1 /* $NetBSD: dfadd.c,v 1.4 2007/02/22 05:46:29 thorpej Exp $ */ 2 3 /* $OpenBSD: dfadd.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 * pmk1.1 27 */ 28 /* 29 * (c) Copyright 1986 HEWLETT-PACKARD COMPANY 30 * 31 * To anyone who acknowledges that this file is provided "AS IS" 32 * without any express or implied warranty: 33 * permission to use, copy, modify, and distribute this file 34 * for any purpose is hereby granted without fee, provided that 35 * the above copyright notice and this notice appears in all 36 * copies, and that the name of Hewlett-Packard Company not be 37 * used in advertising or publicity pertaining to distribution 38 * of the software without specific, written prior permission. 39 * Hewlett-Packard Company makes no representations about the 40 * suitability of this software for any purpose. 41 */ 42 43 #include <sys/cdefs.h> 44 __KERNEL_RCSID(0, "$NetBSD: dfadd.c,v 1.4 2007/02/22 05:46:29 thorpej Exp $"); 45 46 #include "../spmath/float.h" 47 #include "../spmath/dbl_float.h" 48 49 /* 50 * Double_add: add two double precision values. 51 */ 52 int 53 dbl_fadd(leftptr, rightptr, dstptr, status) 54 dbl_floating_point *leftptr, *rightptr, *dstptr; 55 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; 64 register int underflowtrap; 65 66 /* Create local copies of the numbers */ 67 Dbl_copyfromptr(leftptr,leftp1,leftp2); 68 Dbl_copyfromptr(rightptr,rightp1,rightp2); 69 70 /* A zero "save" helps discover equal operands (for later), * 71 * and is used in swapping operands (if needed). */ 72 Dbl_xortointp1(leftp1,rightp1,/*to*/save); 73 74 /* 75 * check first operand for NaN's or infinity 76 */ 77 if ((result_exponent = Dbl_exponent(leftp1)) == DBL_INFINITY_EXPONENT) 78 { 79 if (Dbl_iszero_mantissa(leftp1,leftp2)) 80 { 81 if (Dbl_isnotnan(rightp1,rightp2)) 82 { 83 if (Dbl_isinfinity(rightp1,rightp2) && save!=0) 84 { 85 /* 86 * invalid since operands are opposite signed infinity's 87 */ 88 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 89 Set_invalidflag(); 90 Dbl_makequietnan(resultp1,resultp2); 91 Dbl_copytoptr(resultp1,resultp2,dstptr); 92 return(NOEXCEPTION); 93 } 94 /* 95 * return infinity 96 */ 97 Dbl_copytoptr(leftp1,leftp2,dstptr); 98 return(NOEXCEPTION); 99 } 100 } 101 else 102 { 103 /* 104 * is NaN; signaling or quiet? 105 */ 106 if (Dbl_isone_signaling(leftp1)) 107 { 108 /* trap if INVALIDTRAP enabled */ 109 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 110 /* make NaN quiet */ 111 Set_invalidflag(); 112 Dbl_set_quiet(leftp1); 113 } 114 /* 115 * is second operand a signaling NaN? 116 */ 117 else if (Dbl_is_signalingnan(rightp1)) 118 { 119 /* trap if INVALIDTRAP enabled */ 120 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION); 121 /* make NaN quiet */ 122 Set_invalidflag(); 123 Dbl_set_quiet(rightp1); 124 Dbl_copytoptr(rightp1,rightp2,dstptr); 125 return(NOEXCEPTION); 126 } 127 /* 128 * return quiet NaN 129 */ 130 Dbl_copytoptr(leftp1,leftp2,dstptr); 131 return(NOEXCEPTION); 132 } 133 } /* End left NaN or Infinity processing */ 134 /* 135 * check second operand for NaN's or infinity 136 */ 137 if (Dbl_isinfinity_exponent(rightp1)) 138 { 139 if (Dbl_iszero_mantissa(rightp1,rightp2)) 140 { 141 /* return infinity */ 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 } 179 /* Invariant: left is not smaller than right. */ 180 181 if((right_exponent = Dbl_exponent(rightp1)) == 0) 182 { 183 /* Denormalized operands. First look for zeroes */ 184 if(Dbl_iszero_mantissa(rightp1,rightp2)) 185 { 186 /* right is zero */ 187 if(Dbl_iszero_exponentmantissa(leftp1,leftp2)) 188 { 189 /* Both operands are zeros */ 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 { 336 if(result_exponent==0) 337 { 338 /* Denormalized, exponent should be zero. Left operand * 339 * was normalized, so extent (guard, round) was zero */ 340 goto underflow; 341 } 342 else 343 { 344 /* No further normalization is needed. */ 345 Dbl_set_sign(resultp1,/*using*/sign_save); 346 Ext_leftshiftby1(extent); 347 goto round; 348 } 349 } 350 351 /* Check for denormalized, exponent should be zero. Left * 352 * operand was normalized, so extent (guard, round) was zero */ 353 if(!(underflowtrap = Is_underflowtrap_enabled()) && 354 result_exponent==0) goto underflow; 355 356 /* Shift extension to complete one bit of normalization and 357 * update exponent. */ 358 Ext_leftshiftby1(extent); 359 360 /* Discover first one bit to determine shift amount. Use a 361 * modified binary search. We have already shifted the result 362 * one position right and still not found a one so the remainder 363 * of the extension must be zero and simplifies rounding. */ 364 /* Scan bytes */ 365 while(Dbl_iszero_hiddenhigh7mantissa(resultp1)) 366 { 367 Dbl_leftshiftby8(resultp1,resultp2); 368 if((result_exponent -= 8) <= 0 && !underflowtrap) 369 goto underflow; 370 } 371 /* Now narrow it down to the nibble */ 372 if(Dbl_iszero_hiddenhigh3mantissa(resultp1)) 373 { 374 /* The lower nibble contains the normalizing one */ 375 Dbl_leftshiftby4(resultp1,resultp2); 376 if((result_exponent -= 4) <= 0 && !underflowtrap) 377 goto underflow; 378 } 379 /* Select case were first bit is set (already normalized) 380 * otherwise select the proper shift. */ 381 if((jumpsize = Dbl_hiddenhigh3mantissa(resultp1)) > 7) 382 { 383 /* Already normalized */ 384 if(result_exponent <= 0) goto underflow; 385 Dbl_set_sign(resultp1,/*using*/sign_save); 386 Dbl_set_exponent(resultp1,/*using*/result_exponent); 387 Dbl_copytoptr(resultp1,resultp2,dstptr); 388 return(NOEXCEPTION); 389 } 390 Dbl_sethigh4bits(resultp1,/*using*/sign_save); 391 switch(jumpsize) 392 { 393 case 1: 394 { 395 Dbl_leftshiftby3(resultp1,resultp2); 396 result_exponent -= 3; 397 break; 398 } 399 case 2: 400 case 3: 401 { 402 Dbl_leftshiftby2(resultp1,resultp2); 403 result_exponent -= 2; 404 break; 405 } 406 case 4: 407 case 5: 408 case 6: 409 case 7: 410 { 411 Dbl_leftshiftby1(resultp1,resultp2); 412 result_exponent -= 1; 413 break; 414 } 415 } 416 if(result_exponent > 0) 417 { 418 Dbl_set_exponent(resultp1,/*using*/result_exponent); 419 Dbl_copytoptr(resultp1,resultp2,dstptr); 420 return(NOEXCEPTION); /* Sign bit is already set */ 421 } 422 /* Fixup potential underflows */ 423 underflow: 424 if(Is_underflowtrap_enabled()) 425 { 426 Dbl_set_sign(resultp1,sign_save); 427 Dbl_setwrapped_exponent(resultp1,result_exponent,unfl); 428 Dbl_copytoptr(resultp1,resultp2,dstptr); 429 /* inexact = false */ 430 return(UNDERFLOWEXCEPTION); 431 } 432 /* 433 * Since we cannot get an inexact denormalized result, 434 * we can now return. 435 */ 436 Dbl_fix_overshift(resultp1,resultp2,(1-result_exponent),extent); 437 Dbl_clear_signexponent(resultp1); 438 Dbl_set_sign(resultp1,sign_save); 439 Dbl_copytoptr(resultp1,resultp2,dstptr); 440 return(NOEXCEPTION); 441 } /* end if(hidden...)... */ 442 /* Fall through and round */ 443 } /* end if(save < 0)... */ 444 else 445 { 446 /* Add magnitudes */ 447 Dbl_addition(leftp1,leftp2,rightp1,rightp2,/*to*/resultp1,resultp2); 448 if(Dbl_isone_hiddenoverflow(resultp1)) 449 { 450 /* Prenormalization required. */ 451 Dbl_rightshiftby1_withextent(resultp2,extent,extent); 452 Dbl_arithrightshiftby1(resultp1,resultp2); 453 result_exponent++; 454 } /* end if hiddenoverflow... */ 455 } /* end else ...add magnitudes... */ 456 457 /* Round the result. If the extension is all zeros,then the result is 458 * exact. Otherwise round in the correct direction. No underflow is 459 * possible. If a postnormalization is necessary, then the mantissa is 460 * all zeros so no shift is needed. */ 461 round: 462 if(Ext_isnotzero(extent)) 463 { 464 inexact = true; 465 switch(Rounding_mode()) 466 { 467 case ROUNDNEAREST: /* The default. */ 468 if(Ext_isone_sign(extent)) 469 { 470 /* at least 1/2 ulp */ 471 if(Ext_isnotzero_lower(extent) || 472 Dbl_isone_lowmantissap2(resultp2)) 473 { 474 /* either exactly half way and odd or more than 1/2ulp */ 475 Dbl_increment(resultp1,resultp2); 476 } 477 } 478 break; 479 480 case ROUNDPLUS: 481 if(Dbl_iszero_sign(resultp1)) 482 { 483 /* Round up positive results */ 484 Dbl_increment(resultp1,resultp2); 485 } 486 break; 487 488 case ROUNDMINUS: 489 if(Dbl_isone_sign(resultp1)) 490 { 491 /* Round down negative results */ 492 Dbl_increment(resultp1,resultp2); 493 } 494 495 case ROUNDZERO:; 496 /* truncate is simple */ 497 } /* end switch... */ 498 if(Dbl_isone_hiddenoverflow(resultp1)) result_exponent++; 499 } 500 if(result_exponent == DBL_INFINITY_EXPONENT) 501 { 502 /* Overflow */ 503 if(Is_overflowtrap_enabled()) 504 { 505 Dbl_setwrapped_exponent(resultp1,result_exponent,ovfl); 506 Dbl_copytoptr(resultp1,resultp2,dstptr); 507 if (inexact) { 508 if (Is_inexacttrap_enabled()) 509 return(OVERFLOWEXCEPTION | INEXACTEXCEPTION); 510 else 511 Set_inexactflag(); 512 } 513 return(OVERFLOWEXCEPTION); 514 } 515 else 516 { 517 inexact = true; 518 Set_overflowflag(); 519 Dbl_setoverflow(resultp1,resultp2); 520 } 521 } 522 else Dbl_set_exponent(resultp1,result_exponent); 523 Dbl_copytoptr(resultp1,resultp2,dstptr); 524 if(inexact) { 525 if(Is_inexacttrap_enabled()) 526 return(INEXACTEXCEPTION); 527 else 528 Set_inexactflag(); 529 } 530 return(NOEXCEPTION); 531 } 532