osprey/libm/vlog.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: vlog.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.vlog.c $
 *
 * Revision history:
 *  01-Dec-94 - Original Version
 *
 * Description: source code for vector logarithm function
 *
 * ====================================================================
 * ====================================================================
 */

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

#include "libm.h"

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

#pragma weak vlog = __vlog
#endif

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

extern  const du  __logtabhi[];
extern  const du  __logtablo[];
extern  const du  __log_ru[];

static const long long  twop7 =
{0x4060000000000000ll};

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)};

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

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

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

#define MAXEXP  0x7ffu

#define MINEXP  0x001u


/* ====================================================================
 *
 * FunctionName   vlog
 *
 * Description    computes vector logarithm of arg
 *
 * ====================================================================
 */

#ifdef _SW_PIPELINE

/* If compiler supports software pipelining, use this algorithm; note that
 * denormal args are not supported.
 */

void
__vlog( double  *x, double *y, long count, long stridex, long stridey )
{
unsigned long long ix;
long  i;
int j;
int m;
int k;
double  u;
double  t;
double  xmu;
double  q;
double  l_lead, l_trail;
double  w;
double  result;

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

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

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

    ix = *(unsigned long long *)x;  /* copy arg to a long long */

    m = (ix >> DMANTWIDTH);   /* shift off mantissa */
    j = m - MINEXP;

    m -= DEXPBIAS;

    /* normalize x and compute the nearest 1/128th to x */
  
    ix &= (DSIGNMASK & DEXPMASK); /* mask off sign and exponent 
             * bits of x
             */
    ix |= twop7;  /* set exponent of x to 0x406 */

    /* adjust scaled arg  */

    LL2DBL(ix, w);

    k = ROUND(w);

    u = k;

    k -= 128;

    xmu = twopm7.d*(w - 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));

    /* take care of negative args, NaNs, and Infinities     */

    if ( j >= (MAXEXP-MINEXP) )
      result = Qnan.d;

    if ( *x == 0.0 )
      result = Neginf.d;

    if ( *x == Inf.d )
      result = Inf.d;

    *y = result;

    y += stridey;

    x += stridex;
  }
}

#else

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

unsigned int  ix;

#else

unsigned long long ix;

#endif

long  i;
int j;
int m;
int k;
double  u;
double  t;
double  xmu;
double  q;
double  l_lead, l_trail;
double  w, z;
double  result;

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

  for ( i=0; i<count; i++ )
  {
    /* extract exponent and sign of x for some quick screening */

    z = *x;
    w = z;

#ifdef _32BIT_MACHINE

    DBLHI2INT(w, ix); /* copy arg to an int */
#else
    DBL2LL(w, ix);
#endif
    m = (ix >> DMANTWIDTH);   /* shift off mantissa */
    j = m;

    if ( m == 0 )
    {
      z *= Scaleup.d;
      w = z;

#ifdef _32BIT_MACHINE

      DBLHI2INT(w, ix); /* copy scaled arg to an int   */
#else
      DBL2LL(w, ix);  /* copy scaled arg to a long long */
#endif
      m = (ix >> DMANTWIDTH); /* shift off mantissa */
      m -= 52;  /* adjust for scaling */
    }

    m -= DEXPBIAS;

    /* normalize x and compute the nearest 1/128th to x */
  
    ix &= (DSIGNMASK & DEXPMASK); /* mask off sign and exponent 
             * bits of x
             */
    ix |= twop7;  /* set exponent of x to 0x406 */

    /* adjust scaled arg  */

#ifdef _32BIT_MACHINE

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

    u = k;

    k -= 128;

    xmu = twopm7.d*(w - 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));

    /* take care of negative args, NaNs, and Infinities     */

    if ( j >= MAXEXP )
      result = Qnan.d;

    if ( z == 0.0 )
      result = Neginf.d;

    if ( z == Inf.d )
      result = Inf.d;

    *y = result;

    y += stridey;

    x += stridex;
  }
}
#endif

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