1 /* $NetBSD: dfsub.c,v 1.1 2002/06/05 01:04:24 fredette Exp $ */ 2 3 /* $OpenBSD: dfsub.c,v 1.4 2001/03/29 03:58:17 mickey Exp $ */ 4 5 /* 6 * Copyright 1996 1995 by Open Software Foundation, Inc. 7 * All Rights Reserved 8 * 9 * Permission to use, copy, modify, and distribute this software and 10 * its documentation for any purpose and without fee is hereby granted, 11 * provided that the above copyright notice appears in all copies and 12 * that both the copyright notice and this permission notice appear in 13 * supporting documentation. 14 * 15 * OSF DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE 16 * INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS 17 * FOR A PARTICULAR PURPOSE. 18 * 19 * IN NO EVENT SHALL OSF BE LIABLE FOR ANY SPECIAL, INDIRECT, OR 20 * CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM 21 * LOSS OF USE, DATA OR PROFITS, WHETHER IN ACTION OF CONTRACT, 22 * NEGLIGENCE, OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION 23 * WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. 24 * 25 */ 26 /* 27 * pmk1.1 28 */ 29 /* 30 * (c) Copyright 1986 HEWLETT-PACKARD COMPANY 31 * 32 * To anyone who acknowledges that this file is provided "AS IS" 33 * without any express or implied warranty: 34 * permission to use, copy, modify, and distribute this file 35 * for any purpose is hereby granted without fee, provided that 36 * the above copyright notice and this notice appears in all 37 * copies, and that the name of Hewlett-Packard Company not be 38 * used in advertising or publicity pertaining to distribution 39 * of the software without specific, written prior permission. 40 * Hewlett-Packard Company makes no representations about the 41 * suitability of this software for any purpose. 42 */ 43 44 #include "../spmath/float.h" 45 #include "../spmath/dbl_float.h" 46 47 /* 48 * Double_subtract: subtract two double precision values. 49 */ 50 int 51 dbl_fsub(leftptr, rightptr, dstptr, status) 52 dbl_floating_point *leftptr, *rightptr, *dstptr; 53 unsigned int *status; 54 { 55 register unsigned int signless_upper_left, signless_upper_right, save; 56 register unsigned int leftp1, leftp2, rightp1, rightp2, extent; 57 register unsigned int resultp1 = 0, resultp2 = 0; 58 59 register int result_exponent, right_exponent, diff_exponent; 60 register int sign_save, jumpsize; 61 register int inexact = FALSE, 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 same 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_invert_sign(rightp1); 140 Dbl_copytoptr(rightp1,rightp2,dstptr); 141 return(NOEXCEPTION); 142 } 143 /* 144 * is NaN; signaling or quiet? 145 */ 146 if (Dbl_isone_signaling(rightp1)) 147 { 148 /* trap if INVALIDTRAP enabled */ 149 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 150 /* make NaN quiet */ 151 Set_invalidflag(); 152 Dbl_set_quiet(rightp1); 153 } 154 /* 155 * return quiet NaN 156 */ 157 Dbl_copytoptr(rightp1,rightp2,dstptr); 158 return(NOEXCEPTION); 159 } /* End right NaN or Infinity processing */ 160 161 /* Invariant: Must be dealing with finite numbers */ 162 163 /* Compare operands by removing the sign */ 164 Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); 165 Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); 166 167 /* sign difference selects add or sub operation. */ 168 if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) 169 { 170 /* Set the left operand to the larger one by XOR swap * 171 * First finish the first word using "save" */ 172 Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); 173 Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); 174 Dbl_swap_lower(leftp2,rightp2); 175 result_exponent = Dbl_exponent(leftp1); 176 Dbl_invert_sign(leftp1); 177 } 178 /* Invariant: left is not smaller than right. */ 179 180 if((right_exponent = Dbl_exponent(rightp1)) == 0) 181 { 182 /* Denormalized operands. First look for zeroes */ 183 if(Dbl_iszero_mantissa(rightp1,rightp2)) 184 { 185 /* right is zero */ 186 if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) 187 { 188 /* Both operands are zeros */ 189 Dbl_invert_sign(rightp1); 190 if(Is_rounding_mode(ROUNDMINUS)) 191 { 192 Dbl_or_signs(leftp1,/*with*/rightp1); 193 } 194 else 195 { 196 Dbl_and_signs(leftp1,/*with*/rightp1); 197 } 198 } 199 else 200 { 201 /* Left is not a zero and must be the result. Trapped 202 * underflows are signaled if left is denormalized. Result 203 * is always exact. */ 204 if( (result_exponent == 0) && Is_underflowtrap_enabled() ) 205 { 206 /* need to normalize results mantissa */ 207 sign_save = Dbl_signextendedsign(leftp1); 208 Dbl_leftshiftby1(leftp1,leftp2); 209 Dbl_normalize(leftp1,leftp2,result_exponent); 210 Dbl_set_sign(leftp1,/*using*/sign_save); 211 Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); 212 Dbl_copytoptr(leftp1,leftp2,dstptr); 213 /* inexact = FALSE */ 214 return(UNDERFLOWEXCEPTION); 215 } 216 } 217 Dbl_copytoptr(leftp1,leftp2,dstptr); 218 return(NOEXCEPTION); 219 } 220 221 /* Neither are zeroes */ 222 Dbl_clear_sign(rightp1); /* Exponent is already cleared */ 223 if(result_exponent == 0 ) 224 { 225 /* Both operands are denormalized. The result must be exact 226 * and is simply calculated. A sum could become normalized and a 227 * difference could cancel to a true zero. */ 228 if( (/*signed*/int) save >= 0 ) 229 { 230 Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, 231 /*into*/resultp1,resultp2); 232 if(Dbl_iszero_mantissa(resultp1,resultp2)) 233 { 234 if(Is_rounding_mode(ROUNDMINUS)) 235 { 236 Dbl_setone_sign(resultp1); 237 } 238 else 239 { 240 Dbl_setzero_sign(resultp1); 241 } 242 Dbl_copytoptr(resultp1,resultp2,dstptr); 243 return(NOEXCEPTION); 244 } 245 } 246 else 247 { 248 Dbl_addition(leftp1,leftp2,rightp1,rightp2, 249 /*into*/resultp1,resultp2); 250 if(Dbl_isone_hidden(resultp1)) 251 { 252 Dbl_copytoptr(resultp1,resultp2,dstptr); 253 return(NOEXCEPTION); 254 } 255 } 256 if(Is_underflowtrap_enabled()) 257 { 258 /* need to normalize result */ 259 sign_save = Dbl_signextendedsign(resultp1); 260 Dbl_leftshiftby1(resultp1,resultp2); 261 Dbl_normalize(resultp1,resultp2,result_exponent); 262 Dbl_set_sign(resultp1,/*using*/sign_save); 263 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); 264 Dbl_copytoptr(resultp1,resultp2,dstptr); 265 /* inexact = FALSE */ 266 return(UNDERFLOWEXCEPTION); 267 } 268 Dbl_copytoptr(resultp1,resultp2,dstptr); 269 return(NOEXCEPTION); 270 } 271 right_exponent = 1; /* Set exponent to reflect different bias 272 * with denomalized numbers. */ 273 } 274 else 275 { 276 Dbl_clear_signexponent_set_hidden(rightp1); 277 } 278 Dbl_clear_exponent_set_hidden(leftp1); 279 diff_exponent = result_exponent - right_exponent; 280 281 /* 282 * Special case alignment of operands that would force alignment 283 * beyond the extent of the extension. A further optimization 284 * could special case this but only reduces the path length for this 285 * infrequent case. 286 */ 287 if(diff_exponent > DBL_THRESHOLD) 288 { 289 diff_exponent = DBL_THRESHOLD; 290 } 291 292 /* Align right operand by shifting to right */ 293 Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, 294 /*and lower to*/extent); 295 296 /* Treat sum and difference of the operands separately. */ 297 if( (/*signed*/int) save >= 0 ) 298 { 299 /* 300 * Difference of the two operands. Their can be no overflow. A 301 * borrow can occur out of the hidden bit and force a post 302 * normalization phase. 303 */ 304 Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, 305 /*with*/extent,/*into*/resultp1,resultp2); 306 if(Dbl_iszero_hidden(resultp1)) 307 { 308 /* Handle normalization */ 309 /* A straight foward algorithm would now shift the result 310 * and extension left until the hidden bit becomes one. Not 311 * all of the extension bits need participate in the shift. 312 * Only the two most significant bits (round and guard) are 313 * needed. If only a single shift is needed then the guard 314 * bit becomes a significant low order bit and the extension 315 * must participate in the rounding. If more than a single 316 * shift is needed, then all bits to the right of the guard 317 * bit are zeros, and the guard bit may or may not be zero. */ 318 sign_save = Dbl_signextendedsign(resultp1); 319 Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); 320 321 /* Need to check for a zero result. The sign and exponent 322 * fields have already been zeroed. The more efficient test 323 * of the full object can be used. 324 */ 325 if(Dbl_iszero(resultp1,resultp2)) 326 /* Must have been "x-x" or "x+(-x)". */ 327 { 328 if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); 329 Dbl_copytoptr(resultp1,resultp2,dstptr); 330 return(NOEXCEPTION); 331 } 332 result_exponent--; 333 /* Look to see if normalization is finished. */ 334 if(Dbl_isone_hidden(resultp1)) { 335 if(result_exponent==0) { 336 /* Denormalized, exponent should be zero. Left operand * 337 * was normalized, so extent (guard, round) was zero */ 338 goto underflow; 339 } else { 340 /* No further normalization is needed. */ 341 Dbl_set_sign(resultp1,/*using*/sign_save); 342 Ext_leftshiftby1(extent); 343 goto round; 344 } 345 } 346 347 /* Check for denormalized, exponent should be zero. Left * 348 * operand was normalized, so extent (guard, round) was zero */ 349 if(!(underflowtrap = Is_underflowtrap_enabled()) && 350 result_exponent==0) goto underflow; 351 352 /* Shift extension to complete one bit of normalization and 353 * update exponent. */ 354 Ext_leftshiftby1(extent); 355 356 /* Discover first one bit to determine shift amount. Use a 357 * modified binary search. We have already shifted the result 358 * one position right and still not found a one so the remainder 359 * of the extension must be zero and simplifies rounding. */ 360 /* Scan bytes */ 361 while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) 362 { 363 Dbl_leftshiftby8(resultp1,resultp2); 364 if((result_exponent -= 8) <= 0 && !underflowtrap) 365 goto underflow; 366 } 367 /* Now narrow it down to the nibble */ 368 if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) 369 { 370 /* The lower nibble contains the normalizing one */ 371 Dbl_leftshiftby4(resultp1,resultp2); 372 if((result_exponent -= 4) <= 0 && !underflowtrap) 373 goto underflow; 374 } 375 /* Select case were first bit is set (already normalized) 376 * otherwise select the proper shift. */ 377 if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) 378 { 379 /* Already normalized */ 380 if(result_exponent <= 0) goto underflow; 381 Dbl_set_sign(resultp1,/*using*/sign_save); 382 Dbl_set_exponent(resultp1,/*using*/result_exponent); 383 Dbl_copytoptr(resultp1,resultp2,dstptr); 384 return(NOEXCEPTION); 385 } 386 Dbl_sethigh4bits(resultp1,/*using*/sign_save); 387 switch(jumpsize) 388 { 389 case 1: 390 { 391 Dbl_leftshiftby3(resultp1,resultp2); 392 result_exponent -= 3; 393 break; 394 } 395 case 2: 396 case 3: 397 { 398 Dbl_leftshiftby2(resultp1,resultp2); 399 result_exponent -= 2; 400 break; 401 } 402 case 4: 403 case 5: 404 case 6: 405 case 7: 406 { 407 Dbl_leftshiftby1(resultp1,resultp2); 408 result_exponent -= 1; 409 break; 410 } 411 } 412 if(result_exponent > 0) 413 { 414 Dbl_set_exponent(resultp1,/*using*/result_exponent); 415 Dbl_copytoptr(resultp1,resultp2,dstptr); 416 return(NOEXCEPTION); /* Sign bit is already set */ 417 } 418 /* Fixup potential underflows */ 419 underflow: 420 if(Is_underflowtrap_enabled()) 421 { 422 Dbl_set_sign(resultp1,sign_save); 423 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); 424 Dbl_copytoptr(resultp1,resultp2,dstptr); 425 /* inexact = FALSE */ 426 return(UNDERFLOWEXCEPTION); 427 } 428 /* 429 * Since we cannot get an inexact denormalized result, 430 * we can now return. 431 */ 432 Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); 433 Dbl_clear_signexponent(resultp1); 434 Dbl_set_sign(resultp1,sign_save); 435 Dbl_copytoptr(resultp1,resultp2,dstptr); 436 return(NOEXCEPTION); 437 } /* end if(hidden...)... */ 438 /* Fall through and round */ 439 } /* end if(save >= 0)... */ 440 else 441 { 442 /* Subtract magnitudes */ 443 Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); 444 if(Dbl_isone_hiddenoverflow(resultp1)) 445 { 446 /* Prenormalization required. */ 447 Dbl_rightshiftby1_withextent(resultp2,extent,extent); 448 Dbl_arithrightshiftby1(resultp1,resultp2); 449 result_exponent++; 450 } /* end if hiddenoverflow... */ 451 } /* end else ...subtract magnitudes... */ 452 453 /* Round the result. If the extension is all zeros,then the result is 454 * exact. Otherwise round in the correct direction. No underflow is 455 * possible. If a postnormalization is necessary, then the mantissa is 456 * all zeros so no shift is needed. */ 457 round: 458 if(Ext_isnotzero(extent)) 459 { 460 inexact = TRUE; 461 switch(Rounding_mode()) 462 { 463 case ROUNDNEAREST: /* The default. */ 464 if(Ext_isone_sign(extent)) 465 { 466 /* at least 1/2 ulp */ 467 if(Ext_isnotzero_lower(extent) || 468 Dbl_isone_lowmantissap2(resultp2)) 469 { 470 /* either exactly half way and odd or more than 1/2ulp */ 471 Dbl_increment(resultp1,resultp2); 472 } 473 } 474 break; 475 476 case ROUNDPLUS: 477 if(Dbl_iszero_sign(resultp1)) 478 { 479 /* Round up positive results */ 480 Dbl_increment(resultp1,resultp2); 481 } 482 break; 483 484 case ROUNDMINUS: 485 if(Dbl_isone_sign(resultp1)) 486 { 487 /* Round down negative results */ 488 Dbl_increment(resultp1,resultp2); 489 } 490 491 case ROUNDZERO:; 492 /* truncate is simple */ 493 } /* end switch... */ 494 if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; 495 } 496 if(result_exponent == DBL_INFINITY_EXPONENT) 497 { 498 /* Overflow */ 499 if(Is_overflowtrap_enabled()) 500 { 501 Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); 502 Dbl_copytoptr(resultp1,resultp2,dstptr); 503 if (inexact) { 504 if (Is_inexacttrap_enabled()) 505 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); 506 else 507 Set_inexactflag(); 508 } 509 return(OVERFLOWEXCEPTION); 510 } 511 else 512 { 513 inexact = TRUE; 514 Set_overflowflag(); 515 Dbl_setoverflow(resultp1,resultp2); 516 } 517 } 518 else Dbl_set_exponent(resultp1,result_exponent); 519 Dbl_copytoptr(resultp1,resultp2,dstptr); 520 if(inexact) { 521 if(Is_inexacttrap_enabled()) 522 return(INEXACTEXCEPTION); 523 else 524 Set_inexactflag(); 525 } 526 return(NOEXCEPTION); 527 } 528