1 /* $NetBSD: dfsub.c,v 1.7 2023/07/31 20:48:04 andvar 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 <sys/cdefs.h> 45 __KERNEL_RCSID(0, "$NetBSD: dfsub.c,v 1.7 2023/07/31 20:48:04 andvar Exp $"); 46 47 #include "../spmath/float.h" 48 #include "../spmath/dbl_float.h" 49 50 /* 51 * Double_subtract: subtract two double precision values. 52 */ 53 int 54 dbl_fsub(dbl_floating_point *leftptr, dbl_floating_point *rightptr, 55 dbl_floating_point *dstptr, unsigned int *status) 56 { 57 register unsigned int signless_upper_left, signless_upper_right, save; 58 register unsigned int leftp1, leftp2, rightp1, rightp2, extent; 59 register unsigned int resultp1 = 0, resultp2 = 0; 60 61 register int result_exponent, right_exponent, diff_exponent; 62 register int sign_save, jumpsize; 63 register int inexact = false, underflowtrap; 64 65 /* Create local copies of the numbers */ 66 Dbl_copyfromptr(leftptr,leftp1,leftp2); 67 Dbl_copyfromptr(rightptr,rightp1,rightp2); 68 69 /* A zero "save" helps discover equal operands (for later), * 70 * and is used in swapping operands (if needed). */ 71 Dbl_xortointp1(leftp1,rightp1,/*to*/save); 72 73 /* 74 * check first operand for NaN's or infinity 75 */ 76 if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) 77 { 78 if (Dbl_iszero_mantissa(leftp1,leftp2)) 79 { 80 if (Dbl_isnotnan(rightp1,rightp2)) 81 { 82 if (Dbl_isinfinity(rightp1,rightp2) && save==0) 83 { 84 /* 85 * invalid since operands are same signed infinity's 86 */ 87 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 88 Set_invalidflag(); 89 Dbl_makequietnan(resultp1,resultp2); 90 Dbl_copytoptr(resultp1,resultp2,dstptr); 91 return(NOEXCEPTION); 92 } 93 /* 94 * return infinity 95 */ 96 Dbl_copytoptr(leftp1,leftp2,dstptr); 97 return(NOEXCEPTION); 98 } 99 } 100 else 101 { 102 /* 103 * is NaN; signaling or quiet? 104 */ 105 if (Dbl_isone_signaling(leftp1)) 106 { 107 /* trap if INVALIDTRAP enabled */ 108 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 109 /* make NaN quiet */ 110 Set_invalidflag(); 111 Dbl_set_quiet(leftp1); 112 } 113 /* 114 * is second operand a signaling NaN? 115 */ 116 else if (Dbl_is_signalingnan(rightp1)) 117 { 118 /* trap if INVALIDTRAP enabled */ 119 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 120 /* make NaN quiet */ 121 Set_invalidflag(); 122 Dbl_set_quiet(rightp1); 123 Dbl_copytoptr(rightp1,rightp2,dstptr); 124 return(NOEXCEPTION); 125 } 126 /* 127 * return quiet NaN 128 */ 129 Dbl_copytoptr(leftp1,leftp2,dstptr); 130 return(NOEXCEPTION); 131 } 132 } /* End left NaN or Infinity processing */ 133 /* 134 * check second operand for NaN's or infinity 135 */ 136 if (Dbl_isinfinity_exponent(rightp1)) 137 { 138 if (Dbl_iszero_mantissa(rightp1,rightp2)) 139 { 140 /* return infinity */ 141 Dbl_invert_sign(rightp1); 142 Dbl_copytoptr(rightp1,rightp2,dstptr); 143 return(NOEXCEPTION); 144 } 145 /* 146 * is NaN; signaling or quiet? 147 */ 148 if (Dbl_isone_signaling(rightp1)) 149 { 150 /* trap if INVALIDTRAP enabled */ 151 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 152 /* make NaN quiet */ 153 Set_invalidflag(); 154 Dbl_set_quiet(rightp1); 155 } 156 /* 157 * return quiet NaN 158 */ 159 Dbl_copytoptr(rightp1,rightp2,dstptr); 160 return(NOEXCEPTION); 161 } /* End right NaN or Infinity processing */ 162 163 /* Invariant: Must be dealing with finite numbers */ 164 165 /* Compare operands by removing the sign */ 166 Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); 167 Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); 168 169 /* sign difference selects add or sub operation. */ 170 if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) 171 { 172 /* Set the left operand to the larger one by XOR swap * 173 * First finish the first word using "save" */ 174 Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); 175 Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); 176 Dbl_swap_lower(leftp2,rightp2); 177 result_exponent = Dbl_exponent(leftp1); 178 Dbl_invert_sign(leftp1); 179 } 180 /* Invariant: left is not smaller than right. */ 181 182 if((right_exponent = Dbl_exponent(rightp1)) == 0) 183 { 184 /* Denormalized operands. First look for zeroes */ 185 if(Dbl_iszero_mantissa(rightp1,rightp2)) 186 { 187 /* right is zero */ 188 if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) 189 { 190 /* Both operands are zeros */ 191 Dbl_invert_sign(rightp1); 192 if(Is_rounding_mode(ROUNDMINUS)) 193 { 194 Dbl_or_signs(leftp1,/*with*/rightp1); 195 } 196 else 197 { 198 Dbl_and_signs(leftp1,/*with*/rightp1); 199 } 200 } 201 else 202 { 203 /* Left is not a zero and must be the result. Trapped 204 * underflows are signaled if left is denormalized. Result 205 * is always exact. */ 206 if( (result_exponent == 0) && Is_underflowtrap_enabled() ) 207 { 208 /* need to normalize results mantissa */ 209 sign_save = Dbl_signextendedsign(leftp1); 210 Dbl_leftshiftby1(leftp1,leftp2); 211 Dbl_normalize(leftp1,leftp2,result_exponent); 212 Dbl_set_sign(leftp1,/*using*/sign_save); 213 Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); 214 Dbl_copytoptr(leftp1,leftp2,dstptr); 215 /* inexact = false */ 216 return(UNDERFLOWEXCEPTION); 217 } 218 } 219 Dbl_copytoptr(leftp1,leftp2,dstptr); 220 return(NOEXCEPTION); 221 } 222 223 /* Neither are zeroes */ 224 Dbl_clear_sign(rightp1); /* Exponent is already cleared */ 225 if(result_exponent == 0 ) 226 { 227 /* Both operands are denormalized. The result must be exact 228 * and is simply calculated. A sum could become normalized and a 229 * difference could cancel to a true zero. */ 230 if( (/*signed*/int) save >= 0 ) 231 { 232 Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, 233 /*into*/resultp1,resultp2); 234 if(Dbl_iszero_mantissa(resultp1,resultp2)) 235 { 236 if(Is_rounding_mode(ROUNDMINUS)) 237 { 238 Dbl_setone_sign(resultp1); 239 } 240 else 241 { 242 Dbl_setzero_sign(resultp1); 243 } 244 Dbl_copytoptr(resultp1,resultp2,dstptr); 245 return(NOEXCEPTION); 246 } 247 } 248 else 249 { 250 Dbl_addition(leftp1,leftp2,rightp1,rightp2, 251 /*into*/resultp1,resultp2); 252 if(Dbl_isone_hidden(resultp1)) 253 { 254 Dbl_copytoptr(resultp1,resultp2,dstptr); 255 return(NOEXCEPTION); 256 } 257 } 258 if(Is_underflowtrap_enabled()) 259 { 260 /* need to normalize result */ 261 sign_save = Dbl_signextendedsign(resultp1); 262 Dbl_leftshiftby1(resultp1,resultp2); 263 Dbl_normalize(resultp1,resultp2,result_exponent); 264 Dbl_set_sign(resultp1,/*using*/sign_save); 265 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); 266 Dbl_copytoptr(resultp1,resultp2,dstptr); 267 /* inexact = false */ 268 return(UNDERFLOWEXCEPTION); 269 } 270 Dbl_copytoptr(resultp1,resultp2,dstptr); 271 return(NOEXCEPTION); 272 } 273 right_exponent = 1; /* Set exponent to reflect different bias 274 * with denormalized numbers. */ 275 } 276 else 277 { 278 Dbl_clear_signexponent_set_hidden(rightp1); 279 } 280 Dbl_clear_exponent_set_hidden(leftp1); 281 diff_exponent = result_exponent - right_exponent; 282 283 /* 284 * Special case alignment of operands that would force alignment 285 * beyond the extent of the extension. A further optimization 286 * could special case this but only reduces the path length for this 287 * infrequent case. 288 */ 289 if(diff_exponent > DBL_THRESHOLD) 290 { 291 diff_exponent = DBL_THRESHOLD; 292 } 293 294 /* Align right operand by shifting to right */ 295 Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, 296 /*and lower to*/extent); 297 298 /* Treat sum and difference of the operands separately. */ 299 if( (/*signed*/int) save >= 0 ) 300 { 301 /* 302 * Difference of the two operands. Their can be no overflow. A 303 * borrow can occur out of the hidden bit and force a post 304 * normalization phase. 305 */ 306 Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, 307 /*with*/extent,/*into*/resultp1,resultp2); 308 if(Dbl_iszero_hidden(resultp1)) 309 { 310 /* Handle normalization */ 311 /* A straight forward algorithm would now shift the result 312 * and extension left until the hidden bit becomes one. Not 313 * all of the extension bits need participate in the shift. 314 * Only the two most significant bits (round and guard) are 315 * needed. If only a single shift is needed then the guard 316 * bit becomes a significant low order bit and the extension 317 * must participate in the rounding. If more than a single 318 * shift is needed, then all bits to the right of the guard 319 * bit are zeros, and the guard bit may or may not be zero. */ 320 sign_save = Dbl_signextendedsign(resultp1); 321 Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); 322 323 /* Need to check for a zero result. The sign and exponent 324 * fields have already been zeroed. The more efficient test 325 * of the full object can be used. 326 */ 327 if(Dbl_iszero(resultp1,resultp2)) 328 /* Must have been "x-x" or "x+(-x)". */ 329 { 330 if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); 331 Dbl_copytoptr(resultp1,resultp2,dstptr); 332 return(NOEXCEPTION); 333 } 334 result_exponent--; 335 /* Look to see if normalization is finished. */ 336 if(Dbl_isone_hidden(resultp1)) { 337 if(result_exponent==0) { 338 /* Denormalized, exponent should be zero. Left operand * 339 * was normalized, so extent (guard, round) was zero */ 340 goto underflow; 341 } else { 342 /* No further normalization is needed. */ 343 Dbl_set_sign(resultp1,/*using*/sign_save); 344 Ext_leftshiftby1(extent); 345 goto round; 346 } 347 } 348 349 /* Check for denormalized, exponent should be zero. Left * 350 * operand was normalized, so extent (guard, round) was zero */ 351 if(!(underflowtrap = Is_underflowtrap_enabled()) && 352 result_exponent==0) goto underflow; 353 354 /* Shift extension to complete one bit of normalization and 355 * update exponent. */ 356 Ext_leftshiftby1(extent); 357 358 /* Discover first one bit to determine shift amount. Use a 359 * modified binary search. We have already shifted the result 360 * one position right and still not found a one so the remainder 361 * of the extension must be zero and simplifies rounding. */ 362 /* Scan bytes */ 363 while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) 364 { 365 Dbl_leftshiftby8(resultp1,resultp2); 366 if((result_exponent -= 8) <= 0 && !underflowtrap) 367 goto underflow; 368 } 369 /* Now narrow it down to the nibble */ 370 if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) 371 { 372 /* The lower nibble contains the normalizing one */ 373 Dbl_leftshiftby4(resultp1,resultp2); 374 if((result_exponent -= 4) <= 0 && !underflowtrap) 375 goto underflow; 376 } 377 /* Select case were first bit is set (already normalized) 378 * otherwise select the proper shift. */ 379 if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) 380 { 381 /* Already normalized */ 382 if(result_exponent <= 0) goto underflow; 383 Dbl_set_sign(resultp1,/*using*/sign_save); 384 Dbl_set_exponent(resultp1,/*using*/result_exponent); 385 Dbl_copytoptr(resultp1,resultp2,dstptr); 386 return(NOEXCEPTION); 387 } 388 Dbl_sethigh4bits(resultp1,/*using*/sign_save); 389 switch(jumpsize) 390 { 391 case 1: 392 { 393 Dbl_leftshiftby3(resultp1,resultp2); 394 result_exponent -= 3; 395 break; 396 } 397 case 2: 398 case 3: 399 { 400 Dbl_leftshiftby2(resultp1,resultp2); 401 result_exponent -= 2; 402 break; 403 } 404 case 4: 405 case 5: 406 case 6: 407 case 7: 408 { 409 Dbl_leftshiftby1(resultp1,resultp2); 410 result_exponent -= 1; 411 break; 412 } 413 } 414 if(result_exponent > 0) 415 { 416 Dbl_set_exponent(resultp1,/*using*/result_exponent); 417 Dbl_copytoptr(resultp1,resultp2,dstptr); 418 return(NOEXCEPTION); /* Sign bit is already set */ 419 } 420 /* Fixup potential underflows */ 421 underflow: 422 if(Is_underflowtrap_enabled()) 423 { 424 Dbl_set_sign(resultp1,sign_save); 425 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); 426 Dbl_copytoptr(resultp1,resultp2,dstptr); 427 /* inexact = false */ 428 return(UNDERFLOWEXCEPTION); 429 } 430 /* 431 * Since we cannot get an inexact denormalized result, 432 * we can now return. 433 */ 434 Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); 435 Dbl_clear_signexponent(resultp1); 436 Dbl_set_sign(resultp1,sign_save); 437 Dbl_copytoptr(resultp1,resultp2,dstptr); 438 return(NOEXCEPTION); 439 } /* end if(hidden...)... */ 440 /* Fall through and round */ 441 } /* end if(save >= 0)... */ 442 else 443 { 444 /* Subtract magnitudes */ 445 Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); 446 if(Dbl_isone_hiddenoverflow(resultp1)) 447 { 448 /* Prenormalization required. */ 449 Dbl_rightshiftby1_withextent(resultp2,extent,extent); 450 Dbl_arithrightshiftby1(resultp1,resultp2); 451 result_exponent++; 452 } /* end if hiddenoverflow... */ 453 } /* end else ...subtract magnitudes... */ 454 455 /* Round the result. If the extension is all zeros,then the result is 456 * exact. Otherwise round in the correct direction. No underflow is 457 * possible. If a postnormalization is necessary, then the mantissa is 458 * all zeros so no shift is needed. */ 459 round: 460 if(Ext_isnotzero(extent)) 461 { 462 inexact = true; 463 switch(Rounding_mode()) 464 { 465 case ROUNDNEAREST: /* The default. */ 466 if(Ext_isone_sign(extent)) 467 { 468 /* at least 1/2 ulp */ 469 if(Ext_isnotzero_lower(extent) || 470 Dbl_isone_lowmantissap2(resultp2)) 471 { 472 /* either exactly half way and odd or more than 1/2ulp */ 473 Dbl_increment(resultp1,resultp2); 474 } 475 } 476 break; 477 478 case ROUNDPLUS: 479 if(Dbl_iszero_sign(resultp1)) 480 { 481 /* Round up positive results */ 482 Dbl_increment(resultp1,resultp2); 483 } 484 break; 485 486 case ROUNDMINUS: 487 if(Dbl_isone_sign(resultp1)) 488 { 489 /* Round down negative results */ 490 Dbl_increment(resultp1,resultp2); 491 } 492 493 case ROUNDZERO:; 494 /* truncate is simple */ 495 } /* end switch... */ 496 if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; 497 } 498 if(result_exponent == DBL_INFINITY_EXPONENT) 499 { 500 /* Overflow */ 501 if(Is_overflowtrap_enabled()) 502 { 503 Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); 504 Dbl_copytoptr(resultp1,resultp2,dstptr); 505 if (inexact) { 506 if (Is_inexacttrap_enabled()) 507 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); 508 else 509 Set_inexactflag(); 510 } 511 return(OVERFLOWEXCEPTION); 512 } 513 else 514 { 515 inexact = true; 516 Set_overflowflag(); 517 Dbl_setoverflow(resultp1,resultp2); 518 } 519 } 520 else Dbl_set_exponent(resultp1,result_exponent); 521 Dbl_copytoptr(resultp1,resultp2,dstptr); 522 if(inexact) { 523 if(Is_inexacttrap_enabled()) 524 return(INEXACTEXCEPTION); 525 else 526 Set_inexactflag(); 527 } 528 return(NOEXCEPTION); 529 } 530
Indexes created Thu Sep 25 16:09:42 GMT 2025