osprey/libm/mips/expm1.c

Go to the documentation of this file.

/*
 * 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: expm1.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.expm1.c $
 *
 * Revision history:
 *  09-Jun-93 - Original Version
 *
 * Description: source code for expm1 function
 *
 * ====================================================================
 * ====================================================================
 */

static char *rcs_id = "$Source: /home/bos/bk/kpro64-pending/libm/mips/SCCS/s.expm1.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 Expm1 Function in IEEE
  Floating Point Arithmetic", Peter Tang, ACM Transactions on
  Mathematical Software, Vol. 18, No. 2, June 1992
 */

#if defined(mips) && !defined(__GNUC__)
extern  double  expm1(double);

#pragma weak expm1 = __expm1
#endif

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern double __expm1(double);
#pragma weak expm1
double expm1( double x ) {
  return __expm1( x );
}
#elif defined(__GNUC__)
extern  double  __expm1(double);

double    expm1() __attribute__ ((weak, alias ("__expm1")));

#endif

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

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

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

/* log(1 - 1/4)   */

static const du T1 =
{D(0xbfd26962, 0x1134db93)};

/* log(1 + 1/4)   */

static const du T2 =
{D(0x3fcc8ff7, 0xc79a9a22)};

static const du Twopm100 =
{D(0x39b00000, 0x00000000)};

static const du Twopm7 =
{D(0x3f800000, 0x00000000)};

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

static const du Llimit =
{D(0xc042b708, 0x872320e1)};

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

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

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

static const du m_one =
{D(0xbff00000, 0x00000000)};

/* coefficients for polynomial approximation of exp(x) - 1 on the interval
   (log(1 - 1/4), log(1 + 1/4))
*/

static const du P[] =
{
{D(0x3fc55555, 0x55555549)},
{D(0x3fa55555, 0x555554b6)},
{D(0x3f811111, 0x1111a9f3)},
{D(0x3f56c16c, 0x16ce14c6)},
{D(0x3f2a01a0, 0x1159dd2d)},
{D(0x3efa019f, 0x635825c4)},
{D(0x3ec71e14, 0xbfe3db59)},
{D(0x3e928295, 0x484734ea)},
{D(0x3e5a2836, 0xaa646b96)},
};

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

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

/* 2^(k-7), k = 0, ..., 60    */

static  const fu  twopowm[] =
{
{0x43000000},
{0x42800000},
{0x42000000},
{0x41800000},
{0x41000000},
{0x40800000},
{0x40000000},
{0x3f800000},
{0x3f000000},
{0x3e800000},
{0x3e000000},
{0x3d800000},
{0x3d000000},
{0x3c800000},
{0x3c000000},
{0x3b800000},
{0x3b000000},
{0x3a800000},
{0x3a000000},
{0x39800000},
{0x39000000},
{0x38800000},
{0x38000000},
{0x37800000},
{0x37000000},
{0x36800000},
{0x36000000},
{0x35800000},
{0x35000000},
{0x34800000},
{0x34000000},
{0x33800000},
{0x33000000},
{0x32800000},
{0x32000000},
{0x31800000},
{0x31000000},
{0x30800000},
{0x30000000},
{0x2f800000},
{0x2f000000},
{0x2e800000},
{0x2e000000},
{0x2d800000},
{0x2d000000},
{0x2c800000},
{0x2c000000},
{0x2b800000},
{0x2b000000},
{0x2a800000},
{0x2a000000},
{0x29800000},
{0x29000000},
{0x28800000},
{0x28000000},
{0x27800000},
{0x27000000},
{0x26800000},
{0x26000000},
{0x25800000},
};


/* ====================================================================
 *
 * FunctionName   expm1
 *
 * Description    computes expm1 function of arg
 *
 * ====================================================================
 */

double
__expm1( double x )
{
#ifdef _32BIT_MACHINE

int ix, xpt;
int k, l;

#else

long long ix, xpt;
long long k, l;

#endif

int n, m, j;
double  y1, y2, y;
double  u, v, z;
double  p, q;
double  twopm;
double  twopmm;
double  nd;
double  s, s_lead, s_trail;
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 arg to an int  */
#else
  DBL2LL(x, ix);    /* copy arg to a long long  */
#endif
  xpt = (ix >> DMANTWIDTH); /* shift off mantissa */
  xpt &= 0x7ff;

  if ( xpt < 0x7ff )
  {
    /*    x is finite    */

    if ( (T1.d < x) && (x < T2.d) )
    {
      /* log(1 - 1/4) < x < log(1 + 1/4) */

      if ( xpt >= 0x3c9 )
      {
        /* |x| >= 2^(-54) */

        u = (float)x;
        v = x - u;
        y = u*u*0.5;
        z = v*(x + u)*0.5;

        q = ((((((((P[8].d*x + P[7].d)*x + P[6].d)*x + P[5].d)*x +
        P[4].d)*x + P[3].d)*x + P[2].d)*x + P[1].d)*x +
        P[0].d)*(x*x*x);

        if ( y >= Twopm7.d )
        {
          result = (u + y) + (q + (v + z));
          return ( result );
        }

        result = x + (y + (q + z));

        return ( result );

      }

      return ( x );
    }
    else if ( x > Ulimit.d )
    {
#ifdef _CALL_MATHERR
      exstruct.type = OVERFLOW;
      exstruct.name = "expm1";
      exstruct.arg1 = x;
      exstruct.retval = Inf.d;

      if ( matherr( &exstruct ) == 0 )
      {
        fprintf(stderr, "overflow range error in expm1\n");
        SETERRNO(ERANGE);
      }

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

      return ( Inf.d );
#endif
    }
    else if ( x < Llimit.d )
    {
      return ( m_one.d + Twopm100.d );
    }
    else
    {
      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;

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

      p = (q - y2) + y1;

      k = DEXPBIAS + m;
      k <<= DMANTWIDTH;

#ifdef _32BIT_MACHINE

      twopm = 0.0;
      INT2DBLHI(k, twopm);  /* copy k to MSW of twopm */
#else
      LL2DBL(k, twopm); /* copy k to twopm  */
#endif
      if ( m >= 53 )
      {
        l = DEXPBIAS - m;
        l <<= DMANTWIDTH;

#ifdef _32BIT_MACHINE

        twopmm = 0.0;
        INT2DBLHI(l, twopmm); /* copy l to MSW of twopmm */
#else
        LL2DBL(l, twopmm);  /* copy l to twopmm */
#endif
        s = s_lead + s_trail;
        result = s_lead + (s*p + (s_trail - twopmm));
        result *= twopm;
        return ( result );
      }
      else if ( m >= -7 )
      {
        result = (s_lead - twopowm[m+7].f) +
           (s_lead*p + s_trail*(1.0 + p));
        result *= twopm;
        return ( result );
      }
      else
      {
        s = s_lead + s_trail;
        result = s_lead + (s*p + s_trail);
        result *= twopm;
        result -= 1.0;
        return ( result );
      }
    }
  }
  else if ( x != x )
  {
    /* x is a NaN; return a quiet NaN */

#ifdef _CALL_MATHERR

    exstruct.type = DOMAIN;
    exstruct.name = "expm1";
    exstruct.arg1 = x;
    exstruct.retval = Qnan.d;

    if ( matherr( &exstruct ) == 0 )
    {
      fprintf(stderr, "domain error in expm1\n");
      SETERRNO(EDOM);
    }

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

    return ( Qnan.d );
#endif
  }
  else if ( x == Inf.d )
  {
#ifdef _CALL_MATHERR

    exstruct.type = OVERFLOW;
    exstruct.name = "expm1";
    exstruct.arg1 = x;
    exstruct.retval = Inf.d;

    if ( matherr( &exstruct ) == 0 )
    {
      fprintf(stderr, "overflow range error in expm1\n");
      SETERRNO(ERANGE);
    }

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

    return ( Inf.d );
#endif
  }
  else  /*  x == -inf  */

    return ( m_one.d );
}

#ifdef NO_LONG_DOUBLE

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern long double __expm1l(long double);
long double expm1l( long double x ) { 
  return ( (long double)__expm1((double)x) );
}
#elif defined(__GNUC__)
extern  long double  __expm1l(long double);

long double    expm1l() __attribute__ ((weak, alias ("__expm1l")));

#endif

long double
__expm1l( long double x )
{ 
  return ( (long double)__expm1((double)x) );
}

#endif

---