linux/arch/parisc/math-emu/dfsub.c
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   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/dfsub.c               $Revision: 1.1 $
  26 *
  27 *  Purpose:
  28 *      Double_subtract: subtract two double precision values.
  29 *
  30 *  External Interfaces:
  31 *      dbl_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 "dbl_float.h"
  44
  45/*
  46 * Double_subtract: subtract two double precision values.
  47 */
  48int
  49dbl_fsub(
  50            dbl_floating_point *leftptr,
  51            dbl_floating_point *rightptr,
  52            dbl_floating_point *dstptr,
  53            unsigned int *status)
  54    {
  55    register unsigned int signless_upper_left, signless_upper_right, save;
  56    register unsigned int leftp1, leftp2, rightp1, rightp2, extent;
  57    register unsigned int resultp1 = 0, resultp2 = 0;
  58    
  59    register int result_exponent, right_exponent, diff_exponent;
  60    register int sign_save, jumpsize;
  61    register boolean inexact = FALSE, 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 same 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_invert_sign(rightp1);
 140            Dbl_copytoptr(rightp1,rightp2,dstptr);
 141            return(NOEXCEPTION);
 142            }
 143        /*
 144         * is NaN; signaling or quiet?
 145         */
 146        if (Dbl_isone_signaling(rightp1)) 
 147            {
 148            /* trap if INVALIDTRAP enabled */
 149            if (Is_invalidtrap_enabled()) return(INVALIDEXCEPTION);
 150            /* make NaN quiet */
 151            Set_invalidflag();
 152            Dbl_set_quiet(rightp1);
 153            }
 154        /*
 155         * return quiet NaN
 156         */
 157        Dbl_copytoptr(rightp1,rightp2,dstptr);
 158        return(NOEXCEPTION);
 159        } /* End right NaN or Infinity processing */
 160
 161    /* Invariant: Must be dealing with finite numbers */
 162
 163    /* Compare operands by removing the sign */
 164    Dbl_copytoint_exponentmantissap1(leftp1,signless_upper_left);
 165    Dbl_copytoint_exponentmantissap1(rightp1,signless_upper_right);
 166
 167    /* sign difference selects add or sub operation. */
 168    if(Dbl_ismagnitudeless(leftp2,rightp2,signless_upper_left,signless_upper_right))
 169        {
 170        /* Set the left operand to the larger one by XOR swap *
 171         *  First finish the first word using "save"          */
 172        Dbl_xorfromintp1(save,rightp1,/*to*/rightp1);
 173        Dbl_xorfromintp1(save,leftp1,/*to*/leftp1);
 174        Dbl_swap_lower(leftp2,rightp2);
 175        result_exponent = Dbl_exponent(leftp1);
 176        Dbl_invert_sign(leftp1);
 177        }
 178    /* Invariant:  left is not smaller than right. */ 
 179
 180    if((right_exponent = Dbl_exponent(rightp1)) == 0)
 181        {
 182        /* Denormalized operands.  First look for zeroes */
 183        if(Dbl_iszero_mantissa(rightp1,rightp2)) 
 184            {
 185            /* right is zero */
 186            if(Dbl_iszero_exponentmantissa(leftp1,leftp2))
 187                {
 188                /* Both operands are zeros */
 189                Dbl_invert_sign(rightp1);
 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 forward 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        /* Subtract 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 ...subtract 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 Set_inexactflag();
 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()) return(INEXACTEXCEPTION);
 524        else Set_inexactflag();
 525    return(NOEXCEPTION);
 526    }
 527