1/* $NetBSD: softfloat-macros,v 1.2 2009/02/16 10:23:35 tron Exp $ */ 2/* $FreeBSD$ */ 3 4/* 5=============================================================================== 6 7This C source fragment is part of the SoftFloat IEC/IEEE Floating-point 8Arithmetic Package, Release 2a. 9 10Written by John R. Hauser. This work was made possible in part by the 11International Computer Science Institute, located at Suite 600, 1947 Center 12Street, Berkeley, California 94704. Funding was partially provided by the 13National Science Foundation under grant MIP-9311980. The original version 14of this code was written as part of a project to build a fixed-point vector 15processor in collaboration with the University of California at Berkeley, 16overseen by Profs. Nelson Morgan and John Wawrzynek. More information 17is available through the Web page `http://HTTP.CS.Berkeley.EDU/~jhauser/ 18arithmetic/SoftFloat.html'. 19 20THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort 21has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT 22TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO 23PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY 24AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. 25 26Derivative works are acceptable, even for commercial purposes, so long as 27(1) they include prominent notice that the work is derivative, and (2) they 28include prominent notice akin to these four paragraphs for those parts of 29this code that are retained. 30 31=============================================================================== 32*/ 33 34/* 35------------------------------------------------------------------------------- 36Shifts `a' right by the number of bits given in `count'. If any nonzero 37bits are shifted off, they are ``jammed'' into the least significant bit of 38the result by setting the least significant bit to 1. The value of `count' 39can be arbitrarily large; in particular, if `count' is greater than 32, the 40result will be either 0 or 1, depending on whether `a' is zero or nonzero. 41The result is stored in the location pointed to by `zPtr'. 42------------------------------------------------------------------------------- 43*/ 44INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr ) 45{ 46 bits32 z; 47 48 if ( count == 0 ) { 49 z = a; 50 } 51 else if ( count < 32 ) { 52 z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 ); 53 } 54 else { 55 z = ( a != 0 ); 56 } 57 *zPtr = z; 58 59} 60 61/* 62------------------------------------------------------------------------------- 63Shifts `a' right by the number of bits given in `count'. If any nonzero 64bits are shifted off, they are ``jammed'' into the least significant bit of 65the result by setting the least significant bit to 1. The value of `count' 66can be arbitrarily large; in particular, if `count' is greater than 64, the 67result will be either 0 or 1, depending on whether `a' is zero or nonzero. 68The result is stored in the location pointed to by `zPtr'. 69------------------------------------------------------------------------------- 70*/ 71INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr ) 72{ 73 bits64 z; 74 75 if ( count == 0 ) { 76 z = a; 77 } 78 else if ( count < 64 ) { 79 z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 ); 80 } 81 else { 82 z = ( a != 0 ); 83 } 84 *zPtr = z; 85 86} 87 88/* 89------------------------------------------------------------------------------- 90Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64 91_plus_ the number of bits given in `count'. The shifted result is at most 9264 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The 93bits shifted off form a second 64-bit result as follows: The _last_ bit 94shifted off is the most-significant bit of the extra result, and the other 9563 bits of the extra result are all zero if and only if _all_but_the_last_ 96bits shifted off were all zero. This extra result is stored in the location 97pointed to by `z1Ptr'. The value of `count' can be arbitrarily large. 98 (This routine makes more sense if `a0' and `a1' are considered to form a 99fixed-point value with binary point between `a0' and `a1'. This fixed-point 100value is shifted right by the number of bits given in `count', and the 101integer part of the result is returned at the location pointed to by 102`z0Ptr'. The fractional part of the result may be slightly corrupted as 103described above, and is returned at the location pointed to by `z1Ptr'.) 104------------------------------------------------------------------------------- 105*/ 106INLINE void 107 shift64ExtraRightJamming( 108 bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) 109{ 110 bits64 z0, z1; 111 int8 negCount = ( - count ) & 63; 112 113 if ( count == 0 ) { 114 z1 = a1; 115 z0 = a0; 116 } 117 else if ( count < 64 ) { 118 z1 = ( a0<<negCount ) | ( a1 != 0 ); 119 z0 = a0>>count; 120 } 121 else { 122 if ( count == 64 ) { 123 z1 = a0 | ( a1 != 0 ); 124 } 125 else { 126 z1 = ( ( a0 | a1 ) != 0 ); 127 } 128 z0 = 0; 129 } 130 *z1Ptr = z1; 131 *z0Ptr = z0; 132 133} 134 135/* 136------------------------------------------------------------------------------- 137Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the 138number of bits given in `count'. Any bits shifted off are lost. The value 139of `count' can be arbitrarily large; in particular, if `count' is greater 140than 128, the result will be 0. The result is broken into two 64-bit pieces 141which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. 142------------------------------------------------------------------------------- 143*/ 144INLINE void 145 shift128Right( 146 bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) 147{ 148 bits64 z0, z1; 149 int8 negCount = ( - count ) & 63; 150 151 if ( count == 0 ) { 152 z1 = a1; 153 z0 = a0; 154 } 155 else if ( count < 64 ) { 156 z1 = ( a0<<negCount ) | ( a1>>count ); 157 z0 = a0>>count; 158 } 159 else { 160 z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0; 161 z0 = 0; 162 } 163 *z1Ptr = z1; 164 *z0Ptr = z0; 165 166} 167 168/* 169------------------------------------------------------------------------------- 170Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the 171number of bits given in `count'. If any nonzero bits are shifted off, they 172are ``jammed'' into the least significant bit of the result by setting the 173least significant bit to 1. The value of `count' can be arbitrarily large; 174in particular, if `count' is greater than 128, the result will be either 1750 or 1, depending on whether the concatenation of `a0' and `a1' is zero or 176nonzero. The result is broken into two 64-bit pieces which are stored at 177the locations pointed to by `z0Ptr' and `z1Ptr'. 178------------------------------------------------------------------------------- 179*/ 180INLINE void 181 shift128RightJamming( 182 bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) 183{ 184 bits64 z0, z1; 185 int8 negCount = ( - count ) & 63; 186 187 if ( count == 0 ) { 188 z1 = a1; 189 z0 = a0; 190 } 191 else if ( count < 64 ) { 192 z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 ); 193 z0 = a0>>count; 194 } 195 else { 196 if ( count == 64 ) { 197 z1 = a0 | ( a1 != 0 ); 198 } 199 else if ( count < 128 ) { 200 z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 ); 201 } 202 else { 203 z1 = ( ( a0 | a1 ) != 0 ); 204 } 205 z0 = 0; 206 } 207 *z1Ptr = z1; 208 *z0Ptr = z0; 209 210} 211 212/* 213------------------------------------------------------------------------------- 214Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right 215by 64 _plus_ the number of bits given in `count'. The shifted result is 216at most 128 nonzero bits; these are broken into two 64-bit pieces which are 217stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted 218off form a third 64-bit result as follows: The _last_ bit shifted off is 219the most-significant bit of the extra result, and the other 63 bits of the 220extra result are all zero if and only if _all_but_the_last_ bits shifted off 221were all zero. This extra result is stored in the location pointed to by 222`z2Ptr'. The value of `count' can be arbitrarily large. 223 (This routine makes more sense if `a0', `a1', and `a2' are considered 224to form a fixed-point value with binary point between `a1' and `a2'. This 225fixed-point value is shifted right by the number of bits given in `count', 226and the integer part of the result is returned at the locations pointed to 227by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly 228corrupted as described above, and is returned at the location pointed to by 229`z2Ptr'.) 230------------------------------------------------------------------------------- 231*/ 232INLINE void 233 shift128ExtraRightJamming( 234 bits64 a0, 235 bits64 a1, 236 bits64 a2, 237 int16 count, 238 bits64 *z0Ptr, 239 bits64 *z1Ptr, 240 bits64 *z2Ptr 241 ) 242{ 243 bits64 z0, z1, z2; 244 int8 negCount = ( - count ) & 63; 245 246 if ( count == 0 ) { 247 z2 = a2; 248 z1 = a1; 249 z0 = a0; 250 } 251 else { 252 if ( count < 64 ) { 253 z2 = a1<<negCount; 254 z1 = ( a0<<negCount ) | ( a1>>count ); 255 z0 = a0>>count; 256 } 257 else { 258 if ( count == 64 ) { 259 z2 = a1; 260 z1 = a0; 261 } 262 else { 263 a2 |= a1; 264 if ( count < 128 ) { 265 z2 = a0<<negCount; 266 z1 = a0>>( count & 63 ); 267 } 268 else { 269 z2 = ( count == 128 ) ? a0 : ( a0 != 0 ); 270 z1 = 0; 271 } 272 } 273 z0 = 0; 274 } 275 z2 |= ( a2 != 0 ); 276 } 277 *z2Ptr = z2; 278 *z1Ptr = z1; 279 *z0Ptr = z0; 280 281} 282 283/* 284------------------------------------------------------------------------------- 285Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the 286number of bits given in `count'. Any bits shifted off are lost. The value 287of `count' must be less than 64. The result is broken into two 64-bit 288pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. 289------------------------------------------------------------------------------- 290*/ 291INLINE void 292 shortShift128Left( 293 bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) 294{ 295 296 *z1Ptr = a1<<count; 297 *z0Ptr = 298 ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) ); 299 300} 301 302/* 303------------------------------------------------------------------------------- 304Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left 305by the number of bits given in `count'. Any bits shifted off are lost. 306The value of `count' must be less than 64. The result is broken into three 30764-bit pieces which are stored at the locations pointed to by `z0Ptr', 308`z1Ptr', and `z2Ptr'. 309------------------------------------------------------------------------------- 310*/ 311INLINE void 312 shortShift192Left( 313 bits64 a0, 314 bits64 a1, 315 bits64 a2, 316 int16 count, 317 bits64 *z0Ptr, 318 bits64 *z1Ptr, 319 bits64 *z2Ptr 320 ) 321{ 322 bits64 z0, z1, z2; 323 int8 negCount; 324 325 z2 = a2<<count; 326 z1 = a1<<count; 327 z0 = a0<<count; 328 if ( 0 < count ) { 329 negCount = ( ( - count ) & 63 ); 330 z1 |= a2>>negCount; 331 z0 |= a1>>negCount; 332 } 333 *z2Ptr = z2; 334 *z1Ptr = z1; 335 *z0Ptr = z0; 336 337} 338 339/* 340------------------------------------------------------------------------------- 341Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit 342value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so 343any carry out is lost. The result is broken into two 64-bit pieces which 344are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. 345------------------------------------------------------------------------------- 346*/ 347INLINE void 348 add128( 349 bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) 350{ 351 bits64 z1; 352 353 z1 = a1 + b1; 354 *z1Ptr = z1; 355 *z0Ptr = a0 + b0 + ( z1 < a1 ); 356 357} 358 359/* 360------------------------------------------------------------------------------- 361Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the 362192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is 363modulo 2^192, so any carry out is lost. The result is broken into three 36464-bit pieces which are stored at the locations pointed to by `z0Ptr', 365`z1Ptr', and `z2Ptr'. 366------------------------------------------------------------------------------- 367*/ 368INLINE void 369 add192( 370 bits64 a0, 371 bits64 a1, 372 bits64 a2, 373 bits64 b0, 374 bits64 b1, 375 bits64 b2, 376 bits64 *z0Ptr, 377 bits64 *z1Ptr, 378 bits64 *z2Ptr 379 ) 380{ 381 bits64 z0, z1, z2; 382 int8 carry0, carry1; 383 384 z2 = a2 + b2; 385 carry1 = ( z2 < a2 ); 386 z1 = a1 + b1; 387 carry0 = ( z1 < a1 ); 388 z0 = a0 + b0; 389 z1 += carry1; 390 z0 += ( z1 < (bits64)carry1 ); 391 z0 += carry0; 392 *z2Ptr = z2; 393 *z1Ptr = z1; 394 *z0Ptr = z0; 395 396} 397 398/* 399------------------------------------------------------------------------------- 400Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the 401128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo 4022^128, so any borrow out (carry out) is lost. The result is broken into two 40364-bit pieces which are stored at the locations pointed to by `z0Ptr' and 404`z1Ptr'. 405------------------------------------------------------------------------------- 406*/ 407INLINE void 408 sub128( 409 bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) 410{ 411 412 *z1Ptr = a1 - b1; 413 *z0Ptr = a0 - b0 - ( a1 < b1 ); 414 415} 416 417/* 418------------------------------------------------------------------------------- 419Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2' 420from the 192-bit value formed by concatenating `a0', `a1', and `a2'. 421Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The 422result is broken into three 64-bit pieces which are stored at the locations 423pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'. 424------------------------------------------------------------------------------- 425*/ 426INLINE void 427 sub192( 428 bits64 a0, 429 bits64 a1, 430 bits64 a2, 431 bits64 b0, 432 bits64 b1, 433 bits64 b2, 434 bits64 *z0Ptr, 435 bits64 *z1Ptr, 436 bits64 *z2Ptr 437 ) 438{ 439 bits64 z0, z1, z2; 440 int8 borrow0, borrow1; 441 442 z2 = a2 - b2; 443 borrow1 = ( a2 < b2 ); 444 z1 = a1 - b1; 445 borrow0 = ( a1 < b1 ); 446 z0 = a0 - b0; 447 z0 -= ( z1 < (bits64)borrow1 ); 448 z1 -= borrow1; 449 z0 -= borrow0; 450 *z2Ptr = z2; 451 *z1Ptr = z1; 452 *z0Ptr = z0; 453 454} 455 456/* 457------------------------------------------------------------------------------- 458Multiplies `a' by `b' to obtain a 128-bit product. The product is broken 459into two 64-bit pieces which are stored at the locations pointed to by 460`z0Ptr' and `z1Ptr'. 461------------------------------------------------------------------------------- 462*/ 463INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr ) 464{ 465 bits32 aHigh, aLow, bHigh, bLow; 466 bits64 z0, zMiddleA, zMiddleB, z1; 467 468 aLow = a; 469 aHigh = a>>32; 470 bLow = b; 471 bHigh = b>>32; 472 z1 = ( (bits64) aLow ) * bLow; 473 zMiddleA = ( (bits64) aLow ) * bHigh; 474 zMiddleB = ( (bits64) aHigh ) * bLow; 475 z0 = ( (bits64) aHigh ) * bHigh; 476 zMiddleA += zMiddleB; 477 z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); 478 zMiddleA <<= 32; 479 z1 += zMiddleA; 480 z0 += ( z1 < zMiddleA ); 481 *z1Ptr = z1; 482 *z0Ptr = z0; 483 484} 485 486/* 487------------------------------------------------------------------------------- 488Multiplies the 128-bit value formed by concatenating `a0' and `a1' by 489`b' to obtain a 192-bit product. The product is broken into three 64-bit 490pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and 491`z2Ptr'. 492------------------------------------------------------------------------------- 493*/ 494INLINE void 495 mul128By64To192( 496 bits64 a0, 497 bits64 a1, 498 bits64 b, 499 bits64 *z0Ptr, 500 bits64 *z1Ptr, 501 bits64 *z2Ptr 502 ) 503{ 504 bits64 z0, z1, z2, more1; 505 506 mul64To128( a1, b, &z1, &z2 ); 507 mul64To128( a0, b, &z0, &more1 ); 508 add128( z0, more1, 0, z1, &z0, &z1 ); 509 *z2Ptr = z2; 510 *z1Ptr = z1; 511 *z0Ptr = z0; 512 513} 514 515/* 516------------------------------------------------------------------------------- 517Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the 518128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit 519product. The product is broken into four 64-bit pieces which are stored at 520the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'. 521------------------------------------------------------------------------------- 522*/ 523INLINE void 524 mul128To256( 525 bits64 a0, 526 bits64 a1, 527 bits64 b0, 528 bits64 b1, 529 bits64 *z0Ptr, 530 bits64 *z1Ptr, 531 bits64 *z2Ptr, 532 bits64 *z3Ptr 533 ) 534{ 535 bits64 z0, z1, z2, z3; 536 bits64 more1, more2; 537 538 mul64To128( a1, b1, &z2, &z3 ); 539 mul64To128( a1, b0, &z1, &more2 ); 540 add128( z1, more2, 0, z2, &z1, &z2 ); 541 mul64To128( a0, b0, &z0, &more1 ); 542 add128( z0, more1, 0, z1, &z0, &z1 ); 543 mul64To128( a0, b1, &more1, &more2 ); 544 add128( more1, more2, 0, z2, &more1, &z2 ); 545 add128( z0, z1, 0, more1, &z0, &z1 ); 546 *z3Ptr = z3; 547 *z2Ptr = z2; 548 *z1Ptr = z1; 549 *z0Ptr = z0; 550 551} 552 553/* 554------------------------------------------------------------------------------- 555Returns an approximation to the 64-bit integer quotient obtained by dividing 556`b' into the 128-bit value formed by concatenating `a0' and `a1'. The 557divisor `b' must be at least 2^63. If q is the exact quotient truncated 558toward zero, the approximation returned lies between q and q + 2 inclusive. 559If the exact quotient q is larger than 64 bits, the maximum positive 64-bit 560unsigned integer is returned. 561------------------------------------------------------------------------------- 562*/ 563static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b ) 564{ 565 bits64 b0, b1; 566 bits64 rem0, rem1, term0, term1; 567 bits64 z; 568 569 if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); 570 b0 = b>>32; 571 z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32; 572 mul64To128( b, z, &term0, &term1 ); 573 sub128( a0, a1, term0, term1, &rem0, &rem1 ); 574 while ( ( (sbits64) rem0 ) < 0 ) { 575 z -= LIT64( 0x100000000 ); 576 b1 = b<<32; 577 add128( rem0, rem1, b0, b1, &rem0, &rem1 ); 578 } 579 rem0 = ( rem0<<32 ) | ( rem1>>32 ); 580 z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0; 581 return z; 582 583} 584 585#if !defined(SOFTFLOAT_FOR_GCC) || defined(FLOATX80) || defined(FLOAT128) 586/* 587------------------------------------------------------------------------------- 588Returns an approximation to the square root of the 32-bit significand given 589by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of 590`aExp' (the least significant bit) is 1, the integer returned approximates 5912^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp' 592is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either 593case, the approximation returned lies strictly within +/-2 of the exact 594value. 595------------------------------------------------------------------------------- 596*/ 597static bits32 estimateSqrt32( int16 aExp, bits32 a ) 598{ 599 static const bits16 sqrtOddAdjustments[] = { 600 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, 601 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 602 }; 603 static const bits16 sqrtEvenAdjustments[] = { 604 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, 605 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 606 }; 607 int8 idx; 608 bits32 z; 609 610 idx = ( a>>27 ) & 15; 611 if ( aExp & 1 ) { 612 z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ idx ]; 613 z = ( ( a / z )<<14 ) + ( z<<15 ); 614 a >>= 1; 615 } 616 else { 617 z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ idx ]; 618 z = a / z + z; 619 z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); 620 if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 ); 621 } 622 return ( (bits32) ( ( ( (bits64) a )<<31 ) / z ) ) + ( z>>1 ); 623 624} 625#endif 626 627/* 628------------------------------------------------------------------------------- 629Returns the number of leading 0 bits before the most-significant 1 bit of 630`a'. If `a' is zero, 32 is returned. 631------------------------------------------------------------------------------- 632*/ 633static int8 countLeadingZeros32( bits32 a ) 634{ 635 static const int8 countLeadingZerosHigh[] = { 636 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 637 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 638 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 639 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 640 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 641 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 642 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 643 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 644 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 645 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 646 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 647 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 648 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 649 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 650 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 651 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 652 }; 653 int8 shiftCount; 654 655 shiftCount = 0; 656 if ( a < 0x10000 ) { 657 shiftCount += 16; 658 a <<= 16; 659 } 660 if ( a < 0x1000000 ) { 661 shiftCount += 8; 662 a <<= 8; 663 } 664 shiftCount += countLeadingZerosHigh[ a>>24 ]; 665 return shiftCount; 666 667} 668 669/* 670------------------------------------------------------------------------------- 671Returns the number of leading 0 bits before the most-significant 1 bit of 672`a'. If `a' is zero, 64 is returned. 673------------------------------------------------------------------------------- 674*/ 675static int8 countLeadingZeros64( bits64 a ) 676{ 677 int8 shiftCount; 678 679 shiftCount = 0; 680 if ( a < ( (bits64) 1 )<<32 ) { 681 shiftCount += 32; 682 } 683 else { 684 a >>= 32; 685 } 686 shiftCount += countLeadingZeros32( a ); 687 return shiftCount; 688 689} 690 691/* 692------------------------------------------------------------------------------- 693Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' 694is equal to the 128-bit value formed by concatenating `b0' and `b1'. 695Otherwise, returns 0. 696------------------------------------------------------------------------------- 697*/ 698INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) 699{ 700 701 return ( a0 == b0 ) && ( a1 == b1 ); 702 703} 704 705/* 706------------------------------------------------------------------------------- 707Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less 708than or equal to the 128-bit value formed by concatenating `b0' and `b1'. 709Otherwise, returns 0. 710------------------------------------------------------------------------------- 711*/ 712INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) 713{ 714 715 return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) ); 716 717} 718 719/* 720------------------------------------------------------------------------------- 721Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less 722than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise, 723returns 0. 724------------------------------------------------------------------------------- 725*/ 726INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) 727{ 728 729 return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) ); 730 731} 732 733/* 734------------------------------------------------------------------------------- 735Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is 736not equal to the 128-bit value formed by concatenating `b0' and `b1'. 737Otherwise, returns 0. 738------------------------------------------------------------------------------- 739*/ 740INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) 741{ 742 743 return ( a0 != b0 ) || ( a1 != b1 ); 744 745} 746 747