c_q_mul.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_mul.
 */

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

        double  d;
} du;


/* const1 is 1.0 + 2^(53 - 53/2), i.e. 1.0 + 2^27 */

static  const du        const1 =
{0x41a00000,    0x02000000};

static  const du        twop590 =
{0x64d00000,    0x00000000};

static  const du        twopm590 =
{0x1b100000,    0x00000000};

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

#define NO      0
#define YES     1

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

#pragma weak c_q_mul = __c_q_mul
#define c_q_mul __c_q_mul

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

QUAD
c_q_mul(QUAD x, QUAD y, INT *p_err )
{
INT32   ixhi, iyhi;
INT32   xptxhi, xptyhi;
INT32   xpthi, xptlo;
INT32   scaleup, scaledown;
INT64   iz, iw, iqulp;
double  xhi, xlo, yhi, ylo;
double  xfactor, yfactor;
double  hx, tx, hy, ty;
double  p, q;
double  w, ww;
double  qulp;
QUAD    z, u;
double  rem;
double  a, v, vv;

        /* Avoid underflows and overflows in forming the products
           xhi*const1.d, yhi*const1.d, xhi*yhi, and hx*hy by scaling if
           necessary.  x and y should also be scaled if tx*ty is
           a denormal.
        */

        *p_err = 0;

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

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


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

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

        xpthi = xptxhi;
        xptlo = xptyhi;

        if ( xptxhi < xptyhi )
        {
                xptlo = xptxhi;
                xpthi = xptyhi;
        }

        if ( (0x21a < xptlo) && (xpthi < 0x5fd) )
        {
                /* normal case */

                /* Form the exact product of xhi and yhi using
                 * Dekker's algorithm.
                 */

                p = xhi*const1.d;
        
                hx = (xhi - p) + p;
                tx = xhi - hx;
        
                q = yhi*const1.d;
        
                hy = (yhi - q) + q;
                ty = yhi - hy;
        
                u.hi = xhi*yhi;
                u.lo = (((hx*hy - u.hi) + hx*ty) + hy*tx) + tx*ty;

                /* Add the remaining pieces using the Kahan summation formula. */

                a = xhi*ylo;

                ww = u.lo + a;
                rem = u.lo - ww + a;

                v = u.hi + ww;
                vv = u.hi - v + ww;

                a = xlo*yhi + rem;
                u.lo = vv + a;

                rem = vv - u.lo + a;

                w = v + u.lo;
                ww = v - w + u.lo;

                a = xlo*ylo + rem;

                vv = ww + a;

                z.hi = w + vv;
                DBL2LL(z.hi, iz);
                z.lo = w - z.hi + vv;

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

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

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

                return ( z );
        }
        else
        {
                xfactor = 1.0;
                yfactor = 1.0;
                scaleup = scaledown = NO;

                if ( xptxhi <= 0x21a )
                {
                        xhi *= twop590.d;
                        xlo *= twop590.d;
                        xfactor = twopm590.d;
                        scaleup = YES;
                }

                if ( xptyhi <= 0x21a )
                {
                        yhi *= twop590.d;
                        ylo *= twop590.d;
                        yfactor = twopm590.d;
                        scaleup = YES;
                }

                if ( xptxhi >= 0x5fd )
                {
                        xhi *= twopm590.d;
                        xlo *= twopm590.d;
                        xfactor = twop590.d;
                        scaledown = YES;
                }

                if ( xptyhi >= 0x5fd )
                {
                        yhi *= twopm590.d;
                        ylo *= twopm590.d;
                        yfactor = twop590.d;
                        scaledown = YES;
                }

                if ( (scaleup == YES) && (scaledown == YES) )
                {
                        xfactor = yfactor = 1.0;
                }


                /* Form the exact product of xhi and yhi using
                 * Dekker's algorithm.
                 */

                p = xhi*const1.d;
        
                hx = (xhi - p) + p;
                tx = xhi - hx;
        
                q = yhi*const1.d;
        
                hy = (yhi - q) + q;
                ty = yhi - hy;
        
                u.hi = xhi*yhi;
                u.lo = (((hx*hy - u.hi) + hx*ty) + hy*tx) + tx*ty;

                /* Add the remaining pieces using the Kahan summation formula. */

                a = xhi*ylo;

                ww = u.lo + a;
                rem = u.lo - ww + a;

                v = u.hi + ww;
                vv = u.hi - v + ww;

                a = xlo*yhi + rem;
                u.lo = vv + a;

                rem = vv - u.lo + a;

                w = v + u.lo;
                ww = v - w + u.lo;

                a = xlo*ylo + rem;

                vv = ww + a;

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

                /* Rescale z.hi and z.lo before rounding */

                w = z.hi*xfactor;
                w *= yfactor;

                if ( (w == 0.0) || (fabs(w) == inf.d) )
                {
                        z.hi = w;
                        z.lo = 0.0;

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

                        return ( z );
                }

                ww = z.lo*xfactor;
                ww *= yfactor;

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

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

                /* 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;

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

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

                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;

        goto back;
}