Linus Torvalds | 1da177e | 2005-04-16 15:20:36 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Linux/PA-RISC Project (http://www.parisc-linux.org/) |
| 3 | * |
| 4 | * Floating-point emulation code |
| 5 | * Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org> |
| 6 | * |
| 7 | * This program is free software; you can redistribute it and/or modify |
| 8 | * it under the terms of the GNU General Public License as published by |
| 9 | * the Free Software Foundation; either version 2, or (at your option) |
| 10 | * any later version. |
| 11 | * |
| 12 | * This program is distributed in the hope that it will be useful, |
| 13 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| 14 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| 15 | * GNU General Public License for more details. |
| 16 | * |
| 17 | * You should have received a copy of the GNU General Public License |
| 18 | * along with this program; if not, write to the Free Software |
| 19 | * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA |
| 20 | */ |
| 21 | /* |
| 22 | * BEGIN_DESC |
| 23 | * |
| 24 | * File: |
| 25 | * @(#) pa/spmath/dfadd.c $Revision: 1.1 $ |
| 26 | * |
| 27 | * Purpose: |
| 28 | * Double_add: add two double precision values. |
| 29 | * |
| 30 | * External Interfaces: |
| 31 | * dbl_fadd(leftptr, rightptr, dstptr, status) |
| 32 | * |
| 33 | * Internal Interfaces: |
| 34 | * |
| 35 | * Theory: |
| 36 | * <<please update with a overview of the operation of this file>> |
| 37 | * |
| 38 | * END_DESC |
| 39 | */ |
| 40 | |
| 41 | |
| 42 | #include "float.h" |
| 43 | #include "dbl_float.h" |
| 44 | |
| 45 | /* |
| 46 | * Double_add: add two double precision values. |
| 47 | */ |
| 48 | dbl_fadd( |
| 49 | dbl_floating_point *leftptr, |
| 50 | dbl_floating_point *rightptr, |
| 51 | dbl_floating_point *dstptr, |
| 52 | unsigned int *status) |
| 53 | { |
| 54 | register unsigned int signless_upper_left, signless_upper_right, save; |
| 55 | register unsigned int leftp1, leftp2, rightp1, rightp2, extent; |
| 56 | register unsigned int resultp1 = 0, resultp2 = 0; |
| 57 | |
| 58 | register int result_exponent, right_exponent, diff_exponent; |
| 59 | register int sign_save, jumpsize; |
| 60 | register boolean inexact = FALSE; |
| 61 | register boolean underflowtrap; |
| 62 | |
| 63 | /* Create local copies of the numbers */ |
| 64 | Dbl_copyfromptr(leftptr,leftp1,leftp2); |
| 65 | Dbl_copyfromptr(rightptr,rightp1,rightp2); |
| 66 | |
| 67 | /* A zero "save" helps discover equal operands (for later), * |
| 68 | * and is used in swapping operands (if needed). */ |
| 69 | Dbl_xortointp1(leftp1,rightp1,/*to*/save); |
| 70 | |
| 71 | /* |
| 72 | * check first operand for NaN's or infinity |
| 73 | */ |
| 74 | if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) |
| 75 | { |
| 76 | if (Dbl_iszero_mantissa(leftp1,leftp2)) |
| 77 | { |
| 78 | if (Dbl_isnotnan(rightp1,rightp2)) |
| 79 | { |
| 80 | if (Dbl_isinfinity(rightp1,rightp2) && save!=0) |
| 81 | { |
| 82 | /* |
| 83 | * invalid since operands are opposite signed infinity's |
| 84 | */ |
| 85 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
| 86 | Set_invalidflag(); |
| 87 | Dbl_makequietnan(resultp1,resultp2); |
| 88 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 89 | return(NOEXCEPTION); |
| 90 | } |
| 91 | /* |
| 92 | * return infinity |
| 93 | */ |
| 94 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
| 95 | return(NOEXCEPTION); |
| 96 | } |
| 97 | } |
| 98 | else |
| 99 | { |
| 100 | /* |
| 101 | * is NaN; signaling or quiet? |
| 102 | */ |
| 103 | if (Dbl_isone_signaling(leftp1)) |
| 104 | { |
| 105 | /* trap if INVALIDTRAP enabled */ |
| 106 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
| 107 | /* make NaN quiet */ |
| 108 | Set_invalidflag(); |
| 109 | Dbl_set_quiet(leftp1); |
| 110 | } |
| 111 | /* |
| 112 | * is second operand a signaling NaN? |
| 113 | */ |
| 114 | else if (Dbl_is_signalingnan(rightp1)) |
| 115 | { |
| 116 | /* trap if INVALIDTRAP enabled */ |
| 117 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
| 118 | /* make NaN quiet */ |
| 119 | Set_invalidflag(); |
| 120 | Dbl_set_quiet(rightp1); |
| 121 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
| 122 | return(NOEXCEPTION); |
| 123 | } |
| 124 | /* |
| 125 | * return quiet NaN |
| 126 | */ |
| 127 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
| 128 | return(NOEXCEPTION); |
| 129 | } |
| 130 | } /* End left NaN or Infinity processing */ |
| 131 | /* |
| 132 | * check second operand for NaN's or infinity |
| 133 | */ |
| 134 | if (Dbl_isinfinity_exponent(rightp1)) |
| 135 | { |
| 136 | if (Dbl_iszero_mantissa(rightp1,rightp2)) |
| 137 | { |
| 138 | /* return infinity */ |
| 139 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
| 140 | return(NOEXCEPTION); |
| 141 | } |
| 142 | /* |
| 143 | * is NaN; signaling or quiet? |
| 144 | */ |
| 145 | if (Dbl_isone_signaling(rightp1)) |
| 146 | { |
| 147 | /* trap if INVALIDTRAP enabled */ |
| 148 | if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); |
| 149 | /* make NaN quiet */ |
| 150 | Set_invalidflag(); |
| 151 | Dbl_set_quiet(rightp1); |
| 152 | } |
| 153 | /* |
| 154 | * return quiet NaN |
| 155 | */ |
| 156 | Dbl_copytoptr(rightp1,rightp2,dstptr); |
| 157 | return(NOEXCEPTION); |
| 158 | } /* End right NaN or Infinity processing */ |
| 159 | |
| 160 | /* Invariant: Must be dealing with finite numbers */ |
| 161 | |
| 162 | /* Compare operands by removing the sign */ |
| 163 | Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); |
| 164 | Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); |
| 165 | |
| 166 | /* sign difference selects add or sub operation. */ |
| 167 | if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) |
| 168 | { |
| 169 | /* Set the left operand to the larger one by XOR swap * |
| 170 | * First finish the first word using "save" */ |
| 171 | Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); |
| 172 | Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); |
| 173 | Dbl_swap_lower(leftp2,rightp2); |
| 174 | result_exponent = Dbl_exponent(leftp1); |
| 175 | } |
| 176 | /* Invariant: left is not smaller than right. */ |
| 177 | |
| 178 | if((right_exponent = Dbl_exponent(rightp1)) == 0) |
| 179 | { |
| 180 | /* Denormalized operands. First look for zeroes */ |
| 181 | if(Dbl_iszero_mantissa(rightp1,rightp2)) |
| 182 | { |
| 183 | /* right is zero */ |
| 184 | if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) |
| 185 | { |
| 186 | /* Both operands are zeros */ |
| 187 | if(Is_rounding_mode(ROUNDMINUS)) |
| 188 | { |
| 189 | Dbl_or_signs(leftp1,/*with*/rightp1); |
| 190 | } |
| 191 | else |
| 192 | { |
| 193 | Dbl_and_signs(leftp1,/*with*/rightp1); |
| 194 | } |
| 195 | } |
| 196 | else |
| 197 | { |
| 198 | /* Left is not a zero and must be the result. Trapped |
| 199 | * underflows are signaled if left is denormalized. Result |
| 200 | * is always exact. */ |
| 201 | if( (result_exponent == 0) && Is_underflowtrap_enabled() ) |
| 202 | { |
| 203 | /* need to normalize results mantissa */ |
| 204 | sign_save = Dbl_signextendedsign(leftp1); |
| 205 | Dbl_leftshiftby1(leftp1,leftp2); |
| 206 | Dbl_normalize(leftp1,leftp2,result_exponent); |
| 207 | Dbl_set_sign(leftp1,/*using*/sign_save); |
| 208 | Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); |
| 209 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
| 210 | /* inexact = FALSE */ |
| 211 | return(UNDERFLOWEXCEPTION); |
| 212 | } |
| 213 | } |
| 214 | Dbl_copytoptr(leftp1,leftp2,dstptr); |
| 215 | return(NOEXCEPTION); |
| 216 | } |
| 217 | |
| 218 | /* Neither are zeroes */ |
| 219 | Dbl_clear_sign(rightp1); /* Exponent is already cleared */ |
| 220 | if(result_exponent == 0 ) |
| 221 | { |
| 222 | /* Both operands are denormalized. The result must be exact |
| 223 | * and is simply calculated. A sum could become normalized and a |
| 224 | * difference could cancel to a true zero. */ |
| 225 | if( (/*signed*/int) save < 0 ) |
| 226 | { |
| 227 | Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, |
| 228 | /*into*/resultp1,resultp2); |
| 229 | if(Dbl_iszero_mantissa(resultp1,resultp2)) |
| 230 | { |
| 231 | if(Is_rounding_mode(ROUNDMINUS)) |
| 232 | { |
| 233 | Dbl_setone_sign(resultp1); |
| 234 | } |
| 235 | else |
| 236 | { |
| 237 | Dbl_setzero_sign(resultp1); |
| 238 | } |
| 239 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 240 | return(NOEXCEPTION); |
| 241 | } |
| 242 | } |
| 243 | else |
| 244 | { |
| 245 | Dbl_addition(leftp1,leftp2,rightp1,rightp2, |
| 246 | /*into*/resultp1,resultp2); |
| 247 | if(Dbl_isone_hidden(resultp1)) |
| 248 | { |
| 249 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 250 | return(NOEXCEPTION); |
| 251 | } |
| 252 | } |
| 253 | if(Is_underflowtrap_enabled()) |
| 254 | { |
| 255 | /* need to normalize result */ |
| 256 | sign_save = Dbl_signextendedsign(resultp1); |
| 257 | Dbl_leftshiftby1(resultp1,resultp2); |
| 258 | Dbl_normalize(resultp1,resultp2,result_exponent); |
| 259 | Dbl_set_sign(resultp1,/*using*/sign_save); |
| 260 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); |
| 261 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 262 | /* inexact = FALSE */ |
| 263 | return(UNDERFLOWEXCEPTION); |
| 264 | } |
| 265 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 266 | return(NOEXCEPTION); |
| 267 | } |
| 268 | right_exponent = 1; /* Set exponent to reflect different bias |
| 269 | * with denomalized numbers. */ |
| 270 | } |
| 271 | else |
| 272 | { |
| 273 | Dbl_clear_signexponent_set_hidden(rightp1); |
| 274 | } |
| 275 | Dbl_clear_exponent_set_hidden(leftp1); |
| 276 | diff_exponent = result_exponent - right_exponent; |
| 277 | |
| 278 | /* |
| 279 | * Special case alignment of operands that would force alignment |
| 280 | * beyond the extent of the extension. A further optimization |
| 281 | * could special case this but only reduces the path length for this |
| 282 | * infrequent case. |
| 283 | */ |
| 284 | if(diff_exponent > DBL_THRESHOLD) |
| 285 | { |
| 286 | diff_exponent = DBL_THRESHOLD; |
| 287 | } |
| 288 | |
| 289 | /* Align right operand by shifting to right */ |
| 290 | Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, |
| 291 | /*and lower to*/extent); |
| 292 | |
| 293 | /* Treat sum and difference of the operands separately. */ |
| 294 | if( (/*signed*/int) save < 0 ) |
| 295 | { |
| 296 | /* |
| 297 | * Difference of the two operands. Their can be no overflow. A |
| 298 | * borrow can occur out of the hidden bit and force a post |
| 299 | * normalization phase. |
| 300 | */ |
| 301 | Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, |
| 302 | /*with*/extent,/*into*/resultp1,resultp2); |
| 303 | if(Dbl_iszero_hidden(resultp1)) |
| 304 | { |
| 305 | /* Handle normalization */ |
| 306 | /* A straight foward algorithm would now shift the result |
| 307 | * and extension left until the hidden bit becomes one. Not |
| 308 | * all of the extension bits need participate in the shift. |
| 309 | * Only the two most significant bits (round and guard) are |
| 310 | * needed. If only a single shift is needed then the guard |
| 311 | * bit becomes a significant low order bit and the extension |
| 312 | * must participate in the rounding. If more than a single |
| 313 | * shift is needed, then all bits to the right of the guard |
| 314 | * bit are zeros, and the guard bit may or may not be zero. */ |
| 315 | sign_save = Dbl_signextendedsign(resultp1); |
| 316 | Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); |
| 317 | |
| 318 | /* Need to check for a zero result. The sign and exponent |
| 319 | * fields have already been zeroed. The more efficient test |
| 320 | * of the full object can be used. |
| 321 | */ |
| 322 | if(Dbl_iszero(resultp1,resultp2)) |
| 323 | /* Must have been "x-x" or "x+(-x)". */ |
| 324 | { |
| 325 | if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); |
| 326 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 327 | return(NOEXCEPTION); |
| 328 | } |
| 329 | result_exponent--; |
| 330 | /* Look to see if normalization is finished. */ |
| 331 | if(Dbl_isone_hidden(resultp1)) |
| 332 | { |
| 333 | if(result_exponent==0) |
| 334 | { |
| 335 | /* Denormalized, exponent should be zero. Left operand * |
| 336 | * was normalized, so extent (guard, round) was zero */ |
| 337 | goto underflow; |
| 338 | } |
| 339 | else |
| 340 | { |
| 341 | /* No further normalization is needed. */ |
| 342 | Dbl_set_sign(resultp1,/*using*/sign_save); |
| 343 | Ext_leftshiftby1(extent); |
| 344 | goto round; |
| 345 | } |
| 346 | } |
| 347 | |
| 348 | /* Check for denormalized, exponent should be zero. Left * |
| 349 | * operand was normalized, so extent (guard, round) was zero */ |
| 350 | if(!(underflowtrap = Is_underflowtrap_enabled()) && |
| 351 | result_exponent==0) goto underflow; |
| 352 | |
| 353 | /* Shift extension to complete one bit of normalization and |
| 354 | * update exponent. */ |
| 355 | Ext_leftshiftby1(extent); |
| 356 | |
| 357 | /* Discover first one bit to determine shift amount. Use a |
| 358 | * modified binary search. We have already shifted the result |
| 359 | * one position right and still not found a one so the remainder |
| 360 | * of the extension must be zero and simplifies rounding. */ |
| 361 | /* Scan bytes */ |
| 362 | while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) |
| 363 | { |
| 364 | Dbl_leftshiftby8(resultp1,resultp2); |
| 365 | if((result_exponent -= 8) <= 0 && !underflowtrap) |
| 366 | goto underflow; |
| 367 | } |
| 368 | /* Now narrow it down to the nibble */ |
| 369 | if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) |
| 370 | { |
| 371 | /* The lower nibble contains the normalizing one */ |
| 372 | Dbl_leftshiftby4(resultp1,resultp2); |
| 373 | if((result_exponent -= 4) <= 0 && !underflowtrap) |
| 374 | goto underflow; |
| 375 | } |
| 376 | /* Select case were first bit is set (already normalized) |
| 377 | * otherwise select the proper shift. */ |
| 378 | if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) |
| 379 | { |
| 380 | /* Already normalized */ |
| 381 | if(result_exponent <= 0) goto underflow; |
| 382 | Dbl_set_sign(resultp1,/*using*/sign_save); |
| 383 | Dbl_set_exponent(resultp1,/*using*/result_exponent); |
| 384 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 385 | return(NOEXCEPTION); |
| 386 | } |
| 387 | Dbl_sethigh4bits(resultp1,/*using*/sign_save); |
| 388 | switch(jumpsize) |
| 389 | { |
| 390 | case 1: |
| 391 | { |
| 392 | Dbl_leftshiftby3(resultp1,resultp2); |
| 393 | result_exponent -= 3; |
| 394 | break; |
| 395 | } |
| 396 | case 2: |
| 397 | case 3: |
| 398 | { |
| 399 | Dbl_leftshiftby2(resultp1,resultp2); |
| 400 | result_exponent -= 2; |
| 401 | break; |
| 402 | } |
| 403 | case 4: |
| 404 | case 5: |
| 405 | case 6: |
| 406 | case 7: |
| 407 | { |
| 408 | Dbl_leftshiftby1(resultp1,resultp2); |
| 409 | result_exponent -= 1; |
| 410 | break; |
| 411 | } |
| 412 | } |
| 413 | if(result_exponent > 0) |
| 414 | { |
| 415 | Dbl_set_exponent(resultp1,/*using*/result_exponent); |
| 416 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 417 | return(NOEXCEPTION); /* Sign bit is already set */ |
| 418 | } |
| 419 | /* Fixup potential underflows */ |
| 420 | underflow: |
| 421 | if(Is_underflowtrap_enabled()) |
| 422 | { |
| 423 | Dbl_set_sign(resultp1,sign_save); |
| 424 | Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); |
| 425 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 426 | /* inexact = FALSE */ |
| 427 | return(UNDERFLOWEXCEPTION); |
| 428 | } |
| 429 | /* |
| 430 | * Since we cannot get an inexact denormalized result, |
| 431 | * we can now return. |
| 432 | */ |
| 433 | Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); |
| 434 | Dbl_clear_signexponent(resultp1); |
| 435 | Dbl_set_sign(resultp1,sign_save); |
| 436 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 437 | return(NOEXCEPTION); |
| 438 | } /* end if(hidden...)... */ |
| 439 | /* Fall through and round */ |
| 440 | } /* end if(save < 0)... */ |
| 441 | else |
| 442 | { |
| 443 | /* Add magnitudes */ |
| 444 | Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); |
| 445 | if(Dbl_isone_hiddenoverflow(resultp1)) |
| 446 | { |
| 447 | /* Prenormalization required. */ |
| 448 | Dbl_rightshiftby1_withextent(resultp2,extent,extent); |
| 449 | Dbl_arithrightshiftby1(resultp1,resultp2); |
| 450 | result_exponent++; |
| 451 | } /* end if hiddenoverflow... */ |
| 452 | } /* end else ...add magnitudes... */ |
| 453 | |
| 454 | /* Round the result. If the extension is all zeros,then the result is |
| 455 | * exact. Otherwise round in the correct direction. No underflow is |
| 456 | * possible. If a postnormalization is necessary, then the mantissa is |
| 457 | * all zeros so no shift is needed. */ |
| 458 | round: |
| 459 | if(Ext_isnotzero(extent)) |
| 460 | { |
| 461 | inexact = TRUE; |
| 462 | switch(Rounding_mode()) |
| 463 | { |
| 464 | case ROUNDNEAREST: /* The default. */ |
| 465 | if(Ext_isone_sign(extent)) |
| 466 | { |
| 467 | /* at least 1/2 ulp */ |
| 468 | if(Ext_isnotzero_lower(extent) || |
| 469 | Dbl_isone_lowmantissap2(resultp2)) |
| 470 | { |
| 471 | /* either exactly half way and odd or more than 1/2ulp */ |
| 472 | Dbl_increment(resultp1,resultp2); |
| 473 | } |
| 474 | } |
| 475 | break; |
| 476 | |
| 477 | case ROUNDPLUS: |
| 478 | if(Dbl_iszero_sign(resultp1)) |
| 479 | { |
| 480 | /* Round up positive results */ |
| 481 | Dbl_increment(resultp1,resultp2); |
| 482 | } |
| 483 | break; |
| 484 | |
| 485 | case ROUNDMINUS: |
| 486 | if(Dbl_isone_sign(resultp1)) |
| 487 | { |
| 488 | /* Round down negative results */ |
| 489 | Dbl_increment(resultp1,resultp2); |
| 490 | } |
| 491 | |
| 492 | case ROUNDZERO:; |
| 493 | /* truncate is simple */ |
| 494 | } /* end switch... */ |
| 495 | if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; |
| 496 | } |
| 497 | if(result_exponent == DBL_INFINITY_EXPONENT) |
| 498 | { |
| 499 | /* Overflow */ |
| 500 | if(Is_overflowtrap_enabled()) |
| 501 | { |
| 502 | Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); |
| 503 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 504 | if (inexact) |
| 505 | if (Is_inexacttrap_enabled()) |
| 506 | return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); |
| 507 | else Set_inexactflag(); |
| 508 | return(OVERFLOWEXCEPTION); |
| 509 | } |
| 510 | else |
| 511 | { |
| 512 | inexact = TRUE; |
| 513 | Set_overflowflag(); |
| 514 | Dbl_setoverflow(resultp1,resultp2); |
| 515 | } |
| 516 | } |
| 517 | else Dbl_set_exponent(resultp1,result_exponent); |
| 518 | Dbl_copytoptr(resultp1,resultp2,dstptr); |
| 519 | if(inexact) |
| 520 | if(Is_inexacttrap_enabled()) |
| 521 | return(INEXACTEXCEPTION); |
| 522 | else Set_inexactflag(); |
| 523 | return(NOEXCEPTION); |
| 524 | } |