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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 | // SPDX-License-Identifier: GPL-2.0-or-later /* * Linux/PA-RISC Project (http://www.parisc-linux.org/) * * Floating-point emulation code * Copyright (C) 2001 Hewlett-Packard (Paul Bame) <bame@debian.org> */ /* * BEGIN_DESC * * File: * @(#) pa/spmath/dfsub.c $Revision: 1.1 $ * * Purpose: * Double_subtract: subtract two double precision values. * * External Interfaces: * dbl_fsub(leftptr, rightptr, dstptr, status) * * Internal Interfaces: * * Theory: * <<please update with a overview of the operation of this file>> * * END_DESC */ #include "float.h" #include "dbl_float.h" /* * Double_subtract: subtract two double precision values. */ int dbl_fsub( dbl_floating_point *leftptr, dbl_floating_point *rightptr, dbl_floating_point *dstptr, unsigned int *status) { register unsigned int signless_upper_left, signless_upper_right, save; register unsigned int leftp1, leftp2, rightp1, rightp2, extent; register unsigned int resultp1 = 0, resultp2 = 0; register int result_exponent, right_exponent, diff_exponent; register int sign_save, jumpsize; register boolean inexact = FALSE, underflowtrap; /* Create local copies of the numbers */ Dbl_copyfromptr(leftptr,leftp1,leftp2); Dbl_copyfromptr(rightptr,rightp1,rightp2); /* A zero "save" helps discover equal operands (for later), * * and is used in swapping operands (if needed). */ Dbl_xortointp1(leftp1,rightp1,/*to*/save); /* * check first operand for NaN's or infinity */ if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) { if (Dbl_iszero_mantissa(leftp1,leftp2)) { if (Dbl_isnotnan(rightp1,rightp2)) { if (Dbl_isinfinity(rightp1,rightp2) && save==0) { /* * invalid since operands are same signed infinity's */ if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); Set_invalidflag(); Dbl_makequietnan(resultp1,resultp2); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* * return infinity */ Dbl_copytoptr(leftp1,leftp2,dstptr); return(NOEXCEPTION); } } else { /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(leftp1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(leftp1); } /* * is second operand a signaling NaN? */ else if (Dbl_is_signalingnan(rightp1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(rightp1); Dbl_copytoptr(rightp1,rightp2,dstptr); return(NOEXCEPTION); } /* * return quiet NaN */ Dbl_copytoptr(leftp1,leftp2,dstptr); return(NOEXCEPTION); } } /* End left NaN or Infinity processing */ /* * check second operand for NaN's or infinity */ if (Dbl_isinfinity_exponent(rightp1)) { if (Dbl_iszero_mantissa(rightp1,rightp2)) { /* return infinity */ Dbl_invert_sign(rightp1); Dbl_copytoptr(rightp1,rightp2,dstptr); return(NOEXCEPTION); } /* * is NaN; signaling or quiet? */ if (Dbl_isone_signaling(rightp1)) { /* trap if INVALIDTRAP enabled */ if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); /* make NaN quiet */ Set_invalidflag(); Dbl_set_quiet(rightp1); } /* * return quiet NaN */ Dbl_copytoptr(rightp1,rightp2,dstptr); return(NOEXCEPTION); } /* End right NaN or Infinity processing */ /* Invariant: Must be dealing with finite numbers */ /* Compare operands by removing the sign */ Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left); Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right); /* sign difference selects add or sub operation. */ if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right)) { /* Set the left operand to the larger one by XOR swap * * First finish the first word using "save" */ Dbl_xorfromintp1(save,rightp1,/*to*/rightp1); Dbl_xorfromintp1(save,leftp1,/*to*/leftp1); Dbl_swap_lower(leftp2,rightp2); result_exponent = Dbl_exponent(leftp1); Dbl_invert_sign(leftp1); } /* Invariant: left is not smaller than right. */ if((right_exponent = Dbl_exponent(rightp1)) == 0) { /* Denormalized operands. First look for zeroes */ if(Dbl_iszero_mantissa(rightp1,rightp2)) { /* right is zero */ if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) { /* Both operands are zeros */ Dbl_invert_sign(rightp1); if(Is_rounding_mode(ROUNDMINUS)) { Dbl_or_signs(leftp1,/*with*/rightp1); } else { Dbl_and_signs(leftp1,/*with*/rightp1); } } else { /* Left is not a zero and must be the result. Trapped * underflows are signaled if left is denormalized. Result * is always exact. */ if( (result_exponent == 0) && Is_underflowtrap_enabled() ) { /* need to normalize results mantissa */ sign_save = Dbl_signextendedsign(leftp1); Dbl_leftshiftby1(leftp1,leftp2); Dbl_normalize(leftp1,leftp2,result_exponent); Dbl_set_sign(leftp1,/*using*/sign_save); Dbl_setwrapped_exponent(leftp1,result_exponent,unfl); Dbl_copytoptr(leftp1,leftp2,dstptr); /* inexact = FALSE */ return(UNDERFLOWEXCEPTION); } } Dbl_copytoptr(leftp1,leftp2,dstptr); return(NOEXCEPTION); } /* Neither are zeroes */ Dbl_clear_sign(rightp1); /* Exponent is already cleared */ if(result_exponent == 0 ) { /* Both operands are denormalized. The result must be exact * and is simply calculated. A sum could become normalized and a * difference could cancel to a true zero. */ if( (/*signed*/int) save >= 0 ) { Dbl_subtract(leftp1,leftp2,/*minus*/rightp1,rightp2, /*into*/resultp1,resultp2); if(Dbl_iszero_mantissa(resultp1,resultp2)) { if(Is_rounding_mode(ROUNDMINUS)) { Dbl_setone_sign(resultp1); } else { Dbl_setzero_sign(resultp1); } Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } else { Dbl_addition(leftp1,leftp2,rightp1,rightp2, /*into*/resultp1,resultp2); if(Dbl_isone_hidden(resultp1)) { Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } } if(Is_underflowtrap_enabled()) { /* need to normalize result */ sign_save = Dbl_signextendedsign(resultp1); Dbl_leftshiftby1(resultp1,resultp2); Dbl_normalize(resultp1,resultp2,result_exponent); Dbl_set_sign(resultp1,/*using*/sign_save); Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); Dbl_copytoptr(resultp1,resultp2,dstptr); /* inexact = FALSE */ return(UNDERFLOWEXCEPTION); } Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } right_exponent = 1; /* Set exponent to reflect different bias * with denormalized numbers. */ } else { Dbl_clear_signexponent_set_hidden(rightp1); } Dbl_clear_exponent_set_hidden(leftp1); diff_exponent = result_exponent - right_exponent; /* * Special case alignment of operands that would force alignment * beyond the extent of the extension. A further optimization * could special case this but only reduces the path length for this * infrequent case. */ if(diff_exponent > DBL_THRESHOLD) { diff_exponent = DBL_THRESHOLD; } /* Align right operand by shifting to right */ Dbl_right_align(/*operand*/rightp1,rightp2,/*shifted by*/diff_exponent, /*and lower to*/extent); /* Treat sum and difference of the operands separately. */ if( (/*signed*/int) save >= 0 ) { /* * Difference of the two operands. Their can be no overflow. A * borrow can occur out of the hidden bit and force a post * normalization phase. */ Dbl_subtract_withextension(leftp1,leftp2,/*minus*/rightp1,rightp2, /*with*/extent,/*into*/resultp1,resultp2); if(Dbl_iszero_hidden(resultp1)) { /* Handle normalization */ /* A straight forward algorithm would now shift the result * and extension left until the hidden bit becomes one. Not * all of the extension bits need participate in the shift. * Only the two most significant bits (round and guard) are * needed. If only a single shift is needed then the guard * bit becomes a significant low order bit and the extension * must participate in the rounding. If more than a single * shift is needed, then all bits to the right of the guard * bit are zeros, and the guard bit may or may not be zero. */ sign_save = Dbl_signextendedsign(resultp1); Dbl_leftshiftby1_withextent(resultp1,resultp2,extent,resultp1,resultp2); /* Need to check for a zero result. The sign and exponent * fields have already been zeroed. The more efficient test * of the full object can be used. */ if(Dbl_iszero(resultp1,resultp2)) /* Must have been "x-x" or "x+(-x)". */ { if(Is_rounding_mode(ROUNDMINUS)) Dbl_setone_sign(resultp1); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } result_exponent--; /* Look to see if normalization is finished. */ if(Dbl_isone_hidden(resultp1)) { if(result_exponent==0) { /* Denormalized, exponent should be zero. Left operand * * was normalized, so extent (guard, round) was zero */ goto underflow; } else { /* No further normalization is needed. */ Dbl_set_sign(resultp1,/*using*/sign_save); Ext_leftshiftby1(extent); goto round; } } /* Check for denormalized, exponent should be zero. Left * * operand was normalized, so extent (guard, round) was zero */ if(!(underflowtrap = Is_underflowtrap_enabled()) && result_exponent==0) goto underflow; /* Shift extension to complete one bit of normalization and * update exponent. */ Ext_leftshiftby1(extent); /* Discover first one bit to determine shift amount. Use a * modified binary search. We have already shifted the result * one position right and still not found a one so the remainder * of the extension must be zero and simplifies rounding. */ /* Scan bytes */ while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) { Dbl_leftshiftby8(resultp1,resultp2); if((result_exponent -= 8) <= 0 && !underflowtrap) goto underflow; } /* Now narrow it down to the nibble */ if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) { /* The lower nibble contains the normalizing one */ Dbl_leftshiftby4(resultp1,resultp2); if((result_exponent -= 4) <= 0 && !underflowtrap) goto underflow; } /* Select case were first bit is set (already normalized) * otherwise select the proper shift. */ if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) { /* Already normalized */ if(result_exponent <= 0) goto underflow; Dbl_set_sign(resultp1,/*using*/sign_save); Dbl_set_exponent(resultp1,/*using*/result_exponent); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } Dbl_sethigh4bits(resultp1,/*using*/sign_save); switch(jumpsize) { case 1: { Dbl_leftshiftby3(resultp1,resultp2); result_exponent -= 3; break; } case 2: case 3: { Dbl_leftshiftby2(resultp1,resultp2); result_exponent -= 2; break; } case 4: case 5: case 6: case 7: { Dbl_leftshiftby1(resultp1,resultp2); result_exponent -= 1; break; } } if(result_exponent > 0) { Dbl_set_exponent(resultp1,/*using*/result_exponent); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); /* Sign bit is already set */ } /* Fixup potential underflows */ underflow: if(Is_underflowtrap_enabled()) { Dbl_set_sign(resultp1,sign_save); Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); Dbl_copytoptr(resultp1,resultp2,dstptr); /* inexact = FALSE */ return(UNDERFLOWEXCEPTION); } /* * Since we cannot get an inexact denormalized result, * we can now return. */ Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); Dbl_clear_signexponent(resultp1); Dbl_set_sign(resultp1,sign_save); Dbl_copytoptr(resultp1,resultp2,dstptr); return(NOEXCEPTION); } /* end if(hidden...)... */ /* Fall through and round */ } /* end if(save >= 0)... */ else { /* Subtract magnitudes */ Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); if(Dbl_isone_hiddenoverflow(resultp1)) { /* Prenormalization required. */ Dbl_rightshiftby1_withextent(resultp2,extent,extent); Dbl_arithrightshiftby1(resultp1,resultp2); result_exponent++; } /* end if hiddenoverflow... */ } /* end else ...subtract magnitudes... */ /* Round the result. If the extension is all zeros,then the result is * exact. Otherwise round in the correct direction. No underflow is * possible. If a postnormalization is necessary, then the mantissa is * all zeros so no shift is needed. */ round: if(Ext_isnotzero(extent)) { inexact = TRUE; switch(Rounding_mode()) { case ROUNDNEAREST: /* The default. */ if(Ext_isone_sign(extent)) { /* at least 1/2 ulp */ if(Ext_isnotzero_lower(extent) || Dbl_isone_lowmantissap2(resultp2)) { /* either exactly half way and odd or more than 1/2ulp */ Dbl_increment(resultp1,resultp2); } } break; case ROUNDPLUS: if(Dbl_iszero_sign(resultp1)) { /* Round up positive results */ Dbl_increment(resultp1,resultp2); } break; case ROUNDMINUS: if(Dbl_isone_sign(resultp1)) { /* Round down negative results */ Dbl_increment(resultp1,resultp2); } case ROUNDZERO:; /* truncate is simple */ } /* end switch... */ if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; } if(result_exponent == DBL_INFINITY_EXPONENT) { /* Overflow */ if(Is_overflowtrap_enabled()) { Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); Dbl_copytoptr(resultp1,resultp2,dstptr); if (inexact) if (Is_inexacttrap_enabled()) return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); else Set_inexactflag(); return(OVERFLOWEXCEPTION); } else { inexact = TRUE; Set_overflowflag(); Dbl_setoverflow(resultp1,resultp2); } } else Dbl_set_exponent(resultp1,result_exponent); Dbl_copytoptr(resultp1,resultp2,dstptr); if(inexact) if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION); else Set_inexactflag(); return(NOEXCEPTION); } |