dfsub.c

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/*
 * Linux/PA-RISC Project (http://www.parisc-linux.org/)
 *
 * Floating-point emulation code
 *  Copyright (C) 2001 Hewlett-Packard (Paul Bame) <[email protected]>
 *
 *    This program is free software; you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation; either version 2, or (at your option)
 *    any later version.
 *
 *    This program is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with this program; if not, write to the Free Software
 *    Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */
/*
 * 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 denomalized 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);
    }