1 /* 2 * QEMU float support 3 * 4 * Derived from SoftFloat. 5 */ 6 7 /*============================================================================ 8 9 This C source file is part of the SoftFloat IEC/IEEE Floating-point Arithmetic 10 Package, Release 2b. 11 12 Written by John R. Hauser. This work was made possible in part by the 13 International Computer Science Institute, located at Suite 600, 1947 Center 14 Street, Berkeley, California 94704. Funding was partially provided by the 15 National Science Foundation under grant MIP-9311980. The original version 16 of this code was written as part of a project to build a fixed-point vector 17 processor in collaboration with the University of California at Berkeley, 18 overseen by Profs. Nelson Morgan and John Wawrzynek. More information 19 is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ 20 arithmetic/SoftFloat.html'. 21 22 THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has 23 been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES 24 RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS 25 AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, 26 COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE 27 EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE 28 INSTITUTE (possibly via similar legal warning) AGAINST ALL LOSSES, COSTS, OR 29 OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. 30 31 Derivative works are acceptable, even for commercial purposes, so long as 32 (1) the source code for the derivative work includes prominent notice that 33 the work is derivative, and (2) the source code includes prominent notice with 34 these four paragraphs for those parts of this code that are retained. 35 36 =============================================================================*/ 37 38 /* softfloat (and in particular the code in softfloat-specialize.h) is 39 * target-dependent and needs the TARGET_* macros. 40 */ 41 #include "config.h" 42 43 #include "fpu/softfloat.h" 44 45 /*---------------------------------------------------------------------------- 46 | Primitive arithmetic functions, including multi-word arithmetic, and 47 | division and square root approximations. (Can be specialized to target if 48 | desired.) 49 *----------------------------------------------------------------------------*/ 50 #include "softfloat-macros.h" 51 52 /*---------------------------------------------------------------------------- 53 | Functions and definitions to determine: (1) whether tininess for underflow 54 | is detected before or after rounding by default, (2) what (if anything) 55 | happens when exceptions are raised, (3) how signaling NaNs are distinguished 56 | from quiet NaNs, (4) the default generated quiet NaNs, and (5) how NaNs 57 | are propagated from function inputs to output. These details are target- 58 | specific. 59 *----------------------------------------------------------------------------*/ 60 #include "softfloat-specialize.h" 61 62 void set_float_rounding_mode(int val STATUS_PARAM) 63 { 64 STATUS(float_rounding_mode) = val; 65 } 66 67 void set_float_exception_flags(int val STATUS_PARAM) 68 { 69 STATUS(float_exception_flags) = val; 70 } 71 72 void set_floatx80_rounding_precision(int val STATUS_PARAM) 73 { 74 STATUS(floatx80_rounding_precision) = val; 75 } 76 77 /*---------------------------------------------------------------------------- 78 | Returns the fraction bits of the half-precision floating-point value `a'. 79 *----------------------------------------------------------------------------*/ 80 81 INLINE uint32_t extractFloat16Frac(float16 a) 82 { 83 return float16_val(a) & 0x3ff; 84 } 85 86 /*---------------------------------------------------------------------------- 87 | Returns the exponent bits of the half-precision floating-point value `a'. 88 *----------------------------------------------------------------------------*/ 89 90 INLINE int_fast16_t extractFloat16Exp(float16 a) 91 { 92 return (float16_val(a) >> 10) & 0x1f; 93 } 94 95 /*---------------------------------------------------------------------------- 96 | Returns the sign bit of the single-precision floating-point value `a'. 97 *----------------------------------------------------------------------------*/ 98 99 INLINE flag extractFloat16Sign(float16 a) 100 { 101 return float16_val(a)>>15; 102 } 103 104 /*---------------------------------------------------------------------------- 105 | Takes a 64-bit fixed-point value `absZ' with binary point between bits 6 106 | and 7, and returns the properly rounded 32-bit integer corresponding to the 107 | input. If `zSign' is 1, the input is negated before being converted to an 108 | integer. Bit 63 of `absZ' must be zero. Ordinarily, the fixed-point input 109 | is simply rounded to an integer, with the inexact exception raised if the 110 | input cannot be represented exactly as an integer. However, if the fixed- 111 | point input is too large, the invalid exception is raised and the largest 112 | positive or negative integer is returned. 113 *----------------------------------------------------------------------------*/ 114 115 static int32 roundAndPackInt32( flag zSign, uint64_t absZ STATUS_PARAM) 116 { 117 int8 roundingMode; 118 flag roundNearestEven; 119 int8 roundIncrement, roundBits; 120 int32_t z; 121 122 roundingMode = STATUS(float_rounding_mode); 123 roundNearestEven = ( roundingMode == float_round_nearest_even ); 124 roundIncrement = 0x40; 125 if ( ! roundNearestEven ) { 126 if ( roundingMode == float_round_to_zero ) { 127 roundIncrement = 0; 128 } 129 else { 130 roundIncrement = 0x7F; 131 if ( zSign ) { 132 if ( roundingMode == float_round_up ) roundIncrement = 0; 133 } 134 else { 135 if ( roundingMode == float_round_down ) roundIncrement = 0; 136 } 137 } 138 } 139 roundBits = absZ & 0x7F; 140 absZ = ( absZ + roundIncrement )>>7; 141 absZ &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); 142 z = absZ; 143 if ( zSign ) z = - z; 144 if ( ( absZ>>32 ) || ( z && ( ( z < 0 ) ^ zSign ) ) ) { 145 float_raise( float_flag_invalid STATUS_VAR); 146 return zSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; 147 } 148 if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; 149 return z; 150 151 } 152 153 /*---------------------------------------------------------------------------- 154 | Takes the 128-bit fixed-point value formed by concatenating `absZ0' and 155 | `absZ1', with binary point between bits 63 and 64 (between the input words), 156 | and returns the properly rounded 64-bit integer corresponding to the input. 157 | If `zSign' is 1, the input is negated before being converted to an integer. 158 | Ordinarily, the fixed-point input is simply rounded to an integer, with 159 | the inexact exception raised if the input cannot be represented exactly as 160 | an integer. However, if the fixed-point input is too large, the invalid 161 | exception is raised and the largest positive or negative integer is 162 | returned. 163 *----------------------------------------------------------------------------*/ 164 165 static int64 roundAndPackInt64( flag zSign, uint64_t absZ0, uint64_t absZ1 STATUS_PARAM) 166 { 167 int8 roundingMode; 168 flag roundNearestEven, increment; 169 int64_t z; 170 171 roundingMode = STATUS(float_rounding_mode); 172 roundNearestEven = ( roundingMode == float_round_nearest_even ); 173 increment = ( (int64_t) absZ1 < 0 ); 174 if ( ! roundNearestEven ) { 175 if ( roundingMode == float_round_to_zero ) { 176 increment = 0; 177 } 178 else { 179 if ( zSign ) { 180 increment = ( roundingMode == float_round_down ) && absZ1; 181 } 182 else { 183 increment = ( roundingMode == float_round_up ) && absZ1; 184 } 185 } 186 } 187 if ( increment ) { 188 ++absZ0; 189 if ( absZ0 == 0 ) goto overflow; 190 absZ0 &= ~ ( ( (uint64_t) ( absZ1<<1 ) == 0 ) & roundNearestEven ); 191 } 192 z = absZ0; 193 if ( zSign ) z = - z; 194 if ( z && ( ( z < 0 ) ^ zSign ) ) { 195 overflow: 196 float_raise( float_flag_invalid STATUS_VAR); 197 return 198 zSign ? (int64_t) LIT64( 0x8000000000000000 ) 199 : LIT64( 0x7FFFFFFFFFFFFFFF ); 200 } 201 if ( absZ1 ) STATUS(float_exception_flags) |= float_flag_inexact; 202 return z; 203 204 } 205 206 /*---------------------------------------------------------------------------- 207 | Returns the fraction bits of the single-precision floating-point value `a'. 208 *----------------------------------------------------------------------------*/ 209 210 INLINE uint32_t extractFloat32Frac( float32 a ) 211 { 212 213 return float32_val(a) & 0x007FFFFF; 214 215 } 216 217 /*---------------------------------------------------------------------------- 218 | Returns the exponent bits of the single-precision floating-point value `a'. 219 *----------------------------------------------------------------------------*/ 220 221 INLINE int_fast16_t extractFloat32Exp(float32 a) 222 { 223 224 return ( float32_val(a)>>23 ) & 0xFF; 225 226 } 227 228 /*---------------------------------------------------------------------------- 229 | Returns the sign bit of the single-precision floating-point value `a'. 230 *----------------------------------------------------------------------------*/ 231 232 INLINE flag extractFloat32Sign( float32 a ) 233 { 234 235 return float32_val(a)>>31; 236 237 } 238 239 /*---------------------------------------------------------------------------- 240 | If `a' is denormal and we are in flush-to-zero mode then set the 241 | input-denormal exception and return zero. Otherwise just return the value. 242 *----------------------------------------------------------------------------*/ 243 static float32 float32_squash_input_denormal(float32 a STATUS_PARAM) 244 { 245 if (STATUS(flush_inputs_to_zero)) { 246 if (extractFloat32Exp(a) == 0 && extractFloat32Frac(a) != 0) { 247 float_raise(float_flag_input_denormal STATUS_VAR); 248 return make_float32(float32_val(a) & 0x80000000); 249 } 250 } 251 return a; 252 } 253 254 /*---------------------------------------------------------------------------- 255 | Normalizes the subnormal single-precision floating-point value represented 256 | by the denormalized significand `aSig'. The normalized exponent and 257 | significand are stored at the locations pointed to by `zExpPtr' and 258 | `zSigPtr', respectively. 259 *----------------------------------------------------------------------------*/ 260 261 static void 262 normalizeFloat32Subnormal(uint32_t aSig, int_fast16_t *zExpPtr, uint32_t *zSigPtr) 263 { 264 int8 shiftCount; 265 266 shiftCount = countLeadingZeros32( aSig ) - 8; 267 *zSigPtr = aSig<<shiftCount; 268 *zExpPtr = 1 - shiftCount; 269 270 } 271 272 /*---------------------------------------------------------------------------- 273 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a 274 | single-precision floating-point value, returning the result. After being 275 | shifted into the proper positions, the three fields are simply added 276 | together to form the result. This means that any integer portion of `zSig' 277 | will be added into the exponent. Since a properly normalized significand 278 | will have an integer portion equal to 1, the `zExp' input should be 1 less 279 | than the desired result exponent whenever `zSig' is a complete, normalized 280 | significand. 281 *----------------------------------------------------------------------------*/ 282 283 INLINE float32 packFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig) 284 { 285 286 return make_float32( 287 ( ( (uint32_t) zSign )<<31 ) + ( ( (uint32_t) zExp )<<23 ) + zSig); 288 289 } 290 291 /*---------------------------------------------------------------------------- 292 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 293 | and significand `zSig', and returns the proper single-precision floating- 294 | point value corresponding to the abstract input. Ordinarily, the abstract 295 | value is simply rounded and packed into the single-precision format, with 296 | the inexact exception raised if the abstract input cannot be represented 297 | exactly. However, if the abstract value is too large, the overflow and 298 | inexact exceptions are raised and an infinity or maximal finite value is 299 | returned. If the abstract value is too small, the input value is rounded to 300 | a subnormal number, and the underflow and inexact exceptions are raised if 301 | the abstract input cannot be represented exactly as a subnormal single- 302 | precision floating-point number. 303 | The input significand `zSig' has its binary point between bits 30 304 | and 29, which is 7 bits to the left of the usual location. This shifted 305 | significand must be normalized or smaller. If `zSig' is not normalized, 306 | `zExp' must be 0; in that case, the result returned is a subnormal number, 307 | and it must not require rounding. In the usual case that `zSig' is 308 | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. 309 | The handling of underflow and overflow follows the IEC/IEEE Standard for 310 | Binary Floating-Point Arithmetic. 311 *----------------------------------------------------------------------------*/ 312 313 static float32 roundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM) 314 { 315 int8 roundingMode; 316 flag roundNearestEven; 317 int8 roundIncrement, roundBits; 318 flag isTiny; 319 320 roundingMode = STATUS(float_rounding_mode); 321 roundNearestEven = ( roundingMode == float_round_nearest_even ); 322 roundIncrement = 0x40; 323 if ( ! roundNearestEven ) { 324 if ( roundingMode == float_round_to_zero ) { 325 roundIncrement = 0; 326 } 327 else { 328 roundIncrement = 0x7F; 329 if ( zSign ) { 330 if ( roundingMode == float_round_up ) roundIncrement = 0; 331 } 332 else { 333 if ( roundingMode == float_round_down ) roundIncrement = 0; 334 } 335 } 336 } 337 roundBits = zSig & 0x7F; 338 if ( 0xFD <= (uint16_t) zExp ) { 339 if ( ( 0xFD < zExp ) 340 || ( ( zExp == 0xFD ) 341 && ( (int32_t) ( zSig + roundIncrement ) < 0 ) ) 342 ) { 343 float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); 344 return packFloat32( zSign, 0xFF, - ( roundIncrement == 0 )); 345 } 346 if ( zExp < 0 ) { 347 if (STATUS(flush_to_zero)) { 348 float_raise(float_flag_output_denormal STATUS_VAR); 349 return packFloat32(zSign, 0, 0); 350 } 351 isTiny = 352 ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) 353 || ( zExp < -1 ) 354 || ( zSig + roundIncrement < 0x80000000 ); 355 shift32RightJamming( zSig, - zExp, &zSig ); 356 zExp = 0; 357 roundBits = zSig & 0x7F; 358 if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); 359 } 360 } 361 if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; 362 zSig = ( zSig + roundIncrement )>>7; 363 zSig &= ~ ( ( ( roundBits ^ 0x40 ) == 0 ) & roundNearestEven ); 364 if ( zSig == 0 ) zExp = 0; 365 return packFloat32( zSign, zExp, zSig ); 366 367 } 368 369 /*---------------------------------------------------------------------------- 370 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 371 | and significand `zSig', and returns the proper single-precision floating- 372 | point value corresponding to the abstract input. This routine is just like 373 | `roundAndPackFloat32' except that `zSig' does not have to be normalized. 374 | Bit 31 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' 375 | floating-point exponent. 376 *----------------------------------------------------------------------------*/ 377 378 static float32 379 normalizeRoundAndPackFloat32(flag zSign, int_fast16_t zExp, uint32_t zSig STATUS_PARAM) 380 { 381 int8 shiftCount; 382 383 shiftCount = countLeadingZeros32( zSig ) - 1; 384 return roundAndPackFloat32( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); 385 386 } 387 388 /*---------------------------------------------------------------------------- 389 | Returns the fraction bits of the double-precision floating-point value `a'. 390 *----------------------------------------------------------------------------*/ 391 392 INLINE uint64_t extractFloat64Frac( float64 a ) 393 { 394 395 return float64_val(a) & LIT64( 0x000FFFFFFFFFFFFF ); 396 397 } 398 399 /*---------------------------------------------------------------------------- 400 | Returns the exponent bits of the double-precision floating-point value `a'. 401 *----------------------------------------------------------------------------*/ 402 403 INLINE int_fast16_t extractFloat64Exp(float64 a) 404 { 405 406 return ( float64_val(a)>>52 ) & 0x7FF; 407 408 } 409 410 /*---------------------------------------------------------------------------- 411 | Returns the sign bit of the double-precision floating-point value `a'. 412 *----------------------------------------------------------------------------*/ 413 414 INLINE flag extractFloat64Sign( float64 a ) 415 { 416 417 return float64_val(a)>>63; 418 419 } 420 421 /*---------------------------------------------------------------------------- 422 | If `a' is denormal and we are in flush-to-zero mode then set the 423 | input-denormal exception and return zero. Otherwise just return the value. 424 *----------------------------------------------------------------------------*/ 425 static float64 float64_squash_input_denormal(float64 a STATUS_PARAM) 426 { 427 if (STATUS(flush_inputs_to_zero)) { 428 if (extractFloat64Exp(a) == 0 && extractFloat64Frac(a) != 0) { 429 float_raise(float_flag_input_denormal STATUS_VAR); 430 return make_float64(float64_val(a) & (1ULL << 63)); 431 } 432 } 433 return a; 434 } 435 436 /*---------------------------------------------------------------------------- 437 | Normalizes the subnormal double-precision floating-point value represented 438 | by the denormalized significand `aSig'. The normalized exponent and 439 | significand are stored at the locations pointed to by `zExpPtr' and 440 | `zSigPtr', respectively. 441 *----------------------------------------------------------------------------*/ 442 443 static void 444 normalizeFloat64Subnormal(uint64_t aSig, int_fast16_t *zExpPtr, uint64_t *zSigPtr) 445 { 446 int8 shiftCount; 447 448 shiftCount = countLeadingZeros64( aSig ) - 11; 449 *zSigPtr = aSig<<shiftCount; 450 *zExpPtr = 1 - shiftCount; 451 452 } 453 454 /*---------------------------------------------------------------------------- 455 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a 456 | double-precision floating-point value, returning the result. After being 457 | shifted into the proper positions, the three fields are simply added 458 | together to form the result. This means that any integer portion of `zSig' 459 | will be added into the exponent. Since a properly normalized significand 460 | will have an integer portion equal to 1, the `zExp' input should be 1 less 461 | than the desired result exponent whenever `zSig' is a complete, normalized 462 | significand. 463 *----------------------------------------------------------------------------*/ 464 465 INLINE float64 packFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig) 466 { 467 468 return make_float64( 469 ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<52 ) + zSig); 470 471 } 472 473 /*---------------------------------------------------------------------------- 474 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 475 | and significand `zSig', and returns the proper double-precision floating- 476 | point value corresponding to the abstract input. Ordinarily, the abstract 477 | value is simply rounded and packed into the double-precision format, with 478 | the inexact exception raised if the abstract input cannot be represented 479 | exactly. However, if the abstract value is too large, the overflow and 480 | inexact exceptions are raised and an infinity or maximal finite value is 481 | returned. If the abstract value is too small, the input value is rounded 482 | to a subnormal number, and the underflow and inexact exceptions are raised 483 | if the abstract input cannot be represented exactly as a subnormal double- 484 | precision floating-point number. 485 | The input significand `zSig' has its binary point between bits 62 486 | and 61, which is 10 bits to the left of the usual location. This shifted 487 | significand must be normalized or smaller. If `zSig' is not normalized, 488 | `zExp' must be 0; in that case, the result returned is a subnormal number, 489 | and it must not require rounding. In the usual case that `zSig' is 490 | normalized, `zExp' must be 1 less than the ``true'' floating-point exponent. 491 | The handling of underflow and overflow follows the IEC/IEEE Standard for 492 | Binary Floating-Point Arithmetic. 493 *----------------------------------------------------------------------------*/ 494 495 static float64 roundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM) 496 { 497 int8 roundingMode; 498 flag roundNearestEven; 499 int_fast16_t roundIncrement, roundBits; 500 flag isTiny; 501 502 roundingMode = STATUS(float_rounding_mode); 503 roundNearestEven = ( roundingMode == float_round_nearest_even ); 504 roundIncrement = 0x200; 505 if ( ! roundNearestEven ) { 506 if ( roundingMode == float_round_to_zero ) { 507 roundIncrement = 0; 508 } 509 else { 510 roundIncrement = 0x3FF; 511 if ( zSign ) { 512 if ( roundingMode == float_round_up ) roundIncrement = 0; 513 } 514 else { 515 if ( roundingMode == float_round_down ) roundIncrement = 0; 516 } 517 } 518 } 519 roundBits = zSig & 0x3FF; 520 if ( 0x7FD <= (uint16_t) zExp ) { 521 if ( ( 0x7FD < zExp ) 522 || ( ( zExp == 0x7FD ) 523 && ( (int64_t) ( zSig + roundIncrement ) < 0 ) ) 524 ) { 525 float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); 526 return packFloat64( zSign, 0x7FF, - ( roundIncrement == 0 )); 527 } 528 if ( zExp < 0 ) { 529 if (STATUS(flush_to_zero)) { 530 float_raise(float_flag_output_denormal STATUS_VAR); 531 return packFloat64(zSign, 0, 0); 532 } 533 isTiny = 534 ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) 535 || ( zExp < -1 ) 536 || ( zSig + roundIncrement < LIT64( 0x8000000000000000 ) ); 537 shift64RightJamming( zSig, - zExp, &zSig ); 538 zExp = 0; 539 roundBits = zSig & 0x3FF; 540 if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); 541 } 542 } 543 if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; 544 zSig = ( zSig + roundIncrement )>>10; 545 zSig &= ~ ( ( ( roundBits ^ 0x200 ) == 0 ) & roundNearestEven ); 546 if ( zSig == 0 ) zExp = 0; 547 return packFloat64( zSign, zExp, zSig ); 548 549 } 550 551 /*---------------------------------------------------------------------------- 552 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 553 | and significand `zSig', and returns the proper double-precision floating- 554 | point value corresponding to the abstract input. This routine is just like 555 | `roundAndPackFloat64' except that `zSig' does not have to be normalized. 556 | Bit 63 of `zSig' must be zero, and `zExp' must be 1 less than the ``true'' 557 | floating-point exponent. 558 *----------------------------------------------------------------------------*/ 559 560 static float64 561 normalizeRoundAndPackFloat64(flag zSign, int_fast16_t zExp, uint64_t zSig STATUS_PARAM) 562 { 563 int8 shiftCount; 564 565 shiftCount = countLeadingZeros64( zSig ) - 1; 566 return roundAndPackFloat64( zSign, zExp - shiftCount, zSig<<shiftCount STATUS_VAR); 567 568 } 569 570 /*---------------------------------------------------------------------------- 571 | Returns the fraction bits of the extended double-precision floating-point 572 | value `a'. 573 *----------------------------------------------------------------------------*/ 574 575 INLINE uint64_t extractFloatx80Frac( floatx80 a ) 576 { 577 578 return a.low; 579 580 } 581 582 /*---------------------------------------------------------------------------- 583 | Returns the exponent bits of the extended double-precision floating-point 584 | value `a'. 585 *----------------------------------------------------------------------------*/ 586 587 INLINE int32 extractFloatx80Exp( floatx80 a ) 588 { 589 590 return a.high & 0x7FFF; 591 592 } 593 594 /*---------------------------------------------------------------------------- 595 | Returns the sign bit of the extended double-precision floating-point value 596 | `a'. 597 *----------------------------------------------------------------------------*/ 598 599 INLINE flag extractFloatx80Sign( floatx80 a ) 600 { 601 602 return a.high>>15; 603 604 } 605 606 /*---------------------------------------------------------------------------- 607 | Normalizes the subnormal extended double-precision floating-point value 608 | represented by the denormalized significand `aSig'. The normalized exponent 609 | and significand are stored at the locations pointed to by `zExpPtr' and 610 | `zSigPtr', respectively. 611 *----------------------------------------------------------------------------*/ 612 613 static void 614 normalizeFloatx80Subnormal( uint64_t aSig, int32 *zExpPtr, uint64_t *zSigPtr ) 615 { 616 int8 shiftCount; 617 618 shiftCount = countLeadingZeros64( aSig ); 619 *zSigPtr = aSig<<shiftCount; 620 *zExpPtr = 1 - shiftCount; 621 622 } 623 624 /*---------------------------------------------------------------------------- 625 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into an 626 | extended double-precision floating-point value, returning the result. 627 *----------------------------------------------------------------------------*/ 628 629 INLINE floatx80 packFloatx80( flag zSign, int32 zExp, uint64_t zSig ) 630 { 631 floatx80 z; 632 633 z.low = zSig; 634 z.high = ( ( (uint16_t) zSign )<<15 ) + zExp; 635 return z; 636 637 } 638 639 /*---------------------------------------------------------------------------- 640 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 641 | and extended significand formed by the concatenation of `zSig0' and `zSig1', 642 | and returns the proper extended double-precision floating-point value 643 | corresponding to the abstract input. Ordinarily, the abstract value is 644 | rounded and packed into the extended double-precision format, with the 645 | inexact exception raised if the abstract input cannot be represented 646 | exactly. However, if the abstract value is too large, the overflow and 647 | inexact exceptions are raised and an infinity or maximal finite value is 648 | returned. If the abstract value is too small, the input value is rounded to 649 | a subnormal number, and the underflow and inexact exceptions are raised if 650 | the abstract input cannot be represented exactly as a subnormal extended 651 | double-precision floating-point number. 652 | If `roundingPrecision' is 32 or 64, the result is rounded to the same 653 | number of bits as single or double precision, respectively. Otherwise, the 654 | result is rounded to the full precision of the extended double-precision 655 | format. 656 | The input significand must be normalized or smaller. If the input 657 | significand is not normalized, `zExp' must be 0; in that case, the result 658 | returned is a subnormal number, and it must not require rounding. The 659 | handling of underflow and overflow follows the IEC/IEEE Standard for Binary 660 | Floating-Point Arithmetic. 661 *----------------------------------------------------------------------------*/ 662 663 static floatx80 664 roundAndPackFloatx80( 665 int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 666 STATUS_PARAM) 667 { 668 int8 roundingMode; 669 flag roundNearestEven, increment, isTiny; 670 int64 roundIncrement, roundMask, roundBits; 671 672 roundingMode = STATUS(float_rounding_mode); 673 roundNearestEven = ( roundingMode == float_round_nearest_even ); 674 if ( roundingPrecision == 80 ) goto precision80; 675 if ( roundingPrecision == 64 ) { 676 roundIncrement = LIT64( 0x0000000000000400 ); 677 roundMask = LIT64( 0x00000000000007FF ); 678 } 679 else if ( roundingPrecision == 32 ) { 680 roundIncrement = LIT64( 0x0000008000000000 ); 681 roundMask = LIT64( 0x000000FFFFFFFFFF ); 682 } 683 else { 684 goto precision80; 685 } 686 zSig0 |= ( zSig1 != 0 ); 687 if ( ! roundNearestEven ) { 688 if ( roundingMode == float_round_to_zero ) { 689 roundIncrement = 0; 690 } 691 else { 692 roundIncrement = roundMask; 693 if ( zSign ) { 694 if ( roundingMode == float_round_up ) roundIncrement = 0; 695 } 696 else { 697 if ( roundingMode == float_round_down ) roundIncrement = 0; 698 } 699 } 700 } 701 roundBits = zSig0 & roundMask; 702 if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { 703 if ( ( 0x7FFE < zExp ) 704 || ( ( zExp == 0x7FFE ) && ( zSig0 + roundIncrement < zSig0 ) ) 705 ) { 706 goto overflow; 707 } 708 if ( zExp <= 0 ) { 709 if (STATUS(flush_to_zero)) { 710 float_raise(float_flag_output_denormal STATUS_VAR); 711 return packFloatx80(zSign, 0, 0); 712 } 713 isTiny = 714 ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) 715 || ( zExp < 0 ) 716 || ( zSig0 <= zSig0 + roundIncrement ); 717 shift64RightJamming( zSig0, 1 - zExp, &zSig0 ); 718 zExp = 0; 719 roundBits = zSig0 & roundMask; 720 if ( isTiny && roundBits ) float_raise( float_flag_underflow STATUS_VAR); 721 if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; 722 zSig0 += roundIncrement; 723 if ( (int64_t) zSig0 < 0 ) zExp = 1; 724 roundIncrement = roundMask + 1; 725 if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { 726 roundMask |= roundIncrement; 727 } 728 zSig0 &= ~ roundMask; 729 return packFloatx80( zSign, zExp, zSig0 ); 730 } 731 } 732 if ( roundBits ) STATUS(float_exception_flags) |= float_flag_inexact; 733 zSig0 += roundIncrement; 734 if ( zSig0 < roundIncrement ) { 735 ++zExp; 736 zSig0 = LIT64( 0x8000000000000000 ); 737 } 738 roundIncrement = roundMask + 1; 739 if ( roundNearestEven && ( roundBits<<1 == roundIncrement ) ) { 740 roundMask |= roundIncrement; 741 } 742 zSig0 &= ~ roundMask; 743 if ( zSig0 == 0 ) zExp = 0; 744 return packFloatx80( zSign, zExp, zSig0 ); 745 precision80: 746 increment = ( (int64_t) zSig1 < 0 ); 747 if ( ! roundNearestEven ) { 748 if ( roundingMode == float_round_to_zero ) { 749 increment = 0; 750 } 751 else { 752 if ( zSign ) { 753 increment = ( roundingMode == float_round_down ) && zSig1; 754 } 755 else { 756 increment = ( roundingMode == float_round_up ) && zSig1; 757 } 758 } 759 } 760 if ( 0x7FFD <= (uint32_t) ( zExp - 1 ) ) { 761 if ( ( 0x7FFE < zExp ) 762 || ( ( zExp == 0x7FFE ) 763 && ( zSig0 == LIT64( 0xFFFFFFFFFFFFFFFF ) ) 764 && increment 765 ) 766 ) { 767 roundMask = 0; 768 overflow: 769 float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); 770 if ( ( roundingMode == float_round_to_zero ) 771 || ( zSign && ( roundingMode == float_round_up ) ) 772 || ( ! zSign && ( roundingMode == float_round_down ) ) 773 ) { 774 return packFloatx80( zSign, 0x7FFE, ~ roundMask ); 775 } 776 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 777 } 778 if ( zExp <= 0 ) { 779 isTiny = 780 ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) 781 || ( zExp < 0 ) 782 || ! increment 783 || ( zSig0 < LIT64( 0xFFFFFFFFFFFFFFFF ) ); 784 shift64ExtraRightJamming( zSig0, zSig1, 1 - zExp, &zSig0, &zSig1 ); 785 zExp = 0; 786 if ( isTiny && zSig1 ) float_raise( float_flag_underflow STATUS_VAR); 787 if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; 788 if ( roundNearestEven ) { 789 increment = ( (int64_t) zSig1 < 0 ); 790 } 791 else { 792 if ( zSign ) { 793 increment = ( roundingMode == float_round_down ) && zSig1; 794 } 795 else { 796 increment = ( roundingMode == float_round_up ) && zSig1; 797 } 798 } 799 if ( increment ) { 800 ++zSig0; 801 zSig0 &= 802 ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); 803 if ( (int64_t) zSig0 < 0 ) zExp = 1; 804 } 805 return packFloatx80( zSign, zExp, zSig0 ); 806 } 807 } 808 if ( zSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; 809 if ( increment ) { 810 ++zSig0; 811 if ( zSig0 == 0 ) { 812 ++zExp; 813 zSig0 = LIT64( 0x8000000000000000 ); 814 } 815 else { 816 zSig0 &= ~ ( ( (uint64_t) ( zSig1<<1 ) == 0 ) & roundNearestEven ); 817 } 818 } 819 else { 820 if ( zSig0 == 0 ) zExp = 0; 821 } 822 return packFloatx80( zSign, zExp, zSig0 ); 823 824 } 825 826 /*---------------------------------------------------------------------------- 827 | Takes an abstract floating-point value having sign `zSign', exponent 828 | `zExp', and significand formed by the concatenation of `zSig0' and `zSig1', 829 | and returns the proper extended double-precision floating-point value 830 | corresponding to the abstract input. This routine is just like 831 | `roundAndPackFloatx80' except that the input significand does not have to be 832 | normalized. 833 *----------------------------------------------------------------------------*/ 834 835 static floatx80 836 normalizeRoundAndPackFloatx80( 837 int8 roundingPrecision, flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 838 STATUS_PARAM) 839 { 840 int8 shiftCount; 841 842 if ( zSig0 == 0 ) { 843 zSig0 = zSig1; 844 zSig1 = 0; 845 zExp -= 64; 846 } 847 shiftCount = countLeadingZeros64( zSig0 ); 848 shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); 849 zExp -= shiftCount; 850 return 851 roundAndPackFloatx80( roundingPrecision, zSign, zExp, zSig0, zSig1 STATUS_VAR); 852 853 } 854 855 /*---------------------------------------------------------------------------- 856 | Returns the least-significant 64 fraction bits of the quadruple-precision 857 | floating-point value `a'. 858 *----------------------------------------------------------------------------*/ 859 860 INLINE uint64_t extractFloat128Frac1( float128 a ) 861 { 862 863 return a.low; 864 865 } 866 867 /*---------------------------------------------------------------------------- 868 | Returns the most-significant 48 fraction bits of the quadruple-precision 869 | floating-point value `a'. 870 *----------------------------------------------------------------------------*/ 871 872 INLINE uint64_t extractFloat128Frac0( float128 a ) 873 { 874 875 return a.high & LIT64( 0x0000FFFFFFFFFFFF ); 876 877 } 878 879 /*---------------------------------------------------------------------------- 880 | Returns the exponent bits of the quadruple-precision floating-point value 881 | `a'. 882 *----------------------------------------------------------------------------*/ 883 884 INLINE int32 extractFloat128Exp( float128 a ) 885 { 886 887 return ( a.high>>48 ) & 0x7FFF; 888 889 } 890 891 /*---------------------------------------------------------------------------- 892 | Returns the sign bit of the quadruple-precision floating-point value `a'. 893 *----------------------------------------------------------------------------*/ 894 895 INLINE flag extractFloat128Sign( float128 a ) 896 { 897 898 return a.high>>63; 899 900 } 901 902 /*---------------------------------------------------------------------------- 903 | Normalizes the subnormal quadruple-precision floating-point value 904 | represented by the denormalized significand formed by the concatenation of 905 | `aSig0' and `aSig1'. The normalized exponent is stored at the location 906 | pointed to by `zExpPtr'. The most significant 49 bits of the normalized 907 | significand are stored at the location pointed to by `zSig0Ptr', and the 908 | least significant 64 bits of the normalized significand are stored at the 909 | location pointed to by `zSig1Ptr'. 910 *----------------------------------------------------------------------------*/ 911 912 static void 913 normalizeFloat128Subnormal( 914 uint64_t aSig0, 915 uint64_t aSig1, 916 int32 *zExpPtr, 917 uint64_t *zSig0Ptr, 918 uint64_t *zSig1Ptr 919 ) 920 { 921 int8 shiftCount; 922 923 if ( aSig0 == 0 ) { 924 shiftCount = countLeadingZeros64( aSig1 ) - 15; 925 if ( shiftCount < 0 ) { 926 *zSig0Ptr = aSig1>>( - shiftCount ); 927 *zSig1Ptr = aSig1<<( shiftCount & 63 ); 928 } 929 else { 930 *zSig0Ptr = aSig1<<shiftCount; 931 *zSig1Ptr = 0; 932 } 933 *zExpPtr = - shiftCount - 63; 934 } 935 else { 936 shiftCount = countLeadingZeros64( aSig0 ) - 15; 937 shortShift128Left( aSig0, aSig1, shiftCount, zSig0Ptr, zSig1Ptr ); 938 *zExpPtr = 1 - shiftCount; 939 } 940 941 } 942 943 /*---------------------------------------------------------------------------- 944 | Packs the sign `zSign', the exponent `zExp', and the significand formed 945 | by the concatenation of `zSig0' and `zSig1' into a quadruple-precision 946 | floating-point value, returning the result. After being shifted into the 947 | proper positions, the three fields `zSign', `zExp', and `zSig0' are simply 948 | added together to form the most significant 32 bits of the result. This 949 | means that any integer portion of `zSig0' will be added into the exponent. 950 | Since a properly normalized significand will have an integer portion equal 951 | to 1, the `zExp' input should be 1 less than the desired result exponent 952 | whenever `zSig0' and `zSig1' concatenated form a complete, normalized 953 | significand. 954 *----------------------------------------------------------------------------*/ 955 956 INLINE float128 957 packFloat128( flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 ) 958 { 959 float128 z; 960 961 z.low = zSig1; 962 z.high = ( ( (uint64_t) zSign )<<63 ) + ( ( (uint64_t) zExp )<<48 ) + zSig0; 963 return z; 964 965 } 966 967 /*---------------------------------------------------------------------------- 968 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 969 | and extended significand formed by the concatenation of `zSig0', `zSig1', 970 | and `zSig2', and returns the proper quadruple-precision floating-point value 971 | corresponding to the abstract input. Ordinarily, the abstract value is 972 | simply rounded and packed into the quadruple-precision format, with the 973 | inexact exception raised if the abstract input cannot be represented 974 | exactly. However, if the abstract value is too large, the overflow and 975 | inexact exceptions are raised and an infinity or maximal finite value is 976 | returned. If the abstract value is too small, the input value is rounded to 977 | a subnormal number, and the underflow and inexact exceptions are raised if 978 | the abstract input cannot be represented exactly as a subnormal quadruple- 979 | precision floating-point number. 980 | The input significand must be normalized or smaller. If the input 981 | significand is not normalized, `zExp' must be 0; in that case, the result 982 | returned is a subnormal number, and it must not require rounding. In the 983 | usual case that the input significand is normalized, `zExp' must be 1 less 984 | than the ``true'' floating-point exponent. The handling of underflow and 985 | overflow follows the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 986 *----------------------------------------------------------------------------*/ 987 988 static float128 989 roundAndPackFloat128( 990 flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1, uint64_t zSig2 STATUS_PARAM) 991 { 992 int8 roundingMode; 993 flag roundNearestEven, increment, isTiny; 994 995 roundingMode = STATUS(float_rounding_mode); 996 roundNearestEven = ( roundingMode == float_round_nearest_even ); 997 increment = ( (int64_t) zSig2 < 0 ); 998 if ( ! roundNearestEven ) { 999 if ( roundingMode == float_round_to_zero ) { 1000 increment = 0; 1001 } 1002 else { 1003 if ( zSign ) { 1004 increment = ( roundingMode == float_round_down ) && zSig2; 1005 } 1006 else { 1007 increment = ( roundingMode == float_round_up ) && zSig2; 1008 } 1009 } 1010 } 1011 if ( 0x7FFD <= (uint32_t) zExp ) { 1012 if ( ( 0x7FFD < zExp ) 1013 || ( ( zExp == 0x7FFD ) 1014 && eq128( 1015 LIT64( 0x0001FFFFFFFFFFFF ), 1016 LIT64( 0xFFFFFFFFFFFFFFFF ), 1017 zSig0, 1018 zSig1 1019 ) 1020 && increment 1021 ) 1022 ) { 1023 float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); 1024 if ( ( roundingMode == float_round_to_zero ) 1025 || ( zSign && ( roundingMode == float_round_up ) ) 1026 || ( ! zSign && ( roundingMode == float_round_down ) ) 1027 ) { 1028 return 1029 packFloat128( 1030 zSign, 1031 0x7FFE, 1032 LIT64( 0x0000FFFFFFFFFFFF ), 1033 LIT64( 0xFFFFFFFFFFFFFFFF ) 1034 ); 1035 } 1036 return packFloat128( zSign, 0x7FFF, 0, 0 ); 1037 } 1038 if ( zExp < 0 ) { 1039 if (STATUS(flush_to_zero)) { 1040 float_raise(float_flag_output_denormal STATUS_VAR); 1041 return packFloat128(zSign, 0, 0, 0); 1042 } 1043 isTiny = 1044 ( STATUS(float_detect_tininess) == float_tininess_before_rounding ) 1045 || ( zExp < -1 ) 1046 || ! increment 1047 || lt128( 1048 zSig0, 1049 zSig1, 1050 LIT64( 0x0001FFFFFFFFFFFF ), 1051 LIT64( 0xFFFFFFFFFFFFFFFF ) 1052 ); 1053 shift128ExtraRightJamming( 1054 zSig0, zSig1, zSig2, - zExp, &zSig0, &zSig1, &zSig2 ); 1055 zExp = 0; 1056 if ( isTiny && zSig2 ) float_raise( float_flag_underflow STATUS_VAR); 1057 if ( roundNearestEven ) { 1058 increment = ( (int64_t) zSig2 < 0 ); 1059 } 1060 else { 1061 if ( zSign ) { 1062 increment = ( roundingMode == float_round_down ) && zSig2; 1063 } 1064 else { 1065 increment = ( roundingMode == float_round_up ) && zSig2; 1066 } 1067 } 1068 } 1069 } 1070 if ( zSig2 ) STATUS(float_exception_flags) |= float_flag_inexact; 1071 if ( increment ) { 1072 add128( zSig0, zSig1, 0, 1, &zSig0, &zSig1 ); 1073 zSig1 &= ~ ( ( zSig2 + zSig2 == 0 ) & roundNearestEven ); 1074 } 1075 else { 1076 if ( ( zSig0 | zSig1 ) == 0 ) zExp = 0; 1077 } 1078 return packFloat128( zSign, zExp, zSig0, zSig1 ); 1079 1080 } 1081 1082 /*---------------------------------------------------------------------------- 1083 | Takes an abstract floating-point value having sign `zSign', exponent `zExp', 1084 | and significand formed by the concatenation of `zSig0' and `zSig1', and 1085 | returns the proper quadruple-precision floating-point value corresponding 1086 | to the abstract input. This routine is just like `roundAndPackFloat128' 1087 | except that the input significand has fewer bits and does not have to be 1088 | normalized. In all cases, `zExp' must be 1 less than the ``true'' floating- 1089 | point exponent. 1090 *----------------------------------------------------------------------------*/ 1091 1092 static float128 1093 normalizeRoundAndPackFloat128( 1094 flag zSign, int32 zExp, uint64_t zSig0, uint64_t zSig1 STATUS_PARAM) 1095 { 1096 int8 shiftCount; 1097 uint64_t zSig2; 1098 1099 if ( zSig0 == 0 ) { 1100 zSig0 = zSig1; 1101 zSig1 = 0; 1102 zExp -= 64; 1103 } 1104 shiftCount = countLeadingZeros64( zSig0 ) - 15; 1105 if ( 0 <= shiftCount ) { 1106 zSig2 = 0; 1107 shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); 1108 } 1109 else { 1110 shift128ExtraRightJamming( 1111 zSig0, zSig1, 0, - shiftCount, &zSig0, &zSig1, &zSig2 ); 1112 } 1113 zExp -= shiftCount; 1114 return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR); 1115 1116 } 1117 1118 /*---------------------------------------------------------------------------- 1119 | Returns the result of converting the 32-bit two's complement integer `a' 1120 | to the single-precision floating-point format. The conversion is performed 1121 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1122 *----------------------------------------------------------------------------*/ 1123 1124 float32 int32_to_float32( int32 a STATUS_PARAM ) 1125 { 1126 flag zSign; 1127 1128 if ( a == 0 ) return float32_zero; 1129 if ( a == (int32_t) 0x80000000 ) return packFloat32( 1, 0x9E, 0 ); 1130 zSign = ( a < 0 ); 1131 return normalizeRoundAndPackFloat32( zSign, 0x9C, zSign ? - a : a STATUS_VAR ); 1132 1133 } 1134 1135 /*---------------------------------------------------------------------------- 1136 | Returns the result of converting the 32-bit two's complement integer `a' 1137 | to the double-precision floating-point format. The conversion is performed 1138 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1139 *----------------------------------------------------------------------------*/ 1140 1141 float64 int32_to_float64( int32 a STATUS_PARAM ) 1142 { 1143 flag zSign; 1144 uint32 absA; 1145 int8 shiftCount; 1146 uint64_t zSig; 1147 1148 if ( a == 0 ) return float64_zero; 1149 zSign = ( a < 0 ); 1150 absA = zSign ? - a : a; 1151 shiftCount = countLeadingZeros32( absA ) + 21; 1152 zSig = absA; 1153 return packFloat64( zSign, 0x432 - shiftCount, zSig<<shiftCount ); 1154 1155 } 1156 1157 /*---------------------------------------------------------------------------- 1158 | Returns the result of converting the 32-bit two's complement integer `a' 1159 | to the extended double-precision floating-point format. The conversion 1160 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 1161 | Arithmetic. 1162 *----------------------------------------------------------------------------*/ 1163 1164 floatx80 int32_to_floatx80( int32 a STATUS_PARAM ) 1165 { 1166 flag zSign; 1167 uint32 absA; 1168 int8 shiftCount; 1169 uint64_t zSig; 1170 1171 if ( a == 0 ) return packFloatx80( 0, 0, 0 ); 1172 zSign = ( a < 0 ); 1173 absA = zSign ? - a : a; 1174 shiftCount = countLeadingZeros32( absA ) + 32; 1175 zSig = absA; 1176 return packFloatx80( zSign, 0x403E - shiftCount, zSig<<shiftCount ); 1177 1178 } 1179 1180 /*---------------------------------------------------------------------------- 1181 | Returns the result of converting the 32-bit two's complement integer `a' to 1182 | the quadruple-precision floating-point format. The conversion is performed 1183 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1184 *----------------------------------------------------------------------------*/ 1185 1186 float128 int32_to_float128( int32 a STATUS_PARAM ) 1187 { 1188 flag zSign; 1189 uint32 absA; 1190 int8 shiftCount; 1191 uint64_t zSig0; 1192 1193 if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); 1194 zSign = ( a < 0 ); 1195 absA = zSign ? - a : a; 1196 shiftCount = countLeadingZeros32( absA ) + 17; 1197 zSig0 = absA; 1198 return packFloat128( zSign, 0x402E - shiftCount, zSig0<<shiftCount, 0 ); 1199 1200 } 1201 1202 /*---------------------------------------------------------------------------- 1203 | Returns the result of converting the 64-bit two's complement integer `a' 1204 | to the single-precision floating-point format. The conversion is performed 1205 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1206 *----------------------------------------------------------------------------*/ 1207 1208 float32 int64_to_float32( int64 a STATUS_PARAM ) 1209 { 1210 flag zSign; 1211 uint64 absA; 1212 int8 shiftCount; 1213 1214 if ( a == 0 ) return float32_zero; 1215 zSign = ( a < 0 ); 1216 absA = zSign ? - a : a; 1217 shiftCount = countLeadingZeros64( absA ) - 40; 1218 if ( 0 <= shiftCount ) { 1219 return packFloat32( zSign, 0x95 - shiftCount, absA<<shiftCount ); 1220 } 1221 else { 1222 shiftCount += 7; 1223 if ( shiftCount < 0 ) { 1224 shift64RightJamming( absA, - shiftCount, &absA ); 1225 } 1226 else { 1227 absA <<= shiftCount; 1228 } 1229 return roundAndPackFloat32( zSign, 0x9C - shiftCount, absA STATUS_VAR ); 1230 } 1231 1232 } 1233 1234 float32 uint64_to_float32( uint64 a STATUS_PARAM ) 1235 { 1236 int8 shiftCount; 1237 1238 if ( a == 0 ) return float32_zero; 1239 shiftCount = countLeadingZeros64( a ) - 40; 1240 if ( 0 <= shiftCount ) { 1241 return packFloat32(0, 0x95 - shiftCount, a<<shiftCount); 1242 } 1243 else { 1244 shiftCount += 7; 1245 if ( shiftCount < 0 ) { 1246 shift64RightJamming( a, - shiftCount, &a ); 1247 } 1248 else { 1249 a <<= shiftCount; 1250 } 1251 return roundAndPackFloat32(0, 0x9C - shiftCount, a STATUS_VAR); 1252 } 1253 } 1254 1255 /*---------------------------------------------------------------------------- 1256 | Returns the result of converting the 64-bit two's complement integer `a' 1257 | to the double-precision floating-point format. The conversion is performed 1258 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1259 *----------------------------------------------------------------------------*/ 1260 1261 float64 int64_to_float64( int64 a STATUS_PARAM ) 1262 { 1263 flag zSign; 1264 1265 if ( a == 0 ) return float64_zero; 1266 if ( a == (int64_t) LIT64( 0x8000000000000000 ) ) { 1267 return packFloat64( 1, 0x43E, 0 ); 1268 } 1269 zSign = ( a < 0 ); 1270 return normalizeRoundAndPackFloat64( zSign, 0x43C, zSign ? - a : a STATUS_VAR ); 1271 1272 } 1273 1274 float64 uint64_to_float64(uint64 a STATUS_PARAM) 1275 { 1276 int exp = 0x43C; 1277 1278 if (a == 0) { 1279 return float64_zero; 1280 } 1281 if ((int64_t)a < 0) { 1282 shift64RightJamming(a, 1, &a); 1283 exp += 1; 1284 } 1285 return normalizeRoundAndPackFloat64(0, exp, a STATUS_VAR); 1286 } 1287 1288 /*---------------------------------------------------------------------------- 1289 | Returns the result of converting the 64-bit two's complement integer `a' 1290 | to the extended double-precision floating-point format. The conversion 1291 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 1292 | Arithmetic. 1293 *----------------------------------------------------------------------------*/ 1294 1295 floatx80 int64_to_floatx80( int64 a STATUS_PARAM ) 1296 { 1297 flag zSign; 1298 uint64 absA; 1299 int8 shiftCount; 1300 1301 if ( a == 0 ) return packFloatx80( 0, 0, 0 ); 1302 zSign = ( a < 0 ); 1303 absA = zSign ? - a : a; 1304 shiftCount = countLeadingZeros64( absA ); 1305 return packFloatx80( zSign, 0x403E - shiftCount, absA<<shiftCount ); 1306 1307 } 1308 1309 /*---------------------------------------------------------------------------- 1310 | Returns the result of converting the 64-bit two's complement integer `a' to 1311 | the quadruple-precision floating-point format. The conversion is performed 1312 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1313 *----------------------------------------------------------------------------*/ 1314 1315 float128 int64_to_float128( int64 a STATUS_PARAM ) 1316 { 1317 flag zSign; 1318 uint64 absA; 1319 int8 shiftCount; 1320 int32 zExp; 1321 uint64_t zSig0, zSig1; 1322 1323 if ( a == 0 ) return packFloat128( 0, 0, 0, 0 ); 1324 zSign = ( a < 0 ); 1325 absA = zSign ? - a : a; 1326 shiftCount = countLeadingZeros64( absA ) + 49; 1327 zExp = 0x406E - shiftCount; 1328 if ( 64 <= shiftCount ) { 1329 zSig1 = 0; 1330 zSig0 = absA; 1331 shiftCount -= 64; 1332 } 1333 else { 1334 zSig1 = absA; 1335 zSig0 = 0; 1336 } 1337 shortShift128Left( zSig0, zSig1, shiftCount, &zSig0, &zSig1 ); 1338 return packFloat128( zSign, zExp, zSig0, zSig1 ); 1339 1340 } 1341 1342 float128 uint64_to_float128(uint64 a STATUS_PARAM) 1343 { 1344 if (a == 0) { 1345 return float128_zero; 1346 } 1347 return normalizeRoundAndPackFloat128(0, 0x406E, a, 0 STATUS_VAR); 1348 } 1349 1350 /*---------------------------------------------------------------------------- 1351 | Returns the result of converting the single-precision floating-point value 1352 | `a' to the 32-bit two's complement integer format. The conversion is 1353 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1354 | Arithmetic---which means in particular that the conversion is rounded 1355 | according to the current rounding mode. If `a' is a NaN, the largest 1356 | positive integer is returned. Otherwise, if the conversion overflows, the 1357 | largest integer with the same sign as `a' is returned. 1358 *----------------------------------------------------------------------------*/ 1359 1360 int32 float32_to_int32( float32 a STATUS_PARAM ) 1361 { 1362 flag aSign; 1363 int_fast16_t aExp, shiftCount; 1364 uint32_t aSig; 1365 uint64_t aSig64; 1366 1367 a = float32_squash_input_denormal(a STATUS_VAR); 1368 aSig = extractFloat32Frac( a ); 1369 aExp = extractFloat32Exp( a ); 1370 aSign = extractFloat32Sign( a ); 1371 if ( ( aExp == 0xFF ) && aSig ) aSign = 0; 1372 if ( aExp ) aSig |= 0x00800000; 1373 shiftCount = 0xAF - aExp; 1374 aSig64 = aSig; 1375 aSig64 <<= 32; 1376 if ( 0 < shiftCount ) shift64RightJamming( aSig64, shiftCount, &aSig64 ); 1377 return roundAndPackInt32( aSign, aSig64 STATUS_VAR ); 1378 1379 } 1380 1381 /*---------------------------------------------------------------------------- 1382 | Returns the result of converting the single-precision floating-point value 1383 | `a' to the 32-bit two's complement integer format. The conversion is 1384 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1385 | Arithmetic, except that the conversion is always rounded toward zero. 1386 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 1387 | the conversion overflows, the largest integer with the same sign as `a' is 1388 | returned. 1389 *----------------------------------------------------------------------------*/ 1390 1391 int32 float32_to_int32_round_to_zero( float32 a STATUS_PARAM ) 1392 { 1393 flag aSign; 1394 int_fast16_t aExp, shiftCount; 1395 uint32_t aSig; 1396 int32_t z; 1397 a = float32_squash_input_denormal(a STATUS_VAR); 1398 1399 aSig = extractFloat32Frac( a ); 1400 aExp = extractFloat32Exp( a ); 1401 aSign = extractFloat32Sign( a ); 1402 shiftCount = aExp - 0x9E; 1403 if ( 0 <= shiftCount ) { 1404 if ( float32_val(a) != 0xCF000000 ) { 1405 float_raise( float_flag_invalid STATUS_VAR); 1406 if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) return 0x7FFFFFFF; 1407 } 1408 return (int32_t) 0x80000000; 1409 } 1410 else if ( aExp <= 0x7E ) { 1411 if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 1412 return 0; 1413 } 1414 aSig = ( aSig | 0x00800000 )<<8; 1415 z = aSig>>( - shiftCount ); 1416 if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { 1417 STATUS(float_exception_flags) |= float_flag_inexact; 1418 } 1419 if ( aSign ) z = - z; 1420 return z; 1421 1422 } 1423 1424 /*---------------------------------------------------------------------------- 1425 | Returns the result of converting the single-precision floating-point value 1426 | `a' to the 16-bit two's complement integer format. The conversion is 1427 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1428 | Arithmetic, except that the conversion is always rounded toward zero. 1429 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 1430 | the conversion overflows, the largest integer with the same sign as `a' is 1431 | returned. 1432 *----------------------------------------------------------------------------*/ 1433 1434 int_fast16_t float32_to_int16_round_to_zero(float32 a STATUS_PARAM) 1435 { 1436 flag aSign; 1437 int_fast16_t aExp, shiftCount; 1438 uint32_t aSig; 1439 int32 z; 1440 1441 aSig = extractFloat32Frac( a ); 1442 aExp = extractFloat32Exp( a ); 1443 aSign = extractFloat32Sign( a ); 1444 shiftCount = aExp - 0x8E; 1445 if ( 0 <= shiftCount ) { 1446 if ( float32_val(a) != 0xC7000000 ) { 1447 float_raise( float_flag_invalid STATUS_VAR); 1448 if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { 1449 return 0x7FFF; 1450 } 1451 } 1452 return (int32_t) 0xffff8000; 1453 } 1454 else if ( aExp <= 0x7E ) { 1455 if ( aExp | aSig ) { 1456 STATUS(float_exception_flags) |= float_flag_inexact; 1457 } 1458 return 0; 1459 } 1460 shiftCount -= 0x10; 1461 aSig = ( aSig | 0x00800000 )<<8; 1462 z = aSig>>( - shiftCount ); 1463 if ( (uint32_t) ( aSig<<( shiftCount & 31 ) ) ) { 1464 STATUS(float_exception_flags) |= float_flag_inexact; 1465 } 1466 if ( aSign ) { 1467 z = - z; 1468 } 1469 return z; 1470 1471 } 1472 1473 /*---------------------------------------------------------------------------- 1474 | Returns the result of converting the single-precision floating-point value 1475 | `a' to the 64-bit two's complement integer format. The conversion is 1476 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1477 | Arithmetic---which means in particular that the conversion is rounded 1478 | according to the current rounding mode. If `a' is a NaN, the largest 1479 | positive integer is returned. Otherwise, if the conversion overflows, the 1480 | largest integer with the same sign as `a' is returned. 1481 *----------------------------------------------------------------------------*/ 1482 1483 int64 float32_to_int64( float32 a STATUS_PARAM ) 1484 { 1485 flag aSign; 1486 int_fast16_t aExp, shiftCount; 1487 uint32_t aSig; 1488 uint64_t aSig64, aSigExtra; 1489 a = float32_squash_input_denormal(a STATUS_VAR); 1490 1491 aSig = extractFloat32Frac( a ); 1492 aExp = extractFloat32Exp( a ); 1493 aSign = extractFloat32Sign( a ); 1494 shiftCount = 0xBE - aExp; 1495 if ( shiftCount < 0 ) { 1496 float_raise( float_flag_invalid STATUS_VAR); 1497 if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { 1498 return LIT64( 0x7FFFFFFFFFFFFFFF ); 1499 } 1500 return (int64_t) LIT64( 0x8000000000000000 ); 1501 } 1502 if ( aExp ) aSig |= 0x00800000; 1503 aSig64 = aSig; 1504 aSig64 <<= 40; 1505 shift64ExtraRightJamming( aSig64, 0, shiftCount, &aSig64, &aSigExtra ); 1506 return roundAndPackInt64( aSign, aSig64, aSigExtra STATUS_VAR ); 1507 1508 } 1509 1510 /*---------------------------------------------------------------------------- 1511 | Returns the result of converting the single-precision floating-point value 1512 | `a' to the 64-bit two's complement integer format. The conversion is 1513 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1514 | Arithmetic, except that the conversion is always rounded toward zero. If 1515 | `a' is a NaN, the largest positive integer is returned. Otherwise, if the 1516 | conversion overflows, the largest integer with the same sign as `a' is 1517 | returned. 1518 *----------------------------------------------------------------------------*/ 1519 1520 int64 float32_to_int64_round_to_zero( float32 a STATUS_PARAM ) 1521 { 1522 flag aSign; 1523 int_fast16_t aExp, shiftCount; 1524 uint32_t aSig; 1525 uint64_t aSig64; 1526 int64 z; 1527 a = float32_squash_input_denormal(a STATUS_VAR); 1528 1529 aSig = extractFloat32Frac( a ); 1530 aExp = extractFloat32Exp( a ); 1531 aSign = extractFloat32Sign( a ); 1532 shiftCount = aExp - 0xBE; 1533 if ( 0 <= shiftCount ) { 1534 if ( float32_val(a) != 0xDF000000 ) { 1535 float_raise( float_flag_invalid STATUS_VAR); 1536 if ( ! aSign || ( ( aExp == 0xFF ) && aSig ) ) { 1537 return LIT64( 0x7FFFFFFFFFFFFFFF ); 1538 } 1539 } 1540 return (int64_t) LIT64( 0x8000000000000000 ); 1541 } 1542 else if ( aExp <= 0x7E ) { 1543 if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 1544 return 0; 1545 } 1546 aSig64 = aSig | 0x00800000; 1547 aSig64 <<= 40; 1548 z = aSig64>>( - shiftCount ); 1549 if ( (uint64_t) ( aSig64<<( shiftCount & 63 ) ) ) { 1550 STATUS(float_exception_flags) |= float_flag_inexact; 1551 } 1552 if ( aSign ) z = - z; 1553 return z; 1554 1555 } 1556 1557 /*---------------------------------------------------------------------------- 1558 | Returns the result of converting the single-precision floating-point value 1559 | `a' to the double-precision floating-point format. The conversion is 1560 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1561 | Arithmetic. 1562 *----------------------------------------------------------------------------*/ 1563 1564 float64 float32_to_float64( float32 a STATUS_PARAM ) 1565 { 1566 flag aSign; 1567 int_fast16_t aExp; 1568 uint32_t aSig; 1569 a = float32_squash_input_denormal(a STATUS_VAR); 1570 1571 aSig = extractFloat32Frac( a ); 1572 aExp = extractFloat32Exp( a ); 1573 aSign = extractFloat32Sign( a ); 1574 if ( aExp == 0xFF ) { 1575 if ( aSig ) return commonNaNToFloat64( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 1576 return packFloat64( aSign, 0x7FF, 0 ); 1577 } 1578 if ( aExp == 0 ) { 1579 if ( aSig == 0 ) return packFloat64( aSign, 0, 0 ); 1580 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 1581 --aExp; 1582 } 1583 return packFloat64( aSign, aExp + 0x380, ( (uint64_t) aSig )<<29 ); 1584 1585 } 1586 1587 /*---------------------------------------------------------------------------- 1588 | Returns the result of converting the single-precision floating-point value 1589 | `a' to the extended double-precision floating-point format. The conversion 1590 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 1591 | Arithmetic. 1592 *----------------------------------------------------------------------------*/ 1593 1594 floatx80 float32_to_floatx80( float32 a STATUS_PARAM ) 1595 { 1596 flag aSign; 1597 int_fast16_t aExp; 1598 uint32_t aSig; 1599 1600 a = float32_squash_input_denormal(a STATUS_VAR); 1601 aSig = extractFloat32Frac( a ); 1602 aExp = extractFloat32Exp( a ); 1603 aSign = extractFloat32Sign( a ); 1604 if ( aExp == 0xFF ) { 1605 if ( aSig ) return commonNaNToFloatx80( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 1606 return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 1607 } 1608 if ( aExp == 0 ) { 1609 if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); 1610 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 1611 } 1612 aSig |= 0x00800000; 1613 return packFloatx80( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<40 ); 1614 1615 } 1616 1617 /*---------------------------------------------------------------------------- 1618 | Returns the result of converting the single-precision floating-point value 1619 | `a' to the double-precision floating-point format. The conversion is 1620 | performed according to the IEC/IEEE Standard for Binary Floating-Point 1621 | Arithmetic. 1622 *----------------------------------------------------------------------------*/ 1623 1624 float128 float32_to_float128( float32 a STATUS_PARAM ) 1625 { 1626 flag aSign; 1627 int_fast16_t aExp; 1628 uint32_t aSig; 1629 1630 a = float32_squash_input_denormal(a STATUS_VAR); 1631 aSig = extractFloat32Frac( a ); 1632 aExp = extractFloat32Exp( a ); 1633 aSign = extractFloat32Sign( a ); 1634 if ( aExp == 0xFF ) { 1635 if ( aSig ) return commonNaNToFloat128( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 1636 return packFloat128( aSign, 0x7FFF, 0, 0 ); 1637 } 1638 if ( aExp == 0 ) { 1639 if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); 1640 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 1641 --aExp; 1642 } 1643 return packFloat128( aSign, aExp + 0x3F80, ( (uint64_t) aSig )<<25, 0 ); 1644 1645 } 1646 1647 /*---------------------------------------------------------------------------- 1648 | Rounds the single-precision floating-point value `a' to an integer, and 1649 | returns the result as a single-precision floating-point value. The 1650 | operation is performed according to the IEC/IEEE Standard for Binary 1651 | Floating-Point Arithmetic. 1652 *----------------------------------------------------------------------------*/ 1653 1654 float32 float32_round_to_int( float32 a STATUS_PARAM) 1655 { 1656 flag aSign; 1657 int_fast16_t aExp; 1658 uint32_t lastBitMask, roundBitsMask; 1659 int8 roundingMode; 1660 uint32_t z; 1661 a = float32_squash_input_denormal(a STATUS_VAR); 1662 1663 aExp = extractFloat32Exp( a ); 1664 if ( 0x96 <= aExp ) { 1665 if ( ( aExp == 0xFF ) && extractFloat32Frac( a ) ) { 1666 return propagateFloat32NaN( a, a STATUS_VAR ); 1667 } 1668 return a; 1669 } 1670 if ( aExp <= 0x7E ) { 1671 if ( (uint32_t) ( float32_val(a)<<1 ) == 0 ) return a; 1672 STATUS(float_exception_flags) |= float_flag_inexact; 1673 aSign = extractFloat32Sign( a ); 1674 switch ( STATUS(float_rounding_mode) ) { 1675 case float_round_nearest_even: 1676 if ( ( aExp == 0x7E ) && extractFloat32Frac( a ) ) { 1677 return packFloat32( aSign, 0x7F, 0 ); 1678 } 1679 break; 1680 case float_round_down: 1681 return make_float32(aSign ? 0xBF800000 : 0); 1682 case float_round_up: 1683 return make_float32(aSign ? 0x80000000 : 0x3F800000); 1684 } 1685 return packFloat32( aSign, 0, 0 ); 1686 } 1687 lastBitMask = 1; 1688 lastBitMask <<= 0x96 - aExp; 1689 roundBitsMask = lastBitMask - 1; 1690 z = float32_val(a); 1691 roundingMode = STATUS(float_rounding_mode); 1692 if ( roundingMode == float_round_nearest_even ) { 1693 z += lastBitMask>>1; 1694 if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; 1695 } 1696 else if ( roundingMode != float_round_to_zero ) { 1697 if ( extractFloat32Sign( make_float32(z) ) ^ ( roundingMode == float_round_up ) ) { 1698 z += roundBitsMask; 1699 } 1700 } 1701 z &= ~ roundBitsMask; 1702 if ( z != float32_val(a) ) STATUS(float_exception_flags) |= float_flag_inexact; 1703 return make_float32(z); 1704 1705 } 1706 1707 /*---------------------------------------------------------------------------- 1708 | Returns the result of adding the absolute values of the single-precision 1709 | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated 1710 | before being returned. `zSign' is ignored if the result is a NaN. 1711 | The addition is performed according to the IEC/IEEE Standard for Binary 1712 | Floating-Point Arithmetic. 1713 *----------------------------------------------------------------------------*/ 1714 1715 static float32 addFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) 1716 { 1717 int_fast16_t aExp, bExp, zExp; 1718 uint32_t aSig, bSig, zSig; 1719 int_fast16_t expDiff; 1720 1721 aSig = extractFloat32Frac( a ); 1722 aExp = extractFloat32Exp( a ); 1723 bSig = extractFloat32Frac( b ); 1724 bExp = extractFloat32Exp( b ); 1725 expDiff = aExp - bExp; 1726 aSig <<= 6; 1727 bSig <<= 6; 1728 if ( 0 < expDiff ) { 1729 if ( aExp == 0xFF ) { 1730 if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1731 return a; 1732 } 1733 if ( bExp == 0 ) { 1734 --expDiff; 1735 } 1736 else { 1737 bSig |= 0x20000000; 1738 } 1739 shift32RightJamming( bSig, expDiff, &bSig ); 1740 zExp = aExp; 1741 } 1742 else if ( expDiff < 0 ) { 1743 if ( bExp == 0xFF ) { 1744 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1745 return packFloat32( zSign, 0xFF, 0 ); 1746 } 1747 if ( aExp == 0 ) { 1748 ++expDiff; 1749 } 1750 else { 1751 aSig |= 0x20000000; 1752 } 1753 shift32RightJamming( aSig, - expDiff, &aSig ); 1754 zExp = bExp; 1755 } 1756 else { 1757 if ( aExp == 0xFF ) { 1758 if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1759 return a; 1760 } 1761 if ( aExp == 0 ) { 1762 if (STATUS(flush_to_zero)) { 1763 if (aSig | bSig) { 1764 float_raise(float_flag_output_denormal STATUS_VAR); 1765 } 1766 return packFloat32(zSign, 0, 0); 1767 } 1768 return packFloat32( zSign, 0, ( aSig + bSig )>>6 ); 1769 } 1770 zSig = 0x40000000 + aSig + bSig; 1771 zExp = aExp; 1772 goto roundAndPack; 1773 } 1774 aSig |= 0x20000000; 1775 zSig = ( aSig + bSig )<<1; 1776 --zExp; 1777 if ( (int32_t) zSig < 0 ) { 1778 zSig = aSig + bSig; 1779 ++zExp; 1780 } 1781 roundAndPack: 1782 return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); 1783 1784 } 1785 1786 /*---------------------------------------------------------------------------- 1787 | Returns the result of subtracting the absolute values of the single- 1788 | precision floating-point values `a' and `b'. If `zSign' is 1, the 1789 | difference is negated before being returned. `zSign' is ignored if the 1790 | result is a NaN. The subtraction is performed according to the IEC/IEEE 1791 | Standard for Binary Floating-Point Arithmetic. 1792 *----------------------------------------------------------------------------*/ 1793 1794 static float32 subFloat32Sigs( float32 a, float32 b, flag zSign STATUS_PARAM) 1795 { 1796 int_fast16_t aExp, bExp, zExp; 1797 uint32_t aSig, bSig, zSig; 1798 int_fast16_t expDiff; 1799 1800 aSig = extractFloat32Frac( a ); 1801 aExp = extractFloat32Exp( a ); 1802 bSig = extractFloat32Frac( b ); 1803 bExp = extractFloat32Exp( b ); 1804 expDiff = aExp - bExp; 1805 aSig <<= 7; 1806 bSig <<= 7; 1807 if ( 0 < expDiff ) goto aExpBigger; 1808 if ( expDiff < 0 ) goto bExpBigger; 1809 if ( aExp == 0xFF ) { 1810 if ( aSig | bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1811 float_raise( float_flag_invalid STATUS_VAR); 1812 return float32_default_nan; 1813 } 1814 if ( aExp == 0 ) { 1815 aExp = 1; 1816 bExp = 1; 1817 } 1818 if ( bSig < aSig ) goto aBigger; 1819 if ( aSig < bSig ) goto bBigger; 1820 return packFloat32( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); 1821 bExpBigger: 1822 if ( bExp == 0xFF ) { 1823 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1824 return packFloat32( zSign ^ 1, 0xFF, 0 ); 1825 } 1826 if ( aExp == 0 ) { 1827 ++expDiff; 1828 } 1829 else { 1830 aSig |= 0x40000000; 1831 } 1832 shift32RightJamming( aSig, - expDiff, &aSig ); 1833 bSig |= 0x40000000; 1834 bBigger: 1835 zSig = bSig - aSig; 1836 zExp = bExp; 1837 zSign ^= 1; 1838 goto normalizeRoundAndPack; 1839 aExpBigger: 1840 if ( aExp == 0xFF ) { 1841 if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1842 return a; 1843 } 1844 if ( bExp == 0 ) { 1845 --expDiff; 1846 } 1847 else { 1848 bSig |= 0x40000000; 1849 } 1850 shift32RightJamming( bSig, expDiff, &bSig ); 1851 aSig |= 0x40000000; 1852 aBigger: 1853 zSig = aSig - bSig; 1854 zExp = aExp; 1855 normalizeRoundAndPack: 1856 --zExp; 1857 return normalizeRoundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); 1858 1859 } 1860 1861 /*---------------------------------------------------------------------------- 1862 | Returns the result of adding the single-precision floating-point values `a' 1863 | and `b'. The operation is performed according to the IEC/IEEE Standard for 1864 | Binary Floating-Point Arithmetic. 1865 *----------------------------------------------------------------------------*/ 1866 1867 float32 float32_add( float32 a, float32 b STATUS_PARAM ) 1868 { 1869 flag aSign, bSign; 1870 a = float32_squash_input_denormal(a STATUS_VAR); 1871 b = float32_squash_input_denormal(b STATUS_VAR); 1872 1873 aSign = extractFloat32Sign( a ); 1874 bSign = extractFloat32Sign( b ); 1875 if ( aSign == bSign ) { 1876 return addFloat32Sigs( a, b, aSign STATUS_VAR); 1877 } 1878 else { 1879 return subFloat32Sigs( a, b, aSign STATUS_VAR ); 1880 } 1881 1882 } 1883 1884 /*---------------------------------------------------------------------------- 1885 | Returns the result of subtracting the single-precision floating-point values 1886 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard 1887 | for Binary Floating-Point Arithmetic. 1888 *----------------------------------------------------------------------------*/ 1889 1890 float32 float32_sub( float32 a, float32 b STATUS_PARAM ) 1891 { 1892 flag aSign, bSign; 1893 a = float32_squash_input_denormal(a STATUS_VAR); 1894 b = float32_squash_input_denormal(b STATUS_VAR); 1895 1896 aSign = extractFloat32Sign( a ); 1897 bSign = extractFloat32Sign( b ); 1898 if ( aSign == bSign ) { 1899 return subFloat32Sigs( a, b, aSign STATUS_VAR ); 1900 } 1901 else { 1902 return addFloat32Sigs( a, b, aSign STATUS_VAR ); 1903 } 1904 1905 } 1906 1907 /*---------------------------------------------------------------------------- 1908 | Returns the result of multiplying the single-precision floating-point values 1909 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard 1910 | for Binary Floating-Point Arithmetic. 1911 *----------------------------------------------------------------------------*/ 1912 1913 float32 float32_mul( float32 a, float32 b STATUS_PARAM ) 1914 { 1915 flag aSign, bSign, zSign; 1916 int_fast16_t aExp, bExp, zExp; 1917 uint32_t aSig, bSig; 1918 uint64_t zSig64; 1919 uint32_t zSig; 1920 1921 a = float32_squash_input_denormal(a STATUS_VAR); 1922 b = float32_squash_input_denormal(b STATUS_VAR); 1923 1924 aSig = extractFloat32Frac( a ); 1925 aExp = extractFloat32Exp( a ); 1926 aSign = extractFloat32Sign( a ); 1927 bSig = extractFloat32Frac( b ); 1928 bExp = extractFloat32Exp( b ); 1929 bSign = extractFloat32Sign( b ); 1930 zSign = aSign ^ bSign; 1931 if ( aExp == 0xFF ) { 1932 if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { 1933 return propagateFloat32NaN( a, b STATUS_VAR ); 1934 } 1935 if ( ( bExp | bSig ) == 0 ) { 1936 float_raise( float_flag_invalid STATUS_VAR); 1937 return float32_default_nan; 1938 } 1939 return packFloat32( zSign, 0xFF, 0 ); 1940 } 1941 if ( bExp == 0xFF ) { 1942 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1943 if ( ( aExp | aSig ) == 0 ) { 1944 float_raise( float_flag_invalid STATUS_VAR); 1945 return float32_default_nan; 1946 } 1947 return packFloat32( zSign, 0xFF, 0 ); 1948 } 1949 if ( aExp == 0 ) { 1950 if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); 1951 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 1952 } 1953 if ( bExp == 0 ) { 1954 if ( bSig == 0 ) return packFloat32( zSign, 0, 0 ); 1955 normalizeFloat32Subnormal( bSig, &bExp, &bSig ); 1956 } 1957 zExp = aExp + bExp - 0x7F; 1958 aSig = ( aSig | 0x00800000 )<<7; 1959 bSig = ( bSig | 0x00800000 )<<8; 1960 shift64RightJamming( ( (uint64_t) aSig ) * bSig, 32, &zSig64 ); 1961 zSig = zSig64; 1962 if ( 0 <= (int32_t) ( zSig<<1 ) ) { 1963 zSig <<= 1; 1964 --zExp; 1965 } 1966 return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); 1967 1968 } 1969 1970 /*---------------------------------------------------------------------------- 1971 | Returns the result of dividing the single-precision floating-point value `a' 1972 | by the corresponding value `b'. The operation is performed according to the 1973 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 1974 *----------------------------------------------------------------------------*/ 1975 1976 float32 float32_div( float32 a, float32 b STATUS_PARAM ) 1977 { 1978 flag aSign, bSign, zSign; 1979 int_fast16_t aExp, bExp, zExp; 1980 uint32_t aSig, bSig, zSig; 1981 a = float32_squash_input_denormal(a STATUS_VAR); 1982 b = float32_squash_input_denormal(b STATUS_VAR); 1983 1984 aSig = extractFloat32Frac( a ); 1985 aExp = extractFloat32Exp( a ); 1986 aSign = extractFloat32Sign( a ); 1987 bSig = extractFloat32Frac( b ); 1988 bExp = extractFloat32Exp( b ); 1989 bSign = extractFloat32Sign( b ); 1990 zSign = aSign ^ bSign; 1991 if ( aExp == 0xFF ) { 1992 if ( aSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1993 if ( bExp == 0xFF ) { 1994 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 1995 float_raise( float_flag_invalid STATUS_VAR); 1996 return float32_default_nan; 1997 } 1998 return packFloat32( zSign, 0xFF, 0 ); 1999 } 2000 if ( bExp == 0xFF ) { 2001 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 2002 return packFloat32( zSign, 0, 0 ); 2003 } 2004 if ( bExp == 0 ) { 2005 if ( bSig == 0 ) { 2006 if ( ( aExp | aSig ) == 0 ) { 2007 float_raise( float_flag_invalid STATUS_VAR); 2008 return float32_default_nan; 2009 } 2010 float_raise( float_flag_divbyzero STATUS_VAR); 2011 return packFloat32( zSign, 0xFF, 0 ); 2012 } 2013 normalizeFloat32Subnormal( bSig, &bExp, &bSig ); 2014 } 2015 if ( aExp == 0 ) { 2016 if ( aSig == 0 ) return packFloat32( zSign, 0, 0 ); 2017 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 2018 } 2019 zExp = aExp - bExp + 0x7D; 2020 aSig = ( aSig | 0x00800000 )<<7; 2021 bSig = ( bSig | 0x00800000 )<<8; 2022 if ( bSig <= ( aSig + aSig ) ) { 2023 aSig >>= 1; 2024 ++zExp; 2025 } 2026 zSig = ( ( (uint64_t) aSig )<<32 ) / bSig; 2027 if ( ( zSig & 0x3F ) == 0 ) { 2028 zSig |= ( (uint64_t) bSig * zSig != ( (uint64_t) aSig )<<32 ); 2029 } 2030 return roundAndPackFloat32( zSign, zExp, zSig STATUS_VAR ); 2031 2032 } 2033 2034 /*---------------------------------------------------------------------------- 2035 | Returns the remainder of the single-precision floating-point value `a' 2036 | with respect to the corresponding value `b'. The operation is performed 2037 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 2038 *----------------------------------------------------------------------------*/ 2039 2040 float32 float32_rem( float32 a, float32 b STATUS_PARAM ) 2041 { 2042 flag aSign, zSign; 2043 int_fast16_t aExp, bExp, expDiff; 2044 uint32_t aSig, bSig; 2045 uint32_t q; 2046 uint64_t aSig64, bSig64, q64; 2047 uint32_t alternateASig; 2048 int32_t sigMean; 2049 a = float32_squash_input_denormal(a STATUS_VAR); 2050 b = float32_squash_input_denormal(b STATUS_VAR); 2051 2052 aSig = extractFloat32Frac( a ); 2053 aExp = extractFloat32Exp( a ); 2054 aSign = extractFloat32Sign( a ); 2055 bSig = extractFloat32Frac( b ); 2056 bExp = extractFloat32Exp( b ); 2057 if ( aExp == 0xFF ) { 2058 if ( aSig || ( ( bExp == 0xFF ) && bSig ) ) { 2059 return propagateFloat32NaN( a, b STATUS_VAR ); 2060 } 2061 float_raise( float_flag_invalid STATUS_VAR); 2062 return float32_default_nan; 2063 } 2064 if ( bExp == 0xFF ) { 2065 if ( bSig ) return propagateFloat32NaN( a, b STATUS_VAR ); 2066 return a; 2067 } 2068 if ( bExp == 0 ) { 2069 if ( bSig == 0 ) { 2070 float_raise( float_flag_invalid STATUS_VAR); 2071 return float32_default_nan; 2072 } 2073 normalizeFloat32Subnormal( bSig, &bExp, &bSig ); 2074 } 2075 if ( aExp == 0 ) { 2076 if ( aSig == 0 ) return a; 2077 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 2078 } 2079 expDiff = aExp - bExp; 2080 aSig |= 0x00800000; 2081 bSig |= 0x00800000; 2082 if ( expDiff < 32 ) { 2083 aSig <<= 8; 2084 bSig <<= 8; 2085 if ( expDiff < 0 ) { 2086 if ( expDiff < -1 ) return a; 2087 aSig >>= 1; 2088 } 2089 q = ( bSig <= aSig ); 2090 if ( q ) aSig -= bSig; 2091 if ( 0 < expDiff ) { 2092 q = ( ( (uint64_t) aSig )<<32 ) / bSig; 2093 q >>= 32 - expDiff; 2094 bSig >>= 2; 2095 aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; 2096 } 2097 else { 2098 aSig >>= 2; 2099 bSig >>= 2; 2100 } 2101 } 2102 else { 2103 if ( bSig <= aSig ) aSig -= bSig; 2104 aSig64 = ( (uint64_t) aSig )<<40; 2105 bSig64 = ( (uint64_t) bSig )<<40; 2106 expDiff -= 64; 2107 while ( 0 < expDiff ) { 2108 q64 = estimateDiv128To64( aSig64, 0, bSig64 ); 2109 q64 = ( 2 < q64 ) ? q64 - 2 : 0; 2110 aSig64 = - ( ( bSig * q64 )<<38 ); 2111 expDiff -= 62; 2112 } 2113 expDiff += 64; 2114 q64 = estimateDiv128To64( aSig64, 0, bSig64 ); 2115 q64 = ( 2 < q64 ) ? q64 - 2 : 0; 2116 q = q64>>( 64 - expDiff ); 2117 bSig <<= 6; 2118 aSig = ( ( aSig64>>33 )<<( expDiff - 1 ) ) - bSig * q; 2119 } 2120 do { 2121 alternateASig = aSig; 2122 ++q; 2123 aSig -= bSig; 2124 } while ( 0 <= (int32_t) aSig ); 2125 sigMean = aSig + alternateASig; 2126 if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { 2127 aSig = alternateASig; 2128 } 2129 zSign = ( (int32_t) aSig < 0 ); 2130 if ( zSign ) aSig = - aSig; 2131 return normalizeRoundAndPackFloat32( aSign ^ zSign, bExp, aSig STATUS_VAR ); 2132 2133 } 2134 2135 /*---------------------------------------------------------------------------- 2136 | Returns the result of multiplying the single-precision floating-point values 2137 | `a' and `b' then adding 'c', with no intermediate rounding step after the 2138 | multiplication. The operation is performed according to the IEC/IEEE 2139 | Standard for Binary Floating-Point Arithmetic 754-2008. 2140 | The flags argument allows the caller to select negation of the 2141 | addend, the intermediate product, or the final result. (The difference 2142 | between this and having the caller do a separate negation is that negating 2143 | externally will flip the sign bit on NaNs.) 2144 *----------------------------------------------------------------------------*/ 2145 2146 float32 float32_muladd(float32 a, float32 b, float32 c, int flags STATUS_PARAM) 2147 { 2148 flag aSign, bSign, cSign, zSign; 2149 int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; 2150 uint32_t aSig, bSig, cSig; 2151 flag pInf, pZero, pSign; 2152 uint64_t pSig64, cSig64, zSig64; 2153 uint32_t pSig; 2154 int shiftcount; 2155 flag signflip, infzero; 2156 2157 a = float32_squash_input_denormal(a STATUS_VAR); 2158 b = float32_squash_input_denormal(b STATUS_VAR); 2159 c = float32_squash_input_denormal(c STATUS_VAR); 2160 aSig = extractFloat32Frac(a); 2161 aExp = extractFloat32Exp(a); 2162 aSign = extractFloat32Sign(a); 2163 bSig = extractFloat32Frac(b); 2164 bExp = extractFloat32Exp(b); 2165 bSign = extractFloat32Sign(b); 2166 cSig = extractFloat32Frac(c); 2167 cExp = extractFloat32Exp(c); 2168 cSign = extractFloat32Sign(c); 2169 2170 infzero = ((aExp == 0 && aSig == 0 && bExp == 0xff && bSig == 0) || 2171 (aExp == 0xff && aSig == 0 && bExp == 0 && bSig == 0)); 2172 2173 /* It is implementation-defined whether the cases of (0,inf,qnan) 2174 * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN 2175 * they return if they do), so we have to hand this information 2176 * off to the target-specific pick-a-NaN routine. 2177 */ 2178 if (((aExp == 0xff) && aSig) || 2179 ((bExp == 0xff) && bSig) || 2180 ((cExp == 0xff) && cSig)) { 2181 return propagateFloat32MulAddNaN(a, b, c, infzero STATUS_VAR); 2182 } 2183 2184 if (infzero) { 2185 float_raise(float_flag_invalid STATUS_VAR); 2186 return float32_default_nan; 2187 } 2188 2189 if (flags & float_muladd_negate_c) { 2190 cSign ^= 1; 2191 } 2192 2193 signflip = (flags & float_muladd_negate_result) ? 1 : 0; 2194 2195 /* Work out the sign and type of the product */ 2196 pSign = aSign ^ bSign; 2197 if (flags & float_muladd_negate_product) { 2198 pSign ^= 1; 2199 } 2200 pInf = (aExp == 0xff) || (bExp == 0xff); 2201 pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); 2202 2203 if (cExp == 0xff) { 2204 if (pInf && (pSign ^ cSign)) { 2205 /* addition of opposite-signed infinities => InvalidOperation */ 2206 float_raise(float_flag_invalid STATUS_VAR); 2207 return float32_default_nan; 2208 } 2209 /* Otherwise generate an infinity of the same sign */ 2210 return packFloat32(cSign ^ signflip, 0xff, 0); 2211 } 2212 2213 if (pInf) { 2214 return packFloat32(pSign ^ signflip, 0xff, 0); 2215 } 2216 2217 if (pZero) { 2218 if (cExp == 0) { 2219 if (cSig == 0) { 2220 /* Adding two exact zeroes */ 2221 if (pSign == cSign) { 2222 zSign = pSign; 2223 } else if (STATUS(float_rounding_mode) == float_round_down) { 2224 zSign = 1; 2225 } else { 2226 zSign = 0; 2227 } 2228 return packFloat32(zSign ^ signflip, 0, 0); 2229 } 2230 /* Exact zero plus a denorm */ 2231 if (STATUS(flush_to_zero)) { 2232 float_raise(float_flag_output_denormal STATUS_VAR); 2233 return packFloat32(cSign ^ signflip, 0, 0); 2234 } 2235 } 2236 /* Zero plus something non-zero : just return the something */ 2237 return packFloat32(cSign ^ signflip, cExp, cSig); 2238 } 2239 2240 if (aExp == 0) { 2241 normalizeFloat32Subnormal(aSig, &aExp, &aSig); 2242 } 2243 if (bExp == 0) { 2244 normalizeFloat32Subnormal(bSig, &bExp, &bSig); 2245 } 2246 2247 /* Calculate the actual result a * b + c */ 2248 2249 /* Multiply first; this is easy. */ 2250 /* NB: we subtract 0x7e where float32_mul() subtracts 0x7f 2251 * because we want the true exponent, not the "one-less-than" 2252 * flavour that roundAndPackFloat32() takes. 2253 */ 2254 pExp = aExp + bExp - 0x7e; 2255 aSig = (aSig | 0x00800000) << 7; 2256 bSig = (bSig | 0x00800000) << 8; 2257 pSig64 = (uint64_t)aSig * bSig; 2258 if ((int64_t)(pSig64 << 1) >= 0) { 2259 pSig64 <<= 1; 2260 pExp--; 2261 } 2262 2263 zSign = pSign ^ signflip; 2264 2265 /* Now pSig64 is the significand of the multiply, with the explicit bit in 2266 * position 62. 2267 */ 2268 if (cExp == 0) { 2269 if (!cSig) { 2270 /* Throw out the special case of c being an exact zero now */ 2271 shift64RightJamming(pSig64, 32, &pSig64); 2272 pSig = pSig64; 2273 return roundAndPackFloat32(zSign, pExp - 1, 2274 pSig STATUS_VAR); 2275 } 2276 normalizeFloat32Subnormal(cSig, &cExp, &cSig); 2277 } 2278 2279 cSig64 = (uint64_t)cSig << (62 - 23); 2280 cSig64 |= LIT64(0x4000000000000000); 2281 expDiff = pExp - cExp; 2282 2283 if (pSign == cSign) { 2284 /* Addition */ 2285 if (expDiff > 0) { 2286 /* scale c to match p */ 2287 shift64RightJamming(cSig64, expDiff, &cSig64); 2288 zExp = pExp; 2289 } else if (expDiff < 0) { 2290 /* scale p to match c */ 2291 shift64RightJamming(pSig64, -expDiff, &pSig64); 2292 zExp = cExp; 2293 } else { 2294 /* no scaling needed */ 2295 zExp = cExp; 2296 } 2297 /* Add significands and make sure explicit bit ends up in posn 62 */ 2298 zSig64 = pSig64 + cSig64; 2299 if ((int64_t)zSig64 < 0) { 2300 shift64RightJamming(zSig64, 1, &zSig64); 2301 } else { 2302 zExp--; 2303 } 2304 } else { 2305 /* Subtraction */ 2306 if (expDiff > 0) { 2307 shift64RightJamming(cSig64, expDiff, &cSig64); 2308 zSig64 = pSig64 - cSig64; 2309 zExp = pExp; 2310 } else if (expDiff < 0) { 2311 shift64RightJamming(pSig64, -expDiff, &pSig64); 2312 zSig64 = cSig64 - pSig64; 2313 zExp = cExp; 2314 zSign ^= 1; 2315 } else { 2316 zExp = pExp; 2317 if (cSig64 < pSig64) { 2318 zSig64 = pSig64 - cSig64; 2319 } else if (pSig64 < cSig64) { 2320 zSig64 = cSig64 - pSig64; 2321 zSign ^= 1; 2322 } else { 2323 /* Exact zero */ 2324 zSign = signflip; 2325 if (STATUS(float_rounding_mode) == float_round_down) { 2326 zSign ^= 1; 2327 } 2328 return packFloat32(zSign, 0, 0); 2329 } 2330 } 2331 --zExp; 2332 /* Normalize to put the explicit bit back into bit 62. */ 2333 shiftcount = countLeadingZeros64(zSig64) - 1; 2334 zSig64 <<= shiftcount; 2335 zExp -= shiftcount; 2336 } 2337 shift64RightJamming(zSig64, 32, &zSig64); 2338 return roundAndPackFloat32(zSign, zExp, zSig64 STATUS_VAR); 2339 } 2340 2341 2342 /*---------------------------------------------------------------------------- 2343 | Returns the square root of the single-precision floating-point value `a'. 2344 | The operation is performed according to the IEC/IEEE Standard for Binary 2345 | Floating-Point Arithmetic. 2346 *----------------------------------------------------------------------------*/ 2347 2348 float32 float32_sqrt( float32 a STATUS_PARAM ) 2349 { 2350 flag aSign; 2351 int_fast16_t aExp, zExp; 2352 uint32_t aSig, zSig; 2353 uint64_t rem, term; 2354 a = float32_squash_input_denormal(a STATUS_VAR); 2355 2356 aSig = extractFloat32Frac( a ); 2357 aExp = extractFloat32Exp( a ); 2358 aSign = extractFloat32Sign( a ); 2359 if ( aExp == 0xFF ) { 2360 if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); 2361 if ( ! aSign ) return a; 2362 float_raise( float_flag_invalid STATUS_VAR); 2363 return float32_default_nan; 2364 } 2365 if ( aSign ) { 2366 if ( ( aExp | aSig ) == 0 ) return a; 2367 float_raise( float_flag_invalid STATUS_VAR); 2368 return float32_default_nan; 2369 } 2370 if ( aExp == 0 ) { 2371 if ( aSig == 0 ) return float32_zero; 2372 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 2373 } 2374 zExp = ( ( aExp - 0x7F )>>1 ) + 0x7E; 2375 aSig = ( aSig | 0x00800000 )<<8; 2376 zSig = estimateSqrt32( aExp, aSig ) + 2; 2377 if ( ( zSig & 0x7F ) <= 5 ) { 2378 if ( zSig < 2 ) { 2379 zSig = 0x7FFFFFFF; 2380 goto roundAndPack; 2381 } 2382 aSig >>= aExp & 1; 2383 term = ( (uint64_t) zSig ) * zSig; 2384 rem = ( ( (uint64_t) aSig )<<32 ) - term; 2385 while ( (int64_t) rem < 0 ) { 2386 --zSig; 2387 rem += ( ( (uint64_t) zSig )<<1 ) | 1; 2388 } 2389 zSig |= ( rem != 0 ); 2390 } 2391 shift32RightJamming( zSig, 1, &zSig ); 2392 roundAndPack: 2393 return roundAndPackFloat32( 0, zExp, zSig STATUS_VAR ); 2394 2395 } 2396 2397 /*---------------------------------------------------------------------------- 2398 | Returns the binary exponential of the single-precision floating-point value 2399 | `a'. The operation is performed according to the IEC/IEEE Standard for 2400 | Binary Floating-Point Arithmetic. 2401 | 2402 | Uses the following identities: 2403 | 2404 | 1. ------------------------------------------------------------------------- 2405 | x x*ln(2) 2406 | 2 = e 2407 | 2408 | 2. ------------------------------------------------------------------------- 2409 | 2 3 4 5 n 2410 | x x x x x x x 2411 | e = 1 + --- + --- + --- + --- + --- + ... + --- + ... 2412 | 1! 2! 3! 4! 5! n! 2413 *----------------------------------------------------------------------------*/ 2414 2415 static const float64 float32_exp2_coefficients[15] = 2416 { 2417 const_float64( 0x3ff0000000000000ll ), /* 1 */ 2418 const_float64( 0x3fe0000000000000ll ), /* 2 */ 2419 const_float64( 0x3fc5555555555555ll ), /* 3 */ 2420 const_float64( 0x3fa5555555555555ll ), /* 4 */ 2421 const_float64( 0x3f81111111111111ll ), /* 5 */ 2422 const_float64( 0x3f56c16c16c16c17ll ), /* 6 */ 2423 const_float64( 0x3f2a01a01a01a01all ), /* 7 */ 2424 const_float64( 0x3efa01a01a01a01all ), /* 8 */ 2425 const_float64( 0x3ec71de3a556c734ll ), /* 9 */ 2426 const_float64( 0x3e927e4fb7789f5cll ), /* 10 */ 2427 const_float64( 0x3e5ae64567f544e4ll ), /* 11 */ 2428 const_float64( 0x3e21eed8eff8d898ll ), /* 12 */ 2429 const_float64( 0x3de6124613a86d09ll ), /* 13 */ 2430 const_float64( 0x3da93974a8c07c9dll ), /* 14 */ 2431 const_float64( 0x3d6ae7f3e733b81fll ), /* 15 */ 2432 }; 2433 2434 float32 float32_exp2( float32 a STATUS_PARAM ) 2435 { 2436 flag aSign; 2437 int_fast16_t aExp; 2438 uint32_t aSig; 2439 float64 r, x, xn; 2440 int i; 2441 a = float32_squash_input_denormal(a STATUS_VAR); 2442 2443 aSig = extractFloat32Frac( a ); 2444 aExp = extractFloat32Exp( a ); 2445 aSign = extractFloat32Sign( a ); 2446 2447 if ( aExp == 0xFF) { 2448 if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); 2449 return (aSign) ? float32_zero : a; 2450 } 2451 if (aExp == 0) { 2452 if (aSig == 0) return float32_one; 2453 } 2454 2455 float_raise( float_flag_inexact STATUS_VAR); 2456 2457 /* ******************************* */ 2458 /* using float64 for approximation */ 2459 /* ******************************* */ 2460 x = float32_to_float64(a STATUS_VAR); 2461 x = float64_mul(x, float64_ln2 STATUS_VAR); 2462 2463 xn = x; 2464 r = float64_one; 2465 for (i = 0 ; i < 15 ; i++) { 2466 float64 f; 2467 2468 f = float64_mul(xn, float32_exp2_coefficients[i] STATUS_VAR); 2469 r = float64_add(r, f STATUS_VAR); 2470 2471 xn = float64_mul(xn, x STATUS_VAR); 2472 } 2473 2474 return float64_to_float32(r, status); 2475 } 2476 2477 /*---------------------------------------------------------------------------- 2478 | Returns the binary log of the single-precision floating-point value `a'. 2479 | The operation is performed according to the IEC/IEEE Standard for Binary 2480 | Floating-Point Arithmetic. 2481 *----------------------------------------------------------------------------*/ 2482 float32 float32_log2( float32 a STATUS_PARAM ) 2483 { 2484 flag aSign, zSign; 2485 int_fast16_t aExp; 2486 uint32_t aSig, zSig, i; 2487 2488 a = float32_squash_input_denormal(a STATUS_VAR); 2489 aSig = extractFloat32Frac( a ); 2490 aExp = extractFloat32Exp( a ); 2491 aSign = extractFloat32Sign( a ); 2492 2493 if ( aExp == 0 ) { 2494 if ( aSig == 0 ) return packFloat32( 1, 0xFF, 0 ); 2495 normalizeFloat32Subnormal( aSig, &aExp, &aSig ); 2496 } 2497 if ( aSign ) { 2498 float_raise( float_flag_invalid STATUS_VAR); 2499 return float32_default_nan; 2500 } 2501 if ( aExp == 0xFF ) { 2502 if ( aSig ) return propagateFloat32NaN( a, float32_zero STATUS_VAR ); 2503 return a; 2504 } 2505 2506 aExp -= 0x7F; 2507 aSig |= 0x00800000; 2508 zSign = aExp < 0; 2509 zSig = aExp << 23; 2510 2511 for (i = 1 << 22; i > 0; i >>= 1) { 2512 aSig = ( (uint64_t)aSig * aSig ) >> 23; 2513 if ( aSig & 0x01000000 ) { 2514 aSig >>= 1; 2515 zSig |= i; 2516 } 2517 } 2518 2519 if ( zSign ) 2520 zSig = -zSig; 2521 2522 return normalizeRoundAndPackFloat32( zSign, 0x85, zSig STATUS_VAR ); 2523 } 2524 2525 /*---------------------------------------------------------------------------- 2526 | Returns 1 if the single-precision floating-point value `a' is equal to 2527 | the corresponding value `b', and 0 otherwise. The invalid exception is 2528 | raised if either operand is a NaN. Otherwise, the comparison is performed 2529 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 2530 *----------------------------------------------------------------------------*/ 2531 2532 int float32_eq( float32 a, float32 b STATUS_PARAM ) 2533 { 2534 uint32_t av, bv; 2535 a = float32_squash_input_denormal(a STATUS_VAR); 2536 b = float32_squash_input_denormal(b STATUS_VAR); 2537 2538 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2539 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2540 ) { 2541 float_raise( float_flag_invalid STATUS_VAR); 2542 return 0; 2543 } 2544 av = float32_val(a); 2545 bv = float32_val(b); 2546 return ( av == bv ) || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); 2547 } 2548 2549 /*---------------------------------------------------------------------------- 2550 | Returns 1 if the single-precision floating-point value `a' is less than 2551 | or equal to the corresponding value `b', and 0 otherwise. The invalid 2552 | exception is raised if either operand is a NaN. The comparison is performed 2553 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 2554 *----------------------------------------------------------------------------*/ 2555 2556 int float32_le( float32 a, float32 b STATUS_PARAM ) 2557 { 2558 flag aSign, bSign; 2559 uint32_t av, bv; 2560 a = float32_squash_input_denormal(a STATUS_VAR); 2561 b = float32_squash_input_denormal(b STATUS_VAR); 2562 2563 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2564 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2565 ) { 2566 float_raise( float_flag_invalid STATUS_VAR); 2567 return 0; 2568 } 2569 aSign = extractFloat32Sign( a ); 2570 bSign = extractFloat32Sign( b ); 2571 av = float32_val(a); 2572 bv = float32_val(b); 2573 if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); 2574 return ( av == bv ) || ( aSign ^ ( av < bv ) ); 2575 2576 } 2577 2578 /*---------------------------------------------------------------------------- 2579 | Returns 1 if the single-precision floating-point value `a' is less than 2580 | the corresponding value `b', and 0 otherwise. The invalid exception is 2581 | raised if either operand is a NaN. The comparison is performed according 2582 | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 2583 *----------------------------------------------------------------------------*/ 2584 2585 int float32_lt( float32 a, float32 b STATUS_PARAM ) 2586 { 2587 flag aSign, bSign; 2588 uint32_t av, bv; 2589 a = float32_squash_input_denormal(a STATUS_VAR); 2590 b = float32_squash_input_denormal(b STATUS_VAR); 2591 2592 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2593 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2594 ) { 2595 float_raise( float_flag_invalid STATUS_VAR); 2596 return 0; 2597 } 2598 aSign = extractFloat32Sign( a ); 2599 bSign = extractFloat32Sign( b ); 2600 av = float32_val(a); 2601 bv = float32_val(b); 2602 if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); 2603 return ( av != bv ) && ( aSign ^ ( av < bv ) ); 2604 2605 } 2606 2607 /*---------------------------------------------------------------------------- 2608 | Returns 1 if the single-precision floating-point values `a' and `b' cannot 2609 | be compared, and 0 otherwise. The invalid exception is raised if either 2610 | operand is a NaN. The comparison is performed according to the IEC/IEEE 2611 | Standard for Binary Floating-Point Arithmetic. 2612 *----------------------------------------------------------------------------*/ 2613 2614 int float32_unordered( float32 a, float32 b STATUS_PARAM ) 2615 { 2616 a = float32_squash_input_denormal(a STATUS_VAR); 2617 b = float32_squash_input_denormal(b STATUS_VAR); 2618 2619 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2620 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2621 ) { 2622 float_raise( float_flag_invalid STATUS_VAR); 2623 return 1; 2624 } 2625 return 0; 2626 } 2627 2628 /*---------------------------------------------------------------------------- 2629 | Returns 1 if the single-precision floating-point value `a' is equal to 2630 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 2631 | exception. The comparison is performed according to the IEC/IEEE Standard 2632 | for Binary Floating-Point Arithmetic. 2633 *----------------------------------------------------------------------------*/ 2634 2635 int float32_eq_quiet( float32 a, float32 b STATUS_PARAM ) 2636 { 2637 a = float32_squash_input_denormal(a STATUS_VAR); 2638 b = float32_squash_input_denormal(b STATUS_VAR); 2639 2640 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2641 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2642 ) { 2643 if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { 2644 float_raise( float_flag_invalid STATUS_VAR); 2645 } 2646 return 0; 2647 } 2648 return ( float32_val(a) == float32_val(b) ) || 2649 ( (uint32_t) ( ( float32_val(a) | float32_val(b) )<<1 ) == 0 ); 2650 } 2651 2652 /*---------------------------------------------------------------------------- 2653 | Returns 1 if the single-precision floating-point value `a' is less than or 2654 | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not 2655 | cause an exception. Otherwise, the comparison is performed according to the 2656 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 2657 *----------------------------------------------------------------------------*/ 2658 2659 int float32_le_quiet( float32 a, float32 b STATUS_PARAM ) 2660 { 2661 flag aSign, bSign; 2662 uint32_t av, bv; 2663 a = float32_squash_input_denormal(a STATUS_VAR); 2664 b = float32_squash_input_denormal(b STATUS_VAR); 2665 2666 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2667 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2668 ) { 2669 if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { 2670 float_raise( float_flag_invalid STATUS_VAR); 2671 } 2672 return 0; 2673 } 2674 aSign = extractFloat32Sign( a ); 2675 bSign = extractFloat32Sign( b ); 2676 av = float32_val(a); 2677 bv = float32_val(b); 2678 if ( aSign != bSign ) return aSign || ( (uint32_t) ( ( av | bv )<<1 ) == 0 ); 2679 return ( av == bv ) || ( aSign ^ ( av < bv ) ); 2680 2681 } 2682 2683 /*---------------------------------------------------------------------------- 2684 | Returns 1 if the single-precision floating-point value `a' is less than 2685 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 2686 | exception. Otherwise, the comparison is performed according to the IEC/IEEE 2687 | Standard for Binary Floating-Point Arithmetic. 2688 *----------------------------------------------------------------------------*/ 2689 2690 int float32_lt_quiet( float32 a, float32 b STATUS_PARAM ) 2691 { 2692 flag aSign, bSign; 2693 uint32_t av, bv; 2694 a = float32_squash_input_denormal(a STATUS_VAR); 2695 b = float32_squash_input_denormal(b STATUS_VAR); 2696 2697 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2698 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2699 ) { 2700 if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { 2701 float_raise( float_flag_invalid STATUS_VAR); 2702 } 2703 return 0; 2704 } 2705 aSign = extractFloat32Sign( a ); 2706 bSign = extractFloat32Sign( b ); 2707 av = float32_val(a); 2708 bv = float32_val(b); 2709 if ( aSign != bSign ) return aSign && ( (uint32_t) ( ( av | bv )<<1 ) != 0 ); 2710 return ( av != bv ) && ( aSign ^ ( av < bv ) ); 2711 2712 } 2713 2714 /*---------------------------------------------------------------------------- 2715 | Returns 1 if the single-precision floating-point values `a' and `b' cannot 2716 | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The 2717 | comparison is performed according to the IEC/IEEE Standard for Binary 2718 | Floating-Point Arithmetic. 2719 *----------------------------------------------------------------------------*/ 2720 2721 int float32_unordered_quiet( float32 a, float32 b STATUS_PARAM ) 2722 { 2723 a = float32_squash_input_denormal(a STATUS_VAR); 2724 b = float32_squash_input_denormal(b STATUS_VAR); 2725 2726 if ( ( ( extractFloat32Exp( a ) == 0xFF ) && extractFloat32Frac( a ) ) 2727 || ( ( extractFloat32Exp( b ) == 0xFF ) && extractFloat32Frac( b ) ) 2728 ) { 2729 if ( float32_is_signaling_nan( a ) || float32_is_signaling_nan( b ) ) { 2730 float_raise( float_flag_invalid STATUS_VAR); 2731 } 2732 return 1; 2733 } 2734 return 0; 2735 } 2736 2737 /*---------------------------------------------------------------------------- 2738 | Returns the result of converting the double-precision floating-point value 2739 | `a' to the 32-bit two's complement integer format. The conversion is 2740 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2741 | Arithmetic---which means in particular that the conversion is rounded 2742 | according to the current rounding mode. If `a' is a NaN, the largest 2743 | positive integer is returned. Otherwise, if the conversion overflows, the 2744 | largest integer with the same sign as `a' is returned. 2745 *----------------------------------------------------------------------------*/ 2746 2747 int32 float64_to_int32( float64 a STATUS_PARAM ) 2748 { 2749 flag aSign; 2750 int_fast16_t aExp, shiftCount; 2751 uint64_t aSig; 2752 a = float64_squash_input_denormal(a STATUS_VAR); 2753 2754 aSig = extractFloat64Frac( a ); 2755 aExp = extractFloat64Exp( a ); 2756 aSign = extractFloat64Sign( a ); 2757 if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; 2758 if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); 2759 shiftCount = 0x42C - aExp; 2760 if ( 0 < shiftCount ) shift64RightJamming( aSig, shiftCount, &aSig ); 2761 return roundAndPackInt32( aSign, aSig STATUS_VAR ); 2762 2763 } 2764 2765 /*---------------------------------------------------------------------------- 2766 | Returns the result of converting the double-precision floating-point value 2767 | `a' to the 32-bit two's complement integer format. The conversion is 2768 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2769 | Arithmetic, except that the conversion is always rounded toward zero. 2770 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 2771 | the conversion overflows, the largest integer with the same sign as `a' is 2772 | returned. 2773 *----------------------------------------------------------------------------*/ 2774 2775 int32 float64_to_int32_round_to_zero( float64 a STATUS_PARAM ) 2776 { 2777 flag aSign; 2778 int_fast16_t aExp, shiftCount; 2779 uint64_t aSig, savedASig; 2780 int32_t z; 2781 a = float64_squash_input_denormal(a STATUS_VAR); 2782 2783 aSig = extractFloat64Frac( a ); 2784 aExp = extractFloat64Exp( a ); 2785 aSign = extractFloat64Sign( a ); 2786 if ( 0x41E < aExp ) { 2787 if ( ( aExp == 0x7FF ) && aSig ) aSign = 0; 2788 goto invalid; 2789 } 2790 else if ( aExp < 0x3FF ) { 2791 if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 2792 return 0; 2793 } 2794 aSig |= LIT64( 0x0010000000000000 ); 2795 shiftCount = 0x433 - aExp; 2796 savedASig = aSig; 2797 aSig >>= shiftCount; 2798 z = aSig; 2799 if ( aSign ) z = - z; 2800 if ( ( z < 0 ) ^ aSign ) { 2801 invalid: 2802 float_raise( float_flag_invalid STATUS_VAR); 2803 return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; 2804 } 2805 if ( ( aSig<<shiftCount ) != savedASig ) { 2806 STATUS(float_exception_flags) |= float_flag_inexact; 2807 } 2808 return z; 2809 2810 } 2811 2812 /*---------------------------------------------------------------------------- 2813 | Returns the result of converting the double-precision floating-point value 2814 | `a' to the 16-bit two's complement integer format. The conversion is 2815 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2816 | Arithmetic, except that the conversion is always rounded toward zero. 2817 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 2818 | the conversion overflows, the largest integer with the same sign as `a' is 2819 | returned. 2820 *----------------------------------------------------------------------------*/ 2821 2822 int_fast16_t float64_to_int16_round_to_zero(float64 a STATUS_PARAM) 2823 { 2824 flag aSign; 2825 int_fast16_t aExp, shiftCount; 2826 uint64_t aSig, savedASig; 2827 int32 z; 2828 2829 aSig = extractFloat64Frac( a ); 2830 aExp = extractFloat64Exp( a ); 2831 aSign = extractFloat64Sign( a ); 2832 if ( 0x40E < aExp ) { 2833 if ( ( aExp == 0x7FF ) && aSig ) { 2834 aSign = 0; 2835 } 2836 goto invalid; 2837 } 2838 else if ( aExp < 0x3FF ) { 2839 if ( aExp || aSig ) { 2840 STATUS(float_exception_flags) |= float_flag_inexact; 2841 } 2842 return 0; 2843 } 2844 aSig |= LIT64( 0x0010000000000000 ); 2845 shiftCount = 0x433 - aExp; 2846 savedASig = aSig; 2847 aSig >>= shiftCount; 2848 z = aSig; 2849 if ( aSign ) { 2850 z = - z; 2851 } 2852 if ( ( (int16_t)z < 0 ) ^ aSign ) { 2853 invalid: 2854 float_raise( float_flag_invalid STATUS_VAR); 2855 return aSign ? (int32_t) 0xffff8000 : 0x7FFF; 2856 } 2857 if ( ( aSig<<shiftCount ) != savedASig ) { 2858 STATUS(float_exception_flags) |= float_flag_inexact; 2859 } 2860 return z; 2861 } 2862 2863 /*---------------------------------------------------------------------------- 2864 | Returns the result of converting the double-precision floating-point value 2865 | `a' to the 64-bit two's complement integer format. The conversion is 2866 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2867 | Arithmetic---which means in particular that the conversion is rounded 2868 | according to the current rounding mode. If `a' is a NaN, the largest 2869 | positive integer is returned. Otherwise, if the conversion overflows, the 2870 | largest integer with the same sign as `a' is returned. 2871 *----------------------------------------------------------------------------*/ 2872 2873 int64 float64_to_int64( float64 a STATUS_PARAM ) 2874 { 2875 flag aSign; 2876 int_fast16_t aExp, shiftCount; 2877 uint64_t aSig, aSigExtra; 2878 a = float64_squash_input_denormal(a STATUS_VAR); 2879 2880 aSig = extractFloat64Frac( a ); 2881 aExp = extractFloat64Exp( a ); 2882 aSign = extractFloat64Sign( a ); 2883 if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); 2884 shiftCount = 0x433 - aExp; 2885 if ( shiftCount <= 0 ) { 2886 if ( 0x43E < aExp ) { 2887 float_raise( float_flag_invalid STATUS_VAR); 2888 if ( ! aSign 2889 || ( ( aExp == 0x7FF ) 2890 && ( aSig != LIT64( 0x0010000000000000 ) ) ) 2891 ) { 2892 return LIT64( 0x7FFFFFFFFFFFFFFF ); 2893 } 2894 return (int64_t) LIT64( 0x8000000000000000 ); 2895 } 2896 aSigExtra = 0; 2897 aSig <<= - shiftCount; 2898 } 2899 else { 2900 shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); 2901 } 2902 return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); 2903 2904 } 2905 2906 /*---------------------------------------------------------------------------- 2907 | Returns the result of converting the double-precision floating-point value 2908 | `a' to the 64-bit two's complement integer format. The conversion is 2909 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2910 | Arithmetic, except that the conversion is always rounded toward zero. 2911 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 2912 | the conversion overflows, the largest integer with the same sign as `a' is 2913 | returned. 2914 *----------------------------------------------------------------------------*/ 2915 2916 int64 float64_to_int64_round_to_zero( float64 a STATUS_PARAM ) 2917 { 2918 flag aSign; 2919 int_fast16_t aExp, shiftCount; 2920 uint64_t aSig; 2921 int64 z; 2922 a = float64_squash_input_denormal(a STATUS_VAR); 2923 2924 aSig = extractFloat64Frac( a ); 2925 aExp = extractFloat64Exp( a ); 2926 aSign = extractFloat64Sign( a ); 2927 if ( aExp ) aSig |= LIT64( 0x0010000000000000 ); 2928 shiftCount = aExp - 0x433; 2929 if ( 0 <= shiftCount ) { 2930 if ( 0x43E <= aExp ) { 2931 if ( float64_val(a) != LIT64( 0xC3E0000000000000 ) ) { 2932 float_raise( float_flag_invalid STATUS_VAR); 2933 if ( ! aSign 2934 || ( ( aExp == 0x7FF ) 2935 && ( aSig != LIT64( 0x0010000000000000 ) ) ) 2936 ) { 2937 return LIT64( 0x7FFFFFFFFFFFFFFF ); 2938 } 2939 } 2940 return (int64_t) LIT64( 0x8000000000000000 ); 2941 } 2942 z = aSig<<shiftCount; 2943 } 2944 else { 2945 if ( aExp < 0x3FE ) { 2946 if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 2947 return 0; 2948 } 2949 z = aSig>>( - shiftCount ); 2950 if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { 2951 STATUS(float_exception_flags) |= float_flag_inexact; 2952 } 2953 } 2954 if ( aSign ) z = - z; 2955 return z; 2956 2957 } 2958 2959 /*---------------------------------------------------------------------------- 2960 | Returns the result of converting the double-precision floating-point value 2961 | `a' to the single-precision floating-point format. The conversion is 2962 | performed according to the IEC/IEEE Standard for Binary Floating-Point 2963 | Arithmetic. 2964 *----------------------------------------------------------------------------*/ 2965 2966 float32 float64_to_float32( float64 a STATUS_PARAM ) 2967 { 2968 flag aSign; 2969 int_fast16_t aExp; 2970 uint64_t aSig; 2971 uint32_t zSig; 2972 a = float64_squash_input_denormal(a STATUS_VAR); 2973 2974 aSig = extractFloat64Frac( a ); 2975 aExp = extractFloat64Exp( a ); 2976 aSign = extractFloat64Sign( a ); 2977 if ( aExp == 0x7FF ) { 2978 if ( aSig ) return commonNaNToFloat32( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 2979 return packFloat32( aSign, 0xFF, 0 ); 2980 } 2981 shift64RightJamming( aSig, 22, &aSig ); 2982 zSig = aSig; 2983 if ( aExp || zSig ) { 2984 zSig |= 0x40000000; 2985 aExp -= 0x381; 2986 } 2987 return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); 2988 2989 } 2990 2991 2992 /*---------------------------------------------------------------------------- 2993 | Packs the sign `zSign', exponent `zExp', and significand `zSig' into a 2994 | half-precision floating-point value, returning the result. After being 2995 | shifted into the proper positions, the three fields are simply added 2996 | together to form the result. This means that any integer portion of `zSig' 2997 | will be added into the exponent. Since a properly normalized significand 2998 | will have an integer portion equal to 1, the `zExp' input should be 1 less 2999 | than the desired result exponent whenever `zSig' is a complete, normalized 3000 | significand. 3001 *----------------------------------------------------------------------------*/ 3002 static float16 packFloat16(flag zSign, int_fast16_t zExp, uint16_t zSig) 3003 { 3004 return make_float16( 3005 (((uint32_t)zSign) << 15) + (((uint32_t)zExp) << 10) + zSig); 3006 } 3007 3008 /* Half precision floats come in two formats: standard IEEE and "ARM" format. 3009 The latter gains extra exponent range by omitting the NaN/Inf encodings. */ 3010 3011 float32 float16_to_float32(float16 a, flag ieee STATUS_PARAM) 3012 { 3013 flag aSign; 3014 int_fast16_t aExp; 3015 uint32_t aSig; 3016 3017 aSign = extractFloat16Sign(a); 3018 aExp = extractFloat16Exp(a); 3019 aSig = extractFloat16Frac(a); 3020 3021 if (aExp == 0x1f && ieee) { 3022 if (aSig) { 3023 return commonNaNToFloat32(float16ToCommonNaN(a STATUS_VAR) STATUS_VAR); 3024 } 3025 return packFloat32(aSign, 0xff, 0); 3026 } 3027 if (aExp == 0) { 3028 int8 shiftCount; 3029 3030 if (aSig == 0) { 3031 return packFloat32(aSign, 0, 0); 3032 } 3033 3034 shiftCount = countLeadingZeros32( aSig ) - 21; 3035 aSig = aSig << shiftCount; 3036 aExp = -shiftCount; 3037 } 3038 return packFloat32( aSign, aExp + 0x70, aSig << 13); 3039 } 3040 3041 float16 float32_to_float16(float32 a, flag ieee STATUS_PARAM) 3042 { 3043 flag aSign; 3044 int_fast16_t aExp; 3045 uint32_t aSig; 3046 uint32_t mask; 3047 uint32_t increment; 3048 int8 roundingMode; 3049 a = float32_squash_input_denormal(a STATUS_VAR); 3050 3051 aSig = extractFloat32Frac( a ); 3052 aExp = extractFloat32Exp( a ); 3053 aSign = extractFloat32Sign( a ); 3054 if ( aExp == 0xFF ) { 3055 if (aSig) { 3056 /* Input is a NaN */ 3057 float16 r = commonNaNToFloat16( float32ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 3058 if (!ieee) { 3059 return packFloat16(aSign, 0, 0); 3060 } 3061 return r; 3062 } 3063 /* Infinity */ 3064 if (!ieee) { 3065 float_raise(float_flag_invalid STATUS_VAR); 3066 return packFloat16(aSign, 0x1f, 0x3ff); 3067 } 3068 return packFloat16(aSign, 0x1f, 0); 3069 } 3070 if (aExp == 0 && aSig == 0) { 3071 return packFloat16(aSign, 0, 0); 3072 } 3073 /* Decimal point between bits 22 and 23. */ 3074 aSig |= 0x00800000; 3075 aExp -= 0x7f; 3076 if (aExp < -14) { 3077 mask = 0x00ffffff; 3078 if (aExp >= -24) { 3079 mask >>= 25 + aExp; 3080 } 3081 } else { 3082 mask = 0x00001fff; 3083 } 3084 if (aSig & mask) { 3085 float_raise( float_flag_underflow STATUS_VAR ); 3086 roundingMode = STATUS(float_rounding_mode); 3087 switch (roundingMode) { 3088 case float_round_nearest_even: 3089 increment = (mask + 1) >> 1; 3090 if ((aSig & mask) == increment) { 3091 increment = aSig & (increment << 1); 3092 } 3093 break; 3094 case float_round_up: 3095 increment = aSign ? 0 : mask; 3096 break; 3097 case float_round_down: 3098 increment = aSign ? mask : 0; 3099 break; 3100 default: /* round_to_zero */ 3101 increment = 0; 3102 break; 3103 } 3104 aSig += increment; 3105 if (aSig >= 0x01000000) { 3106 aSig >>= 1; 3107 aExp++; 3108 } 3109 } else if (aExp < -14 3110 && STATUS(float_detect_tininess) == float_tininess_before_rounding) { 3111 float_raise( float_flag_underflow STATUS_VAR); 3112 } 3113 3114 if (ieee) { 3115 if (aExp > 15) { 3116 float_raise( float_flag_overflow | float_flag_inexact STATUS_VAR); 3117 return packFloat16(aSign, 0x1f, 0); 3118 } 3119 } else { 3120 if (aExp > 16) { 3121 float_raise(float_flag_invalid | float_flag_inexact STATUS_VAR); 3122 return packFloat16(aSign, 0x1f, 0x3ff); 3123 } 3124 } 3125 if (aExp < -24) { 3126 return packFloat16(aSign, 0, 0); 3127 } 3128 if (aExp < -14) { 3129 aSig >>= -14 - aExp; 3130 aExp = -14; 3131 } 3132 return packFloat16(aSign, aExp + 14, aSig >> 13); 3133 } 3134 3135 /*---------------------------------------------------------------------------- 3136 | Returns the result of converting the double-precision floating-point value 3137 | `a' to the extended double-precision floating-point format. The conversion 3138 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 3139 | Arithmetic. 3140 *----------------------------------------------------------------------------*/ 3141 3142 floatx80 float64_to_floatx80( float64 a STATUS_PARAM ) 3143 { 3144 flag aSign; 3145 int_fast16_t aExp; 3146 uint64_t aSig; 3147 3148 a = float64_squash_input_denormal(a STATUS_VAR); 3149 aSig = extractFloat64Frac( a ); 3150 aExp = extractFloat64Exp( a ); 3151 aSign = extractFloat64Sign( a ); 3152 if ( aExp == 0x7FF ) { 3153 if ( aSig ) return commonNaNToFloatx80( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 3154 return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 3155 } 3156 if ( aExp == 0 ) { 3157 if ( aSig == 0 ) return packFloatx80( aSign, 0, 0 ); 3158 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3159 } 3160 return 3161 packFloatx80( 3162 aSign, aExp + 0x3C00, ( aSig | LIT64( 0x0010000000000000 ) )<<11 ); 3163 3164 } 3165 3166 /*---------------------------------------------------------------------------- 3167 | Returns the result of converting the double-precision floating-point value 3168 | `a' to the quadruple-precision floating-point format. The conversion is 3169 | performed according to the IEC/IEEE Standard for Binary Floating-Point 3170 | Arithmetic. 3171 *----------------------------------------------------------------------------*/ 3172 3173 float128 float64_to_float128( float64 a STATUS_PARAM ) 3174 { 3175 flag aSign; 3176 int_fast16_t aExp; 3177 uint64_t aSig, zSig0, zSig1; 3178 3179 a = float64_squash_input_denormal(a STATUS_VAR); 3180 aSig = extractFloat64Frac( a ); 3181 aExp = extractFloat64Exp( a ); 3182 aSign = extractFloat64Sign( a ); 3183 if ( aExp == 0x7FF ) { 3184 if ( aSig ) return commonNaNToFloat128( float64ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 3185 return packFloat128( aSign, 0x7FFF, 0, 0 ); 3186 } 3187 if ( aExp == 0 ) { 3188 if ( aSig == 0 ) return packFloat128( aSign, 0, 0, 0 ); 3189 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3190 --aExp; 3191 } 3192 shift128Right( aSig, 0, 4, &zSig0, &zSig1 ); 3193 return packFloat128( aSign, aExp + 0x3C00, zSig0, zSig1 ); 3194 3195 } 3196 3197 /*---------------------------------------------------------------------------- 3198 | Rounds the double-precision floating-point value `a' to an integer, and 3199 | returns the result as a double-precision floating-point value. The 3200 | operation is performed according to the IEC/IEEE Standard for Binary 3201 | Floating-Point Arithmetic. 3202 *----------------------------------------------------------------------------*/ 3203 3204 float64 float64_round_to_int( float64 a STATUS_PARAM ) 3205 { 3206 flag aSign; 3207 int_fast16_t aExp; 3208 uint64_t lastBitMask, roundBitsMask; 3209 int8 roundingMode; 3210 uint64_t z; 3211 a = float64_squash_input_denormal(a STATUS_VAR); 3212 3213 aExp = extractFloat64Exp( a ); 3214 if ( 0x433 <= aExp ) { 3215 if ( ( aExp == 0x7FF ) && extractFloat64Frac( a ) ) { 3216 return propagateFloat64NaN( a, a STATUS_VAR ); 3217 } 3218 return a; 3219 } 3220 if ( aExp < 0x3FF ) { 3221 if ( (uint64_t) ( float64_val(a)<<1 ) == 0 ) return a; 3222 STATUS(float_exception_flags) |= float_flag_inexact; 3223 aSign = extractFloat64Sign( a ); 3224 switch ( STATUS(float_rounding_mode) ) { 3225 case float_round_nearest_even: 3226 if ( ( aExp == 0x3FE ) && extractFloat64Frac( a ) ) { 3227 return packFloat64( aSign, 0x3FF, 0 ); 3228 } 3229 break; 3230 case float_round_down: 3231 return make_float64(aSign ? LIT64( 0xBFF0000000000000 ) : 0); 3232 case float_round_up: 3233 return make_float64( 3234 aSign ? LIT64( 0x8000000000000000 ) : LIT64( 0x3FF0000000000000 )); 3235 } 3236 return packFloat64( aSign, 0, 0 ); 3237 } 3238 lastBitMask = 1; 3239 lastBitMask <<= 0x433 - aExp; 3240 roundBitsMask = lastBitMask - 1; 3241 z = float64_val(a); 3242 roundingMode = STATUS(float_rounding_mode); 3243 if ( roundingMode == float_round_nearest_even ) { 3244 z += lastBitMask>>1; 3245 if ( ( z & roundBitsMask ) == 0 ) z &= ~ lastBitMask; 3246 } 3247 else if ( roundingMode != float_round_to_zero ) { 3248 if ( extractFloat64Sign( make_float64(z) ) ^ ( roundingMode == float_round_up ) ) { 3249 z += roundBitsMask; 3250 } 3251 } 3252 z &= ~ roundBitsMask; 3253 if ( z != float64_val(a) ) 3254 STATUS(float_exception_flags) |= float_flag_inexact; 3255 return make_float64(z); 3256 3257 } 3258 3259 float64 float64_trunc_to_int( float64 a STATUS_PARAM) 3260 { 3261 int oldmode; 3262 float64 res; 3263 oldmode = STATUS(float_rounding_mode); 3264 STATUS(float_rounding_mode) = float_round_to_zero; 3265 res = float64_round_to_int(a STATUS_VAR); 3266 STATUS(float_rounding_mode) = oldmode; 3267 return res; 3268 } 3269 3270 /*---------------------------------------------------------------------------- 3271 | Returns the result of adding the absolute values of the double-precision 3272 | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated 3273 | before being returned. `zSign' is ignored if the result is a NaN. 3274 | The addition is performed according to the IEC/IEEE Standard for Binary 3275 | Floating-Point Arithmetic. 3276 *----------------------------------------------------------------------------*/ 3277 3278 static float64 addFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) 3279 { 3280 int_fast16_t aExp, bExp, zExp; 3281 uint64_t aSig, bSig, zSig; 3282 int_fast16_t expDiff; 3283 3284 aSig = extractFloat64Frac( a ); 3285 aExp = extractFloat64Exp( a ); 3286 bSig = extractFloat64Frac( b ); 3287 bExp = extractFloat64Exp( b ); 3288 expDiff = aExp - bExp; 3289 aSig <<= 9; 3290 bSig <<= 9; 3291 if ( 0 < expDiff ) { 3292 if ( aExp == 0x7FF ) { 3293 if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3294 return a; 3295 } 3296 if ( bExp == 0 ) { 3297 --expDiff; 3298 } 3299 else { 3300 bSig |= LIT64( 0x2000000000000000 ); 3301 } 3302 shift64RightJamming( bSig, expDiff, &bSig ); 3303 zExp = aExp; 3304 } 3305 else if ( expDiff < 0 ) { 3306 if ( bExp == 0x7FF ) { 3307 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3308 return packFloat64( zSign, 0x7FF, 0 ); 3309 } 3310 if ( aExp == 0 ) { 3311 ++expDiff; 3312 } 3313 else { 3314 aSig |= LIT64( 0x2000000000000000 ); 3315 } 3316 shift64RightJamming( aSig, - expDiff, &aSig ); 3317 zExp = bExp; 3318 } 3319 else { 3320 if ( aExp == 0x7FF ) { 3321 if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3322 return a; 3323 } 3324 if ( aExp == 0 ) { 3325 if (STATUS(flush_to_zero)) { 3326 if (aSig | bSig) { 3327 float_raise(float_flag_output_denormal STATUS_VAR); 3328 } 3329 return packFloat64(zSign, 0, 0); 3330 } 3331 return packFloat64( zSign, 0, ( aSig + bSig )>>9 ); 3332 } 3333 zSig = LIT64( 0x4000000000000000 ) + aSig + bSig; 3334 zExp = aExp; 3335 goto roundAndPack; 3336 } 3337 aSig |= LIT64( 0x2000000000000000 ); 3338 zSig = ( aSig + bSig )<<1; 3339 --zExp; 3340 if ( (int64_t) zSig < 0 ) { 3341 zSig = aSig + bSig; 3342 ++zExp; 3343 } 3344 roundAndPack: 3345 return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); 3346 3347 } 3348 3349 /*---------------------------------------------------------------------------- 3350 | Returns the result of subtracting the absolute values of the double- 3351 | precision floating-point values `a' and `b'. If `zSign' is 1, the 3352 | difference is negated before being returned. `zSign' is ignored if the 3353 | result is a NaN. The subtraction is performed according to the IEC/IEEE 3354 | Standard for Binary Floating-Point Arithmetic. 3355 *----------------------------------------------------------------------------*/ 3356 3357 static float64 subFloat64Sigs( float64 a, float64 b, flag zSign STATUS_PARAM ) 3358 { 3359 int_fast16_t aExp, bExp, zExp; 3360 uint64_t aSig, bSig, zSig; 3361 int_fast16_t expDiff; 3362 3363 aSig = extractFloat64Frac( a ); 3364 aExp = extractFloat64Exp( a ); 3365 bSig = extractFloat64Frac( b ); 3366 bExp = extractFloat64Exp( b ); 3367 expDiff = aExp - bExp; 3368 aSig <<= 10; 3369 bSig <<= 10; 3370 if ( 0 < expDiff ) goto aExpBigger; 3371 if ( expDiff < 0 ) goto bExpBigger; 3372 if ( aExp == 0x7FF ) { 3373 if ( aSig | bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3374 float_raise( float_flag_invalid STATUS_VAR); 3375 return float64_default_nan; 3376 } 3377 if ( aExp == 0 ) { 3378 aExp = 1; 3379 bExp = 1; 3380 } 3381 if ( bSig < aSig ) goto aBigger; 3382 if ( aSig < bSig ) goto bBigger; 3383 return packFloat64( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); 3384 bExpBigger: 3385 if ( bExp == 0x7FF ) { 3386 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3387 return packFloat64( zSign ^ 1, 0x7FF, 0 ); 3388 } 3389 if ( aExp == 0 ) { 3390 ++expDiff; 3391 } 3392 else { 3393 aSig |= LIT64( 0x4000000000000000 ); 3394 } 3395 shift64RightJamming( aSig, - expDiff, &aSig ); 3396 bSig |= LIT64( 0x4000000000000000 ); 3397 bBigger: 3398 zSig = bSig - aSig; 3399 zExp = bExp; 3400 zSign ^= 1; 3401 goto normalizeRoundAndPack; 3402 aExpBigger: 3403 if ( aExp == 0x7FF ) { 3404 if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3405 return a; 3406 } 3407 if ( bExp == 0 ) { 3408 --expDiff; 3409 } 3410 else { 3411 bSig |= LIT64( 0x4000000000000000 ); 3412 } 3413 shift64RightJamming( bSig, expDiff, &bSig ); 3414 aSig |= LIT64( 0x4000000000000000 ); 3415 aBigger: 3416 zSig = aSig - bSig; 3417 zExp = aExp; 3418 normalizeRoundAndPack: 3419 --zExp; 3420 return normalizeRoundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); 3421 3422 } 3423 3424 /*---------------------------------------------------------------------------- 3425 | Returns the result of adding the double-precision floating-point values `a' 3426 | and `b'. The operation is performed according to the IEC/IEEE Standard for 3427 | Binary Floating-Point Arithmetic. 3428 *----------------------------------------------------------------------------*/ 3429 3430 float64 float64_add( float64 a, float64 b STATUS_PARAM ) 3431 { 3432 flag aSign, bSign; 3433 a = float64_squash_input_denormal(a STATUS_VAR); 3434 b = float64_squash_input_denormal(b STATUS_VAR); 3435 3436 aSign = extractFloat64Sign( a ); 3437 bSign = extractFloat64Sign( b ); 3438 if ( aSign == bSign ) { 3439 return addFloat64Sigs( a, b, aSign STATUS_VAR ); 3440 } 3441 else { 3442 return subFloat64Sigs( a, b, aSign STATUS_VAR ); 3443 } 3444 3445 } 3446 3447 /*---------------------------------------------------------------------------- 3448 | Returns the result of subtracting the double-precision floating-point values 3449 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard 3450 | for Binary Floating-Point Arithmetic. 3451 *----------------------------------------------------------------------------*/ 3452 3453 float64 float64_sub( float64 a, float64 b STATUS_PARAM ) 3454 { 3455 flag aSign, bSign; 3456 a = float64_squash_input_denormal(a STATUS_VAR); 3457 b = float64_squash_input_denormal(b STATUS_VAR); 3458 3459 aSign = extractFloat64Sign( a ); 3460 bSign = extractFloat64Sign( b ); 3461 if ( aSign == bSign ) { 3462 return subFloat64Sigs( a, b, aSign STATUS_VAR ); 3463 } 3464 else { 3465 return addFloat64Sigs( a, b, aSign STATUS_VAR ); 3466 } 3467 3468 } 3469 3470 /*---------------------------------------------------------------------------- 3471 | Returns the result of multiplying the double-precision floating-point values 3472 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard 3473 | for Binary Floating-Point Arithmetic. 3474 *----------------------------------------------------------------------------*/ 3475 3476 float64 float64_mul( float64 a, float64 b STATUS_PARAM ) 3477 { 3478 flag aSign, bSign, zSign; 3479 int_fast16_t aExp, bExp, zExp; 3480 uint64_t aSig, bSig, zSig0, zSig1; 3481 3482 a = float64_squash_input_denormal(a STATUS_VAR); 3483 b = float64_squash_input_denormal(b STATUS_VAR); 3484 3485 aSig = extractFloat64Frac( a ); 3486 aExp = extractFloat64Exp( a ); 3487 aSign = extractFloat64Sign( a ); 3488 bSig = extractFloat64Frac( b ); 3489 bExp = extractFloat64Exp( b ); 3490 bSign = extractFloat64Sign( b ); 3491 zSign = aSign ^ bSign; 3492 if ( aExp == 0x7FF ) { 3493 if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { 3494 return propagateFloat64NaN( a, b STATUS_VAR ); 3495 } 3496 if ( ( bExp | bSig ) == 0 ) { 3497 float_raise( float_flag_invalid STATUS_VAR); 3498 return float64_default_nan; 3499 } 3500 return packFloat64( zSign, 0x7FF, 0 ); 3501 } 3502 if ( bExp == 0x7FF ) { 3503 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3504 if ( ( aExp | aSig ) == 0 ) { 3505 float_raise( float_flag_invalid STATUS_VAR); 3506 return float64_default_nan; 3507 } 3508 return packFloat64( zSign, 0x7FF, 0 ); 3509 } 3510 if ( aExp == 0 ) { 3511 if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); 3512 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3513 } 3514 if ( bExp == 0 ) { 3515 if ( bSig == 0 ) return packFloat64( zSign, 0, 0 ); 3516 normalizeFloat64Subnormal( bSig, &bExp, &bSig ); 3517 } 3518 zExp = aExp + bExp - 0x3FF; 3519 aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; 3520 bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; 3521 mul64To128( aSig, bSig, &zSig0, &zSig1 ); 3522 zSig0 |= ( zSig1 != 0 ); 3523 if ( 0 <= (int64_t) ( zSig0<<1 ) ) { 3524 zSig0 <<= 1; 3525 --zExp; 3526 } 3527 return roundAndPackFloat64( zSign, zExp, zSig0 STATUS_VAR ); 3528 3529 } 3530 3531 /*---------------------------------------------------------------------------- 3532 | Returns the result of dividing the double-precision floating-point value `a' 3533 | by the corresponding value `b'. The operation is performed according to 3534 | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 3535 *----------------------------------------------------------------------------*/ 3536 3537 float64 float64_div( float64 a, float64 b STATUS_PARAM ) 3538 { 3539 flag aSign, bSign, zSign; 3540 int_fast16_t aExp, bExp, zExp; 3541 uint64_t aSig, bSig, zSig; 3542 uint64_t rem0, rem1; 3543 uint64_t term0, term1; 3544 a = float64_squash_input_denormal(a STATUS_VAR); 3545 b = float64_squash_input_denormal(b STATUS_VAR); 3546 3547 aSig = extractFloat64Frac( a ); 3548 aExp = extractFloat64Exp( a ); 3549 aSign = extractFloat64Sign( a ); 3550 bSig = extractFloat64Frac( b ); 3551 bExp = extractFloat64Exp( b ); 3552 bSign = extractFloat64Sign( b ); 3553 zSign = aSign ^ bSign; 3554 if ( aExp == 0x7FF ) { 3555 if ( aSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3556 if ( bExp == 0x7FF ) { 3557 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3558 float_raise( float_flag_invalid STATUS_VAR); 3559 return float64_default_nan; 3560 } 3561 return packFloat64( zSign, 0x7FF, 0 ); 3562 } 3563 if ( bExp == 0x7FF ) { 3564 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3565 return packFloat64( zSign, 0, 0 ); 3566 } 3567 if ( bExp == 0 ) { 3568 if ( bSig == 0 ) { 3569 if ( ( aExp | aSig ) == 0 ) { 3570 float_raise( float_flag_invalid STATUS_VAR); 3571 return float64_default_nan; 3572 } 3573 float_raise( float_flag_divbyzero STATUS_VAR); 3574 return packFloat64( zSign, 0x7FF, 0 ); 3575 } 3576 normalizeFloat64Subnormal( bSig, &bExp, &bSig ); 3577 } 3578 if ( aExp == 0 ) { 3579 if ( aSig == 0 ) return packFloat64( zSign, 0, 0 ); 3580 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3581 } 3582 zExp = aExp - bExp + 0x3FD; 3583 aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<10; 3584 bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; 3585 if ( bSig <= ( aSig + aSig ) ) { 3586 aSig >>= 1; 3587 ++zExp; 3588 } 3589 zSig = estimateDiv128To64( aSig, 0, bSig ); 3590 if ( ( zSig & 0x1FF ) <= 2 ) { 3591 mul64To128( bSig, zSig, &term0, &term1 ); 3592 sub128( aSig, 0, term0, term1, &rem0, &rem1 ); 3593 while ( (int64_t) rem0 < 0 ) { 3594 --zSig; 3595 add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); 3596 } 3597 zSig |= ( rem1 != 0 ); 3598 } 3599 return roundAndPackFloat64( zSign, zExp, zSig STATUS_VAR ); 3600 3601 } 3602 3603 /*---------------------------------------------------------------------------- 3604 | Returns the remainder of the double-precision floating-point value `a' 3605 | with respect to the corresponding value `b'. The operation is performed 3606 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 3607 *----------------------------------------------------------------------------*/ 3608 3609 float64 float64_rem( float64 a, float64 b STATUS_PARAM ) 3610 { 3611 flag aSign, zSign; 3612 int_fast16_t aExp, bExp, expDiff; 3613 uint64_t aSig, bSig; 3614 uint64_t q, alternateASig; 3615 int64_t sigMean; 3616 3617 a = float64_squash_input_denormal(a STATUS_VAR); 3618 b = float64_squash_input_denormal(b STATUS_VAR); 3619 aSig = extractFloat64Frac( a ); 3620 aExp = extractFloat64Exp( a ); 3621 aSign = extractFloat64Sign( a ); 3622 bSig = extractFloat64Frac( b ); 3623 bExp = extractFloat64Exp( b ); 3624 if ( aExp == 0x7FF ) { 3625 if ( aSig || ( ( bExp == 0x7FF ) && bSig ) ) { 3626 return propagateFloat64NaN( a, b STATUS_VAR ); 3627 } 3628 float_raise( float_flag_invalid STATUS_VAR); 3629 return float64_default_nan; 3630 } 3631 if ( bExp == 0x7FF ) { 3632 if ( bSig ) return propagateFloat64NaN( a, b STATUS_VAR ); 3633 return a; 3634 } 3635 if ( bExp == 0 ) { 3636 if ( bSig == 0 ) { 3637 float_raise( float_flag_invalid STATUS_VAR); 3638 return float64_default_nan; 3639 } 3640 normalizeFloat64Subnormal( bSig, &bExp, &bSig ); 3641 } 3642 if ( aExp == 0 ) { 3643 if ( aSig == 0 ) return a; 3644 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3645 } 3646 expDiff = aExp - bExp; 3647 aSig = ( aSig | LIT64( 0x0010000000000000 ) )<<11; 3648 bSig = ( bSig | LIT64( 0x0010000000000000 ) )<<11; 3649 if ( expDiff < 0 ) { 3650 if ( expDiff < -1 ) return a; 3651 aSig >>= 1; 3652 } 3653 q = ( bSig <= aSig ); 3654 if ( q ) aSig -= bSig; 3655 expDiff -= 64; 3656 while ( 0 < expDiff ) { 3657 q = estimateDiv128To64( aSig, 0, bSig ); 3658 q = ( 2 < q ) ? q - 2 : 0; 3659 aSig = - ( ( bSig>>2 ) * q ); 3660 expDiff -= 62; 3661 } 3662 expDiff += 64; 3663 if ( 0 < expDiff ) { 3664 q = estimateDiv128To64( aSig, 0, bSig ); 3665 q = ( 2 < q ) ? q - 2 : 0; 3666 q >>= 64 - expDiff; 3667 bSig >>= 2; 3668 aSig = ( ( aSig>>1 )<<( expDiff - 1 ) ) - bSig * q; 3669 } 3670 else { 3671 aSig >>= 2; 3672 bSig >>= 2; 3673 } 3674 do { 3675 alternateASig = aSig; 3676 ++q; 3677 aSig -= bSig; 3678 } while ( 0 <= (int64_t) aSig ); 3679 sigMean = aSig + alternateASig; 3680 if ( ( sigMean < 0 ) || ( ( sigMean == 0 ) && ( q & 1 ) ) ) { 3681 aSig = alternateASig; 3682 } 3683 zSign = ( (int64_t) aSig < 0 ); 3684 if ( zSign ) aSig = - aSig; 3685 return normalizeRoundAndPackFloat64( aSign ^ zSign, bExp, aSig STATUS_VAR ); 3686 3687 } 3688 3689 /*---------------------------------------------------------------------------- 3690 | Returns the result of multiplying the double-precision floating-point values 3691 | `a' and `b' then adding 'c', with no intermediate rounding step after the 3692 | multiplication. The operation is performed according to the IEC/IEEE 3693 | Standard for Binary Floating-Point Arithmetic 754-2008. 3694 | The flags argument allows the caller to select negation of the 3695 | addend, the intermediate product, or the final result. (The difference 3696 | between this and having the caller do a separate negation is that negating 3697 | externally will flip the sign bit on NaNs.) 3698 *----------------------------------------------------------------------------*/ 3699 3700 float64 float64_muladd(float64 a, float64 b, float64 c, int flags STATUS_PARAM) 3701 { 3702 flag aSign, bSign, cSign, zSign; 3703 int_fast16_t aExp, bExp, cExp, pExp, zExp, expDiff; 3704 uint64_t aSig, bSig, cSig; 3705 flag pInf, pZero, pSign; 3706 uint64_t pSig0, pSig1, cSig0, cSig1, zSig0, zSig1; 3707 int shiftcount; 3708 flag signflip, infzero; 3709 3710 a = float64_squash_input_denormal(a STATUS_VAR); 3711 b = float64_squash_input_denormal(b STATUS_VAR); 3712 c = float64_squash_input_denormal(c STATUS_VAR); 3713 aSig = extractFloat64Frac(a); 3714 aExp = extractFloat64Exp(a); 3715 aSign = extractFloat64Sign(a); 3716 bSig = extractFloat64Frac(b); 3717 bExp = extractFloat64Exp(b); 3718 bSign = extractFloat64Sign(b); 3719 cSig = extractFloat64Frac(c); 3720 cExp = extractFloat64Exp(c); 3721 cSign = extractFloat64Sign(c); 3722 3723 infzero = ((aExp == 0 && aSig == 0 && bExp == 0x7ff && bSig == 0) || 3724 (aExp == 0x7ff && aSig == 0 && bExp == 0 && bSig == 0)); 3725 3726 /* It is implementation-defined whether the cases of (0,inf,qnan) 3727 * and (inf,0,qnan) raise InvalidOperation or not (and what QNaN 3728 * they return if they do), so we have to hand this information 3729 * off to the target-specific pick-a-NaN routine. 3730 */ 3731 if (((aExp == 0x7ff) && aSig) || 3732 ((bExp == 0x7ff) && bSig) || 3733 ((cExp == 0x7ff) && cSig)) { 3734 return propagateFloat64MulAddNaN(a, b, c, infzero STATUS_VAR); 3735 } 3736 3737 if (infzero) { 3738 float_raise(float_flag_invalid STATUS_VAR); 3739 return float64_default_nan; 3740 } 3741 3742 if (flags & float_muladd_negate_c) { 3743 cSign ^= 1; 3744 } 3745 3746 signflip = (flags & float_muladd_negate_result) ? 1 : 0; 3747 3748 /* Work out the sign and type of the product */ 3749 pSign = aSign ^ bSign; 3750 if (flags & float_muladd_negate_product) { 3751 pSign ^= 1; 3752 } 3753 pInf = (aExp == 0x7ff) || (bExp == 0x7ff); 3754 pZero = ((aExp | aSig) == 0) || ((bExp | bSig) == 0); 3755 3756 if (cExp == 0x7ff) { 3757 if (pInf && (pSign ^ cSign)) { 3758 /* addition of opposite-signed infinities => InvalidOperation */ 3759 float_raise(float_flag_invalid STATUS_VAR); 3760 return float64_default_nan; 3761 } 3762 /* Otherwise generate an infinity of the same sign */ 3763 return packFloat64(cSign ^ signflip, 0x7ff, 0); 3764 } 3765 3766 if (pInf) { 3767 return packFloat64(pSign ^ signflip, 0x7ff, 0); 3768 } 3769 3770 if (pZero) { 3771 if (cExp == 0) { 3772 if (cSig == 0) { 3773 /* Adding two exact zeroes */ 3774 if (pSign == cSign) { 3775 zSign = pSign; 3776 } else if (STATUS(float_rounding_mode) == float_round_down) { 3777 zSign = 1; 3778 } else { 3779 zSign = 0; 3780 } 3781 return packFloat64(zSign ^ signflip, 0, 0); 3782 } 3783 /* Exact zero plus a denorm */ 3784 if (STATUS(flush_to_zero)) { 3785 float_raise(float_flag_output_denormal STATUS_VAR); 3786 return packFloat64(cSign ^ signflip, 0, 0); 3787 } 3788 } 3789 /* Zero plus something non-zero : just return the something */ 3790 return packFloat64(cSign ^ signflip, cExp, cSig); 3791 } 3792 3793 if (aExp == 0) { 3794 normalizeFloat64Subnormal(aSig, &aExp, &aSig); 3795 } 3796 if (bExp == 0) { 3797 normalizeFloat64Subnormal(bSig, &bExp, &bSig); 3798 } 3799 3800 /* Calculate the actual result a * b + c */ 3801 3802 /* Multiply first; this is easy. */ 3803 /* NB: we subtract 0x3fe where float64_mul() subtracts 0x3ff 3804 * because we want the true exponent, not the "one-less-than" 3805 * flavour that roundAndPackFloat64() takes. 3806 */ 3807 pExp = aExp + bExp - 0x3fe; 3808 aSig = (aSig | LIT64(0x0010000000000000))<<10; 3809 bSig = (bSig | LIT64(0x0010000000000000))<<11; 3810 mul64To128(aSig, bSig, &pSig0, &pSig1); 3811 if ((int64_t)(pSig0 << 1) >= 0) { 3812 shortShift128Left(pSig0, pSig1, 1, &pSig0, &pSig1); 3813 pExp--; 3814 } 3815 3816 zSign = pSign ^ signflip; 3817 3818 /* Now [pSig0:pSig1] is the significand of the multiply, with the explicit 3819 * bit in position 126. 3820 */ 3821 if (cExp == 0) { 3822 if (!cSig) { 3823 /* Throw out the special case of c being an exact zero now */ 3824 shift128RightJamming(pSig0, pSig1, 64, &pSig0, &pSig1); 3825 return roundAndPackFloat64(zSign, pExp - 1, 3826 pSig1 STATUS_VAR); 3827 } 3828 normalizeFloat64Subnormal(cSig, &cExp, &cSig); 3829 } 3830 3831 /* Shift cSig and add the explicit bit so [cSig0:cSig1] is the 3832 * significand of the addend, with the explicit bit in position 126. 3833 */ 3834 cSig0 = cSig << (126 - 64 - 52); 3835 cSig1 = 0; 3836 cSig0 |= LIT64(0x4000000000000000); 3837 expDiff = pExp - cExp; 3838 3839 if (pSign == cSign) { 3840 /* Addition */ 3841 if (expDiff > 0) { 3842 /* scale c to match p */ 3843 shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); 3844 zExp = pExp; 3845 } else if (expDiff < 0) { 3846 /* scale p to match c */ 3847 shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); 3848 zExp = cExp; 3849 } else { 3850 /* no scaling needed */ 3851 zExp = cExp; 3852 } 3853 /* Add significands and make sure explicit bit ends up in posn 126 */ 3854 add128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); 3855 if ((int64_t)zSig0 < 0) { 3856 shift128RightJamming(zSig0, zSig1, 1, &zSig0, &zSig1); 3857 } else { 3858 zExp--; 3859 } 3860 shift128RightJamming(zSig0, zSig1, 64, &zSig0, &zSig1); 3861 return roundAndPackFloat64(zSign, zExp, zSig1 STATUS_VAR); 3862 } else { 3863 /* Subtraction */ 3864 if (expDiff > 0) { 3865 shift128RightJamming(cSig0, cSig1, expDiff, &cSig0, &cSig1); 3866 sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); 3867 zExp = pExp; 3868 } else if (expDiff < 0) { 3869 shift128RightJamming(pSig0, pSig1, -expDiff, &pSig0, &pSig1); 3870 sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); 3871 zExp = cExp; 3872 zSign ^= 1; 3873 } else { 3874 zExp = pExp; 3875 if (lt128(cSig0, cSig1, pSig0, pSig1)) { 3876 sub128(pSig0, pSig1, cSig0, cSig1, &zSig0, &zSig1); 3877 } else if (lt128(pSig0, pSig1, cSig0, cSig1)) { 3878 sub128(cSig0, cSig1, pSig0, pSig1, &zSig0, &zSig1); 3879 zSign ^= 1; 3880 } else { 3881 /* Exact zero */ 3882 zSign = signflip; 3883 if (STATUS(float_rounding_mode) == float_round_down) { 3884 zSign ^= 1; 3885 } 3886 return packFloat64(zSign, 0, 0); 3887 } 3888 } 3889 --zExp; 3890 /* Do the equivalent of normalizeRoundAndPackFloat64() but 3891 * starting with the significand in a pair of uint64_t. 3892 */ 3893 if (zSig0) { 3894 shiftcount = countLeadingZeros64(zSig0) - 1; 3895 shortShift128Left(zSig0, zSig1, shiftcount, &zSig0, &zSig1); 3896 if (zSig1) { 3897 zSig0 |= 1; 3898 } 3899 zExp -= shiftcount; 3900 } else { 3901 shiftcount = countLeadingZeros64(zSig1) - 1; 3902 zSig0 = zSig1 << shiftcount; 3903 zExp -= (shiftcount + 64); 3904 } 3905 return roundAndPackFloat64(zSign, zExp, zSig0 STATUS_VAR); 3906 } 3907 } 3908 3909 /*---------------------------------------------------------------------------- 3910 | Returns the square root of the double-precision floating-point value `a'. 3911 | The operation is performed according to the IEC/IEEE Standard for Binary 3912 | Floating-Point Arithmetic. 3913 *----------------------------------------------------------------------------*/ 3914 3915 float64 float64_sqrt( float64 a STATUS_PARAM ) 3916 { 3917 flag aSign; 3918 int_fast16_t aExp, zExp; 3919 uint64_t aSig, zSig, doubleZSig; 3920 uint64_t rem0, rem1, term0, term1; 3921 a = float64_squash_input_denormal(a STATUS_VAR); 3922 3923 aSig = extractFloat64Frac( a ); 3924 aExp = extractFloat64Exp( a ); 3925 aSign = extractFloat64Sign( a ); 3926 if ( aExp == 0x7FF ) { 3927 if ( aSig ) return propagateFloat64NaN( a, a STATUS_VAR ); 3928 if ( ! aSign ) return a; 3929 float_raise( float_flag_invalid STATUS_VAR); 3930 return float64_default_nan; 3931 } 3932 if ( aSign ) { 3933 if ( ( aExp | aSig ) == 0 ) return a; 3934 float_raise( float_flag_invalid STATUS_VAR); 3935 return float64_default_nan; 3936 } 3937 if ( aExp == 0 ) { 3938 if ( aSig == 0 ) return float64_zero; 3939 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3940 } 3941 zExp = ( ( aExp - 0x3FF )>>1 ) + 0x3FE; 3942 aSig |= LIT64( 0x0010000000000000 ); 3943 zSig = estimateSqrt32( aExp, aSig>>21 ); 3944 aSig <<= 9 - ( aExp & 1 ); 3945 zSig = estimateDiv128To64( aSig, 0, zSig<<32 ) + ( zSig<<30 ); 3946 if ( ( zSig & 0x1FF ) <= 5 ) { 3947 doubleZSig = zSig<<1; 3948 mul64To128( zSig, zSig, &term0, &term1 ); 3949 sub128( aSig, 0, term0, term1, &rem0, &rem1 ); 3950 while ( (int64_t) rem0 < 0 ) { 3951 --zSig; 3952 doubleZSig -= 2; 3953 add128( rem0, rem1, zSig>>63, doubleZSig | 1, &rem0, &rem1 ); 3954 } 3955 zSig |= ( ( rem0 | rem1 ) != 0 ); 3956 } 3957 return roundAndPackFloat64( 0, zExp, zSig STATUS_VAR ); 3958 3959 } 3960 3961 /*---------------------------------------------------------------------------- 3962 | Returns the binary log of the double-precision floating-point value `a'. 3963 | The operation is performed according to the IEC/IEEE Standard for Binary 3964 | Floating-Point Arithmetic. 3965 *----------------------------------------------------------------------------*/ 3966 float64 float64_log2( float64 a STATUS_PARAM ) 3967 { 3968 flag aSign, zSign; 3969 int_fast16_t aExp; 3970 uint64_t aSig, aSig0, aSig1, zSig, i; 3971 a = float64_squash_input_denormal(a STATUS_VAR); 3972 3973 aSig = extractFloat64Frac( a ); 3974 aExp = extractFloat64Exp( a ); 3975 aSign = extractFloat64Sign( a ); 3976 3977 if ( aExp == 0 ) { 3978 if ( aSig == 0 ) return packFloat64( 1, 0x7FF, 0 ); 3979 normalizeFloat64Subnormal( aSig, &aExp, &aSig ); 3980 } 3981 if ( aSign ) { 3982 float_raise( float_flag_invalid STATUS_VAR); 3983 return float64_default_nan; 3984 } 3985 if ( aExp == 0x7FF ) { 3986 if ( aSig ) return propagateFloat64NaN( a, float64_zero STATUS_VAR ); 3987 return a; 3988 } 3989 3990 aExp -= 0x3FF; 3991 aSig |= LIT64( 0x0010000000000000 ); 3992 zSign = aExp < 0; 3993 zSig = (uint64_t)aExp << 52; 3994 for (i = 1LL << 51; i > 0; i >>= 1) { 3995 mul64To128( aSig, aSig, &aSig0, &aSig1 ); 3996 aSig = ( aSig0 << 12 ) | ( aSig1 >> 52 ); 3997 if ( aSig & LIT64( 0x0020000000000000 ) ) { 3998 aSig >>= 1; 3999 zSig |= i; 4000 } 4001 } 4002 4003 if ( zSign ) 4004 zSig = -zSig; 4005 return normalizeRoundAndPackFloat64( zSign, 0x408, zSig STATUS_VAR ); 4006 } 4007 4008 /*---------------------------------------------------------------------------- 4009 | Returns 1 if the double-precision floating-point value `a' is equal to the 4010 | corresponding value `b', and 0 otherwise. The invalid exception is raised 4011 | if either operand is a NaN. Otherwise, the comparison is performed 4012 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4013 *----------------------------------------------------------------------------*/ 4014 4015 int float64_eq( float64 a, float64 b STATUS_PARAM ) 4016 { 4017 uint64_t av, bv; 4018 a = float64_squash_input_denormal(a STATUS_VAR); 4019 b = float64_squash_input_denormal(b STATUS_VAR); 4020 4021 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4022 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4023 ) { 4024 float_raise( float_flag_invalid STATUS_VAR); 4025 return 0; 4026 } 4027 av = float64_val(a); 4028 bv = float64_val(b); 4029 return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); 4030 4031 } 4032 4033 /*---------------------------------------------------------------------------- 4034 | Returns 1 if the double-precision floating-point value `a' is less than or 4035 | equal to the corresponding value `b', and 0 otherwise. The invalid 4036 | exception is raised if either operand is a NaN. The comparison is performed 4037 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4038 *----------------------------------------------------------------------------*/ 4039 4040 int float64_le( float64 a, float64 b STATUS_PARAM ) 4041 { 4042 flag aSign, bSign; 4043 uint64_t av, bv; 4044 a = float64_squash_input_denormal(a STATUS_VAR); 4045 b = float64_squash_input_denormal(b STATUS_VAR); 4046 4047 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4048 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4049 ) { 4050 float_raise( float_flag_invalid STATUS_VAR); 4051 return 0; 4052 } 4053 aSign = extractFloat64Sign( a ); 4054 bSign = extractFloat64Sign( b ); 4055 av = float64_val(a); 4056 bv = float64_val(b); 4057 if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); 4058 return ( av == bv ) || ( aSign ^ ( av < bv ) ); 4059 4060 } 4061 4062 /*---------------------------------------------------------------------------- 4063 | Returns 1 if the double-precision floating-point value `a' is less than 4064 | the corresponding value `b', and 0 otherwise. The invalid exception is 4065 | raised if either operand is a NaN. The comparison is performed according 4066 | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4067 *----------------------------------------------------------------------------*/ 4068 4069 int float64_lt( float64 a, float64 b STATUS_PARAM ) 4070 { 4071 flag aSign, bSign; 4072 uint64_t av, bv; 4073 4074 a = float64_squash_input_denormal(a STATUS_VAR); 4075 b = float64_squash_input_denormal(b STATUS_VAR); 4076 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4077 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4078 ) { 4079 float_raise( float_flag_invalid STATUS_VAR); 4080 return 0; 4081 } 4082 aSign = extractFloat64Sign( a ); 4083 bSign = extractFloat64Sign( b ); 4084 av = float64_val(a); 4085 bv = float64_val(b); 4086 if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); 4087 return ( av != bv ) && ( aSign ^ ( av < bv ) ); 4088 4089 } 4090 4091 /*---------------------------------------------------------------------------- 4092 | Returns 1 if the double-precision floating-point values `a' and `b' cannot 4093 | be compared, and 0 otherwise. The invalid exception is raised if either 4094 | operand is a NaN. The comparison is performed according to the IEC/IEEE 4095 | Standard for Binary Floating-Point Arithmetic. 4096 *----------------------------------------------------------------------------*/ 4097 4098 int float64_unordered( float64 a, float64 b STATUS_PARAM ) 4099 { 4100 a = float64_squash_input_denormal(a STATUS_VAR); 4101 b = float64_squash_input_denormal(b STATUS_VAR); 4102 4103 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4104 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4105 ) { 4106 float_raise( float_flag_invalid STATUS_VAR); 4107 return 1; 4108 } 4109 return 0; 4110 } 4111 4112 /*---------------------------------------------------------------------------- 4113 | Returns 1 if the double-precision floating-point value `a' is equal to the 4114 | corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 4115 | exception.The comparison is performed according to the IEC/IEEE Standard 4116 | for Binary Floating-Point Arithmetic. 4117 *----------------------------------------------------------------------------*/ 4118 4119 int float64_eq_quiet( float64 a, float64 b STATUS_PARAM ) 4120 { 4121 uint64_t av, bv; 4122 a = float64_squash_input_denormal(a STATUS_VAR); 4123 b = float64_squash_input_denormal(b STATUS_VAR); 4124 4125 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4126 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4127 ) { 4128 if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { 4129 float_raise( float_flag_invalid STATUS_VAR); 4130 } 4131 return 0; 4132 } 4133 av = float64_val(a); 4134 bv = float64_val(b); 4135 return ( av == bv ) || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); 4136 4137 } 4138 4139 /*---------------------------------------------------------------------------- 4140 | Returns 1 if the double-precision floating-point value `a' is less than or 4141 | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not 4142 | cause an exception. Otherwise, the comparison is performed according to the 4143 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4144 *----------------------------------------------------------------------------*/ 4145 4146 int float64_le_quiet( float64 a, float64 b STATUS_PARAM ) 4147 { 4148 flag aSign, bSign; 4149 uint64_t av, bv; 4150 a = float64_squash_input_denormal(a STATUS_VAR); 4151 b = float64_squash_input_denormal(b STATUS_VAR); 4152 4153 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4154 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4155 ) { 4156 if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { 4157 float_raise( float_flag_invalid STATUS_VAR); 4158 } 4159 return 0; 4160 } 4161 aSign = extractFloat64Sign( a ); 4162 bSign = extractFloat64Sign( b ); 4163 av = float64_val(a); 4164 bv = float64_val(b); 4165 if ( aSign != bSign ) return aSign || ( (uint64_t) ( ( av | bv )<<1 ) == 0 ); 4166 return ( av == bv ) || ( aSign ^ ( av < bv ) ); 4167 4168 } 4169 4170 /*---------------------------------------------------------------------------- 4171 | Returns 1 if the double-precision floating-point value `a' is less than 4172 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 4173 | exception. Otherwise, the comparison is performed according to the IEC/IEEE 4174 | Standard for Binary Floating-Point Arithmetic. 4175 *----------------------------------------------------------------------------*/ 4176 4177 int float64_lt_quiet( float64 a, float64 b STATUS_PARAM ) 4178 { 4179 flag aSign, bSign; 4180 uint64_t av, bv; 4181 a = float64_squash_input_denormal(a STATUS_VAR); 4182 b = float64_squash_input_denormal(b STATUS_VAR); 4183 4184 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4185 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4186 ) { 4187 if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { 4188 float_raise( float_flag_invalid STATUS_VAR); 4189 } 4190 return 0; 4191 } 4192 aSign = extractFloat64Sign( a ); 4193 bSign = extractFloat64Sign( b ); 4194 av = float64_val(a); 4195 bv = float64_val(b); 4196 if ( aSign != bSign ) return aSign && ( (uint64_t) ( ( av | bv )<<1 ) != 0 ); 4197 return ( av != bv ) && ( aSign ^ ( av < bv ) ); 4198 4199 } 4200 4201 /*---------------------------------------------------------------------------- 4202 | Returns 1 if the double-precision floating-point values `a' and `b' cannot 4203 | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The 4204 | comparison is performed according to the IEC/IEEE Standard for Binary 4205 | Floating-Point Arithmetic. 4206 *----------------------------------------------------------------------------*/ 4207 4208 int float64_unordered_quiet( float64 a, float64 b STATUS_PARAM ) 4209 { 4210 a = float64_squash_input_denormal(a STATUS_VAR); 4211 b = float64_squash_input_denormal(b STATUS_VAR); 4212 4213 if ( ( ( extractFloat64Exp( a ) == 0x7FF ) && extractFloat64Frac( a ) ) 4214 || ( ( extractFloat64Exp( b ) == 0x7FF ) && extractFloat64Frac( b ) ) 4215 ) { 4216 if ( float64_is_signaling_nan( a ) || float64_is_signaling_nan( b ) ) { 4217 float_raise( float_flag_invalid STATUS_VAR); 4218 } 4219 return 1; 4220 } 4221 return 0; 4222 } 4223 4224 /*---------------------------------------------------------------------------- 4225 | Returns the result of converting the extended double-precision floating- 4226 | point value `a' to the 32-bit two's complement integer format. The 4227 | conversion is performed according to the IEC/IEEE Standard for Binary 4228 | Floating-Point Arithmetic---which means in particular that the conversion 4229 | is rounded according to the current rounding mode. If `a' is a NaN, the 4230 | largest positive integer is returned. Otherwise, if the conversion 4231 | overflows, the largest integer with the same sign as `a' is returned. 4232 *----------------------------------------------------------------------------*/ 4233 4234 int32 floatx80_to_int32( floatx80 a STATUS_PARAM ) 4235 { 4236 flag aSign; 4237 int32 aExp, shiftCount; 4238 uint64_t aSig; 4239 4240 aSig = extractFloatx80Frac( a ); 4241 aExp = extractFloatx80Exp( a ); 4242 aSign = extractFloatx80Sign( a ); 4243 if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; 4244 shiftCount = 0x4037 - aExp; 4245 if ( shiftCount <= 0 ) shiftCount = 1; 4246 shift64RightJamming( aSig, shiftCount, &aSig ); 4247 return roundAndPackInt32( aSign, aSig STATUS_VAR ); 4248 4249 } 4250 4251 /*---------------------------------------------------------------------------- 4252 | Returns the result of converting the extended double-precision floating- 4253 | point value `a' to the 32-bit two's complement integer format. The 4254 | conversion is performed according to the IEC/IEEE Standard for Binary 4255 | Floating-Point Arithmetic, except that the conversion is always rounded 4256 | toward zero. If `a' is a NaN, the largest positive integer is returned. 4257 | Otherwise, if the conversion overflows, the largest integer with the same 4258 | sign as `a' is returned. 4259 *----------------------------------------------------------------------------*/ 4260 4261 int32 floatx80_to_int32_round_to_zero( floatx80 a STATUS_PARAM ) 4262 { 4263 flag aSign; 4264 int32 aExp, shiftCount; 4265 uint64_t aSig, savedASig; 4266 int32_t z; 4267 4268 aSig = extractFloatx80Frac( a ); 4269 aExp = extractFloatx80Exp( a ); 4270 aSign = extractFloatx80Sign( a ); 4271 if ( 0x401E < aExp ) { 4272 if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) aSign = 0; 4273 goto invalid; 4274 } 4275 else if ( aExp < 0x3FFF ) { 4276 if ( aExp || aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 4277 return 0; 4278 } 4279 shiftCount = 0x403E - aExp; 4280 savedASig = aSig; 4281 aSig >>= shiftCount; 4282 z = aSig; 4283 if ( aSign ) z = - z; 4284 if ( ( z < 0 ) ^ aSign ) { 4285 invalid: 4286 float_raise( float_flag_invalid STATUS_VAR); 4287 return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; 4288 } 4289 if ( ( aSig<<shiftCount ) != savedASig ) { 4290 STATUS(float_exception_flags) |= float_flag_inexact; 4291 } 4292 return z; 4293 4294 } 4295 4296 /*---------------------------------------------------------------------------- 4297 | Returns the result of converting the extended double-precision floating- 4298 | point value `a' to the 64-bit two's complement integer format. The 4299 | conversion is performed according to the IEC/IEEE Standard for Binary 4300 | Floating-Point Arithmetic---which means in particular that the conversion 4301 | is rounded according to the current rounding mode. If `a' is a NaN, 4302 | the largest positive integer is returned. Otherwise, if the conversion 4303 | overflows, the largest integer with the same sign as `a' is returned. 4304 *----------------------------------------------------------------------------*/ 4305 4306 int64 floatx80_to_int64( floatx80 a STATUS_PARAM ) 4307 { 4308 flag aSign; 4309 int32 aExp, shiftCount; 4310 uint64_t aSig, aSigExtra; 4311 4312 aSig = extractFloatx80Frac( a ); 4313 aExp = extractFloatx80Exp( a ); 4314 aSign = extractFloatx80Sign( a ); 4315 shiftCount = 0x403E - aExp; 4316 if ( shiftCount <= 0 ) { 4317 if ( shiftCount ) { 4318 float_raise( float_flag_invalid STATUS_VAR); 4319 if ( ! aSign 4320 || ( ( aExp == 0x7FFF ) 4321 && ( aSig != LIT64( 0x8000000000000000 ) ) ) 4322 ) { 4323 return LIT64( 0x7FFFFFFFFFFFFFFF ); 4324 } 4325 return (int64_t) LIT64( 0x8000000000000000 ); 4326 } 4327 aSigExtra = 0; 4328 } 4329 else { 4330 shift64ExtraRightJamming( aSig, 0, shiftCount, &aSig, &aSigExtra ); 4331 } 4332 return roundAndPackInt64( aSign, aSig, aSigExtra STATUS_VAR ); 4333 4334 } 4335 4336 /*---------------------------------------------------------------------------- 4337 | Returns the result of converting the extended double-precision floating- 4338 | point value `a' to the 64-bit two's complement integer format. The 4339 | conversion is performed according to the IEC/IEEE Standard for Binary 4340 | Floating-Point Arithmetic, except that the conversion is always rounded 4341 | toward zero. If `a' is a NaN, the largest positive integer is returned. 4342 | Otherwise, if the conversion overflows, the largest integer with the same 4343 | sign as `a' is returned. 4344 *----------------------------------------------------------------------------*/ 4345 4346 int64 floatx80_to_int64_round_to_zero( floatx80 a STATUS_PARAM ) 4347 { 4348 flag aSign; 4349 int32 aExp, shiftCount; 4350 uint64_t aSig; 4351 int64 z; 4352 4353 aSig = extractFloatx80Frac( a ); 4354 aExp = extractFloatx80Exp( a ); 4355 aSign = extractFloatx80Sign( a ); 4356 shiftCount = aExp - 0x403E; 4357 if ( 0 <= shiftCount ) { 4358 aSig &= LIT64( 0x7FFFFFFFFFFFFFFF ); 4359 if ( ( a.high != 0xC03E ) || aSig ) { 4360 float_raise( float_flag_invalid STATUS_VAR); 4361 if ( ! aSign || ( ( aExp == 0x7FFF ) && aSig ) ) { 4362 return LIT64( 0x7FFFFFFFFFFFFFFF ); 4363 } 4364 } 4365 return (int64_t) LIT64( 0x8000000000000000 ); 4366 } 4367 else if ( aExp < 0x3FFF ) { 4368 if ( aExp | aSig ) STATUS(float_exception_flags) |= float_flag_inexact; 4369 return 0; 4370 } 4371 z = aSig>>( - shiftCount ); 4372 if ( (uint64_t) ( aSig<<( shiftCount & 63 ) ) ) { 4373 STATUS(float_exception_flags) |= float_flag_inexact; 4374 } 4375 if ( aSign ) z = - z; 4376 return z; 4377 4378 } 4379 4380 /*---------------------------------------------------------------------------- 4381 | Returns the result of converting the extended double-precision floating- 4382 | point value `a' to the single-precision floating-point format. The 4383 | conversion is performed according to the IEC/IEEE Standard for Binary 4384 | Floating-Point Arithmetic. 4385 *----------------------------------------------------------------------------*/ 4386 4387 float32 floatx80_to_float32( floatx80 a STATUS_PARAM ) 4388 { 4389 flag aSign; 4390 int32 aExp; 4391 uint64_t aSig; 4392 4393 aSig = extractFloatx80Frac( a ); 4394 aExp = extractFloatx80Exp( a ); 4395 aSign = extractFloatx80Sign( a ); 4396 if ( aExp == 0x7FFF ) { 4397 if ( (uint64_t) ( aSig<<1 ) ) { 4398 return commonNaNToFloat32( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 4399 } 4400 return packFloat32( aSign, 0xFF, 0 ); 4401 } 4402 shift64RightJamming( aSig, 33, &aSig ); 4403 if ( aExp || aSig ) aExp -= 0x3F81; 4404 return roundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); 4405 4406 } 4407 4408 /*---------------------------------------------------------------------------- 4409 | Returns the result of converting the extended double-precision floating- 4410 | point value `a' to the double-precision floating-point format. The 4411 | conversion is performed according to the IEC/IEEE Standard for Binary 4412 | Floating-Point Arithmetic. 4413 *----------------------------------------------------------------------------*/ 4414 4415 float64 floatx80_to_float64( floatx80 a STATUS_PARAM ) 4416 { 4417 flag aSign; 4418 int32 aExp; 4419 uint64_t aSig, zSig; 4420 4421 aSig = extractFloatx80Frac( a ); 4422 aExp = extractFloatx80Exp( a ); 4423 aSign = extractFloatx80Sign( a ); 4424 if ( aExp == 0x7FFF ) { 4425 if ( (uint64_t) ( aSig<<1 ) ) { 4426 return commonNaNToFloat64( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 4427 } 4428 return packFloat64( aSign, 0x7FF, 0 ); 4429 } 4430 shift64RightJamming( aSig, 1, &zSig ); 4431 if ( aExp || aSig ) aExp -= 0x3C01; 4432 return roundAndPackFloat64( aSign, aExp, zSig STATUS_VAR ); 4433 4434 } 4435 4436 /*---------------------------------------------------------------------------- 4437 | Returns the result of converting the extended double-precision floating- 4438 | point value `a' to the quadruple-precision floating-point format. The 4439 | conversion is performed according to the IEC/IEEE Standard for Binary 4440 | Floating-Point Arithmetic. 4441 *----------------------------------------------------------------------------*/ 4442 4443 float128 floatx80_to_float128( floatx80 a STATUS_PARAM ) 4444 { 4445 flag aSign; 4446 int_fast16_t aExp; 4447 uint64_t aSig, zSig0, zSig1; 4448 4449 aSig = extractFloatx80Frac( a ); 4450 aExp = extractFloatx80Exp( a ); 4451 aSign = extractFloatx80Sign( a ); 4452 if ( ( aExp == 0x7FFF ) && (uint64_t) ( aSig<<1 ) ) { 4453 return commonNaNToFloat128( floatx80ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 4454 } 4455 shift128Right( aSig<<1, 0, 16, &zSig0, &zSig1 ); 4456 return packFloat128( aSign, aExp, zSig0, zSig1 ); 4457 4458 } 4459 4460 /*---------------------------------------------------------------------------- 4461 | Rounds the extended double-precision floating-point value `a' to an integer, 4462 | and returns the result as an extended quadruple-precision floating-point 4463 | value. The operation is performed according to the IEC/IEEE Standard for 4464 | Binary Floating-Point Arithmetic. 4465 *----------------------------------------------------------------------------*/ 4466 4467 floatx80 floatx80_round_to_int( floatx80 a STATUS_PARAM ) 4468 { 4469 flag aSign; 4470 int32 aExp; 4471 uint64_t lastBitMask, roundBitsMask; 4472 int8 roundingMode; 4473 floatx80 z; 4474 4475 aExp = extractFloatx80Exp( a ); 4476 if ( 0x403E <= aExp ) { 4477 if ( ( aExp == 0x7FFF ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) { 4478 return propagateFloatx80NaN( a, a STATUS_VAR ); 4479 } 4480 return a; 4481 } 4482 if ( aExp < 0x3FFF ) { 4483 if ( ( aExp == 0 ) 4484 && ( (uint64_t) ( extractFloatx80Frac( a )<<1 ) == 0 ) ) { 4485 return a; 4486 } 4487 STATUS(float_exception_flags) |= float_flag_inexact; 4488 aSign = extractFloatx80Sign( a ); 4489 switch ( STATUS(float_rounding_mode) ) { 4490 case float_round_nearest_even: 4491 if ( ( aExp == 0x3FFE ) && (uint64_t) ( extractFloatx80Frac( a )<<1 ) 4492 ) { 4493 return 4494 packFloatx80( aSign, 0x3FFF, LIT64( 0x8000000000000000 ) ); 4495 } 4496 break; 4497 case float_round_down: 4498 return 4499 aSign ? 4500 packFloatx80( 1, 0x3FFF, LIT64( 0x8000000000000000 ) ) 4501 : packFloatx80( 0, 0, 0 ); 4502 case float_round_up: 4503 return 4504 aSign ? packFloatx80( 1, 0, 0 ) 4505 : packFloatx80( 0, 0x3FFF, LIT64( 0x8000000000000000 ) ); 4506 } 4507 return packFloatx80( aSign, 0, 0 ); 4508 } 4509 lastBitMask = 1; 4510 lastBitMask <<= 0x403E - aExp; 4511 roundBitsMask = lastBitMask - 1; 4512 z = a; 4513 roundingMode = STATUS(float_rounding_mode); 4514 if ( roundingMode == float_round_nearest_even ) { 4515 z.low += lastBitMask>>1; 4516 if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; 4517 } 4518 else if ( roundingMode != float_round_to_zero ) { 4519 if ( extractFloatx80Sign( z ) ^ ( roundingMode == float_round_up ) ) { 4520 z.low += roundBitsMask; 4521 } 4522 } 4523 z.low &= ~ roundBitsMask; 4524 if ( z.low == 0 ) { 4525 ++z.high; 4526 z.low = LIT64( 0x8000000000000000 ); 4527 } 4528 if ( z.low != a.low ) STATUS(float_exception_flags) |= float_flag_inexact; 4529 return z; 4530 4531 } 4532 4533 /*---------------------------------------------------------------------------- 4534 | Returns the result of adding the absolute values of the extended double- 4535 | precision floating-point values `a' and `b'. If `zSign' is 1, the sum is 4536 | negated before being returned. `zSign' is ignored if the result is a NaN. 4537 | The addition is performed according to the IEC/IEEE Standard for Binary 4538 | Floating-Point Arithmetic. 4539 *----------------------------------------------------------------------------*/ 4540 4541 static floatx80 addFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM) 4542 { 4543 int32 aExp, bExp, zExp; 4544 uint64_t aSig, bSig, zSig0, zSig1; 4545 int32 expDiff; 4546 4547 aSig = extractFloatx80Frac( a ); 4548 aExp = extractFloatx80Exp( a ); 4549 bSig = extractFloatx80Frac( b ); 4550 bExp = extractFloatx80Exp( b ); 4551 expDiff = aExp - bExp; 4552 if ( 0 < expDiff ) { 4553 if ( aExp == 0x7FFF ) { 4554 if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4555 return a; 4556 } 4557 if ( bExp == 0 ) --expDiff; 4558 shift64ExtraRightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); 4559 zExp = aExp; 4560 } 4561 else if ( expDiff < 0 ) { 4562 if ( bExp == 0x7FFF ) { 4563 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4564 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4565 } 4566 if ( aExp == 0 ) ++expDiff; 4567 shift64ExtraRightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); 4568 zExp = bExp; 4569 } 4570 else { 4571 if ( aExp == 0x7FFF ) { 4572 if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { 4573 return propagateFloatx80NaN( a, b STATUS_VAR ); 4574 } 4575 return a; 4576 } 4577 zSig1 = 0; 4578 zSig0 = aSig + bSig; 4579 if ( aExp == 0 ) { 4580 normalizeFloatx80Subnormal( zSig0, &zExp, &zSig0 ); 4581 goto roundAndPack; 4582 } 4583 zExp = aExp; 4584 goto shiftRight1; 4585 } 4586 zSig0 = aSig + bSig; 4587 if ( (int64_t) zSig0 < 0 ) goto roundAndPack; 4588 shiftRight1: 4589 shift64ExtraRightJamming( zSig0, zSig1, 1, &zSig0, &zSig1 ); 4590 zSig0 |= LIT64( 0x8000000000000000 ); 4591 ++zExp; 4592 roundAndPack: 4593 return 4594 roundAndPackFloatx80( 4595 STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); 4596 4597 } 4598 4599 /*---------------------------------------------------------------------------- 4600 | Returns the result of subtracting the absolute values of the extended 4601 | double-precision floating-point values `a' and `b'. If `zSign' is 1, the 4602 | difference is negated before being returned. `zSign' is ignored if the 4603 | result is a NaN. The subtraction is performed according to the IEC/IEEE 4604 | Standard for Binary Floating-Point Arithmetic. 4605 *----------------------------------------------------------------------------*/ 4606 4607 static floatx80 subFloatx80Sigs( floatx80 a, floatx80 b, flag zSign STATUS_PARAM ) 4608 { 4609 int32 aExp, bExp, zExp; 4610 uint64_t aSig, bSig, zSig0, zSig1; 4611 int32 expDiff; 4612 floatx80 z; 4613 4614 aSig = extractFloatx80Frac( a ); 4615 aExp = extractFloatx80Exp( a ); 4616 bSig = extractFloatx80Frac( b ); 4617 bExp = extractFloatx80Exp( b ); 4618 expDiff = aExp - bExp; 4619 if ( 0 < expDiff ) goto aExpBigger; 4620 if ( expDiff < 0 ) goto bExpBigger; 4621 if ( aExp == 0x7FFF ) { 4622 if ( (uint64_t) ( ( aSig | bSig )<<1 ) ) { 4623 return propagateFloatx80NaN( a, b STATUS_VAR ); 4624 } 4625 float_raise( float_flag_invalid STATUS_VAR); 4626 z.low = floatx80_default_nan_low; 4627 z.high = floatx80_default_nan_high; 4628 return z; 4629 } 4630 if ( aExp == 0 ) { 4631 aExp = 1; 4632 bExp = 1; 4633 } 4634 zSig1 = 0; 4635 if ( bSig < aSig ) goto aBigger; 4636 if ( aSig < bSig ) goto bBigger; 4637 return packFloatx80( STATUS(float_rounding_mode) == float_round_down, 0, 0 ); 4638 bExpBigger: 4639 if ( bExp == 0x7FFF ) { 4640 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4641 return packFloatx80( zSign ^ 1, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4642 } 4643 if ( aExp == 0 ) ++expDiff; 4644 shift128RightJamming( aSig, 0, - expDiff, &aSig, &zSig1 ); 4645 bBigger: 4646 sub128( bSig, 0, aSig, zSig1, &zSig0, &zSig1 ); 4647 zExp = bExp; 4648 zSign ^= 1; 4649 goto normalizeRoundAndPack; 4650 aExpBigger: 4651 if ( aExp == 0x7FFF ) { 4652 if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4653 return a; 4654 } 4655 if ( bExp == 0 ) --expDiff; 4656 shift128RightJamming( bSig, 0, expDiff, &bSig, &zSig1 ); 4657 aBigger: 4658 sub128( aSig, 0, bSig, zSig1, &zSig0, &zSig1 ); 4659 zExp = aExp; 4660 normalizeRoundAndPack: 4661 return 4662 normalizeRoundAndPackFloatx80( 4663 STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); 4664 4665 } 4666 4667 /*---------------------------------------------------------------------------- 4668 | Returns the result of adding the extended double-precision floating-point 4669 | values `a' and `b'. The operation is performed according to the IEC/IEEE 4670 | Standard for Binary Floating-Point Arithmetic. 4671 *----------------------------------------------------------------------------*/ 4672 4673 floatx80 floatx80_add( floatx80 a, floatx80 b STATUS_PARAM ) 4674 { 4675 flag aSign, bSign; 4676 4677 aSign = extractFloatx80Sign( a ); 4678 bSign = extractFloatx80Sign( b ); 4679 if ( aSign == bSign ) { 4680 return addFloatx80Sigs( a, b, aSign STATUS_VAR ); 4681 } 4682 else { 4683 return subFloatx80Sigs( a, b, aSign STATUS_VAR ); 4684 } 4685 4686 } 4687 4688 /*---------------------------------------------------------------------------- 4689 | Returns the result of subtracting the extended double-precision floating- 4690 | point values `a' and `b'. The operation is performed according to the 4691 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4692 *----------------------------------------------------------------------------*/ 4693 4694 floatx80 floatx80_sub( floatx80 a, floatx80 b STATUS_PARAM ) 4695 { 4696 flag aSign, bSign; 4697 4698 aSign = extractFloatx80Sign( a ); 4699 bSign = extractFloatx80Sign( b ); 4700 if ( aSign == bSign ) { 4701 return subFloatx80Sigs( a, b, aSign STATUS_VAR ); 4702 } 4703 else { 4704 return addFloatx80Sigs( a, b, aSign STATUS_VAR ); 4705 } 4706 4707 } 4708 4709 /*---------------------------------------------------------------------------- 4710 | Returns the result of multiplying the extended double-precision floating- 4711 | point values `a' and `b'. The operation is performed according to the 4712 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4713 *----------------------------------------------------------------------------*/ 4714 4715 floatx80 floatx80_mul( floatx80 a, floatx80 b STATUS_PARAM ) 4716 { 4717 flag aSign, bSign, zSign; 4718 int32 aExp, bExp, zExp; 4719 uint64_t aSig, bSig, zSig0, zSig1; 4720 floatx80 z; 4721 4722 aSig = extractFloatx80Frac( a ); 4723 aExp = extractFloatx80Exp( a ); 4724 aSign = extractFloatx80Sign( a ); 4725 bSig = extractFloatx80Frac( b ); 4726 bExp = extractFloatx80Exp( b ); 4727 bSign = extractFloatx80Sign( b ); 4728 zSign = aSign ^ bSign; 4729 if ( aExp == 0x7FFF ) { 4730 if ( (uint64_t) ( aSig<<1 ) 4731 || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { 4732 return propagateFloatx80NaN( a, b STATUS_VAR ); 4733 } 4734 if ( ( bExp | bSig ) == 0 ) goto invalid; 4735 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4736 } 4737 if ( bExp == 0x7FFF ) { 4738 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4739 if ( ( aExp | aSig ) == 0 ) { 4740 invalid: 4741 float_raise( float_flag_invalid STATUS_VAR); 4742 z.low = floatx80_default_nan_low; 4743 z.high = floatx80_default_nan_high; 4744 return z; 4745 } 4746 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4747 } 4748 if ( aExp == 0 ) { 4749 if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); 4750 normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); 4751 } 4752 if ( bExp == 0 ) { 4753 if ( bSig == 0 ) return packFloatx80( zSign, 0, 0 ); 4754 normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); 4755 } 4756 zExp = aExp + bExp - 0x3FFE; 4757 mul64To128( aSig, bSig, &zSig0, &zSig1 ); 4758 if ( 0 < (int64_t) zSig0 ) { 4759 shortShift128Left( zSig0, zSig1, 1, &zSig0, &zSig1 ); 4760 --zExp; 4761 } 4762 return 4763 roundAndPackFloatx80( 4764 STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); 4765 4766 } 4767 4768 /*---------------------------------------------------------------------------- 4769 | Returns the result of dividing the extended double-precision floating-point 4770 | value `a' by the corresponding value `b'. The operation is performed 4771 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4772 *----------------------------------------------------------------------------*/ 4773 4774 floatx80 floatx80_div( floatx80 a, floatx80 b STATUS_PARAM ) 4775 { 4776 flag aSign, bSign, zSign; 4777 int32 aExp, bExp, zExp; 4778 uint64_t aSig, bSig, zSig0, zSig1; 4779 uint64_t rem0, rem1, rem2, term0, term1, term2; 4780 floatx80 z; 4781 4782 aSig = extractFloatx80Frac( a ); 4783 aExp = extractFloatx80Exp( a ); 4784 aSign = extractFloatx80Sign( a ); 4785 bSig = extractFloatx80Frac( b ); 4786 bExp = extractFloatx80Exp( b ); 4787 bSign = extractFloatx80Sign( b ); 4788 zSign = aSign ^ bSign; 4789 if ( aExp == 0x7FFF ) { 4790 if ( (uint64_t) ( aSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4791 if ( bExp == 0x7FFF ) { 4792 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4793 goto invalid; 4794 } 4795 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4796 } 4797 if ( bExp == 0x7FFF ) { 4798 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4799 return packFloatx80( zSign, 0, 0 ); 4800 } 4801 if ( bExp == 0 ) { 4802 if ( bSig == 0 ) { 4803 if ( ( aExp | aSig ) == 0 ) { 4804 invalid: 4805 float_raise( float_flag_invalid STATUS_VAR); 4806 z.low = floatx80_default_nan_low; 4807 z.high = floatx80_default_nan_high; 4808 return z; 4809 } 4810 float_raise( float_flag_divbyzero STATUS_VAR); 4811 return packFloatx80( zSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 4812 } 4813 normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); 4814 } 4815 if ( aExp == 0 ) { 4816 if ( aSig == 0 ) return packFloatx80( zSign, 0, 0 ); 4817 normalizeFloatx80Subnormal( aSig, &aExp, &aSig ); 4818 } 4819 zExp = aExp - bExp + 0x3FFE; 4820 rem1 = 0; 4821 if ( bSig <= aSig ) { 4822 shift128Right( aSig, 0, 1, &aSig, &rem1 ); 4823 ++zExp; 4824 } 4825 zSig0 = estimateDiv128To64( aSig, rem1, bSig ); 4826 mul64To128( bSig, zSig0, &term0, &term1 ); 4827 sub128( aSig, rem1, term0, term1, &rem0, &rem1 ); 4828 while ( (int64_t) rem0 < 0 ) { 4829 --zSig0; 4830 add128( rem0, rem1, 0, bSig, &rem0, &rem1 ); 4831 } 4832 zSig1 = estimateDiv128To64( rem1, 0, bSig ); 4833 if ( (uint64_t) ( zSig1<<1 ) <= 8 ) { 4834 mul64To128( bSig, zSig1, &term1, &term2 ); 4835 sub128( rem1, 0, term1, term2, &rem1, &rem2 ); 4836 while ( (int64_t) rem1 < 0 ) { 4837 --zSig1; 4838 add128( rem1, rem2, 0, bSig, &rem1, &rem2 ); 4839 } 4840 zSig1 |= ( ( rem1 | rem2 ) != 0 ); 4841 } 4842 return 4843 roundAndPackFloatx80( 4844 STATUS(floatx80_rounding_precision), zSign, zExp, zSig0, zSig1 STATUS_VAR ); 4845 4846 } 4847 4848 /*---------------------------------------------------------------------------- 4849 | Returns the remainder of the extended double-precision floating-point value 4850 | `a' with respect to the corresponding value `b'. The operation is performed 4851 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 4852 *----------------------------------------------------------------------------*/ 4853 4854 floatx80 floatx80_rem( floatx80 a, floatx80 b STATUS_PARAM ) 4855 { 4856 flag aSign, zSign; 4857 int32 aExp, bExp, expDiff; 4858 uint64_t aSig0, aSig1, bSig; 4859 uint64_t q, term0, term1, alternateASig0, alternateASig1; 4860 floatx80 z; 4861 4862 aSig0 = extractFloatx80Frac( a ); 4863 aExp = extractFloatx80Exp( a ); 4864 aSign = extractFloatx80Sign( a ); 4865 bSig = extractFloatx80Frac( b ); 4866 bExp = extractFloatx80Exp( b ); 4867 if ( aExp == 0x7FFF ) { 4868 if ( (uint64_t) ( aSig0<<1 ) 4869 || ( ( bExp == 0x7FFF ) && (uint64_t) ( bSig<<1 ) ) ) { 4870 return propagateFloatx80NaN( a, b STATUS_VAR ); 4871 } 4872 goto invalid; 4873 } 4874 if ( bExp == 0x7FFF ) { 4875 if ( (uint64_t) ( bSig<<1 ) ) return propagateFloatx80NaN( a, b STATUS_VAR ); 4876 return a; 4877 } 4878 if ( bExp == 0 ) { 4879 if ( bSig == 0 ) { 4880 invalid: 4881 float_raise( float_flag_invalid STATUS_VAR); 4882 z.low = floatx80_default_nan_low; 4883 z.high = floatx80_default_nan_high; 4884 return z; 4885 } 4886 normalizeFloatx80Subnormal( bSig, &bExp, &bSig ); 4887 } 4888 if ( aExp == 0 ) { 4889 if ( (uint64_t) ( aSig0<<1 ) == 0 ) return a; 4890 normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); 4891 } 4892 bSig |= LIT64( 0x8000000000000000 ); 4893 zSign = aSign; 4894 expDiff = aExp - bExp; 4895 aSig1 = 0; 4896 if ( expDiff < 0 ) { 4897 if ( expDiff < -1 ) return a; 4898 shift128Right( aSig0, 0, 1, &aSig0, &aSig1 ); 4899 expDiff = 0; 4900 } 4901 q = ( bSig <= aSig0 ); 4902 if ( q ) aSig0 -= bSig; 4903 expDiff -= 64; 4904 while ( 0 < expDiff ) { 4905 q = estimateDiv128To64( aSig0, aSig1, bSig ); 4906 q = ( 2 < q ) ? q - 2 : 0; 4907 mul64To128( bSig, q, &term0, &term1 ); 4908 sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); 4909 shortShift128Left( aSig0, aSig1, 62, &aSig0, &aSig1 ); 4910 expDiff -= 62; 4911 } 4912 expDiff += 64; 4913 if ( 0 < expDiff ) { 4914 q = estimateDiv128To64( aSig0, aSig1, bSig ); 4915 q = ( 2 < q ) ? q - 2 : 0; 4916 q >>= 64 - expDiff; 4917 mul64To128( bSig, q<<( 64 - expDiff ), &term0, &term1 ); 4918 sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); 4919 shortShift128Left( 0, bSig, 64 - expDiff, &term0, &term1 ); 4920 while ( le128( term0, term1, aSig0, aSig1 ) ) { 4921 ++q; 4922 sub128( aSig0, aSig1, term0, term1, &aSig0, &aSig1 ); 4923 } 4924 } 4925 else { 4926 term1 = 0; 4927 term0 = bSig; 4928 } 4929 sub128( term0, term1, aSig0, aSig1, &alternateASig0, &alternateASig1 ); 4930 if ( lt128( alternateASig0, alternateASig1, aSig0, aSig1 ) 4931 || ( eq128( alternateASig0, alternateASig1, aSig0, aSig1 ) 4932 && ( q & 1 ) ) 4933 ) { 4934 aSig0 = alternateASig0; 4935 aSig1 = alternateASig1; 4936 zSign = ! zSign; 4937 } 4938 return 4939 normalizeRoundAndPackFloatx80( 4940 80, zSign, bExp + expDiff, aSig0, aSig1 STATUS_VAR ); 4941 4942 } 4943 4944 /*---------------------------------------------------------------------------- 4945 | Returns the square root of the extended double-precision floating-point 4946 | value `a'. The operation is performed according to the IEC/IEEE Standard 4947 | for Binary Floating-Point Arithmetic. 4948 *----------------------------------------------------------------------------*/ 4949 4950 floatx80 floatx80_sqrt( floatx80 a STATUS_PARAM ) 4951 { 4952 flag aSign; 4953 int32 aExp, zExp; 4954 uint64_t aSig0, aSig1, zSig0, zSig1, doubleZSig0; 4955 uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; 4956 floatx80 z; 4957 4958 aSig0 = extractFloatx80Frac( a ); 4959 aExp = extractFloatx80Exp( a ); 4960 aSign = extractFloatx80Sign( a ); 4961 if ( aExp == 0x7FFF ) { 4962 if ( (uint64_t) ( aSig0<<1 ) ) return propagateFloatx80NaN( a, a STATUS_VAR ); 4963 if ( ! aSign ) return a; 4964 goto invalid; 4965 } 4966 if ( aSign ) { 4967 if ( ( aExp | aSig0 ) == 0 ) return a; 4968 invalid: 4969 float_raise( float_flag_invalid STATUS_VAR); 4970 z.low = floatx80_default_nan_low; 4971 z.high = floatx80_default_nan_high; 4972 return z; 4973 } 4974 if ( aExp == 0 ) { 4975 if ( aSig0 == 0 ) return packFloatx80( 0, 0, 0 ); 4976 normalizeFloatx80Subnormal( aSig0, &aExp, &aSig0 ); 4977 } 4978 zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFF; 4979 zSig0 = estimateSqrt32( aExp, aSig0>>32 ); 4980 shift128Right( aSig0, 0, 2 + ( aExp & 1 ), &aSig0, &aSig1 ); 4981 zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); 4982 doubleZSig0 = zSig0<<1; 4983 mul64To128( zSig0, zSig0, &term0, &term1 ); 4984 sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); 4985 while ( (int64_t) rem0 < 0 ) { 4986 --zSig0; 4987 doubleZSig0 -= 2; 4988 add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); 4989 } 4990 zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); 4991 if ( ( zSig1 & LIT64( 0x3FFFFFFFFFFFFFFF ) ) <= 5 ) { 4992 if ( zSig1 == 0 ) zSig1 = 1; 4993 mul64To128( doubleZSig0, zSig1, &term1, &term2 ); 4994 sub128( rem1, 0, term1, term2, &rem1, &rem2 ); 4995 mul64To128( zSig1, zSig1, &term2, &term3 ); 4996 sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); 4997 while ( (int64_t) rem1 < 0 ) { 4998 --zSig1; 4999 shortShift128Left( 0, zSig1, 1, &term2, &term3 ); 5000 term3 |= 1; 5001 term2 |= doubleZSig0; 5002 add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); 5003 } 5004 zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); 5005 } 5006 shortShift128Left( 0, zSig1, 1, &zSig0, &zSig1 ); 5007 zSig0 |= doubleZSig0; 5008 return 5009 roundAndPackFloatx80( 5010 STATUS(floatx80_rounding_precision), 0, zExp, zSig0, zSig1 STATUS_VAR ); 5011 5012 } 5013 5014 /*---------------------------------------------------------------------------- 5015 | Returns 1 if the extended double-precision floating-point value `a' is equal 5016 | to the corresponding value `b', and 0 otherwise. The invalid exception is 5017 | raised if either operand is a NaN. Otherwise, the comparison is performed 5018 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5019 *----------------------------------------------------------------------------*/ 5020 5021 int floatx80_eq( floatx80 a, floatx80 b STATUS_PARAM ) 5022 { 5023 5024 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5025 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5026 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5027 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5028 ) { 5029 float_raise( float_flag_invalid STATUS_VAR); 5030 return 0; 5031 } 5032 return 5033 ( a.low == b.low ) 5034 && ( ( a.high == b.high ) 5035 || ( ( a.low == 0 ) 5036 && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) 5037 ); 5038 5039 } 5040 5041 /*---------------------------------------------------------------------------- 5042 | Returns 1 if the extended double-precision floating-point value `a' is 5043 | less than or equal to the corresponding value `b', and 0 otherwise. The 5044 | invalid exception is raised if either operand is a NaN. The comparison is 5045 | performed according to the IEC/IEEE Standard for Binary Floating-Point 5046 | Arithmetic. 5047 *----------------------------------------------------------------------------*/ 5048 5049 int floatx80_le( floatx80 a, floatx80 b STATUS_PARAM ) 5050 { 5051 flag aSign, bSign; 5052 5053 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5054 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5055 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5056 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5057 ) { 5058 float_raise( float_flag_invalid STATUS_VAR); 5059 return 0; 5060 } 5061 aSign = extractFloatx80Sign( a ); 5062 bSign = extractFloatx80Sign( b ); 5063 if ( aSign != bSign ) { 5064 return 5065 aSign 5066 || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 5067 == 0 ); 5068 } 5069 return 5070 aSign ? le128( b.high, b.low, a.high, a.low ) 5071 : le128( a.high, a.low, b.high, b.low ); 5072 5073 } 5074 5075 /*---------------------------------------------------------------------------- 5076 | Returns 1 if the extended double-precision floating-point value `a' is 5077 | less than the corresponding value `b', and 0 otherwise. The invalid 5078 | exception is raised if either operand is a NaN. The comparison is performed 5079 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5080 *----------------------------------------------------------------------------*/ 5081 5082 int floatx80_lt( floatx80 a, floatx80 b STATUS_PARAM ) 5083 { 5084 flag aSign, bSign; 5085 5086 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5087 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5088 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5089 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5090 ) { 5091 float_raise( float_flag_invalid STATUS_VAR); 5092 return 0; 5093 } 5094 aSign = extractFloatx80Sign( a ); 5095 bSign = extractFloatx80Sign( b ); 5096 if ( aSign != bSign ) { 5097 return 5098 aSign 5099 && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 5100 != 0 ); 5101 } 5102 return 5103 aSign ? lt128( b.high, b.low, a.high, a.low ) 5104 : lt128( a.high, a.low, b.high, b.low ); 5105 5106 } 5107 5108 /*---------------------------------------------------------------------------- 5109 | Returns 1 if the extended double-precision floating-point values `a' and `b' 5110 | cannot be compared, and 0 otherwise. The invalid exception is raised if 5111 | either operand is a NaN. The comparison is performed according to the 5112 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5113 *----------------------------------------------------------------------------*/ 5114 int floatx80_unordered( floatx80 a, floatx80 b STATUS_PARAM ) 5115 { 5116 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5117 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5118 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5119 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5120 ) { 5121 float_raise( float_flag_invalid STATUS_VAR); 5122 return 1; 5123 } 5124 return 0; 5125 } 5126 5127 /*---------------------------------------------------------------------------- 5128 | Returns 1 if the extended double-precision floating-point value `a' is 5129 | equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not 5130 | cause an exception. The comparison is performed according to the IEC/IEEE 5131 | Standard for Binary Floating-Point Arithmetic. 5132 *----------------------------------------------------------------------------*/ 5133 5134 int floatx80_eq_quiet( floatx80 a, floatx80 b STATUS_PARAM ) 5135 { 5136 5137 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5138 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5139 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5140 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5141 ) { 5142 if ( floatx80_is_signaling_nan( a ) 5143 || floatx80_is_signaling_nan( b ) ) { 5144 float_raise( float_flag_invalid STATUS_VAR); 5145 } 5146 return 0; 5147 } 5148 return 5149 ( a.low == b.low ) 5150 && ( ( a.high == b.high ) 5151 || ( ( a.low == 0 ) 5152 && ( (uint16_t) ( ( a.high | b.high )<<1 ) == 0 ) ) 5153 ); 5154 5155 } 5156 5157 /*---------------------------------------------------------------------------- 5158 | Returns 1 if the extended double-precision floating-point value `a' is less 5159 | than or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs 5160 | do not cause an exception. Otherwise, the comparison is performed according 5161 | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5162 *----------------------------------------------------------------------------*/ 5163 5164 int floatx80_le_quiet( floatx80 a, floatx80 b STATUS_PARAM ) 5165 { 5166 flag aSign, bSign; 5167 5168 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5169 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5170 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5171 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5172 ) { 5173 if ( floatx80_is_signaling_nan( a ) 5174 || floatx80_is_signaling_nan( b ) ) { 5175 float_raise( float_flag_invalid STATUS_VAR); 5176 } 5177 return 0; 5178 } 5179 aSign = extractFloatx80Sign( a ); 5180 bSign = extractFloatx80Sign( b ); 5181 if ( aSign != bSign ) { 5182 return 5183 aSign 5184 || ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 5185 == 0 ); 5186 } 5187 return 5188 aSign ? le128( b.high, b.low, a.high, a.low ) 5189 : le128( a.high, a.low, b.high, b.low ); 5190 5191 } 5192 5193 /*---------------------------------------------------------------------------- 5194 | Returns 1 if the extended double-precision floating-point value `a' is less 5195 | than the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause 5196 | an exception. Otherwise, the comparison is performed according to the 5197 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5198 *----------------------------------------------------------------------------*/ 5199 5200 int floatx80_lt_quiet( floatx80 a, floatx80 b STATUS_PARAM ) 5201 { 5202 flag aSign, bSign; 5203 5204 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5205 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5206 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5207 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5208 ) { 5209 if ( floatx80_is_signaling_nan( a ) 5210 || floatx80_is_signaling_nan( b ) ) { 5211 float_raise( float_flag_invalid STATUS_VAR); 5212 } 5213 return 0; 5214 } 5215 aSign = extractFloatx80Sign( a ); 5216 bSign = extractFloatx80Sign( b ); 5217 if ( aSign != bSign ) { 5218 return 5219 aSign 5220 && ( ( ( (uint16_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 5221 != 0 ); 5222 } 5223 return 5224 aSign ? lt128( b.high, b.low, a.high, a.low ) 5225 : lt128( a.high, a.low, b.high, b.low ); 5226 5227 } 5228 5229 /*---------------------------------------------------------------------------- 5230 | Returns 1 if the extended double-precision floating-point values `a' and `b' 5231 | cannot be compared, and 0 otherwise. Quiet NaNs do not cause an exception. 5232 | The comparison is performed according to the IEC/IEEE Standard for Binary 5233 | Floating-Point Arithmetic. 5234 *----------------------------------------------------------------------------*/ 5235 int floatx80_unordered_quiet( floatx80 a, floatx80 b STATUS_PARAM ) 5236 { 5237 if ( ( ( extractFloatx80Exp( a ) == 0x7FFF ) 5238 && (uint64_t) ( extractFloatx80Frac( a )<<1 ) ) 5239 || ( ( extractFloatx80Exp( b ) == 0x7FFF ) 5240 && (uint64_t) ( extractFloatx80Frac( b )<<1 ) ) 5241 ) { 5242 if ( floatx80_is_signaling_nan( a ) 5243 || floatx80_is_signaling_nan( b ) ) { 5244 float_raise( float_flag_invalid STATUS_VAR); 5245 } 5246 return 1; 5247 } 5248 return 0; 5249 } 5250 5251 /*---------------------------------------------------------------------------- 5252 | Returns the result of converting the quadruple-precision floating-point 5253 | value `a' to the 32-bit two's complement integer format. The conversion 5254 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5255 | Arithmetic---which means in particular that the conversion is rounded 5256 | according to the current rounding mode. If `a' is a NaN, the largest 5257 | positive integer is returned. Otherwise, if the conversion overflows, the 5258 | largest integer with the same sign as `a' is returned. 5259 *----------------------------------------------------------------------------*/ 5260 5261 int32 float128_to_int32( float128 a STATUS_PARAM ) 5262 { 5263 flag aSign; 5264 int32 aExp, shiftCount; 5265 uint64_t aSig0, aSig1; 5266 5267 aSig1 = extractFloat128Frac1( a ); 5268 aSig0 = extractFloat128Frac0( a ); 5269 aExp = extractFloat128Exp( a ); 5270 aSign = extractFloat128Sign( a ); 5271 if ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) aSign = 0; 5272 if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); 5273 aSig0 |= ( aSig1 != 0 ); 5274 shiftCount = 0x4028 - aExp; 5275 if ( 0 < shiftCount ) shift64RightJamming( aSig0, shiftCount, &aSig0 ); 5276 return roundAndPackInt32( aSign, aSig0 STATUS_VAR ); 5277 5278 } 5279 5280 /*---------------------------------------------------------------------------- 5281 | Returns the result of converting the quadruple-precision floating-point 5282 | value `a' to the 32-bit two's complement integer format. The conversion 5283 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5284 | Arithmetic, except that the conversion is always rounded toward zero. If 5285 | `a' is a NaN, the largest positive integer is returned. Otherwise, if the 5286 | conversion overflows, the largest integer with the same sign as `a' is 5287 | returned. 5288 *----------------------------------------------------------------------------*/ 5289 5290 int32 float128_to_int32_round_to_zero( float128 a STATUS_PARAM ) 5291 { 5292 flag aSign; 5293 int32 aExp, shiftCount; 5294 uint64_t aSig0, aSig1, savedASig; 5295 int32_t z; 5296 5297 aSig1 = extractFloat128Frac1( a ); 5298 aSig0 = extractFloat128Frac0( a ); 5299 aExp = extractFloat128Exp( a ); 5300 aSign = extractFloat128Sign( a ); 5301 aSig0 |= ( aSig1 != 0 ); 5302 if ( 0x401E < aExp ) { 5303 if ( ( aExp == 0x7FFF ) && aSig0 ) aSign = 0; 5304 goto invalid; 5305 } 5306 else if ( aExp < 0x3FFF ) { 5307 if ( aExp || aSig0 ) STATUS(float_exception_flags) |= float_flag_inexact; 5308 return 0; 5309 } 5310 aSig0 |= LIT64( 0x0001000000000000 ); 5311 shiftCount = 0x402F - aExp; 5312 savedASig = aSig0; 5313 aSig0 >>= shiftCount; 5314 z = aSig0; 5315 if ( aSign ) z = - z; 5316 if ( ( z < 0 ) ^ aSign ) { 5317 invalid: 5318 float_raise( float_flag_invalid STATUS_VAR); 5319 return aSign ? (int32_t) 0x80000000 : 0x7FFFFFFF; 5320 } 5321 if ( ( aSig0<<shiftCount ) != savedASig ) { 5322 STATUS(float_exception_flags) |= float_flag_inexact; 5323 } 5324 return z; 5325 5326 } 5327 5328 /*---------------------------------------------------------------------------- 5329 | Returns the result of converting the quadruple-precision floating-point 5330 | value `a' to the 64-bit two's complement integer format. The conversion 5331 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5332 | Arithmetic---which means in particular that the conversion is rounded 5333 | according to the current rounding mode. If `a' is a NaN, the largest 5334 | positive integer is returned. Otherwise, if the conversion overflows, the 5335 | largest integer with the same sign as `a' is returned. 5336 *----------------------------------------------------------------------------*/ 5337 5338 int64 float128_to_int64( float128 a STATUS_PARAM ) 5339 { 5340 flag aSign; 5341 int32 aExp, shiftCount; 5342 uint64_t aSig0, aSig1; 5343 5344 aSig1 = extractFloat128Frac1( a ); 5345 aSig0 = extractFloat128Frac0( a ); 5346 aExp = extractFloat128Exp( a ); 5347 aSign = extractFloat128Sign( a ); 5348 if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); 5349 shiftCount = 0x402F - aExp; 5350 if ( shiftCount <= 0 ) { 5351 if ( 0x403E < aExp ) { 5352 float_raise( float_flag_invalid STATUS_VAR); 5353 if ( ! aSign 5354 || ( ( aExp == 0x7FFF ) 5355 && ( aSig1 || ( aSig0 != LIT64( 0x0001000000000000 ) ) ) 5356 ) 5357 ) { 5358 return LIT64( 0x7FFFFFFFFFFFFFFF ); 5359 } 5360 return (int64_t) LIT64( 0x8000000000000000 ); 5361 } 5362 shortShift128Left( aSig0, aSig1, - shiftCount, &aSig0, &aSig1 ); 5363 } 5364 else { 5365 shift64ExtraRightJamming( aSig0, aSig1, shiftCount, &aSig0, &aSig1 ); 5366 } 5367 return roundAndPackInt64( aSign, aSig0, aSig1 STATUS_VAR ); 5368 5369 } 5370 5371 /*---------------------------------------------------------------------------- 5372 | Returns the result of converting the quadruple-precision floating-point 5373 | value `a' to the 64-bit two's complement integer format. The conversion 5374 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5375 | Arithmetic, except that the conversion is always rounded toward zero. 5376 | If `a' is a NaN, the largest positive integer is returned. Otherwise, if 5377 | the conversion overflows, the largest integer with the same sign as `a' is 5378 | returned. 5379 *----------------------------------------------------------------------------*/ 5380 5381 int64 float128_to_int64_round_to_zero( float128 a STATUS_PARAM ) 5382 { 5383 flag aSign; 5384 int32 aExp, shiftCount; 5385 uint64_t aSig0, aSig1; 5386 int64 z; 5387 5388 aSig1 = extractFloat128Frac1( a ); 5389 aSig0 = extractFloat128Frac0( a ); 5390 aExp = extractFloat128Exp( a ); 5391 aSign = extractFloat128Sign( a ); 5392 if ( aExp ) aSig0 |= LIT64( 0x0001000000000000 ); 5393 shiftCount = aExp - 0x402F; 5394 if ( 0 < shiftCount ) { 5395 if ( 0x403E <= aExp ) { 5396 aSig0 &= LIT64( 0x0000FFFFFFFFFFFF ); 5397 if ( ( a.high == LIT64( 0xC03E000000000000 ) ) 5398 && ( aSig1 < LIT64( 0x0002000000000000 ) ) ) { 5399 if ( aSig1 ) STATUS(float_exception_flags) |= float_flag_inexact; 5400 } 5401 else { 5402 float_raise( float_flag_invalid STATUS_VAR); 5403 if ( ! aSign || ( ( aExp == 0x7FFF ) && ( aSig0 | aSig1 ) ) ) { 5404 return LIT64( 0x7FFFFFFFFFFFFFFF ); 5405 } 5406 } 5407 return (int64_t) LIT64( 0x8000000000000000 ); 5408 } 5409 z = ( aSig0<<shiftCount ) | ( aSig1>>( ( - shiftCount ) & 63 ) ); 5410 if ( (uint64_t) ( aSig1<<shiftCount ) ) { 5411 STATUS(float_exception_flags) |= float_flag_inexact; 5412 } 5413 } 5414 else { 5415 if ( aExp < 0x3FFF ) { 5416 if ( aExp | aSig0 | aSig1 ) { 5417 STATUS(float_exception_flags) |= float_flag_inexact; 5418 } 5419 return 0; 5420 } 5421 z = aSig0>>( - shiftCount ); 5422 if ( aSig1 5423 || ( shiftCount && (uint64_t) ( aSig0<<( shiftCount & 63 ) ) ) ) { 5424 STATUS(float_exception_flags) |= float_flag_inexact; 5425 } 5426 } 5427 if ( aSign ) z = - z; 5428 return z; 5429 5430 } 5431 5432 /*---------------------------------------------------------------------------- 5433 | Returns the result of converting the quadruple-precision floating-point 5434 | value `a' to the single-precision floating-point format. The conversion 5435 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5436 | Arithmetic. 5437 *----------------------------------------------------------------------------*/ 5438 5439 float32 float128_to_float32( float128 a STATUS_PARAM ) 5440 { 5441 flag aSign; 5442 int32 aExp; 5443 uint64_t aSig0, aSig1; 5444 uint32_t zSig; 5445 5446 aSig1 = extractFloat128Frac1( a ); 5447 aSig0 = extractFloat128Frac0( a ); 5448 aExp = extractFloat128Exp( a ); 5449 aSign = extractFloat128Sign( a ); 5450 if ( aExp == 0x7FFF ) { 5451 if ( aSig0 | aSig1 ) { 5452 return commonNaNToFloat32( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 5453 } 5454 return packFloat32( aSign, 0xFF, 0 ); 5455 } 5456 aSig0 |= ( aSig1 != 0 ); 5457 shift64RightJamming( aSig0, 18, &aSig0 ); 5458 zSig = aSig0; 5459 if ( aExp || zSig ) { 5460 zSig |= 0x40000000; 5461 aExp -= 0x3F81; 5462 } 5463 return roundAndPackFloat32( aSign, aExp, zSig STATUS_VAR ); 5464 5465 } 5466 5467 /*---------------------------------------------------------------------------- 5468 | Returns the result of converting the quadruple-precision floating-point 5469 | value `a' to the double-precision floating-point format. The conversion 5470 | is performed according to the IEC/IEEE Standard for Binary Floating-Point 5471 | Arithmetic. 5472 *----------------------------------------------------------------------------*/ 5473 5474 float64 float128_to_float64( float128 a STATUS_PARAM ) 5475 { 5476 flag aSign; 5477 int32 aExp; 5478 uint64_t aSig0, aSig1; 5479 5480 aSig1 = extractFloat128Frac1( a ); 5481 aSig0 = extractFloat128Frac0( a ); 5482 aExp = extractFloat128Exp( a ); 5483 aSign = extractFloat128Sign( a ); 5484 if ( aExp == 0x7FFF ) { 5485 if ( aSig0 | aSig1 ) { 5486 return commonNaNToFloat64( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 5487 } 5488 return packFloat64( aSign, 0x7FF, 0 ); 5489 } 5490 shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); 5491 aSig0 |= ( aSig1 != 0 ); 5492 if ( aExp || aSig0 ) { 5493 aSig0 |= LIT64( 0x4000000000000000 ); 5494 aExp -= 0x3C01; 5495 } 5496 return roundAndPackFloat64( aSign, aExp, aSig0 STATUS_VAR ); 5497 5498 } 5499 5500 /*---------------------------------------------------------------------------- 5501 | Returns the result of converting the quadruple-precision floating-point 5502 | value `a' to the extended double-precision floating-point format. The 5503 | conversion is performed according to the IEC/IEEE Standard for Binary 5504 | Floating-Point Arithmetic. 5505 *----------------------------------------------------------------------------*/ 5506 5507 floatx80 float128_to_floatx80( float128 a STATUS_PARAM ) 5508 { 5509 flag aSign; 5510 int32 aExp; 5511 uint64_t aSig0, aSig1; 5512 5513 aSig1 = extractFloat128Frac1( a ); 5514 aSig0 = extractFloat128Frac0( a ); 5515 aExp = extractFloat128Exp( a ); 5516 aSign = extractFloat128Sign( a ); 5517 if ( aExp == 0x7FFF ) { 5518 if ( aSig0 | aSig1 ) { 5519 return commonNaNToFloatx80( float128ToCommonNaN( a STATUS_VAR ) STATUS_VAR ); 5520 } 5521 return packFloatx80( aSign, 0x7FFF, LIT64( 0x8000000000000000 ) ); 5522 } 5523 if ( aExp == 0 ) { 5524 if ( ( aSig0 | aSig1 ) == 0 ) return packFloatx80( aSign, 0, 0 ); 5525 normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); 5526 } 5527 else { 5528 aSig0 |= LIT64( 0x0001000000000000 ); 5529 } 5530 shortShift128Left( aSig0, aSig1, 15, &aSig0, &aSig1 ); 5531 return roundAndPackFloatx80( 80, aSign, aExp, aSig0, aSig1 STATUS_VAR ); 5532 5533 } 5534 5535 /*---------------------------------------------------------------------------- 5536 | Rounds the quadruple-precision floating-point value `a' to an integer, and 5537 | returns the result as a quadruple-precision floating-point value. The 5538 | operation is performed according to the IEC/IEEE Standard for Binary 5539 | Floating-Point Arithmetic. 5540 *----------------------------------------------------------------------------*/ 5541 5542 float128 float128_round_to_int( float128 a STATUS_PARAM ) 5543 { 5544 flag aSign; 5545 int32 aExp; 5546 uint64_t lastBitMask, roundBitsMask; 5547 int8 roundingMode; 5548 float128 z; 5549 5550 aExp = extractFloat128Exp( a ); 5551 if ( 0x402F <= aExp ) { 5552 if ( 0x406F <= aExp ) { 5553 if ( ( aExp == 0x7FFF ) 5554 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) 5555 ) { 5556 return propagateFloat128NaN( a, a STATUS_VAR ); 5557 } 5558 return a; 5559 } 5560 lastBitMask = 1; 5561 lastBitMask = ( lastBitMask<<( 0x406E - aExp ) )<<1; 5562 roundBitsMask = lastBitMask - 1; 5563 z = a; 5564 roundingMode = STATUS(float_rounding_mode); 5565 if ( roundingMode == float_round_nearest_even ) { 5566 if ( lastBitMask ) { 5567 add128( z.high, z.low, 0, lastBitMask>>1, &z.high, &z.low ); 5568 if ( ( z.low & roundBitsMask ) == 0 ) z.low &= ~ lastBitMask; 5569 } 5570 else { 5571 if ( (int64_t) z.low < 0 ) { 5572 ++z.high; 5573 if ( (uint64_t) ( z.low<<1 ) == 0 ) z.high &= ~1; 5574 } 5575 } 5576 } 5577 else if ( roundingMode != float_round_to_zero ) { 5578 if ( extractFloat128Sign( z ) 5579 ^ ( roundingMode == float_round_up ) ) { 5580 add128( z.high, z.low, 0, roundBitsMask, &z.high, &z.low ); 5581 } 5582 } 5583 z.low &= ~ roundBitsMask; 5584 } 5585 else { 5586 if ( aExp < 0x3FFF ) { 5587 if ( ( ( (uint64_t) ( a.high<<1 ) ) | a.low ) == 0 ) return a; 5588 STATUS(float_exception_flags) |= float_flag_inexact; 5589 aSign = extractFloat128Sign( a ); 5590 switch ( STATUS(float_rounding_mode) ) { 5591 case float_round_nearest_even: 5592 if ( ( aExp == 0x3FFE ) 5593 && ( extractFloat128Frac0( a ) 5594 | extractFloat128Frac1( a ) ) 5595 ) { 5596 return packFloat128( aSign, 0x3FFF, 0, 0 ); 5597 } 5598 break; 5599 case float_round_down: 5600 return 5601 aSign ? packFloat128( 1, 0x3FFF, 0, 0 ) 5602 : packFloat128( 0, 0, 0, 0 ); 5603 case float_round_up: 5604 return 5605 aSign ? packFloat128( 1, 0, 0, 0 ) 5606 : packFloat128( 0, 0x3FFF, 0, 0 ); 5607 } 5608 return packFloat128( aSign, 0, 0, 0 ); 5609 } 5610 lastBitMask = 1; 5611 lastBitMask <<= 0x402F - aExp; 5612 roundBitsMask = lastBitMask - 1; 5613 z.low = 0; 5614 z.high = a.high; 5615 roundingMode = STATUS(float_rounding_mode); 5616 if ( roundingMode == float_round_nearest_even ) { 5617 z.high += lastBitMask>>1; 5618 if ( ( ( z.high & roundBitsMask ) | a.low ) == 0 ) { 5619 z.high &= ~ lastBitMask; 5620 } 5621 } 5622 else if ( roundingMode != float_round_to_zero ) { 5623 if ( extractFloat128Sign( z ) 5624 ^ ( roundingMode == float_round_up ) ) { 5625 z.high |= ( a.low != 0 ); 5626 z.high += roundBitsMask; 5627 } 5628 } 5629 z.high &= ~ roundBitsMask; 5630 } 5631 if ( ( z.low != a.low ) || ( z.high != a.high ) ) { 5632 STATUS(float_exception_flags) |= float_flag_inexact; 5633 } 5634 return z; 5635 5636 } 5637 5638 /*---------------------------------------------------------------------------- 5639 | Returns the result of adding the absolute values of the quadruple-precision 5640 | floating-point values `a' and `b'. If `zSign' is 1, the sum is negated 5641 | before being returned. `zSign' is ignored if the result is a NaN. 5642 | The addition is performed according to the IEC/IEEE Standard for Binary 5643 | Floating-Point Arithmetic. 5644 *----------------------------------------------------------------------------*/ 5645 5646 static float128 addFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) 5647 { 5648 int32 aExp, bExp, zExp; 5649 uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; 5650 int32 expDiff; 5651 5652 aSig1 = extractFloat128Frac1( a ); 5653 aSig0 = extractFloat128Frac0( a ); 5654 aExp = extractFloat128Exp( a ); 5655 bSig1 = extractFloat128Frac1( b ); 5656 bSig0 = extractFloat128Frac0( b ); 5657 bExp = extractFloat128Exp( b ); 5658 expDiff = aExp - bExp; 5659 if ( 0 < expDiff ) { 5660 if ( aExp == 0x7FFF ) { 5661 if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5662 return a; 5663 } 5664 if ( bExp == 0 ) { 5665 --expDiff; 5666 } 5667 else { 5668 bSig0 |= LIT64( 0x0001000000000000 ); 5669 } 5670 shift128ExtraRightJamming( 5671 bSig0, bSig1, 0, expDiff, &bSig0, &bSig1, &zSig2 ); 5672 zExp = aExp; 5673 } 5674 else if ( expDiff < 0 ) { 5675 if ( bExp == 0x7FFF ) { 5676 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5677 return packFloat128( zSign, 0x7FFF, 0, 0 ); 5678 } 5679 if ( aExp == 0 ) { 5680 ++expDiff; 5681 } 5682 else { 5683 aSig0 |= LIT64( 0x0001000000000000 ); 5684 } 5685 shift128ExtraRightJamming( 5686 aSig0, aSig1, 0, - expDiff, &aSig0, &aSig1, &zSig2 ); 5687 zExp = bExp; 5688 } 5689 else { 5690 if ( aExp == 0x7FFF ) { 5691 if ( aSig0 | aSig1 | bSig0 | bSig1 ) { 5692 return propagateFloat128NaN( a, b STATUS_VAR ); 5693 } 5694 return a; 5695 } 5696 add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); 5697 if ( aExp == 0 ) { 5698 if (STATUS(flush_to_zero)) { 5699 if (zSig0 | zSig1) { 5700 float_raise(float_flag_output_denormal STATUS_VAR); 5701 } 5702 return packFloat128(zSign, 0, 0, 0); 5703 } 5704 return packFloat128( zSign, 0, zSig0, zSig1 ); 5705 } 5706 zSig2 = 0; 5707 zSig0 |= LIT64( 0x0002000000000000 ); 5708 zExp = aExp; 5709 goto shiftRight1; 5710 } 5711 aSig0 |= LIT64( 0x0001000000000000 ); 5712 add128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); 5713 --zExp; 5714 if ( zSig0 < LIT64( 0x0002000000000000 ) ) goto roundAndPack; 5715 ++zExp; 5716 shiftRight1: 5717 shift128ExtraRightJamming( 5718 zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); 5719 roundAndPack: 5720 return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); 5721 5722 } 5723 5724 /*---------------------------------------------------------------------------- 5725 | Returns the result of subtracting the absolute values of the quadruple- 5726 | precision floating-point values `a' and `b'. If `zSign' is 1, the 5727 | difference is negated before being returned. `zSign' is ignored if the 5728 | result is a NaN. The subtraction is performed according to the IEC/IEEE 5729 | Standard for Binary Floating-Point Arithmetic. 5730 *----------------------------------------------------------------------------*/ 5731 5732 static float128 subFloat128Sigs( float128 a, float128 b, flag zSign STATUS_PARAM) 5733 { 5734 int32 aExp, bExp, zExp; 5735 uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1; 5736 int32 expDiff; 5737 float128 z; 5738 5739 aSig1 = extractFloat128Frac1( a ); 5740 aSig0 = extractFloat128Frac0( a ); 5741 aExp = extractFloat128Exp( a ); 5742 bSig1 = extractFloat128Frac1( b ); 5743 bSig0 = extractFloat128Frac0( b ); 5744 bExp = extractFloat128Exp( b ); 5745 expDiff = aExp - bExp; 5746 shortShift128Left( aSig0, aSig1, 14, &aSig0, &aSig1 ); 5747 shortShift128Left( bSig0, bSig1, 14, &bSig0, &bSig1 ); 5748 if ( 0 < expDiff ) goto aExpBigger; 5749 if ( expDiff < 0 ) goto bExpBigger; 5750 if ( aExp == 0x7FFF ) { 5751 if ( aSig0 | aSig1 | bSig0 | bSig1 ) { 5752 return propagateFloat128NaN( a, b STATUS_VAR ); 5753 } 5754 float_raise( float_flag_invalid STATUS_VAR); 5755 z.low = float128_default_nan_low; 5756 z.high = float128_default_nan_high; 5757 return z; 5758 } 5759 if ( aExp == 0 ) { 5760 aExp = 1; 5761 bExp = 1; 5762 } 5763 if ( bSig0 < aSig0 ) goto aBigger; 5764 if ( aSig0 < bSig0 ) goto bBigger; 5765 if ( bSig1 < aSig1 ) goto aBigger; 5766 if ( aSig1 < bSig1 ) goto bBigger; 5767 return packFloat128( STATUS(float_rounding_mode) == float_round_down, 0, 0, 0 ); 5768 bExpBigger: 5769 if ( bExp == 0x7FFF ) { 5770 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5771 return packFloat128( zSign ^ 1, 0x7FFF, 0, 0 ); 5772 } 5773 if ( aExp == 0 ) { 5774 ++expDiff; 5775 } 5776 else { 5777 aSig0 |= LIT64( 0x4000000000000000 ); 5778 } 5779 shift128RightJamming( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); 5780 bSig0 |= LIT64( 0x4000000000000000 ); 5781 bBigger: 5782 sub128( bSig0, bSig1, aSig0, aSig1, &zSig0, &zSig1 ); 5783 zExp = bExp; 5784 zSign ^= 1; 5785 goto normalizeRoundAndPack; 5786 aExpBigger: 5787 if ( aExp == 0x7FFF ) { 5788 if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5789 return a; 5790 } 5791 if ( bExp == 0 ) { 5792 --expDiff; 5793 } 5794 else { 5795 bSig0 |= LIT64( 0x4000000000000000 ); 5796 } 5797 shift128RightJamming( bSig0, bSig1, expDiff, &bSig0, &bSig1 ); 5798 aSig0 |= LIT64( 0x4000000000000000 ); 5799 aBigger: 5800 sub128( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1 ); 5801 zExp = aExp; 5802 normalizeRoundAndPack: 5803 --zExp; 5804 return normalizeRoundAndPackFloat128( zSign, zExp - 14, zSig0, zSig1 STATUS_VAR ); 5805 5806 } 5807 5808 /*---------------------------------------------------------------------------- 5809 | Returns the result of adding the quadruple-precision floating-point values 5810 | `a' and `b'. The operation is performed according to the IEC/IEEE Standard 5811 | for Binary Floating-Point Arithmetic. 5812 *----------------------------------------------------------------------------*/ 5813 5814 float128 float128_add( float128 a, float128 b STATUS_PARAM ) 5815 { 5816 flag aSign, bSign; 5817 5818 aSign = extractFloat128Sign( a ); 5819 bSign = extractFloat128Sign( b ); 5820 if ( aSign == bSign ) { 5821 return addFloat128Sigs( a, b, aSign STATUS_VAR ); 5822 } 5823 else { 5824 return subFloat128Sigs( a, b, aSign STATUS_VAR ); 5825 } 5826 5827 } 5828 5829 /*---------------------------------------------------------------------------- 5830 | Returns the result of subtracting the quadruple-precision floating-point 5831 | values `a' and `b'. The operation is performed according to the IEC/IEEE 5832 | Standard for Binary Floating-Point Arithmetic. 5833 *----------------------------------------------------------------------------*/ 5834 5835 float128 float128_sub( float128 a, float128 b STATUS_PARAM ) 5836 { 5837 flag aSign, bSign; 5838 5839 aSign = extractFloat128Sign( a ); 5840 bSign = extractFloat128Sign( b ); 5841 if ( aSign == bSign ) { 5842 return subFloat128Sigs( a, b, aSign STATUS_VAR ); 5843 } 5844 else { 5845 return addFloat128Sigs( a, b, aSign STATUS_VAR ); 5846 } 5847 5848 } 5849 5850 /*---------------------------------------------------------------------------- 5851 | Returns the result of multiplying the quadruple-precision floating-point 5852 | values `a' and `b'. The operation is performed according to the IEC/IEEE 5853 | Standard for Binary Floating-Point Arithmetic. 5854 *----------------------------------------------------------------------------*/ 5855 5856 float128 float128_mul( float128 a, float128 b STATUS_PARAM ) 5857 { 5858 flag aSign, bSign, zSign; 5859 int32 aExp, bExp, zExp; 5860 uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2, zSig3; 5861 float128 z; 5862 5863 aSig1 = extractFloat128Frac1( a ); 5864 aSig0 = extractFloat128Frac0( a ); 5865 aExp = extractFloat128Exp( a ); 5866 aSign = extractFloat128Sign( a ); 5867 bSig1 = extractFloat128Frac1( b ); 5868 bSig0 = extractFloat128Frac0( b ); 5869 bExp = extractFloat128Exp( b ); 5870 bSign = extractFloat128Sign( b ); 5871 zSign = aSign ^ bSign; 5872 if ( aExp == 0x7FFF ) { 5873 if ( ( aSig0 | aSig1 ) 5874 || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { 5875 return propagateFloat128NaN( a, b STATUS_VAR ); 5876 } 5877 if ( ( bExp | bSig0 | bSig1 ) == 0 ) goto invalid; 5878 return packFloat128( zSign, 0x7FFF, 0, 0 ); 5879 } 5880 if ( bExp == 0x7FFF ) { 5881 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5882 if ( ( aExp | aSig0 | aSig1 ) == 0 ) { 5883 invalid: 5884 float_raise( float_flag_invalid STATUS_VAR); 5885 z.low = float128_default_nan_low; 5886 z.high = float128_default_nan_high; 5887 return z; 5888 } 5889 return packFloat128( zSign, 0x7FFF, 0, 0 ); 5890 } 5891 if ( aExp == 0 ) { 5892 if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); 5893 normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); 5894 } 5895 if ( bExp == 0 ) { 5896 if ( ( bSig0 | bSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); 5897 normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); 5898 } 5899 zExp = aExp + bExp - 0x4000; 5900 aSig0 |= LIT64( 0x0001000000000000 ); 5901 shortShift128Left( bSig0, bSig1, 16, &bSig0, &bSig1 ); 5902 mul128To256( aSig0, aSig1, bSig0, bSig1, &zSig0, &zSig1, &zSig2, &zSig3 ); 5903 add128( zSig0, zSig1, aSig0, aSig1, &zSig0, &zSig1 ); 5904 zSig2 |= ( zSig3 != 0 ); 5905 if ( LIT64( 0x0002000000000000 ) <= zSig0 ) { 5906 shift128ExtraRightJamming( 5907 zSig0, zSig1, zSig2, 1, &zSig0, &zSig1, &zSig2 ); 5908 ++zExp; 5909 } 5910 return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); 5911 5912 } 5913 5914 /*---------------------------------------------------------------------------- 5915 | Returns the result of dividing the quadruple-precision floating-point value 5916 | `a' by the corresponding value `b'. The operation is performed according to 5917 | the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 5918 *----------------------------------------------------------------------------*/ 5919 5920 float128 float128_div( float128 a, float128 b STATUS_PARAM ) 5921 { 5922 flag aSign, bSign, zSign; 5923 int32 aExp, bExp, zExp; 5924 uint64_t aSig0, aSig1, bSig0, bSig1, zSig0, zSig1, zSig2; 5925 uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; 5926 float128 z; 5927 5928 aSig1 = extractFloat128Frac1( a ); 5929 aSig0 = extractFloat128Frac0( a ); 5930 aExp = extractFloat128Exp( a ); 5931 aSign = extractFloat128Sign( a ); 5932 bSig1 = extractFloat128Frac1( b ); 5933 bSig0 = extractFloat128Frac0( b ); 5934 bExp = extractFloat128Exp( b ); 5935 bSign = extractFloat128Sign( b ); 5936 zSign = aSign ^ bSign; 5937 if ( aExp == 0x7FFF ) { 5938 if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5939 if ( bExp == 0x7FFF ) { 5940 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5941 goto invalid; 5942 } 5943 return packFloat128( zSign, 0x7FFF, 0, 0 ); 5944 } 5945 if ( bExp == 0x7FFF ) { 5946 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 5947 return packFloat128( zSign, 0, 0, 0 ); 5948 } 5949 if ( bExp == 0 ) { 5950 if ( ( bSig0 | bSig1 ) == 0 ) { 5951 if ( ( aExp | aSig0 | aSig1 ) == 0 ) { 5952 invalid: 5953 float_raise( float_flag_invalid STATUS_VAR); 5954 z.low = float128_default_nan_low; 5955 z.high = float128_default_nan_high; 5956 return z; 5957 } 5958 float_raise( float_flag_divbyzero STATUS_VAR); 5959 return packFloat128( zSign, 0x7FFF, 0, 0 ); 5960 } 5961 normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); 5962 } 5963 if ( aExp == 0 ) { 5964 if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( zSign, 0, 0, 0 ); 5965 normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); 5966 } 5967 zExp = aExp - bExp + 0x3FFD; 5968 shortShift128Left( 5969 aSig0 | LIT64( 0x0001000000000000 ), aSig1, 15, &aSig0, &aSig1 ); 5970 shortShift128Left( 5971 bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); 5972 if ( le128( bSig0, bSig1, aSig0, aSig1 ) ) { 5973 shift128Right( aSig0, aSig1, 1, &aSig0, &aSig1 ); 5974 ++zExp; 5975 } 5976 zSig0 = estimateDiv128To64( aSig0, aSig1, bSig0 ); 5977 mul128By64To192( bSig0, bSig1, zSig0, &term0, &term1, &term2 ); 5978 sub192( aSig0, aSig1, 0, term0, term1, term2, &rem0, &rem1, &rem2 ); 5979 while ( (int64_t) rem0 < 0 ) { 5980 --zSig0; 5981 add192( rem0, rem1, rem2, 0, bSig0, bSig1, &rem0, &rem1, &rem2 ); 5982 } 5983 zSig1 = estimateDiv128To64( rem1, rem2, bSig0 ); 5984 if ( ( zSig1 & 0x3FFF ) <= 4 ) { 5985 mul128By64To192( bSig0, bSig1, zSig1, &term1, &term2, &term3 ); 5986 sub192( rem1, rem2, 0, term1, term2, term3, &rem1, &rem2, &rem3 ); 5987 while ( (int64_t) rem1 < 0 ) { 5988 --zSig1; 5989 add192( rem1, rem2, rem3, 0, bSig0, bSig1, &rem1, &rem2, &rem3 ); 5990 } 5991 zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); 5992 } 5993 shift128ExtraRightJamming( zSig0, zSig1, 0, 15, &zSig0, &zSig1, &zSig2 ); 5994 return roundAndPackFloat128( zSign, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); 5995 5996 } 5997 5998 /*---------------------------------------------------------------------------- 5999 | Returns the remainder of the quadruple-precision floating-point value `a' 6000 | with respect to the corresponding value `b'. The operation is performed 6001 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 6002 *----------------------------------------------------------------------------*/ 6003 6004 float128 float128_rem( float128 a, float128 b STATUS_PARAM ) 6005 { 6006 flag aSign, zSign; 6007 int32 aExp, bExp, expDiff; 6008 uint64_t aSig0, aSig1, bSig0, bSig1, q, term0, term1, term2; 6009 uint64_t allZero, alternateASig0, alternateASig1, sigMean1; 6010 int64_t sigMean0; 6011 float128 z; 6012 6013 aSig1 = extractFloat128Frac1( a ); 6014 aSig0 = extractFloat128Frac0( a ); 6015 aExp = extractFloat128Exp( a ); 6016 aSign = extractFloat128Sign( a ); 6017 bSig1 = extractFloat128Frac1( b ); 6018 bSig0 = extractFloat128Frac0( b ); 6019 bExp = extractFloat128Exp( b ); 6020 if ( aExp == 0x7FFF ) { 6021 if ( ( aSig0 | aSig1 ) 6022 || ( ( bExp == 0x7FFF ) && ( bSig0 | bSig1 ) ) ) { 6023 return propagateFloat128NaN( a, b STATUS_VAR ); 6024 } 6025 goto invalid; 6026 } 6027 if ( bExp == 0x7FFF ) { 6028 if ( bSig0 | bSig1 ) return propagateFloat128NaN( a, b STATUS_VAR ); 6029 return a; 6030 } 6031 if ( bExp == 0 ) { 6032 if ( ( bSig0 | bSig1 ) == 0 ) { 6033 invalid: 6034 float_raise( float_flag_invalid STATUS_VAR); 6035 z.low = float128_default_nan_low; 6036 z.high = float128_default_nan_high; 6037 return z; 6038 } 6039 normalizeFloat128Subnormal( bSig0, bSig1, &bExp, &bSig0, &bSig1 ); 6040 } 6041 if ( aExp == 0 ) { 6042 if ( ( aSig0 | aSig1 ) == 0 ) return a; 6043 normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); 6044 } 6045 expDiff = aExp - bExp; 6046 if ( expDiff < -1 ) return a; 6047 shortShift128Left( 6048 aSig0 | LIT64( 0x0001000000000000 ), 6049 aSig1, 6050 15 - ( expDiff < 0 ), 6051 &aSig0, 6052 &aSig1 6053 ); 6054 shortShift128Left( 6055 bSig0 | LIT64( 0x0001000000000000 ), bSig1, 15, &bSig0, &bSig1 ); 6056 q = le128( bSig0, bSig1, aSig0, aSig1 ); 6057 if ( q ) sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); 6058 expDiff -= 64; 6059 while ( 0 < expDiff ) { 6060 q = estimateDiv128To64( aSig0, aSig1, bSig0 ); 6061 q = ( 4 < q ) ? q - 4 : 0; 6062 mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); 6063 shortShift192Left( term0, term1, term2, 61, &term1, &term2, &allZero ); 6064 shortShift128Left( aSig0, aSig1, 61, &aSig0, &allZero ); 6065 sub128( aSig0, 0, term1, term2, &aSig0, &aSig1 ); 6066 expDiff -= 61; 6067 } 6068 if ( -64 < expDiff ) { 6069 q = estimateDiv128To64( aSig0, aSig1, bSig0 ); 6070 q = ( 4 < q ) ? q - 4 : 0; 6071 q >>= - expDiff; 6072 shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); 6073 expDiff += 52; 6074 if ( expDiff < 0 ) { 6075 shift128Right( aSig0, aSig1, - expDiff, &aSig0, &aSig1 ); 6076 } 6077 else { 6078 shortShift128Left( aSig0, aSig1, expDiff, &aSig0, &aSig1 ); 6079 } 6080 mul128By64To192( bSig0, bSig1, q, &term0, &term1, &term2 ); 6081 sub128( aSig0, aSig1, term1, term2, &aSig0, &aSig1 ); 6082 } 6083 else { 6084 shift128Right( aSig0, aSig1, 12, &aSig0, &aSig1 ); 6085 shift128Right( bSig0, bSig1, 12, &bSig0, &bSig1 ); 6086 } 6087 do { 6088 alternateASig0 = aSig0; 6089 alternateASig1 = aSig1; 6090 ++q; 6091 sub128( aSig0, aSig1, bSig0, bSig1, &aSig0, &aSig1 ); 6092 } while ( 0 <= (int64_t) aSig0 ); 6093 add128( 6094 aSig0, aSig1, alternateASig0, alternateASig1, (uint64_t *)&sigMean0, &sigMean1 ); 6095 if ( ( sigMean0 < 0 ) 6096 || ( ( ( sigMean0 | sigMean1 ) == 0 ) && ( q & 1 ) ) ) { 6097 aSig0 = alternateASig0; 6098 aSig1 = alternateASig1; 6099 } 6100 zSign = ( (int64_t) aSig0 < 0 ); 6101 if ( zSign ) sub128( 0, 0, aSig0, aSig1, &aSig0, &aSig1 ); 6102 return 6103 normalizeRoundAndPackFloat128( aSign ^ zSign, bExp - 4, aSig0, aSig1 STATUS_VAR ); 6104 6105 } 6106 6107 /*---------------------------------------------------------------------------- 6108 | Returns the square root of the quadruple-precision floating-point value `a'. 6109 | The operation is performed according to the IEC/IEEE Standard for Binary 6110 | Floating-Point Arithmetic. 6111 *----------------------------------------------------------------------------*/ 6112 6113 float128 float128_sqrt( float128 a STATUS_PARAM ) 6114 { 6115 flag aSign; 6116 int32 aExp, zExp; 6117 uint64_t aSig0, aSig1, zSig0, zSig1, zSig2, doubleZSig0; 6118 uint64_t rem0, rem1, rem2, rem3, term0, term1, term2, term3; 6119 float128 z; 6120 6121 aSig1 = extractFloat128Frac1( a ); 6122 aSig0 = extractFloat128Frac0( a ); 6123 aExp = extractFloat128Exp( a ); 6124 aSign = extractFloat128Sign( a ); 6125 if ( aExp == 0x7FFF ) { 6126 if ( aSig0 | aSig1 ) return propagateFloat128NaN( a, a STATUS_VAR ); 6127 if ( ! aSign ) return a; 6128 goto invalid; 6129 } 6130 if ( aSign ) { 6131 if ( ( aExp | aSig0 | aSig1 ) == 0 ) return a; 6132 invalid: 6133 float_raise( float_flag_invalid STATUS_VAR); 6134 z.low = float128_default_nan_low; 6135 z.high = float128_default_nan_high; 6136 return z; 6137 } 6138 if ( aExp == 0 ) { 6139 if ( ( aSig0 | aSig1 ) == 0 ) return packFloat128( 0, 0, 0, 0 ); 6140 normalizeFloat128Subnormal( aSig0, aSig1, &aExp, &aSig0, &aSig1 ); 6141 } 6142 zExp = ( ( aExp - 0x3FFF )>>1 ) + 0x3FFE; 6143 aSig0 |= LIT64( 0x0001000000000000 ); 6144 zSig0 = estimateSqrt32( aExp, aSig0>>17 ); 6145 shortShift128Left( aSig0, aSig1, 13 - ( aExp & 1 ), &aSig0, &aSig1 ); 6146 zSig0 = estimateDiv128To64( aSig0, aSig1, zSig0<<32 ) + ( zSig0<<30 ); 6147 doubleZSig0 = zSig0<<1; 6148 mul64To128( zSig0, zSig0, &term0, &term1 ); 6149 sub128( aSig0, aSig1, term0, term1, &rem0, &rem1 ); 6150 while ( (int64_t) rem0 < 0 ) { 6151 --zSig0; 6152 doubleZSig0 -= 2; 6153 add128( rem0, rem1, zSig0>>63, doubleZSig0 | 1, &rem0, &rem1 ); 6154 } 6155 zSig1 = estimateDiv128To64( rem1, 0, doubleZSig0 ); 6156 if ( ( zSig1 & 0x1FFF ) <= 5 ) { 6157 if ( zSig1 == 0 ) zSig1 = 1; 6158 mul64To128( doubleZSig0, zSig1, &term1, &term2 ); 6159 sub128( rem1, 0, term1, term2, &rem1, &rem2 ); 6160 mul64To128( zSig1, zSig1, &term2, &term3 ); 6161 sub192( rem1, rem2, 0, 0, term2, term3, &rem1, &rem2, &rem3 ); 6162 while ( (int64_t) rem1 < 0 ) { 6163 --zSig1; 6164 shortShift128Left( 0, zSig1, 1, &term2, &term3 ); 6165 term3 |= 1; 6166 term2 |= doubleZSig0; 6167 add192( rem1, rem2, rem3, 0, term2, term3, &rem1, &rem2, &rem3 ); 6168 } 6169 zSig1 |= ( ( rem1 | rem2 | rem3 ) != 0 ); 6170 } 6171 shift128ExtraRightJamming( zSig0, zSig1, 0, 14, &zSig0, &zSig1, &zSig2 ); 6172 return roundAndPackFloat128( 0, zExp, zSig0, zSig1, zSig2 STATUS_VAR ); 6173 6174 } 6175 6176 /*---------------------------------------------------------------------------- 6177 | Returns 1 if the quadruple-precision floating-point value `a' is equal to 6178 | the corresponding value `b', and 0 otherwise. The invalid exception is 6179 | raised if either operand is a NaN. Otherwise, the comparison is performed 6180 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 6181 *----------------------------------------------------------------------------*/ 6182 6183 int float128_eq( float128 a, float128 b STATUS_PARAM ) 6184 { 6185 6186 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6187 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6188 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6189 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6190 ) { 6191 float_raise( float_flag_invalid STATUS_VAR); 6192 return 0; 6193 } 6194 return 6195 ( a.low == b.low ) 6196 && ( ( a.high == b.high ) 6197 || ( ( a.low == 0 ) 6198 && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) 6199 ); 6200 6201 } 6202 6203 /*---------------------------------------------------------------------------- 6204 | Returns 1 if the quadruple-precision floating-point value `a' is less than 6205 | or equal to the corresponding value `b', and 0 otherwise. The invalid 6206 | exception is raised if either operand is a NaN. The comparison is performed 6207 | according to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 6208 *----------------------------------------------------------------------------*/ 6209 6210 int float128_le( float128 a, float128 b STATUS_PARAM ) 6211 { 6212 flag aSign, bSign; 6213 6214 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6215 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6216 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6217 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6218 ) { 6219 float_raise( float_flag_invalid STATUS_VAR); 6220 return 0; 6221 } 6222 aSign = extractFloat128Sign( a ); 6223 bSign = extractFloat128Sign( b ); 6224 if ( aSign != bSign ) { 6225 return 6226 aSign 6227 || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 6228 == 0 ); 6229 } 6230 return 6231 aSign ? le128( b.high, b.low, a.high, a.low ) 6232 : le128( a.high, a.low, b.high, b.low ); 6233 6234 } 6235 6236 /*---------------------------------------------------------------------------- 6237 | Returns 1 if the quadruple-precision floating-point value `a' is less than 6238 | the corresponding value `b', and 0 otherwise. The invalid exception is 6239 | raised if either operand is a NaN. The comparison is performed according 6240 | to the IEC/IEEE Standard for Binary Floating-Point Arithmetic. 6241 *----------------------------------------------------------------------------*/ 6242 6243 int float128_lt( float128 a, float128 b STATUS_PARAM ) 6244 { 6245 flag aSign, bSign; 6246 6247 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6248 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6249 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6250 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6251 ) { 6252 float_raise( float_flag_invalid STATUS_VAR); 6253 return 0; 6254 } 6255 aSign = extractFloat128Sign( a ); 6256 bSign = extractFloat128Sign( b ); 6257 if ( aSign != bSign ) { 6258 return 6259 aSign 6260 && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 6261 != 0 ); 6262 } 6263 return 6264 aSign ? lt128( b.high, b.low, a.high, a.low ) 6265 : lt128( a.high, a.low, b.high, b.low ); 6266 6267 } 6268 6269 /*---------------------------------------------------------------------------- 6270 | Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot 6271 | be compared, and 0 otherwise. The invalid exception is raised if either 6272 | operand is a NaN. The comparison is performed according to the IEC/IEEE 6273 | Standard for Binary Floating-Point Arithmetic. 6274 *----------------------------------------------------------------------------*/ 6275 6276 int float128_unordered( float128 a, float128 b STATUS_PARAM ) 6277 { 6278 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6279 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6280 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6281 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6282 ) { 6283 float_raise( float_flag_invalid STATUS_VAR); 6284 return 1; 6285 } 6286 return 0; 6287 } 6288 6289 /*---------------------------------------------------------------------------- 6290 | Returns 1 if the quadruple-precision floating-point value `a' is equal to 6291 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 6292 | exception. The comparison is performed according to the IEC/IEEE Standard 6293 | for Binary Floating-Point Arithmetic. 6294 *----------------------------------------------------------------------------*/ 6295 6296 int float128_eq_quiet( float128 a, float128 b STATUS_PARAM ) 6297 { 6298 6299 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6300 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6301 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6302 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6303 ) { 6304 if ( float128_is_signaling_nan( a ) 6305 || float128_is_signaling_nan( b ) ) { 6306 float_raise( float_flag_invalid STATUS_VAR); 6307 } 6308 return 0; 6309 } 6310 return 6311 ( a.low == b.low ) 6312 && ( ( a.high == b.high ) 6313 || ( ( a.low == 0 ) 6314 && ( (uint64_t) ( ( a.high | b.high )<<1 ) == 0 ) ) 6315 ); 6316 6317 } 6318 6319 /*---------------------------------------------------------------------------- 6320 | Returns 1 if the quadruple-precision floating-point value `a' is less than 6321 | or equal to the corresponding value `b', and 0 otherwise. Quiet NaNs do not 6322 | cause an exception. Otherwise, the comparison is performed according to the 6323 | IEC/IEEE Standard for Binary Floating-Point Arithmetic. 6324 *----------------------------------------------------------------------------*/ 6325 6326 int float128_le_quiet( float128 a, float128 b STATUS_PARAM ) 6327 { 6328 flag aSign, bSign; 6329 6330 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6331 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6332 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6333 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6334 ) { 6335 if ( float128_is_signaling_nan( a ) 6336 || float128_is_signaling_nan( b ) ) { 6337 float_raise( float_flag_invalid STATUS_VAR); 6338 } 6339 return 0; 6340 } 6341 aSign = extractFloat128Sign( a ); 6342 bSign = extractFloat128Sign( b ); 6343 if ( aSign != bSign ) { 6344 return 6345 aSign 6346 || ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 6347 == 0 ); 6348 } 6349 return 6350 aSign ? le128( b.high, b.low, a.high, a.low ) 6351 : le128( a.high, a.low, b.high, b.low ); 6352 6353 } 6354 6355 /*---------------------------------------------------------------------------- 6356 | Returns 1 if the quadruple-precision floating-point value `a' is less than 6357 | the corresponding value `b', and 0 otherwise. Quiet NaNs do not cause an 6358 | exception. Otherwise, the comparison is performed according to the IEC/IEEE 6359 | Standard for Binary Floating-Point Arithmetic. 6360 *----------------------------------------------------------------------------*/ 6361 6362 int float128_lt_quiet( float128 a, float128 b STATUS_PARAM ) 6363 { 6364 flag aSign, bSign; 6365 6366 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6367 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6368 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6369 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6370 ) { 6371 if ( float128_is_signaling_nan( a ) 6372 || float128_is_signaling_nan( b ) ) { 6373 float_raise( float_flag_invalid STATUS_VAR); 6374 } 6375 return 0; 6376 } 6377 aSign = extractFloat128Sign( a ); 6378 bSign = extractFloat128Sign( b ); 6379 if ( aSign != bSign ) { 6380 return 6381 aSign 6382 && ( ( ( (uint64_t) ( ( a.high | b.high )<<1 ) ) | a.low | b.low ) 6383 != 0 ); 6384 } 6385 return 6386 aSign ? lt128( b.high, b.low, a.high, a.low ) 6387 : lt128( a.high, a.low, b.high, b.low ); 6388 6389 } 6390 6391 /*---------------------------------------------------------------------------- 6392 | Returns 1 if the quadruple-precision floating-point values `a' and `b' cannot 6393 | be compared, and 0 otherwise. Quiet NaNs do not cause an exception. The 6394 | comparison is performed according to the IEC/IEEE Standard for Binary 6395 | Floating-Point Arithmetic. 6396 *----------------------------------------------------------------------------*/ 6397 6398 int float128_unordered_quiet( float128 a, float128 b STATUS_PARAM ) 6399 { 6400 if ( ( ( extractFloat128Exp( a ) == 0x7FFF ) 6401 && ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) 6402 || ( ( extractFloat128Exp( b ) == 0x7FFF ) 6403 && ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) ) 6404 ) { 6405 if ( float128_is_signaling_nan( a ) 6406 || float128_is_signaling_nan( b ) ) { 6407 float_raise( float_flag_invalid STATUS_VAR); 6408 } 6409 return 1; 6410 } 6411 return 0; 6412 } 6413 6414 /* misc functions */ 6415 float32 uint32_to_float32( uint32 a STATUS_PARAM ) 6416 { 6417 return int64_to_float32(a STATUS_VAR); 6418 } 6419 6420 float64 uint32_to_float64( uint32 a STATUS_PARAM ) 6421 { 6422 return int64_to_float64(a STATUS_VAR); 6423 } 6424 6425 uint32 float32_to_uint32( float32 a STATUS_PARAM ) 6426 { 6427 int64_t v; 6428 uint32 res; 6429 6430 v = float32_to_int64(a STATUS_VAR); 6431 if (v < 0) { 6432 res = 0; 6433 float_raise( float_flag_invalid STATUS_VAR); 6434 } else if (v > 0xffffffff) { 6435 res = 0xffffffff; 6436 float_raise( float_flag_invalid STATUS_VAR); 6437 } else { 6438 res = v; 6439 } 6440 return res; 6441 } 6442 6443 uint32 float32_to_uint32_round_to_zero( float32 a STATUS_PARAM ) 6444 { 6445 int64_t v; 6446 uint32 res; 6447 6448 v = float32_to_int64_round_to_zero(a STATUS_VAR); 6449 if (v < 0) { 6450 res = 0; 6451 float_raise( float_flag_invalid STATUS_VAR); 6452 } else if (v > 0xffffffff) { 6453 res = 0xffffffff; 6454 float_raise( float_flag_invalid STATUS_VAR); 6455 } else { 6456 res = v; 6457 } 6458 return res; 6459 } 6460 6461 uint_fast16_t float32_to_uint16_round_to_zero(float32 a STATUS_PARAM) 6462 { 6463 int64_t v; 6464 uint_fast16_t res; 6465 6466 v = float32_to_int64_round_to_zero(a STATUS_VAR); 6467 if (v < 0) { 6468 res = 0; 6469 float_raise( float_flag_invalid STATUS_VAR); 6470 } else if (v > 0xffff) { 6471 res = 0xffff; 6472 float_raise( float_flag_invalid STATUS_VAR); 6473 } else { 6474 res = v; 6475 } 6476 return res; 6477 } 6478 6479 uint32 float64_to_uint32( float64 a STATUS_PARAM ) 6480 { 6481 int64_t v; 6482 uint32 res; 6483 6484 v = float64_to_int64(a STATUS_VAR); 6485 if (v < 0) { 6486 res = 0; 6487 float_raise( float_flag_invalid STATUS_VAR); 6488 } else if (v > 0xffffffff) { 6489 res = 0xffffffff; 6490 float_raise( float_flag_invalid STATUS_VAR); 6491 } else { 6492 res = v; 6493 } 6494 return res; 6495 } 6496 6497 uint32 float64_to_uint32_round_to_zero( float64 a STATUS_PARAM ) 6498 { 6499 int64_t v; 6500 uint32 res; 6501 6502 v = float64_to_int64_round_to_zero(a STATUS_VAR); 6503 if (v < 0) { 6504 res = 0; 6505 float_raise( float_flag_invalid STATUS_VAR); 6506 } else if (v > 0xffffffff) { 6507 res = 0xffffffff; 6508 float_raise( float_flag_invalid STATUS_VAR); 6509 } else { 6510 res = v; 6511 } 6512 return res; 6513 } 6514 6515 uint_fast16_t float64_to_uint16_round_to_zero(float64 a STATUS_PARAM) 6516 { 6517 int64_t v; 6518 uint_fast16_t res; 6519 6520 v = float64_to_int64_round_to_zero(a STATUS_VAR); 6521 if (v < 0) { 6522 res = 0; 6523 float_raise( float_flag_invalid STATUS_VAR); 6524 } else if (v > 0xffff) { 6525 res = 0xffff; 6526 float_raise( float_flag_invalid STATUS_VAR); 6527 } else { 6528 res = v; 6529 } 6530 return res; 6531 } 6532 6533 /* FIXME: This looks broken. */ 6534 uint64_t float64_to_uint64 (float64 a STATUS_PARAM) 6535 { 6536 int64_t v; 6537 6538 v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); 6539 v += float64_val(a); 6540 v = float64_to_int64(make_float64(v) STATUS_VAR); 6541 6542 return v - INT64_MIN; 6543 } 6544 6545 uint64_t float64_to_uint64_round_to_zero (float64 a STATUS_PARAM) 6546 { 6547 int64_t v; 6548 6549 v = float64_val(int64_to_float64(INT64_MIN STATUS_VAR)); 6550 v += float64_val(a); 6551 v = float64_to_int64_round_to_zero(make_float64(v) STATUS_VAR); 6552 6553 return v - INT64_MIN; 6554 } 6555 6556 #define COMPARE(s, nan_exp) \ 6557 INLINE int float ## s ## _compare_internal( float ## s a, float ## s b, \ 6558 int is_quiet STATUS_PARAM ) \ 6559 { \ 6560 flag aSign, bSign; \ 6561 uint ## s ## _t av, bv; \ 6562 a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ 6563 b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ 6564 \ 6565 if (( ( extractFloat ## s ## Exp( a ) == nan_exp ) && \ 6566 extractFloat ## s ## Frac( a ) ) || \ 6567 ( ( extractFloat ## s ## Exp( b ) == nan_exp ) && \ 6568 extractFloat ## s ## Frac( b ) )) { \ 6569 if (!is_quiet || \ 6570 float ## s ## _is_signaling_nan( a ) || \ 6571 float ## s ## _is_signaling_nan( b ) ) { \ 6572 float_raise( float_flag_invalid STATUS_VAR); \ 6573 } \ 6574 return float_relation_unordered; \ 6575 } \ 6576 aSign = extractFloat ## s ## Sign( a ); \ 6577 bSign = extractFloat ## s ## Sign( b ); \ 6578 av = float ## s ## _val(a); \ 6579 bv = float ## s ## _val(b); \ 6580 if ( aSign != bSign ) { \ 6581 if ( (uint ## s ## _t) ( ( av | bv )<<1 ) == 0 ) { \ 6582 /* zero case */ \ 6583 return float_relation_equal; \ 6584 } else { \ 6585 return 1 - (2 * aSign); \ 6586 } \ 6587 } else { \ 6588 if (av == bv) { \ 6589 return float_relation_equal; \ 6590 } else { \ 6591 return 1 - 2 * (aSign ^ ( av < bv )); \ 6592 } \ 6593 } \ 6594 } \ 6595 \ 6596 int float ## s ## _compare( float ## s a, float ## s b STATUS_PARAM ) \ 6597 { \ 6598 return float ## s ## _compare_internal(a, b, 0 STATUS_VAR); \ 6599 } \ 6600 \ 6601 int float ## s ## _compare_quiet( float ## s a, float ## s b STATUS_PARAM ) \ 6602 { \ 6603 return float ## s ## _compare_internal(a, b, 1 STATUS_VAR); \ 6604 } 6605 6606 COMPARE(32, 0xff) 6607 COMPARE(64, 0x7ff) 6608 6609 INLINE int floatx80_compare_internal( floatx80 a, floatx80 b, 6610 int is_quiet STATUS_PARAM ) 6611 { 6612 flag aSign, bSign; 6613 6614 if (( ( extractFloatx80Exp( a ) == 0x7fff ) && 6615 ( extractFloatx80Frac( a )<<1 ) ) || 6616 ( ( extractFloatx80Exp( b ) == 0x7fff ) && 6617 ( extractFloatx80Frac( b )<<1 ) )) { 6618 if (!is_quiet || 6619 floatx80_is_signaling_nan( a ) || 6620 floatx80_is_signaling_nan( b ) ) { 6621 float_raise( float_flag_invalid STATUS_VAR); 6622 } 6623 return float_relation_unordered; 6624 } 6625 aSign = extractFloatx80Sign( a ); 6626 bSign = extractFloatx80Sign( b ); 6627 if ( aSign != bSign ) { 6628 6629 if ( ( ( (uint16_t) ( ( a.high | b.high ) << 1 ) ) == 0) && 6630 ( ( a.low | b.low ) == 0 ) ) { 6631 /* zero case */ 6632 return float_relation_equal; 6633 } else { 6634 return 1 - (2 * aSign); 6635 } 6636 } else { 6637 if (a.low == b.low && a.high == b.high) { 6638 return float_relation_equal; 6639 } else { 6640 return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); 6641 } 6642 } 6643 } 6644 6645 int floatx80_compare( floatx80 a, floatx80 b STATUS_PARAM ) 6646 { 6647 return floatx80_compare_internal(a, b, 0 STATUS_VAR); 6648 } 6649 6650 int floatx80_compare_quiet( floatx80 a, floatx80 b STATUS_PARAM ) 6651 { 6652 return floatx80_compare_internal(a, b, 1 STATUS_VAR); 6653 } 6654 6655 INLINE int float128_compare_internal( float128 a, float128 b, 6656 int is_quiet STATUS_PARAM ) 6657 { 6658 flag aSign, bSign; 6659 6660 if (( ( extractFloat128Exp( a ) == 0x7fff ) && 6661 ( extractFloat128Frac0( a ) | extractFloat128Frac1( a ) ) ) || 6662 ( ( extractFloat128Exp( b ) == 0x7fff ) && 6663 ( extractFloat128Frac0( b ) | extractFloat128Frac1( b ) ) )) { 6664 if (!is_quiet || 6665 float128_is_signaling_nan( a ) || 6666 float128_is_signaling_nan( b ) ) { 6667 float_raise( float_flag_invalid STATUS_VAR); 6668 } 6669 return float_relation_unordered; 6670 } 6671 aSign = extractFloat128Sign( a ); 6672 bSign = extractFloat128Sign( b ); 6673 if ( aSign != bSign ) { 6674 if ( ( ( ( a.high | b.high )<<1 ) | a.low | b.low ) == 0 ) { 6675 /* zero case */ 6676 return float_relation_equal; 6677 } else { 6678 return 1 - (2 * aSign); 6679 } 6680 } else { 6681 if (a.low == b.low && a.high == b.high) { 6682 return float_relation_equal; 6683 } else { 6684 return 1 - 2 * (aSign ^ ( lt128( a.high, a.low, b.high, b.low ) )); 6685 } 6686 } 6687 } 6688 6689 int float128_compare( float128 a, float128 b STATUS_PARAM ) 6690 { 6691 return float128_compare_internal(a, b, 0 STATUS_VAR); 6692 } 6693 6694 int float128_compare_quiet( float128 a, float128 b STATUS_PARAM ) 6695 { 6696 return float128_compare_internal(a, b, 1 STATUS_VAR); 6697 } 6698 6699 /* min() and max() functions. These can't be implemented as 6700 * 'compare and pick one input' because that would mishandle 6701 * NaNs and +0 vs -0. 6702 */ 6703 #define MINMAX(s, nan_exp) \ 6704 INLINE float ## s float ## s ## _minmax(float ## s a, float ## s b, \ 6705 int ismin STATUS_PARAM ) \ 6706 { \ 6707 flag aSign, bSign; \ 6708 uint ## s ## _t av, bv; \ 6709 a = float ## s ## _squash_input_denormal(a STATUS_VAR); \ 6710 b = float ## s ## _squash_input_denormal(b STATUS_VAR); \ 6711 if (float ## s ## _is_any_nan(a) || \ 6712 float ## s ## _is_any_nan(b)) { \ 6713 return propagateFloat ## s ## NaN(a, b STATUS_VAR); \ 6714 } \ 6715 aSign = extractFloat ## s ## Sign(a); \ 6716 bSign = extractFloat ## s ## Sign(b); \ 6717 av = float ## s ## _val(a); \ 6718 bv = float ## s ## _val(b); \ 6719 if (aSign != bSign) { \ 6720 if (ismin) { \ 6721 return aSign ? a : b; \ 6722 } else { \ 6723 return aSign ? b : a; \ 6724 } \ 6725 } else { \ 6726 if (ismin) { \ 6727 return (aSign ^ (av < bv)) ? a : b; \ 6728 } else { \ 6729 return (aSign ^ (av < bv)) ? b : a; \ 6730 } \ 6731 } \ 6732 } \ 6733 \ 6734 float ## s float ## s ## _min(float ## s a, float ## s b STATUS_PARAM) \ 6735 { \ 6736 return float ## s ## _minmax(a, b, 1 STATUS_VAR); \ 6737 } \ 6738 \ 6739 float ## s float ## s ## _max(float ## s a, float ## s b STATUS_PARAM) \ 6740 { \ 6741 return float ## s ## _minmax(a, b, 0 STATUS_VAR); \ 6742 } 6743 6744 MINMAX(32, 0xff) 6745 MINMAX(64, 0x7ff) 6746 6747 6748 /* Multiply A by 2 raised to the power N. */ 6749 float32 float32_scalbn( float32 a, int n STATUS_PARAM ) 6750 { 6751 flag aSign; 6752 int16_t aExp; 6753 uint32_t aSig; 6754 6755 a = float32_squash_input_denormal(a STATUS_VAR); 6756 aSig = extractFloat32Frac( a ); 6757 aExp = extractFloat32Exp( a ); 6758 aSign = extractFloat32Sign( a ); 6759 6760 if ( aExp == 0xFF ) { 6761 if ( aSig ) { 6762 return propagateFloat32NaN( a, a STATUS_VAR ); 6763 } 6764 return a; 6765 } 6766 if ( aExp != 0 ) 6767 aSig |= 0x00800000; 6768 else if ( aSig == 0 ) 6769 return a; 6770 6771 if (n > 0x200) { 6772 n = 0x200; 6773 } else if (n < -0x200) { 6774 n = -0x200; 6775 } 6776 6777 aExp += n - 1; 6778 aSig <<= 7; 6779 return normalizeRoundAndPackFloat32( aSign, aExp, aSig STATUS_VAR ); 6780 } 6781 6782 float64 float64_scalbn( float64 a, int n STATUS_PARAM ) 6783 { 6784 flag aSign; 6785 int16_t aExp; 6786 uint64_t aSig; 6787 6788 a = float64_squash_input_denormal(a STATUS_VAR); 6789 aSig = extractFloat64Frac( a ); 6790 aExp = extractFloat64Exp( a ); 6791 aSign = extractFloat64Sign( a ); 6792 6793 if ( aExp == 0x7FF ) { 6794 if ( aSig ) { 6795 return propagateFloat64NaN( a, a STATUS_VAR ); 6796 } 6797 return a; 6798 } 6799 if ( aExp != 0 ) 6800 aSig |= LIT64( 0x0010000000000000 ); 6801 else if ( aSig == 0 ) 6802 return a; 6803 6804 if (n > 0x1000) { 6805 n = 0x1000; 6806 } else if (n < -0x1000) { 6807 n = -0x1000; 6808 } 6809 6810 aExp += n - 1; 6811 aSig <<= 10; 6812 return normalizeRoundAndPackFloat64( aSign, aExp, aSig STATUS_VAR ); 6813 } 6814 6815 floatx80 floatx80_scalbn( floatx80 a, int n STATUS_PARAM ) 6816 { 6817 flag aSign; 6818 int32_t aExp; 6819 uint64_t aSig; 6820 6821 aSig = extractFloatx80Frac( a ); 6822 aExp = extractFloatx80Exp( a ); 6823 aSign = extractFloatx80Sign( a ); 6824 6825 if ( aExp == 0x7FFF ) { 6826 if ( aSig<<1 ) { 6827 return propagateFloatx80NaN( a, a STATUS_VAR ); 6828 } 6829 return a; 6830 } 6831 6832 if (aExp == 0 && aSig == 0) 6833 return a; 6834 6835 if (n > 0x10000) { 6836 n = 0x10000; 6837 } else if (n < -0x10000) { 6838 n = -0x10000; 6839 } 6840 6841 aExp += n; 6842 return normalizeRoundAndPackFloatx80( STATUS(floatx80_rounding_precision), 6843 aSign, aExp, aSig, 0 STATUS_VAR ); 6844 } 6845 6846 float128 float128_scalbn( float128 a, int n STATUS_PARAM ) 6847 { 6848 flag aSign; 6849 int32_t aExp; 6850 uint64_t aSig0, aSig1; 6851 6852 aSig1 = extractFloat128Frac1( a ); 6853 aSig0 = extractFloat128Frac0( a ); 6854 aExp = extractFloat128Exp( a ); 6855 aSign = extractFloat128Sign( a ); 6856 if ( aExp == 0x7FFF ) { 6857 if ( aSig0 | aSig1 ) { 6858 return propagateFloat128NaN( a, a STATUS_VAR ); 6859 } 6860 return a; 6861 } 6862 if ( aExp != 0 ) 6863 aSig0 |= LIT64( 0x0001000000000000 ); 6864 else if ( aSig0 == 0 && aSig1 == 0 ) 6865 return a; 6866 6867 if (n > 0x10000) { 6868 n = 0x10000; 6869 } else if (n < -0x10000) { 6870 n = -0x10000; 6871 } 6872 6873 aExp += n - 1; 6874 return normalizeRoundAndPackFloat128( aSign, aExp, aSig0, aSig1 6875 STATUS_VAR ); 6876 6877 } 6878