| 1 | /*--------------------------------------------------------------------------- |
| 2 | * |
| 3 | * Ryu floating-point output for single precision. |
| 4 | * |
| 5 | * Portions Copyright (c) 2018-2019, 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 | |
| 43 | #include "ryu_common.h" |
| 44 | #include "digit_table.h" |
| 45 | |
| 46 | #define FLOAT_MANTISSA_BITS 23 |
| 47 | #define FLOAT_EXPONENT_BITS 8 |
| 48 | #define FLOAT_BIAS 127 |
| 49 | |
| 50 | /* |
| 51 | * This table is generated (by the upstream) by PrintFloatLookupTable, |
| 52 | * and modified (by us) to add UINT64CONST. |
| 53 | */ |
| 54 | #define FLOAT_POW5_INV_BITCOUNT 59 |
| 55 | static const uint64 FLOAT_POW5_INV_SPLIT[31] = { |
| 56 | UINT64CONST(576460752303423489), UINT64CONST(461168601842738791), UINT64CONST(368934881474191033), UINT64CONST(295147905179352826), |
| 57 | UINT64CONST(472236648286964522), UINT64CONST(377789318629571618), UINT64CONST(302231454903657294), UINT64CONST(483570327845851670), |
| 58 | UINT64CONST(386856262276681336), UINT64CONST(309485009821345069), UINT64CONST(495176015714152110), UINT64CONST(396140812571321688), |
| 59 | UINT64CONST(316912650057057351), UINT64CONST(507060240091291761), UINT64CONST(405648192073033409), UINT64CONST(324518553658426727), |
| 60 | UINT64CONST(519229685853482763), UINT64CONST(415383748682786211), UINT64CONST(332306998946228969), UINT64CONST(531691198313966350), |
| 61 | UINT64CONST(425352958651173080), UINT64CONST(340282366920938464), UINT64CONST(544451787073501542), UINT64CONST(435561429658801234), |
| 62 | UINT64CONST(348449143727040987), UINT64CONST(557518629963265579), UINT64CONST(446014903970612463), UINT64CONST(356811923176489971), |
| 63 | UINT64CONST(570899077082383953), UINT64CONST(456719261665907162), UINT64CONST(365375409332725730) |
| 64 | }; |
| 65 | #define FLOAT_POW5_BITCOUNT 61 |
| 66 | static const uint64 FLOAT_POW5_SPLIT[47] = { |
| 67 | UINT64CONST(1152921504606846976), UINT64CONST(1441151880758558720), UINT64CONST(1801439850948198400), UINT64CONST(2251799813685248000), |
| 68 | UINT64CONST(1407374883553280000), UINT64CONST(1759218604441600000), UINT64CONST(2199023255552000000), UINT64CONST(1374389534720000000), |
| 69 | UINT64CONST(1717986918400000000), UINT64CONST(2147483648000000000), UINT64CONST(1342177280000000000), UINT64CONST(1677721600000000000), |
| 70 | UINT64CONST(2097152000000000000), UINT64CONST(1310720000000000000), UINT64CONST(1638400000000000000), UINT64CONST(2048000000000000000), |
| 71 | UINT64CONST(1280000000000000000), UINT64CONST(1600000000000000000), UINT64CONST(2000000000000000000), UINT64CONST(1250000000000000000), |
| 72 | UINT64CONST(1562500000000000000), UINT64CONST(1953125000000000000), UINT64CONST(1220703125000000000), UINT64CONST(1525878906250000000), |
| 73 | UINT64CONST(1907348632812500000), UINT64CONST(1192092895507812500), UINT64CONST(1490116119384765625), UINT64CONST(1862645149230957031), |
| 74 | UINT64CONST(1164153218269348144), UINT64CONST(1455191522836685180), UINT64CONST(1818989403545856475), UINT64CONST(2273736754432320594), |
| 75 | UINT64CONST(1421085471520200371), UINT64CONST(1776356839400250464), UINT64CONST(2220446049250313080), UINT64CONST(1387778780781445675), |
| 76 | UINT64CONST(1734723475976807094), UINT64CONST(2168404344971008868), UINT64CONST(1355252715606880542), UINT64CONST(1694065894508600678), |
| 77 | UINT64CONST(2117582368135750847), UINT64CONST(1323488980084844279), UINT64CONST(1654361225106055349), UINT64CONST(2067951531382569187), |
| 78 | UINT64CONST(1292469707114105741), UINT64CONST(1615587133892632177), UINT64CONST(2019483917365790221) |
| 79 | }; |
| 80 | |
| 81 | static inline uint32 |
| 82 | pow5Factor(uint32 value) |
| 83 | { |
| 84 | uint32 count = 0; |
| 85 | |
| 86 | for (;;) |
| 87 | { |
| 88 | Assert(value != 0); |
| 89 | const uint32 q = value / 5; |
| 90 | const uint32 r = value % 5; |
| 91 | |
| 92 | if (r != 0) |
| 93 | break; |
| 94 | |
| 95 | value = q; |
| 96 | ++count; |
| 97 | } |
| 98 | return count; |
| 99 | } |
| 100 | |
| 101 | /* Returns true if value is divisible by 5^p. */ |
| 102 | static inline bool |
| 103 | multipleOfPowerOf5(const uint32 value, const uint32 p) |
| 104 | { |
| 105 | return pow5Factor(value) >= p; |
| 106 | } |
| 107 | |
| 108 | /* Returns true if value is divisible by 2^p. */ |
| 109 | static inline bool |
| 110 | multipleOfPowerOf2(const uint32 value, const uint32 p) |
| 111 | { |
| 112 | /* return __builtin_ctz(value) >= p; */ |
| 113 | return (value & ((1u << p) - 1)) == 0; |
| 114 | } |
| 115 | |
| 116 | /* |
| 117 | * It seems to be slightly faster to avoid uint128_t here, although the |
| 118 | * generated code for uint128_t looks slightly nicer. |
| 119 | */ |
| 120 | static inline uint32 |
| 121 | mulShift(const uint32 m, const uint64 factor, const int32 shift) |
| 122 | { |
| 123 | /* |
| 124 | * The casts here help MSVC to avoid calls to the __allmul library |
| 125 | * function. |
| 126 | */ |
| 127 | const uint32 factorLo = (uint32) (factor); |
| 128 | const uint32 factorHi = (uint32) (factor >> 32); |
| 129 | const uint64 bits0 = (uint64) m * factorLo; |
| 130 | const uint64 bits1 = (uint64) m * factorHi; |
| 131 | |
| 132 | Assert(shift > 32); |
| 133 | |
| 134 | #ifdef RYU_32_BIT_PLATFORM |
| 135 | |
| 136 | /* |
| 137 | * On 32-bit platforms we can avoid a 64-bit shift-right since we only |
| 138 | * need the upper 32 bits of the result and the shift value is > 32. |
| 139 | */ |
| 140 | const uint32 bits0Hi = (uint32) (bits0 >> 32); |
| 141 | uint32 bits1Lo = (uint32) (bits1); |
| 142 | uint32 bits1Hi = (uint32) (bits1 >> 32); |
| 143 | |
| 144 | bits1Lo += bits0Hi; |
| 145 | bits1Hi += (bits1Lo < bits0Hi); |
| 146 | |
| 147 | const int32 s = shift - 32; |
| 148 | |
| 149 | return (bits1Hi << (32 - s)) | (bits1Lo >> s); |
| 150 | |
| 151 | #else /* RYU_32_BIT_PLATFORM */ |
| 152 | |
| 153 | const uint64 sum = (bits0 >> 32) + bits1; |
| 154 | const uint64 shiftedSum = sum >> (shift - 32); |
| 155 | |
| 156 | Assert(shiftedSum <= PG_UINT32_MAX); |
| 157 | return (uint32) shiftedSum; |
| 158 | |
| 159 | #endif /* RYU_32_BIT_PLATFORM */ |
| 160 | } |
| 161 | |
| 162 | static inline uint32 |
| 163 | mulPow5InvDivPow2(const uint32 m, const uint32 q, const int32 j) |
| 164 | { |
| 165 | return mulShift(m, FLOAT_POW5_INV_SPLIT[q], j); |
| 166 | } |
| 167 | |
| 168 | static inline uint32 |
| 169 | mulPow5divPow2(const uint32 m, const uint32 i, const int32 j) |
| 170 | { |
| 171 | return mulShift(m, FLOAT_POW5_SPLIT[i], j); |
| 172 | } |
| 173 | |
| 174 | static inline uint32 |
| 175 | decimalLength(const uint32 v) |
| 176 | { |
| 177 | /* Function precondition: v is not a 10-digit number. */ |
| 178 | /* (9 digits are sufficient for round-tripping.) */ |
| 179 | Assert(v < 1000000000); |
| 180 | if (v >= 100000000) |
| 181 | { |
| 182 | return 9; |
| 183 | } |
| 184 | if (v >= 10000000) |
| 185 | { |
| 186 | return 8; |
| 187 | } |
| 188 | if (v >= 1000000) |
| 189 | { |
| 190 | return 7; |
| 191 | } |
| 192 | if (v >= 100000) |
| 193 | { |
| 194 | return 6; |
| 195 | } |
| 196 | if (v >= 10000) |
| 197 | { |
| 198 | return 5; |
| 199 | } |
| 200 | if (v >= 1000) |
| 201 | { |
| 202 | return 4; |
| 203 | } |
| 204 | if (v >= 100) |
| 205 | { |
| 206 | return 3; |
| 207 | } |
| 208 | if (v >= 10) |
| 209 | { |
| 210 | return 2; |
| 211 | } |
| 212 | return 1; |
| 213 | } |
| 214 | |
| 215 | /* A floating decimal representing m * 10^e. */ |
| 216 | typedef struct floating_decimal_32 |
| 217 | { |
| 218 | uint32 mantissa; |
| 219 | int32 exponent; |
| 220 | } floating_decimal_32; |
| 221 | |
| 222 | static inline floating_decimal_32 |
| 223 | f2d(const uint32 ieeeMantissa, const uint32 ieeeExponent) |
| 224 | { |
| 225 | int32 e2; |
| 226 | uint32 m2; |
| 227 | |
| 228 | if (ieeeExponent == 0) |
| 229 | { |
| 230 | /* We subtract 2 so that the bounds computation has 2 additional bits. */ |
| 231 | e2 = 1 - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2; |
| 232 | m2 = ieeeMantissa; |
| 233 | } |
| 234 | else |
| 235 | { |
| 236 | e2 = ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS - 2; |
| 237 | m2 = (1u << FLOAT_MANTISSA_BITS) | ieeeMantissa; |
| 238 | } |
| 239 | |
| 240 | #if STRICTLY_SHORTEST |
| 241 | const bool even = (m2 & 1) == 0; |
| 242 | const bool acceptBounds = even; |
| 243 | #else |
| 244 | const bool acceptBounds = false; |
| 245 | #endif |
| 246 | |
| 247 | /* Step 2: Determine the interval of legal decimal representations. */ |
| 248 | const uint32 mv = 4 * m2; |
| 249 | const uint32 mp = 4 * m2 + 2; |
| 250 | |
| 251 | /* Implicit bool -> int conversion. True is 1, false is 0. */ |
| 252 | const uint32 mmShift = ieeeMantissa != 0 || ieeeExponent <= 1; |
| 253 | const uint32 mm = 4 * m2 - 1 - mmShift; |
| 254 | |
| 255 | /* Step 3: Convert to a decimal power base using 64-bit arithmetic. */ |
| 256 | uint32 vr, |
| 257 | vp, |
| 258 | vm; |
| 259 | int32 e10; |
| 260 | bool vmIsTrailingZeros = false; |
| 261 | bool vrIsTrailingZeros = false; |
| 262 | uint8 lastRemovedDigit = 0; |
| 263 | |
| 264 | if (e2 >= 0) |
| 265 | { |
| 266 | const uint32 q = log10Pow2(e2); |
| 267 | |
| 268 | e10 = q; |
| 269 | |
| 270 | const int32 k = FLOAT_POW5_INV_BITCOUNT + pow5bits(q) - 1; |
| 271 | const int32 i = -e2 + q + k; |
| 272 | |
| 273 | vr = mulPow5InvDivPow2(mv, q, i); |
| 274 | vp = mulPow5InvDivPow2(mp, q, i); |
| 275 | vm = mulPow5InvDivPow2(mm, q, i); |
| 276 | |
| 277 | if (q != 0 && (vp - 1) / 10 <= vm / 10) |
| 278 | { |
| 279 | /* |
| 280 | * We need to know one removed digit even if we are not going to |
| 281 | * loop below. We could use q = X - 1 above, except that would |
| 282 | * require 33 bits for the result, and we've found that 32-bit |
| 283 | * arithmetic is faster even on 64-bit machines. |
| 284 | */ |
| 285 | const int32 l = FLOAT_POW5_INV_BITCOUNT + pow5bits(q - 1) - 1; |
| 286 | |
| 287 | lastRemovedDigit = (uint8) (mulPow5InvDivPow2(mv, q - 1, -e2 + q - 1 + l) % 10); |
| 288 | } |
| 289 | if (q <= 9) |
| 290 | { |
| 291 | /* |
| 292 | * The largest power of 5 that fits in 24 bits is 5^10, but q <= 9 |
| 293 | * seems to be safe as well. |
| 294 | * |
| 295 | * Only one of mp, mv, and mm can be a multiple of 5, if any. |
| 296 | */ |
| 297 | if (mv % 5 == 0) |
| 298 | { |
| 299 | vrIsTrailingZeros = multipleOfPowerOf5(mv, q); |
| 300 | } |
| 301 | else if (acceptBounds) |
| 302 | { |
| 303 | vmIsTrailingZeros = multipleOfPowerOf5(mm, q); |
| 304 | } |
| 305 | else |
| 306 | { |
| 307 | vp -= multipleOfPowerOf5(mp, q); |
| 308 | } |
| 309 | } |
| 310 | } |
| 311 | else |
| 312 | { |
| 313 | const uint32 q = log10Pow5(-e2); |
| 314 | |
| 315 | e10 = q + e2; |
| 316 | |
| 317 | const int32 i = -e2 - q; |
| 318 | const int32 k = pow5bits(i) - FLOAT_POW5_BITCOUNT; |
| 319 | int32 j = q - k; |
| 320 | |
| 321 | vr = mulPow5divPow2(mv, i, j); |
| 322 | vp = mulPow5divPow2(mp, i, j); |
| 323 | vm = mulPow5divPow2(mm, i, j); |
| 324 | |
| 325 | if (q != 0 && (vp - 1) / 10 <= vm / 10) |
| 326 | { |
| 327 | j = q - 1 - (pow5bits(i + 1) - FLOAT_POW5_BITCOUNT); |
| 328 | lastRemovedDigit = (uint8) (mulPow5divPow2(mv, i + 1, j) % 10); |
| 329 | } |
| 330 | if (q <= 1) |
| 331 | { |
| 332 | /* |
| 333 | * {vr,vp,vm} is trailing zeros if {mv,mp,mm} has at least q |
| 334 | * trailing 0 bits. |
| 335 | */ |
| 336 | /* mv = 4 * m2, so it always has at least two trailing 0 bits. */ |
| 337 | vrIsTrailingZeros = true; |
| 338 | if (acceptBounds) |
| 339 | { |
| 340 | /* |
| 341 | * mm = mv - 1 - mmShift, so it has 1 trailing 0 bit iff |
| 342 | * mmShift == 1. |
| 343 | */ |
| 344 | vmIsTrailingZeros = mmShift == 1; |
| 345 | } |
| 346 | else |
| 347 | { |
| 348 | /* |
| 349 | * mp = mv + 2, so it always has at least one trailing 0 bit. |
| 350 | */ |
| 351 | --vp; |
| 352 | } |
| 353 | } |
| 354 | else if (q < 31) |
| 355 | { |
| 356 | /* TODO(ulfjack):Use a tighter bound here. */ |
| 357 | vrIsTrailingZeros = multipleOfPowerOf2(mv, q - 1); |
| 358 | } |
| 359 | } |
| 360 | |
| 361 | /* |
| 362 | * Step 4: Find the shortest decimal representation in the interval of |
| 363 | * legal representations. |
| 364 | */ |
| 365 | uint32 removed = 0; |
| 366 | uint32 output; |
| 367 | |
| 368 | if (vmIsTrailingZeros || vrIsTrailingZeros) |
| 369 | { |
| 370 | /* General case, which happens rarely (~4.0%). */ |
| 371 | while (vp / 10 > vm / 10) |
| 372 | { |
| 373 | vmIsTrailingZeros &= vm - (vm / 10) * 10 == 0; |
| 374 | vrIsTrailingZeros &= lastRemovedDigit == 0; |
| 375 | lastRemovedDigit = (uint8) (vr % 10); |
| 376 | vr /= 10; |
| 377 | vp /= 10; |
| 378 | vm /= 10; |
| 379 | ++removed; |
| 380 | } |
| 381 | if (vmIsTrailingZeros) |
| 382 | { |
| 383 | while (vm % 10 == 0) |
| 384 | { |
| 385 | vrIsTrailingZeros &= lastRemovedDigit == 0; |
| 386 | lastRemovedDigit = (uint8) (vr % 10); |
| 387 | vr /= 10; |
| 388 | vp /= 10; |
| 389 | vm /= 10; |
| 390 | ++removed; |
| 391 | } |
| 392 | } |
| 393 | |
| 394 | if (vrIsTrailingZeros && lastRemovedDigit == 5 && vr % 2 == 0) |
| 395 | { |
| 396 | /* Round even if the exact number is .....50..0. */ |
| 397 | lastRemovedDigit = 4; |
| 398 | } |
| 399 | |
| 400 | /* |
| 401 | * We need to take vr + 1 if vr is outside bounds or we need to round |
| 402 | * up. |
| 403 | */ |
| 404 | output = vr + ((vr == vm && (!acceptBounds || !vmIsTrailingZeros)) || lastRemovedDigit >= 5); |
| 405 | } |
| 406 | else |
| 407 | { |
| 408 | /* |
| 409 | * Specialized for the common case (~96.0%). Percentages below are |
| 410 | * relative to this. |
| 411 | * |
| 412 | * Loop iterations below (approximately): 0: 13.6%, 1: 70.7%, 2: |
| 413 | * 14.1%, 3: 1.39%, 4: 0.14%, 5+: 0.01% |
| 414 | */ |
| 415 | while (vp / 10 > vm / 10) |
| 416 | { |
| 417 | lastRemovedDigit = (uint8) (vr % 10); |
| 418 | vr /= 10; |
| 419 | vp /= 10; |
| 420 | vm /= 10; |
| 421 | ++removed; |
| 422 | } |
| 423 | |
| 424 | /* |
| 425 | * We need to take vr + 1 if vr is outside bounds or we need to round |
| 426 | * up. |
| 427 | */ |
| 428 | output = vr + (vr == vm || lastRemovedDigit >= 5); |
| 429 | } |
| 430 | |
| 431 | const int32 exp = e10 + removed; |
| 432 | |
| 433 | floating_decimal_32 fd; |
| 434 | |
| 435 | fd.exponent = exp; |
| 436 | fd.mantissa = output; |
| 437 | return fd; |
| 438 | } |
| 439 | |
| 440 | static inline int |
| 441 | to_chars_f(const floating_decimal_32 v, const uint32 olength, char *const result) |
| 442 | { |
| 443 | /* Step 5: Print the decimal representation. */ |
| 444 | int index = 0; |
| 445 | |
| 446 | uint32 output = v.mantissa; |
| 447 | int32 exp = v.exponent; |
| 448 | |
| 449 | /*---- |
| 450 | * On entry, mantissa * 10^exp is the result to be output. |
| 451 | * Caller has already done the - sign if needed. |
| 452 | * |
| 453 | * We want to insert the point somewhere depending on the output length |
| 454 | * and exponent, which might mean adding zeros: |
| 455 | * |
| 456 | * exp | format |
| 457 | * 1+ | ddddddddd000000 |
| 458 | * 0 | ddddddddd |
| 459 | * -1 .. -len+1 | dddddddd.d to d.ddddddddd |
| 460 | * -len ... | 0.ddddddddd to 0.000dddddd |
| 461 | */ |
| 462 | uint32 i = 0; |
| 463 | int32 nexp = exp + olength; |
| 464 | |
| 465 | if (nexp <= 0) |
| 466 | { |
| 467 | /* -nexp is number of 0s to add after '.' */ |
| 468 | Assert(nexp >= -3); |
| 469 | /* 0.000ddddd */ |
| 470 | index = 2 - nexp; |
| 471 | /* copy 8 bytes rather than 5 to let compiler optimize */ |
| 472 | memcpy(result, "0.000000" , 8); |
| 473 | } |
| 474 | else if (exp < 0) |
| 475 | { |
| 476 | /* |
| 477 | * dddd.dddd; leave space at the start and move the '.' in after |
| 478 | */ |
| 479 | index = 1; |
| 480 | } |
| 481 | else |
| 482 | { |
| 483 | /* |
| 484 | * We can save some code later by pre-filling with zeros. We know that |
| 485 | * there can be no more than 6 output digits in this form, otherwise |
| 486 | * we would not choose fixed-point output. memset 8 rather than 6 |
| 487 | * bytes to let the compiler optimize it. |
| 488 | */ |
| 489 | Assert(exp < 6 && exp + olength <= 6); |
| 490 | memset(result, '0', 8); |
| 491 | } |
| 492 | |
| 493 | while (output >= 10000) |
| 494 | { |
| 495 | const uint32 c = output - 10000 * (output / 10000); |
| 496 | const uint32 c0 = (c % 100) << 1; |
| 497 | const uint32 c1 = (c / 100) << 1; |
| 498 | |
| 499 | output /= 10000; |
| 500 | |
| 501 | memcpy(result + index + olength - i - 2, DIGIT_TABLE + c0, 2); |
| 502 | memcpy(result + index + olength - i - 4, DIGIT_TABLE + c1, 2); |
| 503 | i += 4; |
| 504 | } |
| 505 | if (output >= 100) |
| 506 | { |
| 507 | const uint32 c = (output % 100) << 1; |
| 508 | |
| 509 | output /= 100; |
| 510 | memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2); |
| 511 | i += 2; |
| 512 | } |
| 513 | if (output >= 10) |
| 514 | { |
| 515 | const uint32 c = output << 1; |
| 516 | |
| 517 | memcpy(result + index + olength - i - 2, DIGIT_TABLE + c, 2); |
| 518 | } |
| 519 | else |
| 520 | { |
| 521 | result[index] = (char) ('0' + output); |
| 522 | } |
| 523 | |
| 524 | if (index == 1) |
| 525 | { |
| 526 | /* |
| 527 | * nexp is 1..6 here, representing the number of digits before the |
| 528 | * point. A value of 7+ is not possible because we switch to |
| 529 | * scientific notation when the display exponent reaches 6. |
| 530 | */ |
| 531 | Assert(nexp < 7); |
| 532 | /* gcc only seems to want to optimize memmove for small 2^n */ |
| 533 | if (nexp & 4) |
| 534 | { |
| 535 | memmove(result + index - 1, result + index, 4); |
| 536 | index += 4; |
| 537 | } |
| 538 | if (nexp & 2) |
| 539 | { |
| 540 | memmove(result + index - 1, result + index, 2); |
| 541 | index += 2; |
| 542 | } |
| 543 | if (nexp & 1) |
| 544 | { |
| 545 | result[index - 1] = result[index]; |
| 546 | } |
| 547 | result[nexp] = '.'; |
| 548 | index = olength + 1; |
| 549 | } |
| 550 | else if (exp >= 0) |
| 551 | { |
| 552 | /* we supplied the trailing zeros earlier, now just set the length. */ |
| 553 | index = olength + exp; |
| 554 | } |
| 555 | else |
| 556 | { |
| 557 | index = olength + (2 - nexp); |
| 558 | } |
| 559 | |
| 560 | return index; |
| 561 | } |
| 562 | |
| 563 | static inline int |
| 564 | to_chars(const floating_decimal_32 v, const bool sign, char *const result) |
| 565 | { |
| 566 | /* Step 5: Print the decimal representation. */ |
| 567 | int index = 0; |
| 568 | |
| 569 | uint32 output = v.mantissa; |
| 570 | uint32 olength = decimalLength(output); |
| 571 | int32 exp = v.exponent + olength - 1; |
| 572 | |
| 573 | if (sign) |
| 574 | result[index++] = '-'; |
| 575 | |
| 576 | /* |
| 577 | * The thresholds for fixed-point output are chosen to match printf |
| 578 | * defaults. Beware that both the code of to_chars_f and the value of |
| 579 | * FLOAT_SHORTEST_DECIMAL_LEN are sensitive to these thresholds. |
| 580 | */ |
| 581 | if (exp >= -4 && exp < 6) |
| 582 | return to_chars_f(v, olength, result + index) + sign; |
| 583 | |
| 584 | /* |
| 585 | * If v.exponent is exactly 0, we might have reached here via the small |
| 586 | * integer fast path, in which case v.mantissa might contain trailing |
| 587 | * (decimal) zeros. For scientific notation we need to move these zeros |
| 588 | * into the exponent. (For fixed point this doesn't matter, which is why |
| 589 | * we do this here rather than above.) |
| 590 | * |
| 591 | * Since we already calculated the display exponent (exp) above based on |
| 592 | * the old decimal length, that value does not change here. Instead, we |
| 593 | * just reduce the display length for each digit removed. |
| 594 | * |
| 595 | * If we didn't get here via the fast path, the raw exponent will not |
| 596 | * usually be 0, and there will be no trailing zeros, so we pay no more |
| 597 | * than one div10/multiply extra cost. We claw back half of that by |
| 598 | * checking for divisibility by 2 before dividing by 10. |
| 599 | */ |
| 600 | if (v.exponent == 0) |
| 601 | { |
| 602 | while ((output & 1) == 0) |
| 603 | { |
| 604 | const uint32 q = output / 10; |
| 605 | const uint32 r = output - 10 * q; |
| 606 | |
| 607 | if (r != 0) |
| 608 | break; |
| 609 | output = q; |
| 610 | --olength; |
| 611 | } |
| 612 | } |
| 613 | |
| 614 | /*---- |
| 615 | * Print the decimal digits. |
| 616 | * The following code is equivalent to: |
| 617 | * |
| 618 | * for (uint32 i = 0; i < olength - 1; ++i) { |
| 619 | * const uint32 c = output % 10; output /= 10; |
| 620 | * result[index + olength - i] = (char) ('0' + c); |
| 621 | * } |
| 622 | * result[index] = '0' + output % 10; |
| 623 | */ |
| 624 | uint32 i = 0; |
| 625 | |
| 626 | while (output >= 10000) |
| 627 | { |
| 628 | const uint32 c = output - 10000 * (output / 10000); |
| 629 | const uint32 c0 = (c % 100) << 1; |
| 630 | const uint32 c1 = (c / 100) << 1; |
| 631 | |
| 632 | output /= 10000; |
| 633 | |
| 634 | memcpy(result + index + olength - i - 1, DIGIT_TABLE + c0, 2); |
| 635 | memcpy(result + index + olength - i - 3, DIGIT_TABLE + c1, 2); |
| 636 | i += 4; |
| 637 | } |
| 638 | if (output >= 100) |
| 639 | { |
| 640 | const uint32 c = (output % 100) << 1; |
| 641 | |
| 642 | output /= 100; |
| 643 | memcpy(result + index + olength - i - 1, DIGIT_TABLE + c, 2); |
| 644 | i += 2; |
| 645 | } |
| 646 | if (output >= 10) |
| 647 | { |
| 648 | const uint32 c = output << 1; |
| 649 | |
| 650 | /* |
| 651 | * We can't use memcpy here: the decimal dot goes between these two |
| 652 | * digits. |
| 653 | */ |
| 654 | result[index + olength - i] = DIGIT_TABLE[c + 1]; |
| 655 | result[index] = DIGIT_TABLE[c]; |
| 656 | } |
| 657 | else |
| 658 | { |
| 659 | result[index] = (char) ('0' + output); |
| 660 | } |
| 661 | |
| 662 | /* Print decimal point if needed. */ |
| 663 | if (olength > 1) |
| 664 | { |
| 665 | result[index + 1] = '.'; |
| 666 | index += olength + 1; |
| 667 | } |
| 668 | else |
| 669 | { |
| 670 | ++index; |
| 671 | } |
| 672 | |
| 673 | /* Print the exponent. */ |
| 674 | result[index++] = 'e'; |
| 675 | if (exp < 0) |
| 676 | { |
| 677 | result[index++] = '-'; |
| 678 | exp = -exp; |
| 679 | } |
| 680 | else |
| 681 | result[index++] = '+'; |
| 682 | |
| 683 | memcpy(result + index, DIGIT_TABLE + 2 * exp, 2); |
| 684 | index += 2; |
| 685 | |
| 686 | return index; |
| 687 | } |
| 688 | |
| 689 | static inline bool |
| 690 | f2d_small_int(const uint32 ieeeMantissa, |
| 691 | const uint32 ieeeExponent, |
| 692 | floating_decimal_32 *v) |
| 693 | { |
| 694 | const int32 e2 = (int32) ieeeExponent - FLOAT_BIAS - FLOAT_MANTISSA_BITS; |
| 695 | |
| 696 | /* |
| 697 | * Avoid using multiple "return false;" here since it tends to provoke the |
| 698 | * compiler into inlining multiple copies of f2d, which is undesirable. |
| 699 | */ |
| 700 | |
| 701 | if (e2 >= -FLOAT_MANTISSA_BITS && e2 <= 0) |
| 702 | { |
| 703 | /*---- |
| 704 | * Since 2^23 <= m2 < 2^24 and 0 <= -e2 <= 23: |
| 705 | * 1 <= f = m2 / 2^-e2 < 2^24. |
| 706 | * |
| 707 | * Test if the lower -e2 bits of the significand are 0, i.e. whether |
| 708 | * the fraction is 0. We can use ieeeMantissa here, since the implied |
| 709 | * 1 bit can never be tested by this; the implied 1 can only be part |
| 710 | * of a fraction if e2 < -FLOAT_MANTISSA_BITS which we already |
| 711 | * checked. (e.g. 0.5 gives ieeeMantissa == 0 and e2 == -24) |
| 712 | */ |
| 713 | const uint32 mask = (1U << -e2) - 1; |
| 714 | const uint32 fraction = ieeeMantissa & mask; |
| 715 | |
| 716 | if (fraction == 0) |
| 717 | { |
| 718 | /*---- |
| 719 | * f is an integer in the range [1, 2^24). |
| 720 | * Note: mantissa might contain trailing (decimal) 0's. |
| 721 | * Note: since 2^24 < 10^9, there is no need to adjust |
| 722 | * decimalLength(). |
| 723 | */ |
| 724 | const uint32 m2 = (1U << FLOAT_MANTISSA_BITS) | ieeeMantissa; |
| 725 | |
| 726 | v->mantissa = m2 >> -e2; |
| 727 | v->exponent = 0; |
| 728 | return true; |
| 729 | } |
| 730 | } |
| 731 | |
| 732 | return false; |
| 733 | } |
| 734 | |
| 735 | /* |
| 736 | * Store the shortest decimal representation of the given float as an |
| 737 | * UNTERMINATED string in the caller's supplied buffer (which must be at least |
| 738 | * FLOAT_SHORTEST_DECIMAL_LEN-1 bytes long). |
| 739 | * |
| 740 | * Returns the number of bytes stored. |
| 741 | */ |
| 742 | int |
| 743 | float_to_shortest_decimal_bufn(float f, char *result) |
| 744 | { |
| 745 | /* |
| 746 | * Step 1: Decode the floating-point number, and unify normalized and |
| 747 | * subnormal cases. |
| 748 | */ |
| 749 | const uint32 bits = float_to_bits(f); |
| 750 | |
| 751 | /* Decode bits into sign, mantissa, and exponent. */ |
| 752 | const bool ieeeSign = ((bits >> (FLOAT_MANTISSA_BITS + FLOAT_EXPONENT_BITS)) & 1) != 0; |
| 753 | const uint32 ieeeMantissa = bits & ((1u << FLOAT_MANTISSA_BITS) - 1); |
| 754 | const uint32 ieeeExponent = (bits >> FLOAT_MANTISSA_BITS) & ((1u << FLOAT_EXPONENT_BITS) - 1); |
| 755 | |
| 756 | /* Case distinction; exit early for the easy cases. */ |
| 757 | if (ieeeExponent == ((1u << FLOAT_EXPONENT_BITS) - 1u) || (ieeeExponent == 0 && ieeeMantissa == 0)) |
| 758 | { |
| 759 | return copy_special_str(result, ieeeSign, (ieeeExponent != 0), (ieeeMantissa != 0)); |
| 760 | } |
| 761 | |
| 762 | floating_decimal_32 v; |
| 763 | const bool isSmallInt = f2d_small_int(ieeeMantissa, ieeeExponent, &v); |
| 764 | |
| 765 | if (!isSmallInt) |
| 766 | { |
| 767 | v = f2d(ieeeMantissa, ieeeExponent); |
| 768 | } |
| 769 | |
| 770 | return to_chars(v, ieeeSign, result); |
| 771 | } |
| 772 | |
| 773 | /* |
| 774 | * Store the shortest decimal representation of the given float as a |
| 775 | * null-terminated string in the caller's supplied buffer (which must be at |
| 776 | * least FLOAT_SHORTEST_DECIMAL_LEN bytes long). |
| 777 | * |
| 778 | * Returns the string length. |
| 779 | */ |
| 780 | int |
| 781 | float_to_shortest_decimal_buf(float f, char *result) |
| 782 | { |
| 783 | const int index = float_to_shortest_decimal_bufn(f, result); |
| 784 | |
| 785 | /* Terminate the string. */ |
| 786 | Assert(index < FLOAT_SHORTEST_DECIMAL_LEN); |
| 787 | result[index] = '\0'; |
| 788 | return index; |
| 789 | } |
| 790 | |
| 791 | /* |
| 792 | * Return the shortest decimal representation as a null-terminated palloc'd |
| 793 | * string (outside the backend, uses malloc() instead). |
| 794 | * |
| 795 | * Caller is responsible for freeing the result. |
| 796 | */ |
| 797 | char * |
| 798 | float_to_shortest_decimal(float f) |
| 799 | { |
| 800 | char *const result = (char *) palloc(FLOAT_SHORTEST_DECIMAL_LEN); |
| 801 | |
| 802 | float_to_shortest_decimal_buf(f, result); |
| 803 | return result; |
| 804 | } |
| 805 | |