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1.1 ! root 1: ! 2: /*============================================================================ ! 3: ! 4: This C source fragment is part of the SoftFloat IEC/IEEE Floating-point ! 5: Arithmetic Package, Release 2b. ! 6: ! 7: Written by John R. Hauser. This work was made possible in part by the ! 8: International Computer Science Institute, located at Suite 600, 1947 Center ! 9: Street, Berkeley, California 94704. Funding was partially provided by the ! 10: National Science Foundation under grant MIP-9311980. The original version ! 11: of this code was written as part of a project to build a fixed-point vector ! 12: processor in collaboration with the University of California at Berkeley, ! 13: overseen by Profs. Nelson Morgan and John Wawrzynek. More information ! 14: is available through the Web page `http://www.cs.berkeley.edu/~jhauser/ ! 15: arithmetic/SoftFloat.html'. ! 16: ! 17: THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort has ! 18: been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT TIMES ! 19: RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO PERSONS ! 20: AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ALL LOSSES, ! 21: COSTS, OR OTHER PROBLEMS THEY INCUR DUE TO THE SOFTWARE, AND WHO FURTHERMORE ! 22: EFFECTIVELY INDEMNIFY JOHN HAUSER AND THE INTERNATIONAL COMPUTER SCIENCE ! 23: INSTITUTE (possibly via similar legal notice) AGAINST ALL LOSSES, COSTS, OR ! 24: OTHER PROBLEMS INCURRED BY THEIR CUSTOMERS AND CLIENTS DUE TO THE SOFTWARE. ! 25: ! 26: Derivative works are acceptable, even for commercial purposes, so long as ! 27: (1) the source code for the derivative work includes prominent notice that ! 28: the work is derivative, and (2) the source code includes prominent notice with ! 29: these four paragraphs for those parts of this code that are retained. ! 30: ! 31: =============================================================================*/ ! 32: ! 33: /*---------------------------------------------------------------------------- ! 34: | Shifts `a' right by the number of bits given in `count'. If any nonzero ! 35: | bits are shifted off, they are ``jammed'' into the least significant bit of ! 36: | the result by setting the least significant bit to 1. The value of `count' ! 37: | can be arbitrarily large; in particular, if `count' is greater than 32, the ! 38: | result will be either 0 or 1, depending on whether `a' is zero or nonzero. ! 39: | The result is stored in the location pointed to by `zPtr'. ! 40: *----------------------------------------------------------------------------*/ ! 41: ! 42: INLINE void shift32RightJamming( bits32 a, int16 count, bits32 *zPtr ) ! 43: { ! 44: bits32 z; ! 45: ! 46: if ( count == 0 ) { ! 47: z = a; ! 48: } ! 49: else if ( count < 32 ) { ! 50: z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 ); ! 51: } ! 52: else { ! 53: z = ( a != 0 ); ! 54: } ! 55: *zPtr = z; ! 56: ! 57: } ! 58: ! 59: /*---------------------------------------------------------------------------- ! 60: | Shifts `a' right by the number of bits given in `count'. If any nonzero ! 61: | bits are shifted off, they are ``jammed'' into the least significant bit of ! 62: | the result by setting the least significant bit to 1. The value of `count' ! 63: | can be arbitrarily large; in particular, if `count' is greater than 64, the ! 64: | result will be either 0 or 1, depending on whether `a' is zero or nonzero. ! 65: | The result is stored in the location pointed to by `zPtr'. ! 66: *----------------------------------------------------------------------------*/ ! 67: ! 68: INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr ) ! 69: { ! 70: bits64 z; ! 71: ! 72: if ( count == 0 ) { ! 73: z = a; ! 74: } ! 75: else if ( count < 64 ) { ! 76: z = ( a>>count ) | ( ( a<<( ( - count ) & 63 ) ) != 0 ); ! 77: } ! 78: else { ! 79: z = ( a != 0 ); ! 80: } ! 81: *zPtr = z; ! 82: ! 83: } ! 84: ! 85: /*---------------------------------------------------------------------------- ! 86: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64 ! 87: | _plus_ the number of bits given in `count'. The shifted result is at most ! 88: | 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The ! 89: | bits shifted off form a second 64-bit result as follows: The _last_ bit ! 90: | shifted off is the most-significant bit of the extra result, and the other ! 91: | 63 bits of the extra result are all zero if and only if _all_but_the_last_ ! 92: | bits shifted off were all zero. This extra result is stored in the location ! 93: | pointed to by `z1Ptr'. The value of `count' can be arbitrarily large. ! 94: | (This routine makes more sense if `a0' and `a1' are considered to form ! 95: | a fixed-point value with binary point between `a0' and `a1'. This fixed- ! 96: | point value is shifted right by the number of bits given in `count', and ! 97: | the integer part of the result is returned at the location pointed to by ! 98: | `z0Ptr'. The fractional part of the result may be slightly corrupted as ! 99: | described above, and is returned at the location pointed to by `z1Ptr'.) ! 100: *----------------------------------------------------------------------------*/ ! 101: ! 102: INLINE void ! 103: shift64ExtraRightJamming( ! 104: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) ! 105: { ! 106: bits64 z0, z1; ! 107: int8 negCount = ( - count ) & 63; ! 108: ! 109: if ( count == 0 ) { ! 110: z1 = a1; ! 111: z0 = a0; ! 112: } ! 113: else if ( count < 64 ) { ! 114: z1 = ( a0<<negCount ) | ( a1 != 0 ); ! 115: z0 = a0>>count; ! 116: } ! 117: else { ! 118: if ( count == 64 ) { ! 119: z1 = a0 | ( a1 != 0 ); ! 120: } ! 121: else { ! 122: z1 = ( ( a0 | a1 ) != 0 ); ! 123: } ! 124: z0 = 0; ! 125: } ! 126: *z1Ptr = z1; ! 127: *z0Ptr = z0; ! 128: ! 129: } ! 130: ! 131: /*---------------------------------------------------------------------------- ! 132: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the ! 133: | number of bits given in `count'. Any bits shifted off are lost. The value ! 134: | of `count' can be arbitrarily large; in particular, if `count' is greater ! 135: | than 128, the result will be 0. The result is broken into two 64-bit pieces ! 136: | which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. ! 137: *----------------------------------------------------------------------------*/ ! 138: ! 139: INLINE void ! 140: shift128Right( ! 141: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) ! 142: { ! 143: bits64 z0, z1; ! 144: int8 negCount = ( - count ) & 63; ! 145: ! 146: if ( count == 0 ) { ! 147: z1 = a1; ! 148: z0 = a0; ! 149: } ! 150: else if ( count < 64 ) { ! 151: z1 = ( a0<<negCount ) | ( a1>>count ); ! 152: z0 = a0>>count; ! 153: } ! 154: else { ! 155: z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0; ! 156: z0 = 0; ! 157: } ! 158: *z1Ptr = z1; ! 159: *z0Ptr = z0; ! 160: ! 161: } ! 162: ! 163: /*---------------------------------------------------------------------------- ! 164: | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the ! 165: | number of bits given in `count'. If any nonzero bits are shifted off, they ! 166: | are ``jammed'' into the least significant bit of the result by setting the ! 167: | least significant bit to 1. The value of `count' can be arbitrarily large; ! 168: | in particular, if `count' is greater than 128, the result will be either ! 169: | 0 or 1, depending on whether the concatenation of `a0' and `a1' is zero or ! 170: | nonzero. The result is broken into two 64-bit pieces which are stored at ! 171: | the locations pointed to by `z0Ptr' and `z1Ptr'. ! 172: *----------------------------------------------------------------------------*/ ! 173: ! 174: INLINE void ! 175: shift128RightJamming( ! 176: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) ! 177: { ! 178: bits64 z0, z1; ! 179: int8 negCount = ( - count ) & 63; ! 180: ! 181: if ( count == 0 ) { ! 182: z1 = a1; ! 183: z0 = a0; ! 184: } ! 185: else if ( count < 64 ) { ! 186: z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 ); ! 187: z0 = a0>>count; ! 188: } ! 189: else { ! 190: if ( count == 64 ) { ! 191: z1 = a0 | ( a1 != 0 ); ! 192: } ! 193: else if ( count < 128 ) { ! 194: z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 ); ! 195: } ! 196: else { ! 197: z1 = ( ( a0 | a1 ) != 0 ); ! 198: } ! 199: z0 = 0; ! 200: } ! 201: *z1Ptr = z1; ! 202: *z0Ptr = z0; ! 203: ! 204: } ! 205: ! 206: /*---------------------------------------------------------------------------- ! 207: | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right ! 208: | by 64 _plus_ the number of bits given in `count'. The shifted result is ! 209: | at most 128 nonzero bits; these are broken into two 64-bit pieces which are ! 210: | stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted ! 211: | off form a third 64-bit result as follows: The _last_ bit shifted off is ! 212: | the most-significant bit of the extra result, and the other 63 bits of the ! 213: | extra result are all zero if and only if _all_but_the_last_ bits shifted off ! 214: | were all zero. This extra result is stored in the location pointed to by ! 215: | `z2Ptr'. The value of `count' can be arbitrarily large. ! 216: | (This routine makes more sense if `a0', `a1', and `a2' are considered ! 217: | to form a fixed-point value with binary point between `a1' and `a2'. This ! 218: | fixed-point value is shifted right by the number of bits given in `count', ! 219: | and the integer part of the result is returned at the locations pointed to ! 220: | by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly ! 221: | corrupted as described above, and is returned at the location pointed to by ! 222: | `z2Ptr'.) ! 223: *----------------------------------------------------------------------------*/ ! 224: ! 225: INLINE void ! 226: shift128ExtraRightJamming( ! 227: bits64 a0, ! 228: bits64 a1, ! 229: bits64 a2, ! 230: int16 count, ! 231: bits64 *z0Ptr, ! 232: bits64 *z1Ptr, ! 233: bits64 *z2Ptr ! 234: ) ! 235: { ! 236: bits64 z0, z1, z2; ! 237: int8 negCount = ( - count ) & 63; ! 238: ! 239: if ( count == 0 ) { ! 240: z2 = a2; ! 241: z1 = a1; ! 242: z0 = a0; ! 243: } ! 244: else { ! 245: if ( count < 64 ) { ! 246: z2 = a1<<negCount; ! 247: z1 = ( a0<<negCount ) | ( a1>>count ); ! 248: z0 = a0>>count; ! 249: } ! 250: else { ! 251: if ( count == 64 ) { ! 252: z2 = a1; ! 253: z1 = a0; ! 254: } ! 255: else { ! 256: a2 |= a1; ! 257: if ( count < 128 ) { ! 258: z2 = a0<<negCount; ! 259: z1 = a0>>( count & 63 ); ! 260: } ! 261: else { ! 262: z2 = ( count == 128 ) ? a0 : ( a0 != 0 ); ! 263: z1 = 0; ! 264: } ! 265: } ! 266: z0 = 0; ! 267: } ! 268: z2 |= ( a2 != 0 ); ! 269: } ! 270: *z2Ptr = z2; ! 271: *z1Ptr = z1; ! 272: *z0Ptr = z0; ! 273: ! 274: } ! 275: ! 276: /*---------------------------------------------------------------------------- ! 277: | Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the ! 278: | number of bits given in `count'. Any bits shifted off are lost. The value ! 279: | of `count' must be less than 64. The result is broken into two 64-bit ! 280: | pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. ! 281: *----------------------------------------------------------------------------*/ ! 282: ! 283: INLINE void ! 284: shortShift128Left( ! 285: bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) ! 286: { ! 287: ! 288: *z1Ptr = a1<<count; ! 289: *z0Ptr = ! 290: ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) ); ! 291: ! 292: } ! 293: ! 294: /*---------------------------------------------------------------------------- ! 295: | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left ! 296: | by the number of bits given in `count'. Any bits shifted off are lost. ! 297: | The value of `count' must be less than 64. The result is broken into three ! 298: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr', ! 299: | `z1Ptr', and `z2Ptr'. ! 300: *----------------------------------------------------------------------------*/ ! 301: ! 302: INLINE void ! 303: shortShift192Left( ! 304: bits64 a0, ! 305: bits64 a1, ! 306: bits64 a2, ! 307: int16 count, ! 308: bits64 *z0Ptr, ! 309: bits64 *z1Ptr, ! 310: bits64 *z2Ptr ! 311: ) ! 312: { ! 313: bits64 z0, z1, z2; ! 314: int8 negCount; ! 315: ! 316: z2 = a2<<count; ! 317: z1 = a1<<count; ! 318: z0 = a0<<count; ! 319: if ( 0 < count ) { ! 320: negCount = ( ( - count ) & 63 ); ! 321: z1 |= a2>>negCount; ! 322: z0 |= a1>>negCount; ! 323: } ! 324: *z2Ptr = z2; ! 325: *z1Ptr = z1; ! 326: *z0Ptr = z0; ! 327: ! 328: } ! 329: ! 330: /*---------------------------------------------------------------------------- ! 331: | Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit ! 332: | value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so ! 333: | any carry out is lost. The result is broken into two 64-bit pieces which ! 334: | are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. ! 335: *----------------------------------------------------------------------------*/ ! 336: ! 337: INLINE void ! 338: add128( ! 339: bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) ! 340: { ! 341: bits64 z1; ! 342: ! 343: z1 = a1 + b1; ! 344: *z1Ptr = z1; ! 345: *z0Ptr = a0 + b0 + ( z1 < a1 ); ! 346: ! 347: } ! 348: ! 349: /*---------------------------------------------------------------------------- ! 350: | Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the ! 351: | 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is ! 352: | modulo 2^192, so any carry out is lost. The result is broken into three ! 353: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr', ! 354: | `z1Ptr', and `z2Ptr'. ! 355: *----------------------------------------------------------------------------*/ ! 356: ! 357: INLINE void ! 358: add192( ! 359: bits64 a0, ! 360: bits64 a1, ! 361: bits64 a2, ! 362: bits64 b0, ! 363: bits64 b1, ! 364: bits64 b2, ! 365: bits64 *z0Ptr, ! 366: bits64 *z1Ptr, ! 367: bits64 *z2Ptr ! 368: ) ! 369: { ! 370: bits64 z0, z1, z2; ! 371: int8 carry0, carry1; ! 372: ! 373: z2 = a2 + b2; ! 374: carry1 = ( z2 < a2 ); ! 375: z1 = a1 + b1; ! 376: carry0 = ( z1 < a1 ); ! 377: z0 = a0 + b0; ! 378: z1 += carry1; ! 379: z0 += ( z1 < carry1 ); ! 380: z0 += carry0; ! 381: *z2Ptr = z2; ! 382: *z1Ptr = z1; ! 383: *z0Ptr = z0; ! 384: ! 385: } ! 386: ! 387: /*---------------------------------------------------------------------------- ! 388: | Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the ! 389: | 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo ! 390: | 2^128, so any borrow out (carry out) is lost. The result is broken into two ! 391: | 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and ! 392: | `z1Ptr'. ! 393: *----------------------------------------------------------------------------*/ ! 394: ! 395: INLINE void ! 396: sub128( ! 397: bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) ! 398: { ! 399: ! 400: *z1Ptr = a1 - b1; ! 401: *z0Ptr = a0 - b0 - ( a1 < b1 ); ! 402: ! 403: } ! 404: ! 405: /*---------------------------------------------------------------------------- ! 406: | Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2' ! 407: | from the 192-bit value formed by concatenating `a0', `a1', and `a2'. ! 408: | Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The ! 409: | result is broken into three 64-bit pieces which are stored at the locations ! 410: | pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'. ! 411: *----------------------------------------------------------------------------*/ ! 412: ! 413: INLINE void ! 414: sub192( ! 415: bits64 a0, ! 416: bits64 a1, ! 417: bits64 a2, ! 418: bits64 b0, ! 419: bits64 b1, ! 420: bits64 b2, ! 421: bits64 *z0Ptr, ! 422: bits64 *z1Ptr, ! 423: bits64 *z2Ptr ! 424: ) ! 425: { ! 426: bits64 z0, z1, z2; ! 427: int8 borrow0, borrow1; ! 428: ! 429: z2 = a2 - b2; ! 430: borrow1 = ( a2 < b2 ); ! 431: z1 = a1 - b1; ! 432: borrow0 = ( a1 < b1 ); ! 433: z0 = a0 - b0; ! 434: z0 -= ( z1 < borrow1 ); ! 435: z1 -= borrow1; ! 436: z0 -= borrow0; ! 437: *z2Ptr = z2; ! 438: *z1Ptr = z1; ! 439: *z0Ptr = z0; ! 440: ! 441: } ! 442: ! 443: /*---------------------------------------------------------------------------- ! 444: | Multiplies `a' by `b' to obtain a 128-bit product. The product is broken ! 445: | into two 64-bit pieces which are stored at the locations pointed to by ! 446: | `z0Ptr' and `z1Ptr'. ! 447: *----------------------------------------------------------------------------*/ ! 448: ! 449: INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr ) ! 450: { ! 451: bits32 aHigh, aLow, bHigh, bLow; ! 452: bits64 z0, zMiddleA, zMiddleB, z1; ! 453: ! 454: aLow = a; ! 455: aHigh = a>>32; ! 456: bLow = b; ! 457: bHigh = b>>32; ! 458: z1 = ( (bits64) aLow ) * bLow; ! 459: zMiddleA = ( (bits64) aLow ) * bHigh; ! 460: zMiddleB = ( (bits64) aHigh ) * bLow; ! 461: z0 = ( (bits64) aHigh ) * bHigh; ! 462: zMiddleA += zMiddleB; ! 463: z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); ! 464: zMiddleA <<= 32; ! 465: z1 += zMiddleA; ! 466: z0 += ( z1 < zMiddleA ); ! 467: *z1Ptr = z1; ! 468: *z0Ptr = z0; ! 469: ! 470: } ! 471: ! 472: /*---------------------------------------------------------------------------- ! 473: | Multiplies the 128-bit value formed by concatenating `a0' and `a1' by ! 474: | `b' to obtain a 192-bit product. The product is broken into three 64-bit ! 475: | pieces which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and ! 476: | `z2Ptr'. ! 477: *----------------------------------------------------------------------------*/ ! 478: ! 479: INLINE void ! 480: mul128By64To192( ! 481: bits64 a0, ! 482: bits64 a1, ! 483: bits64 b, ! 484: bits64 *z0Ptr, ! 485: bits64 *z1Ptr, ! 486: bits64 *z2Ptr ! 487: ) ! 488: { ! 489: bits64 z0, z1, z2, more1; ! 490: ! 491: mul64To128( a1, b, &z1, &z2 ); ! 492: mul64To128( a0, b, &z0, &more1 ); ! 493: add128( z0, more1, 0, z1, &z0, &z1 ); ! 494: *z2Ptr = z2; ! 495: *z1Ptr = z1; ! 496: *z0Ptr = z0; ! 497: ! 498: } ! 499: ! 500: /*---------------------------------------------------------------------------- ! 501: | Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the ! 502: | 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit ! 503: | product. The product is broken into four 64-bit pieces which are stored at ! 504: | the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'. ! 505: *----------------------------------------------------------------------------*/ ! 506: ! 507: INLINE void ! 508: mul128To256( ! 509: bits64 a0, ! 510: bits64 a1, ! 511: bits64 b0, ! 512: bits64 b1, ! 513: bits64 *z0Ptr, ! 514: bits64 *z1Ptr, ! 515: bits64 *z2Ptr, ! 516: bits64 *z3Ptr ! 517: ) ! 518: { ! 519: bits64 z0, z1, z2, z3; ! 520: bits64 more1, more2; ! 521: ! 522: mul64To128( a1, b1, &z2, &z3 ); ! 523: mul64To128( a1, b0, &z1, &more2 ); ! 524: add128( z1, more2, 0, z2, &z1, &z2 ); ! 525: mul64To128( a0, b0, &z0, &more1 ); ! 526: add128( z0, more1, 0, z1, &z0, &z1 ); ! 527: mul64To128( a0, b1, &more1, &more2 ); ! 528: add128( more1, more2, 0, z2, &more1, &z2 ); ! 529: add128( z0, z1, 0, more1, &z0, &z1 ); ! 530: *z3Ptr = z3; ! 531: *z2Ptr = z2; ! 532: *z1Ptr = z1; ! 533: *z0Ptr = z0; ! 534: ! 535: } ! 536: ! 537: /*---------------------------------------------------------------------------- ! 538: | Returns an approximation to the 64-bit integer quotient obtained by dividing ! 539: | `b' into the 128-bit value formed by concatenating `a0' and `a1'. The ! 540: | divisor `b' must be at least 2^63. If q is the exact quotient truncated ! 541: | toward zero, the approximation returned lies between q and q + 2 inclusive. ! 542: | If the exact quotient q is larger than 64 bits, the maximum positive 64-bit ! 543: | unsigned integer is returned. ! 544: *----------------------------------------------------------------------------*/ ! 545: ! 546: static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b ) ! 547: { ! 548: bits64 b0, b1; ! 549: bits64 rem0, rem1, term0, term1; ! 550: bits64 z; ! 551: ! 552: if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); ! 553: b0 = b>>32; ! 554: z = ( b0<<32 <= a0 ) ? LIT64( 0xFFFFFFFF00000000 ) : ( a0 / b0 )<<32; ! 555: mul64To128( b, z, &term0, &term1 ); ! 556: sub128( a0, a1, term0, term1, &rem0, &rem1 ); ! 557: while ( ( (sbits64) rem0 ) < 0 ) { ! 558: z -= LIT64( 0x100000000 ); ! 559: b1 = b<<32; ! 560: add128( rem0, rem1, b0, b1, &rem0, &rem1 ); ! 561: } ! 562: rem0 = ( rem0<<32 ) | ( rem1>>32 ); ! 563: z |= ( b0<<32 <= rem0 ) ? 0xFFFFFFFF : rem0 / b0; ! 564: return z; ! 565: ! 566: } ! 567: ! 568: /*---------------------------------------------------------------------------- ! 569: | Returns an approximation to the square root of the 32-bit significand given ! 570: | by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of ! 571: | `aExp' (the least significant bit) is 1, the integer returned approximates ! 572: | 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp' ! 573: | is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either ! 574: | case, the approximation returned lies strictly within +/-2 of the exact ! 575: | value. ! 576: *----------------------------------------------------------------------------*/ ! 577: ! 578: static bits32 estimateSqrt32( int16 aExp, bits32 a ) ! 579: { ! 580: static const bits16 sqrtOddAdjustments[] = { ! 581: 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, ! 582: 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 ! 583: }; ! 584: static const bits16 sqrtEvenAdjustments[] = { ! 585: 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, ! 586: 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 ! 587: }; ! 588: int8 index; ! 589: bits32 z; ! 590: ! 591: index = ( a>>27 ) & 15; ! 592: if ( aExp & 1 ) { ! 593: z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ]; ! 594: z = ( ( a / z )<<14 ) + ( z<<15 ); ! 595: a >>= 1; ! 596: } ! 597: else { ! 598: z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ]; ! 599: z = a / z + z; ! 600: z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); ! 601: if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 ); ! 602: } ! 603: return ( (bits32) ( ( ( (bits64) a )<<31 ) / z ) ) + ( z>>1 ); ! 604: ! 605: } ! 606: ! 607: /*---------------------------------------------------------------------------- ! 608: | Returns the number of leading 0 bits before the most-significant 1 bit of ! 609: | `a'. If `a' is zero, 32 is returned. ! 610: *----------------------------------------------------------------------------*/ ! 611: ! 612: static int8 countLeadingZeros32( bits32 a ) ! 613: { ! 614: static const int8 countLeadingZerosHigh[] = { ! 615: 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, ! 616: 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, ! 617: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ! 618: 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, ! 619: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ! 620: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ! 621: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ! 622: 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ! 623: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 624: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 625: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 626: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 627: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 628: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 629: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ! 630: 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ! 631: }; ! 632: int8 shiftCount; ! 633: ! 634: shiftCount = 0; ! 635: if ( a < 0x10000 ) { ! 636: shiftCount += 16; ! 637: a <<= 16; ! 638: } ! 639: if ( a < 0x1000000 ) { ! 640: shiftCount += 8; ! 641: a <<= 8; ! 642: } ! 643: shiftCount += countLeadingZerosHigh[ a>>24 ]; ! 644: return shiftCount; ! 645: ! 646: } ! 647: ! 648: /*---------------------------------------------------------------------------- ! 649: | Returns the number of leading 0 bits before the most-significant 1 bit of ! 650: | `a'. If `a' is zero, 64 is returned. ! 651: *----------------------------------------------------------------------------*/ ! 652: ! 653: static int8 countLeadingZeros64( bits64 a ) ! 654: { ! 655: int8 shiftCount; ! 656: ! 657: shiftCount = 0; ! 658: if ( a < ( (bits64) 1 )<<32 ) { ! 659: shiftCount += 32; ! 660: } ! 661: else { ! 662: a >>= 32; ! 663: } ! 664: shiftCount += countLeadingZeros32( a ); ! 665: return shiftCount; ! 666: ! 667: } ! 668: ! 669: /*---------------------------------------------------------------------------- ! 670: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' ! 671: | is equal to the 128-bit value formed by concatenating `b0' and `b1'. ! 672: | Otherwise, returns 0. ! 673: *----------------------------------------------------------------------------*/ ! 674: ! 675: INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) ! 676: { ! 677: ! 678: return ( a0 == b0 ) && ( a1 == b1 ); ! 679: ! 680: } ! 681: ! 682: /*---------------------------------------------------------------------------- ! 683: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less ! 684: | than or equal to the 128-bit value formed by concatenating `b0' and `b1'. ! 685: | Otherwise, returns 0. ! 686: *----------------------------------------------------------------------------*/ ! 687: ! 688: INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) ! 689: { ! 690: ! 691: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) ); ! 692: ! 693: } ! 694: ! 695: /*---------------------------------------------------------------------------- ! 696: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less ! 697: | than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise, ! 698: | returns 0. ! 699: *----------------------------------------------------------------------------*/ ! 700: ! 701: INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) ! 702: { ! 703: ! 704: return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) ); ! 705: ! 706: } ! 707: ! 708: /*---------------------------------------------------------------------------- ! 709: | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is ! 710: | not equal to the 128-bit value formed by concatenating `b0' and `b1'. ! 711: | Otherwise, returns 0. ! 712: *----------------------------------------------------------------------------*/ ! 713: ! 714: INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) ! 715: { ! 716: ! 717: return ( a0 != b0 ) || ( a1 != b1 ); ! 718: ! 719: } ! 720:
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