TLA Line data Source code
1 : // Copyright 2018 Ulf Adams
2 : //
3 : // The contents of this file may be used under the terms of the Apache License,
4 : // Version 2.0.
5 : //
6 : // (See accompanying file LICENSE-Apache or copy at
7 : // http://www.apache.org/licenses/LICENSE-2.0)
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 : // Runtime compiler options:
19 : // -DRYU_DEBUG Generate verbose debugging output to stdout.
20 : //
21 : // -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
22 : // depending on your compiler.
23 : //
24 : // -DRYU_OPTIMIZE_SIZE Use smaller lookup tables. Instead of storing every
25 : // required power of 5, only store every 26th entry, and compute
26 : // intermediate values with a multiplication. This reduces the lookup table
27 : // size by about 10x (only one case, and only double) at the cost of some
28 : // performance. Currently requires MSVC intrinsics.
29 :
30 : /*
31 : This is a derivative work
32 : */
33 :
34 : #ifndef BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
35 : #define BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
36 :
37 : #include <boost/json/detail/ryu/ryu.hpp>
38 : #include <cstdlib>
39 : #include <cstring>
40 :
41 : #ifdef RYU_DEBUG
42 : #include <stdio.h>
43 : #endif
44 :
45 : // ABSL avoids uint128_t on Win32 even if __SIZEOF_INT128__ is defined.
46 : // Let's do the same for now.
47 : #if defined(__SIZEOF_INT128__) && !defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS)
48 : #define BOOST_JSON_RYU_HAS_UINT128
49 : #elif defined(_MSC_VER) && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
50 : #define BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS
51 : #endif
52 :
53 : #include <boost/json/detail/ryu/detail/common.hpp>
54 : #include <boost/json/detail/ryu/detail/digit_table.hpp>
55 : #include <boost/json/detail/ryu/detail/d2s.hpp>
56 : #include <boost/json/detail/ryu/detail/d2s_intrinsics.hpp>
57 :
58 : namespace boost {
59 : namespace json {
60 : namespace detail {
61 :
62 : namespace ryu {
63 : namespace detail {
64 :
65 : // We need a 64x128-bit multiplication and a subsequent 128-bit shift.
66 : // Multiplication:
67 : // The 64-bit factor is variable and passed in, the 128-bit factor comes
68 : // from a lookup table. We know that the 64-bit factor only has 55
69 : // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
70 : // factor only has 124 significant bits (i.e., the 4 topmost bits are
71 : // zeros).
72 : // Shift:
73 : // In principle, the multiplication result requires 55 + 124 = 179 bits to
74 : // represent. However, we then shift this value to the right by j, which is
75 : // at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
76 : // bits. This means that we only need the topmost 64 significant bits of
77 : // the 64x128-bit multiplication.
78 : //
79 : // There are several ways to do this:
80 : // 1. Best case: the compiler exposes a 128-bit type.
81 : // We perform two 64x64-bit multiplications, add the higher 64 bits of the
82 : // lower result to the higher result, and shift by j - 64 bits.
83 : //
84 : // We explicitly cast from 64-bit to 128-bit, so the compiler can tell
85 : // that these are only 64-bit inputs, and can map these to the best
86 : // possible sequence of assembly instructions.
87 : // x64 machines happen to have matching assembly instructions for
88 : // 64x64-bit multiplications and 128-bit shifts.
89 : //
90 : // 2. Second best case: the compiler exposes intrinsics for the x64 assembly
91 : // instructions mentioned in 1.
92 : //
93 : // 3. We only have 64x64 bit instructions that return the lower 64 bits of
94 : // the result, i.e., we have to use plain C.
95 : // Our inputs are less than the full width, so we have three options:
96 : // a. Ignore this fact and just implement the intrinsics manually.
97 : // b. Split both into 31-bit pieces, which guarantees no internal overflow,
98 : // but requires extra work upfront (unless we change the lookup table).
99 : // c. Split only the first factor into 31-bit pieces, which also guarantees
100 : // no internal overflow, but requires extra work since the intermediate
101 : // results are not perfectly aligned.
102 : #if defined(BOOST_JSON_RYU_HAS_UINT128)
103 :
104 : // Best case: use 128-bit type.
105 : inline
106 : std::uint64_t
107 HIT 786 : mulShift(
108 : const std::uint64_t m,
109 : const std::uint64_t* const mul,
110 : const std::int32_t j) noexcept
111 : {
112 786 : const uint128_t b0 = ((uint128_t) m) * mul[0];
113 786 : const uint128_t b2 = ((uint128_t) m) * mul[1];
114 786 : return (std::uint64_t) (((b0 >> 64) + b2) >> (j - 64));
115 : }
116 :
117 : inline
118 : uint64_t
119 262 : mulShiftAll(
120 : const std::uint64_t m,
121 : const std::uint64_t* const mul,
122 : std::int32_t const j,
123 : std::uint64_t* const vp,
124 : std::uint64_t* const vm,
125 : const std::uint32_t mmShift) noexcept
126 : {
127 : // m <<= 2;
128 : // uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
129 : // uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
130 : //
131 : // uint128_t hi = (b0 >> 64) + b2;
132 : // uint128_t lo = b0 & 0xffffffffffffffffull;
133 : // uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
134 : // uint128_t vpLo = lo + (factor << 1);
135 : // *vp = (std::uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
136 : // uint128_t vmLo = lo - (factor << mmShift);
137 : // *vm = (std::uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
138 : // return (std::uint64_t) (hi >> (j - 64));
139 262 : *vp = mulShift(4 * m + 2, mul, j);
140 262 : *vm = mulShift(4 * m - 1 - mmShift, mul, j);
141 262 : return mulShift(4 * m, mul, j);
142 : }
143 :
144 : #elif defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
145 :
146 : inline
147 : std::uint64_t
148 : mulShift(
149 : const std::uint64_t m,
150 : const std::uint64_t* const mul,
151 : const std::int32_t j) noexcept
152 : {
153 : // m is maximum 55 bits
154 : std::uint64_t high1; // 128
155 : std::uint64_t const low1 = umul128(m, mul[1], &high1); // 64
156 : std::uint64_t high0; // 64
157 : umul128(m, mul[0], &high0); // 0
158 : std::uint64_t const sum = high0 + low1;
159 : if (sum < high0)
160 : ++high1; // overflow into high1
161 : return shiftright128(sum, high1, j - 64);
162 : }
163 :
164 : inline
165 : std::uint64_t
166 : mulShiftAll(
167 : const std::uint64_t m,
168 : const std::uint64_t* const mul,
169 : const std::int32_t j,
170 : std::uint64_t* const vp,
171 : std::uint64_t* const vm,
172 : const std::uint32_t mmShift) noexcept
173 : {
174 : *vp = mulShift(4 * m + 2, mul, j);
175 : *vm = mulShift(4 * m - 1 - mmShift, mul, j);
176 : return mulShift(4 * m, mul, j);
177 : }
178 :
179 : #else // !defined(BOOST_JSON_RYU_HAS_UINT128) && !defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
180 :
181 : inline
182 : std::uint64_t
183 : mulShiftAll(
184 : std::uint64_t m,
185 : const std::uint64_t* const mul,
186 : const std::int32_t j,
187 : std::uint64_t* const vp,
188 : std::uint64_t* const vm,
189 : const std::uint32_t mmShift)
190 : {
191 : m <<= 1;
192 : // m is maximum 55 bits
193 : std::uint64_t tmp;
194 : std::uint64_t const lo = umul128(m, mul[0], &tmp);
195 : std::uint64_t hi;
196 : std::uint64_t const mid = tmp + umul128(m, mul[1], &hi);
197 : hi += mid < tmp; // overflow into hi
198 :
199 : const std::uint64_t lo2 = lo + mul[0];
200 : const std::uint64_t mid2 = mid + mul[1] + (lo2 < lo);
201 : const std::uint64_t hi2 = hi + (mid2 < mid);
202 : *vp = shiftright128(mid2, hi2, (std::uint32_t)(j - 64 - 1));
203 :
204 : if (mmShift == 1)
205 : {
206 : const std::uint64_t lo3 = lo - mul[0];
207 : const std::uint64_t mid3 = mid - mul[1] - (lo3 > lo);
208 : const std::uint64_t hi3 = hi - (mid3 > mid);
209 : *vm = shiftright128(mid3, hi3, (std::uint32_t)(j - 64 - 1));
210 : }
211 : else
212 : {
213 : const std::uint64_t lo3 = lo + lo;
214 : const std::uint64_t mid3 = mid + mid + (lo3 < lo);
215 : const std::uint64_t hi3 = hi + hi + (mid3 < mid);
216 : const std::uint64_t lo4 = lo3 - mul[0];
217 : const std::uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
218 : const std::uint64_t hi4 = hi3 - (mid4 > mid3);
219 : *vm = shiftright128(mid4, hi4, (std::uint32_t)(j - 64));
220 : }
221 :
222 : return shiftright128(mid, hi, (std::uint32_t)(j - 64 - 1));
223 : }
224 :
225 : #endif // BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS
226 :
227 : inline
228 : std::uint32_t
229 538 : decimalLength17(
230 : const std::uint64_t v)
231 : {
232 : // This is slightly faster than a loop.
233 : // The average output length is 16.38 digits, so we check high-to-low.
234 : // Function precondition: v is not an 18, 19, or 20-digit number.
235 : // (17 digits are sufficient for round-tripping.)
236 538 : BOOST_ASSERT(v < 100000000000000000L);
237 538 : if (v >= 10000000000000000L) { return 17; }
238 528 : if (v >= 1000000000000000L) { return 16; }
239 509 : if (v >= 100000000000000L) { return 15; }
240 505 : if (v >= 10000000000000L) { return 14; }
241 500 : if (v >= 1000000000000L) { return 13; }
242 494 : if (v >= 100000000000L) { return 12; }
243 489 : if (v >= 10000000000L) { return 11; }
244 484 : if (v >= 1000000000L) { return 10; }
245 474 : if (v >= 100000000L) { return 9; }
246 467 : if (v >= 10000000L) { return 8; }
247 461 : if (v >= 1000000L) { return 7; }
248 455 : if (v >= 100000L) { return 6; }
249 450 : if (v >= 10000L) { return 5; }
250 445 : if (v >= 1000L) { return 4; }
251 439 : if (v >= 100L) { return 3; }
252 421 : if (v >= 10L) { return 2; }
253 415 : return 1;
254 : }
255 :
256 : // A floating decimal representing m * 10^e.
257 : struct floating_decimal_64
258 : {
259 : std::uint64_t mantissa;
260 : // Decimal exponent's range is -324 to 308
261 : // inclusive, and can fit in a short if needed.
262 : std::int32_t exponent;
263 : };
264 :
265 : inline
266 : floating_decimal_64
267 262 : d2d(
268 : const std::uint64_t ieeeMantissa,
269 : const std::uint32_t ieeeExponent)
270 : {
271 : std::int32_t e2;
272 : std::uint64_t m2;
273 262 : if (ieeeExponent == 0)
274 : {
275 : // We subtract 2 so that the bounds computation has 2 additional bits.
276 15 : e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
277 15 : m2 = ieeeMantissa;
278 : }
279 : else
280 : {
281 247 : e2 = (std::int32_t)ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
282 247 : m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
283 : }
284 262 : const bool even = (m2 & 1) == 0;
285 262 : const bool acceptBounds = even;
286 :
287 : #ifdef RYU_DEBUG
288 : printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
289 : #endif
290 :
291 : // Step 2: Determine the interval of valid decimal representations.
292 262 : const std::uint64_t mv = 4 * m2;
293 : // Implicit bool -> int conversion. True is 1, false is 0.
294 262 : const std::uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
295 : // We would compute mp and mm like this:
296 : // uint64_t mp = 4 * m2 + 2;
297 : // uint64_t mm = mv - 1 - mmShift;
298 :
299 : // Step 3: Convert to a decimal power base using 128-bit arithmetic.
300 : std::uint64_t vr, vp, vm;
301 : std::int32_t e10;
302 262 : bool vmIsTrailingZeros = false;
303 262 : bool vrIsTrailingZeros = false;
304 262 : if (e2 >= 0) {
305 : // I tried special-casing q == 0, but there was no effect on performance.
306 : // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
307 128 : const std::uint32_t q = log10Pow2(e2) - (e2 > 3);
308 128 : e10 = (std::int32_t)q;
309 128 : const std::int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t)q) - 1;
310 128 : const std::int32_t i = -e2 + (std::int32_t)q + k;
311 : #if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
312 : uint64_t pow5[2];
313 : double_computeInvPow5(q, pow5);
314 : vr = mulShiftAll(m2, pow5, i, &vp, &vm, mmShift);
315 : #else
316 128 : vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT()[q], i, &vp, &vm, mmShift);
317 : #endif
318 : #ifdef RYU_DEBUG
319 : printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
320 : printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
321 : #endif
322 128 : if (q <= 21)
323 : {
324 : // This should use q <= 22, but I think 21 is also safe. Smaller values
325 : // may still be safe, but it's more difficult to reason about them.
326 : // Only one of mp, mv, and mm can be a multiple of 5, if any.
327 114 : const std::uint32_t mvMod5 = ((std::uint32_t)mv) - 5 * ((std::uint32_t)div5(mv));
328 114 : if (mvMod5 == 0)
329 : {
330 86 : vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
331 : }
332 28 : else if (acceptBounds)
333 : {
334 : // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
335 : // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
336 : // <=> true && pow5Factor(mm) >= q, since e2 >= q.
337 11 : vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
338 : }
339 : else
340 : {
341 : // Same as min(e2 + 1, pow5Factor(mp)) >= q.
342 17 : vp -= multipleOfPowerOf5(mv + 2, q);
343 : }
344 : }
345 : }
346 : else
347 : {
348 : // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
349 134 : const std::uint32_t q = log10Pow5(-e2) - (-e2 > 1);
350 134 : e10 = (std::int32_t)q + e2;
351 134 : const std::int32_t i = -e2 - (std::int32_t)q;
352 134 : const std::int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
353 134 : const std::int32_t j = (std::int32_t)q - k;
354 : #if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
355 : std::uint64_t pow5[2];
356 : double_computePow5(i, pow5);
357 : vr = mulShiftAll(m2, pow5, j, &vp, &vm, mmShift);
358 : #else
359 134 : vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT()[i], j, &vp, &vm, mmShift);
360 : #endif
361 : #ifdef RYU_DEBUG
362 : printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
363 : printf("%u %d %d %d\n", q, i, k, j);
364 : printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
365 : #endif
366 134 : if (q <= 1)
367 : {
368 : // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
369 : // mv = 4 * m2, so it always has at least two trailing 0 bits.
370 3 : vrIsTrailingZeros = true;
371 3 : if (acceptBounds)
372 : {
373 : // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
374 3 : vmIsTrailingZeros = mmShift == 1;
375 : }
376 : else
377 : {
378 : // mp = mv + 2, so it always has at least one trailing 0 bit.
379 MIS 0 : --vp;
380 : }
381 : }
382 HIT 131 : else if (q < 63)
383 : {
384 : // TODO(ulfjack): Use a tighter bound here.
385 : // We want to know if the full product has at least q trailing zeros.
386 : // We need to compute min(p2(mv), p5(mv) - e2) >= q
387 : // <=> p2(mv) >= q && p5(mv) - e2 >= q
388 : // <=> p2(mv) >= q (because -e2 >= q)
389 96 : vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
390 : #ifdef RYU_DEBUG
391 : printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
392 : #endif
393 : }
394 : }
395 : #ifdef RYU_DEBUG
396 : printf("e10=%d\n", e10);
397 : printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
398 : printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
399 : printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
400 : #endif
401 :
402 : // Step 4: Find the shortest decimal representation in the interval of valid representations.
403 262 : std::int32_t removed = 0;
404 262 : std::uint8_t lastRemovedDigit = 0;
405 : std::uint64_t output;
406 : // On average, we remove ~2 digits.
407 262 : if (vmIsTrailingZeros || vrIsTrailingZeros)
408 : {
409 : // General case, which happens rarely (~0.7%).
410 : for (;;)
411 : {
412 1663 : const std::uint64_t vpDiv10 = div10(vp);
413 1663 : const std::uint64_t vmDiv10 = div10(vm);
414 1663 : if (vpDiv10 <= vmDiv10)
415 94 : break;
416 1569 : const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
417 1569 : const std::uint64_t vrDiv10 = div10(vr);
418 1569 : const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
419 1569 : vmIsTrailingZeros &= vmMod10 == 0;
420 1569 : vrIsTrailingZeros &= lastRemovedDigit == 0;
421 1569 : lastRemovedDigit = (uint8_t)vrMod10;
422 1569 : vr = vrDiv10;
423 1569 : vp = vpDiv10;
424 1569 : vm = vmDiv10;
425 1569 : ++removed;
426 1569 : }
427 : #ifdef RYU_DEBUG
428 : printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
429 : printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
430 : #endif
431 94 : if (vmIsTrailingZeros)
432 : {
433 : for (;;)
434 : {
435 3 : const std::uint64_t vmDiv10 = div10(vm);
436 3 : const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
437 3 : if (vmMod10 != 0)
438 2 : break;
439 1 : const std::uint64_t vpDiv10 = div10(vp);
440 1 : const std::uint64_t vrDiv10 = div10(vr);
441 1 : const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
442 1 : vrIsTrailingZeros &= lastRemovedDigit == 0;
443 1 : lastRemovedDigit = (uint8_t)vrMod10;
444 1 : vr = vrDiv10;
445 1 : vp = vpDiv10;
446 1 : vm = vmDiv10;
447 1 : ++removed;
448 1 : }
449 : }
450 : #ifdef RYU_DEBUG
451 : printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
452 : printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
453 : #endif
454 94 : if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
455 : {
456 : // Round even if the exact number is .....50..0.
457 1 : lastRemovedDigit = 4;
458 : }
459 : // We need to take vr + 1 if vr is outside bounds or we need to round up.
460 94 : output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
461 94 : }
462 : else
463 : {
464 : // Specialized for the common case (~99.3%). Percentages below are relative to this.
465 168 : bool roundUp = false;
466 168 : const std::uint64_t vpDiv100 = div100(vp);
467 168 : const std::uint64_t vmDiv100 = div100(vm);
468 168 : if (vpDiv100 > vmDiv100)
469 : {
470 : // Optimization: remove two digits at a time (~86.2%).
471 161 : const std::uint64_t vrDiv100 = div100(vr);
472 161 : const std::uint32_t vrMod100 = ((std::uint32_t)vr) - 100 * ((std::uint32_t)vrDiv100);
473 161 : roundUp = vrMod100 >= 50;
474 161 : vr = vrDiv100;
475 161 : vp = vpDiv100;
476 161 : vm = vmDiv100;
477 161 : removed += 2;
478 : }
479 : // Loop iterations below (approximately), without optimization above:
480 : // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
481 : // Loop iterations below (approximately), with optimization above:
482 : // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
483 : for (;;)
484 : {
485 2256 : const std::uint64_t vpDiv10 = div10(vp);
486 2256 : const std::uint64_t vmDiv10 = div10(vm);
487 2256 : if (vpDiv10 <= vmDiv10)
488 168 : break;
489 2088 : const std::uint64_t vrDiv10 = div10(vr);
490 2088 : const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
491 2088 : roundUp = vrMod10 >= 5;
492 2088 : vr = vrDiv10;
493 2088 : vp = vpDiv10;
494 2088 : vm = vmDiv10;
495 2088 : ++removed;
496 2088 : }
497 : #ifdef RYU_DEBUG
498 : printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
499 : printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
500 : #endif
501 : // We need to take vr + 1 if vr is outside bounds or we need to round up.
502 168 : output = vr + (vr == vm || roundUp);
503 : }
504 262 : const std::int32_t exp = e10 + removed;
505 :
506 : #ifdef RYU_DEBUG
507 : printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
508 : printf("O=%" PRIu64 "\n", output);
509 : printf("EXP=%d\n", exp);
510 : #endif
511 :
512 : floating_decimal_64 fd;
513 262 : fd.exponent = exp;
514 262 : fd.mantissa = output;
515 262 : return fd;
516 : }
517 :
518 : inline
519 : int
520 538 : to_chars(
521 : const floating_decimal_64 v,
522 : const bool sign,
523 : char* const result)
524 : {
525 : // Step 5: Print the decimal representation.
526 538 : int index = 0;
527 538 : if (sign)
528 129 : result[index++] = '-';
529 :
530 538 : std::uint64_t output = v.mantissa;
531 538 : std::uint32_t const olength = decimalLength17(output);
532 :
533 : #ifdef RYU_DEBUG
534 : printf("DIGITS=%" PRIu64 "\n", v.mantissa);
535 : printf("OLEN=%u\n", olength);
536 : printf("EXP=%u\n", v.exponent + olength);
537 : #endif
538 :
539 : // Print the decimal digits.
540 : // The following code is equivalent to:
541 : // for (uint32_t i = 0; i < olength - 1; ++i) {
542 : // const uint32_t c = output % 10; output /= 10;
543 : // result[index + olength - i] = (char) ('0' + c);
544 : // }
545 : // result[index] = '0' + output % 10;
546 :
547 538 : std::uint32_t i = 0;
548 : // We prefer 32-bit operations, even on 64-bit platforms.
549 : // We have at most 17 digits, and uint32_t can store 9 digits.
550 : // If output doesn't fit into uint32_t, we cut off 8 digits,
551 : // so the rest will fit into uint32_t.
552 538 : if ((output >> 32) != 0)
553 : {
554 : // Expensive 64-bit division.
555 59 : std::uint64_t const q = div1e8(output);
556 59 : std::uint32_t output2 = ((std::uint32_t)output) - 100000000 * ((std::uint32_t)q);
557 59 : output = q;
558 :
559 59 : const std::uint32_t c = output2 % 10000;
560 59 : output2 /= 10000;
561 59 : const std::uint32_t d = output2 % 10000;
562 59 : const std::uint32_t c0 = (c % 100) << 1;
563 59 : const std::uint32_t c1 = (c / 100) << 1;
564 59 : const std::uint32_t d0 = (d % 100) << 1;
565 59 : const std::uint32_t d1 = (d / 100) << 1;
566 59 : std::memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
567 59 : std::memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
568 59 : std::memcpy(result + index + olength - i - 5, DIGIT_TABLE() + d0, 2);
569 59 : std::memcpy(result + index + olength - i - 7, DIGIT_TABLE() + d1, 2);
570 59 : i += 8;
571 : }
572 538 : uint32_t output2 = (std::uint32_t)output;
573 638 : while (output2 >= 10000)
574 : {
575 : #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
576 : const uint32_t c = output2 - 10000 * (output2 / 10000);
577 : #else
578 100 : const uint32_t c = output2 % 10000;
579 : #endif
580 100 : output2 /= 10000;
581 100 : const uint32_t c0 = (c % 100) << 1;
582 100 : const uint32_t c1 = (c / 100) << 1;
583 100 : memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
584 100 : memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
585 100 : i += 4;
586 : }
587 538 : if (output2 >= 100) {
588 69 : const uint32_t c = (output2 % 100) << 1;
589 69 : output2 /= 100;
590 69 : memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c, 2);
591 69 : i += 2;
592 : }
593 538 : if (output2 >= 10) {
594 62 : const uint32_t c = output2 << 1;
595 : // We can't use memcpy here: the decimal dot goes between these two digits.
596 62 : result[index + olength - i] = DIGIT_TABLE()[c + 1];
597 62 : result[index] = DIGIT_TABLE()[c];
598 : }
599 : else {
600 476 : result[index] = (char)('0' + output2);
601 : }
602 :
603 : // Print decimal point if needed.
604 538 : if (olength > 1) {
605 123 : result[index + 1] = '.';
606 123 : index += olength + 1;
607 : }
608 : else {
609 415 : ++index;
610 : }
611 :
612 : // Print the exponent.
613 538 : result[index++] = 'E';
614 538 : int32_t exp = v.exponent + (int32_t)olength - 1;
615 538 : if (exp < 0) {
616 92 : result[index++] = '-';
617 92 : exp = -exp;
618 : }
619 :
620 538 : if (exp >= 100) {
621 33 : const int32_t c = exp % 10;
622 33 : memcpy(result + index, DIGIT_TABLE() + 2 * (exp / 10), 2);
623 33 : result[index + 2] = (char)('0' + c);
624 33 : index += 3;
625 : }
626 505 : else if (exp >= 10) {
627 180 : memcpy(result + index, DIGIT_TABLE() + 2 * exp, 2);
628 180 : index += 2;
629 : }
630 : else {
631 325 : result[index++] = (char)('0' + exp);
632 : }
633 :
634 538 : return index;
635 : }
636 :
637 538 : static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
638 : floating_decimal_64* const v) {
639 538 : const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
640 538 : const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
641 :
642 538 : if (e2 > 0) {
643 : // f = m2 * 2^e2 >= 2^53 is an integer.
644 : // Ignore this case for now.
645 131 : return false;
646 : }
647 :
648 407 : if (e2 < -52) {
649 : // f < 1.
650 92 : return false;
651 : }
652 :
653 : // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
654 : // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
655 315 : const uint64_t mask = (1ull << -e2) - 1;
656 315 : const uint64_t fraction = m2 & mask;
657 315 : if (fraction != 0) {
658 39 : return false;
659 : }
660 :
661 : // f is an integer in the range [1, 2^53).
662 : // Note: mantissa might contain trailing (decimal) 0's.
663 : // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
664 276 : v->mantissa = m2 >> -e2;
665 276 : v->exponent = 0;
666 276 : return true;
667 : }
668 :
669 : } // detail
670 :
671 : int
672 609 : d2s_buffered_n(
673 : double f,
674 : char* result,
675 : bool allow_infinity_and_nan) noexcept
676 : {
677 : using namespace detail;
678 : // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
679 609 : std::uint64_t const bits = double_to_bits(f);
680 :
681 : #ifdef RYU_DEBUG
682 : printf("IN=");
683 : for (std::int32_t bit = 63; bit >= 0; --bit) {
684 : printf("%d", (int)((bits >> bit) & 1));
685 : }
686 : printf("\n");
687 : #endif
688 :
689 : // Decode bits into sign, mantissa, and exponent.
690 609 : const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
691 609 : const std::uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
692 609 : const std::uint32_t ieeeExponent = (std::uint32_t)((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
693 : // Case distinction; exit early for the easy cases.
694 609 : if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
695 : // We changed how special numbers are output by default
696 71 : if (allow_infinity_and_nan)
697 11 : return copy_special_str(result, ieeeSign, ieeeExponent != 0, ieeeMantissa != 0);
698 : else
699 60 : return copy_special_str_conforming(result, ieeeSign, ieeeExponent != 0, ieeeMantissa != 0);
700 :
701 : }
702 :
703 : floating_decimal_64 v;
704 538 : const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
705 538 : if (isSmallInt) {
706 : // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
707 : // For scientific notation we need to move these zeros into the exponent.
708 : // (This is not needed for fixed-point notation, so it might be beneficial to trim
709 : // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
710 : for (;;) {
711 698 : std::uint64_t const q = div10(v.mantissa);
712 698 : std::uint32_t const r = ((std::uint32_t) v.mantissa) - 10 * ((std::uint32_t) q);
713 698 : if (r != 0)
714 276 : break;
715 422 : v.mantissa = q;
716 422 : ++v.exponent;
717 422 : }
718 : }
719 : else {
720 262 : v = d2d(ieeeMantissa, ieeeExponent);
721 : }
722 :
723 538 : return to_chars(v, ieeeSign, result);
724 : }
725 :
726 : } // ryu
727 :
728 : } // detail
729 : } // namespace json
730 : } // namespace boost
731 :
732 : #endif
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