c_q_add.c

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/*

  Copyright (C) 2000, 2001 Silicon Graphics, Inc.  All Rights Reserved.

  This program is free software; you can redistribute it and/or modify it
  under the terms of version 2 of the GNU General Public License as
  published by the Free Software Foundation.

  This program is distributed in the hope that it would be useful, but
  WITHOUT ANY WARRANTY; without even the implied warranty of
  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  

  Further, this software is distributed without any warranty that it is
  free of the rightful claim of any third person regarding infringement 
  or the like.  Any license provided herein, whether implied or 
  otherwise, applies only to this software file.  Patent licenses, if 
  any, provided herein do not apply to combinations of this program with 
  other software, or any other product whatsoever.  

  You should have received a copy of the GNU General Public License along
  with this program; if not, write the Free Software Foundation, Inc., 59
  Temple Place - Suite 330, Boston MA 02111-1307, USA.

  Contact information:  Silicon Graphics, Inc., 1600 Amphitheatre Pky,
  Mountain View, CA 94043, or:

  http://www.sgi.com

  For further information regarding this notice, see:

  http://oss.sgi.com/projects/GenInfo/NoticeExplan

*/


/* =======================================================================
 * =======================================================================
 *
 *
 * =======================================================================
 * =======================================================================
 */


#include "defs.h"
#include "quad.h"

/* note that this routine must be kept in sync with the corresponding libc
 * routine, q_add.
 */

typedef union
{
        struct
        {
                UINT32 hi;
                UINT32 lo;
        } word;

        double  d;
} du;

static const du         twop914 =
{0x79100000,    0x00000000};

static const du         inf =
{0x7ff00000,    0x00000000};

extern  QUAD    c_q_add(QUAD, QUAD, INT *);

#pragma weak c_q_add = __c_q_add
#define c_q_add __c_q_add

double  fabs(double);
#pragma intrinsic (fabs)

QUAD
c_q_add(QUAD x, QUAD y, INT *p_err )
{
double  xhi, xlo, yhi, ylo;
INT32   ixhi, iyhi;
INT32   xptxhi, xptyhi;
INT64   iz, iw, iqulp;
double  w, ww;
double  u, uu;
double  qulp;
QUAD    z;
double  tmp1, tmp2, lo, rem;

        /* adapted from T. J. Dekker's add2 subroutine */

        *p_err = 0;

        xhi = x.hi; xlo = x.lo;
        yhi = y.hi; ylo = y.lo;

        iyhi = *(INT32 *)&yhi;
        xptyhi = (iyhi >> 20);
        xptyhi &= 0x7ff;

        ixhi = *(INT32 *)&xhi;
        xptxhi = (ixhi >> 20);
        xptxhi &= 0x7ff;

#ifdef QUAD_DEBUG
        printf("c_q_add: xhi = %08x%08x\n", *(INT32 *)&xhi, *((INT32 *)&xhi + 1));
        printf("c_q_add: xlo = %08x%08x\n", *(INT32 *)&xlo, *((INT32 *)&xlo + 1));
        printf("c_q_add: yhi = %08x%08x\n", *(INT32 *)&yhi, *((INT32 *)&yhi + 1));
        printf("c_q_add: ylo = %08x%08x\n", *(INT32 *)&ylo, *((INT32 *)&ylo + 1));
#endif

        if ( xptxhi < xptyhi )
        {
                tmp1 = xhi;
                xhi = yhi;
                yhi = tmp1;
                xptxhi = xptyhi;
        }

        if ( fabs(xlo) < fabs(ylo) )
        {
                tmp2 = xlo;
                xlo = ylo;
                ylo = tmp2;
        }

        if ( xptxhi < 0x7fd )
        {
                z.hi = xhi + yhi;
                z.lo = xhi - z.hi + yhi;

                u = xlo + ylo;
                uu = xlo - u + ylo;

                lo = z.lo + u;

                w =  z.hi + lo;
                ww = z.hi - w + lo;

                rem = z.lo - lo + u;

                ww += rem + uu;
                z.hi = w + ww;
                DBL2LL( z.hi, iz );
                z.lo = w - z.hi + ww;

                /* if necessary, round z.lo so that the sum of z.hi and z.lo has at most
                   107 significant bits
                */

                /* first, compute a quarter ulp of z */

                iw = (iz >> DMANTWIDTH);
                iqulp = (iw & 0x7ff);
                iqulp -= 54;
                iqulp <<= DMANTWIDTH;

                if ( iqulp > 0 )
                {
                        LL2DBL( iqulp, qulp );
                        iw <<= DMANTWIDTH;

                        /* Note that the size of an ulp changes at a
                         * power of two.
                         */

                        if ( iw == iz )
                                goto fix;

                        if ( fabs(z.lo) >= qulp )
                        {
                                qulp = 0.0;
                        }
                        else if ( z.lo < 0.0 )
                                qulp = -qulp;

                        z.lo += qulp;
                        z.lo -= qulp;
                }


#ifdef QUAD_DEBUG
        printf("q_add: z.hi = %08x%08x\n", *(INT32 *)&z.hi, *((INT32 *)&z.hi + 1));
        printf("q_add: z.lo = %08x%08x\n", *(INT32 *)&z.lo, *((INT32 *)&z.lo + 1));
#endif

                return ( z );
        }
        else if ( xptxhi == 0x7ff )
        {
                z.hi = xhi + yhi;
                z.lo = 0.0;

#ifdef QUAD_DEBUG
        printf("q_add: z.hi = %08x%08x\n", *(INT32 *)&z.hi, *((INT32 *)&z.hi + 1));
        printf("q_add: z.lo = %08x%08x\n", *(INT32 *)&z.lo, *((INT32 *)&z.lo + 1));
#endif

                return ( z );
        }
        else
        {
                if ( fabs(yhi) < twop914.d )
                {
                        z.hi = xhi;
                        z.lo = xlo;

#ifdef QUAD_DEBUG
        printf("q_add: z.hi = %08x%08x\n", *(INT32 *)&z.hi, *((INT32 *)&z.hi + 1));
        printf("q_add: z.lo = %08x%08x\n", *(INT32 *)&z.lo, *((INT32 *)&z.lo + 1));
#endif

                        return ( z );
                }

                /*      avoid overflow in intermediate computations by 
                        computing 4.0*(.25*x + .25*y)
                */

                xhi *= 0.25;
                xlo *= 0.25;
                yhi *= 0.25;
                ylo *= 0.25;

                z.hi = xhi + yhi;
                z.lo = xhi - z.hi + yhi;

                u = xlo + ylo;
                uu = xlo - u + ylo;

                lo = z.lo + u;

                w =  z.hi + lo;
                ww = z.hi - w + lo;

                rem = z.lo - lo + u;

                ww += rem + uu;
                z.hi = w + ww;
                DBL2LL( z.hi, iz );
                z.lo = w - z.hi + ww;

                /* if necessary, round z.lo so that the sum of z.hi and z.lo has at most
                   107 significant bits
                */

                /* first, compute a quarter ulp of z */

                iw = (iz >> DMANTWIDTH);
                iqulp = (iw & 0x7ff);
                iqulp -= 54;
                iqulp <<= DMANTWIDTH;

                if ( iqulp > 0 )
                {
                        LL2DBL( iqulp, qulp );
                        iw <<= DMANTWIDTH;

                        /* Note that the size of an ulp changes at a
                         * power of two.
                         */

                        if ( iw == iz )
                                goto fix2;

                        if ( fabs(z.lo) >= qulp )
                        {
                                qulp = 0.0;
                        }
                        else if ( z.lo < 0.0 )
                                qulp = -qulp;

                        z.lo += qulp;
                        z.lo -= qulp;
                }

                z.hi *= 4.0;

                if ( fabs(z.hi) == inf.d )
                {
                        z.lo = 0.0;
                        return ( z );
                }

                z.lo *= 4.0;

                return ( z );

        }

fix:
        if ( ((z.hi > 0.0) && (z.lo < 0.0)) || ((z.hi < 0.0) && (z.lo > 0.0)) )
                qulp *= 0.5;

        if ( fabs(z.lo) >= qulp )
        {
                qulp = 0.0;
        }
        else if ( z.lo < 0.0 )
                qulp = -qulp;

        z.lo += qulp;
        z.lo -= qulp;

        return ( z );

fix2:
        if ( ((z.hi > 0.0) && (z.lo < 0.0)) || ((z.hi < 0.0) && (z.lo > 0.0)) )
                qulp *= 0.5;

        if ( fabs(z.lo) >= qulp )
        {
                qulp = 0.0;
        }
        else if ( z.lo < 0.0 )
                qulp = -qulp;

        z.lo += qulp;
        z.lo -= qulp;

        z.hi *= 4.0;

        if ( fabs(z.hi) == inf.d )
        {
                z.lo = 0.0;
                return ( z );
        }

        z.lo *= 4.0;

        return ( z );
}