Coverage Report

Created: 2025-07-03 06:49

/src/postgres/src/common/d2s.c
Line
Count
Source (jump to first uncovered line)
1
/*---------------------------------------------------------------------------
2
 *
3
 * Ryu floating-point output for double precision.
4
 *
5
 * Portions Copyright (c) 2018-2025, PostgreSQL Global Development Group
6
 *
7
 * IDENTIFICATION
8
 *    src/common/d2s.c
9
 *
10
 * This is a modification of code taken from github.com/ulfjack/ryu under the
11
 * terms of the Boost license (not the Apache license). The original copyright
12
 * notice follows:
13
 *
14
 * Copyright 2018 Ulf Adams
15
 *
16
 * The contents of this file may be used under the terms of the Apache
17
 * License, Version 2.0.
18
 *
19
 *     (See accompanying file LICENSE-Apache or copy at
20
 *      http://www.apache.org/licenses/LICENSE-2.0)
21
 *
22
 * Alternatively, the contents of this file may be used under the terms of the
23
 * Boost Software License, Version 1.0.
24
 *
25
 *     (See accompanying file LICENSE-Boost or copy at
26
 *      https://www.boost.org/LICENSE_1_0.txt)
27
 *
28
 * Unless required by applicable law or agreed to in writing, this software is
29
 * distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
30
 * KIND, either express or implied.
31
 *
32
 *---------------------------------------------------------------------------
33
 */
34
35
/*
36
 *  Runtime compiler options:
37
 *
38
 *  -DRYU_ONLY_64_BIT_OPS Avoid using uint128 or 64-bit intrinsics. Slower,
39
 *      depending on your compiler.
40
 */
41
42
#ifndef FRONTEND
43
#include "postgres.h"
44
#else
45
#include "postgres_fe.h"
46
#endif
47
48
#include "common/shortest_dec.h"
49
50
/*
51
 * For consistency, we use 128-bit types if and only if the rest of PG also
52
 * does, even though we could use them here without worrying about the
53
 * alignment concerns that apply elsewhere.
54
 */
55
#if !defined(HAVE_INT128) && defined(_MSC_VER) \
56
  && !defined(RYU_ONLY_64_BIT_OPS) && defined(_M_X64)
57
#define HAS_64_BIT_INTRINSICS
58
#endif
59
60
#include "ryu_common.h"
61
#include "digit_table.h"
62
#include "d2s_full_table.h"
63
#include "d2s_intrinsics.h"
64
65
0
#define DOUBLE_MANTISSA_BITS 52
66
0
#define DOUBLE_EXPONENT_BITS 11
67
0
#define DOUBLE_BIAS 1023
68
69
0
#define DOUBLE_POW5_INV_BITCOUNT 122
70
0
#define DOUBLE_POW5_BITCOUNT 121
71
72
73
static inline uint32
74
pow5Factor(uint64 value)
75
0
{
76
0
  uint32    count = 0;
77
78
0
  for (;;)
79
0
  {
80
0
    Assert(value != 0);
81
0
    const uint64 q = div5(value);
82
0
    const uint32 r = (uint32) (value - 5 * q);
83
84
0
    if (r != 0)
85
0
      break;
86
87
0
    value = q;
88
0
    ++count;
89
0
  }
90
0
  return count;
91
0
}
92
93
/*  Returns true if value is divisible by 5^p. */
94
static inline bool
95
multipleOfPowerOf5(const uint64 value, const uint32 p)
96
0
{
97
  /*
98
   * I tried a case distinction on p, but there was no performance
99
   * difference.
100
   */
101
0
  return pow5Factor(value) >= p;
102
0
}
103
104
/*  Returns true if value is divisible by 2^p. */
105
static inline bool
106
multipleOfPowerOf2(const uint64 value, const uint32 p)
107
0
{
108
  /* return __builtin_ctzll(value) >= p; */
109
0
  return (value & ((UINT64CONST(1) << p) - 1)) == 0;
110
0
}
111
112
/*
113
 * We need a 64x128-bit multiplication and a subsequent 128-bit shift.
114
 *
115
 * Multiplication:
116
 *
117
 *    The 64-bit factor is variable and passed in, the 128-bit factor comes
118
 *    from a lookup table. We know that the 64-bit factor only has 55
119
 *    significant bits (i.e., the 9 topmost bits are zeros). The 128-bit
120
 *    factor only has 124 significant bits (i.e., the 4 topmost bits are
121
 *    zeros).
122
 *
123
 * Shift:
124
 *
125
 *    In principle, the multiplication result requires 55 + 124 = 179 bits to
126
 *    represent. However, we then shift this value to the right by j, which is
127
 *    at least j >= 115, so the result is guaranteed to fit into 179 - 115 =
128
 *    64 bits. This means that we only need the topmost 64 significant bits of
129
 *    the 64x128-bit multiplication.
130
 *
131
 * There are several ways to do this:
132
 *
133
 *  1. Best case: the compiler exposes a 128-bit type.
134
 *     We perform two 64x64-bit multiplications, add the higher 64 bits of the
135
 *     lower result to the higher result, and shift by j - 64 bits.
136
 *
137
 *     We explicitly cast from 64-bit to 128-bit, so the compiler can tell
138
 *     that these are only 64-bit inputs, and can map these to the best
139
 *     possible sequence of assembly instructions. x86-64 machines happen to
140
 *     have matching assembly instructions for 64x64-bit multiplications and
141
 *     128-bit shifts.
142
 *
143
 *  2. Second best case: the compiler exposes intrinsics for the x86-64
144
 *     assembly instructions mentioned in 1.
145
 *
146
 *  3. We only have 64x64 bit instructions that return the lower 64 bits of
147
 *     the result, i.e., we have to use plain C.
148
 *
149
 *     Our inputs are less than the full width, so we have three options:
150
 *     a. Ignore this fact and just implement the intrinsics manually.
151
 *     b. Split both into 31-bit pieces, which guarantees no internal
152
 *        overflow, but requires extra work upfront (unless we change the
153
 *        lookup table).
154
 *     c. Split only the first factor into 31-bit pieces, which also
155
 *        guarantees no internal overflow, but requires extra work since the
156
 *        intermediate results are not perfectly aligned.
157
 */
158
#if defined(HAVE_INT128)
159
160
/*  Best case: use 128-bit type. */
161
static inline uint64
162
mulShift(const uint64 m, const uint64 *const mul, const int32 j)
163
0
{
164
0
  const uint128 b0 = ((uint128) m) * mul[0];
165
0
  const uint128 b2 = ((uint128) m) * mul[1];
166
167
0
  return (uint64) (((b0 >> 64) + b2) >> (j - 64));
168
0
}
169
170
static inline uint64
171
mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
172
      uint64 *const vp, uint64 *const vm, const uint32 mmShift)
173
0
{
174
0
  *vp = mulShift(4 * m + 2, mul, j);
175
0
  *vm = mulShift(4 * m - 1 - mmShift, mul, j);
176
0
  return mulShift(4 * m, mul, j);
177
0
}
178
179
#elif defined(HAS_64_BIT_INTRINSICS)
180
181
static inline uint64
182
mulShift(const uint64 m, const uint64 *const mul, const int32 j)
183
{
184
  /* m is maximum 55 bits */
185
  uint64    high1;
186
187
  /* 128 */
188
  const uint64 low1 = umul128(m, mul[1], &high1);
189
190
  /* 64 */
191
  uint64    high0;
192
  uint64    sum;
193
194
  /* 64 */
195
  umul128(m, mul[0], &high0);
196
  /* 0 */
197
  sum = high0 + low1;
198
199
  if (sum < high0)
200
  {
201
    ++high1;
202
    /* overflow into high1 */
203
  }
204
  return shiftright128(sum, high1, j - 64);
205
}
206
207
static inline uint64
208
mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
209
      uint64 *const vp, uint64 *const vm, const uint32 mmShift)
210
{
211
  *vp = mulShift(4 * m + 2, mul, j);
212
  *vm = mulShift(4 * m - 1 - mmShift, mul, j);
213
  return mulShift(4 * m, mul, j);
214
}
215
216
#else             /* // !defined(HAVE_INT128) &&
217
                 * !defined(HAS_64_BIT_INTRINSICS) */
218
219
static inline uint64
220
mulShiftAll(uint64 m, const uint64 *const mul, const int32 j,
221
      uint64 *const vp, uint64 *const vm, const uint32 mmShift)
222
{
223
  m <<= 1;          /* m is maximum 55 bits */
224
225
  uint64    tmp;
226
  const uint64 lo = umul128(m, mul[0], &tmp);
227
  uint64    hi;
228
  const uint64 mid = tmp + umul128(m, mul[1], &hi);
229
230
  hi += mid < tmp;      /* overflow into hi */
231
232
  const uint64 lo2 = lo + mul[0];
233
  const uint64 mid2 = mid + mul[1] + (lo2 < lo);
234
  const uint64 hi2 = hi + (mid2 < mid);
235
236
  *vp = shiftright128(mid2, hi2, j - 64 - 1);
237
238
  if (mmShift == 1)
239
  {
240
    const uint64 lo3 = lo - mul[0];
241
    const uint64 mid3 = mid - mul[1] - (lo3 > lo);
242
    const uint64 hi3 = hi - (mid3 > mid);
243
244
    *vm = shiftright128(mid3, hi3, j - 64 - 1);
245
  }
246
  else
247
  {
248
    const uint64 lo3 = lo + lo;
249
    const uint64 mid3 = mid + mid + (lo3 < lo);
250
    const uint64 hi3 = hi + hi + (mid3 < mid);
251
    const uint64 lo4 = lo3 - mul[0];
252
    const uint64 mid4 = mid3 - mul[1] - (lo4 > lo3);
253
    const uint64 hi4 = hi3 - (mid4 > mid3);
254
255
    *vm = shiftright128(mid4, hi4, j - 64);
256
  }
257
258
  return shiftright128(mid, hi, j - 64 - 1);
259
}
260
261
#endif              /* // HAS_64_BIT_INTRINSICS */
262
263
static inline uint32
264
decimalLength(const uint64 v)
265
0
{
266
  /* This is slightly faster than a loop. */
267
  /* The average output length is 16.38 digits, so we check high-to-low. */
268
  /* Function precondition: v is not an 18, 19, or 20-digit number. */
269
  /* (17 digits are sufficient for round-tripping.) */
270
0
  Assert(v < 100000000000000000L);
271
0
  if (v >= 10000000000000000L)
272
0
  {
273
0
    return 17;
274
0
  }
275
0
  if (v >= 1000000000000000L)
276
0
  {
277
0
    return 16;
278
0
  }
279
0
  if (v >= 100000000000000L)
280
0
  {
281
0
    return 15;
282
0
  }
283
0
  if (v >= 10000000000000L)
284
0
  {
285
0
    return 14;
286
0
  }
287
0
  if (v >= 1000000000000L)
288
0
  {
289
0
    return 13;
290
0
  }
291
0
  if (v >= 100000000000L)
292
0
  {
293
0
    return 12;
294
0
  }
295
0
  if (v >= 10000000000L)
296
0
  {
297
0
    return 11;
298
0
  }
299
0
  if (v >= 1000000000L)
300
0
  {
301
0
    return 10;
302
0
  }
303
0
  if (v >= 100000000L)
304
0
  {
305
0
    return 9;
306
0
  }
307
0
  if (v >= 10000000L)
308
0
  {
309
0
    return 8;
310
0
  }
311
0
  if (v >= 1000000L)
312
0
  {
313
0
    return 7;
314
0
  }
315
0
  if (v >= 100000L)
316
0
  {
317
0
    return 6;
318
0
  }
319
0
  if (v >= 10000L)
320
0
  {
321
0
    return 5;
322
0
  }
323
0
  if (v >= 1000L)
324
0
  {
325
0
    return 4;
326
0
  }
327
0
  if (v >= 100L)
328
0
  {
329
0
    return 3;
330
0
  }
331
0
  if (v >= 10L)
332
0
  {
333
0
    return 2;
334
0
  }
335
0
  return 1;
336
0
}
337
338
/*  A floating decimal representing m * 10^e. */
339
typedef struct floating_decimal_64
340
{
341
  uint64    mantissa;
342
  int32   exponent;
343
} floating_decimal_64;
344
345
static inline floating_decimal_64
346
d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
347
0
{
348
0
  int32   e2;
349
0
  uint64    m2;
350
351
0
  if (ieeeExponent == 0)
352
0
  {
353
    /* We subtract 2 so that the bounds computation has 2 additional bits. */
354
0
    e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
355
0
    m2 = ieeeMantissa;
356
0
  }
357
0
  else
358
0
  {
359
0
    e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
360
0
    m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
361
0
  }
362
363
#if STRICTLY_SHORTEST
364
  const bool  even = (m2 & 1) == 0;
365
  const bool  acceptBounds = even;
366
#else
367
0
  const bool  acceptBounds = false;
368
0
#endif
369
370
  /* Step 2: Determine the interval of legal decimal representations. */
371
0
  const uint64 mv = 4 * m2;
372
373
  /* Implicit bool -> int conversion. True is 1, false is 0. */
374
0
  const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
375
376
  /* We would compute mp and mm like this: */
377
  /* uint64 mp = 4 * m2 + 2; */
378
  /* uint64 mm = mv - 1 - mmShift; */
379
380
  /* Step 3: Convert to a decimal power base using 128-bit arithmetic. */
381
0
  uint64    vr,
382
0
        vp,
383
0
        vm;
384
0
  int32   e10;
385
0
  bool    vmIsTrailingZeros = false;
386
0
  bool    vrIsTrailingZeros = false;
387
388
0
  if (e2 >= 0)
389
0
  {
390
    /*
391
     * I tried special-casing q == 0, but there was no effect on
392
     * performance.
393
     *
394
     * This expr is slightly faster than max(0, log10Pow2(e2) - 1).
395
     */
396
0
    const uint32 q = log10Pow2(e2) - (e2 > 3);
397
0
    const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
398
0
    const int32 i = -e2 + q + k;
399
400
0
    e10 = q;
401
402
0
    vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
403
404
0
    if (q <= 21)
405
0
    {
406
      /*
407
       * This should use q <= 22, but I think 21 is also safe. Smaller
408
       * values may still be safe, but it's more difficult to reason
409
       * about them.
410
       *
411
       * Only one of mp, mv, and mm can be a multiple of 5, if any.
412
       */
413
0
      const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
414
415
0
      if (mvMod5 == 0)
416
0
      {
417
0
        vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
418
0
      }
419
0
      else if (acceptBounds)
420
0
      {
421
        /*----
422
         * Same as min(e2 + (~mm & 1), pow5Factor(mm)) >= q
423
         * <=> e2 + (~mm & 1) >= q && pow5Factor(mm) >= q
424
         * <=> true && pow5Factor(mm) >= q, since e2 >= q.
425
         *----
426
         */
427
0
        vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
428
0
      }
429
0
      else
430
0
      {
431
        /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
432
0
        vp -= multipleOfPowerOf5(mv + 2, q);
433
0
      }
434
0
    }
435
0
  }
436
0
  else
437
0
  {
438
    /*
439
     * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
440
     */
441
0
    const uint32 q = log10Pow5(-e2) - (-e2 > 1);
442
0
    const int32 i = -e2 - q;
443
0
    const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
444
0
    const int32 j = q - k;
445
446
0
    e10 = q + e2;
447
448
0
    vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
449
450
0
    if (q <= 1)
451
0
    {
452
      /*
453
       * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
454
       * trailing 0 bits.
455
       */
456
      /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
457
0
      vrIsTrailingZeros = true;
458
0
      if (acceptBounds)
459
0
      {
460
        /*
461
         * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
462
         * mmShift == 1.
463
         */
464
0
        vmIsTrailingZeros = mmShift == 1;
465
0
      }
466
0
      else
467
0
      {
468
        /*
469
         * mp = mv + 2, so it always has at least one trailing 0 bit.
470
         */
471
0
        --vp;
472
0
      }
473
0
    }
474
0
    else if (q < 63)
475
0
    {
476
      /* TODO(ulfjack):Use a tighter bound here. */
477
      /*
478
       * We need to compute min(ntz(mv), pow5Factor(mv) - e2) >= q - 1
479
       */
480
      /* <=> ntz(mv) >= q - 1 && pow5Factor(mv) - e2 >= q - 1 */
481
      /* <=> ntz(mv) >= q - 1 (e2 is negative and -e2 >= q) */
482
      /* <=> (mv & ((1 << (q - 1)) - 1)) == 0 */
483
484
      /*
485
       * We also need to make sure that the left shift does not
486
       * overflow.
487
       */
488
0
      vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
489
0
    }
490
0
  }
491
492
  /*
493
   * Step 4: Find the shortest decimal representation in the interval of
494
   * legal representations.
495
   */
496
0
  uint32    removed = 0;
497
0
  uint8   lastRemovedDigit = 0;
498
0
  uint64    output;
499
500
  /* On average, we remove ~2 digits. */
501
0
  if (vmIsTrailingZeros || vrIsTrailingZeros)
502
0
  {
503
    /* General case, which happens rarely (~0.7%). */
504
0
    for (;;)
505
0
    {
506
0
      const uint64 vpDiv10 = div10(vp);
507
0
      const uint64 vmDiv10 = div10(vm);
508
509
0
      if (vpDiv10 <= vmDiv10)
510
0
        break;
511
512
0
      const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
513
0
      const uint64 vrDiv10 = div10(vr);
514
0
      const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
515
516
0
      vmIsTrailingZeros &= vmMod10 == 0;
517
0
      vrIsTrailingZeros &= lastRemovedDigit == 0;
518
0
      lastRemovedDigit = (uint8) vrMod10;
519
0
      vr = vrDiv10;
520
0
      vp = vpDiv10;
521
0
      vm = vmDiv10;
522
0
      ++removed;
523
0
    }
524
525
0
    if (vmIsTrailingZeros)
526
0
    {
527
0
      for (;;)
528
0
      {
529
0
        const uint64 vmDiv10 = div10(vm);
530
0
        const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
531
532
0
        if (vmMod10 != 0)
533
0
          break;
534
535
0
        const uint64 vpDiv10 = div10(vp);
536
0
        const uint64 vrDiv10 = div10(vr);
537
0
        const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
538
539
0
        vrIsTrailingZeros &= lastRemovedDigit == 0;
540
0
        lastRemovedDigit = (uint8) vrMod10;
541
0
        vr = vrDiv10;
542
0
        vp = vpDiv10;
543
0
        vm = vmDiv10;
544
0
        ++removed;
545
0
      }
546
0
    }
547
548
0
    if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
549
0
    {
550
      /* Round even if the exact number is .....50..0. */
551
0
      lastRemovedDigit = 4;
552
0
    }
553
554
    /*
555
     * We need to take vr + 1 if vr is outside bounds or we need to round
556
     * up.
557
     */
558
0
    output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
559
0
  }
560
0
  else
561
0
  {
562
    /*
563
     * Specialized for the common case (~99.3%). Percentages below are
564
     * relative to this.
565
     */
566
0
    bool    roundUp = false;
567
0
    const uint64 vpDiv100 = div100(vp);
568
0
    const uint64 vmDiv100 = div100(vm);
569
570
0
    if (vpDiv100 > vmDiv100)
571
0
    {
572
      /* Optimization:remove two digits at a time(~86.2 %). */
573
0
      const uint64 vrDiv100 = div100(vr);
574
0
      const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
575
576
0
      roundUp = vrMod100 >= 50;
577
0
      vr = vrDiv100;
578
0
      vp = vpDiv100;
579
0
      vm = vmDiv100;
580
0
      removed += 2;
581
0
    }
582
583
    /*----
584
     * Loop iterations below (approximately), without optimization
585
     * above:
586
     *
587
     * 0: 0.03%, 1: 13.8%, 2: 70.6%, 3: 14.0%, 4: 1.40%, 5: 0.14%,
588
     * 6+: 0.02%
589
     *
590
     * Loop iterations below (approximately), with optimization
591
     * above:
592
     *
593
     * 0: 70.6%, 1: 27.8%, 2: 1.40%, 3: 0.14%, 4+: 0.02%
594
     *----
595
     */
596
0
    for (;;)
597
0
    {
598
0
      const uint64 vpDiv10 = div10(vp);
599
0
      const uint64 vmDiv10 = div10(vm);
600
601
0
      if (vpDiv10 <= vmDiv10)
602
0
        break;
603
604
0
      const uint64 vrDiv10 = div10(vr);
605
0
      const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
606
607
0
      roundUp = vrMod10 >= 5;
608
0
      vr = vrDiv10;
609
0
      vp = vpDiv10;
610
0
      vm = vmDiv10;
611
0
      ++removed;
612
0
    }
613
614
    /*
615
     * We need to take vr + 1 if vr is outside bounds or we need to round
616
     * up.
617
     */
618
0
    output = vr + (vr == vm || roundUp);
619
0
  }
620
621
0
  const int32 exp = e10 + removed;
622
623
0
  floating_decimal_64 fd;
624
625
0
  fd.exponent = exp;
626
0
  fd.mantissa = output;
627
0
  return fd;
628
0
}
629
630
static inline int
631
to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
632
0
{
633
  /* Step 5: Print the decimal representation. */
634
0
  int     index = 0;
635
636
0
  uint64    output = v.mantissa;
637
0
  int32   exp = v.exponent;
638
639
  /*----
640
   * On entry, mantissa * 10^exp is the result to be output.
641
   * Caller has already done the - sign if needed.
642
   *
643
   * We want to insert the point somewhere depending on the output length
644
   * and exponent, which might mean adding zeros:
645
   *
646
   *            exp  | format
647
   *            1+   |  ddddddddd000000
648
   *            0    |  ddddddddd
649
   *  -1 .. -len+1   |  dddddddd.d to d.ddddddddd
650
   *  -len ...       |  0.ddddddddd to 0.000dddddd
651
   */
652
0
  uint32    i = 0;
653
0
  int32   nexp = exp + olength;
654
655
0
  if (nexp <= 0)
656
0
  {
657
    /* -nexp is number of 0s to add after '.' */
658
0
    Assert(nexp >= -3);
659
    /* 0.000ddddd */
660
0
    index = 2 - nexp;
661
    /* won't need more than this many 0s */
662
0
    memcpy(result, "0.000000", 8);
663
0
  }
664
0
  else if (exp < 0)
665
0
  {
666
    /*
667
     * dddd.dddd; leave space at the start and move the '.' in after
668
     */
669
0
    index = 1;
670
0
  }
671
0
  else
672
0
  {
673
    /*
674
     * We can save some code later by pre-filling with zeros. We know that
675
     * there can be no more than 16 output digits in this form, otherwise
676
     * we would not choose fixed-point output.
677
     */
678
0
    Assert(exp < 16 && exp + olength <= 16);
679
0
    memset(result, '0', 16);
680
0
  }
681
682
  /*
683
   * We prefer 32-bit operations, even on 64-bit platforms. We have at most
684
   * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
685
   * uint32, we cut off 8 digits, so the rest will fit into uint32.
686
   */
687
0
  if ((output >> 32) != 0)
688
0
  {
689
    /* Expensive 64-bit division. */
690
0
    const uint64 q = div1e8(output);
691
0
    uint32    output2 = (uint32) (output - 100000000 * q);
692
0
    const uint32 c = output2 % 10000;
693
694
0
    output = q;
695
0
    output2 /= 10000;
696
697
0
    const uint32 d = output2 % 10000;
698
0
    const uint32 c0 = (c % 100) << 1;
699
0
    const uint32 c1 = (c / 100) << 1;
700
0
    const uint32 d0 = (d % 100) << 1;
701
0
    const uint32 d1 = (d / 100) << 1;
702
703
0
    memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
704
0
    memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
705
0
    memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
706
0
    memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
707
0
    i += 8;
708
0
  }
709
710
0
  uint32    output2 = (uint32) output;
711
712
0
  while (output2 >= 10000)
713
0
  {
714
0
    const uint32 c = output2 - 10000 * (output2 / 10000);
715
0
    const uint32 c0 = (c % 100) << 1;
716
0
    const uint32 c1 = (c / 100) << 1;
717
718
0
    output2 /= 10000;
719
0
    memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
720
0
    memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
721
0
    i += 4;
722
0
  }
723
0
  if (output2 >= 100)
724
0
  {
725
0
    const uint32 c = (output2 % 100) << 1;
726
727
0
    output2 /= 100;
728
0
    memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
729
0
    i += 2;
730
0
  }
731
0
  if (output2 >= 10)
732
0
  {
733
0
    const uint32 c = output2 << 1;
734
735
0
    memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
736
0
  }
737
0
  else
738
0
  {
739
0
    result[index] = (char) ('0' + output2);
740
0
  }
741
742
0
  if (index == 1)
743
0
  {
744
    /*
745
     * nexp is 1..15 here, representing the number of digits before the
746
     * point. A value of 16 is not possible because we switch to
747
     * scientific notation when the display exponent reaches 15.
748
     */
749
0
    Assert(nexp < 16);
750
    /* gcc only seems to want to optimize memmove for small 2^n */
751
0
    if (nexp & 8)
752
0
    {
753
0
      memmove(result + index - 1, result + index, 8);
754
0
      index += 8;
755
0
    }
756
0
    if (nexp & 4)
757
0
    {
758
0
      memmove(result + index - 1, result + index, 4);
759
0
      index += 4;
760
0
    }
761
0
    if (nexp & 2)
762
0
    {
763
0
      memmove(result + index - 1, result + index, 2);
764
0
      index += 2;
765
0
    }
766
0
    if (nexp & 1)
767
0
    {
768
0
      result[index - 1] = result[index];
769
0
    }
770
0
    result[nexp] = '.';
771
0
    index = olength + 1;
772
0
  }
773
0
  else if (exp >= 0)
774
0
  {
775
    /* we supplied the trailing zeros earlier, now just set the length. */
776
0
    index = olength + exp;
777
0
  }
778
0
  else
779
0
  {
780
0
    index = olength + (2 - nexp);
781
0
  }
782
783
0
  return index;
784
0
}
785
786
static inline int
787
to_chars(floating_decimal_64 v, const bool sign, char *const result)
788
0
{
789
  /* Step 5: Print the decimal representation. */
790
0
  int     index = 0;
791
792
0
  uint64    output = v.mantissa;
793
0
  uint32    olength = decimalLength(output);
794
0
  int32   exp = v.exponent + olength - 1;
795
796
0
  if (sign)
797
0
  {
798
0
    result[index++] = '-';
799
0
  }
800
801
  /*
802
   * The thresholds for fixed-point output are chosen to match printf
803
   * defaults. Beware that both the code of to_chars_df and the value of
804
   * DOUBLE_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
805
   */
806
0
  if (exp >= -4 && exp < 15)
807
0
    return to_chars_df(v, olength, result + index) + sign;
808
809
  /*
810
   * If v.exponent is exactly 0, we might have reached here via the small
811
   * integer fast path, in which case v.mantissa might contain trailing
812
   * (decimal) zeros. For scientific notation we need to move these zeros
813
   * into the exponent. (For fixed point this doesn't matter, which is why
814
   * we do this here rather than above.)
815
   *
816
   * Since we already calculated the display exponent (exp) above based on
817
   * the old decimal length, that value does not change here. Instead, we
818
   * just reduce the display length for each digit removed.
819
   *
820
   * If we didn't get here via the fast path, the raw exponent will not
821
   * usually be 0, and there will be no trailing zeros, so we pay no more
822
   * than one div10/multiply extra cost. We claw back half of that by
823
   * checking for divisibility by 2 before dividing by 10.
824
   */
825
0
  if (v.exponent == 0)
826
0
  {
827
0
    while ((output & 1) == 0)
828
0
    {
829
0
      const uint64 q = div10(output);
830
0
      const uint32 r = (uint32) (output - 10 * q);
831
832
0
      if (r != 0)
833
0
        break;
834
0
      output = q;
835
0
      --olength;
836
0
    }
837
0
  }
838
839
  /*----
840
   * Print the decimal digits.
841
   *
842
   * The following code is equivalent to:
843
   *
844
   * for (uint32 i = 0; i < olength - 1; ++i) {
845
   *   const uint32 c = output % 10; output /= 10;
846
   *   result[index + olength - i] = (char) ('0' + c);
847
   * }
848
   * result[index] = '0' + output % 10;
849
   *----
850
   */
851
852
0
  uint32    i = 0;
853
854
  /*
855
   * We prefer 32-bit operations, even on 64-bit platforms. We have at most
856
   * 17 digits, and uint32 can store 9 digits. If output doesn't fit into
857
   * uint32, we cut off 8 digits, so the rest will fit into uint32.
858
   */
859
0
  if ((output >> 32) != 0)
860
0
  {
861
    /* Expensive 64-bit division. */
862
0
    const uint64 q = div1e8(output);
863
0
    uint32    output2 = (uint32) (output - 100000000 * q);
864
865
0
    output = q;
866
867
0
    const uint32 c = output2 % 10000;
868
869
0
    output2 /= 10000;
870
871
0
    const uint32 d = output2 % 10000;
872
0
    const uint32 c0 = (c % 100) << 1;
873
0
    const uint32 c1 = (c / 100) << 1;
874
0
    const uint32 d0 = (d % 100) << 1;
875
0
    const uint32 d1 = (d / 100) << 1;
876
877
0
    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
878
0
    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
879
0
    memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
880
0
    memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
881
0
    i += 8;
882
0
  }
883
884
0
  uint32    output2 = (uint32) output;
885
886
0
  while (output2 >= 10000)
887
0
  {
888
0
    const uint32 c = output2 - 10000 * (output2 / 10000);
889
890
0
    output2 /= 10000;
891
892
0
    const uint32 c0 = (c % 100) << 1;
893
0
    const uint32 c1 = (c / 100) << 1;
894
895
0
    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
896
0
    memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
897
0
    i += 4;
898
0
  }
899
0
  if (output2 >= 100)
900
0
  {
901
0
    const uint32 c = (output2 % 100) << 1;
902
903
0
    output2 /= 100;
904
0
    memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
905
0
    i += 2;
906
0
  }
907
0
  if (output2 >= 10)
908
0
  {
909
0
    const uint32 c = output2 << 1;
910
911
    /*
912
     * We can't use memcpy here: the decimal dot goes between these two
913
     * digits.
914
     */
915
0
    result[index + olength - i] = DIGIT_TABLE[c + 1];
916
0
    result[index] = DIGIT_TABLE[c];
917
0
  }
918
0
  else
919
0
  {
920
0
    result[index] = (char) ('0' + output2);
921
0
  }
922
923
  /* Print decimal point if needed. */
924
0
  if (olength > 1)
925
0
  {
926
0
    result[index + 1] = '.';
927
0
    index += olength + 1;
928
0
  }
929
0
  else
930
0
  {
931
0
    ++index;
932
0
  }
933
934
  /* Print the exponent. */
935
0
  result[index++] = 'e';
936
0
  if (exp < 0)
937
0
  {
938
0
    result[index++] = '-';
939
0
    exp = -exp;
940
0
  }
941
0
  else
942
0
    result[index++] = '+';
943
944
0
  if (exp >= 100)
945
0
  {
946
0
    const int32 c = exp % 10;
947
948
0
    memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
949
0
    result[index + 2] = (char) ('0' + c);
950
0
    index += 3;
951
0
  }
952
0
  else
953
0
  {
954
0
    memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
955
0
    index += 2;
956
0
  }
957
958
0
  return index;
959
0
}
960
961
static inline bool
962
d2d_small_int(const uint64 ieeeMantissa,
963
        const uint32 ieeeExponent,
964
        floating_decimal_64 *v)
965
0
{
966
0
  const int32 e2 = (int32) ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS;
967
968
  /*
969
   * Avoid using multiple "return false;" here since it tends to provoke the
970
   * compiler into inlining multiple copies of d2d, which is undesirable.
971
   */
972
973
0
  if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
974
0
  {
975
    /*----
976
     * Since 2^52 <= m2 < 2^53 and 0 <= -e2 <= 52:
977
     *   1 <= f = m2 / 2^-e2 < 2^53.
978
     *
979
     * Test if the lower -e2 bits of the significand are 0, i.e. whether
980
     * the fraction is 0. We can use ieeeMantissa here, since the implied
981
     * 1 bit can never be tested by this; the implied 1 can only be part
982
     * of a fraction if e2 < -DOUBLE_MANTISSA_BITS which we already
983
     * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -53)
984
     */
985
0
    const uint64 mask = (UINT64CONST(1) << -e2) - 1;
986
0
    const uint64 fraction = ieeeMantissa & mask;
987
988
0
    if (fraction == 0)
989
0
    {
990
      /*----
991
       * f is an integer in the range [1, 2^53).
992
       * Note: mantissa might contain trailing (decimal) 0's.
993
       * Note: since 2^53 < 10^16, there is no need to adjust
994
       * decimalLength().
995
       */
996
0
      const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
997
998
0
      v->mantissa = m2 >> -e2;
999
0
      v->exponent = 0;
1000
0
      return true;
1001
0
    }
1002
0
  }
1003
1004
0
  return false;
1005
0
}
1006
1007
/*
1008
 * Store the shortest decimal representation of the given double as an
1009
 * UNTERMINATED string in the caller's supplied buffer (which must be at least
1010
 * DOUBLE_SHORTEST_DECIMAL_LEN-1 bytes long).
1011
 *
1012
 * Returns the number of bytes stored.
1013
 */
1014
int
1015
double_to_shortest_decimal_bufn(double f, char *result)
1016
0
{
1017
  /*
1018
   * Step 1: Decode the floating-point number, and unify normalized and
1019
   * subnormal cases.
1020
   */
1021
0
  const uint64 bits = double_to_bits(f);
1022
1023
  /* Decode bits into sign, mantissa, and exponent. */
1024
0
  const bool  ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
1025
0
  const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
1026
0
  const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
1027
1028
  /* Case distinction; exit early for the easy cases. */
1029
0
  if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
1030
0
  {
1031
0
    return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
1032
0
  }
1033
1034
0
  floating_decimal_64 v;
1035
0
  const bool  isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
1036
1037
0
  if (!isSmallInt)
1038
0
  {
1039
0
    v = d2d(ieeeMantissa, ieeeExponent);
1040
0
  }
1041
1042
0
  return to_chars(v, ieeeSign, result);
1043
0
}
1044
1045
/*
1046
 * Store the shortest decimal representation of the given double as a
1047
 * null-terminated string in the caller's supplied buffer (which must be at
1048
 * least DOUBLE_SHORTEST_DECIMAL_LEN bytes long).
1049
 *
1050
 * Returns the string length.
1051
 */
1052
int
1053
double_to_shortest_decimal_buf(double f, char *result)
1054
0
{
1055
0
  const int index = double_to_shortest_decimal_bufn(f, result);
1056
1057
  /* Terminate the string. */
1058
0
  Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
1059
0
  result[index] = '\0';
1060
0
  return index;
1061
0
}
1062
1063
/*
1064
 * Return the shortest decimal representation as a null-terminated palloc'd
1065
 * string (outside the backend, uses malloc() instead).
1066
 *
1067
 * Caller is responsible for freeing the result.
1068
 */
1069
char *
1070
double_to_shortest_decimal(double f)
1071
0
{
1072
0
  char     *const result = (char *) palloc(DOUBLE_SHORTEST_DECIMAL_LEN);
1073
1074
0
  double_to_shortest_decimal_buf(f, result);
1075
0
  return result;
1076
0
}