arch/parisc/math-emu/dfadd.c

   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 forward 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 }