TLA Line data Source code
1 : /*---------------------------------------------------------------------------
2 : *
3 : * Ryu floating-point output for single precision.
4 : *
5 : * Portions Copyright (c) 2018-2023, PostgreSQL Global Development Group
6 : *
7 : * IDENTIFICATION
8 : * src/common/f2s.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 : #ifndef FRONTEND
36 : #include "postgres.h"
37 : #else
38 : #include "postgres_fe.h"
39 : #endif
40 :
41 : #include "common/shortest_dec.h"
42 : #include "digit_table.h"
43 : #include "ryu_common.h"
44 :
45 : #define FLOAT_MANTISSA_BITS 23
46 : #define FLOAT_EXPONENT_BITS 8
47 : #define FLOAT_BIAS 127
48 :
49 : /*
50 : * This table is generated (by the upstream) by PrintFloatLookupTable,
51 : * and modified (by us) to add UINT64CONST.
52 : */
53 : #define FLOAT_POW5_INV_BITCOUNT 59
54 : static const uint64 FLOAT_POW5_INV_SPLIT[31] = {
55 : UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826),
56 : UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670),
57 : UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688),
58 : UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727),
59 : UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350),
60 : UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234),
61 : UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971),
62 : UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730)
63 : };
64 : #define FLOAT_POW5_BITCOUNT 61
65 : static const uint64 FLOAT_POW5_SPLIT[47] = {
66 : UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000),
67 : UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000),
68 : UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000),
69 : UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000),
70 : UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000),
71 : UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000),
72 : UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031),
73 : UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594),
74 : UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675),
75 : UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678),
76 : UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187),
77 : UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221)
78 : };
79 :
80 : static inline uint32
81 CBC 354 : pow5Factor(uint32 value)
82 : {
83 354 : uint32 count = 0;
84 :
85 : for (;;)
86 825 : {
87 1179 : Assert(value != 0);
88 1179 : const uint32 q = value / 5;
89 1179 : const uint32 r = value % 5;
90 :
91 1179 : if (r != 0)
92 354 : break;
93 :
94 825 : value = q;
95 825 : ++count;
96 : }
97 354 : return count;
98 : }
99 :
100 : /* Returns true if value is divisible by 5^p. */
101 : static inline bool
102 354 : multipleOfPowerOf5(const uint32 value, const uint32 p)
103 : {
104 354 : return pow5Factor(value) >= p;
105 : }
106 :
107 : /* Returns true if value is divisible by 2^p. */
108 : static inline bool
109 4157 : multipleOfPowerOf2(const uint32 value, const uint32 p)
110 : {
111 : /* return __builtin_ctz(value) >= p; */
112 4157 : return (value & ((1u << p) - 1)) == 0;
113 : }
114 :
115 : /*
116 : * It seems to be slightly faster to avoid uint128_t here, although the
117 : * generated code for uint128_t looks slightly nicer.
118 : */
119 : static inline uint32
120 18250 : mulShift(const uint32 m, const uint64 factor, const int32 shift)
121 : {
122 : /*
123 : * The casts here help MSVC to avoid calls to the __allmul library
124 : * function.
125 : */
126 18250 : const uint32 factorLo = (uint32) (factor);
127 18250 : const uint32 factorHi = (uint32) (factor >> 32);
128 18250 : const uint64 bits0 = (uint64) m * factorLo;
129 18250 : const uint64 bits1 = (uint64) m * factorHi;
130 :
131 18250 : Assert(shift > 32);
132 :
133 : #ifdef RYU_32_BIT_PLATFORM
134 :
135 : /*
136 : * On 32-bit platforms we can avoid a 64-bit shift-right since we only
137 : * need the upper 32 bits of the result and the shift value is > 32.
138 : */
139 : const uint32 bits0Hi = (uint32) (bits0 >> 32);
140 : uint32 bits1Lo = (uint32) (bits1);
141 : uint32 bits1Hi = (uint32) (bits1 >> 32);
142 :
143 : bits1Lo += bits0Hi;
144 : bits1Hi += (bits1Lo < bits0Hi);
145 :
146 : const int32 s = shift - 32;
147 :
148 : return (bits1Hi << (32 - s)) | (bits1Lo >> s);
149 :
150 : #else /* RYU_32_BIT_PLATFORM */
151 :
152 18250 : const uint64 sum = (bits0 >> 32) + bits1;
153 18250 : const uint64 shiftedSum = sum >> (shift - 32);
154 :
155 18250 : Assert(shiftedSum <= PG_UINT32_MAX);
156 18250 : return (uint32) shiftedSum;
157 :
158 : #endif /* RYU_32_BIT_PLATFORM */
159 : }
160 :
161 : static inline uint32
162 2010 : mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j)
163 : {
164 2010 : return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j);
165 : }
166 :
167 : static inline uint32
168 16240 : mulPow5divPow2(const uint32 m, const uint32 i, const int32 j)
169 : {
170 16240 : return mulShift(m, FLOAT_POW5_SPLIT[i], j);
171 : }
172 :
173 : static inline uint32
174 9480 : decimalLength(const uint32 v)
175 : {
176 : /* Function precondition: v is not a 10-digit number. */
177 : /* (9 digits are sufficient for round-tripping.) */
178 9480 : Assert(v < 1000000000);
179 9480 : if (v >= 100000000)
180 : {
181 165 : return 9;
182 : }
183 9315 : if (v >= 10000000)
184 : {
185 2700 : return 8;
186 : }
187 6615 : if (v >= 1000000)
188 : {
189 1453 : return 7;
190 : }
191 5162 : if (v >= 100000)
192 : {
193 136 : return 6;
194 : }
195 5026 : if (v >= 10000)
196 : {
197 228 : return 5;
198 : }
199 4798 : if (v >= 1000)
200 : {
201 388 : return 4;
202 : }
203 4410 : if (v >= 100)
204 : {
205 1830 : return 3;
206 : }
207 2580 : if (v >= 10)
208 : {
209 435 : return 2;
210 : }
211 2145 : return 1;
212 : }
213 :
214 : /* A floating decimal representing m * 10^e. */
215 : typedef struct floating_decimal_32
216 : {
217 : uint32 mantissa;
218 : int32 exponent;
219 : } floating_decimal_32;
220 :
221 : static inline floating_decimal_32
222 5727 : f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent)
223 : {
224 : int32 e2;
225 : uint32 m2;
226 :
227 5727 : if (ieeeExponent == 0)
228 : {
229 : /* We subtract 2 so that the bounds computation has 2 additional bits. */
230 63 : e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
231 63 : m2 = ieeeMantissa;
232 : }
233 : else
234 : {
235 5664 : e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2;
236 5664 : m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa;
237 : }
238 :
239 : #if STRICTLY_SHORTEST
240 : const bool even = (m2 & 1) == 0;
241 : const bool acceptBounds = even;
242 : #else
243 5727 : const bool acceptBounds = false;
244 : #endif
245 :
246 : /* Step 2: Determine the interval of legal decimal representations. */
247 5727 : const uint32 mv = 4 * m2;
248 5727 : const uint32 mp = 4 * m2 + 2;
249 :
250 : /* Implicit bool -> int conversion. True is 1, false is 0. */
251 5727 : const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1;
252 5727 : const uint32 mm = 4 * m2 - 1 - mmShift;
253 :
254 : /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */
255 : uint32 vr,
256 : vp,
257 : vm;
258 : int32 e10;
259 5727 : bool vmIsTrailingZeros = false;
260 5727 : bool vrIsTrailingZeros = false;
261 5727 : uint8 lastRemovedDigit = 0;
262 :
263 5727 : if (e2 >= 0)
264 : {
265 610 : const uint32 q = log10Pow2(e2);
266 :
267 610 : e10 = q;
268 :
269 610 : const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1;
270 610 : const int32 i = -e2 + q + k;
271 :
272 610 : vr = mulPow5InvDivPow2(mv, q, i);
273 610 : vp = mulPow5InvDivPow2(mp, q, i);
274 610 : vm = mulPow5InvDivPow2(mm, q, i);
275 :
276 610 : if (q != 0 && (vp - 1) / 10 <= vm / 10)
277 : {
278 : /*
279 : * We need to know one removed digit even if we are not going to
280 : * loop below. We could use q = X - 1 above, except that would
281 : * require 33 bits for the result, and we've found that 32-bit
282 : * arithmetic is faster even on 64-bit machines.
283 : */
284 180 : const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1;
285 :
286 180 : lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10);
287 : }
288 610 : if (q <= 9)
289 : {
290 : /*
291 : * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9
292 : * seems to be safe as well.
293 : *
294 : * Only one of mp, mv, and mm can be a multiple of 5, if any.
295 : */
296 354 : if (mv % 5 == 0)
297 : {
298 60 : vrIsTrailingZeros = multipleOfPowerOf5(mv, q);
299 : }
300 294 : else if (acceptBounds)
301 : {
302 UBC 0 : vmIsTrailingZeros = multipleOfPowerOf5(mm, q);
303 : }
304 : else
305 : {
306 CBC 294 : vp -= multipleOfPowerOf5(mp, q);
307 : }
308 : }
309 : }
310 : else
311 : {
312 5117 : const uint32 q = log10Pow5(-e2);
313 :
314 5117 : e10 = q + e2;
315 :
316 5117 : const int32 i = -e2 - q;
317 5117 : const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT;
318 5117 : int32 j = q - k;
319 :
320 5117 : vr = mulPow5divPow2(mv, i, j);
321 5117 : vp = mulPow5divPow2(mp, i, j);
322 5117 : vm = mulPow5divPow2(mm, i, j);
323 :
324 5117 : if (q != 0 && (vp - 1) / 10 <= vm / 10)
325 : {
326 889 : j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT);
327 889 : lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10);
328 : }
329 5117 : if (q <= 1)
330 : {
331 : /*
332 : * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q
333 : * trailing 0 bits.
334 : */
335 : /* mv = 4 * m2, so it always has at least two trailing 0 bits. */
336 15 : vrIsTrailingZeros = true;
337 15 : if (acceptBounds)
338 : {
339 : /*
340 : * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff
341 : * mmShift == 1.
342 : */
343 UBC 0 : vmIsTrailingZeros = mmShift == 1;
344 : }
345 : else
346 : {
347 : /*
348 : * mp = mv + 2, so it always has at least one trailing 0 bit.
349 : */
350 CBC 15 : --vp;
351 : }
352 : }
353 5102 : else if (q < 31)
354 : {
355 : /* TODO(ulfjack):Use a tighter bound here. */
356 4157 : vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1);
357 : }
358 : }
359 :
360 : /*
361 : * Step 4: Find the shortest decimal representation in the interval of
362 : * legal representations.
363 : */
364 5727 : uint32 removed = 0;
365 : uint32 output;
366 :
367 5727 : if (vmIsTrailingZeros || vrIsTrailingZeros)
368 : {
369 : /* General case, which happens rarely (~4.0%). */
370 1898 : while (vp / 10 > vm / 10)
371 : {
372 1557 : vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0;
373 1557 : vrIsTrailingZeros &= lastRemovedDigit == 0;
374 1557 : lastRemovedDigit = (uint8) (vr % 10);
375 1557 : vr /= 10;
376 1557 : vp /= 10;
377 1557 : vm /= 10;
378 1557 : ++removed;
379 : }
380 341 : if (vmIsTrailingZeros)
381 : {
382 UBC 0 : while (vm % 10 == 0)
383 : {
384 0 : vrIsTrailingZeros &= lastRemovedDigit == 0;
385 0 : lastRemovedDigit = (uint8) (vr % 10);
386 0 : vr /= 10;
387 0 : vp /= 10;
388 0 : vm /= 10;
389 0 : ++removed;
390 : }
391 : }
392 :
393 CBC 341 : if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0)
394 : {
395 : /* Round even if the exact number is .....50..0. */
396 90 : lastRemovedDigit = 4;
397 : }
398 :
399 : /*
400 : * We need to take vr + 1 if vr is outside bounds or we need to round
401 : * up.
402 : */
403 341 : output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5);
404 : }
405 : else
406 : {
407 : /*
408 : * Specialized for the common case (~96.0%). Percentages below are
409 : * relative to this.
410 : *
411 : * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2:
412 : * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01%
413 : */
414 16227 : while (vp / 10 > vm / 10)
415 : {
416 10841 : lastRemovedDigit = (uint8) (vr % 10);
417 10841 : vr /= 10;
418 10841 : vp /= 10;
419 10841 : vm /= 10;
420 10841 : ++removed;
421 : }
422 :
423 : /*
424 : * We need to take vr + 1 if vr is outside bounds or we need to round
425 : * up.
426 : */
427 5386 : output = vr + (vr == vm || lastRemovedDigit >= 5);
428 : }
429 :
430 5727 : const int32 exp = e10 + removed;
431 :
432 : floating_decimal_32 fd;
433 :
434 5727 : fd.exponent = exp;
435 5727 : fd.mantissa = output;
436 5727 : return fd;
437 : }
438 :
439 : static inline int
440 7685 : to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result)
441 : {
442 : /* Step 5: Print the decimal representation. */
443 7685 : int index = 0;
444 :
445 7685 : uint32 output = v.mantissa;
446 7685 : int32 exp = v.exponent;
447 :
448 : /*----
449 : * On entry, mantissa * 10^exp is the result to be output.
450 : * Caller has already done the - sign if needed.
451 : *
452 : * We want to insert the point somewhere depending on the output length
453 : * and exponent, which might mean adding zeros:
454 : *
455 : * exp | format
456 : * 1+ | ddddddddd000000
457 : * 0 | ddddddddd
458 : * -1 .. -len+1 | dddddddd.d to d.ddddddddd
459 : * -len ... | 0.ddddddddd to 0.000dddddd
460 : */
461 7685 : uint32 i = 0;
462 7685 : int32 nexp = exp + olength;
463 :
464 7685 : if (nexp <= 0)
465 : {
466 : /* -nexp is number of 0s to add after '.' */
467 2335 : Assert(nexp >= -3);
468 : /* 0.000ddddd */
469 2335 : index = 2 - nexp;
470 : /* copy 8 bytes rather than 5 to let compiler optimize */
471 2335 : memcpy(result, "0.000000", 8);
472 : }
473 5350 : else if (exp < 0)
474 : {
475 : /*
476 : * dddd.dddd; leave space at the start and move the '.' in after
477 : */
478 1672 : index = 1;
479 : }
480 : else
481 : {
482 : /*
483 : * We can save some code later by pre-filling with zeros. We know that
484 : * there can be no more than 6 output digits in this form, otherwise
485 : * we would not choose fixed-point output. memset 8 rather than 6
486 : * bytes to let the compiler optimize it.
487 : */
488 3678 : Assert(exp < 6 && exp + olength <= 6);
489 3678 : memset(result, '0', 8);
490 : }
491 :
492 10937 : while (output >= 10000)
493 : {
494 3252 : const uint32 c = output - 10000 * (output / 10000);
495 3252 : const uint32 c0 = (c % 100) << 1;
496 3252 : const uint32 c1 = (c / 100) << 1;
497 :
498 3252 : output /= 10000;
499 :
500 3252 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2);
501 3252 : memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2);
502 3252 : i += 4;
503 : }
504 7685 : if (output >= 100)
505 : {
506 4941 : const uint32 c = (output % 100) << 1;
507 :
508 4941 : output /= 100;
509 4941 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
510 4941 : i += 2;
511 : }
512 7685 : if (output >= 10)
513 : {
514 2676 : const uint32 c = output << 1;
515 :
516 2676 : memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2);
517 : }
518 : else
519 : {
520 5009 : result[index] = (char) ('0' + output);
521 : }
522 :
523 7685 : if (index == 1)
524 : {
525 : /*
526 : * nexp is 1..6 here, representing the number of digits before the
527 : * point. A value of 7+ is not possible because we switch to
528 : * scientific notation when the display exponent reaches 6.
529 : */
530 1672 : Assert(nexp < 7);
531 : /* gcc only seems to want to optimize memmove for small 2^n */
532 1672 : if (nexp & 4)
533 : {
534 227 : memmove(result + index - 1, result + index, 4);
535 227 : index += 4;
536 : }
537 1672 : if (nexp & 2)
538 : {
539 400 : memmove(result + index - 1, result + index, 2);
540 400 : index += 2;
541 : }
542 1672 : if (nexp & 1)
543 : {
544 1268 : result[index - 1] = result[index];
545 : }
546 1672 : result[nexp] = '.';
547 1672 : index = olength + 1;
548 : }
549 6013 : else if (exp >= 0)
550 : {
551 : /* we supplied the trailing zeros earlier, now just set the length. */
552 3678 : index = olength + exp;
553 : }
554 : else
555 : {
556 2335 : index = olength + (2 - nexp);
557 : }
558 :
559 7685 : return index;
560 : }
561 :
562 : static inline int
563 9480 : to_chars(const floating_decimal_32 v, const bool sign, char *const result)
564 : {
565 : /* Step 5: Print the decimal representation. */
566 9480 : int index = 0;
567 :
568 9480 : uint32 output = v.mantissa;
569 9480 : uint32 olength = decimalLength(output);
570 9480 : int32 exp = v.exponent + olength - 1;
571 :
572 9480 : if (sign)
573 713 : result[index++] = '-';
574 :
575 : /*
576 : * The thresholds for fixed-point output are chosen to match printf
577 : * defaults. Beware that both the code of to_chars_f and the value of
578 : * FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds.
579 : */
580 9480 : if (exp >= -4 && exp < 6)
581 7685 : return to_chars_f(v, olength, result + index) + sign;
582 :
583 : /*
584 : * If v.exponent is exactly 0, we might have reached here via the small
585 : * integer fast path, in which case v.mantissa might contain trailing
586 : * (decimal) zeros. For scientific notation we need to move these zeros
587 : * into the exponent. (For fixed point this doesn't matter, which is why
588 : * we do this here rather than above.)
589 : *
590 : * Since we already calculated the display exponent (exp) above based on
591 : * the old decimal length, that value does not change here. Instead, we
592 : * just reduce the display length for each digit removed.
593 : *
594 : * If we didn't get here via the fast path, the raw exponent will not
595 : * usually be 0, and there will be no trailing zeros, so we pay no more
596 : * than one div10/multiply extra cost. We claw back half of that by
597 : * checking for divisibility by 2 before dividing by 10.
598 : */
599 1795 : if (v.exponent == 0)
600 : {
601 345 : while ((output & 1) == 0)
602 : {
603 285 : const uint32 q = output / 10;
604 285 : const uint32 r = output - 10 * q;
605 :
606 285 : if (r != 0)
607 90 : break;
608 195 : output = q;
609 195 : --olength;
610 : }
611 : }
612 :
613 : /*----
614 : * Print the decimal digits.
615 : * The following code is equivalent to:
616 : *
617 : * for (uint32 i = 0; i < olength - 1; ++i) {
618 : * const uint32 c = output % 10; output /= 10;
619 : * result[index + olength - i] = (char) ('0' + c);
620 : * }
621 : * result[index] = '0' + output % 10;
622 : */
623 1795 : uint32 i = 0;
624 :
625 3360 : while (output >= 10000)
626 : {
627 1565 : const uint32 c = output - 10000 * (output / 10000);
628 1565 : const uint32 c0 = (c % 100) << 1;
629 1565 : const uint32 c1 = (c / 100) << 1;
630 :
631 1565 : output /= 10000;
632 :
633 1565 : memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2);
634 1565 : memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2);
635 1565 : i += 4;
636 : }
637 1795 : if (output >= 100)
638 : {
639 1400 : const uint32 c = (output % 100) << 1;
640 :
641 1400 : output /= 100;
642 1400 : memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2);
643 1400 : i += 2;
644 : }
645 1795 : if (output >= 10)
646 : {
647 968 : const uint32 c = output << 1;
648 :
649 : /*
650 : * We can't use memcpy here: the decimal dot goes between these two
651 : * digits.
652 : */
653 968 : result[index + olength - i] = DIGIT_TABLE[c + 1];
654 968 : result[index] = DIGIT_TABLE[c];
655 : }
656 : else
657 : {
658 827 : result[index] = (char) ('0' + output);
659 : }
660 :
661 : /* Print decimal point if needed. */
662 1795 : if (olength > 1)
663 : {
664 1553 : result[index + 1] = '.';
665 1553 : index += olength + 1;
666 : }
667 : else
668 : {
669 242 : ++index;
670 : }
671 :
672 : /* Print the exponent. */
673 1795 : result[index++] = 'e';
674 1795 : if (exp < 0)
675 : {
676 1080 : result[index++] = '-';
677 1080 : exp = -exp;
678 : }
679 : else
680 715 : result[index++] = '+';
681 :
682 1795 : memcpy(result + index, DIGIT_TABLE + 2 * exp, 2);
683 1795 : index += 2;
684 :
685 1795 : return index;
686 : }
687 :
688 : static inline bool
689 9480 : f2d_small_int(const uint32 ieeeMantissa,
690 : const uint32 ieeeExponent,
691 : floating_decimal_32 *v)
692 : {
693 9480 : const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS;
694 :
695 : /*
696 : * Avoid using multiple "return false;" here since it tends to provoke the
697 : * compiler into inlining multiple copies of f2d, which is undesirable.
698 : */
699 :
700 9480 : if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0)
701 : {
702 : /*----
703 : * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23:
704 : * 1 <= f = m2 / 2^-e2 < 2^24.
705 : *
706 : * Test if the lower -e2 bits of the significand are 0, i.e. whether
707 : * the fraction is 0. We can use ieeeMantissa here, since the implied
708 : * 1 bit can never be tested by this; the implied 1 can only be part
709 : * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already
710 : * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24)
711 : */
712 5440 : const uint32 mask = (1U << -e2) - 1;
713 5440 : const uint32 fraction = ieeeMantissa & mask;
714 :
715 5440 : if (fraction == 0)
716 : {
717 : /*----
718 : * f is an integer in the range [1, 2^24).
719 : * Note: mantissa might contain trailing (decimal) 0's.
720 : * Note: since 2^24 < 10^9, there is no need to adjust
721 : * decimalLength().
722 : */
723 3753 : const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa;
724 :
725 3753 : v->mantissa = m2 >> -e2;
726 3753 : v->exponent = 0;
727 3753 : return true;
728 : }
729 : }
730 :
731 5727 : return false;
732 : }
733 :
734 : /*
735 : * Store the shortest decimal representation of the given float as an
736 : * UNTERMINATED string in the caller's supplied buffer (which must be at least
737 : * FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long).
738 : *
739 : * Returns the number of bytes stored.
740 : */
741 : int
742 11992 : float_to_shortest_decimal_bufn(float f, char *result)
743 : {
744 : /*
745 : * Step 1: Decode the floating-point number, and unify normalized and
746 : * subnormal cases.
747 : */
748 11992 : const uint32 bits = float_to_bits(f);
749 :
750 : /* Decode bits into sign, mantissa, and exponent. */
751 11992 : const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0;
752 11992 : const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1);
753 11992 : const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1);
754 :
755 : /* Case distinction; exit early for the easy cases. */
756 11992 : if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0))
757 : {
758 2512 : return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0));
759 : }
760 :
761 : floating_decimal_32 v;
762 9480 : const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v);
763 :
764 9480 : if (!isSmallInt)
765 : {
766 5727 : v = f2d(ieeeMantissa, ieeeExponent);
767 : }
768 :
769 9480 : return to_chars(v, ieeeSign, result);
770 : }
771 :
772 : /*
773 : * Store the shortest decimal representation of the given float as a
774 : * null-terminated string in the caller's supplied buffer (which must be at
775 : * least FLOAT_SHORTEST_DECIMAL_LEN bytes long).
776 : *
777 : * Returns the string length.
778 : */
779 : int
780 11992 : float_to_shortest_decimal_buf(float f, char *result)
781 : {
782 11992 : const int index = float_to_shortest_decimal_bufn(f, result);
783 :
784 : /* Terminate the string. */
785 11992 : Assert(index < FLOAT_SHORTEST_DECIMAL_LEN);
786 11992 : result[index] = '\0';
787 11992 : return index;
788 : }
789 :
790 : /*
791 : * Return the shortest decimal representation as a null-terminated palloc'd
792 : * string (outside the backend, uses malloc() instead).
793 : *
794 : * Caller is responsible for freeing the result.
795 : */
796 : char *
797 UBC 0 : float_to_shortest_decimal(float f)
798 : {
799 0 : char *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN);
800 :
801 0 : float_to_shortest_decimal_buf(f, result);
802 0 : return result;
803 : }
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