osprey/libm/mips/exp.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: exp.c
 * $Revision: 1.5 $
 * $Date: 04/12/21 14:58:21-08:00 $
 * $Author: bos@eng-25.internal.keyresearch.com $
 * $Source: /home/bos/bk/kpro64-pending/libm/mips/SCCS/s.exp.c $
 *
 * Revision history:
 *  09-Jun-93 - Original Version
 *
 * Description: source code for exp function
 *
 * ====================================================================
 * ====================================================================
 */

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

#ifdef _CALL_MATHERR
#include <stdio.h>
#include <math.h>
#include <errno.h>
#endif

#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  double  exp(double);

#pragma weak exp = __exp
#endif

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern double __exp(double);
#pragma weak exp
double exp( double x ) {
  return __exp( x );
}
#elif defined(__GNUC__)
extern  double  __exp(double);

double    exp() __attribute__ ((weak, alias ("__exp")));

#endif

extern  const du  _exptabhi[];
extern  const du  _exptablo[];

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

static const  du  Inf =
{D(0x7ff00000, 0x00000000)};

static const du Ulimit =
{D(0x40862e42, 0xfefa39ef)};

static const du Llimit =
{D(0xc0874910, 0xd52d3051)};

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

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

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

static const du one =
{D(0x3ff00000, 0x00000000)};

/* 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   exp
 *
 * Description    computes exponential of arg
 *
 * ====================================================================
 */

double
__exp( double x )
{
#ifdef _32BIT_MACHINE

int ix, xpt;
int l;

#else

long long ix, xpt;
long long l;

#endif

double  y1, y2, y;
double  p, q;
int n, m, j;
int m1, m2;
double  nd;
double  s, s_lead, s_trail;
double  twopm;
double  twopm1, twopm2;
double  result;
#ifdef _CALL_MATHERR
struct exception  exstruct;
#endif

  /* extract exponent of x for some quick screening */

#ifdef _32BIT_MACHINE

  DBLHI2INT(x, ix); /* copy MSW of x to ix  */
#else
  DBL2LL(x, ix);    /* copy x to ix */
#endif

  xpt = (ix >> DMANTWIDTH);
  xpt &= 0x7ff;

  if ( xpt < 0x408 )
  {
    /*      |x| < 512.0 */

    if ( xpt >= 0x3c8 )
    {
      /* |x| >= 2^(-54) */

      /* reduce x to +/- log(2)/64     */

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

      y1 = x - nd*ln2by32hi.d;
      y2 = nd*ln2by32lo.d;
      y = y1 - y2;

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

      s_lead = _exptabhi[j].d;
      s_trail = _exptablo[j].d;
      s = s_lead + s_trail;

      l = m + DEXPBIAS;
      l <<= DMANTWIDTH;

#ifdef _32BIT_MACHINE

      twopm = 0.0;
      INT2DBLHI(l, twopm);  /* copy MSW of l to twopm */
#else
      LL2DBL(l, twopm); /* copy l to twopm  */
#endif
      q = ((((P[6].d*y + P[5].d)*y + P[4].d)*y + P[3].d)*y +
        P[2].d)*(y*y);

      p = (q - y2) + y1;

      result = s_lead + (s_trail + s*p);
      result *= twopm;
      return ( result );
    }

    return ( one.d + x );
  }

  if ( x != x )
  {
    /* x is a NaN; return a quiet NaN */

#ifdef _CALL_MATHERR

    exstruct.type = DOMAIN;
    exstruct.name = "exp";
    exstruct.arg1 = x;
    exstruct.retval = Qnan.d;

    if ( matherr( &exstruct ) == 0 )
    {
      fprintf(stderr, "domain error in exp\n");
      SETERRNO(EDOM);
    }

    return ( exstruct.retval );
#else
    NAN_SETERRNO(EDOM);

    return ( Qnan.d );
#endif
  }

  if ( x > Ulimit.d )
  {
#ifdef _CALL_MATHERR

    exstruct.type = OVERFLOW;
    exstruct.name = "exp";
    exstruct.arg1 = x;
    exstruct.retval = Inf.d;

    if ( matherr( &exstruct ) == 0 )
    {
      fprintf(stderr, "overflow error in exp\n");
      SETERRNO(ERANGE);
    }

    return ( exstruct.retval );
#else
    SETERRNO(ERANGE);

    return ( Inf.d );
#endif
  }

  if ( x < Llimit.d )
  {
#ifdef _CALL_MATHERR

    exstruct.type = UNDERFLOW;
    exstruct.name = "exp";
    exstruct.arg1 = x;
    exstruct.retval = 0.0;

    if ( matherr( &exstruct ) == 0 )
    {
      fprintf(stderr, "underflow error in exp\n");
      SETERRNO(ERANGE);
    }

    return ( exstruct.retval );
#else
    SETERRNO(ERANGE);

    return ( 0.0 );
#endif
  }

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

  /* reduce x to +/- log(2)/64     */

  y1 = x - nd*ln2by32hi.d;
  y2 = nd*ln2by32lo.d;
  y = 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*y + P[5].d)*y + P[4].d)*y + P[3].d)*y +
    P[2].d)*(y*y);

  p = (q - y2) + y1;

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

  /* must be more careful here when forming 2^m*result;
     the exponent may underflow or overflow
  */

  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;

  return ( result );
}

#ifdef NO_LONG_DOUBLE

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern  long double  __expl(long double);
long double expl( long double x ) { 
  return ( (long double)__exp((double)x) );
}
#elif defined(__GNUC__)
extern  long double  __expl(long double);

long double    expl() __attribute__ ((weak, alias ("__expl")));

#endif

long double
__expl( long double x )
{ 
  return ( (long double)__exp((double)x) );
}

#endif

---