arch/parisc/math-emu/sfsub.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/sfsub.c               $Revision: 1.1 $
  26  *
  27  *  Purpose:
  28  *      Single_subtract: subtract two single precision values.
  29  *
  30  *  External Interfaces:
  31  *      sgl_fsub(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 "sgl_float.h"
  44
  45 /*
  46  * Single_subtract: subtract two single precision values.
  47  */
  48 int
  49 sgl_fsub(
  50             sgl_floating_point *leftptr,
  51             sgl_floating_point *rightptr,
  52             sgl_floating_point *dstptr,
  53             unsigned int *status)
  54     {
  55     register unsigned int left, right, result, extent;
  56     register unsigned int signless_upper_left, signless_upper_right, save;
  57
  58     register int result_exponent, right_exponent, diff_exponent;
  59     register int sign_save, jumpsize;
  60     register boolean inexact = FALSE, underflowtrap;
  61
  62     /* Create local copies of the numbers */
  63     left = *leftptr;
  64     right = *rightptr;
  65
  66     /* A zero "save" helps discover equal operands (for later),  *
  67      * and is used in swapping operands (if needed).             */
  68     Sgl_xortointp1(left,right,/*to*/save);
  69
  70     /*
  71      * check first operand for NaN's or infinity
  72      */
  73     if ((result_exponent = Sgl_exponent(left)) == SGL_INFINITY_EXPONENT)
  74         {
  75         if (Sgl_iszero_mantissa(left))
  76             {
  77             if (Sgl_isnotnan(right))
  78                 {
  79                 if (Sgl_isinfinity(right) && save==0)
  80                     {
  81                     /*
  82                      * invalid since operands are same signed infinity's
  83                      */
  84                     if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
  85                     Set_invalidflag();
  86                     Sgl_makequietnan(result);
  87                     *dstptr = result;
  88                     return(NOEXCEPTION);
  89                     }
  90                 /*
  91                  * return infinity
  92                  */
  93                 *dstptr = left;
  94                 return(NOEXCEPTION);
  95                 }
  96             }
  97         else
  98             {
  99             /*
 100              * is NaN; signaling or quiet?
 101              */
 102             if (Sgl_isone_signaling(left))
 103                 {
 104                 /* trap if INVALIDTRAP enabled */
 105                 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
 106                 /* make NaN quiet */
 107                 Set_invalidflag();
 108                 Sgl_set_quiet(left);
 109                 }
 110             /*
 111              * is second operand a signaling NaN?
 112              */
 113             else if (Sgl_is_signalingnan(right))
 114                 {
 115                 /* trap if INVALIDTRAP enabled */
 116                 if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
 117                 /* make NaN quiet */
 118                 Set_invalidflag();
 119                 Sgl_set_quiet(right);
 120                 *dstptr = right;
 121                 return(NOEXCEPTION);
 122                 }
 123             /*
 124              * return quiet NaN
 125              */
 126             *dstptr = left;
 127             return(NOEXCEPTION);
 128             }
 129         } /* End left NaN or Infinity processing */
 130     /*
 131      * check second operand for NaN's or infinity
 132      */
 133     if (Sgl_isinfinity_exponent(right))
 134         {
 135         if (Sgl_iszero_mantissa(right))
 136             {
 137             /* return infinity */
 138             Sgl_invert_sign(right);
 139             *dstptr = right;
 140             return(NOEXCEPTION);
 141             }
 142         /*
 143          * is NaN; signaling or quiet?
 144          */
 145         if (Sgl_isone_signaling(right))
 146             {
 147             /* trap if INVALIDTRAP enabled */
 148             if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
 149             /* make NaN quiet */
 150             Set_invalidflag();
 151             Sgl_set_quiet(right);
 152             }
 153         /*
 154          * return quiet NaN
 155          */
 156         *dstptr = right;
 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     Sgl_copytoint_exponentmantissa(left,signless_upper_left);
 164     Sgl_copytoint_exponentmantissa(right,signless_upper_right);
 165
 166     /* sign difference selects sub or add operation. */
 167     if(Sgl_ismagnitudeless(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         Sgl_xorfromintp1(save,right,/*to*/right);
 172         Sgl_xorfromintp1(save,left,/*to*/left);
 173         result_exponent = Sgl_exponent(left);
 174         Sgl_invert_sign(left);
 175         }
 176     /* Invariant:  left is not smaller than right. */
 177
 178     if((right_exponent = Sgl_exponent(right)) == 0)
 179         {
 180         /* Denormalized operands.  First look for zeroes */
 181         if(Sgl_iszero_mantissa(right))
 182             {
 183             /* right is zero */
 184             if(Sgl_iszero_exponentmantissa(left))
 185                 {
 186                 /* Both operands are zeros */
 187                 Sgl_invert_sign(right);
 188                 if(Is_rounding_mode(ROUNDMINUS))
 189                     {
 190                     Sgl_or_signs(left,/*with*/right);
 191                     }
 192                 else
 193                     {
 194                     Sgl_and_signs(left,/*with*/right);
 195                     }
 196                 }
 197             else
 198                 {
 199                 /* Left is not a zero and must be the result.  Trapped
 200                  * underflows are signaled if left is denormalized.  Result
 201                  * is always exact. */
 202                 if( (result_exponent == 0) && Is_underflowtrap_enabled() )
 203                     {
 204                     /* need to normalize results mantissa */
 205                     sign_save = Sgl_signextendedsign(left);
 206                     Sgl_leftshiftby1(left);
 207                     Sgl_normalize(left,result_exponent);
 208                     Sgl_set_sign(left,/*using*/sign_save);
 209                     Sgl_setwrapped_exponent(left,result_exponent,unfl);
 210                     *dstptr = left;
 211                     /* inexact = FALSE */
 212                     return(UNDERFLOWEXCEPTION);
 213                     }
 214                 }
 215             *dstptr = left;
 216             return(NOEXCEPTION);
 217             }
 218
 219         /* Neither are zeroes */
 220         Sgl_clear_sign(right);  /* Exponent is already cleared */
 221         if(result_exponent == 0 )
 222             {
 223             /* Both operands are denormalized.  The result must be exact
 224              * and is simply calculated.  A sum could become normalized and a
 225              * difference could cancel to a true zero. */
 226             if( (/*signed*/int) save >= 0 )
 227                 {
 228                 Sgl_subtract(left,/*minus*/right,/*into*/result);
 229                 if(Sgl_iszero_mantissa(result))
 230                     {
 231                     if(Is_rounding_mode(ROUNDMINUS))
 232                         {
 233                         Sgl_setone_sign(result);
 234                         }
 235                     else
 236                         {
 237                         Sgl_setzero_sign(result);
 238                         }
 239                     *dstptr = result;
 240                     return(NOEXCEPTION);
 241                     }
 242                 }
 243             else
 244                 {
 245                 Sgl_addition(left,right,/*into*/result);
 246                 if(Sgl_isone_hidden(result))
 247                     {
 248                     *dstptr = result;
 249                     return(NOEXCEPTION);
 250                     }
 251                 }
 252             if(Is_underflowtrap_enabled())
 253                 {
 254                 /* need to normalize result */
 255                 sign_save = Sgl_signextendedsign(result);
 256                 Sgl_leftshiftby1(result);
 257                 Sgl_normalize(result,result_exponent);
 258                 Sgl_set_sign(result,/*using*/sign_save);
 259                 Sgl_setwrapped_exponent(result,result_exponent,unfl);
 260                 *dstptr = result;
 261                 /* inexact = FALSE */
 262                 return(UNDERFLOWEXCEPTION);
 263                 }
 264             *dstptr = result;
 265             return(NOEXCEPTION);
 266             }
 267         right_exponent = 1;     /* Set exponent to reflect different bias
 268                                  * with denomalized numbers. */
 269         }
 270     else
 271         {
 272         Sgl_clear_signexponent_set_hidden(right);
 273         }
 274     Sgl_clear_exponent_set_hidden(left);
 275     diff_exponent = result_exponent - right_exponent;
 276
 277     /*
 278      * Special case alignment of operands that would force alignment
 279      * beyond the extent of the extension.  A further optimization
 280      * could special case this but only reduces the path length for this
 281      * infrequent case.
 282      */
 283     if(diff_exponent > SGL_THRESHOLD)
 284         {
 285         diff_exponent = SGL_THRESHOLD;
 286         }
 287
 288     /* Align right operand by shifting to right */
 289     Sgl_right_align(/*operand*/right,/*shifted by*/diff_exponent,
 290       /*and lower to*/extent);
 291
 292     /* Treat sum and difference of the operands separately. */
 293     if( (/*signed*/int) save >= 0 )
 294         {
 295         /*
 296          * Difference of the two operands.  Their can be no overflow.  A
 297          * borrow can occur out of the hidden bit and force a post
 298          * normalization phase.
 299          */
 300         Sgl_subtract_withextension(left,/*minus*/right,/*with*/extent,/*into*/result);
 301         if(Sgl_iszero_hidden(result))
 302             {
 303             /* Handle normalization */
 304             /* A straightforward algorithm would now shift the result
 305              * and extension left until the hidden bit becomes one.  Not
 306              * all of the extension bits need participate in the shift.
 307              * Only the two most significant bits (round and guard) are
 308              * needed.  If only a single shift is needed then the guard
 309              * bit becomes a significant low order bit and the extension
 310              * must participate in the rounding.  If more than a single
 311              * shift is needed, then all bits to the right of the guard
 312              * bit are zeros, and the guard bit may or may not be zero. */
 313             sign_save = Sgl_signextendedsign(result);
 314             Sgl_leftshiftby1_withextent(result,extent,result);
 315
 316             /* Need to check for a zero result.  The sign and exponent
 317              * fields have already been zeroed.  The more efficient test
 318              * of the full object can be used.
 319              */
 320             if(Sgl_iszero(result))
 321                 /* Must have been "x-x" or "x+(-x)". */
 322                 {
 323                 if(Is_rounding_mode(ROUNDMINUS)) Sgl_setone_sign(result);
 324                 *dstptr = result;
 325                 return(NOEXCEPTION);
 326                 }
 327             result_exponent--;
 328             /* Look to see if normalization is finished. */
 329             if(Sgl_isone_hidden(result))
 330                 {
 331                 if(result_exponent==0)
 332                     {
 333                     /* Denormalized, exponent should be zero.  Left operand *
 334                      * was normalized, so extent (guard, round) was zero    */
 335                     goto underflow;
 336                     }
 337                 else
 338                     {
 339                     /* No further normalization is needed. */
 340                     Sgl_set_sign(result,/*using*/sign_save);
 341                     Ext_leftshiftby1(extent);
 342                     goto round;
 343                     }
 344                 }
 345
 346             /* Check for denormalized, exponent should be zero.  Left    *
 347              * operand was normalized, so extent (guard, round) was zero */
 348             if(!(underflowtrap = Is_underflowtrap_enabled()) &&
 349                result_exponent==0) goto underflow;
 350
 351             /* Shift extension to complete one bit of normalization and
 352              * update exponent. */
 353             Ext_leftshiftby1(extent);
 354
 355             /* Discover first one bit to determine shift amount.  Use a
 356              * modified binary search.  We have already shifted the result
 357              * one position right and still not found a one so the remainder
 358              * of the extension must be zero and simplifies rounding. */
 359             /* Scan bytes */
 360             while(Sgl_iszero_hiddenhigh7mantissa(result))
 361                 {
 362                 Sgl_leftshiftby8(result);
 363                 if((result_exponent -= 8) <= 0  && !underflowtrap)
 364                     goto underflow;
 365                 }
 366             /* Now narrow it down to the nibble */
 367             if(Sgl_iszero_hiddenhigh3mantissa(result))
 368                 {
 369                 /* The lower nibble contains the normalizing one */
 370                 Sgl_leftshiftby4(result);
 371                 if((result_exponent -= 4) <= 0 && !underflowtrap)
 372                     goto underflow;
 373                 }
 374             /* Select case were first bit is set (already normalized)
 375              * otherwise select the proper shift. */
 376             if((jumpsize = Sgl_hiddenhigh3mantissa(result)) > 7)
 377                 {
 378                 /* Already normalized */
 379                 if(result_exponent <= 0) goto underflow;
 380                 Sgl_set_sign(result,/*using*/sign_save);
 381                 Sgl_set_exponent(result,/*using*/result_exponent);
 382                 *dstptr = result;
 383                 return(NOEXCEPTION);
 384                 }
 385             Sgl_sethigh4bits(result,/*using*/sign_save);
 386             switch(jumpsize)
 387                 {
 388                 case 1:
 389                     {
 390                     Sgl_leftshiftby3(result);
 391                     result_exponent -= 3;
 392                     break;
 393                     }
 394                 case 2:
 395                 case 3:
 396                     {
 397                     Sgl_leftshiftby2(result);
 398                     result_exponent -= 2;
 399                     break;
 400                     }
 401                 case 4:
 402                 case 5:
 403                 case 6:
 404                 case 7:
 405                     {
 406                     Sgl_leftshiftby1(result);
 407                     result_exponent -= 1;
 408                     break;
 409                     }
 410                 }
 411             if(result_exponent > 0)
 412                 {
 413                 Sgl_set_exponent(result,/*using*/result_exponent);
 414                 *dstptr = result;       /* Sign bit is already set */
 415                 return(NOEXCEPTION);
 416                 }
 417             /* Fixup potential underflows */
 418           underflow:
 419             if(Is_underflowtrap_enabled())
 420                 {
 421                 Sgl_set_sign(result,sign_save);
 422                 Sgl_setwrapped_exponent(result,result_exponent,unfl);
 423                 *dstptr = result;
 424                 /* inexact = FALSE */
 425                 return(UNDERFLOWEXCEPTION);
 426                 }
 427             /*
 428              * Since we cannot get an inexact denormalized result,
 429              * we can now return.
 430              */
 431             Sgl_right_align(result,/*by*/(1-result_exponent),extent);
 432             Sgl_clear_signexponent(result);
 433             Sgl_set_sign(result,sign_save);
 434             *dstptr = result;
 435             return(NOEXCEPTION);
 436             } /* end if(hidden...)... */
 437         /* Fall through and round */
 438         } /* end if(save >= 0)... */
 439     else
 440         {
 441         /* Add magnitudes */
 442         Sgl_addition(left,right,/*to*/result);
 443         if(Sgl_isone_hiddenoverflow(result))
 444             {
 445             /* Prenormalization required. */
 446             Sgl_rightshiftby1_withextent(result,extent,extent);
 447             Sgl_arithrightshiftby1(result);
 448             result_exponent++;
 449             } /* end if hiddenoverflow... */
 450         } /* end else ...sub magnitudes... */
 451
 452     /* Round the result.  If the extension is all zeros,then the result is
 453      * exact.  Otherwise round in the correct direction.  No underflow is
 454      * possible. If a postnormalization is necessary, then the mantissa is
 455      * all zeros so no shift is needed. */
 456   round:
 457     if(Ext_isnotzero(extent))
 458         {
 459         inexact = TRUE;
 460         switch(Rounding_mode())
 461             {
 462             case ROUNDNEAREST: /* The default. */
 463             if(Ext_isone_sign(extent))
 464                 {
 465                 /* at least 1/2 ulp */
 466                 if(Ext_isnotzero_lower(extent)  ||
 467                   Sgl_isone_lowmantissa(result))
 468                     {
 469                     /* either exactly half way and odd or more than 1/2ulp */
 470                     Sgl_increment(result);
 471                     }
 472                 }
 473             break;
 474
 475             case ROUNDPLUS:
 476             if(Sgl_iszero_sign(result))
 477                 {
 478                 /* Round up positive results */
 479                 Sgl_increment(result);
 480                 }
 481             break;
 482
 483             case ROUNDMINUS:
 484             if(Sgl_isone_sign(result))
 485                 {
 486                 /* Round down negative results */
 487                 Sgl_increment(result);
 488                 }
 489
 490             case ROUNDZERO:;
 491             /* truncate is simple */
 492             } /* end switch... */
 493         if(Sgl_isone_hiddenoverflow(result)) result_exponent++;
 494         }
 495     if(result_exponent == SGL_INFINITY_EXPONENT)
 496         {
 497         /* Overflow */
 498         if(Is_overflowtrap_enabled())
 499             {
 500             Sgl_setwrapped_exponent(result,result_exponent,ovfl);
 501             *dstptr = result;
 502             if (inexact)
 503                 if (Is_inexacttrap_enabled())
 504                     return(OVERFLOWEXCEPTION | INEXACTEXCEPTION);
 505                 else Set_inexactflag();
 506             return(OVERFLOWEXCEPTION);
 507             }
 508         else
 509             {
 510             Set_overflowflag();
 511             inexact = TRUE;
 512             Sgl_setoverflow(result);
 513             }
 514         }
 515     else Sgl_set_exponent(result,result_exponent);
 516     *dstptr = result;
 517     if(inexact)
 518         if(Is_inexacttrap_enabled()) return(INEXACTEXCEPTION);
 519         else Set_inexactflag();
 520     return(NOEXCEPTION);
 521     }