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 + 
    static carrier_uint float_to_carrier(T x) noexcept
 
88 + 
    {
 
89 + 
        carrier_uint u;
 
90 + 
        std::memcpy(&u, &x, sizeof(carrier_uint));
 
91 + 
        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 + 
    static constexpr unsigned extract_exponent_bits(carrier_uint u) noexcept
 
98 + 
    {
 
99 + 
        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 + 
    static constexpr carrier_uint remove_exponent_bits(carrier_uint u, unsigned int exponent_bits) noexcept
 
112 + 
    {
 
113 + 
        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 + 
    static constexpr carrier_uint remove_sign_bit_and_shift(carrier_uint u) noexcept {
 
118 + 
        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 + 
    static constexpr bool is_nonzero(carrier_uint u) noexcept
 
141 + 
    {
 
142 + 
        return (u << 1) != 0;
 
143 + 
    }
 
144 +
 
145 + 
    static constexpr bool is_positive(carrier_uint u) noexcept
 
146 + 
    {
 
147 + 
        return u < (carrier_uint(1) << (format::significand_bits + format::exponent_bits));
 
148 + 
    }
 
149 +
 
150 + 
    static constexpr bool is_negative(carrier_uint u) noexcept
 
151 + 
    {
 
152 + 
        return !is_positive(u);
 
153 + 
    }
 
154 +
 
155 + 
    static constexpr bool is_finite(unsigned exponent_bits) noexcept
 
156 + 
    {
 
157 + 
        return exponent_bits != ((1u << format::exponent_bits) - 1);
 
158 + 
    }
 
159 +
 
160 + 
    static constexpr bool has_all_zero_significand_bits(carrier_uint u) noexcept
 
161 + 
    {
 
162 + 
        return (u << 1) == 0;
 
163 + 
    }
 
164 +
 
165 + 
    static constexpr bool has_even_significand_bits(carrier_uint u) noexcept
 
166 + 
    {
 
167 + 
        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 + 
    constexpr explicit dragonbox_float_bits(T float_value) noexcept
 
194 + 
        : 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 + 
    constexpr unsigned int extract_exponent_bits() const noexcept
 
205 + 
    {
 
206 + 
        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 + 
    constexpr auto remove_exponent_bits(unsigned int exponent_bits) const noexcept -> dragonbox_signed_significand_bits<type, traits_type>
 
219 + 
    {
 
220 + 
        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 + 
    constexpr bool is_nonzero() const noexcept
 
247 + 
    {
 
248 + 
        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 + 
    constexpr bool is_finite(unsigned exponent_bits) const noexcept
 
262 + 
    {
 
263 + 
        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 + 
    constexpr explicit dragonbox_signed_significand_bits(carrier_uint bit_pattern) noexcept
 
288 + 
        : u{bit_pattern} {}
 
289 +
 
290 + 
    // Shift the obtained signed significand bits to the left by 1 to remove the sign bit.
 
291 + 
    constexpr carrier_uint remove_sign_bit_and_shift() const noexcept
 
292 + 
    {
 
293 + 
        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 + 
    constexpr bool is_negative() const noexcept
 
302 + 
    {
 
303 + 
        return traits_type::is_negative(u);
 
304 + 
    }
 
305 +
 
306 + 
    constexpr bool has_all_zero_significand_bits() const noexcept
 
307 + 
    {
 
308 + 
        return traits_type::has_all_zero_significand_bits(u);
 
309 + 
    }
 
310 +
 
311 + 
    constexpr bool has_even_significand_bits() const noexcept
 
312 + 
    {
 
313 + 
        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 + 
        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 + 
            BOOST_ASSERT(n <= compute_power(UINT32_C(10), N + 1));
 
349 +
 
350 + 
            using info = divide_by_pow10_info<N>;
 
351 + 
            n *= info::magic_number;
 
352 +
 
353 + 
            constexpr auto mask = std::uint32_t(std::uint32_t(1) << info::shift_amount) - 1;
 
354 + 
            bool result = ((n & mask) < info::magic_number);
 
355 +
 
356 + 
            n >>= info::shift_amount;
 
357 + 
            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 + 
        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 + 
            else BOOST_IF_CONSTEXPR (std::is_same<UInt, std::uint64_t>::value && N == 3 && n_max <= UINT64_C(15534100272597517998))
 
415 + 
            {
 
416 + 
                return static_cast<UInt>(umul128_upper64(n, UINT64_C(2361183241434822607)) >> 7);
 
417 + 
            }
 
418 + 
            else
 
419 + 
            {
 
420 + 
                auto divisor = compute_power(static_cast<UInt>(10), N);
 
421 + 
                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},
 
554 + 
        {0x8dd01fad907ffc3b, 0xae3da7d97f6792e4}, {0xb1442798f49ffb4a, 0x99cd11cfdf41779d},
 
555 + 
        {0xdd95317f31c7fa1d, 0x40405643d711d584}, {0x8a7d3eef7f1cfc52, 0x482835ea666b2573},
 
556 + 
        {0xad1c8eab5ee43b66, 0xda3243650005eed0}, {0xd863b256369d4a40, 0x90bed43e40076a83},
 
557 + 
        {0x873e4f75e2224e68, 0x5a7744a6e804a292}, {0xa90de3535aaae202, 0x711515d0a205cb37},
 
558 + 
        {0xd3515c2831559a83, 0x0d5a5b44ca873e04}, {0x8412d9991ed58091, 0xe858790afe9486c3},
 
559 + 
        {0xa5178fff668ae0b6, 0x626e974dbe39a873}, {0xce5d73ff402d98e3, 0xfb0a3d212dc81290},
 
560 + 
        {0x80fa687f881c7f8e, 0x7ce66634bc9d0b9a}, {0xa139029f6a239f72, 0x1c1fffc1ebc44e81},
 
561 + 
        {0xc987434744ac874e, 0xa327ffb266b56221}, {0xfbe9141915d7a922, 0x4bf1ff9f0062baa9},
 
562 + 
        {0x9d71ac8fada6c9b5, 0x6f773fc3603db4aa}, {0xc4ce17b399107c22, 0xcb550fb4384d21d4},
 
563 + 
        {0xf6019da07f549b2b, 0x7e2a53a146606a49}, {0x99c102844f94e0fb, 0x2eda7444cbfc426e},
 
564 + 
        {0xc0314325637a1939, 0xfa911155fefb5309}, {0xf03d93eebc589f88, 0x793555ab7eba27cb},
 
565 + 
        {0x96267c7535b763b5, 0x4bc1558b2f3458df}, {0xbbb01b9283253ca2, 0x9eb1aaedfb016f17},
 
566 + 
        {0xea9c227723ee8bcb, 0x465e15a979c1cadd}, {0x92a1958a7675175f, 0x0bfacd89ec191eca},
 
567 + 
        {0xb749faed14125d36, 0xcef980ec671f667c}, {0xe51c79a85916f484, 0x82b7e12780e7401b},
 
568 + 
        {0x8f31cc0937ae58d2, 0xd1b2ecb8b0908811}, {0xb2fe3f0b8599ef07, 0x861fa7e6dcb4aa16},
 
569 + 
        {0xdfbdcece67006ac9, 0x67a791e093e1d49b}, {0x8bd6a141006042bd, 0xe0c8bb2c5c6d24e1},
 
570 + 
        {0xaecc49914078536d, 0x58fae9f773886e19}, {0xda7f5bf590966848, 0xaf39a475506a899f},
 
571 + 
        {0x888f99797a5e012d, 0x6d8406c952429604}, {0xaab37fd7d8f58178, 0xc8e5087ba6d33b84},
 
572 + 
        {0xd5605fcdcf32e1d6, 0xfb1e4a9a90880a65}, {0x855c3be0a17fcd26, 0x5cf2eea09a550680},
 
573 + 
        {0xa6b34ad8c9dfc06f, 0xf42faa48c0ea481f}, {0xd0601d8efc57b08b, 0xf13b94daf124da27},
 
574 + 
        {0x823c12795db6ce57, 0x76c53d08d6b70859}, {0xa2cb1717b52481ed, 0x54768c4b0c64ca6f},
 
575 + 
        {0xcb7ddcdda26da268, 0xa9942f5dcf7dfd0a}, {0xfe5d54150b090b02, 0xd3f93b35435d7c4d},
 
576 + 
        {0x9efa548d26e5a6e1, 0xc47bc5014a1a6db0}, {0xc6b8e9b0709f109a, 0x359ab6419ca1091c},
 
577 + 
        {0xf867241c8cc6d4c0, 0xc30163d203c94b63}, {0x9b407691d7fc44f8, 0x79e0de63425dcf1e},
 
578 + 
        {0xc21094364dfb5636, 0x985915fc12f542e5}, {0xf294b943e17a2bc4, 0x3e6f5b7b17b2939e},
 
579 + 
        {0x979cf3ca6cec5b5a, 0xa705992ceecf9c43}, {0xbd8430bd08277231, 0x50c6ff782a838354},
 
580 + 
        {0xece53cec4a314ebd, 0xa4f8bf5635246429}, {0x940f4613ae5ed136, 0x871b7795e136be9a},
 
581 + 
        {0xb913179899f68584, 0x28e2557b59846e40}, {0xe757dd7ec07426e5, 0x331aeada2fe589d0},
 
582 + 
        {0x9096ea6f3848984f, 0x3ff0d2c85def7622}, {0xb4bca50b065abe63, 0x0fed077a756b53aa},
 
583 + 
        {0xe1ebce4dc7f16dfb, 0xd3e8495912c62895}, {0x8d3360f09cf6e4bd, 0x64712dd7abbbd95d},
 
584 + 
        {0xb080392cc4349dec, 0xbd8d794d96aacfb4}, {0xdca04777f541c567, 0xecf0d7a0fc5583a1},
 
585 + 
        {0x89e42caaf9491b60, 0xf41686c49db57245}, {0xac5d37d5b79b6239, 0x311c2875c522ced6},
 
586 + 
        {0xd77485cb25823ac7, 0x7d633293366b828c}, {0x86a8d39ef77164bc, 0xae5dff9c02033198},
 
587 + 
        {0xa8530886b54dbdeb, 0xd9f57f830283fdfd}, {0xd267caa862a12d66, 0xd072df63c324fd7c},
 
588 + 
        {0x8380dea93da4bc60, 0x4247cb9e59f71e6e}, {0xa46116538d0deb78, 0x52d9be85f074e609},
 
589 + 
        {0xcd795be870516656, 0x67902e276c921f8c}, {0x806bd9714632dff6, 0x00ba1cd8a3db53b7},
 
590 + 
        {0xa086cfcd97bf97f3, 0x80e8a40eccd228a5}, {0xc8a883c0fdaf7df0, 0x6122cd128006b2ce},
 
591 + 
        {0xfad2a4b13d1b5d6c, 0x796b805720085f82}, {0x9cc3a6eec6311a63, 0xcbe3303674053bb1},
 
592 + 
        {0xc3f490aa77bd60fc, 0xbedbfc4411068a9d}, {0xf4f1b4d515acb93b, 0xee92fb5515482d45},
 
593 + 
        {0x991711052d8bf3c5, 0x751bdd152d4d1c4b}, {0xbf5cd54678eef0b6, 0xd262d45a78a0635e},
 
594 + 
        {0xef340a98172aace4, 0x86fb897116c87c35}, {0x9580869f0e7aac0e, 0xd45d35e6ae3d4da1},
 
595 + 
        {0xbae0a846d2195712, 0x8974836059cca10a}, {0xe998d258869facd7, 0x2bd1a438703fc94c},
 
596 + 
        {0x91ff83775423cc06, 0x7b6306a34627ddd0}, {0xb67f6455292cbf08, 0x1a3bc84c17b1d543},
 
597 + 
        {0xe41f3d6a7377eeca, 0x20caba5f1d9e4a94}, {0x8e938662882af53e, 0x547eb47b7282ee9d},
 
598 + 
        {0xb23867fb2a35b28d, 0xe99e619a4f23aa44}, {0xdec681f9f4c31f31, 0x6405fa00e2ec94d5},
 
599 + 
        {0x8b3c113c38f9f37e, 0xde83bc408dd3dd05}, {0xae0b158b4738705e, 0x9624ab50b148d446},
 
600 + 
        {0xd98ddaee19068c76, 0x3badd624dd9b0958}, {0x87f8a8d4cfa417c9, 0xe54ca5d70a80e5d7},
 
601 + 
        {0xa9f6d30a038d1dbc, 0x5e9fcf4ccd211f4d}, {0xd47487cc8470652b, 0x7647c32000696720},
 
602 + 
        {0x84c8d4dfd2c63f3b, 0x29ecd9f40041e074}, {0xa5fb0a17c777cf09, 0xf468107100525891},
 
603 + 
        {0xcf79cc9db955c2cc, 0x7182148d4066eeb5}, {0x81ac1fe293d599bf, 0xc6f14cd848405531},
 
604 + 
        {0xa21727db38cb002f, 0xb8ada00e5a506a7d}, {0xca9cf1d206fdc03b, 0xa6d90811f0e4851d},
 
605 + 
        {0xfd442e4688bd304a, 0x908f4a166d1da664}, {0x9e4a9cec15763e2e, 0x9a598e4e043287ff},
 
606 + 
        {0xc5dd44271ad3cdba, 0x40eff1e1853f29fe}, {0xf7549530e188c128, 0xd12bee59e68ef47d},
 
607 + 
        {0x9a94dd3e8cf578b9, 0x82bb74f8301958cf}, {0xc13a148e3032d6e7, 0xe36a52363c1faf02},
 
608 + 
        {0xf18899b1bc3f8ca1, 0xdc44e6c3cb279ac2}, {0x96f5600f15a7b7e5, 0x29ab103a5ef8c0ba},
 
609 + 
        {0xbcb2b812db11a5de, 0x7415d448f6b6f0e8}, {0xebdf661791d60f56, 0x111b495b3464ad22},
 
610 + 
        {0x936b9fcebb25c995, 0xcab10dd900beec35}, {0xb84687c269ef3bfb, 0x3d5d514f40eea743},
 
611 + 
        {0xe65829b3046b0afa, 0x0cb4a5a3112a5113}, {0x8ff71a0fe2c2e6dc, 0x47f0e785eaba72ac},
 
612 + 
        {0xb3f4e093db73a093, 0x59ed216765690f57}, {0xe0f218b8d25088b8, 0x306869c13ec3532d},
 
613 + 
        {0x8c974f7383725573, 0x1e414218c73a13fc}, {0xafbd2350644eeacf, 0xe5d1929ef90898fb},
 
614 + 
        {0xdbac6c247d62a583, 0xdf45f746b74abf3a}, {0x894bc396ce5da772, 0x6b8bba8c328eb784},
 
615 + 
        {0xab9eb47c81f5114f, 0x066ea92f3f326565}, {0xd686619ba27255a2, 0xc80a537b0efefebe},
 
616 + 
        {0x8613fd0145877585, 0xbd06742ce95f5f37}, {0xa798fc4196e952e7, 0x2c48113823b73705},
 
617 + 
        {0xd17f3b51fca3a7a0, 0xf75a15862ca504c6}, {0x82ef85133de648c4, 0x9a984d73dbe722fc},
 
618 + 
        {0xa3ab66580d5fdaf5, 0xc13e60d0d2e0ebbb}, {0xcc963fee10b7d1b3, 0x318df905079926a9},
 
619 + 
        {0xffbbcfe994e5c61f, 0xfdf17746497f7053}, {0x9fd561f1fd0f9bd3, 0xfeb6ea8bedefa634},
 
620 + 
        {0xc7caba6e7c5382c8, 0xfe64a52ee96b8fc1}, {0xf9bd690a1b68637b, 0x3dfdce7aa3c673b1},
 
621 + 
        {0x9c1661a651213e2d, 0x06bea10ca65c084f}, {0xc31bfa0fe5698db8, 0x486e494fcff30a63},
 
622 + 
        {0xf3e2f893dec3f126, 0x5a89dba3c3efccfb}, {0x986ddb5c6b3a76b7, 0xf89629465a75e01d},
 
623 + 
        {0xbe89523386091465, 0xf6bbb397f1135824}, {0xee2ba6c0678b597f, 0x746aa07ded582e2d},
 
624 + 
        {0x94db483840b717ef, 0xa8c2a44eb4571cdd}, {0xba121a4650e4ddeb, 0x92f34d62616ce414},
 
625 + 
        {0xe896a0d7e51e1566, 0x77b020baf9c81d18}, {0x915e2486ef32cd60, 0x0ace1474dc1d122f},
 
626 + 
        {0xb5b5ada8aaff80b8, 0x0d819992132456bb}, {0xe3231912d5bf60e6, 0x10e1fff697ed6c6a},
 
627 + 
        {0x8df5efabc5979c8f, 0xca8d3ffa1ef463c2}, {0xb1736b96b6fd83b3, 0xbd308ff8a6b17cb3},
 
628 + 
        {0xddd0467c64bce4a0, 0xac7cb3f6d05ddbdf}, {0x8aa22c0dbef60ee4, 0x6bcdf07a423aa96c},
 
629 + 
        {0xad4ab7112eb3929d, 0x86c16c98d2c953c7}, {0xd89d64d57a607744, 0xe871c7bf077ba8b8},
 
630 + 
        {0x87625f056c7c4a8b, 0x11471cd764ad4973}, {0xa93af6c6c79b5d2d, 0xd598e40d3dd89bd0},
 
631 + 
        {0xd389b47879823479, 0x4aff1d108d4ec2c4}, {0x843610cb4bf160cb, 0xcedf722a585139bb},
 
632 + 
        {0xa54394fe1eedb8fe, 0xc2974eb4ee658829}, {0xce947a3da6a9273e, 0x733d226229feea33},
 
633 + 
        {0x811ccc668829b887, 0x0806357d5a3f5260}, {0xa163ff802a3426a8, 0xca07c2dcb0cf26f8},
 
634 + 
        {0xc9bcff6034c13052, 0xfc89b393dd02f0b6}, {0xfc2c3f3841f17c67, 0xbbac2078d443ace3},
 
635 + 
        {0x9d9ba7832936edc0, 0xd54b944b84aa4c0e}, {0xc5029163f384a931, 0x0a9e795e65d4df12},
 
636 + 
        {0xf64335bcf065d37d, 0x4d4617b5ff4a16d6}, {0x99ea0196163fa42e, 0x504bced1bf8e4e46},
 
637 + 
        {0xc06481fb9bcf8d39, 0xe45ec2862f71e1d7}, {0xf07da27a82c37088, 0x5d767327bb4e5a4d},
 
638 + 
        {0x964e858c91ba2655, 0x3a6a07f8d510f870}, {0xbbe226efb628afea, 0x890489f70a55368c},
 
639 + 
        {0xeadab0aba3b2dbe5, 0x2b45ac74ccea842f}, {0x92c8ae6b464fc96f, 0x3b0b8bc90012929e},
 
640 + 
        {0xb77ada0617e3bbcb, 0x09ce6ebb40173745}, {0xe55990879ddcaabd, 0xcc420a6a101d0516},
 
641 + 
        {0x8f57fa54c2a9eab6, 0x9fa946824a12232e}, {0xb32df8e9f3546564, 0x47939822dc96abfa},
 
642 + 
        {0xdff9772470297ebd, 0x59787e2b93bc56f8}, {0x8bfbea76c619ef36, 0x57eb4edb3c55b65b},
 
643 + 
        {0xaefae51477a06b03, 0xede622920b6b23f2}, {0xdab99e59958885c4, 0xe95fab368e45ecee},
 
644 + 
        {0x88b402f7fd75539b, 0x11dbcb0218ebb415}, {0xaae103b5fcd2a881, 0xd652bdc29f26a11a},
 
645 + 
        {0xd59944a37c0752a2, 0x4be76d3346f04960}, {0x857fcae62d8493a5, 0x6f70a4400c562ddc},
 
646 + 
        {0xa6dfbd9fb8e5b88e, 0xcb4ccd500f6bb953}, {0xd097ad07a71f26b2, 0x7e2000a41346a7a8},
 
647 + 
        {0x825ecc24c873782f, 0x8ed400668c0c28c9}, {0xa2f67f2dfa90563b, 0x728900802f0f32fb},
 
648 + 
        {0xcbb41ef979346bca, 0x4f2b40a03ad2ffba}, {0xfea126b7d78186bc, 0xe2f610c84987bfa9},
 
649 + 
        {0x9f24b832e6b0f436, 0x0dd9ca7d2df4d7ca}, {0xc6ede63fa05d3143, 0x91503d1c79720dbc},
 
650 + 
        {0xf8a95fcf88747d94, 0x75a44c6397ce912b}, {0x9b69dbe1b548ce7c, 0xc986afbe3ee11abb},
 
651 + 
        {0xc24452da229b021b, 0xfbe85badce996169}, {0xf2d56790ab41c2a2, 0xfae27299423fb9c4},
 
652 + 
        {0x97c560ba6b0919a5, 0xdccd879fc967d41b}, {0xbdb6b8e905cb600f, 0x5400e987bbc1c921},
 
653 + 
        {0xed246723473e3813, 0x290123e9aab23b69}, {0x9436c0760c86e30b, 0xf9a0b6720aaf6522},
 
654 + 
        {0xb94470938fa89bce, 0xf808e40e8d5b3e6a}, {0xe7958cb87392c2c2, 0xb60b1d1230b20e05},
 
655 + 
        {0x90bd77f3483bb9b9, 0xb1c6f22b5e6f48c3}, {0xb4ecd5f01a4aa828, 0x1e38aeb6360b1af4},
 
656 + 
        {0xe2280b6c20dd5232, 0x25c6da63c38de1b1}, {0x8d590723948a535f, 0x579c487e5a38ad0f},
 
657 + 
        {0xb0af48ec79ace837, 0x2d835a9df0c6d852}, {0xdcdb1b2798182244, 0xf8e431456cf88e66},
 
658 + 
        {0x8a08f0f8bf0f156b, 0x1b8e9ecb641b5900}, {0xac8b2d36eed2dac5, 0xe272467e3d222f40},
 
659 + 
        {0xd7adf884aa879177, 0x5b0ed81dcc6abb10}, {0x86ccbb52ea94baea, 0x98e947129fc2b4ea},
 
660 + 
        {0xa87fea27a539e9a5, 0x3f2398d747b36225}, {0xd29fe4b18e88640e, 0x8eec7f0d19a03aae},
 
661 + 
        {0x83a3eeeef9153e89, 0x1953cf68300424ad}, {0xa48ceaaab75a8e2b, 0x5fa8c3423c052dd8},
 
662 + 
        {0xcdb02555653131b6, 0x3792f412cb06794e}, {0x808e17555f3ebf11, 0xe2bbd88bbee40bd1},
 
663 + 
        {0xa0b19d2ab70e6ed6, 0x5b6aceaeae9d0ec5}, {0xc8de047564d20a8b, 0xf245825a5a445276},
 
664 + 
        {0xfb158592be068d2e, 0xeed6e2f0f0d56713}, {0x9ced737bb6c4183d, 0x55464dd69685606c},
 
665 + 
        {0xc428d05aa4751e4c, 0xaa97e14c3c26b887}, {0xf53304714d9265df, 0xd53dd99f4b3066a9},
 
666 + 
        {0x993fe2c6d07b7fab, 0xe546a8038efe402a}, {0xbf8fdb78849a5f96, 0xde98520472bdd034},
 
667 + 
        {0xef73d256a5c0f77c, 0x963e66858f6d4441}, {0x95a8637627989aad, 0xdde7001379a44aa9},
 
668 + 
        {0xbb127c53b17ec159, 0x5560c018580d5d53}, {0xe9d71b689dde71af, 0xaab8f01e6e10b4a7},
 
669 + 
        {0x9226712162ab070d, 0xcab3961304ca70e9}, {0xb6b00d69bb55c8d1, 0x3d607b97c5fd0d23},
 
670 + 
        {0xe45c10c42a2b3b05, 0x8cb89a7db77c506b}, {0x8eb98a7a9a5b04e3, 0x77f3608e92adb243},
 
671 + 
        {0xb267ed1940f1c61c, 0x55f038b237591ed4}, {0xdf01e85f912e37a3, 0x6b6c46dec52f6689},
 
672 + 
        {0x8b61313bbabce2c6, 0x2323ac4b3b3da016}, {0xae397d8aa96c1b77, 0xabec975e0a0d081b},
 
673 + 
        {0xd9c7dced53c72255, 0x96e7bd358c904a22}, {0x881cea14545c7575, 0x7e50d64177da2e55},
 
674 + 
        {0xaa242499697392d2, 0xdde50bd1d5d0b9ea}, {0xd4ad2dbfc3d07787, 0x955e4ec64b44e865},
 
675 + 
        {0x84ec3c97da624ab4, 0xbd5af13bef0b113f}, {0xa6274bbdd0fadd61, 0xecb1ad8aeacdd58f},
 
676 + 
        {0xcfb11ead453994ba, 0x67de18eda5814af3}, {0x81ceb32c4b43fcf4, 0x80eacf948770ced8},
 
677 + 
        {0xa2425ff75e14fc31, 0xa1258379a94d028e}, {0xcad2f7f5359a3b3e, 0x096ee45813a04331},
 
678 + 
        {0xfd87b5f28300ca0d, 0x8bca9d6e188853fd}, {0x9e74d1b791e07e48, 0x775ea264cf55347e},
 
679 + 
        {0xc612062576589dda, 0x95364afe032a819e}, {0xf79687aed3eec551, 0x3a83ddbd83f52205},
 
680 + 
        {0x9abe14cd44753b52, 0xc4926a9672793543}, {0xc16d9a0095928a27, 0x75b7053c0f178294},
 
681 + 
        {0xf1c90080baf72cb1, 0x5324c68b12dd6339}, {0x971da05074da7bee, 0xd3f6fc16ebca5e04},
 
682 + 
        {0xbce5086492111aea, 0x88f4bb1ca6bcf585}, {0xec1e4a7db69561a5, 0x2b31e9e3d06c32e6},
 
683 + 
        {0x9392ee8e921d5d07, 0x3aff322e62439fd0}, {0xb877aa3236a4b449, 0x09befeb9fad487c3},
 
684 + 
        {0xe69594bec44de15b, 0x4c2ebe687989a9b4}, {0x901d7cf73ab0acd9, 0x0f9d37014bf60a11},
 
685 + 
        {0xb424dc35095cd80f, 0x538484c19ef38c95}, {0xe12e13424bb40e13, 0x2865a5f206b06fba},
 
686 + 
        {0x8cbccc096f5088cb, 0xf93f87b7442e45d4}, {0xafebff0bcb24aafe, 0xf78f69a51539d749},
 
687 + 
        {0xdbe6fecebdedd5be, 0xb573440e5a884d1c}, {0x89705f4136b4a597, 0x31680a88f8953031},
 
688 + 
        {0xabcc77118461cefc, 0xfdc20d2b36ba7c3e}, {0xd6bf94d5e57a42bc, 0x3d32907604691b4d},
 
689 + 
        {0x8637bd05af6c69b5, 0xa63f9a49c2c1b110}, {0xa7c5ac471b478423, 0x0fcf80dc33721d54},
 
690 + 
        {0xd1b71758e219652b, 0xd3c36113404ea4a9}, {0x83126e978d4fdf3b, 0x645a1cac083126ea},
 
691 + 
        {0xa3d70a3d70a3d70a, 0x3d70a3d70a3d70a4}, {0xcccccccccccccccc, 0xcccccccccccccccd},
 
692 + 
        {0x8000000000000000, 0x0000000000000000}, {0xa000000000000000, 0x0000000000000000},
 
693 + 
        {0xc800000000000000, 0x0000000000000000}, {0xfa00000000000000, 0x0000000000000000},
 
694 + 
        {0x9c40000000000000, 0x0000000000000000}, {0xc350000000000000, 0x0000000000000000},
 
695 + 
        {0xf424000000000000, 0x0000000000000000}, {0x9896800000000000, 0x0000000000000000},
 
696 + 
        {0xbebc200000000000, 0x0000000000000000}, {0xee6b280000000000, 0x0000000000000000},
 
697 + 
        {0x9502f90000000000, 0x0000000000000000}, {0xba43b74000000000, 0x0000000000000000},
 
698 + 
        {0xe8d4a51000000000, 0x0000000000000000}, {0x9184e72a00000000, 0x0000000000000000},
 
699 + 
        {0xb5e620f480000000, 0x0000000000000000}, {0xe35fa931a0000000, 0x0000000000000000},
 
700 + 
        {0x8e1bc9bf04000000, 0x0000000000000000}, {0xb1a2bc2ec5000000, 0x0000000000000000},
 
701 + 
        {0xde0b6b3a76400000, 0x0000000000000000}, {0x8ac7230489e80000, 0x0000000000000000},
 
702 + 
        {0xad78ebc5ac620000, 0x0000000000000000}, {0xd8d726b7177a8000, 0x0000000000000000},
 
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 + 
        static BOOST_CXX14_CONSTEXPR void handle_sign(SignedSignificandBits s, ReturnType& r) noexcept
 
900 + 
        {
 
901 + 
            r.is_negative = s.is_negative();
 
902 + 
        }
 
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 + 
            r.exponent += Impl::remove_trailing_zeros(r.significand);
 
931 + 
        }
 
932 +
 
933 + 
        template <typename Impl, typename ReturnType>
 
934 + 
        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 + 
            constexpr bool include_left_endpoint() const noexcept { return is_closed; }
 
973 + 
            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 + 
            static constexpr bool include_left_endpoint() noexcept { return true; }
 
988 + 
            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 + 
            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 + 
            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 + 
            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 + 
        static constexpr bool prefer_round_down(ReturnType const& r) noexcept
 
1399 + 
        {
 
1400 + 
            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 + 
        static constexpr typename cache_format::cache_entry_type get_cache(int k) noexcept
 
1453 + 
        {
 
1454 + 
            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 + 
    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 + 
        ReturnType ret_value = {};
 
1603 + 
        IntervalType interval_type{additional_args...};
 
1604 +
 
1605 + 
        // Compute k and beta.
 
1606 + 
        const int minus_k = log::floor_log10_pow2(exponent) - kappa;
 
1607 + 
        const auto cache = CachePolicy::template get_cache<format>(-minus_k);
 
1608 + 
        const int beta = exponent + log::floor_log2_pow10(-minus_k);
 
1609 +
 
1610 + 
        // Compute zi and deltai.
 
1611 + 
        // 10^kappa <= deltai < 10^(kappa + 1)
 
1612 + 
        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 + 
        const auto z_res = compute_mul((two_fc | 1) << beta, cache);
 
1624 + 
        const auto zi = z_res.result;
 
1625 + 
        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 + 
        BOOST_CXX14_CONSTEXPR auto big_divisor = compute_power(std::uint32_t(10), kappa + 1);
 
1632 + 
        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 + 
        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 + 
        auto r = std::uint32_t(zi - big_divisor * ret_value.significand);
 
1643 +
 
1644 + 
        if (r < deltai)
 
1645 + 
        {
 
1646 + 
            // Exclude the right endpoint if necessary.
 
1647 + 
            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 + 
                    --ret_value.significand;
 
1661 + 
                    r = big_divisor;
 
1662 +
 
1663 + 
                    goto small_divisor_case_label;
 
1664 + 
                }
 
1665 + 
            }
 
1666 + 
        }
 
1667 + 
        else if (r > deltai)
 
1668 + 
        {
 
1669 + 
            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 + 
            const auto x_res = compute_mul_parity(two_fc - 1, cache, beta);
 
1677 + 
            const auto xi_parity = x_res.parity;
 
1678 + 
            const auto x_is_integer = x_res.is_integer;
 
1679 +
 
1680 + 
            if (!(xi_parity | (x_is_integer & interval_type.include_left_endpoint())))
 
1681 + 
            {
 
1682 + 
                goto small_divisor_case_label;
 
1683 + 
            }
 
1684 + 
        }
 
1685 + 
        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 + 
        return ret_value;
 
1690 +
 
1691 +
 
1692 + 
        //////////////////////////////////////////////////////////////////////
 
1693 + 
        // Step 3: Find the significand with the smaller divisor
 
1694 + 
        //////////////////////////////////////////////////////////////////////
 
1695 +
 
1696 + 
    small_divisor_case_label:
 
1697 + 
        TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
 
1698 + 
        ret_value.significand *= 10;
 
1699 + 
        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 + 
            auto dist = r - (deltai / 2) + (small_divisor / 2);
 
1729 + 
            const bool approx_y_parity = ((dist ^ (small_divisor / 2)) & 1) != 0;
 
1730 +
 
1731 + 
            // Is dist divisible by 10^kappa?
 
1732 + 
            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 + 
            ret_value.significand += dist;
 
1736 +
 
1737 + 
            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 + 
                const auto y_res = compute_mul_parity(two_fc, cache, beta);
 
1748 + 
                const auto yi_parity = y_res.parity;
 
1749 + 
                const auto is_y_integer = y_res.is_integer;
 
1750 +
 
1751 + 
                if (yi_parity != approx_y_parity)
 
1752 + 
                {
 
1753 + 
                    --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 + 
                    if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) & is_y_integer)
 
1761 + 
                    {
 
1762 + 
                        --ret_value.significand;
 
1763 + 
                    }
 
1764 + 
                }
 
1765 + 
            }
 
1766 + 
        }
 
1767 +
 
1768 + 
        return ret_value;
 
1769 + 
    }
 
1770 +
 
1771 + 
    template <typename ReturnType, typename IntervalType, typename TrailingZeroPolicy,
 
1772 + 
              typename BinaryToDecimalRoundingPolicy, typename CachePolicy, typename... AdditionalArgs>
 
1773 + 
    BOOST_JSON_SAFEBUFFERS static ReturnType compute_nearest_shorter(const int exponent, AdditionalArgs... additional_args) noexcept
 
1774 + 
    {
 
1775 + 
        ReturnType ret_value = {};
 
1776 + 
        IntervalType interval_type{additional_args...};
 
1777 +
 
1778 + 
        // Compute k and beta.
 
1779 + 
        const int minus_k = log::floor_log10_pow2_minus_log10_4_over_3(exponent);
 
1780 + 
        const int beta = exponent + log::floor_log2_pow10(-minus_k);
 
1781 +
 
1782 + 
        // Compute xi and zi.
 
1783 + 
        const auto cache = CachePolicy::template get_cache<format>(-minus_k);
 
1784 +
 
1785 + 
        auto xi = compute_left_endpoint_for_shorter_interval_case(cache, beta);
 
1786 + 
        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 + 
        if (!interval_type.include_right_endpoint() && is_right_endpoint_integer_shorter_interval(exponent))
 
1791 + 
        {
 
1792 + 
            --zi;
 
1793 + 
        }
 
1794 + 
        // If we don't accept the left endpoint or
 
1795 + 
        // if the left endpoint is not an integer, increase it.
 
1796 + 
        if (!interval_type.include_left_endpoint() || !is_left_endpoint_integer_shorter_interval(exponent))
 
1797 + 
        {
 
1798 + 
            ++xi;
 
1799 + 
        }
 
1800 +
 
1801 + 
        // Try bigger divisor.
 
1802 + 
        ret_value.significand = zi / 10;
 
1803 +
 
1804 + 
        // If succeed, remove trailing zeros if necessary and return.
 
1805 + 
        if (ret_value.significand * 10 >= xi)
 
1806 + 
        {
 
1807 + 
            ret_value.exponent = minus_k + 1;
 
1808 + 
            TrailingZeroPolicy::template on_trailing_zeros<impl>(ret_value);
 
1809 + 
            return ret_value;
 
1810 + 
        }
 
1811 +
 
1812 + 
        // Otherwise, compute the round-up of y.
 
1813 + 
        TrailingZeroPolicy::template no_trailing_zeros<impl>(ret_value);
 
1814 + 
        ret_value.significand = compute_round_up_for_shorter_interval_case(cache, beta);
 
1815 + 
        ret_value.exponent = minus_k;
 
1816 +
 
1817 + 
        // When tie occurs, choose one of them according to the rule.
 
1818 + 
        if (BinaryToDecimalRoundingPolicy::prefer_round_down(ret_value) &&
 
1819 + 
            exponent >= shorter_interval_tie_lower_threshold &&
 
1820 + 
            exponent <= shorter_interval_tie_upper_threshold)
 
1821 + 
        {
 
1822 + 
            --ret_value.significand;
 
1823 + 
        }
 
1824 + 
        else if (ret_value.significand < xi)
 
1825 + 
        {
 
1826 + 
            ++ret_value.significand;
 
1827 + 
        }
 
1828 +
 
1829 + 
        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 + 
        if (n == 0)
 
2011 + 
        {
 
2012 + 
            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 + 
            constexpr auto magic_number = UINT64_C(12379400392853802749);
 
2054 + 
            auto nm = umul128(n, magic_number);
 
2055 +
 
2056 + 
            // Is n is divisible by 10^8?
 
2057 + 
            if ((nm.high & ((std::uint64_t(1) << (90 - 64)) - 1)) == 0 &&
 
2058 + 
                nm.low < magic_number) {
 
2059 + 
                // If yes, work with the quotient.
 
2060 + 
                auto n32 = static_cast<std::uint32_t>(nm.high >> (90 - 64));
 
2061 +
 
2062 + 
                constexpr auto mod_inv_5 = UINT32_C(0xcccccccd);
 
2063 + 
                constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
 
2064 +
 
2065 + 
                int s = 8;
 
2066 + 
                while (true)
 
2067 + 
                {
 
2068 + 
                    auto q = boost::core::rotr(n32 * mod_inv_25, 2);
 
2069 + 
                    if (q <= (std::numeric_limits<std::uint32_t>::max)() / 100)
 
2070 + 
                    {
 
2071 + 
                        n32 = q;
 
2072 + 
                        s += 2;
 
2073 + 
                    }
 
2074 + 
                    else
 
2075 + 
                    {
 
2076 + 
                        break;
 
2077 + 
                    }
 
2078 + 
                }
 
2079 +
 
2080 + 
                auto q = boost::core::rotr(n32 * mod_inv_5, 1);
 
2081 + 
                if (q <= (std::numeric_limits<std::uint32_t>::max)() / 10)
 
2082 + 
                {
 
2083 + 
                    n32 = q;
 
2084 + 
                    s |= 1;
 
2085 + 
                }
 
2086 +
 
2087 + 
                n = n32;
 
2088 + 
                return s;
 
2089 + 
            }
 
2090 +
 
2091 + 
            // If n is not divisible by 10^8, work with n itself.
 
2092 + 
            constexpr auto mod_inv_5 = UINT64_C(0xcccccccccccccccd);
 
2093 + 
            constexpr auto mod_inv_25 = mod_inv_5 * mod_inv_5;
 
2094 +
 
2095 + 
            int s = 0;
 
2096 + 
            while (true)
 
2097 + 
            {
 
2098 + 
                auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_25, 2));
 
2099 + 
                if (q <= (std::numeric_limits<std::uint64_t>::max)() / 100)
 
2100 + 
                {
 
2101 + 
                    n = q;
 
2102 + 
                    s += 2;
 
2103 + 
                }
 
2104 + 
                else
 
2105 + 
                {
 
2106 + 
                    break;
 
2107 + 
                }
 
2108 + 
            }
 
2109 +
 
2110 + 
            auto q = static_cast<carrier_uint>(boost::core::rotr(n * mod_inv_5, 1));
 
2111 + 
            if (q <= (std::numeric_limits<std::uint64_t>::max)() / 10)
 
2112 + 
            {
 
2113 + 
                n = q;
 
2114 + 
                s |= 1;
 
2115 + 
            }
 
2116 +
 
2117 + 
            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 + 
    static compute_mul_result compute_mul(carrier_uint u, cache_entry_type const& cache) noexcept
 
2130 + 
    {
 
2131 + 
        auto r = umul192_upper128(u, cache);
 
2132 + 
        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 + 
    static constexpr std::uint32_t compute_delta(cache_entry_type const& cache,
 
2144 + 
                                                    int beta) noexcept
 
2145 + 
    {
 
2146 + 
        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 + 
    static compute_mul_parity_result compute_mul_parity(carrier_uint two_f,
 
2160 + 
                                                        cache_entry_type const& cache,
 
2161 + 
                                                        int beta) noexcept
 
2162 + 
    {
 
2163 + 
        auto r = umul192_lower128(two_f, cache);
 
2164 + 
        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 + 
    static constexpr carrier_uint compute_left_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
 
2175 + 
    {
 
2176 + 
        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 + 
    static constexpr carrier_uint compute_right_endpoint_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
 
2187 + 
    {
 
2188 + 
        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 + 
    static constexpr carrier_uint compute_round_up_for_shorter_interval_case(cache_entry_type const& cache, int beta) noexcept
 
2199 + 
    {
 
2200 + 
        return ((cache.high >> (carrier_bits - significand_bits - 2 - beta)) + 1) / 2;
 
2201 + 
    }
 
2202 +
 
2203 + 
    static constexpr bool is_right_endpoint_integer_shorter_interval(int exponent) noexcept
 
2204 + 
    {
 
2205 + 
        return exponent >= case_shorter_interval_right_endpoint_lower_threshold &&
 
2206 + 
                exponent <= case_shorter_interval_right_endpoint_upper_threshold;
 
2207 + 
    }
 
2208 +
 
2209 + 
    static constexpr bool is_left_endpoint_integer_shorter_interval(int exponent) noexcept
 
2210 + 
    {
 
2211 + 
        return exponent >= case_shorter_interval_left_endpoint_lower_threshold &&
 
2212 + 
                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 + 
    return_type ret = policy_holder::template delegate<return_type>(dragonbox_signed_significand_bits,
 
2250 + 
        [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 + 
            constexpr auto tag = decltype(interval_type_provider)::tag;
 
2253 +
 
2254 + 
            auto two_fc = dragonbox_signed_significand_bits.remove_sign_bit_and_shift();
 
2255 + 
            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 + 
                if (exponent != 0) {
 
2260 + 
                    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 + 
                    if (two_fc == 0) {
 
2292 + 
                        return decltype(interval_type_provider)::template invoke_shorter_interval_case<return_type>(
 
2293 + 
                            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 + 
                                        typename policy_holder::cache_policy>(
 
2303 + 
                                        exponent);
 
2304 + 
                            });
 
2305 + 
                    }
 
2306 +
 
2307 + 
                    two_fc |= (decltype(two_fc)(1) << (format::significand_bits + 1));
 
2308 + 
                }
 
2309 + 
                // Is the input a subnormal number?
 
2310 + 
                else {
 
2311 + 
                    exponent = format::min_exponent - format::significand_bits;
 
2312 + 
                }
 
2313 +
 
2314 + 
                return decltype(interval_type_provider)::template invoke_normal_interval_case<return_type>(
 
2315 + 
                    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 + 
                                typename policy_holder::cache_policy>(two_fc, exponent, additional_args);
 
2323 + 
                    });
 
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 + 
    policy_holder::handle_sign(dragonbox_signed_significand_bits, ret);
 
2368 + 
    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