1 // Copyright 2018 Ulf Adams
3 // The contents of this file may be used under the terms of the Apache License,
6 // (See accompanying file LICENSE-Apache or copy at
7 // http://www.apache.org/licenses/LICENSE-2.0)
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)
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.
18 // Runtime compiler options:
19 // -DRYU_DEBUG Generate verbose debugging output to stdout.
21 // -DRYU_ONLY_64_BIT_OPS Avoid using uint128_t or 64-bit intrinsics. Slower,
22 // depending on your compiler.
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.
31 This is a derivative work
34 #ifndef BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
35 #define BOOST_JSON_DETAIL_RYU_IMPL_D2S_IPP
37 #include <boost/json/detail/ryu/ryu.hpp>
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
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>
64 // We need a 64x128-bit multiplication and a subsequent 128-bit shift.
66 // The 64-bit factor is variable and passed in, the 128-bit factor comes
67 // from a lookup table. We know that the 64-bit factor only has 55
68 // significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
69 // factor only has 124 significant bits (i.e., the 4 topmost bits are
72 // In principle, the multiplication result requires 55 + 124 = 179 bits to
73 // represent. However, we then shift this value to the right by j, which is
74 // at least j >= 115, so the result is guaranteed to fit into 179 - 115 = 64
75 // bits. This means that we only need the topmost 64 significant bits of
76 // the 64x128-bit multiplication.
78 // There are several ways to do this:
79 // 1. Best case: the compiler exposes a 128-bit type.
80 // We perform two 64x64-bit multiplications, add the higher 64 bits of the
81 // lower result to the higher result, and shift by j - 64 bits.
83 // We explicitly cast from 64-bit to 128-bit, so the compiler can tell
84 // that these are only 64-bit inputs, and can map these to the best
85 // possible sequence of assembly instructions.
86 // x64 machines happen to have matching assembly instructions for
87 // 64x64-bit multiplications and 128-bit shifts.
89 // 2. Second best case: the compiler exposes intrinsics for the x64 assembly
90 // instructions mentioned in 1.
92 // 3. We only have 64x64 bit instructions that return the lower 64 bits of
93 // the result, i.e., we have to use plain C.
94 // Our inputs are less than the full width, so we have three options:
95 // a. Ignore this fact and just implement the intrinsics manually.
96 // b. Split both into 31-bit pieces, which guarantees no internal overflow,
97 // but requires extra work upfront (unless we change the lookup table).
98 // c. Split only the first factor into 31-bit pieces, which also guarantees
99 // no internal overflow, but requires extra work since the intermediate
100 // results are not perfectly aligned.
101 #if defined(BOOST_JSON_RYU_HAS_UINT128)
103 // Best case: use 128-bit type.
107 const std::uint64_t m,
108 const std::uint64_t* const mul,
109 const std::int32_t j) noexcept
111 const uint128_t b0 = ((uint128_t) m) * mul[0];
112 const uint128_t b2 = ((uint128_t) m) * mul[1];
113 return (std::uint64_t) (((b0 >> 64) + b2) >> (j - 64));
119 const std::uint64_t m,
120 const std::uint64_t* const mul,
121 std::int32_t const j,
122 std::uint64_t* const vp,
123 std::uint64_t* const vm,
124 const std::uint32_t mmShift) noexcept
127 // uint128_t b0 = ((uint128_t) m) * mul[0]; // 0
128 // uint128_t b2 = ((uint128_t) m) * mul[1]; // 64
130 // uint128_t hi = (b0 >> 64) + b2;
131 // uint128_t lo = b0 & 0xffffffffffffffffull;
132 // uint128_t factor = (((uint128_t) mul[1]) << 64) + mul[0];
133 // uint128_t vpLo = lo + (factor << 1);
134 // *vp = (std::uint64_t) ((hi + (vpLo >> 64)) >> (j - 64));
135 // uint128_t vmLo = lo - (factor << mmShift);
136 // *vm = (std::uint64_t) ((hi + (vmLo >> 64) - (((uint128_t) 1ull) << 64)) >> (j - 64));
137 // return (std::uint64_t) (hi >> (j - 64));
138 *vp = mulShift(4 * m + 2, mul, j);
139 *vm = mulShift(4 * m - 1 - mmShift, mul, j);
140 return mulShift(4 * m, mul, j);
143 #elif defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
148 const std::uint64_t m,
149 const std::uint64_t* const mul,
150 const std::int32_t j) noexcept
152 // m is maximum 55 bits
153 std::uint64_t high1; // 128
154 std::uint64_t const low1 = umul128(m, mul[1], &high1); // 64
155 std::uint64_t high0; // 64
156 umul128(m, mul[0], &high0); // 0
157 std::uint64_t const sum = high0 + low1;
159 ++high1; // overflow into high1
160 return shiftright128(sum, high1, j - 64);
166 const std::uint64_t m,
167 const std::uint64_t* const mul,
168 const std::int32_t j,
169 std::uint64_t* const vp,
170 std::uint64_t* const vm,
171 const std::uint32_t mmShift) noexcept
173 *vp = mulShift(4 * m + 2, mul, j);
174 *vm = mulShift(4 * m - 1 - mmShift, mul, j);
175 return mulShift(4 * m, mul, j);
178 #else // !defined(BOOST_JSON_RYU_HAS_UINT128) && !defined(BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS)
184 const std::uint64_t* const mul,
185 const std::int32_t j,
186 std::uint64_t* const vp,
187 std::uint64_t* const vm,
188 const std::uint32_t mmShift)
191 // m is maximum 55 bits
193 std::uint64_t const lo = umul128(m, mul[0], &tmp);
195 std::uint64_t const mid = tmp + umul128(m, mul[1], &hi);
196 hi += mid < tmp; // overflow into hi
198 const std::uint64_t lo2 = lo + mul[0];
199 const std::uint64_t mid2 = mid + mul[1] + (lo2 < lo);
200 const std::uint64_t hi2 = hi + (mid2 < mid);
201 *vp = shiftright128(mid2, hi2, (std::uint32_t)(j - 64 - 1));
205 const std::uint64_t lo3 = lo - mul[0];
206 const std::uint64_t mid3 = mid - mul[1] - (lo3 > lo);
207 const std::uint64_t hi3 = hi - (mid3 > mid);
208 *vm = shiftright128(mid3, hi3, (std::uint32_t)(j - 64 - 1));
212 const std::uint64_t lo3 = lo + lo;
213 const std::uint64_t mid3 = mid + mid + (lo3 < lo);
214 const std::uint64_t hi3 = hi + hi + (mid3 < mid);
215 const std::uint64_t lo4 = lo3 - mul[0];
216 const std::uint64_t mid4 = mid3 - mul[1] - (lo4 > lo3);
217 const std::uint64_t hi4 = hi3 - (mid4 > mid3);
218 *vm = shiftright128(mid4, hi4, (std::uint32_t)(j - 64));
221 return shiftright128(mid, hi, (std::uint32_t)(j - 64 - 1));
224 #endif // BOOST_JSON_RYU_HAS_64_BIT_INTRINSICS
229 const std::uint64_t v)
231 // This is slightly faster than a loop.
232 // The average output length is 16.38 digits, so we check high-to-low.
233 // Function precondition: v is not an 18, 19, or 20-digit number.
234 // (17 digits are sufficient for round-tripping.)
235 BOOST_ASSERT(v < 100000000000000000L);
236 if (v >= 10000000000000000L) { return 17; }
237 if (v >= 1000000000000000L) { return 16; }
238 if (v >= 100000000000000L) { return 15; }
239 if (v >= 10000000000000L) { return 14; }
240 if (v >= 1000000000000L) { return 13; }
241 if (v >= 100000000000L) { return 12; }
242 if (v >= 10000000000L) { return 11; }
243 if (v >= 1000000000L) { return 10; }
244 if (v >= 100000000L) { return 9; }
245 if (v >= 10000000L) { return 8; }
246 if (v >= 1000000L) { return 7; }
247 if (v >= 100000L) { return 6; }
248 if (v >= 10000L) { return 5; }
249 if (v >= 1000L) { return 4; }
250 if (v >= 100L) { return 3; }
251 if (v >= 10L) { return 2; }
255 // A floating decimal representing m * 10^e.
256 struct floating_decimal_64
258 std::uint64_t mantissa;
259 // Decimal exponent's range is -324 to 308
260 // inclusive, and can fit in a short if needed.
261 std::int32_t exponent;
267 const std::uint64_t ieeeMantissa,
268 const std::uint32_t ieeeExponent)
272 if (ieeeExponent == 0)
274 // We subtract 2 so that the bounds computation has 2 additional bits.
275 e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
280 e2 = (std::int32_t)ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
281 m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
283 const bool even = (m2 & 1) == 0;
284 const bool acceptBounds = even;
287 printf("-> %" PRIu64 " * 2^%d\n", m2, e2 + 2);
290 // Step 2: Determine the interval of valid decimal representations.
291 const std::uint64_t mv = 4 * m2;
292 // Implicit bool -> int conversion. True is 1, false is 0.
293 const std::uint32_t mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
294 // We would compute mp and mm like this:
295 // uint64_t mp = 4 * m2 + 2;
296 // uint64_t mm = mv - 1 - mmShift;
298 // Step 3: Convert to a decimal power base using 128-bit arithmetic.
299 std::uint64_t vr, vp, vm;
301 bool vmIsTrailingZeros = false;
302 bool vrIsTrailingZeros = false;
304 // I tried special-casing q == 0, but there was no effect on performance.
305 // This expression is slightly faster than max(0, log10Pow2(e2) - 1).
306 const std::uint32_t q = log10Pow2(e2) - (e2 > 3);
307 e10 = (std::int32_t)q;
308 const std::int32_t k = DOUBLE_POW5_INV_BITCOUNT + pow5bits((int32_t)q) - 1;
309 const std::int32_t i = -e2 + (std::int32_t)q + k;
310 #if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
312 double_computeInvPow5(q, pow5);
313 vr = mulShiftAll(m2, pow5, i, &vp, &vm, mmShift);
315 vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT()[q], i, &vp, &vm, mmShift);
318 printf("%" PRIu64 " * 2^%d / 10^%u\n", mv, e2, q);
319 printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
323 // This should use q <= 22, but I think 21 is also safe. Smaller values
324 // may still be safe, but it's more difficult to reason about them.
325 // Only one of mp, mv, and mm can be a multiple of 5, if any.
326 const std::uint32_t mvMod5 = ((std::uint32_t)mv) - 5 * ((std::uint32_t)div5(mv));
329 vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
331 else if (acceptBounds)
333 // Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
334 // <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
335 // <=> true && pow5Factor(mm) >= q, since e2 >= q.
336 vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
340 // Same as min(e2 + 1, pow5Factor(mp)) >= q.
341 vp -= multipleOfPowerOf5(mv + 2, q);
347 // This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
348 const std::uint32_t q = log10Pow5(-e2) - (-e2 > 1);
349 e10 = (std::int32_t)q + e2;
350 const std::int32_t i = -e2 - (std::int32_t)q;
351 const std::int32_t k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
352 const std::int32_t j = (std::int32_t)q - k;
353 #if defined(BOOST_JSON_RYU_OPTIMIZE_SIZE)
354 std::uint64_t pow5[2];
355 double_computePow5(i, pow5);
356 vr = mulShiftAll(m2, pow5, j, &vp, &vm, mmShift);
358 vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT()[i], j, &vp, &vm, mmShift);
361 printf("%" PRIu64 " * 5^%d / 10^%u\n", mv, -e2, q);
362 printf("%u %d %d %d\n", q, i, k, j);
363 printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
367 // {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q trailing 0 bits.
368 // mv = 4 * m2, so it always has at least two trailing 0 bits.
369 vrIsTrailingZeros = true;
372 // mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff mmShift == 1.
373 vmIsTrailingZeros = mmShift == 1;
377 // mp = mv + 2, so it always has at least one trailing 0 bit.
383 // TODO(ulfjack): Use a tighter bound here.
384 // We want to know if the full product has at least q trailing zeros.
385 // We need to compute min(p2(mv), p5(mv) - e2) >= q
386 // <=> p2(mv) >= q && p5(mv) - e2 >= q
387 // <=> p2(mv) >= q (because -e2 >= q)
388 vrIsTrailingZeros = multipleOfPowerOf2(mv, q);
390 printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
395 printf("e10=%d\n", e10);
396 printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
397 printf("vm is trailing zeros=%s\n", vmIsTrailingZeros ? "true" : "false");
398 printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
401 // Step 4: Find the shortest decimal representation in the interval of valid representations.
402 std::int32_t removed = 0;
403 std::uint8_t lastRemovedDigit = 0;
404 std::uint64_t output;
405 // On average, we remove ~2 digits.
406 if (vmIsTrailingZeros || vrIsTrailingZeros)
408 // General case, which happens rarely (~0.7%).
411 const std::uint64_t vpDiv10 = div10(vp);
412 const std::uint64_t vmDiv10 = div10(vm);
413 if (vpDiv10 <= vmDiv10)
415 const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
416 const std::uint64_t vrDiv10 = div10(vr);
417 const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
418 vmIsTrailingZeros &= vmMod10 == 0;
419 vrIsTrailingZeros &= lastRemovedDigit == 0;
420 lastRemovedDigit = (uint8_t)vrMod10;
427 printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
428 printf("d-10=%s\n", vmIsTrailingZeros ? "true" : "false");
430 if (vmIsTrailingZeros)
434 const std::uint64_t vmDiv10 = div10(vm);
435 const std::uint32_t vmMod10 = ((std::uint32_t)vm) - 10 * ((std::uint32_t)vmDiv10);
438 const std::uint64_t vpDiv10 = div10(vp);
439 const std::uint64_t vrDiv10 = div10(vr);
440 const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
441 vrIsTrailingZeros &= lastRemovedDigit == 0;
442 lastRemovedDigit = (uint8_t)vrMod10;
450 printf("%" PRIu64 " %d\n", vr, lastRemovedDigit);
451 printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
453 if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
455 // Round even if the exact number is .....50..0.
456 lastRemovedDigit = 4;
458 // We need to take vr + 1 if vr is outside bounds or we need to round up.
459 output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
463 // Specialized for the common case (~99.3%). Percentages below are relative to this.
464 bool roundUp = false;
465 const std::uint64_t vpDiv100 = div100(vp);
466 const std::uint64_t vmDiv100 = div100(vm);
467 if (vpDiv100 > vmDiv100)
469 // Optimization: remove two digits at a time (~86.2%).
470 const std::uint64_t vrDiv100 = div100(vr);
471 const std::uint32_t vrMod100 = ((std::uint32_t)vr) - 100 * ((std::uint32_t)vrDiv100);
472 roundUp = vrMod100 >= 50;
478 // Loop iterations below (approximately), without optimization above:
479 // 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%, 6+: 0.02%
480 // Loop iterations below (approximately), with optimization above:
481 // 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
484 const std::uint64_t vpDiv10 = div10(vp);
485 const std::uint64_t vmDiv10 = div10(vm);
486 if (vpDiv10 <= vmDiv10)
488 const std::uint64_t vrDiv10 = div10(vr);
489 const std::uint32_t vrMod10 = ((std::uint32_t)vr) - 10 * ((std::uint32_t)vrDiv10);
490 roundUp = vrMod10 >= 5;
497 printf("%" PRIu64 " roundUp=%s\n", vr, roundUp ? "true" : "false");
498 printf("vr is trailing zeros=%s\n", vrIsTrailingZeros ? "true" : "false");
500 // We need to take vr + 1 if vr is outside bounds or we need to round up.
501 output = vr + (vr == vm || roundUp);
503 const std::int32_t exp = e10 + removed;
506 printf("V+=%" PRIu64 "\nV =%" PRIu64 "\nV-=%" PRIu64 "\n", vp, vr, vm);
507 printf("O=%" PRIu64 "\n", output);
508 printf("EXP=%d\n", exp);
511 floating_decimal_64 fd;
513 fd.mantissa = output;
520 const floating_decimal_64 v,
524 // Step 5: Print the decimal representation.
527 result[index++] = '-';
529 std::uint64_t output = v.mantissa;
530 std::uint32_t const olength = decimalLength17(output);
533 printf("DIGITS=%" PRIu64 "\n", v.mantissa);
534 printf("OLEN=%u\n", olength);
535 printf("EXP=%u\n", v.exponent + olength);
538 // Print the decimal digits.
539 // The following code is equivalent to:
540 // for (uint32_t i = 0; i < olength - 1; ++i) {
541 // const uint32_t c = output % 10; output /= 10;
542 // result[index + olength - i] = (char) ('0' + c);
544 // result[index] = '0' + output % 10;
547 // We prefer 32-bit operations, even on 64-bit platforms.
548 // We have at most 17 digits, and uint32_t can store 9 digits.
549 // If output doesn't fit into uint32_t, we cut off 8 digits,
550 // so the rest will fit into uint32_t.
551 if ((output >> 32) != 0)
553 // Expensive 64-bit division.
554 std::uint64_t const q = div1e8(output);
555 std::uint32_t output2 = ((std::uint32_t)output) - 100000000 * ((std::uint32_t)q);
558 const std::uint32_t c = output2 % 10000;
560 const std::uint32_t d = output2 % 10000;
561 const std::uint32_t c0 = (c % 100) << 1;
562 const std::uint32_t c1 = (c / 100) << 1;
563 const std::uint32_t d0 = (d % 100) << 1;
564 const std::uint32_t d1 = (d / 100) << 1;
565 std::memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
566 std::memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
567 std::memcpy(result + index + olength - i - 5, DIGIT_TABLE() + d0, 2);
568 std::memcpy(result + index + olength - i - 7, DIGIT_TABLE() + d1, 2);
571 uint32_t output2 = (std::uint32_t)output;
572 while (output2 >= 10000)
574 #ifdef __clang__ // https://bugs.llvm.org/show_bug.cgi?id=38217
575 const uint32_t c = output2 - 10000 * (output2 / 10000);
577 const uint32_t c = output2 % 10000;
580 const uint32_t c0 = (c % 100) << 1;
581 const uint32_t c1 = (c / 100) << 1;
582 memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c0, 2);
583 memcpy(result + index + olength - i - 3, DIGIT_TABLE() + c1, 2);
586 if (output2 >= 100) {
587 const uint32_t c = (output2 % 100) << 1;
589 memcpy(result + index + olength - i - 1, DIGIT_TABLE() + c, 2);
593 const uint32_t c = output2 << 1;
594 // We can't use memcpy here: the decimal dot goes between these two digits.
595 result[index + olength - i] = DIGIT_TABLE()[c + 1];
596 result[index] = DIGIT_TABLE()[c];
599 result[index] = (char)('0' + output2);
602 // Print decimal point if needed.
604 result[index + 1] = '.';
605 index += olength + 1;
611 // Print the exponent.
612 result[index++] = 'E';
613 int32_t exp = v.exponent + (int32_t)olength - 1;
615 result[index++] = '-';
620 const int32_t c = exp % 10;
621 memcpy(result + index, DIGIT_TABLE() + 2 * (exp / 10), 2);
622 result[index + 2] = (char)('0' + c);
625 else if (exp >= 10) {
626 memcpy(result + index, DIGIT_TABLE() + 2 * exp, 2);
630 result[index++] = (char)('0' + exp);
636 static inline bool d2d_small_int(const uint64_t ieeeMantissa, const uint32_t ieeeExponent,
637 floating_decimal_64* const v) {
638 const uint64_t m2 = (1ull << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
639 const int32_t e2 = (int32_t) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
642 // f = m2 * 2^e2 >= 2^53 is an integer.
643 // Ignore this case for now.
652 // Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52: 1 <= f = m2 / 2^-e2 < 2^53.
653 // Test if the lower -e2 bits of the significand are 0, i.e. whether the fraction is 0.
654 const uint64_t mask = (1ull << -e2) - 1;
655 const uint64_t fraction = m2 & mask;
660 // f is an integer in the range [1, 2^53).
661 // Note: mantissa might contain trailing (decimal) 0's.
662 // Note: since 2^53 < 10^16, there is no need to adjust decimalLength17().
663 v->mantissa = m2 >> -e2;
673 char* result) noexcept
675 using namespace detail;
676 // Step 1: Decode the floating-point number, and unify normalized and subnormal cases.
677 std::uint64_t const bits = double_to_bits(f);
681 for (std::int32_t bit = 63; bit >= 0; --bit) {
682 printf("%d", (int)((bits >> bit) & 1));
687 // Decode bits into sign, mantissa, and exponent.
688 const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
689 const std::uint64_t ieeeMantissa = bits & ((1ull << DOUBLE_MANTISSA_BITS) - 1);
690 const std::uint32_t ieeeExponent = (std::uint32_t)((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
691 // Case distinction; exit early for the easy cases.
692 if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) {
693 return copy_special_str(result, ieeeSign, ieeeExponent != 0, ieeeMantissa != 0);
696 floating_decimal_64 v;
697 const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
699 // For small integers in the range [1, 2^53), v.mantissa might contain trailing (decimal) zeros.
700 // For scientific notation we need to move these zeros into the exponent.
701 // (This is not needed for fixed-point notation, so it might be beneficial to trim
702 // trailing zeros in to_chars only if needed - once fixed-point notation output is implemented.)
704 std::uint64_t const q = div10(v.mantissa);
705 std::uint32_t const r = ((std::uint32_t) v.mantissa) - 10 * ((std::uint32_t) q);
713 v = d2d(ieeeMantissa, ieeeExponent);
716 return to_chars(v, ieeeSign, result);