Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | |
| 2 | /* |
| 3 | =============================================================================== |
| 4 | |
| 5 | This C source fragment is part of the SoftFloat IEC/IEEE Floating-point |
| 6 | Arithmetic Package, Release 2. |
| 7 | |
| 8 | Written by John R. Hauser. This work was made possible in part by the |
| 9 | International Computer Science Institute, located at Suite 600, 1947 Center |
| 10 | Street, Berkeley, California 94704. Funding was partially provided by the |
| 11 | National Science Foundation under grant MIP-9311980. The original version |
| 12 | of this code was written as part of a project to build a fixed-point vector |
| 13 | processor in collaboration with the University of California at Berkeley, |
| 14 | overseen by Profs. Nelson Morgan and John Wawrzynek. More information |
Justin P. Mattock | 50a23e6 | 2010-10-16 10:36:23 -0700 | [diff] [blame] | 15 | is available through the web page |
| 16 | http://www.jhauser.us/arithmetic/SoftFloat-2b/SoftFloat-source.txt |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 17 | |
| 18 | THIS SOFTWARE IS DISTRIBUTED AS IS, FOR FREE. Although reasonable effort |
| 19 | has been made to avoid it, THIS SOFTWARE MAY CONTAIN FAULTS THAT WILL AT |
| 20 | TIMES RESULT IN INCORRECT BEHAVIOR. USE OF THIS SOFTWARE IS RESTRICTED TO |
| 21 | PERSONS AND ORGANIZATIONS WHO CAN AND WILL TAKE FULL RESPONSIBILITY FOR ANY |
| 22 | AND ALL LOSSES, COSTS, OR OTHER PROBLEMS ARISING FROM ITS USE. |
| 23 | |
| 24 | Derivative works are acceptable, even for commercial purposes, so long as |
| 25 | (1) they include prominent notice that the work is derivative, and (2) they |
| 26 | include prominent notice akin to these three paragraphs for those parts of |
| 27 | this code that are retained. |
| 28 | |
| 29 | =============================================================================== |
| 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 | if ( count == 0 ) { |
| 46 | z = a; |
| 47 | } |
| 48 | else if ( count < 32 ) { |
| 49 | z = ( a>>count ) | ( ( a<<( ( - count ) & 31 ) ) != 0 ); |
| 50 | } |
| 51 | else { |
| 52 | z = ( a != 0 ); |
| 53 | } |
| 54 | *zPtr = z; |
| 55 | } |
| 56 | |
| 57 | /* |
| 58 | ------------------------------------------------------------------------------- |
| 59 | Shifts `a' right by the number of bits given in `count'. If any nonzero |
| 60 | bits are shifted off, they are ``jammed'' into the least significant bit of |
| 61 | the result by setting the least significant bit to 1. The value of `count' |
| 62 | can be arbitrarily large; in particular, if `count' is greater than 64, the |
| 63 | result will be either 0 or 1, depending on whether `a' is zero or nonzero. |
| 64 | The result is stored in the location pointed to by `zPtr'. |
| 65 | ------------------------------------------------------------------------------- |
| 66 | */ |
| 67 | INLINE void shift64RightJamming( bits64 a, int16 count, bits64 *zPtr ) |
| 68 | { |
| 69 | bits64 z; |
| 70 | |
| 71 | __asm__("@shift64RightJamming -- start"); |
| 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 | __asm__("@shift64RightJamming -- end"); |
| 82 | *zPtr = z; |
| 83 | } |
| 84 | |
| 85 | /* |
| 86 | ------------------------------------------------------------------------------- |
| 87 | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by 64 |
| 88 | _plus_ the number of bits given in `count'. The shifted result is at most |
| 89 | 64 nonzero bits; this is stored at the location pointed to by `z0Ptr'. The |
| 90 | bits shifted off form a second 64-bit result as follows: The _last_ bit |
| 91 | shifted off is the most-significant bit of the extra result, and the other |
| 92 | 63 bits of the extra result are all zero if and only if _all_but_the_last_ |
| 93 | bits shifted off were all zero. This extra result is stored in the location |
| 94 | pointed to by `z1Ptr'. The value of `count' can be arbitrarily large. |
| 95 | (This routine makes more sense if `a0' and `a1' are considered to form a |
| 96 | fixed-point value with binary point between `a0' and `a1'. This fixed-point |
| 97 | value is shifted right by the number of bits given in `count', and the |
| 98 | integer part of the result is returned at the location pointed to by |
| 99 | `z0Ptr'. The fractional part of the result may be slightly corrupted as |
| 100 | described above, and is returned at the location pointed to by `z1Ptr'.) |
| 101 | ------------------------------------------------------------------------------- |
| 102 | */ |
| 103 | INLINE void |
| 104 | shift64ExtraRightJamming( |
| 105 | bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 106 | { |
| 107 | bits64 z0, z1; |
| 108 | int8 negCount = ( - count ) & 63; |
| 109 | |
| 110 | if ( count == 0 ) { |
| 111 | z1 = a1; |
| 112 | z0 = a0; |
| 113 | } |
| 114 | else if ( count < 64 ) { |
| 115 | z1 = ( a0<<negCount ) | ( a1 != 0 ); |
| 116 | z0 = a0>>count; |
| 117 | } |
| 118 | else { |
| 119 | if ( count == 64 ) { |
| 120 | z1 = a0 | ( a1 != 0 ); |
| 121 | } |
| 122 | else { |
| 123 | z1 = ( ( a0 | a1 ) != 0 ); |
| 124 | } |
| 125 | z0 = 0; |
| 126 | } |
| 127 | *z1Ptr = z1; |
| 128 | *z0Ptr = z0; |
| 129 | |
| 130 | } |
| 131 | |
| 132 | /* |
| 133 | ------------------------------------------------------------------------------- |
| 134 | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the |
| 135 | number of bits given in `count'. Any bits shifted off are lost. The value |
| 136 | of `count' can be arbitrarily large; in particular, if `count' is greater |
| 137 | than 128, the result will be 0. The result is broken into two 64-bit pieces |
| 138 | which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. |
| 139 | ------------------------------------------------------------------------------- |
| 140 | */ |
| 141 | INLINE void |
| 142 | shift128Right( |
| 143 | bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 144 | { |
| 145 | bits64 z0, z1; |
| 146 | int8 negCount = ( - count ) & 63; |
| 147 | |
| 148 | if ( count == 0 ) { |
| 149 | z1 = a1; |
| 150 | z0 = a0; |
| 151 | } |
| 152 | else if ( count < 64 ) { |
| 153 | z1 = ( a0<<negCount ) | ( a1>>count ); |
| 154 | z0 = a0>>count; |
| 155 | } |
| 156 | else { |
| 157 | z1 = ( count < 64 ) ? ( a0>>( count & 63 ) ) : 0; |
| 158 | z0 = 0; |
| 159 | } |
| 160 | *z1Ptr = z1; |
| 161 | *z0Ptr = z0; |
| 162 | |
| 163 | } |
| 164 | |
| 165 | /* |
| 166 | ------------------------------------------------------------------------------- |
| 167 | Shifts the 128-bit value formed by concatenating `a0' and `a1' right by the |
| 168 | number of bits given in `count'. If any nonzero bits are shifted off, they |
| 169 | are ``jammed'' into the least significant bit of the result by setting the |
| 170 | least significant bit to 1. The value of `count' can be arbitrarily large; |
| 171 | in particular, if `count' is greater than 128, the result will be either 0 |
| 172 | or 1, depending on whether the concatenation of `a0' and `a1' is zero or |
| 173 | nonzero. The result is broken into two 64-bit pieces which are stored at |
| 174 | the locations pointed to by `z0Ptr' and `z1Ptr'. |
| 175 | ------------------------------------------------------------------------------- |
| 176 | */ |
| 177 | INLINE void |
| 178 | shift128RightJamming( |
| 179 | bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 180 | { |
| 181 | bits64 z0, z1; |
| 182 | int8 negCount = ( - count ) & 63; |
| 183 | |
| 184 | if ( count == 0 ) { |
| 185 | z1 = a1; |
| 186 | z0 = a0; |
| 187 | } |
| 188 | else if ( count < 64 ) { |
| 189 | z1 = ( a0<<negCount ) | ( a1>>count ) | ( ( a1<<negCount ) != 0 ); |
| 190 | z0 = a0>>count; |
| 191 | } |
| 192 | else { |
| 193 | if ( count == 64 ) { |
| 194 | z1 = a0 | ( a1 != 0 ); |
| 195 | } |
| 196 | else if ( count < 128 ) { |
| 197 | z1 = ( a0>>( count & 63 ) ) | ( ( ( a0<<negCount ) | a1 ) != 0 ); |
| 198 | } |
| 199 | else { |
| 200 | z1 = ( ( a0 | a1 ) != 0 ); |
| 201 | } |
| 202 | z0 = 0; |
| 203 | } |
| 204 | *z1Ptr = z1; |
| 205 | *z0Ptr = z0; |
| 206 | |
| 207 | } |
| 208 | |
| 209 | /* |
| 210 | ------------------------------------------------------------------------------- |
| 211 | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' right |
| 212 | by 64 _plus_ the number of bits given in `count'. The shifted result is |
| 213 | at most 128 nonzero bits; these are broken into two 64-bit pieces which are |
| 214 | stored at the locations pointed to by `z0Ptr' and `z1Ptr'. The bits shifted |
| 215 | off form a third 64-bit result as follows: The _last_ bit shifted off is |
| 216 | the most-significant bit of the extra result, and the other 63 bits of the |
| 217 | extra result are all zero if and only if _all_but_the_last_ bits shifted off |
| 218 | were all zero. This extra result is stored in the location pointed to by |
| 219 | `z2Ptr'. The value of `count' can be arbitrarily large. |
| 220 | (This routine makes more sense if `a0', `a1', and `a2' are considered |
| 221 | to form a fixed-point value with binary point between `a1' and `a2'. This |
| 222 | fixed-point value is shifted right by the number of bits given in `count', |
| 223 | and the integer part of the result is returned at the locations pointed to |
| 224 | by `z0Ptr' and `z1Ptr'. The fractional part of the result may be slightly |
| 225 | corrupted as described above, and is returned at the location pointed to by |
| 226 | `z2Ptr'.) |
| 227 | ------------------------------------------------------------------------------- |
| 228 | */ |
| 229 | INLINE void |
| 230 | shift128ExtraRightJamming( |
| 231 | bits64 a0, |
| 232 | bits64 a1, |
| 233 | bits64 a2, |
| 234 | int16 count, |
| 235 | bits64 *z0Ptr, |
| 236 | bits64 *z1Ptr, |
| 237 | bits64 *z2Ptr |
| 238 | ) |
| 239 | { |
| 240 | bits64 z0, z1, z2; |
| 241 | int8 negCount = ( - count ) & 63; |
| 242 | |
| 243 | if ( count == 0 ) { |
| 244 | z2 = a2; |
| 245 | z1 = a1; |
| 246 | z0 = a0; |
| 247 | } |
| 248 | else { |
| 249 | if ( count < 64 ) { |
| 250 | z2 = a1<<negCount; |
| 251 | z1 = ( a0<<negCount ) | ( a1>>count ); |
| 252 | z0 = a0>>count; |
| 253 | } |
| 254 | else { |
| 255 | if ( count == 64 ) { |
| 256 | z2 = a1; |
| 257 | z1 = a0; |
| 258 | } |
| 259 | else { |
| 260 | a2 |= a1; |
| 261 | if ( count < 128 ) { |
| 262 | z2 = a0<<negCount; |
| 263 | z1 = a0>>( count & 63 ); |
| 264 | } |
| 265 | else { |
| 266 | z2 = ( count == 128 ) ? a0 : ( a0 != 0 ); |
| 267 | z1 = 0; |
| 268 | } |
| 269 | } |
| 270 | z0 = 0; |
| 271 | } |
| 272 | z2 |= ( a2 != 0 ); |
| 273 | } |
| 274 | *z2Ptr = z2; |
| 275 | *z1Ptr = z1; |
| 276 | *z0Ptr = z0; |
| 277 | |
| 278 | } |
| 279 | |
| 280 | /* |
| 281 | ------------------------------------------------------------------------------- |
| 282 | Shifts the 128-bit value formed by concatenating `a0' and `a1' left by the |
| 283 | number of bits given in `count'. Any bits shifted off are lost. The value |
| 284 | of `count' must be less than 64. The result is broken into two 64-bit |
| 285 | pieces which are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. |
| 286 | ------------------------------------------------------------------------------- |
| 287 | */ |
| 288 | INLINE void |
| 289 | shortShift128Left( |
| 290 | bits64 a0, bits64 a1, int16 count, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 291 | { |
| 292 | |
| 293 | *z1Ptr = a1<<count; |
| 294 | *z0Ptr = |
| 295 | ( count == 0 ) ? a0 : ( a0<<count ) | ( a1>>( ( - count ) & 63 ) ); |
| 296 | |
| 297 | } |
| 298 | |
| 299 | /* |
| 300 | ------------------------------------------------------------------------------- |
| 301 | Shifts the 192-bit value formed by concatenating `a0', `a1', and `a2' left |
| 302 | by the number of bits given in `count'. Any bits shifted off are lost. |
| 303 | The value of `count' must be less than 64. The result is broken into three |
| 304 | 64-bit pieces which are stored at the locations pointed to by `z0Ptr', |
| 305 | `z1Ptr', and `z2Ptr'. |
| 306 | ------------------------------------------------------------------------------- |
| 307 | */ |
| 308 | INLINE void |
| 309 | shortShift192Left( |
| 310 | bits64 a0, |
| 311 | bits64 a1, |
| 312 | bits64 a2, |
| 313 | int16 count, |
| 314 | bits64 *z0Ptr, |
| 315 | bits64 *z1Ptr, |
| 316 | bits64 *z2Ptr |
| 317 | ) |
| 318 | { |
| 319 | bits64 z0, z1, z2; |
| 320 | int8 negCount; |
| 321 | |
| 322 | z2 = a2<<count; |
| 323 | z1 = a1<<count; |
| 324 | z0 = a0<<count; |
| 325 | if ( 0 < count ) { |
| 326 | negCount = ( ( - count ) & 63 ); |
| 327 | z1 |= a2>>negCount; |
| 328 | z0 |= a1>>negCount; |
| 329 | } |
| 330 | *z2Ptr = z2; |
| 331 | *z1Ptr = z1; |
| 332 | *z0Ptr = z0; |
| 333 | |
| 334 | } |
| 335 | |
| 336 | /* |
| 337 | ------------------------------------------------------------------------------- |
| 338 | Adds the 128-bit value formed by concatenating `a0' and `a1' to the 128-bit |
| 339 | value formed by concatenating `b0' and `b1'. Addition is modulo 2^128, so |
| 340 | any carry out is lost. The result is broken into two 64-bit pieces which |
| 341 | are stored at the locations pointed to by `z0Ptr' and `z1Ptr'. |
| 342 | ------------------------------------------------------------------------------- |
| 343 | */ |
| 344 | INLINE void |
| 345 | add128( |
| 346 | bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 347 | { |
| 348 | bits64 z1; |
| 349 | |
| 350 | z1 = a1 + b1; |
| 351 | *z1Ptr = z1; |
| 352 | *z0Ptr = a0 + b0 + ( z1 < a1 ); |
| 353 | |
| 354 | } |
| 355 | |
| 356 | /* |
| 357 | ------------------------------------------------------------------------------- |
| 358 | Adds the 192-bit value formed by concatenating `a0', `a1', and `a2' to the |
| 359 | 192-bit value formed by concatenating `b0', `b1', and `b2'. Addition is |
| 360 | modulo 2^192, so any carry out is lost. The result is broken into three |
| 361 | 64-bit pieces which are stored at the locations pointed to by `z0Ptr', |
| 362 | `z1Ptr', and `z2Ptr'. |
| 363 | ------------------------------------------------------------------------------- |
| 364 | */ |
| 365 | INLINE void |
| 366 | add192( |
| 367 | bits64 a0, |
| 368 | bits64 a1, |
| 369 | bits64 a2, |
| 370 | bits64 b0, |
| 371 | bits64 b1, |
| 372 | bits64 b2, |
| 373 | bits64 *z0Ptr, |
| 374 | bits64 *z1Ptr, |
| 375 | bits64 *z2Ptr |
| 376 | ) |
| 377 | { |
| 378 | bits64 z0, z1, z2; |
| 379 | int8 carry0, carry1; |
| 380 | |
| 381 | z2 = a2 + b2; |
| 382 | carry1 = ( z2 < a2 ); |
| 383 | z1 = a1 + b1; |
| 384 | carry0 = ( z1 < a1 ); |
| 385 | z0 = a0 + b0; |
| 386 | z1 += carry1; |
| 387 | z0 += ( z1 < carry1 ); |
| 388 | z0 += carry0; |
| 389 | *z2Ptr = z2; |
| 390 | *z1Ptr = z1; |
| 391 | *z0Ptr = z0; |
| 392 | |
| 393 | } |
| 394 | |
| 395 | /* |
| 396 | ------------------------------------------------------------------------------- |
| 397 | Subtracts the 128-bit value formed by concatenating `b0' and `b1' from the |
| 398 | 128-bit value formed by concatenating `a0' and `a1'. Subtraction is modulo |
| 399 | 2^128, so any borrow out (carry out) is lost. The result is broken into two |
| 400 | 64-bit pieces which are stored at the locations pointed to by `z0Ptr' and |
| 401 | `z1Ptr'. |
| 402 | ------------------------------------------------------------------------------- |
| 403 | */ |
| 404 | INLINE void |
| 405 | sub128( |
| 406 | bits64 a0, bits64 a1, bits64 b0, bits64 b1, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 407 | { |
| 408 | |
| 409 | *z1Ptr = a1 - b1; |
| 410 | *z0Ptr = a0 - b0 - ( a1 < b1 ); |
| 411 | |
| 412 | } |
| 413 | |
| 414 | /* |
| 415 | ------------------------------------------------------------------------------- |
| 416 | Subtracts the 192-bit value formed by concatenating `b0', `b1', and `b2' |
| 417 | from the 192-bit value formed by concatenating `a0', `a1', and `a2'. |
| 418 | Subtraction is modulo 2^192, so any borrow out (carry out) is lost. The |
| 419 | result is broken into three 64-bit pieces which are stored at the locations |
| 420 | pointed to by `z0Ptr', `z1Ptr', and `z2Ptr'. |
| 421 | ------------------------------------------------------------------------------- |
| 422 | */ |
| 423 | INLINE void |
| 424 | sub192( |
| 425 | bits64 a0, |
| 426 | bits64 a1, |
| 427 | bits64 a2, |
| 428 | bits64 b0, |
| 429 | bits64 b1, |
| 430 | bits64 b2, |
| 431 | bits64 *z0Ptr, |
| 432 | bits64 *z1Ptr, |
| 433 | bits64 *z2Ptr |
| 434 | ) |
| 435 | { |
| 436 | bits64 z0, z1, z2; |
| 437 | int8 borrow0, borrow1; |
| 438 | |
| 439 | z2 = a2 - b2; |
| 440 | borrow1 = ( a2 < b2 ); |
| 441 | z1 = a1 - b1; |
| 442 | borrow0 = ( a1 < b1 ); |
| 443 | z0 = a0 - b0; |
| 444 | z0 -= ( z1 < borrow1 ); |
| 445 | z1 -= borrow1; |
| 446 | z0 -= borrow0; |
| 447 | *z2Ptr = z2; |
| 448 | *z1Ptr = z1; |
| 449 | *z0Ptr = z0; |
| 450 | |
| 451 | } |
| 452 | |
| 453 | /* |
| 454 | ------------------------------------------------------------------------------- |
| 455 | Multiplies `a' by `b' to obtain a 128-bit product. The product is broken |
| 456 | into two 64-bit pieces which are stored at the locations pointed to by |
| 457 | `z0Ptr' and `z1Ptr'. |
| 458 | ------------------------------------------------------------------------------- |
| 459 | */ |
| 460 | INLINE void mul64To128( bits64 a, bits64 b, bits64 *z0Ptr, bits64 *z1Ptr ) |
| 461 | { |
| 462 | bits32 aHigh, aLow, bHigh, bLow; |
| 463 | bits64 z0, zMiddleA, zMiddleB, z1; |
| 464 | |
| 465 | aLow = a; |
| 466 | aHigh = a>>32; |
| 467 | bLow = b; |
| 468 | bHigh = b>>32; |
| 469 | z1 = ( (bits64) aLow ) * bLow; |
| 470 | zMiddleA = ( (bits64) aLow ) * bHigh; |
| 471 | zMiddleB = ( (bits64) aHigh ) * bLow; |
| 472 | z0 = ( (bits64) aHigh ) * bHigh; |
| 473 | zMiddleA += zMiddleB; |
| 474 | z0 += ( ( (bits64) ( zMiddleA < zMiddleB ) )<<32 ) + ( zMiddleA>>32 ); |
| 475 | zMiddleA <<= 32; |
| 476 | z1 += zMiddleA; |
| 477 | z0 += ( z1 < zMiddleA ); |
| 478 | *z1Ptr = z1; |
| 479 | *z0Ptr = z0; |
| 480 | |
| 481 | } |
| 482 | |
| 483 | /* |
| 484 | ------------------------------------------------------------------------------- |
| 485 | Multiplies the 128-bit value formed by concatenating `a0' and `a1' by `b' to |
| 486 | obtain a 192-bit product. The product is broken into three 64-bit pieces |
| 487 | which are stored at the locations pointed to by `z0Ptr', `z1Ptr', and |
| 488 | `z2Ptr'. |
| 489 | ------------------------------------------------------------------------------- |
| 490 | */ |
| 491 | INLINE void |
| 492 | mul128By64To192( |
| 493 | bits64 a0, |
| 494 | bits64 a1, |
| 495 | bits64 b, |
| 496 | bits64 *z0Ptr, |
| 497 | bits64 *z1Ptr, |
| 498 | bits64 *z2Ptr |
| 499 | ) |
| 500 | { |
| 501 | bits64 z0, z1, z2, more1; |
| 502 | |
| 503 | mul64To128( a1, b, &z1, &z2 ); |
| 504 | mul64To128( a0, b, &z0, &more1 ); |
| 505 | add128( z0, more1, 0, z1, &z0, &z1 ); |
| 506 | *z2Ptr = z2; |
| 507 | *z1Ptr = z1; |
| 508 | *z0Ptr = z0; |
| 509 | |
| 510 | } |
| 511 | |
| 512 | /* |
| 513 | ------------------------------------------------------------------------------- |
| 514 | Multiplies the 128-bit value formed by concatenating `a0' and `a1' to the |
| 515 | 128-bit value formed by concatenating `b0' and `b1' to obtain a 256-bit |
| 516 | product. The product is broken into four 64-bit pieces which are stored at |
| 517 | the locations pointed to by `z0Ptr', `z1Ptr', `z2Ptr', and `z3Ptr'. |
| 518 | ------------------------------------------------------------------------------- |
| 519 | */ |
| 520 | INLINE void |
| 521 | mul128To256( |
| 522 | bits64 a0, |
| 523 | bits64 a1, |
| 524 | bits64 b0, |
| 525 | bits64 b1, |
| 526 | bits64 *z0Ptr, |
| 527 | bits64 *z1Ptr, |
| 528 | bits64 *z2Ptr, |
| 529 | bits64 *z3Ptr |
| 530 | ) |
| 531 | { |
| 532 | bits64 z0, z1, z2, z3; |
| 533 | bits64 more1, more2; |
| 534 | |
| 535 | mul64To128( a1, b1, &z2, &z3 ); |
| 536 | mul64To128( a1, b0, &z1, &more2 ); |
| 537 | add128( z1, more2, 0, z2, &z1, &z2 ); |
| 538 | mul64To128( a0, b0, &z0, &more1 ); |
| 539 | add128( z0, more1, 0, z1, &z0, &z1 ); |
| 540 | mul64To128( a0, b1, &more1, &more2 ); |
| 541 | add128( more1, more2, 0, z2, &more1, &z2 ); |
| 542 | add128( z0, z1, 0, more1, &z0, &z1 ); |
| 543 | *z3Ptr = z3; |
| 544 | *z2Ptr = z2; |
| 545 | *z1Ptr = z1; |
| 546 | *z0Ptr = z0; |
| 547 | |
| 548 | } |
| 549 | |
| 550 | /* |
| 551 | ------------------------------------------------------------------------------- |
| 552 | Returns an approximation to the 64-bit integer quotient obtained by dividing |
| 553 | `b' into the 128-bit value formed by concatenating `a0' and `a1'. The |
| 554 | divisor `b' must be at least 2^63. If q is the exact quotient truncated |
| 555 | toward zero, the approximation returned lies between q and q + 2 inclusive. |
| 556 | If the exact quotient q is larger than 64 bits, the maximum positive 64-bit |
| 557 | unsigned integer is returned. |
| 558 | ------------------------------------------------------------------------------- |
| 559 | */ |
| 560 | static bits64 estimateDiv128To64( bits64 a0, bits64 a1, bits64 b ) |
| 561 | { |
| 562 | bits64 b0, b1; |
| 563 | bits64 rem0, rem1, term0, term1; |
| 564 | bits64 z; |
| 565 | if ( b <= a0 ) return LIT64( 0xFFFFFFFFFFFFFFFF ); |
Nicolas Pitre | c1241c4c | 2005-06-23 21:56:46 +0100 | [diff] [blame] | 566 | b0 = b>>32; /* hence b0 is 32 bits wide now */ |
| 567 | if ( b0<<32 <= a0 ) { |
| 568 | z = LIT64( 0xFFFFFFFF00000000 ); |
| 569 | } else { |
| 570 | z = a0; |
| 571 | do_div( z, b0 ); |
| 572 | z <<= 32; |
| 573 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 574 | mul64To128( b, z, &term0, &term1 ); |
| 575 | sub128( a0, a1, term0, term1, &rem0, &rem1 ); |
| 576 | while ( ( (sbits64) rem0 ) < 0 ) { |
| 577 | z -= LIT64( 0x100000000 ); |
| 578 | b1 = b<<32; |
| 579 | add128( rem0, rem1, b0, b1, &rem0, &rem1 ); |
| 580 | } |
| 581 | rem0 = ( rem0<<32 ) | ( rem1>>32 ); |
Nicolas Pitre | c1241c4c | 2005-06-23 21:56:46 +0100 | [diff] [blame] | 582 | if ( b0<<32 <= rem0 ) { |
| 583 | z |= 0xFFFFFFFF; |
| 584 | } else { |
| 585 | do_div( rem0, b0 ); |
| 586 | z |= rem0; |
| 587 | } |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 588 | return z; |
| 589 | |
| 590 | } |
| 591 | |
| 592 | /* |
| 593 | ------------------------------------------------------------------------------- |
| 594 | Returns an approximation to the square root of the 32-bit significand given |
| 595 | by `a'. Considered as an integer, `a' must be at least 2^31. If bit 0 of |
| 596 | `aExp' (the least significant bit) is 1, the integer returned approximates |
| 597 | 2^31*sqrt(`a'/2^31), where `a' is considered an integer. If bit 0 of `aExp' |
| 598 | is 0, the integer returned approximates 2^31*sqrt(`a'/2^30). In either |
| 599 | case, the approximation returned lies strictly within +/-2 of the exact |
| 600 | value. |
| 601 | ------------------------------------------------------------------------------- |
| 602 | */ |
| 603 | static bits32 estimateSqrt32( int16 aExp, bits32 a ) |
| 604 | { |
| 605 | static const bits16 sqrtOddAdjustments[] = { |
| 606 | 0x0004, 0x0022, 0x005D, 0x00B1, 0x011D, 0x019F, 0x0236, 0x02E0, |
| 607 | 0x039C, 0x0468, 0x0545, 0x0631, 0x072B, 0x0832, 0x0946, 0x0A67 |
| 608 | }; |
| 609 | static const bits16 sqrtEvenAdjustments[] = { |
| 610 | 0x0A2D, 0x08AF, 0x075A, 0x0629, 0x051A, 0x0429, 0x0356, 0x029E, |
| 611 | 0x0200, 0x0179, 0x0109, 0x00AF, 0x0068, 0x0034, 0x0012, 0x0002 |
| 612 | }; |
| 613 | int8 index; |
| 614 | bits32 z; |
Nicolas Pitre | c1241c4c | 2005-06-23 21:56:46 +0100 | [diff] [blame] | 615 | bits64 A; |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 616 | |
| 617 | index = ( a>>27 ) & 15; |
| 618 | if ( aExp & 1 ) { |
| 619 | z = 0x4000 + ( a>>17 ) - sqrtOddAdjustments[ index ]; |
| 620 | z = ( ( a / z )<<14 ) + ( z<<15 ); |
| 621 | a >>= 1; |
| 622 | } |
| 623 | else { |
| 624 | z = 0x8000 + ( a>>17 ) - sqrtEvenAdjustments[ index ]; |
| 625 | z = a / z + z; |
| 626 | z = ( 0x20000 <= z ) ? 0xFFFF8000 : ( z<<15 ); |
| 627 | if ( z <= a ) return (bits32) ( ( (sbits32) a )>>1 ); |
| 628 | } |
Nicolas Pitre | c1241c4c | 2005-06-23 21:56:46 +0100 | [diff] [blame] | 629 | A = ( (bits64) a )<<31; |
| 630 | do_div( A, z ); |
| 631 | return ( (bits32) A ) + ( z>>1 ); |
Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 632 | |
| 633 | } |
| 634 | |
| 635 | /* |
| 636 | ------------------------------------------------------------------------------- |
| 637 | Returns the number of leading 0 bits before the most-significant 1 bit |
| 638 | of `a'. If `a' is zero, 32 is returned. |
| 639 | ------------------------------------------------------------------------------- |
| 640 | */ |
| 641 | static int8 countLeadingZeros32( bits32 a ) |
| 642 | { |
| 643 | static const int8 countLeadingZerosHigh[] = { |
| 644 | 8, 7, 6, 6, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, |
| 645 | 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, |
| 646 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, |
| 647 | 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, |
| 648 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 649 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 650 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 651 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, |
| 652 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 653 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 654 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 655 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 656 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 657 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 658 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, |
| 659 | 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 |
| 660 | }; |
| 661 | int8 shiftCount; |
| 662 | |
| 663 | shiftCount = 0; |
| 664 | if ( a < 0x10000 ) { |
| 665 | shiftCount += 16; |
| 666 | a <<= 16; |
| 667 | } |
| 668 | if ( a < 0x1000000 ) { |
| 669 | shiftCount += 8; |
| 670 | a <<= 8; |
| 671 | } |
| 672 | shiftCount += countLeadingZerosHigh[ a>>24 ]; |
| 673 | return shiftCount; |
| 674 | |
| 675 | } |
| 676 | |
| 677 | /* |
| 678 | ------------------------------------------------------------------------------- |
| 679 | Returns the number of leading 0 bits before the most-significant 1 bit |
| 680 | of `a'. If `a' is zero, 64 is returned. |
| 681 | ------------------------------------------------------------------------------- |
| 682 | */ |
| 683 | static int8 countLeadingZeros64( bits64 a ) |
| 684 | { |
| 685 | int8 shiftCount; |
| 686 | |
| 687 | shiftCount = 0; |
| 688 | if ( a < ( (bits64) 1 )<<32 ) { |
| 689 | shiftCount += 32; |
| 690 | } |
| 691 | else { |
| 692 | a >>= 32; |
| 693 | } |
| 694 | shiftCount += countLeadingZeros32( a ); |
| 695 | return shiftCount; |
| 696 | |
| 697 | } |
| 698 | |
| 699 | /* |
| 700 | ------------------------------------------------------------------------------- |
| 701 | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' |
| 702 | is equal to the 128-bit value formed by concatenating `b0' and `b1'. |
| 703 | Otherwise, returns 0. |
| 704 | ------------------------------------------------------------------------------- |
| 705 | */ |
| 706 | INLINE flag eq128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) |
| 707 | { |
| 708 | |
| 709 | return ( a0 == b0 ) && ( a1 == b1 ); |
| 710 | |
| 711 | } |
| 712 | |
| 713 | /* |
| 714 | ------------------------------------------------------------------------------- |
| 715 | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less |
| 716 | than or equal to the 128-bit value formed by concatenating `b0' and `b1'. |
| 717 | Otherwise, returns 0. |
| 718 | ------------------------------------------------------------------------------- |
| 719 | */ |
| 720 | INLINE flag le128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) |
| 721 | { |
| 722 | |
| 723 | return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 <= b1 ) ); |
| 724 | |
| 725 | } |
| 726 | |
| 727 | /* |
| 728 | ------------------------------------------------------------------------------- |
| 729 | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is less |
| 730 | than the 128-bit value formed by concatenating `b0' and `b1'. Otherwise, |
| 731 | returns 0. |
| 732 | ------------------------------------------------------------------------------- |
| 733 | */ |
| 734 | INLINE flag lt128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) |
| 735 | { |
| 736 | |
| 737 | return ( a0 < b0 ) || ( ( a0 == b0 ) && ( a1 < b1 ) ); |
| 738 | |
| 739 | } |
| 740 | |
| 741 | /* |
| 742 | ------------------------------------------------------------------------------- |
| 743 | Returns 1 if the 128-bit value formed by concatenating `a0' and `a1' is |
| 744 | not equal to the 128-bit value formed by concatenating `b0' and `b1'. |
| 745 | Otherwise, returns 0. |
| 746 | ------------------------------------------------------------------------------- |
| 747 | */ |
| 748 | INLINE flag ne128( bits64 a0, bits64 a1, bits64 b0, bits64 b1 ) |
| 749 | { |
| 750 | |
| 751 | return ( a0 != b0 ) || ( a1 != b1 ); |
| 752 | |
| 753 | } |
| 754 | |