osprey/libm/mips/log.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: log.c
 * $Revision: 1.5 $
 * $Date: 04/12/21 14:58:22-08:00 $
 * $Author: bos@eng-25.internal.keyresearch.com $
 * $Source: /home/bos/bk/kpro64-pending/libm/mips/SCCS/s.log.c $
 *
 * Revision history:
 *  09-Jun-93 - Original Version
 *
 * Description: source code for log function
 *
 * ====================================================================
 * ====================================================================
 */

static char *rcs_id = "$Source: /home/bos/bk/kpro64-pending/libm/mips/SCCS/s.log.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 Logarithm Function in IEEE
  Floating-Point Arithmetic", Peter Tang, Argonne National Laboratory,
  ACM Transactions on Mathematical Software, Vol. 16, No. 4,
  Dec. 1990
*/

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

#pragma weak log = __log
#endif

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

double    log() __attribute__ ((weak, alias ("__log")));

#endif

extern  const du  _logtabhi[];
extern  const du  _logtablo[];
extern  const du  _log_ru[];

#ifdef _32BIT_MACHINE

/* exp(-1/16) */

static const int  lim1 =
{0x3fee0fab};

/* exp(1/16) */

static const int  lim2 =
{0x3ff1082b};

static const int  twop7 =
{0x40600000};

#else

/* exp(-1/16) */

static const long long  lim1 =
{0x3fee0fabfbc702a3ll};

/* exp(1/16) */

static const long long  lim2 =
{0x3ff1082b577d34eell};

static const long long  twop7 =
{0x4060000000000000ll};

#endif

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

static const  du  Neginf =
{D(0xfff00000, 0x00000000)};

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

static  const du  twopm7 =
{D(0x3f800000, 0x00000000)};

static const du log2_lead =
{D(0x3fe62e42, 0xfefa4000)};

static const du log2_trail =
{D(0xbd48432a, 0x1b0e2634)};

static const du Scaleup =
{D(0x43300000, 0x00000000)};

/* coefficients for polynomial approximation of log(1 + t) on +/- 1/256   */

static const du P[] =
{
{D(0x3ff00000, 0x00000000)},
{D(0xbfe00000, 0x00000001)},
{D(0x3fd55555, 0x55509ba5)},
{D(0xbfcfffff, 0xffeb6526)},
{D(0x3fc999b4, 0xdfed6fe4)},
{D(0xbfc55576, 0x66472e04)},
};

/* coefficients for polynomial approximation of log((1 + x/2)/(1 - x/2)) on 
   +/- 2*tanh(1/32)
*/

static const du Q[] =
{
{D(0x3ff00000, 0x00000000)},
{D(0x3fb55555, 0x555554ed)},
{D(0x3f899999, 0x99b929bd)},
{D(0x3f624923, 0x14d70150)},
{D(0x3f3c7ff7, 0xdaa9e72e)},
};


/* ====================================================================
 *
 * FunctionName   log
 *
 * Description    computes logarithm of arg
 *
 * ====================================================================
 */

double
__log( double x )
{
#ifdef _32BIT_MACHINE

int ix, m;

#else

long long ix, m;

#endif

int k;
double  g, u, v, x1, x2;
double  u1, u2;
double  t;
double  xmu;
double  q;
double  result;
double  l_lead, l_trail;
#ifdef _CALL_MATHERR
struct exception  exstruct;
#endif


  /* extract exponent and sign 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
  m = (ix >> DMANTWIDTH);

  if ( (0 < m) && (m < 0x7ff) )
  {
    /* x is positive and finite */

    m -= DEXPBIAS;
L:
    if ( (ix >= lim2) || (ix <= lim1) )
    {
      /* normalize x and compute the nearest 1/128th to x */

      ix &= DEXPMASK; /* mask off exponent bits of x */
      ix |= twop7;  /* set exponent of x to 0x406 */

#ifdef _32BIT_MACHINE

      INT2DBLHI(ix, x);
#else
      LL2DBL(ix, x);
#endif
      k = ROUND(x);

      u = k;

      k -= 128;

      xmu = twopm7.d*(x - u);

      t = _log_ru[k].d*xmu;

      /* avoid loss of significance for values of x near two
         by adjusting index; effectively u is divided by two.
         The logtable has been adjusted for this.
      */

      if ( k > 64 )
        m++;

      q = ((((P[5].d*t + P[4].d)*t + P[3].d)*t + 
          P[2].d)*t + P[1].d)*(t*t);

      l_lead = _logtabhi[k].d;
      l_trail = _logtablo[k].d;

      l_lead += m*log2_lead.d;
      l_trail += m*log2_trail.d;

      result = l_lead + (t + (q + l_trail));

      return ( result );
    }

    if ( x == 1.0 )
      return ( 0.0 );

    x = x - 1.0;

    g = 1.0/(2.0 + x);

    u = x*g;
    u = u + u;
    v = u*u;

    q = (((Q[4].d*v + Q[3].d)*v + Q[2].d)*v +
      Q[1].d)*(v*u);

    u1 = (float)u;  /* round u to 24 bits */
    x1 = (float)x;  /* round x to 24 bits */

    x2 = x - x1;
    u2 = x - u1;
    u2 = u2 + u2;
    u2 = ((u2 - u1*x1) - u1*x2)*g;

    result = u1 + (u2 + q);

    return ( result );
  }

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

#ifdef _CALL_MATHERR

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

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

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

    return ( Qnan.d );
#endif
  }

  if ( x == Neginf.d )
  {
#ifdef _CALL_MATHERR

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

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

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

    return ( Qnan.d );
#endif
  }

  if ( x == 0.0 )
  {
zeroarg:

#ifdef _CALL_MATHERR

    exstruct.type = OVERFLOW;
    exstruct.name = "log";
    exstruct.arg1 = x;
    exstruct.retval = Neginf.d;

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

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

    return ( Neginf.d );
#endif
  }

  if ( x == Inf.d )
  {
#ifdef _CALL_MATHERR

    exstruct.type = DOMAIN;
    exstruct.name = "log";
    exstruct.arg1 = x;
    exstruct.retval = Inf.d;

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

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

    return ( Inf.d );
#endif
  }

  if ( x < 0.0 )
  {
#ifdef _CALL_MATHERR

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

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

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

    return ( Qnan.d );
#endif
  }

  /* take care of denormals by scaling them up and adjusting the unbiased
     exponent of x
  */

  x *= Scaleup.d;

  if ( x == 0.0 )
    goto zeroarg;

#ifdef _32BIT_MACHINE

  DBLHI2INT(x, ix); /* copy MSW of x to ix  */
#else
  DBL2LL(x, ix);    /* copy x to ix */
#endif
  m = (ix >> DMANTWIDTH); /* shift off mantissa */
  m -= DEXPBIAS;
  m -= 52;  /* adjust for scaling */
  goto L;
}

#ifdef NO_LONG_DOUBLE

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

long double    logl() __attribute__ ((weak, alias ("__logl")));

#endif

long double
__logl( long double x )
{ 
  return ( (long double)__log((double)x) );
}

#endif

---