TLA Line data Source code
1 : /*---------------------------------------------------------------------------
2 : *
3 : * Ryu floating-point output for double precision.
4 : *
5 : * Portions Copyright (c) 2018-2023, 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 : #define DOUBLE_MANTISSA_BITS 52
66 : #define DOUBLE_EXPONENT_BITS 11
67 : #define DOUBLE_BIAS 1023
68 :
69 : #define DOUBLE_POW5_INV_BITCOUNT 122
70 : #define DOUBLE_POW5_BITCOUNT 121
71 :
72 :
73 : static inline uint32
74 CBC 698 : pow5Factor(uint64 value)
75 : {
76 698 : uint32 count = 0;
77 :
78 : for (;;)
79 2265 : {
80 2963 : Assert(value != 0);
81 2963 : const uint64 q = div5(value);
82 2963 : const uint32 r = (uint32) (value - 5 * q);
83 :
84 2963 : if (r != 0)
85 698 : break;
86 :
87 2265 : value = q;
88 2265 : ++count;
89 : }
90 698 : return count;
91 : }
92 :
93 : /* Returns true if value is divisible by 5^p. */
94 : static inline bool
95 698 : multipleOfPowerOf5(const uint64 value, const uint32 p)
96 : {
97 : /*
98 : * I tried a case distinction on p, but there was no performance
99 : * difference.
100 : */
101 698 : return pow5Factor(value) >= p;
102 : }
103 :
104 : /* Returns true if value is divisible by 2^p. */
105 : static inline bool
106 795340 : multipleOfPowerOf2(const uint64 value, const uint32 p)
107 : {
108 : /* return __builtin_ctzll(value) >= p; */
109 795340 : return (value & ((UINT64CONST(1) << p) - 1)) == 0;
110 : }
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 2390298 : mulShift(const uint64 m, const uint64 *const mul, const int32 j)
163 : {
164 2390298 : const uint128 b0 = ((uint128) m) * mul[0];
165 2390298 : const uint128 b2 = ((uint128) m) * mul[1];
166 :
167 2390298 : return (uint64) (((b0 >> 64) + b2) >> (j - 64));
168 : }
169 :
170 : static inline uint64
171 796766 : mulShiftAll(const uint64 m, const uint64 *const mul, const int32 j,
172 : uint64 *const vp, uint64 *const vm, const uint32 mmShift)
173 : {
174 796766 : *vp = mulShift(4 * m + 2, mul, j);
175 796766 : *vm = mulShift(4 * m - 1 - mmShift, mul, j);
176 796766 : return mulShift(4 * m, mul, j);
177 : }
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 1980847 : decimalLength(const uint64 v)
265 : {
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 1980847 : Assert(v < 100000000000000000L);
271 1980847 : if (v >= 10000000000000000L)
272 : {
273 141097 : return 17;
274 : }
275 1839750 : if (v >= 1000000000000000L)
276 : {
277 332181 : return 16;
278 : }
279 1507569 : if (v >= 100000000000000L)
280 : {
281 30843 : return 15;
282 : }
283 1476726 : if (v >= 10000000000000L)
284 : {
285 5458 : return 14;
286 : }
287 1471268 : if (v >= 1000000000000L)
288 : {
289 176 : return 13;
290 : }
291 1471092 : if (v >= 100000000000L)
292 : {
293 65 : return 12;
294 : }
295 1471027 : if (v >= 10000000000L)
296 : {
297 69 : return 11;
298 : }
299 1470958 : if (v >= 1000000000L)
300 : {
301 21754 : return 10;
302 : }
303 1449204 : if (v >= 100000000L)
304 : {
305 23283 : return 9;
306 : }
307 1425921 : if (v >= 10000000L)
308 : {
309 2678 : return 8;
310 : }
311 1423243 : if (v >= 1000000L)
312 : {
313 56850 : return 7;
314 : }
315 1366393 : if (v >= 100000L)
316 : {
317 6225 : return 6;
318 : }
319 1360168 : if (v >= 10000L)
320 : {
321 183596 : return 5;
322 : }
323 1176572 : if (v >= 1000L)
324 : {
325 362322 : return 4;
326 : }
327 814250 : if (v >= 100L)
328 : {
329 673199 : return 3;
330 : }
331 141051 : if (v >= 10L)
332 : {
333 122054 : return 2;
334 : }
335 18997 : return 1;
336 : }
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 796766 : d2d(const uint64 ieeeMantissa, const uint32 ieeeExponent)
347 : {
348 : int32 e2;
349 : uint64 m2;
350 :
351 796766 : if (ieeeExponent == 0)
352 : {
353 : /* We subtract 2 so that the bounds computation has 2 additional bits. */
354 63 : e2 = 1 - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
355 63 : m2 = ieeeMantissa;
356 : }
357 : else
358 : {
359 796703 : e2 = ieeeExponent - DOUBLE_BIAS - DOUBLE_MANTISSA_BITS - 2;
360 796703 : m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
361 : }
362 :
363 : #if STRICTLY_SHORTEST
364 : const bool even = (m2 & 1) == 0;
365 : const bool acceptBounds = even;
366 : #else
367 796766 : const bool acceptBounds = false;
368 : #endif
369 :
370 : /* Step 2: Determine the interval of legal decimal representations. */
371 796766 : const uint64 mv = 4 * m2;
372 :
373 : /* Implicit bool -> int conversion. True is 1, false is 0. */
374 796766 : 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 : uint64 vr,
382 : vp,
383 : vm;
384 : int32 e10;
385 796766 : bool vmIsTrailingZeros = false;
386 796766 : bool vrIsTrailingZeros = false;
387 :
388 796766 : if (e2 >= 0)
389 : {
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 : */
396 992 : const uint32 q = log10Pow2(e2) - (e2 > 3);
397 992 : const int32 k = DOUBLE_POW5_INV_BITCOUNT + pow5bits(q) - 1;
398 992 : const int32 i = -e2 + q + k;
399 :
400 992 : e10 = q;
401 :
402 992 : vr = mulShiftAll(m2, DOUBLE_POW5_INV_SPLIT[q], i, &vp, &vm, mmShift);
403 :
404 992 : if (q <= 21)
405 : {
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 : */
413 698 : const uint32 mvMod5 = (uint32) (mv - 5 * div5(mv));
414 :
415 698 : if (mvMod5 == 0)
416 : {
417 105 : vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
418 : }
419 593 : else if (acceptBounds)
420 : {
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 UBC 0 : vmIsTrailingZeros = multipleOfPowerOf5(mv - 1 - mmShift, q);
428 : }
429 : else
430 : {
431 : /* Same as min(e2 + 1, pow5Factor(mp)) >= q. */
432 CBC 593 : vp -= multipleOfPowerOf5(mv + 2, q);
433 : }
434 : }
435 : }
436 : else
437 : {
438 : /*
439 : * This expression is slightly faster than max(0, log10Pow5(-e2) - 1).
440 : */
441 795774 : const uint32 q = log10Pow5(-e2) - (-e2 > 1);
442 795774 : const int32 i = -e2 - q;
443 795774 : const int32 k = pow5bits(i) - DOUBLE_POW5_BITCOUNT;
444 795774 : const int32 j = q - k;
445 :
446 795774 : e10 = q + e2;
447 :
448 795774 : vr = mulShiftAll(m2, DOUBLE_POW5_SPLIT[i], j, &vp, &vm, mmShift);
449 :
450 795774 : if (q <= 1)
451 : {
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 60 : vrIsTrailingZeros = true;
458 60 : if (acceptBounds)
459 : {
460 : /*
461 : * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
462 : * mmShift == 1.
463 : */
464 UBC 0 : vmIsTrailingZeros = mmShift == 1;
465 : }
466 : else
467 : {
468 : /*
469 : * mp = mv + 2, so it always has at least one trailing 0 bit.
470 : */
471 CBC 60 : --vp;
472 : }
473 : }
474 795714 : else if (q < 63)
475 : {
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 795340 : vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
489 : }
490 : }
491 :
492 : /*
493 : * Step 4: Find the shortest decimal representation in the interval of
494 : * legal representations.
495 : */
496 796766 : uint32 removed = 0;
497 796766 : uint8 lastRemovedDigit = 0;
498 : uint64 output;
499 :
500 : /* On average, we remove ~2 digits. */
501 796766 : if (vmIsTrailingZeros || vrIsTrailingZeros)
502 : {
503 : /* General case, which happens rarely (~0.7%). */
504 : for (;;)
505 2275371 : {
506 2434995 : const uint64 vpDiv10 = div10(vp);
507 2434995 : const uint64 vmDiv10 = div10(vm);
508 :
509 2434995 : if (vpDiv10 <= vmDiv10)
510 159624 : break;
511 :
512 2275371 : const uint32 vmMod10 = (uint32) (vm - 10 * vmDiv10);
513 2275371 : const uint64 vrDiv10 = div10(vr);
514 2275371 : const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
515 :
516 2275371 : vmIsTrailingZeros &= vmMod10 == 0;
517 2275371 : vrIsTrailingZeros &= lastRemovedDigit == 0;
518 2275371 : lastRemovedDigit = (uint8) vrMod10;
519 2275371 : vr = vrDiv10;
520 2275371 : vp = vpDiv10;
521 2275371 : vm = vmDiv10;
522 2275371 : ++removed;
523 : }
524 :
525 159624 : if (vmIsTrailingZeros)
526 : {
527 : for (;;)
528 UBC 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 : }
546 : }
547 :
548 CBC 159624 : if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
549 : {
550 : /* Round even if the exact number is .....50..0. */
551 15 : lastRemovedDigit = 4;
552 : }
553 :
554 : /*
555 : * We need to take vr + 1 if vr is outside bounds or we need to round
556 : * up.
557 : */
558 159624 : output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
559 : }
560 : else
561 : {
562 : /*
563 : * Specialized for the common case (~99.3%). Percentages below are
564 : * relative to this.
565 : */
566 637142 : bool roundUp = false;
567 637142 : const uint64 vpDiv100 = div100(vp);
568 637142 : const uint64 vmDiv100 = div100(vm);
569 :
570 637142 : if (vpDiv100 > vmDiv100)
571 : {
572 : /* Optimization:remove two digits at a time(~86.2 %). */
573 569809 : const uint64 vrDiv100 = div100(vr);
574 569809 : const uint32 vrMod100 = (uint32) (vr - 100 * vrDiv100);
575 :
576 569809 : roundUp = vrMod100 >= 50;
577 569809 : vr = vrDiv100;
578 569809 : vp = vpDiv100;
579 569809 : vm = vmDiv100;
580 569809 : removed += 2;
581 : }
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 : for (;;)
597 1471376 : {
598 2108518 : const uint64 vpDiv10 = div10(vp);
599 2108518 : const uint64 vmDiv10 = div10(vm);
600 :
601 2108518 : if (vpDiv10 <= vmDiv10)
602 637142 : break;
603 :
604 1471376 : const uint64 vrDiv10 = div10(vr);
605 1471376 : const uint32 vrMod10 = (uint32) (vr - 10 * vrDiv10);
606 :
607 1471376 : roundUp = vrMod10 >= 5;
608 1471376 : vr = vrDiv10;
609 1471376 : vp = vpDiv10;
610 1471376 : vm = vmDiv10;
611 1471376 : ++removed;
612 : }
613 :
614 : /*
615 : * We need to take vr + 1 if vr is outside bounds or we need to round
616 : * up.
617 : */
618 637142 : output = vr + (vr == vm || roundUp);
619 : }
620 :
621 796766 : const int32 exp = e10 + removed;
622 :
623 : floating_decimal_64 fd;
624 :
625 796766 : fd.exponent = exp;
626 796766 : fd.mantissa = output;
627 796766 : return fd;
628 : }
629 :
630 : static inline int
631 1979049 : to_chars_df(const floating_decimal_64 v, const uint32 olength, char *const result)
632 : {
633 : /* Step 5: Print the decimal representation. */
634 1979049 : int index = 0;
635 :
636 1979049 : uint64 output = v.mantissa;
637 1979049 : 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 1979049 : uint32 i = 0;
653 1979049 : int32 nexp = exp + olength;
654 :
655 1979049 : if (nexp <= 0)
656 : {
657 : /* -nexp is number of 0s to add after '.' */
658 129825 : Assert(nexp >= -3);
659 : /* 0.000ddddd */
660 129825 : index = 2 - nexp;
661 : /* won't need more than this many 0s */
662 129825 : memcpy(result, "0.000000", 8);
663 : }
664 1849224 : else if (exp < 0)
665 : {
666 : /*
667 : * dddd.dddd; leave space at the start and move the '.' in after
668 : */
669 665188 : index = 1;
670 : }
671 : else
672 : {
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 1184036 : Assert(exp < 16 && exp + olength <= 16);
679 1184036 : memset(result, '0', 16);
680 : }
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 1979049 : if ((output >> 32) != 0)
688 : {
689 : /* Expensive 64-bit division. */
690 508619 : const uint64 q = div1e8(output);
691 508619 : uint32 output2 = (uint32) (output - 100000000 * q);
692 508619 : const uint32 c = output2 % 10000;
693 :
694 508619 : output = q;
695 508619 : output2 /= 10000;
696 :
697 508619 : const uint32 d = output2 % 10000;
698 508619 : const uint32 c0 = (c % 100) << 1;
699 508619 : const uint32 c1 = (c / 100) << 1;
700 508619 : const uint32 d0 = (d % 100) << 1;
701 508619 : const uint32 d1 = (d / 100) << 1;
702 :
703 508619 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
704 508619 : memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
705 508619 : memcpy(result + index + olength - i - 6, DIGIT_TABLE + d0, 2);
706 508619 : memcpy(result + index + olength - i - 8, DIGIT_TABLE + d1, 2);
707 508619 : i += 8;
708 : }
709 :
710 1979049 : uint32 output2 = (uint32) output;
711 :
712 2967189 : while (output2 >= 10000)
713 : {
714 988140 : const uint32 c = output2 - 10000 * (output2 / 10000);
715 988140 : const uint32 c0 = (c % 100) << 1;
716 988140 : const uint32 c1 = (c / 100) << 1;
717 :
718 988140 : output2 /= 10000;
719 988140 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
720 988140 : memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
721 988140 : i += 4;
722 : }
723 1979049 : if (output2 >= 100)
724 : {
725 1457639 : const uint32 c = (output2 % 100) << 1;
726 :
727 1457639 : output2 /= 100;
728 1457639 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
729 1457639 : i += 2;
730 : }
731 1979049 : if (output2 >= 10)
732 : {
733 851969 : const uint32 c = output2 << 1;
734 :
735 851969 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
736 : }
737 : else
738 : {
739 1127080 : result[index] = (char) ('0' + output2);
740 : }
741 :
742 1979049 : if (index == 1)
743 : {
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 665188 : Assert(nexp < 16);
750 : /* gcc only seems to want to optimize memmove for small 2^n */
751 665188 : if (nexp & 8)
752 : {
753 380 : memmove(result + index - 1, result + index, 8);
754 380 : index += 8;
755 : }
756 665188 : if (nexp & 4)
757 : {
758 3094 : memmove(result + index - 1, result + index, 4);
759 3094 : index += 4;
760 : }
761 665188 : if (nexp & 2)
762 : {
763 656173 : memmove(result + index - 1, result + index, 2);
764 656173 : index += 2;
765 : }
766 665188 : if (nexp & 1)
767 : {
768 551499 : result[index - 1] = result[index];
769 : }
770 665188 : result[nexp] = '.';
771 665188 : index = olength + 1;
772 : }
773 1313861 : else if (exp >= 0)
774 : {
775 : /* we supplied the trailing zeros earlier, now just set the length. */
776 1184036 : index = olength + exp;
777 : }
778 : else
779 : {
780 129825 : index = olength + (2 - nexp);
781 : }
782 :
783 1979049 : return index;
784 : }
785 :
786 : static inline int
787 1980847 : to_chars(floating_decimal_64 v, const bool sign, char *const result)
788 : {
789 : /* Step 5: Print the decimal representation. */
790 1980847 : int index = 0;
791 :
792 1980847 : uint64 output = v.mantissa;
793 1980847 : uint32 olength = decimalLength(output);
794 1980847 : int32 exp = v.exponent + olength - 1;
795 :
796 1980847 : if (sign)
797 : {
798 65609 : result[index++] = '-';
799 : }
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 1980847 : if (exp >= -4 && exp < 15)
807 1979049 : 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 1798 : if (v.exponent == 0)
826 : {
827 555 : while ((output & 1) == 0)
828 : {
829 513 : const uint64 q = div10(output);
830 513 : const uint32 r = (uint32) (output - 10 * q);
831 :
832 513 : if (r != 0)
833 288 : break;
834 225 : output = q;
835 225 : --olength;
836 : }
837 : }
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 1798 : 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 1798 : if ((output >> 32) != 0)
860 : {
861 : /* Expensive 64-bit division. */
862 1330 : const uint64 q = div1e8(output);
863 1330 : uint32 output2 = (uint32) (output - 100000000 * q);
864 :
865 1330 : output = q;
866 :
867 1330 : const uint32 c = output2 % 10000;
868 :
869 1330 : output2 /= 10000;
870 :
871 1330 : const uint32 d = output2 % 10000;
872 1330 : const uint32 c0 = (c % 100) << 1;
873 1330 : const uint32 c1 = (c / 100) << 1;
874 1330 : const uint32 d0 = (d % 100) << 1;
875 1330 : const uint32 d1 = (d / 100) << 1;
876 :
877 1330 : memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
878 1330 : memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
879 1330 : memcpy(result + index + olength - i - 5, DIGIT_TABLE + d0, 2);
880 1330 : memcpy(result + index + olength - i - 7, DIGIT_TABLE + d1, 2);
881 1330 : i += 8;
882 : }
883 :
884 1798 : uint32 output2 = (uint32) output;
885 :
886 3768 : while (output2 >= 10000)
887 : {
888 1970 : const uint32 c = output2 - 10000 * (output2 / 10000);
889 :
890 1970 : output2 /= 10000;
891 :
892 1970 : const uint32 c0 = (c % 100) << 1;
893 1970 : const uint32 c1 = (c / 100) << 1;
894 :
895 1970 : memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
896 1970 : memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
897 1970 : i += 4;
898 : }
899 1798 : if (output2 >= 100)
900 : {
901 553 : const uint32 c = (output2 % 100) << 1;
902 :
903 553 : output2 /= 100;
904 553 : memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
905 553 : i += 2;
906 : }
907 1798 : if (output2 >= 10)
908 : {
909 753 : const uint32 c = output2 << 1;
910 :
911 : /*
912 : * We can't use memcpy here: the decimal dot goes between these two
913 : * digits.
914 : */
915 753 : result[index + olength - i] = DIGIT_TABLE[c + 1];
916 753 : result[index] = DIGIT_TABLE[c];
917 : }
918 : else
919 : {
920 1045 : result[index] = (char) ('0' + output2);
921 : }
922 :
923 : /* Print decimal point if needed. */
924 1798 : if (olength > 1)
925 : {
926 1399 : result[index + 1] = '.';
927 1399 : index += olength + 1;
928 : }
929 : else
930 : {
931 399 : ++index;
932 : }
933 :
934 : /* Print the exponent. */
935 1798 : result[index++] = 'e';
936 1798 : if (exp < 0)
937 : {
938 686 : result[index++] = '-';
939 686 : exp = -exp;
940 : }
941 : else
942 1112 : result[index++] = '+';
943 :
944 1798 : if (exp >= 100)
945 : {
946 596 : const int32 c = exp % 10;
947 :
948 596 : memcpy(result + index, DIGIT_TABLE + 2 * (exp / 10), 2);
949 596 : result[index + 2] = (char) ('0' + c);
950 596 : index += 3;
951 : }
952 : else
953 : {
954 1202 : memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
955 1202 : index += 2;
956 : }
957 :
958 1798 : return index;
959 : }
960 :
961 : static inline bool
962 1980847 : d2d_small_int(const uint64 ieeeMantissa,
963 : const uint32 ieeeExponent,
964 : floating_decimal_64 *v)
965 : {
966 1980847 : 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 1980847 : if (e2 >= -DOUBLE_MANTISSA_BITS && e2 <= 0)
974 : {
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 1849284 : const uint64 mask = (UINT64CONST(1) << -e2) - 1;
986 1849284 : const uint64 fraction = ieeeMantissa & mask;
987 :
988 1849284 : if (fraction == 0)
989 : {
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 1184081 : const uint64 m2 = (UINT64CONST(1) << DOUBLE_MANTISSA_BITS) | ieeeMantissa;
997 :
998 1184081 : v->mantissa = m2 >> -e2;
999 1184081 : v->exponent = 0;
1000 1184081 : return true;
1001 : }
1002 : }
1003 :
1004 796766 : return false;
1005 : }
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 1984142 : double_to_shortest_decimal_bufn(double f, char *result)
1016 : {
1017 : /*
1018 : * Step 1: Decode the floating-point number, and unify normalized and
1019 : * subnormal cases.
1020 : */
1021 1984142 : const uint64 bits = double_to_bits(f);
1022 :
1023 : /* Decode bits into sign, mantissa, and exponent. */
1024 1984142 : const bool ieeeSign = ((bits >> (DOUBLE_MANTISSA_BITS + DOUBLE_EXPONENT_BITS)) & 1) != 0;
1025 1984142 : const uint64 ieeeMantissa = bits & ((UINT64CONST(1) << DOUBLE_MANTISSA_BITS) - 1);
1026 1984142 : const uint32 ieeeExponent = (uint32) ((bits >> DOUBLE_MANTISSA_BITS) & ((1u << DOUBLE_EXPONENT_BITS) - 1));
1027 :
1028 : /* Case distinction; exit early for the easy cases. */
1029 1984142 : if (ieeeExponent == ((1u << DOUBLE_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
1030 : {
1031 3295 : return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
1032 : }
1033 :
1034 : floating_decimal_64 v;
1035 1980847 : const bool isSmallInt = d2d_small_int(ieeeMantissa, ieeeExponent, &v);
1036 :
1037 1980847 : if (!isSmallInt)
1038 : {
1039 796766 : v = d2d(ieeeMantissa, ieeeExponent);
1040 : }
1041 :
1042 1980847 : return to_chars(v, ieeeSign, result);
1043 : }
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 1984142 : double_to_shortest_decimal_buf(double f, char *result)
1054 : {
1055 1984142 : const int index = double_to_shortest_decimal_bufn(f, result);
1056 :
1057 : /* Terminate the string. */
1058 1984142 : Assert(index < DOUBLE_SHORTEST_DECIMAL_LEN);
1059 1984142 : result[index] = '\0';
1060 1984142 : return index;
1061 : }
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 UBC 0 : double_to_shortest_decimal(double f)
1071 : {
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 : }
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