :
860 : template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::cache_bits;
861 : template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::min_k;
862 : template <bool b> constexpr int cache_holder_ieee754_binary64_impl<b>::max_k;
863 : template <bool b> constexpr typename cache_holder_ieee754_binary64_impl<b>::cache_entry_type cache_holder_ieee754_binary64_impl<b>::cache[];
864 :
865 : #endif
866 :
867 : #if (!defined(BOOST_MSVC) || BOOST_MSVC != 1900)
868 : using cache_holder_ieee754_binary64 = cache_holder_ieee754_binary64_impl<true>;
869 : #endif
870 :
871 : ////////////////////////////////////////////////////////////////////////////////////////
872 : // Policies.
873 : ////////////////////////////////////////////////////////////////////////////////////////
874 :
875 : // Forward declare the implementation class.
876 : template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>>
877 : struct impl;
878 :
879 : namespace policy_impl {
880 : // Sign policies.
881 : namespace sign {
882 : struct base {};
883 :
884 : struct ignore : base
885 : {
886 : using sign_policy = ignore;
887 : static constexpr bool return_has_sign = false;
888 :
889 : template <typename SignedSignificandBits, typename ReturnType>
890 : static BOOST_CXX14_CONSTEXPR void handle_sign(SignedSignificandBits, ReturnType&) noexcept {}
891 : };
892 :
893 : struct return_sign : base
894 : {
895 : using sign_policy = return_sign;
896 : static constexpr bool return_has_sign = true;
897 :
898 : template <typename SignedSignificandBits, typename ReturnType>
899 444 : static BOOST_CXX14_CONSTEXPR void handle_sign(SignedSignificandBits s, ReturnType& r) noexcept
900 : {
901 444 : r.is_negative = s.is_negative();
902 444 : }
903 : };
904 : }
905 :
906 : // Trailing zero policies.
907 : namespace trailing_zero {
908 : struct base {};
909 :
910 : struct ignore : base
911 : {
912 : using trailing_zero_policy = ignore;
913 : static constexpr bool report_trailing_zeros = false;
914 :
915 : template <typename Impl, typename ReturnType>
916 : static BOOST_CXX14_CONSTEXPR void on_trailing_zeros(ReturnType&) noexcept {}
917 :
918 : template <typename Impl, typename ReturnType>
919 : static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType&) noexcept {}
920 : };
921 :
922 : struct remove : base
923 : {
924 : using trailing_zero_policy = remove;
925 : static constexpr bool report_trailing_zeros = false;
926 :
927 : template <typename Impl, typename ReturnType>
928 : BOOST_FORCEINLINE static void on_trailing_zeros(ReturnType& r) noexcept
929 : {
930 886 : r.exponent += Impl::remove_trailing_zeros(r.significand);
931 443 : }
932 :
933 : template <typename Impl, typename ReturnType>
934 1 : static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType&) noexcept {}
935 : };
936 :
937 : struct report : base
938 : {
939 : using trailing_zero_policy = report;
940 : static constexpr bool report_trailing_zeros = true;
941 :
942 : template <typename Impl, typename ReturnType>
943 : static BOOST_CXX14_CONSTEXPR void on_trailing_zeros(ReturnType& r) noexcept
944 : {
945 : r.may_have_trailing_zeros = true;
946 : }
947 :
948 : template <typename Impl, typename ReturnType>
949 : static BOOST_CXX14_CONSTEXPR void no_trailing_zeros(ReturnType& r) noexcept
950 : {
951 : r.may_have_trailing_zeros = false;
952 : }
953 : };
954 : }
955 :
956 : // Decimal-to-binary rounding mode policies.
957 : namespace decimal_to_binary_rounding {
958 : struct base {};
959 :
960 : enum class tag_t
961 : {
962 : to_nearest,
963 : left_closed_directed,
964 : right_closed_directed
965 : };
966 :
967 : namespace interval_type {
968 : struct symmetric_boundary
969 : {
970 : static constexpr bool is_symmetric = true;
971 : bool is_closed;
972 0 : constexpr bool include_left_endpoint() const noexcept { return is_closed; }
973 9 : constexpr bool include_right_endpoint() const noexcept { return is_closed; }
974 : };
975 :
976 : struct asymmetric_boundary
977 : {
978 : static constexpr bool is_symmetric = false;
979 : bool is_left_closed;
980 : constexpr bool include_left_endpoint() const noexcept { return is_left_closed; }
981 : constexpr bool include_right_endpoint() const noexcept { return !is_left_closed; }
982 : };
983 :
984 : struct closed
985 : {
986 : static constexpr bool is_symmetric = true;
987 138 : static constexpr bool include_left_endpoint() noexcept { return true; }
988 138 : static constexpr bool include_right_endpoint() noexcept { return true; }
989 : };
990 :
991 : struct open
992 : {
993 : static constexpr bool is_symmetric = true;
994 : static constexpr bool include_left_endpoint() noexcept { return false; }
995 : static constexpr bool include_right_endpoint() noexcept { return false; }
996 : };
997 :
998 : struct left_closed_right_open
999 : {
1000 : static constexpr bool is_symmetric = false;
1001 : static constexpr bool include_left_endpoint() noexcept { return true; }
1002 : static constexpr bool include_right_endpoint() noexcept { return false; }
1003 : };
1004 :
1005 : struct right_closed_left_open
1006 : {
1007 : static constexpr bool is_symmetric = false;
1008 : static constexpr bool include_left_endpoint() noexcept { return false; }
1009 : static constexpr bool include_right_endpoint() noexcept { return true; }
1010 : };
1011 : }
1012 :
1013 : template <typename T>
1014 : struct return_type : return_type<decltype(&T::operator())>
1015 : {};
1016 :
1017 : struct nearest_to_even : base
1018 : {
1019 : using decimal_to_binary_rounding_policy = nearest_to_even;
1020 : static constexpr auto tag = tag_t::to_nearest;
1021 : using normal_interval_type = interval_type::symmetric_boundary;
1022 : using shorter_interval_type = interval_type::closed;
1023 :
1024 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1025 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func f) noexcept
1026 : {
1027 444 : return f(nearest_to_even{});
1028 : }
1029 :
1030 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1031 : BOOST_FORCEINLINE static constexpr ReturnType
1032 : invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept
1033 : {
1034 306 : return f(s.has_even_significand_bits());
1035 : }
1036 :
1037 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1038 : BOOST_FORCEINLINE static constexpr ReturnType
1039 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1040 : {
1041 138 : return f();
1042 : }
1043 : };
1044 :
1045 : struct nearest_to_odd : base
1046 : {
1047 : using decimal_to_binary_rounding_policy = nearest_to_odd;
1048 : static constexpr auto tag = tag_t::to_nearest;
1049 : using normal_interval_type = interval_type::symmetric_boundary;
1050 : using shorter_interval_type = interval_type::open;
1051 :
1052 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1053 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1054 : {
1055 : return f(nearest_to_odd{});
1056 : }
1057 :
1058 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1059 : BOOST_FORCEINLINE static constexpr ReturnType
1060 : invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept
1061 : {
1062 : return f(!s.has_even_significand_bits());
1063 : }
1064 :
1065 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1066 : BOOST_FORCEINLINE static constexpr ReturnType
1067 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1068 : {
1069 : return f();
1070 : }
1071 : };
1072 :
1073 : struct nearest_toward_plus_infinity : base
1074 : {
1075 : using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity;
1076 : static constexpr auto tag = tag_t::to_nearest;
1077 : using normal_interval_type = interval_type::asymmetric_boundary;
1078 : using shorter_interval_type = interval_type::asymmetric_boundary;
1079 :
1080 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1081 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1082 : {
1083 : return f(nearest_toward_plus_infinity{});
1084 : }
1085 :
1086 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1087 : BOOST_FORCEINLINE static constexpr ReturnType
1088 : invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept
1089 : {
1090 : return f(!s.is_negative());
1091 : }
1092 :
1093 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1094 : BOOST_FORCEINLINE static constexpr ReturnType
1095 : invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept
1096 : {
1097 : return f(!s.is_negative());
1098 : }
1099 : };
1100 :
1101 : struct nearest_toward_minus_infinity : base
1102 : {
1103 : using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity;
1104 : static constexpr auto tag = tag_t::to_nearest;
1105 : using normal_interval_type = interval_type::asymmetric_boundary;
1106 : using shorter_interval_type = interval_type::asymmetric_boundary;
1107 :
1108 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1109 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1110 : {
1111 : return f(nearest_toward_minus_infinity{});
1112 : }
1113 :
1114 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1115 : BOOST_FORCEINLINE static constexpr ReturnType
1116 : invoke_normal_interval_case(SignedSignificandBits s, Func&& f) noexcept
1117 : {
1118 : return f(s.is_negative());
1119 : }
1120 :
1121 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1122 : BOOST_FORCEINLINE static constexpr ReturnType
1123 : invoke_shorter_interval_case(SignedSignificandBits s, Func&& f) noexcept
1124 : {
1125 : return f(s.is_negative());
1126 : }
1127 : };
1128 :
1129 : struct nearest_toward_zero : base
1130 : {
1131 : using decimal_to_binary_rounding_policy = nearest_toward_zero;
1132 : static constexpr auto tag = tag_t::to_nearest;
1133 : using normal_interval_type = interval_type::right_closed_left_open;
1134 : using shorter_interval_type = interval_type::right_closed_left_open;
1135 :
1136 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1137 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1138 : {
1139 : return f(nearest_toward_zero{});
1140 : }
1141 :
1142 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1143 : BOOST_FORCEINLINE static constexpr ReturnType
1144 : invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept
1145 : {
1146 : return f();
1147 : }
1148 :
1149 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1150 : BOOST_FORCEINLINE static constexpr ReturnType
1151 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1152 : {
1153 : return f();
1154 : }
1155 : };
1156 :
1157 : struct nearest_away_from_zero : base
1158 : {
1159 : using decimal_to_binary_rounding_policy = nearest_away_from_zero;
1160 : static constexpr auto tag = tag_t::to_nearest;
1161 : using normal_interval_type = interval_type::left_closed_right_open;
1162 : using shorter_interval_type = interval_type::left_closed_right_open;
1163 :
1164 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1165 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1166 : {
1167 : return f(nearest_away_from_zero{});
1168 : }
1169 :
1170 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1171 : BOOST_FORCEINLINE static constexpr ReturnType
1172 : invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept
1173 : {
1174 : return f();
1175 : }
1176 :
1177 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1178 : BOOST_FORCEINLINE static constexpr ReturnType
1179 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1180 : {
1181 : return f();
1182 : }
1183 : };
1184 :
1185 : struct nearest_always_closed
1186 : {
1187 : static constexpr auto tag = tag_t::to_nearest;
1188 : using normal_interval_type = interval_type::closed;
1189 : using shorter_interval_type = interval_type::closed;
1190 :
1191 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1192 : BOOST_FORCEINLINE static constexpr ReturnType
1193 : invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept
1194 : {
1195 : return f();
1196 : }
1197 :
1198 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1199 : BOOST_FORCEINLINE static constexpr ReturnType
1200 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1201 : {
1202 : return f();
1203 : }
1204 : };
1205 :
1206 : struct nearest_always_open
1207 : {
1208 : static constexpr auto tag = tag_t::to_nearest;
1209 : using normal_interval_type = interval_type::open;
1210 : using shorter_interval_type = interval_type::open;
1211 :
1212 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1213 : BOOST_FORCEINLINE static constexpr ReturnType
1214 : invoke_normal_interval_case(SignedSignificandBits, Func&& f) noexcept
1215 : {
1216 : return f();
1217 : }
1218 :
1219 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1220 : BOOST_FORCEINLINE static constexpr ReturnType
1221 : invoke_shorter_interval_case(SignedSignificandBits, Func&& f) noexcept
1222 : {
1223 : return f();
1224 : }
1225 : };
1226 :
1227 : struct nearest_to_even_static_boundary : base
1228 : {
1229 : using decimal_to_binary_rounding_policy = nearest_to_even_static_boundary;
1230 :
1231 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1232 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1233 : {
1234 : if (s.has_even_significand_bits())
1235 : {
1236 : return f(nearest_always_closed{});
1237 : }
1238 : else
1239 : {
1240 : return f(nearest_always_open{});
1241 : }
1242 : }
1243 : };
1244 :
1245 : struct nearest_to_odd_static_boundary : base
1246 : {
1247 : using decimal_to_binary_rounding_policy = nearest_to_odd_static_boundary;
1248 :
1249 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1250 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1251 : {
1252 : if (s.has_even_significand_bits())
1253 : {
1254 : return f(nearest_always_open{});
1255 : }
1256 : else
1257 : {
1258 : return f(nearest_always_closed{});
1259 : }
1260 : }
1261 : };
1262 : struct nearest_toward_plus_infinity_static_boundary : base
1263 : {
1264 : using decimal_to_binary_rounding_policy = nearest_toward_plus_infinity_static_boundary;
1265 :
1266 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1267 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1268 : {
1269 : if (s.is_negative())
1270 : {
1271 : return f(nearest_toward_zero{});
1272 : }
1273 : else
1274 : {
1275 : return f(nearest_away_from_zero{});
1276 : }
1277 : }
1278 : };
1279 :
1280 : struct nearest_toward_minus_infinity_static_boundary : base
1281 : {
1282 : using decimal_to_binary_rounding_policy = nearest_toward_minus_infinity_static_boundary;
1283 :
1284 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1285 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1286 : {
1287 : if (s.is_negative())
1288 : {
1289 : return f(nearest_away_from_zero{});
1290 : }
1291 : else
1292 : {
1293 : return f(nearest_toward_zero{});
1294 : }
1295 : }
1296 : };
1297 :
1298 : struct left_closed_directed
1299 : {
1300 : static constexpr auto tag = tag_t::left_closed_directed;
1301 : };
1302 : struct right_closed_directed
1303 : {
1304 : static constexpr auto tag = tag_t::right_closed_directed;
1305 : };
1306 :
1307 : struct toward_plus_infinity : base
1308 : {
1309 : using decimal_to_binary_rounding_policy = toward_plus_infinity;
1310 :
1311 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1312 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1313 : {
1314 : if (s.is_negative())
1315 : {
1316 : return f(left_closed_directed{});
1317 : }
1318 : else
1319 : {
1320 : return f(right_closed_directed{});
1321 : }
1322 : }
1323 : };
1324 :
1325 : struct toward_minus_infinity : base
1326 : {
1327 : using decimal_to_binary_rounding_policy = toward_minus_infinity;
1328 :
1329 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1330 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits s, Func&& f) noexcept
1331 : {
1332 : if (s.is_negative())
1333 : {
1334 : return f(right_closed_directed{});
1335 : }
1336 : else
1337 : {
1338 : return f(left_closed_directed{});
1339 : }
1340 : }
1341 : };
1342 :
1343 : struct toward_zero : base
1344 : {
1345 : using decimal_to_binary_rounding_policy = toward_zero;
1346 :
1347 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1348 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1349 : {
1350 : return f(left_closed_directed{});
1351 : }
1352 : };
1353 :
1354 : struct away_from_zero : base
1355 : {
1356 : using decimal_to_binary_rounding_policy = away_from_zero;
1357 :
1358 : template <typename ReturnType, typename SignedSignificandBits, typename Func>
1359 : BOOST_FORCEINLINE static ReturnType delegate(SignedSignificandBits, Func&& f) noexcept
1360 : {
1361 : return f(right_closed_directed{});
1362 : }
1363 : };
1364 : }
1365 :
1366 : // Binary-to-decimal rounding policies.
1367 : // (Always assumes nearest rounding modes.)
1368 : namespace binary_to_decimal_rounding {
1369 : struct base {};
1370 :
1371 : enum class tag_t
1372 : {
1373 : do_not_care,
1374 : to_even,
1375 : to_odd,
1376 : away_from_zero,
1377 : toward_zero
1378 : };
1379 :
1380 : struct do_not_care : base
1381 : {
1382 : using binary_to_decimal_rounding_policy = do_not_care;
1383 : static constexpr auto tag = tag_t::do_not_care;
1384 :
1385 : template <typename ReturnType>
1386 : static constexpr bool prefer_round_down(ReturnType const&) noexcept
1387 : {
1388 : return false;
1389 : }
1390 : };
1391 :
1392 : struct to_even : base
1393 : {
1394 : using binary_to_decimal_rounding_policy = to_even;
1395 : static constexpr auto tag = tag_t::to_even;
1396 :
1397 : template <typename ReturnType>
1398 0 : static constexpr bool prefer_round_down(ReturnType const& r) noexcept
1399 : {
1400 0 : return r.significand % 2 != 0;
1401 : }
1402 : };
1403 :
1404 : struct to_odd : base
1405 : {
1406 : using binary_to_decimal_rounding_policy = to_odd;
1407 : static constexpr auto tag = tag_t::to_odd;
1408 :
1409 : template <typename ReturnType>
1410 : static constexpr bool prefer_round_down(ReturnType const& r) noexcept
1411 : {
1412 : return r.significand % 2 == 0;
1413 : }
1414 : };
1415 :
1416 : struct away_from_zero : base
1417 : {
1418 : using binary_to_decimal_rounding_policy = away_from_zero;
1419 : static constexpr auto tag = tag_t::away_from_zero;
1420 :
1421 : template <typename ReturnType>
1422 : static constexpr bool prefer_round_down(ReturnType const&) noexcept
1423 : {
1424 : return false;
1425 : }
1426 : };
1427 :
1428 : struct toward_zero : base
1429 : {
1430 : using binary_to_decimal_rounding_policy = toward_zero;
1431 : static constexpr auto tag = tag_t::toward_zero;
1432 :
1433 : template <typename ReturnType>
1434 : static constexpr bool prefer_round_down(ReturnType const&) noexcept
1435 : {
1436 : return true;
1437 : }
1438 : };
1439 : }
1440 :
1441 : // Cache policies.
1442 : namespace cache {
1443 : struct base {};
1444 :
1445 : struct full : base
1446 : {
1447 : using cache_policy = full;
1448 :
1449 : template <typename FloatFormat, typename cache_format = typename std::conditional<std::is_same<FloatFormat, ieee754_binary32>::value,
1450 : cache_holder_ieee754_binary32,
1451 : cache_holder_ieee754_binary64>::type>
1452 444 : static constexpr typename cache_format::cache_entry_type get_cache(int k) noexcept
1453 : {
1454 444 : return cache_format::cache[std::size_t(k - cache_format::min_k)];
1455 : }
1456 : };
1457 : }
1458 : }
1459 :
1460 : namespace policy {
1461 : namespace sign {
1462 : BOOST_INLINE_VARIABLE constexpr auto ignore = detail::policy_impl::sign::ignore{};
1463 : BOOST_INLINE_VARIABLE constexpr auto return_sign = detail::policy_impl::sign::return_sign{};
1464 : }
1465 :
1466 : namespace trailing_zero {
1467 : BOOST_INLINE_VARIABLE constexpr auto ignore = detail::policy_impl::trailing_zero::ignore{};
1468 : BOOST_INLINE_VARIABLE constexpr auto remove = detail::policy_impl::trailing_zero::remove{};
1469 : BOOST_INLINE_VARIABLE constexpr auto report = detail::policy_impl::trailing_zero::report{};
1470 : }
1471 :
1472 : namespace decimal_to_binary_rounding {
1473 : BOOST_INLINE_VARIABLE constexpr auto nearest_to_even =
1474 : detail::policy_impl::decimal_to_binary_rounding::nearest_to_even{};
1475 : BOOST_INLINE_VARIABLE constexpr auto nearest_to_odd =
1476 : detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd{};
1477 : BOOST_INLINE_VARIABLE constexpr auto nearest_toward_plus_infinity =
1478 : detail::policy_impl::decimal_to_binary_rounding::nearest_toward_plus_infinity{};
1479 : BOOST_INLINE_VARIABLE constexpr auto nearest_toward_minus_infinity =
1480 : detail::policy_impl::decimal_to_binary_rounding::nearest_toward_minus_infinity{};
1481 : BOOST_INLINE_VARIABLE constexpr auto nearest_toward_zero =
1482 : detail::policy_impl::decimal_to_binary_rounding::nearest_toward_zero{};
1483 : BOOST_INLINE_VARIABLE constexpr auto nearest_away_from_zero =
1484 : detail::policy_impl::decimal_to_binary_rounding::nearest_away_from_zero{};
1485 :
1486 : BOOST_INLINE_VARIABLE constexpr auto nearest_to_even_static_boundary =
1487 : detail::policy_impl::decimal_to_binary_rounding::nearest_to_even_static_boundary{};
1488 : BOOST_INLINE_VARIABLE constexpr auto nearest_to_odd_static_boundary =
1489 : detail::policy_impl::decimal_to_binary_rounding::nearest_to_odd_static_boundary{};
1490 : BOOST_INLINE_VARIABLE constexpr auto nearest_toward_plus_infinity_static_boundary =
1491 : detail::policy_impl::decimal_to_binary_rounding::
1492 : nearest_toward_plus_infinity_static_boundary{};
1493 : BOOST_INLINE_VARIABLE constexpr auto nearest_toward_minus_infinity_static_boundary =
1494 : detail::policy_impl::decimal_to_binary_rounding::
1495 : nearest_toward_minus_infinity_static_boundary{};
1496 :
1497 : BOOST_INLINE_VARIABLE constexpr auto toward_plus_infinity =
1498 : detail::policy_impl::decimal_to_binary_rounding::toward_plus_infinity{};
1499 : BOOST_INLINE_VARIABLE constexpr auto toward_minus_infinity =
1500 : detail::policy_impl::decimal_to_binary_rounding::toward_minus_infinity{};
1501 : BOOST_INLINE_VARIABLE constexpr auto toward_zero =
1502 : detail::policy_impl::decimal_to_binary_rounding::toward_zero{};
1503 : BOOST_INLINE_VARIABLE constexpr auto away_from_zero =
1504 : detail::policy_impl::decimal_to_binary_rounding::away_from_zero{};
1505 : }
1506 :
1507 : namespace binary_to_decimal_rounding {
1508 : BOOST_INLINE_VARIABLE constexpr auto do_not_care =
1509 : detail::policy_impl::binary_to_decimal_rounding::do_not_care{};
1510 : BOOST_INLINE_VARIABLE constexpr auto to_even =
1511 : detail::policy_impl::binary_to_decimal_rounding::to_even{};
1512 : BOOST_INLINE_VARIABLE constexpr auto to_odd =
1513 : detail::policy_impl::binary_to_decimal_rounding::to_odd{};
1514 : BOOST_INLINE_VARIABLE constexpr auto away_from_zero =
1515 : detail::policy_impl::binary_to_decimal_rounding::away_from_zero{};
1516 : BOOST_INLINE_VARIABLE constexpr auto toward_zero =
1517 : detail::policy_impl::binary_to_decimal_rounding::toward_zero{};
1518 : }
1519 :
1520 : namespace cache {
1521 : BOOST_INLINE_VARIABLE constexpr auto full = detail::policy_impl::cache::full{};
1522 : }
1523 : } // Namespace Policy
1524 :
1525 : ////////////////////////////////////////////////////////////////////////////////////////
1526 : // The main algorithm.
1527 : ////////////////////////////////////////////////////////////////////////////////////////
1528 :
1529 : template <typename Float, typename FloatTraits>
1530 : struct impl : private FloatTraits, private FloatTraits::format
1531 : {
1532 : using format = typename FloatTraits::format;
1533 : using carrier_uint = typename FloatTraits::carrier_uint;
1534 :
1535 : using FloatTraits::carrier_bits;
1536 : using format::significand_bits;
1537 : using format::min_exponent;
1538 : using format::max_exponent;
1539 : using format::exponent_bias;
1540 : using format::decimal_digits;
1541 :
1542 : static constexpr int kappa = std::is_same<format, ieee754_binary32>::value ? 1 : 2;
1543 : static_assert(kappa >= 1, "Kappa must be >= 1");
1544 : // static_assert(carrier_bits >= significand_bits + 2 + log::floor_log2_pow10(kappa + 1));
1545 :
1546 : static constexpr int min_k_a = -log::floor_log10_pow2_minus_log10_4_over_3(int(max_exponent - significand_bits));
1547 : static constexpr int min_k_b = -log::floor_log10_pow2(int(max_exponent - significand_bits)) + kappa;
1548 : static constexpr int min_k = min_k_a < min_k_b ? min_k_a : min_k_b;
1549 : // static_assert(min_k >= cache_holder<format>::min_k, "Min k is not in the cache");
1550 :
1551 : static constexpr int max_k_a = -log::floor_log10_pow2_minus_log10_4_over_3(int(min_exponent - significand_bits /*+ 1*/));
1552 : static constexpr int max_k_b = -log::floor_log10_pow2(int(min_exponent - significand_bits)) + kappa;
1553 : static constexpr int max_k = max_k_a > max_k_b ? max_k_a : max_k_b;
1554 :
1555 : using cache_format = typename std::conditional<std::is_same<format, ieee754_binary32>::value,
1556 : cache_holder_ieee754_binary32,
1557 : cache_holder_ieee754_binary64>::type;
1558 : using cache_entry_type = typename cache_format::cache_entry_type;
1559 : static constexpr auto cache_bits = cache_format::cache_bits;
1560 :
1561 : static constexpr int case_shorter_interval_left_endpoint_lower_threshold = 2;
1562 : static BOOST_CXX14_CONSTEXPR const int case_shorter_interval_left_endpoint_upper_threshold = 3;
1563 : //2 + log::floor_log2(compute_power(10, count_factors<5>((carrier_uint(1) << (significand_bits + 2)) - 1) + 1) / 3);
1564 :
1565 : static constexpr int case_shorter_interval_right_endpoint_lower_threshold = 0;
1566 : static BOOST_CXX14_CONSTEXPR const int case_shorter_interval_right_endpoint_upper_threshold = 3;
1567 : //2 + log::floor_log2(compute_power(10, count_factors<5>((carrier_uint(1) << (significand_bits + 1)) + 1) + 1) / 3);
1568 :
1569 : static constexpr int shorter_interval_tie_lower_threshold =
1570 : -log::floor_log5_pow2_minus_log5_3(significand_bits + 4) - 2 - significand_bits;
1571 : static constexpr int shorter_interval_tie_upper_threshold =
1572 : -log::floor_log5_pow2(significand_bits + 2) - 2 - significand_bits;
1573 :
1574 : struct compute_mul_result
1575 : {
1576 : carrier_uint result;
1577 : bool is_integer;
1578 : };
1579 :
1580 : struct compute_mul_parity_result
1581 : {
1582 : bool parity;
1583 : bool is_integer;
1584 : };
1585 :
1586 : //// The main algorithm assumes the input is a normal/subnormal finite number
1587 :
1588 : #if defined(__GNUC__) && (__GNUC__ < 5) && !defined(__clang__)
1589 : # pragma GCC diagnostic push
1590 : # pragma GCC diagnostic ignored "-Wmissing-field-initializers"
1591 : #endif
1592 :
1593 : template <typename ReturnType, typename IntervalType, typename TrailingZeroPolicy,
1594 : typename BinaryToDecimalRoundingPolicy, typename CachePolicy, typename... AdditionalArgs>
1595 306 : BOOST_JSON_SAFEBUFFERS static ReturnType compute_nearest_normal(carrier_uint const two_fc, const int exponent,
1596 : AdditionalArgs... additional_args) noexcept
1597 : {
1598 : //////////////////////////////////////////////////////////////////////
1599 : // Step 1: Schubfach multiplier calculation
1600 : //////////////////////////////////////////////////////////////////////
1601 :
1602 306 : ReturnType ret_value = {};
1603 306 : IntervalType interval_type{additional_args...};
1604 :
1605 : // Compute k and beta.
1606 306 : const int minus_k = log::floor_log10_pow2(exponent) - kappa;
1607 306 : const auto cache = CachePolicy::template get_cache<format>(-minus_k);
1608 306 : const int beta = exponent + log::floor_log2_pow10(-minus_k);
1609 :
1610 : // Compute zi and deltai.
1611 : // 10^kappa <= deltai < 10^(kappa + 1)
1612 306 : const auto deltai = compute_delta(cache, beta);
1613 : // For the case of binary32, the result of integer check is not correct for
1614 : // 29711844 * 2^-82
1615 : // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
1616 : // and 29711844 * 2^-81
1617 : // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17,
1618 : // and they are the unique counterexamples. However, since 29711844 is even,
1619 : // this does not cause any problem for the endpoints calculations; it can only
1620 : // cause a problem when we need to perform integer check for the center.
1621 : // Fortunately, with these inputs, that branch is never executed, so we are fine.
1622 : //const auto [zi, is_z_integer] = compute_mul((two_fc | 1) << beta, cache);
1623 306 : const auto z_res = compute_mul((two_fc | 1) << beta, cache);
1624 306 : const auto zi = z_res.result;
1625 306 : const auto is_z_integer = z_res.is_integer;
1626 :
1627 : //////////////////////////////////////////////////////////////////////
1628 : // Step 2: Try larger divisor; remove trailing zeros if necessary
1629 : //////////////////////////////////////////////////////////////////////
1630 :
1631 306 : BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);
1632 306 : BOOST_CXX14_CONSTEXPR auto small_divisor = compute_power(std::uint32_t(10), kappa);
1633 :
1634 : // Using an upper bound on zi, we might be able to optimize the division
1635 : // better than the compiler; we are computing zi / big_divisor here.
1636 : #ifdef BOOST_NO_CXX14_CONSTEXPR
1637 306 : ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, zi);
1638 : #else
1639 : ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(zi);
1640 : #endif
1641 :
1642 306 : auto r = std::uint32_t(zi - big_divisor * ret_value.significand);
1643 :
1644 306 : if (r < deltai)
1645 : {
1646 : // Exclude the right endpoint if necessary.
1647 305 : if (r == 0 && (is_z_integer & !interval_type.include_right_endpoint()))
1648 : {
1649 : BOOST_IF_CONSTEXPR (BinaryToDecimalRoundingPolicy::tag == policy_impl::binary_to_decimal_rounding::tag_t::do_not_care)
1650 : {
1651 : ret_value.significand *= 10;
1652 : ret_value.exponent = minus_k + kappa;
1653 : --ret_value.significand;
1654 : TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
1655 :
1656 : return ret_value;
1657 : }
1658 : else
1659 : {
1660 0 : --ret_value.significand;
1661 0 : r = big_divisor;
1662 :
1663 0 : goto small_divisor_case_label;
1664 : }
1665 : }
1666 : }
1667 1 : else if (r > deltai)
1668 : {
1669 1 : goto small_divisor_case_label;
1670 : }
1671 : else
1672 : {
1673 : // r == deltai; compare fractional parts.
1674 : // const auto [xi_parity, x_is_integer] =
1675 : // compute_mul_parity(two_fc - 1, cache, beta);
1676 0 : const auto x_res = compute_mul_parity(two_fc - 1, cache, beta);
1677 0 : const auto xi_parity = x_res.parity;
1678 0 : const auto x_is_integer = x_res.is_integer;
1679 :
1680 0 : if (!(xi_parity | (x_is_integer & interval_type.include_left_endpoint())))
1681 : {
1682 0 : goto small_divisor_case_label;
1683 : }
1684 : }
1685 305 : ret_value.exponent = minus_k + kappa + 1;
1686 :
1687 : // We may need to remove trailing zeros.
1688 : TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
1689 305 : return ret_value;
1690 :
1691 :
1692 : //////////////////////////////////////////////////////////////////////
1693 : // Step 3: Find the significand with the smaller divisor
1694 : //////////////////////////////////////////////////////////////////////
1695 :
1696 1 : small_divisor_case_label:
1697 1 : TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
1698 1 : ret_value.significand *= 10;
1699 1 : ret_value.exponent = minus_k + kappa;
1700 :
1701 : BOOST_IF_CONSTEXPR (BinaryToDecimalRoundingPolicy::tag == policy_impl::binary_to_decimal_rounding::tag_t::do_not_care)
1702 : {
1703 : // Normally, we want to compute
1704 : // ret_value.significand += r / small_divisor
1705 : // and return, but we need to take care of the case that the resulting
1706 : // value is exactly the right endpoint, while that is not included in the
1707 : // interval.
1708 : if (!interval_type.include_right_endpoint())
1709 : {
1710 : // Is r divisible by 10^kappa?
1711 : if (is_z_integer && div::check_divisibility_and_divide_by_pow10<kappa>(r))
1712 : {
1713 : // This should be in the interval.
1714 : ret_value.significand += r - 1;
1715 : }
1716 : else
1717 : {
1718 : ret_value.significand += r;
1719 : }
1720 : }
1721 : else
1722 : {
1723 : ret_value.significand += div::small_division_by_pow10<kappa>(r);
1724 : }
1725 : }
1726 : else
1727 : {
1728 1 : auto dist = r - (deltai / 2) + (small_divisor / 2);
1729 1 : const bool approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0;
1730 :
1731 : // Is dist divisible by 10^kappa?
1732 1 : const bool divisible_by_small_divisor = div::check_divisibility_and_divide_by_pow10<kappa>(dist);
1733 :
1734 : // Add dist / 10^kappa to the significand.
1735 1 : ret_value.significand += dist;
1736 :
1737 1 : if (divisible_by_small_divisor)
1738 : {
1739 : // Check z^(f) >= epsilon^(f).
1740 : // We have either yi == zi - epsiloni or yi == (zi - epsiloni) - 1,
1741 : // where yi == zi - epsiloni if and only if z^(f) >= epsilon^(f).
1742 : // Since there are only 2 possibilities, we only need to care about the
1743 : // parity. Also, zi and r should have the same parity since the divisor is
1744 : // an even number.
1745 : //const auto [yi_parity, is_y_integer] =
1746 : // compute_mul_parity(two_fc, cache, beta);
1747 0 : const auto y_res = compute_mul_parity(two_fc, cache, beta);
1748 0 : const auto yi_parity = y_res.parity;
1749 0 : const auto is_y_integer = y_res.is_integer;
1750 :
1751 0 : if (yi_parity != approx_y_parity)
1752 : {
1753 0 : --ret_value.significand;
1754 : }
1755 : else
1756 : {
1757 : // If z^(f) >= epsilon^(f), we might have a tie
1758 : // when z^(f) == epsilon^(f), or equivalently, when y is an integer.
1759 : // For tie-to-up case, we can just choose the upper one.
1760 0 : if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) & is_y_integer)
1761 : {
1762 0 : --ret_value.significand;
1763 : }
1764 : }
1765 : }
1766 : }
1767 :
1768 1 : return ret_value;
1769 : }
1770 :
1771 : template <typename ReturnType, typename IntervalType, typename TrailingZeroPolicy,
1772 : typename BinaryToDecimalRoundingPolicy, typename CachePolicy, typename... AdditionalArgs>
1773 138 : BOOST_JSON_SAFEBUFFERS static ReturnType compute_nearest_shorter(const int exponent, AdditionalArgs... additional_args) noexcept
1774 : {
1775 138 : ReturnType ret_value = {};
1776 : IntervalType interval_type{additional_args...};
1777 :
1778 : // Compute k and beta.
1779 138 : const int minus_k = log::floor_log10_pow2_minus_log10_4_over_3(exponent);
1780 138 : const int beta = exponent + log::floor_log2_pow10(-minus_k);
1781 :
1782 : // Compute xi and zi.
1783 138 : const auto cache = CachePolicy::template get_cache<format>(-minus_k);
1784 :
1785 138 : auto xi = compute_left_endpoint_for_shorter_interval_case(cache, beta);
1786 138 : auto zi = compute_right_endpoint_for_shorter_interval_case(cache, beta);
1787 :
1788 : // If we don't accept the right endpoint and
1789 : // if the right endpoint is an integer, decrease it.
1790 138 : if (!interval_type.include_right_endpoint() && is_right_endpoint_integer_shorter_interval(exponent))
1791 : {
1792 0 : --zi;
1793 : }
1794 : // If we don't accept the left endpoint or
1795 : // if the left endpoint is not an integer, increase it.
1796 138 : if (!interval_type.include_left_endpoint() || !is_left_endpoint_integer_shorter_interval(exponent))
1797 : {
1798 138 : ++xi;
1799 : }
1800 :
1801 : // Try bigger divisor.
1802 138 : ret_value.significand = zi / 10;
1803 :
1804 : // If succeed, remove trailing zeros if necessary and return.
1805 138 : if (ret_value.significand * 10 >= xi)
1806 : {
1807 138 : ret_value.exponent = minus_k + 1;
1808 : TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
1809 138 : return ret_value;
1810 : }
1811 :
1812 : // Otherwise, compute the round-up of y.
1813 0 : TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
1814 0 : ret_value.significand = compute_round_up_for_shorter_interval_case(cache, beta);
1815 0 : ret_value.exponent = minus_k;
1816 :
1817 : // When tie occurs, choose one of them according to the rule.
1818 0 : if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) &&
1819 0 : exponent >= shorter_interval_tie_lower_threshold &&
1820 : exponent <= shorter_interval_tie_upper_threshold)
1821 : {
1822 0 : --ret_value.significand;
1823 : }
1824 0 : else if (ret_value.significand < xi)
1825 : {
1826 0 : ++ret_value.significand;
1827 : }
1828 :
1829 0 : return ret_value;
1830 : }
1831 :
1832 : #if defined(__GNUC__) && (__GNUC__ < 5) && !defined(__clang__)
1833 : # pragma GCC diagnostic pop
1834 : #endif
1835 :
1836 : template <class ReturnType, class TrailingZeroPolicy, class CachePolicy>
1837 : BOOST_JSON_SAFEBUFFERS static ReturnType compute_left_closed_directed(carrier_uint const two_fc, int exponent) noexcept
1838 : {
1839 : //////////////////////////////////////////////////////////////////////
1840 : // Step 1: Schubfach multiplier calculation
1841 : //////////////////////////////////////////////////////////////////////
1842 :
1843 : ReturnType ret_value;
1844 :
1845 : // Compute k and beta.
1846 : const int minus_k = log::floor_log10_pow2(exponent) - kappa;
1847 : const auto cache = CachePolicy::template get_cache<format>(-minus_k);
1848 : const int beta = exponent + log::floor_log2_pow10(-minus_k);
1849 :
1850 : // Compute xi and deltai.
1851 : // 10^kappa <= deltai < 10^(kappa + 1)
1852 : const auto deltai = compute_delta(cache, beta);
1853 : //auto [xi, is_x_integer] = compute_mul(two_fc << beta, cache);
1854 : const auto x_res = compute_mul(two_fc << beta, cache);
1855 : auto xi = x_res.result;
1856 : auto is_x_integer = x_res.is_integer;
1857 :
1858 : // Deal with the unique exceptional cases
1859 : // 29711844 * 2^-82
1860 : // = 6.1442653300000000008655037797566933477355632930994033813476... * 10^-18
1861 : // and 29711844 * 2^-81
1862 : // = 1.2288530660000000001731007559513386695471126586198806762695... * 10^-17
1863 : // for binary32.
1864 : BOOST_IF_CONSTEXPR (std::is_same<format, ieee754_binary32>::value)
1865 : {
1866 : if (exponent <= -80)
1867 : {
1868 : is_x_integer = false;
1869 : }
1870 : }
1871 :
1872 : if (!is_x_integer)
1873 : {
1874 : ++xi;
1875 : }
1876 :
1877 : //////////////////////////////////////////////////////////////////////
1878 : // Step 2: Try larger divisor; remove trailing zeros if necessary
1879 : //////////////////////////////////////////////////////////////////////
1880 :
1881 : BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);
1882 :
1883 : // Using an upper bound on xi, we might be able to optimize the division
1884 : // better than the compiler; we are computing xi / big_divisor here.
1885 :
1886 : #ifdef BOOST_NO_CXX14_CONSTEXPR
1887 : ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, xi);
1888 : #else
1889 : ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(xi);
1890 : #endif
1891 :
1892 : auto r = std::uint32_t(xi - big_divisor * ret_value.significand);
1893 :
1894 : if (r != 0)
1895 : {
1896 : ++ret_value.significand;
1897 : r = big_divisor - r;
1898 : }
1899 :
1900 : if (r > deltai)
1901 : {
1902 : goto small_divisor_case_label;
1903 : }
1904 : else if (r == deltai)
1905 : {
1906 : // Compare the fractional parts.
1907 : // This branch is never taken for the exceptional cases
1908 : // 2f_c = 29711482, e = -81
1909 : // (6.1442649164096937243516663440523473127541365101933479309082... * 10^-18)
1910 : // and 2f_c = 29711482, e = -80
1911 : // (1.2288529832819387448703332688104694625508273020386695861816... * 10^-17).
1912 : //const auto [zi_parity, is_z_integer] =
1913 : // compute_mul_parity(two_fc + 2, cache, beta);
1914 : const auto z_res = compute_mul_parity(two_fc + 2, cache, beta);
1915 : if (z_res.parity || z_res.is_integer)
1916 : {
1917 : goto small_divisor_case_label;
1918 : }
1919 : }
1920 :
1921 : // The ceiling is inside, so we are done.
1922 : ret_value.exponent = minus_k + kappa + 1;
1923 : TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
1924 : return ret_value;
1925 :
1926 :
1927 : //////////////////////////////////////////////////////////////////////
1928 : // Step 3: Find the significand with the smaller divisor
1929 : //////////////////////////////////////////////////////////////////////
1930 :
1931 : small_divisor_case_label:
1932 : ret_value.significand *= 10;
1933 : ret_value.significand -= div::small_division_by_pow10<kappa>(r);
1934 : ret_value.exponent = minus_k + kappa;
1935 : TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
1936 : return ret_value;
1937 : }
1938 :
1939 : template <typename ReturnType, typename TrailingZeroPolicy, typename CachePolicy>
1940 : BOOST_JSON_SAFEBUFFERS static ReturnType compute_right_closed_directed(carrier_uint const two_fc, const int exponent, bool shorter_interval) noexcept
1941 : {
1942 : //////////////////////////////////////////////////////////////////////
1943 : // Step 1: Schubfach multiplier calculation
1944 : //////////////////////////////////////////////////////////////////////
1945 :
1946 : ReturnType ret_value;
1947 :
1948 : // Compute k and beta.
1949 : const int minus_k = log::floor_log10_pow2(exponent - (shorter_interval ? 1 : 0)) - kappa;
1950 : const auto cache = CachePolicy::template get_cache<format>(-minus_k);
1951 : const int beta = exponent + log::floor_log2_pow10(-minus_k);
1952 :
1953 : // Compute zi and deltai.
1954 : // 10^kappa <= deltai < 10^(kappa + 1)
1955 : const auto deltai = shorter_interval ? compute_delta(cache, beta - 1) : compute_delta(cache, beta);
1956 : carrier_uint const zi = compute_mul(two_fc << beta, cache).result;
1957 :
1958 :
1959 : //////////////////////////////////////////////////////////////////////
1960 : // Step 2: Try larger divisor; remove trailing zeros if necessary
1961 : //////////////////////////////////////////////////////////////////////
1962 :
1963 : BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);
1964 :
1965 : // Using an upper bound on zi, we might be able to optimize the division better than
1966 : // the compiler; we are computing zi / big_divisor here.
1967 : #ifdef BOOST_NO_CXX14_CONSTEXPR
1968 : ret_value.significand = div::divide_by_pow10<carrier_uint>(kappa + 1, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1, zi);
1969 : #else
1970 : ret_value.significand = div::divide_by_pow10<kappa + 1, carrier_uint, (carrier_uint(1) << (significand_bits + 1)) * big_divisor - 1>(zi);
1971 : #endif
1972 :
1973 : const auto r = std::uint32_t(zi - big_divisor * ret_value.significand);
1974 :
1975 : if (r > deltai)
1976 : {
1977 : goto small_divisor_case_label;
1978 : }
1979 : else if (r == deltai)
1980 : {
1981 : // Compare the fractional parts.
1982 : if (!compute_mul_parity(two_fc - (shorter_interval ? 1 : 2), cache, beta).parity)
1983 : {
1984 : goto small_divisor_case_label;
1985 : }
1986 : }
1987 :
1988 : // The floor is inside, so we are done.
1989 : ret_value.exponent = minus_k + kappa + 1;
1990 : TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
1991 : return ret_value;
1992 :
1993 :
1994 : //////////////////////////////////////////////////////////////////////
1995 : // Step 3: Find the significand with the small divisor
1996 : //////////////////////////////////////////////////////////////////////
1997 :
1998 : small_divisor_case_label:
1999 : ret_value.significand *= 10;
2000 : ret_value.significand += div::small_division_by_pow10<kappa>(r);
2001 : ret_value.exponent = minus_k + kappa;
2002 : TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
2003 :
2004 : return ret_value;
2005 : }
2006 :
2007 : // Remove trailing zeros from n and return the number of zeros removed.
2008 : BOOST_FORCEINLINE static int remove_trailing_zeros(carrier_uint& n) noexcept
2009 : {
2010 443 : if (n == 0)
2011 : {
2012 0 : return 0;
2013 : }
2014 :
2015 : BOOST_IF_CONSTEXPR (std::is_same<format, ieee754_binary32>::value)
2016 : {
2017 : constexpr auto mod_inv_5 = UINT32_C(0xcccccccd);
2018 : constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
2019 :
2020 : int s = 0;
2021 : while (true)
2022 : {
2023 : auto q = boost::core::rotr(n * mod_inv_25, 2);
2024 : if (q <= (std::numeric_limits<std::uint32_t>::max)() / 100)
2025 : {
2026 : n = q;
2027 : s += 2;
2028 : }
2029 : else
2030 : {
2031 : break;
2032 : }
2033 : }
2034 : auto q = boost::core::rotr(n * mod_inv_5, 1);
2035 : if (q <= (std::numeric_limits<std::uint32_t>::max)() / 10)
2036 : {
2037 : n = q;
2038 : s |= 1;
2039 : }
2040 :
2041 : return s;
2042 : }
2043 : else
2044 : {
2045 : // Static assertion does not work unless if constexpr is supported
2046 : // static_assert(std::is_same<format, ieee754_binary64>::value, "Must be a double type");
2047 :
2048 : // Divide by 10^8 and reduce to 32-bits if divisible.
2049 : // Since ret_value.significand <= (2^53 * 1000 - 1) / 1000 < 10^16,
2050 : // n is at most of 16 digits.
2051 :
2052 : // This magic number is ceil(2^90 / 10^8).
2053 443 : constexpr auto magic_number = UINT64_C(12379400392853802749);
2054 443 : auto nm = umul128(n, magic_number);
2055 :
2056 : // Is n is divisible by 10^8?
2057 443 : if ((nm.high & ((std::uint64_t(1) << (90 - 64)) - 1)) == 0 &&
2058 440 : nm.low < magic_number) {
2059 : // If yes, work with the quotient.
2060 440 : auto n32 = static_cast<std::uint32_t>(nm.high >> (90 - 64));
2061 :
2062 440 : constexpr auto mod_inv_5 = UINT32_C(0xcccccccd);
2063 440 : constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
2064 :
2065 440 : int s = 8;
2066 1306 : while (true)
2067 : {
2068 1746 : auto q = boost::core::rotr(n32 * mod_inv_25, 2);
2069 1746 : if (q <= (std::numeric_limits<std::uint32_t>::max)() / 100)
2070 : {
2071 1306 : n32 = q;
2072 1306 : s += 2;
2073 : }
2074 : else
2075 : {
2076 440 : break;
2077 : }
2078 : }
2079 :
2080 440 : auto q = boost::core::rotr(n32 * mod_inv_5, 1);
2081 440 : if (q <= (std::numeric_limits<std::uint32_t>::max)() / 10)
2082 : {
2083 400 : n32 = q;
2084 400 : s |= 1;
2085 : }
2086 :
2087 440 : n = n32;
2088 440 : return s;
2089 : }
2090 :
2091 : // If n is not divisible by 10^8, work with n itself.
2092 3 : constexpr auto mod_inv_5 = UINT64_C(0xcccccccccccccccd);
2093 3 : constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
2094 :
2095 3 : int s = 0;
2096 0 : while (true)
2097 : {
2098 3 : auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_25, 2));
2099 3 : if (q <= (std::numeric_limits<std::uint64_t>::max)() / 100)
2100 : {
2101 0 : n = q;
2102 0 : s += 2;
2103 : }
2104 : else
2105 : {
2106 3 : break;
2107 : }
2108 : }
2109 :
2110 3 : auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_5, 1));
2111 3 : if (q <= (std::numeric_limits<std::uint64_t>::max)() / 10)
2112 : {
2113 0 : n = q;
2114 0 : s |= 1;
2115 : }
2116 :
2117 3 : return s;
2118 : }
2119 : }
2120 :
2121 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2122 : static compute_mul_result compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept
2123 : {
2124 : auto r = umul96_upper64(u, cache);
2125 : return {carrier_uint(r >> 32), carrier_uint(r) == 0};
2126 : }
2127 :
2128 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2129 306 : static compute_mul_result compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept
2130 : {
2131 306 : auto r = umul192_upper128(u, cache);
2132 306 : return {r.high, r.low == 0};
2133 : }
2134 :
2135 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2136 : static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
2137 : int beta) noexcept
2138 : {
2139 : return std::uint32_t(cache >> (cache_bits - 1 - beta));
2140 : }
2141 :
2142 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2143 306 : static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
2144 : int beta) noexcept
2145 : {
2146 306 : return std::uint32_t(cache.high >> (carrier_bits - 1 - beta));
2147 : }
2148 :
2149 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2150 : static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
2151 : cache_entry_type const& cache,
2152 : int beta) noexcept
2153 : {
2154 : auto r = umul96_lower64(two_f, cache);
2155 : return {((r >> (64 - beta)) & 1) != 0, std::uint32_t(r >> (32 - beta)) == 0};
2156 : }
2157 :
2158 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2159 0 : static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
2160 : cache_entry_type const& cache,
2161 : int beta) noexcept
2162 : {
2163 0 : auto r = umul192_lower128(two_f, cache);
2164 0 : return {((r.high >> (64 - beta)) & 1) != 0, ((r.high << beta) | (r.low >> (64 - beta))) == 0};
2165 : }
2166 :
2167 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2168 : static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2169 : {
2170 : return carrier_uint((cache - (cache >> (significand_bits + 2))) >> (cache_bits - significand_bits - 1 - beta));
2171 : }
2172 :
2173 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2174 138 : static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2175 : {
2176 138 : return (cache.high - (cache.high >> (significand_bits + 2))) >> (carrier_bits - significand_bits - 1 - beta);
2177 : }
2178 :
2179 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2180 : static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2181 : {
2182 : return carrier_uint((cache + (cache >> (significand_bits + 1))) >> (cache_bits - significand_bits - 1 - beta));
2183 : }
2184 :
2185 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2186 138 : static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2187 : {
2188 138 : return (cache.high + (cache.high >> (significand_bits + 1))) >> (carrier_bits - significand_bits - 1 - beta);
2189 : }
2190 :
2191 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary32>::value, bool>::type = true>
2192 : static constexpr carrier_uint compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2193 : {
2194 : return (carrier_uint(cache >> (cache_bits - significand_bits - 2 - beta)) + 1) / 2;
2195 : }
2196 :
2197 : template <typename local_format = format, typename std::enable_if<std::is_same<local_format, ieee754_binary64>::value, bool>::type = true>
2198 0 : static constexpr carrier_uint compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
2199 : {
2200 0 : return ((cache.high >> (carrier_bits - significand_bits - 2 - beta)) + 1) / 2;
2201 : }
2202 :
2203 0 : static constexpr bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept
2204 : {
2205 0 : return exponent >= case_shorter_interval_right_endpoint_lower_threshold &&
2206 0 : exponent <= case_shorter_interval_right_endpoint_upper_threshold;
2207 : }
2208 :
2209 138 : static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept
2210 : {
2211 138 : return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
2212 138 : exponent <= case_shorter_interval_left_endpoint_upper_threshold;
2213 : }
2214 : };
2215 :
2216 :
2217 : ////////////////////////////////////////////////////////////////////////////////////////
2218 : // Policy holder.
2219 : ////////////////////////////////////////////////////////////////////////////////////////
2220 :
2221 : namespace policy_impl {
2222 : template <typename... Policies>
2223 : struct policy_holder : Policies... {};
2224 : }
2225 :
2226 : ////////////////////////////////////////////////////////////////////////////////////////
2227 : // The interface function.
2228 : ////////////////////////////////////////////////////////////////////////////////////////
2229 :
2230 : #ifdef BOOST_MSVC
2231 : # pragma warning(push)
2232 : # pragma warning(disable: 4100) // Unreferenced formal parameter (interval_type_provider)
2233 : # pragma warning(disable: 4189) // Local variable is initializaed but unused (tag)
2234 : #endif
2235 :
2236 : template <typename Float, typename FloatTraits = dragonbox_float_traits<Float>>
2237 : BOOST_FORCEINLINE BOOST_JSON_SAFEBUFFERS auto
2238 : to_decimal(dragonbox_signed_significand_bits<Float, FloatTraits> dragonbox_signed_significand_bits,
2239 : unsigned int exponent_bits) noexcept
2240 : -> decimal_fp<typename FloatTraits::carrier_uint, true, false>
2241 : {
2242 : // Build policy holder type.
2243 : using namespace policy_impl;
2244 :
2245 : using policy_holder = policy_holder<decimal_to_binary_rounding::nearest_to_even, binary_to_decimal_rounding::to_even, cache::full, sign::return_sign, trailing_zero::remove>;
2246 :
2247 : using return_type = decimal_fp<typename FloatTraits::carrier_uint, policy_holder::return_has_sign, policy_holder::report_trailing_zeros>;
2248 :
2249 444 : return_type ret = policy_holder::template delegate<return_type>(dragonbox_signed_significand_bits,
2250 444 : [exponent_bits, dragonbox_signed_significand_bits](policy_impl::decimal_to_binary_rounding::nearest_to_even interval_type_provider) {
2251 : using format = typename FloatTraits::format;
2252 444 : constexpr auto tag = decltype(interval_type_provider)::tag;
2253 :
2254 444 : auto two_fc = dragonbox_signed_significand_bits.remove_sign_bit_and_shift();
2255 444 : auto exponent = int(exponent_bits);
2256 :
2257 : BOOST_IF_CONSTEXPR (tag == decimal_to_binary_rounding::tag_t::to_nearest) { // NOLINT: if constexpr not always false
2258 : // Is the input a normal number?
2259 444 : if (exponent != 0) {
2260 433 : exponent += format::exponent_bias - format::significand_bits;
2261 :
2262 : // Shorter interval case; proceed like Schubfach.
2263 : // One might think this condition is wrong, since when exponent_bits == 1
2264 : // and two_fc == 0, the interval is actually regular. However, it turns out
2265 : // that this seemingly wrong condition is actually fine, because the end
2266 : // result is anyway the same.
2267 : //
2268 : // [binary32]
2269 : // (fc-1/2) * 2^e = 1.175'494'28... * 10^-38
2270 : // (fc-1/4) * 2^e = 1.175'494'31... * 10^-38
2271 : // fc * 2^e = 1.175'494'35... * 10^-38
2272 : // (fc+1/2) * 2^e = 1.175'494'42... * 10^-38
2273 : //
2274 : // Hence, shorter_interval_case will return 1.175'494'4 * 10^-38.
2275 : // 1.175'494'3 * 10^-38 is also a correct shortest representation that will
2276 : // be rejected if we assume shorter interval, but 1.175'494'4 * 10^-38 is
2277 : // closer to the true value so it doesn't matter.
2278 : //
2279 : // [binary64]
2280 : // (fc-1/2) * 2^e = 2.225'073'858'507'201'13... * 10^-308
2281 : // (fc-1/4) * 2^e = 2.225'073'858'507'201'25... * 10^-308
2282 : // fc * 2^e = 2.225'073'858'507'201'38... * 10^-308
2283 : // (fc+1/2) * 2^e = 2.225'073'858'507'201'63... * 10^-308
2284 : //
2285 : // Hence, shorter_interval_case will return 2.225'073'858'507'201'4 *
2286 : // 10^-308. This is indeed of the shortest length, and it is the unique one
2287 : // closest to the true value among valid representations of the same length.
2288 : static_assert(std::is_same<format, ieee754_binary32>::value ||
2289 : std::is_same<format, ieee754_binary64>::value, "Format must be IEEE754 binary 32 or 64");
2290 :
2291 433 : if (two_fc == 0) {
2292 138 : return decltype(interval_type_provider)::template invoke_shorter_interval_case<return_type>(
2293 276 : dragonbox_signed_significand_bits, [exponent]() {
2294 : return detail::impl<Float, FloatTraits>::
2295 : template compute_nearest_shorter<
2296 : return_type,
2297 : typename decltype(interval_type_provider)::
2298 : shorter_interval_type,
2299 : typename policy_holder::trailing_zero_policy,
2300 : typename policy_holder::
2301 : binary_to_decimal_rounding_policy,
2302 138 : typename policy_holder::cache_policy>(
2303 138 : exponent);
2304 138 : });
2305 : }
2306 :
2307 295 : two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
2308 : }
2309 : // Is the input a subnormal number?
2310 : else {
2311 11 : exponent = format::min_exponent - format::significand_bits;
2312 : }
2313 :
2314 306 : return decltype(interval_type_provider)::template invoke_normal_interval_case<return_type>(
2315 612 : dragonbox_signed_significand_bits, [two_fc, exponent](bool additional_args) {
2316 : return detail::impl<Float, FloatTraits>::
2317 : template compute_nearest_normal<
2318 : return_type,
2319 : typename decltype(interval_type_provider)::normal_interval_type,
2320 : typename policy_holder::trailing_zero_policy,
2321 : typename policy_holder::binary_to_decimal_rounding_policy,
2322 306 : typename policy_holder::cache_policy>(two_fc, exponent, additional_args);
2323 306 : });
2324 : }
2325 : else BOOST_IF_CONSTEXPR (tag == decimal_to_binary_rounding::tag_t::left_closed_directed) // NOLINT: if constexpr not always false
2326 : {
2327 : // Is the input a normal number?
2328 : if (exponent != 0) {
2329 : exponent += format::exponent_bias - format::significand_bits;
2330 : two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
2331 : }
2332 : // Is the input a subnormal number?
2333 : else {
2334 : exponent = format::min_exponent - format::significand_bits;
2335 : }
2336 :
2337 : return detail::impl<Float>::template compute_left_closed_directed<
2338 : return_type, typename policy_holder::trailing_zero_policy,
2339 : typename policy_holder::cache_policy>(two_fc, exponent);
2340 : }
2341 : else
2342 : {
2343 : // Assertion does not work unless if constexpr is defined
2344 : // static_assert(tag == decimal_to_binary_rounding::tag_t::right_closed_directed, "Tag should be right_closed_direction");
2345 :
2346 : bool shorter_interval = false;
2347 :
2348 : // Is the input a normal number?
2349 : if (exponent != 0) {
2350 : if (two_fc == 0 && exponent != 1) {
2351 : shorter_interval = true;
2352 : }
2353 : exponent += format::exponent_bias - format::significand_bits;
2354 : two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
2355 : }
2356 : // Is the input a subnormal number?
2357 : else {
2358 : exponent = format::min_exponent - format::significand_bits;
2359 : }
2360 :
2361 : return detail::impl<Float>::template compute_right_closed_directed<
2362 : return_type, typename policy_holder::trailing_zero_policy,
2363 : typename policy_holder::cache_policy>(two_fc, exponent, shorter_interval);
2364 : }
2365 : });
2366 :
2367 444 : policy_holder::handle_sign(dragonbox_signed_significand_bits, ret);
2368 444 : return ret;
2369 : }
2370 :
2371 : #ifdef BOOST_MSVC
2372 : # pragma warning(pop)
2373 : #endif
2374 :
2375 : namespace to_chars_detail {
2376 :
2377 : std::size_t dragon_box_print_chars(
2378 : dragonbox_float_traits<double>::carrier_uint significand,
2379 : int exponent,
2380 : char* first,
2381 : char* last) noexcept;
2382 :
2383 : }
2384 :
2385 : } // namespace detail
2386 : } // namespace json
2387 : } // namespace boost
2388 :
2389 : #ifdef BOOST_MSVC
2390 : # pragma warning(pop)
2391 :
2392 : #endif
2393 :
2394 : #endif // BOOST_JSON_DETAIL_DRAGONBOX_DRAGONBOX_HPP
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