osprey/libm/vexp.c

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/*
 * Copyright 2003, 2004, 2005, 2006 PathScale, Inc.  All Rights Reserved.
 */

/*

  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 2.1 of the GNU Lesser 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 Lesser 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

*/


/* ====================================================================
 * ====================================================================
 *
 * Module: vexp.c
 * $Revision: 1.5 $
 * $Date: 04/12/21 14:58:20-08:00 $
 * $Author: bos@eng-25.internal.keyresearch.com $
 * $Source: /home/bos/bk/kpro64-pending/libm/SCCS/s.vexp.c $
 *
 * Revision history:
 *  01-Dec-94 - Original Version
 *
 * Description: source code for vector exponential function
 *
 * ====================================================================
 * ====================================================================
 */

static char *rcs_id = "$Source: /home/bos/bk/kpro64-pending/libm/SCCS/s.vexp.c $ $Revision: 1.5 $";

#include "libm.h"

/*  Algorithm adapted from
  "Table-driven Implementation of the Exponential Function in
  IEEE Floating Point Arithmetic", Peter Tang, ACM Transactions on
  Mathematical Software, Vol. 15, No. 2, June 1989
 */

#if defined(mips) && !defined(__GNUC__)
extern  void  vexp(double *, double *, long, long, long);

#pragma weak vexp = __vexp
#endif

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern void __vexp( double *x, double *y, long count, long stridex,
  long stridey );
#pragma weak vexp
void vexp( double *x, double *y, long count, long stridex, long stridey ) {
  __vexp(x, y, count, stridex, stridey);
}
#elif defined(__GNUC__)
extern  void  __vexp(double *, double *, long, long, long);
void    vexp() __attribute__ ((weak, alias ("__vexp")));
#endif

extern  const du  __exptabhi[];
extern  const du  __exptablo[];

static const du Ulimit =
{D(0x40862e42, 0xfefa3940)};

static const du Llimit =
{D(0xc0874910, 0xd52d3052)};

static const du rln2by32 =
{D(0x40471547, 0x652b82fe)};

static const du ln2by32hi =
{D(0x3f962e42, 0xfef00000)};

static const du ln2by32lo =
{D(0x3d8473de, 0x6af278ed)};

static const du Twopm54 =
{D(0x3c900000, 0x00000000)};

static const  du  Qnan =
{D(QNANHI, QNANLO)};

/* coefficients for polynomial approximation of exp on +/- log(2)/64     */

static const du P[] =
{
{D(0x3ff00000, 0x00000000)},
{D(0x3ff00000, 0x00000000)},
{D(0x3fe00000, 0x00000000)},
{D(0x3fc55555, 0x55548f7c)},
{D(0x3fa55555, 0x55545d4e)},
{D(0x3f811115, 0xb7aa905e)},
{D(0x3f56c172, 0x8d739765)},
};


/* ====================================================================
 *
 * FunctionName   vexp
 *
 * Description    computes vector exponential of arg
 *
 * ====================================================================
 */

void
__vexp( double  *x, double *y, long count, long stridex, long stridey )
{
#ifdef _32BIT_MACHINE

int l;

#else

long long l;

#endif

long i;
int m, m1, m2;
int j, n;
double  w;
double  y1, y2, z;
double  p, q;
double  dx;
double  nd;
double  s, s_lead, s_trail;
double  twopm1, twopm2;
double  result;

  /* i = 0, 1, ..., n-1; y[i*stridey] = exp(x[i*stridex]) */

  for ( i=0; i<count; i++ )
  {
#ifdef _PREFETCH
#pragma prefetch_ref=*(x+8)
#pragma prefetch_ref=*(y+8)
#endif

    dx = w = *x;

    if ( dx != dx )
      dx = 0.0;

    if ( dx > Ulimit.d )
      dx = Ulimit.d;
      
    if ( dx < Llimit.d )
      dx = Llimit.d;

    if ( fabs(dx) < Twopm54.d )
      dx = 0.0;
  
    /* reduce dx to +/- log(2)/64     */

    nd = dx*rln2by32.d;
    n = ROUND(nd);
    nd = n;

    y1 = dx - nd*ln2by32hi.d;
    y2 = nd*ln2by32lo.d;
    z = y1 - y2;

    j = n & 0x1f;
    m = n >> 5;

    s_lead = __exptabhi[j].d;
    s_trail = __exptablo[j].d;
    s = s_lead + s_trail;

    q = ((((P[6].d*z + P[5].d)*z + P[4].d)*z + P[3].d)*z +
      P[2].d)*(z*z);

    p = (q - y2) + y1;

    result = s_lead + (s_trail + s*p);

    m1 = (m >> 1);
    m2 = m - m1;

#ifdef _32BIT_MACHINE

    twopm1 = 0.0;
    l = m1 + DEXPBIAS;
    l <<= DMANTWIDTH;

    INT2DBLHI(l, twopm1);

    twopm2 = 0.0;
    l = m2 + DEXPBIAS;
    l <<= DMANTWIDTH;

    INT2DBLHI(l, twopm2);
#else
    l = m1 + DEXPBIAS;
    l <<= DMANTWIDTH;

    LL2DBL(l, twopm1);

    l = m2 + DEXPBIAS;
    l <<= DMANTWIDTH;

    LL2DBL(l, twopm2);
#endif
    result *= twopm1;
    result *= twopm2;

    if ( w != w )
      result = Qnan.d;

    *y = result;

    x += stridex;
    y += stridey;
  }
}

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