1 | #pragma once |
2 | |
3 | #include <array> // array |
4 | #include <cassert> // assert |
5 | #include <ciso646> // or, and, not |
6 | #include <cmath> // signbit, isfinite |
7 | #include <cstdint> // intN_t, uintN_t |
8 | #include <cstring> // memcpy, memmove |
9 | #include <limits> // numeric_limits |
10 | #include <type_traits> // conditional |
11 | #include <nlohmann/detail/macro_scope.hpp> |
12 | |
13 | namespace nlohmann |
14 | { |
15 | namespace detail |
16 | { |
17 | |
18 | /*! |
19 | @brief implements the Grisu2 algorithm for binary to decimal floating-point |
20 | conversion. |
21 | |
22 | This implementation is a slightly modified version of the reference |
23 | implementation which may be obtained from |
24 | http://florian.loitsch.com/publications (bench.tar.gz). |
25 | |
26 | The code is distributed under the MIT license, Copyright (c) 2009 Florian Loitsch. |
27 | |
28 | For a detailed description of the algorithm see: |
29 | |
30 | [1] Loitsch, "Printing Floating-Point Numbers Quickly and Accurately with |
31 | Integers", Proceedings of the ACM SIGPLAN 2010 Conference on Programming |
32 | Language Design and Implementation, PLDI 2010 |
33 | [2] Burger, Dybvig, "Printing Floating-Point Numbers Quickly and Accurately", |
34 | Proceedings of the ACM SIGPLAN 1996 Conference on Programming Language |
35 | Design and Implementation, PLDI 1996 |
36 | */ |
37 | namespace dtoa_impl |
38 | { |
39 | |
40 | template <typename Target, typename Source> |
41 | Target reinterpret_bits(const Source source) |
42 | { |
43 | static_assert(sizeof(Target) == sizeof(Source), "size mismatch" ); |
44 | |
45 | Target target; |
46 | std::memcpy(&target, &source, sizeof(Source)); |
47 | return target; |
48 | } |
49 | |
50 | struct diyfp // f * 2^e |
51 | { |
52 | static constexpr int kPrecision = 64; // = q |
53 | |
54 | std::uint64_t f = 0; |
55 | int e = 0; |
56 | |
57 | constexpr diyfp(std::uint64_t f_, int e_) noexcept : f(f_), e(e_) {} |
58 | |
59 | /*! |
60 | @brief returns x - y |
61 | @pre x.e == y.e and x.f >= y.f |
62 | */ |
63 | static diyfp sub(const diyfp& x, const diyfp& y) noexcept |
64 | { |
65 | assert(x.e == y.e); |
66 | assert(x.f >= y.f); |
67 | |
68 | return {x.f - y.f, x.e}; |
69 | } |
70 | |
71 | /*! |
72 | @brief returns x * y |
73 | @note The result is rounded. (Only the upper q bits are returned.) |
74 | */ |
75 | static diyfp mul(const diyfp& x, const diyfp& y) noexcept |
76 | { |
77 | static_assert(kPrecision == 64, "internal error" ); |
78 | |
79 | // Computes: |
80 | // f = round((x.f * y.f) / 2^q) |
81 | // e = x.e + y.e + q |
82 | |
83 | // Emulate the 64-bit * 64-bit multiplication: |
84 | // |
85 | // p = u * v |
86 | // = (u_lo + 2^32 u_hi) (v_lo + 2^32 v_hi) |
87 | // = (u_lo v_lo ) + 2^32 ((u_lo v_hi ) + (u_hi v_lo )) + 2^64 (u_hi v_hi ) |
88 | // = (p0 ) + 2^32 ((p1 ) + (p2 )) + 2^64 (p3 ) |
89 | // = (p0_lo + 2^32 p0_hi) + 2^32 ((p1_lo + 2^32 p1_hi) + (p2_lo + 2^32 p2_hi)) + 2^64 (p3 ) |
90 | // = (p0_lo ) + 2^32 (p0_hi + p1_lo + p2_lo ) + 2^64 (p1_hi + p2_hi + p3) |
91 | // = (p0_lo ) + 2^32 (Q ) + 2^64 (H ) |
92 | // = (p0_lo ) + 2^32 (Q_lo + 2^32 Q_hi ) + 2^64 (H ) |
93 | // |
94 | // (Since Q might be larger than 2^32 - 1) |
95 | // |
96 | // = (p0_lo + 2^32 Q_lo) + 2^64 (Q_hi + H) |
97 | // |
98 | // (Q_hi + H does not overflow a 64-bit int) |
99 | // |
100 | // = p_lo + 2^64 p_hi |
101 | |
102 | const std::uint64_t u_lo = x.f & 0xFFFFFFFFu; |
103 | const std::uint64_t u_hi = x.f >> 32u; |
104 | const std::uint64_t v_lo = y.f & 0xFFFFFFFFu; |
105 | const std::uint64_t v_hi = y.f >> 32u; |
106 | |
107 | const std::uint64_t p0 = u_lo * v_lo; |
108 | const std::uint64_t p1 = u_lo * v_hi; |
109 | const std::uint64_t p2 = u_hi * v_lo; |
110 | const std::uint64_t p3 = u_hi * v_hi; |
111 | |
112 | const std::uint64_t p0_hi = p0 >> 32u; |
113 | const std::uint64_t p1_lo = p1 & 0xFFFFFFFFu; |
114 | const std::uint64_t p1_hi = p1 >> 32u; |
115 | const std::uint64_t p2_lo = p2 & 0xFFFFFFFFu; |
116 | const std::uint64_t p2_hi = p2 >> 32u; |
117 | |
118 | std::uint64_t Q = p0_hi + p1_lo + p2_lo; |
119 | |
120 | // The full product might now be computed as |
121 | // |
122 | // p_hi = p3 + p2_hi + p1_hi + (Q >> 32) |
123 | // p_lo = p0_lo + (Q << 32) |
124 | // |
125 | // But in this particular case here, the full p_lo is not required. |
126 | // Effectively we only need to add the highest bit in p_lo to p_hi (and |
127 | // Q_hi + 1 does not overflow). |
128 | |
129 | Q += std::uint64_t{1} << (64u - 32u - 1u); // round, ties up |
130 | |
131 | const std::uint64_t h = p3 + p2_hi + p1_hi + (Q >> 32u); |
132 | |
133 | return {h, x.e + y.e + 64}; |
134 | } |
135 | |
136 | /*! |
137 | @brief normalize x such that the significand is >= 2^(q-1) |
138 | @pre x.f != 0 |
139 | */ |
140 | static diyfp normalize(diyfp x) noexcept |
141 | { |
142 | assert(x.f != 0); |
143 | |
144 | while ((x.f >> 63u) == 0) |
145 | { |
146 | x.f <<= 1u; |
147 | x.e--; |
148 | } |
149 | |
150 | return x; |
151 | } |
152 | |
153 | /*! |
154 | @brief normalize x such that the result has the exponent E |
155 | @pre e >= x.e and the upper e - x.e bits of x.f must be zero. |
156 | */ |
157 | static diyfp normalize_to(const diyfp& x, const int target_exponent) noexcept |
158 | { |
159 | const int delta = x.e - target_exponent; |
160 | |
161 | assert(delta >= 0); |
162 | assert(((x.f << delta) >> delta) == x.f); |
163 | |
164 | return {x.f << delta, target_exponent}; |
165 | } |
166 | }; |
167 | |
168 | struct boundaries |
169 | { |
170 | diyfp w; |
171 | diyfp minus; |
172 | diyfp plus; |
173 | }; |
174 | |
175 | /*! |
176 | Compute the (normalized) diyfp representing the input number 'value' and its |
177 | boundaries. |
178 | |
179 | @pre value must be finite and positive |
180 | */ |
181 | template <typename FloatType> |
182 | boundaries compute_boundaries(FloatType value) |
183 | { |
184 | assert(std::isfinite(value)); |
185 | assert(value > 0); |
186 | |
187 | // Convert the IEEE representation into a diyfp. |
188 | // |
189 | // If v is denormal: |
190 | // value = 0.F * 2^(1 - bias) = ( F) * 2^(1 - bias - (p-1)) |
191 | // If v is normalized: |
192 | // value = 1.F * 2^(E - bias) = (2^(p-1) + F) * 2^(E - bias - (p-1)) |
193 | |
194 | static_assert(std::numeric_limits<FloatType>::is_iec559, |
195 | "internal error: dtoa_short requires an IEEE-754 floating-point implementation" ); |
196 | |
197 | constexpr int kPrecision = std::numeric_limits<FloatType>::digits; // = p (includes the hidden bit) |
198 | constexpr int kBias = std::numeric_limits<FloatType>::max_exponent - 1 + (kPrecision - 1); |
199 | constexpr int kMinExp = 1 - kBias; |
200 | constexpr std::uint64_t kHiddenBit = std::uint64_t{1} << (kPrecision - 1); // = 2^(p-1) |
201 | |
202 | using bits_type = typename std::conditional<kPrecision == 24, std::uint32_t, std::uint64_t >::type; |
203 | |
204 | const std::uint64_t bits = reinterpret_bits<bits_type>(value); |
205 | const std::uint64_t E = bits >> (kPrecision - 1); |
206 | const std::uint64_t F = bits & (kHiddenBit - 1); |
207 | |
208 | const bool is_denormal = E == 0; |
209 | const diyfp v = is_denormal |
210 | ? diyfp(F, kMinExp) |
211 | : diyfp(F + kHiddenBit, static_cast<int>(E) - kBias); |
212 | |
213 | // Compute the boundaries m- and m+ of the floating-point value |
214 | // v = f * 2^e. |
215 | // |
216 | // Determine v- and v+, the floating-point predecessor and successor if v, |
217 | // respectively. |
218 | // |
219 | // v- = v - 2^e if f != 2^(p-1) or e == e_min (A) |
220 | // = v - 2^(e-1) if f == 2^(p-1) and e > e_min (B) |
221 | // |
222 | // v+ = v + 2^e |
223 | // |
224 | // Let m- = (v- + v) / 2 and m+ = (v + v+) / 2. All real numbers _strictly_ |
225 | // between m- and m+ round to v, regardless of how the input rounding |
226 | // algorithm breaks ties. |
227 | // |
228 | // ---+-------------+-------------+-------------+-------------+--- (A) |
229 | // v- m- v m+ v+ |
230 | // |
231 | // -----------------+------+------+-------------+-------------+--- (B) |
232 | // v- m- v m+ v+ |
233 | |
234 | const bool lower_boundary_is_closer = F == 0 and E > 1; |
235 | const diyfp m_plus = diyfp(2 * v.f + 1, v.e - 1); |
236 | const diyfp m_minus = lower_boundary_is_closer |
237 | ? diyfp(4 * v.f - 1, v.e - 2) // (B) |
238 | : diyfp(2 * v.f - 1, v.e - 1); // (A) |
239 | |
240 | // Determine the normalized w+ = m+. |
241 | const diyfp w_plus = diyfp::normalize(m_plus); |
242 | |
243 | // Determine w- = m- such that e_(w-) = e_(w+). |
244 | const diyfp w_minus = diyfp::normalize_to(m_minus, w_plus.e); |
245 | |
246 | return {diyfp::normalize(v), w_minus, w_plus}; |
247 | } |
248 | |
249 | // Given normalized diyfp w, Grisu needs to find a (normalized) cached |
250 | // power-of-ten c, such that the exponent of the product c * w = f * 2^e lies |
251 | // within a certain range [alpha, gamma] (Definition 3.2 from [1]) |
252 | // |
253 | // alpha <= e = e_c + e_w + q <= gamma |
254 | // |
255 | // or |
256 | // |
257 | // f_c * f_w * 2^alpha <= f_c 2^(e_c) * f_w 2^(e_w) * 2^q |
258 | // <= f_c * f_w * 2^gamma |
259 | // |
260 | // Since c and w are normalized, i.e. 2^(q-1) <= f < 2^q, this implies |
261 | // |
262 | // 2^(q-1) * 2^(q-1) * 2^alpha <= c * w * 2^q < 2^q * 2^q * 2^gamma |
263 | // |
264 | // or |
265 | // |
266 | // 2^(q - 2 + alpha) <= c * w < 2^(q + gamma) |
267 | // |
268 | // The choice of (alpha,gamma) determines the size of the table and the form of |
269 | // the digit generation procedure. Using (alpha,gamma)=(-60,-32) works out well |
270 | // in practice: |
271 | // |
272 | // The idea is to cut the number c * w = f * 2^e into two parts, which can be |
273 | // processed independently: An integral part p1, and a fractional part p2: |
274 | // |
275 | // f * 2^e = ( (f div 2^-e) * 2^-e + (f mod 2^-e) ) * 2^e |
276 | // = (f div 2^-e) + (f mod 2^-e) * 2^e |
277 | // = p1 + p2 * 2^e |
278 | // |
279 | // The conversion of p1 into decimal form requires a series of divisions and |
280 | // modulos by (a power of) 10. These operations are faster for 32-bit than for |
281 | // 64-bit integers, so p1 should ideally fit into a 32-bit integer. This can be |
282 | // achieved by choosing |
283 | // |
284 | // -e >= 32 or e <= -32 := gamma |
285 | // |
286 | // In order to convert the fractional part |
287 | // |
288 | // p2 * 2^e = p2 / 2^-e = d[-1] / 10^1 + d[-2] / 10^2 + ... |
289 | // |
290 | // into decimal form, the fraction is repeatedly multiplied by 10 and the digits |
291 | // d[-i] are extracted in order: |
292 | // |
293 | // (10 * p2) div 2^-e = d[-1] |
294 | // (10 * p2) mod 2^-e = d[-2] / 10^1 + ... |
295 | // |
296 | // The multiplication by 10 must not overflow. It is sufficient to choose |
297 | // |
298 | // 10 * p2 < 16 * p2 = 2^4 * p2 <= 2^64. |
299 | // |
300 | // Since p2 = f mod 2^-e < 2^-e, |
301 | // |
302 | // -e <= 60 or e >= -60 := alpha |
303 | |
304 | constexpr int kAlpha = -60; |
305 | constexpr int kGamma = -32; |
306 | |
307 | struct cached_power // c = f * 2^e ~= 10^k |
308 | { |
309 | std::uint64_t f; |
310 | int e; |
311 | int k; |
312 | }; |
313 | |
314 | /*! |
315 | For a normalized diyfp w = f * 2^e, this function returns a (normalized) cached |
316 | power-of-ten c = f_c * 2^e_c, such that the exponent of the product w * c |
317 | satisfies (Definition 3.2 from [1]) |
318 | |
319 | alpha <= e_c + e + q <= gamma. |
320 | */ |
321 | inline cached_power get_cached_power_for_binary_exponent(int e) |
322 | { |
323 | // Now |
324 | // |
325 | // alpha <= e_c + e + q <= gamma (1) |
326 | // ==> f_c * 2^alpha <= c * 2^e * 2^q |
327 | // |
328 | // and since the c's are normalized, 2^(q-1) <= f_c, |
329 | // |
330 | // ==> 2^(q - 1 + alpha) <= c * 2^(e + q) |
331 | // ==> 2^(alpha - e - 1) <= c |
332 | // |
333 | // If c were an exact power of ten, i.e. c = 10^k, one may determine k as |
334 | // |
335 | // k = ceil( log_10( 2^(alpha - e - 1) ) ) |
336 | // = ceil( (alpha - e - 1) * log_10(2) ) |
337 | // |
338 | // From the paper: |
339 | // "In theory the result of the procedure could be wrong since c is rounded, |
340 | // and the computation itself is approximated [...]. In practice, however, |
341 | // this simple function is sufficient." |
342 | // |
343 | // For IEEE double precision floating-point numbers converted into |
344 | // normalized diyfp's w = f * 2^e, with q = 64, |
345 | // |
346 | // e >= -1022 (min IEEE exponent) |
347 | // -52 (p - 1) |
348 | // -52 (p - 1, possibly normalize denormal IEEE numbers) |
349 | // -11 (normalize the diyfp) |
350 | // = -1137 |
351 | // |
352 | // and |
353 | // |
354 | // e <= +1023 (max IEEE exponent) |
355 | // -52 (p - 1) |
356 | // -11 (normalize the diyfp) |
357 | // = 960 |
358 | // |
359 | // This binary exponent range [-1137,960] results in a decimal exponent |
360 | // range [-307,324]. One does not need to store a cached power for each |
361 | // k in this range. For each such k it suffices to find a cached power |
362 | // such that the exponent of the product lies in [alpha,gamma]. |
363 | // This implies that the difference of the decimal exponents of adjacent |
364 | // table entries must be less than or equal to |
365 | // |
366 | // floor( (gamma - alpha) * log_10(2) ) = 8. |
367 | // |
368 | // (A smaller distance gamma-alpha would require a larger table.) |
369 | |
370 | // NB: |
371 | // Actually this function returns c, such that -60 <= e_c + e + 64 <= -34. |
372 | |
373 | constexpr int kCachedPowersMinDecExp = -300; |
374 | constexpr int kCachedPowersDecStep = 8; |
375 | |
376 | static constexpr std::array<cached_power, 79> kCachedPowers = |
377 | { |
378 | { |
379 | { 0xAB70FE17C79AC6CA, -1060, -300 }, |
380 | { 0xFF77B1FCBEBCDC4F, -1034, -292 }, |
381 | { 0xBE5691EF416BD60C, -1007, -284 }, |
382 | { 0x8DD01FAD907FFC3C, -980, -276 }, |
383 | { 0xD3515C2831559A83, -954, -268 }, |
384 | { 0x9D71AC8FADA6C9B5, -927, -260 }, |
385 | { 0xEA9C227723EE8BCB, -901, -252 }, |
386 | { 0xAECC49914078536D, -874, -244 }, |
387 | { 0x823C12795DB6CE57, -847, -236 }, |
388 | { 0xC21094364DFB5637, -821, -228 }, |
389 | { 0x9096EA6F3848984F, -794, -220 }, |
390 | { 0xD77485CB25823AC7, -768, -212 }, |
391 | { 0xA086CFCD97BF97F4, -741, -204 }, |
392 | { 0xEF340A98172AACE5, -715, -196 }, |
393 | { 0xB23867FB2A35B28E, -688, -188 }, |
394 | { 0x84C8D4DFD2C63F3B, -661, -180 }, |
395 | { 0xC5DD44271AD3CDBA, -635, -172 }, |
396 | { 0x936B9FCEBB25C996, -608, -164 }, |
397 | { 0xDBAC6C247D62A584, -582, -156 }, |
398 | { 0xA3AB66580D5FDAF6, -555, -148 }, |
399 | { 0xF3E2F893DEC3F126, -529, -140 }, |
400 | { 0xB5B5ADA8AAFF80B8, -502, -132 }, |
401 | { 0x87625F056C7C4A8B, -475, -124 }, |
402 | { 0xC9BCFF6034C13053, -449, -116 }, |
403 | { 0x964E858C91BA2655, -422, -108 }, |
404 | { 0xDFF9772470297EBD, -396, -100 }, |
405 | { 0xA6DFBD9FB8E5B88F, -369, -92 }, |
406 | { 0xF8A95FCF88747D94, -343, -84 }, |
407 | { 0xB94470938FA89BCF, -316, -76 }, |
408 | { 0x8A08F0F8BF0F156B, -289, -68 }, |
409 | { 0xCDB02555653131B6, -263, -60 }, |
410 | { 0x993FE2C6D07B7FAC, -236, -52 }, |
411 | { 0xE45C10C42A2B3B06, -210, -44 }, |
412 | { 0xAA242499697392D3, -183, -36 }, |
413 | { 0xFD87B5F28300CA0E, -157, -28 }, |
414 | { 0xBCE5086492111AEB, -130, -20 }, |
415 | { 0x8CBCCC096F5088CC, -103, -12 }, |
416 | { 0xD1B71758E219652C, -77, -4 }, |
417 | { 0x9C40000000000000, -50, 4 }, |
418 | { 0xE8D4A51000000000, -24, 12 }, |
419 | { 0xAD78EBC5AC620000, 3, 20 }, |
420 | { 0x813F3978F8940984, 30, 28 }, |
421 | { 0xC097CE7BC90715B3, 56, 36 }, |
422 | { 0x8F7E32CE7BEA5C70, 83, 44 }, |
423 | { 0xD5D238A4ABE98068, 109, 52 }, |
424 | { 0x9F4F2726179A2245, 136, 60 }, |
425 | { 0xED63A231D4C4FB27, 162, 68 }, |
426 | { 0xB0DE65388CC8ADA8, 189, 76 }, |
427 | { 0x83C7088E1AAB65DB, 216, 84 }, |
428 | { 0xC45D1DF942711D9A, 242, 92 }, |
429 | { 0x924D692CA61BE758, 269, 100 }, |
430 | { 0xDA01EE641A708DEA, 295, 108 }, |
431 | { 0xA26DA3999AEF774A, 322, 116 }, |
432 | { 0xF209787BB47D6B85, 348, 124 }, |
433 | { 0xB454E4A179DD1877, 375, 132 }, |
434 | { 0x865B86925B9BC5C2, 402, 140 }, |
435 | { 0xC83553C5C8965D3D, 428, 148 }, |
436 | { 0x952AB45CFA97A0B3, 455, 156 }, |
437 | { 0xDE469FBD99A05FE3, 481, 164 }, |
438 | { 0xA59BC234DB398C25, 508, 172 }, |
439 | { 0xF6C69A72A3989F5C, 534, 180 }, |
440 | { 0xB7DCBF5354E9BECE, 561, 188 }, |
441 | { 0x88FCF317F22241E2, 588, 196 }, |
442 | { 0xCC20CE9BD35C78A5, 614, 204 }, |
443 | { 0x98165AF37B2153DF, 641, 212 }, |
444 | { 0xE2A0B5DC971F303A, 667, 220 }, |
445 | { 0xA8D9D1535CE3B396, 694, 228 }, |
446 | { 0xFB9B7CD9A4A7443C, 720, 236 }, |
447 | { 0xBB764C4CA7A44410, 747, 244 }, |
448 | { 0x8BAB8EEFB6409C1A, 774, 252 }, |
449 | { 0xD01FEF10A657842C, 800, 260 }, |
450 | { 0x9B10A4E5E9913129, 827, 268 }, |
451 | { 0xE7109BFBA19C0C9D, 853, 276 }, |
452 | { 0xAC2820D9623BF429, 880, 284 }, |
453 | { 0x80444B5E7AA7CF85, 907, 292 }, |
454 | { 0xBF21E44003ACDD2D, 933, 300 }, |
455 | { 0x8E679C2F5E44FF8F, 960, 308 }, |
456 | { 0xD433179D9C8CB841, 986, 316 }, |
457 | { 0x9E19DB92B4E31BA9, 1013, 324 }, |
458 | } |
459 | }; |
460 | |
461 | // This computation gives exactly the same results for k as |
462 | // k = ceil((kAlpha - e - 1) * 0.30102999566398114) |
463 | // for |e| <= 1500, but doesn't require floating-point operations. |
464 | // NB: log_10(2) ~= 78913 / 2^18 |
465 | assert(e >= -1500); |
466 | assert(e <= 1500); |
467 | const int f = kAlpha - e - 1; |
468 | const int k = (f * 78913) / (1 << 18) + static_cast<int>(f > 0); |
469 | |
470 | const int index = (-kCachedPowersMinDecExp + k + (kCachedPowersDecStep - 1)) / kCachedPowersDecStep; |
471 | assert(index >= 0); |
472 | assert(static_cast<std::size_t>(index) < kCachedPowers.size()); |
473 | |
474 | const cached_power cached = kCachedPowers[static_cast<std::size_t>(index)]; |
475 | assert(kAlpha <= cached.e + e + 64); |
476 | assert(kGamma >= cached.e + e + 64); |
477 | |
478 | return cached; |
479 | } |
480 | |
481 | /*! |
482 | For n != 0, returns k, such that pow10 := 10^(k-1) <= n < 10^k. |
483 | For n == 0, returns 1 and sets pow10 := 1. |
484 | */ |
485 | inline int find_largest_pow10(const std::uint32_t n, std::uint32_t& pow10) |
486 | { |
487 | // LCOV_EXCL_START |
488 | if (n >= 1000000000) |
489 | { |
490 | pow10 = 1000000000; |
491 | return 10; |
492 | } |
493 | // LCOV_EXCL_STOP |
494 | else if (n >= 100000000) |
495 | { |
496 | pow10 = 100000000; |
497 | return 9; |
498 | } |
499 | else if (n >= 10000000) |
500 | { |
501 | pow10 = 10000000; |
502 | return 8; |
503 | } |
504 | else if (n >= 1000000) |
505 | { |
506 | pow10 = 1000000; |
507 | return 7; |
508 | } |
509 | else if (n >= 100000) |
510 | { |
511 | pow10 = 100000; |
512 | return 6; |
513 | } |
514 | else if (n >= 10000) |
515 | { |
516 | pow10 = 10000; |
517 | return 5; |
518 | } |
519 | else if (n >= 1000) |
520 | { |
521 | pow10 = 1000; |
522 | return 4; |
523 | } |
524 | else if (n >= 100) |
525 | { |
526 | pow10 = 100; |
527 | return 3; |
528 | } |
529 | else if (n >= 10) |
530 | { |
531 | pow10 = 10; |
532 | return 2; |
533 | } |
534 | else |
535 | { |
536 | pow10 = 1; |
537 | return 1; |
538 | } |
539 | } |
540 | |
541 | inline void grisu2_round(char* buf, int len, std::uint64_t dist, std::uint64_t delta, |
542 | std::uint64_t rest, std::uint64_t ten_k) |
543 | { |
544 | assert(len >= 1); |
545 | assert(dist <= delta); |
546 | assert(rest <= delta); |
547 | assert(ten_k > 0); |
548 | |
549 | // <--------------------------- delta ----> |
550 | // <---- dist ---------> |
551 | // --------------[------------------+-------------------]-------------- |
552 | // M- w M+ |
553 | // |
554 | // ten_k |
555 | // <------> |
556 | // <---- rest ----> |
557 | // --------------[------------------+----+--------------]-------------- |
558 | // w V |
559 | // = buf * 10^k |
560 | // |
561 | // ten_k represents a unit-in-the-last-place in the decimal representation |
562 | // stored in buf. |
563 | // Decrement buf by ten_k while this takes buf closer to w. |
564 | |
565 | // The tests are written in this order to avoid overflow in unsigned |
566 | // integer arithmetic. |
567 | |
568 | while (rest < dist |
569 | and delta - rest >= ten_k |
570 | and (rest + ten_k < dist or dist - rest > rest + ten_k - dist)) |
571 | { |
572 | assert(buf[len - 1] != '0'); |
573 | buf[len - 1]--; |
574 | rest += ten_k; |
575 | } |
576 | } |
577 | |
578 | /*! |
579 | Generates V = buffer * 10^decimal_exponent, such that M- <= V <= M+. |
580 | M- and M+ must be normalized and share the same exponent -60 <= e <= -32. |
581 | */ |
582 | inline void grisu2_digit_gen(char* buffer, int& length, int& decimal_exponent, |
583 | diyfp M_minus, diyfp w, diyfp M_plus) |
584 | { |
585 | static_assert(kAlpha >= -60, "internal error" ); |
586 | static_assert(kGamma <= -32, "internal error" ); |
587 | |
588 | // Generates the digits (and the exponent) of a decimal floating-point |
589 | // number V = buffer * 10^decimal_exponent in the range [M-, M+]. The diyfp's |
590 | // w, M- and M+ share the same exponent e, which satisfies alpha <= e <= gamma. |
591 | // |
592 | // <--------------------------- delta ----> |
593 | // <---- dist ---------> |
594 | // --------------[------------------+-------------------]-------------- |
595 | // M- w M+ |
596 | // |
597 | // Grisu2 generates the digits of M+ from left to right and stops as soon as |
598 | // V is in [M-,M+]. |
599 | |
600 | assert(M_plus.e >= kAlpha); |
601 | assert(M_plus.e <= kGamma); |
602 | |
603 | std::uint64_t delta = diyfp::sub(M_plus, M_minus).f; // (significand of (M+ - M-), implicit exponent is e) |
604 | std::uint64_t dist = diyfp::sub(M_plus, w ).f; // (significand of (M+ - w ), implicit exponent is e) |
605 | |
606 | // Split M+ = f * 2^e into two parts p1 and p2 (note: e < 0): |
607 | // |
608 | // M+ = f * 2^e |
609 | // = ((f div 2^-e) * 2^-e + (f mod 2^-e)) * 2^e |
610 | // = ((p1 ) * 2^-e + (p2 )) * 2^e |
611 | // = p1 + p2 * 2^e |
612 | |
613 | const diyfp one(std::uint64_t{1} << -M_plus.e, M_plus.e); |
614 | |
615 | auto p1 = static_cast<std::uint32_t>(M_plus.f >> -one.e); // p1 = f div 2^-e (Since -e >= 32, p1 fits into a 32-bit int.) |
616 | std::uint64_t p2 = M_plus.f & (one.f - 1); // p2 = f mod 2^-e |
617 | |
618 | // 1) |
619 | // |
620 | // Generate the digits of the integral part p1 = d[n-1]...d[1]d[0] |
621 | |
622 | assert(p1 > 0); |
623 | |
624 | std::uint32_t pow10; |
625 | const int k = find_largest_pow10(p1, pow10); |
626 | |
627 | // 10^(k-1) <= p1 < 10^k, pow10 = 10^(k-1) |
628 | // |
629 | // p1 = (p1 div 10^(k-1)) * 10^(k-1) + (p1 mod 10^(k-1)) |
630 | // = (d[k-1] ) * 10^(k-1) + (p1 mod 10^(k-1)) |
631 | // |
632 | // M+ = p1 + p2 * 2^e |
633 | // = d[k-1] * 10^(k-1) + (p1 mod 10^(k-1)) + p2 * 2^e |
634 | // = d[k-1] * 10^(k-1) + ((p1 mod 10^(k-1)) * 2^-e + p2) * 2^e |
635 | // = d[k-1] * 10^(k-1) + ( rest) * 2^e |
636 | // |
637 | // Now generate the digits d[n] of p1 from left to right (n = k-1,...,0) |
638 | // |
639 | // p1 = d[k-1]...d[n] * 10^n + d[n-1]...d[0] |
640 | // |
641 | // but stop as soon as |
642 | // |
643 | // rest * 2^e = (d[n-1]...d[0] * 2^-e + p2) * 2^e <= delta * 2^e |
644 | |
645 | int n = k; |
646 | while (n > 0) |
647 | { |
648 | // Invariants: |
649 | // M+ = buffer * 10^n + (p1 + p2 * 2^e) (buffer = 0 for n = k) |
650 | // pow10 = 10^(n-1) <= p1 < 10^n |
651 | // |
652 | const std::uint32_t d = p1 / pow10; // d = p1 div 10^(n-1) |
653 | const std::uint32_t r = p1 % pow10; // r = p1 mod 10^(n-1) |
654 | // |
655 | // M+ = buffer * 10^n + (d * 10^(n-1) + r) + p2 * 2^e |
656 | // = (buffer * 10 + d) * 10^(n-1) + (r + p2 * 2^e) |
657 | // |
658 | assert(d <= 9); |
659 | buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d |
660 | // |
661 | // M+ = buffer * 10^(n-1) + (r + p2 * 2^e) |
662 | // |
663 | p1 = r; |
664 | n--; |
665 | // |
666 | // M+ = buffer * 10^n + (p1 + p2 * 2^e) |
667 | // pow10 = 10^n |
668 | // |
669 | |
670 | // Now check if enough digits have been generated. |
671 | // Compute |
672 | // |
673 | // p1 + p2 * 2^e = (p1 * 2^-e + p2) * 2^e = rest * 2^e |
674 | // |
675 | // Note: |
676 | // Since rest and delta share the same exponent e, it suffices to |
677 | // compare the significands. |
678 | const std::uint64_t rest = (std::uint64_t{p1} << -one.e) + p2; |
679 | if (rest <= delta) |
680 | { |
681 | // V = buffer * 10^n, with M- <= V <= M+. |
682 | |
683 | decimal_exponent += n; |
684 | |
685 | // We may now just stop. But instead look if the buffer could be |
686 | // decremented to bring V closer to w. |
687 | // |
688 | // pow10 = 10^n is now 1 ulp in the decimal representation V. |
689 | // The rounding procedure works with diyfp's with an implicit |
690 | // exponent of e. |
691 | // |
692 | // 10^n = (10^n * 2^-e) * 2^e = ulp * 2^e |
693 | // |
694 | const std::uint64_t ten_n = std::uint64_t{pow10} << -one.e; |
695 | grisu2_round(buffer, length, dist, delta, rest, ten_n); |
696 | |
697 | return; |
698 | } |
699 | |
700 | pow10 /= 10; |
701 | // |
702 | // pow10 = 10^(n-1) <= p1 < 10^n |
703 | // Invariants restored. |
704 | } |
705 | |
706 | // 2) |
707 | // |
708 | // The digits of the integral part have been generated: |
709 | // |
710 | // M+ = d[k-1]...d[1]d[0] + p2 * 2^e |
711 | // = buffer + p2 * 2^e |
712 | // |
713 | // Now generate the digits of the fractional part p2 * 2^e. |
714 | // |
715 | // Note: |
716 | // No decimal point is generated: the exponent is adjusted instead. |
717 | // |
718 | // p2 actually represents the fraction |
719 | // |
720 | // p2 * 2^e |
721 | // = p2 / 2^-e |
722 | // = d[-1] / 10^1 + d[-2] / 10^2 + ... |
723 | // |
724 | // Now generate the digits d[-m] of p1 from left to right (m = 1,2,...) |
725 | // |
726 | // p2 * 2^e = d[-1]d[-2]...d[-m] * 10^-m |
727 | // + 10^-m * (d[-m-1] / 10^1 + d[-m-2] / 10^2 + ...) |
728 | // |
729 | // using |
730 | // |
731 | // 10^m * p2 = ((10^m * p2) div 2^-e) * 2^-e + ((10^m * p2) mod 2^-e) |
732 | // = ( d) * 2^-e + ( r) |
733 | // |
734 | // or |
735 | // 10^m * p2 * 2^e = d + r * 2^e |
736 | // |
737 | // i.e. |
738 | // |
739 | // M+ = buffer + p2 * 2^e |
740 | // = buffer + 10^-m * (d + r * 2^e) |
741 | // = (buffer * 10^m + d) * 10^-m + 10^-m * r * 2^e |
742 | // |
743 | // and stop as soon as 10^-m * r * 2^e <= delta * 2^e |
744 | |
745 | assert(p2 > delta); |
746 | |
747 | int m = 0; |
748 | for (;;) |
749 | { |
750 | // Invariant: |
751 | // M+ = buffer * 10^-m + 10^-m * (d[-m-1] / 10 + d[-m-2] / 10^2 + ...) * 2^e |
752 | // = buffer * 10^-m + 10^-m * (p2 ) * 2^e |
753 | // = buffer * 10^-m + 10^-m * (1/10 * (10 * p2) ) * 2^e |
754 | // = buffer * 10^-m + 10^-m * (1/10 * ((10*p2 div 2^-e) * 2^-e + (10*p2 mod 2^-e)) * 2^e |
755 | // |
756 | assert(p2 <= (std::numeric_limits<std::uint64_t>::max)() / 10); |
757 | p2 *= 10; |
758 | const std::uint64_t d = p2 >> -one.e; // d = (10 * p2) div 2^-e |
759 | const std::uint64_t r = p2 & (one.f - 1); // r = (10 * p2) mod 2^-e |
760 | // |
761 | // M+ = buffer * 10^-m + 10^-m * (1/10 * (d * 2^-e + r) * 2^e |
762 | // = buffer * 10^-m + 10^-m * (1/10 * (d + r * 2^e)) |
763 | // = (buffer * 10 + d) * 10^(-m-1) + 10^(-m-1) * r * 2^e |
764 | // |
765 | assert(d <= 9); |
766 | buffer[length++] = static_cast<char>('0' + d); // buffer := buffer * 10 + d |
767 | // |
768 | // M+ = buffer * 10^(-m-1) + 10^(-m-1) * r * 2^e |
769 | // |
770 | p2 = r; |
771 | m++; |
772 | // |
773 | // M+ = buffer * 10^-m + 10^-m * p2 * 2^e |
774 | // Invariant restored. |
775 | |
776 | // Check if enough digits have been generated. |
777 | // |
778 | // 10^-m * p2 * 2^e <= delta * 2^e |
779 | // p2 * 2^e <= 10^m * delta * 2^e |
780 | // p2 <= 10^m * delta |
781 | delta *= 10; |
782 | dist *= 10; |
783 | if (p2 <= delta) |
784 | { |
785 | break; |
786 | } |
787 | } |
788 | |
789 | // V = buffer * 10^-m, with M- <= V <= M+. |
790 | |
791 | decimal_exponent -= m; |
792 | |
793 | // 1 ulp in the decimal representation is now 10^-m. |
794 | // Since delta and dist are now scaled by 10^m, we need to do the |
795 | // same with ulp in order to keep the units in sync. |
796 | // |
797 | // 10^m * 10^-m = 1 = 2^-e * 2^e = ten_m * 2^e |
798 | // |
799 | const std::uint64_t ten_m = one.f; |
800 | grisu2_round(buffer, length, dist, delta, p2, ten_m); |
801 | |
802 | // By construction this algorithm generates the shortest possible decimal |
803 | // number (Loitsch, Theorem 6.2) which rounds back to w. |
804 | // For an input number of precision p, at least |
805 | // |
806 | // N = 1 + ceil(p * log_10(2)) |
807 | // |
808 | // decimal digits are sufficient to identify all binary floating-point |
809 | // numbers (Matula, "In-and-Out conversions"). |
810 | // This implies that the algorithm does not produce more than N decimal |
811 | // digits. |
812 | // |
813 | // N = 17 for p = 53 (IEEE double precision) |
814 | // N = 9 for p = 24 (IEEE single precision) |
815 | } |
816 | |
817 | /*! |
818 | v = buf * 10^decimal_exponent |
819 | len is the length of the buffer (number of decimal digits) |
820 | The buffer must be large enough, i.e. >= max_digits10. |
821 | */ |
822 | JSON_HEDLEY_NON_NULL(1) |
823 | inline void grisu2(char* buf, int& len, int& decimal_exponent, |
824 | diyfp m_minus, diyfp v, diyfp m_plus) |
825 | { |
826 | assert(m_plus.e == m_minus.e); |
827 | assert(m_plus.e == v.e); |
828 | |
829 | // --------(-----------------------+-----------------------)-------- (A) |
830 | // m- v m+ |
831 | // |
832 | // --------------------(-----------+-----------------------)-------- (B) |
833 | // m- v m+ |
834 | // |
835 | // First scale v (and m- and m+) such that the exponent is in the range |
836 | // [alpha, gamma]. |
837 | |
838 | const cached_power cached = get_cached_power_for_binary_exponent(m_plus.e); |
839 | |
840 | const diyfp c_minus_k(cached.f, cached.e); // = c ~= 10^-k |
841 | |
842 | // The exponent of the products is = v.e + c_minus_k.e + q and is in the range [alpha,gamma] |
843 | const diyfp w = diyfp::mul(v, c_minus_k); |
844 | const diyfp w_minus = diyfp::mul(m_minus, c_minus_k); |
845 | const diyfp w_plus = diyfp::mul(m_plus, c_minus_k); |
846 | |
847 | // ----(---+---)---------------(---+---)---------------(---+---)---- |
848 | // w- w w+ |
849 | // = c*m- = c*v = c*m+ |
850 | // |
851 | // diyfp::mul rounds its result and c_minus_k is approximated too. w, w- and |
852 | // w+ are now off by a small amount. |
853 | // In fact: |
854 | // |
855 | // w - v * 10^k < 1 ulp |
856 | // |
857 | // To account for this inaccuracy, add resp. subtract 1 ulp. |
858 | // |
859 | // --------+---[---------------(---+---)---------------]---+-------- |
860 | // w- M- w M+ w+ |
861 | // |
862 | // Now any number in [M-, M+] (bounds included) will round to w when input, |
863 | // regardless of how the input rounding algorithm breaks ties. |
864 | // |
865 | // And digit_gen generates the shortest possible such number in [M-, M+]. |
866 | // Note that this does not mean that Grisu2 always generates the shortest |
867 | // possible number in the interval (m-, m+). |
868 | const diyfp M_minus(w_minus.f + 1, w_minus.e); |
869 | const diyfp M_plus (w_plus.f - 1, w_plus.e ); |
870 | |
871 | decimal_exponent = -cached.k; // = -(-k) = k |
872 | |
873 | grisu2_digit_gen(buf, len, decimal_exponent, M_minus, w, M_plus); |
874 | } |
875 | |
876 | /*! |
877 | v = buf * 10^decimal_exponent |
878 | len is the length of the buffer (number of decimal digits) |
879 | The buffer must be large enough, i.e. >= max_digits10. |
880 | */ |
881 | template <typename FloatType> |
882 | JSON_HEDLEY_NON_NULL(1) |
883 | void grisu2(char* buf, int& len, int& decimal_exponent, FloatType value) |
884 | { |
885 | static_assert(diyfp::kPrecision >= std::numeric_limits<FloatType>::digits + 3, |
886 | "internal error: not enough precision" ); |
887 | |
888 | assert(std::isfinite(value)); |
889 | assert(value > 0); |
890 | |
891 | // If the neighbors (and boundaries) of 'value' are always computed for double-precision |
892 | // numbers, all float's can be recovered using strtod (and strtof). However, the resulting |
893 | // decimal representations are not exactly "short". |
894 | // |
895 | // The documentation for 'std::to_chars' (https://en.cppreference.com/w/cpp/utility/to_chars) |
896 | // says "value is converted to a string as if by std::sprintf in the default ("C") locale" |
897 | // and since sprintf promotes float's to double's, I think this is exactly what 'std::to_chars' |
898 | // does. |
899 | // On the other hand, the documentation for 'std::to_chars' requires that "parsing the |
900 | // representation using the corresponding std::from_chars function recovers value exactly". That |
901 | // indicates that single precision floating-point numbers should be recovered using |
902 | // 'std::strtof'. |
903 | // |
904 | // NB: If the neighbors are computed for single-precision numbers, there is a single float |
905 | // (7.0385307e-26f) which can't be recovered using strtod. The resulting double precision |
906 | // value is off by 1 ulp. |
907 | #if 0 |
908 | const boundaries w = compute_boundaries(static_cast<double>(value)); |
909 | #else |
910 | const boundaries w = compute_boundaries(value); |
911 | #endif |
912 | |
913 | grisu2(buf, len, decimal_exponent, w.minus, w.w, w.plus); |
914 | } |
915 | |
916 | /*! |
917 | @brief appends a decimal representation of e to buf |
918 | @return a pointer to the element following the exponent. |
919 | @pre -1000 < e < 1000 |
920 | */ |
921 | JSON_HEDLEY_NON_NULL(1) |
922 | JSON_HEDLEY_RETURNS_NON_NULL |
923 | inline char* append_exponent(char* buf, int e) |
924 | { |
925 | assert(e > -1000); |
926 | assert(e < 1000); |
927 | |
928 | if (e < 0) |
929 | { |
930 | e = -e; |
931 | *buf++ = '-'; |
932 | } |
933 | else |
934 | { |
935 | *buf++ = '+'; |
936 | } |
937 | |
938 | auto k = static_cast<std::uint32_t>(e); |
939 | if (k < 10) |
940 | { |
941 | // Always print at least two digits in the exponent. |
942 | // This is for compatibility with printf("%g"). |
943 | *buf++ = '0'; |
944 | *buf++ = static_cast<char>('0' + k); |
945 | } |
946 | else if (k < 100) |
947 | { |
948 | *buf++ = static_cast<char>('0' + k / 10); |
949 | k %= 10; |
950 | *buf++ = static_cast<char>('0' + k); |
951 | } |
952 | else |
953 | { |
954 | *buf++ = static_cast<char>('0' + k / 100); |
955 | k %= 100; |
956 | *buf++ = static_cast<char>('0' + k / 10); |
957 | k %= 10; |
958 | *buf++ = static_cast<char>('0' + k); |
959 | } |
960 | |
961 | return buf; |
962 | } |
963 | |
964 | /*! |
965 | @brief prettify v = buf * 10^decimal_exponent |
966 | |
967 | If v is in the range [10^min_exp, 10^max_exp) it will be printed in fixed-point |
968 | notation. Otherwise it will be printed in exponential notation. |
969 | |
970 | @pre min_exp < 0 |
971 | @pre max_exp > 0 |
972 | */ |
973 | JSON_HEDLEY_NON_NULL(1) |
974 | JSON_HEDLEY_RETURNS_NON_NULL |
975 | inline char* format_buffer(char* buf, int len, int decimal_exponent, |
976 | int min_exp, int max_exp) |
977 | { |
978 | assert(min_exp < 0); |
979 | assert(max_exp > 0); |
980 | |
981 | const int k = len; |
982 | const int n = len + decimal_exponent; |
983 | |
984 | // v = buf * 10^(n-k) |
985 | // k is the length of the buffer (number of decimal digits) |
986 | // n is the position of the decimal point relative to the start of the buffer. |
987 | |
988 | if (k <= n and n <= max_exp) |
989 | { |
990 | // digits[000] |
991 | // len <= max_exp + 2 |
992 | |
993 | std::memset(buf + k, '0', static_cast<size_t>(n - k)); |
994 | // Make it look like a floating-point number (#362, #378) |
995 | buf[n + 0] = '.'; |
996 | buf[n + 1] = '0'; |
997 | return buf + (n + 2); |
998 | } |
999 | |
1000 | if (0 < n and n <= max_exp) |
1001 | { |
1002 | // dig.its |
1003 | // len <= max_digits10 + 1 |
1004 | |
1005 | assert(k > n); |
1006 | |
1007 | std::memmove(buf + (n + 1), buf + n, static_cast<size_t>(k - n)); |
1008 | buf[n] = '.'; |
1009 | return buf + (k + 1); |
1010 | } |
1011 | |
1012 | if (min_exp < n and n <= 0) |
1013 | { |
1014 | // 0.[000]digits |
1015 | // len <= 2 + (-min_exp - 1) + max_digits10 |
1016 | |
1017 | std::memmove(buf + (2 + -n), buf, static_cast<size_t>(k)); |
1018 | buf[0] = '0'; |
1019 | buf[1] = '.'; |
1020 | std::memset(buf + 2, '0', static_cast<size_t>(-n)); |
1021 | return buf + (2 + (-n) + k); |
1022 | } |
1023 | |
1024 | if (k == 1) |
1025 | { |
1026 | // dE+123 |
1027 | // len <= 1 + 5 |
1028 | |
1029 | buf += 1; |
1030 | } |
1031 | else |
1032 | { |
1033 | // d.igitsE+123 |
1034 | // len <= max_digits10 + 1 + 5 |
1035 | |
1036 | std::memmove(buf + 2, buf + 1, static_cast<size_t>(k - 1)); |
1037 | buf[1] = '.'; |
1038 | buf += 1 + k; |
1039 | } |
1040 | |
1041 | *buf++ = 'e'; |
1042 | return append_exponent(buf, n - 1); |
1043 | } |
1044 | |
1045 | } // namespace dtoa_impl |
1046 | |
1047 | /*! |
1048 | @brief generates a decimal representation of the floating-point number value in [first, last). |
1049 | |
1050 | The format of the resulting decimal representation is similar to printf's %g |
1051 | format. Returns an iterator pointing past-the-end of the decimal representation. |
1052 | |
1053 | @note The input number must be finite, i.e. NaN's and Inf's are not supported. |
1054 | @note The buffer must be large enough. |
1055 | @note The result is NOT null-terminated. |
1056 | */ |
1057 | template <typename FloatType> |
1058 | JSON_HEDLEY_NON_NULL(1, 2) |
1059 | JSON_HEDLEY_RETURNS_NON_NULL |
1060 | char* to_chars(char* first, const char* last, FloatType value) |
1061 | { |
1062 | static_cast<void>(last); // maybe unused - fix warning |
1063 | assert(std::isfinite(value)); |
1064 | |
1065 | // Use signbit(value) instead of (value < 0) since signbit works for -0. |
1066 | if (std::signbit(value)) |
1067 | { |
1068 | value = -value; |
1069 | *first++ = '-'; |
1070 | } |
1071 | |
1072 | if (value == 0) // +-0 |
1073 | { |
1074 | *first++ = '0'; |
1075 | // Make it look like a floating-point number (#362, #378) |
1076 | *first++ = '.'; |
1077 | *first++ = '0'; |
1078 | return first; |
1079 | } |
1080 | |
1081 | assert(last - first >= std::numeric_limits<FloatType>::max_digits10); |
1082 | |
1083 | // Compute v = buffer * 10^decimal_exponent. |
1084 | // The decimal digits are stored in the buffer, which needs to be interpreted |
1085 | // as an unsigned decimal integer. |
1086 | // len is the length of the buffer, i.e. the number of decimal digits. |
1087 | int len = 0; |
1088 | int decimal_exponent = 0; |
1089 | dtoa_impl::grisu2(first, len, decimal_exponent, value); |
1090 | |
1091 | assert(len <= std::numeric_limits<FloatType>::max_digits10); |
1092 | |
1093 | // Format the buffer like printf("%.*g", prec, value) |
1094 | constexpr int kMinExp = -4; |
1095 | // Use digits10 here to increase compatibility with version 2. |
1096 | constexpr int kMaxExp = std::numeric_limits<FloatType>::digits10; |
1097 | |
1098 | assert(last - first >= kMaxExp + 2); |
1099 | assert(last - first >= 2 + (-kMinExp - 1) + std::numeric_limits<FloatType>::max_digits10); |
1100 | assert(last - first >= std::numeric_limits<FloatType>::max_digits10 + 6); |
1101 | |
1102 | return dtoa_impl::format_buffer(first, len, decimal_exponent, kMinExp, kMaxExp); |
1103 | } |
1104 | |
1105 | } // namespace detail |
1106 | } // namespace nlohmann |
1107 | |