osprey/libm/mips/acosf.c

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/*
 * Copyright 2003, 2004 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: acosf.c
 * $Revision: 1.1.1.1 $
 * $Date: 2005/10/21 19:00:00 $
 * $Author: marcel $
 * $Source: /proj/osprey/CVS/open64/osprey1.0/libm/mips/acosf.c,v $
 *
 * Revision history:
 *  09-Jun-93 - Original Version
 *
 * Description: source code for acosf function
 *
 * ====================================================================
 * ====================================================================
 */

static char *rcs_id = "$Source: /proj/osprey/CVS/open64/osprey1.0/libm/mips/acosf.c,v $ $Revision: 1.1.1.1 $";

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

#include "libm.h"

#if defined(mips) && !defined(__GNUC__)
extern  float facos(float);
extern  float acosf(float);

#pragma weak facos = __acosf
#pragma weak acosf = __acosf
#endif

#if defined(BUILD_OS_DARWIN) /* Mach-O doesn't support aliases */
extern float __acosf(float);
#pragma weak acosf
float acosf( float x ) {
  return __acosf(x);
}
#elif defined(__GNUC__)
extern  float  __acosf(float);
float    acosf(float) __attribute__ ((weak, alias ("__acosf")));
#endif

/* coefficients for polynomial approximation of asin on +/- 0.5    */

static const du P[] =
{
{D(0x3ff00000, 0x00000000)},
{D(0x3fc5555c, 0x88342cb0)},
{D(0x3fb3301e, 0x4681bb77)},
{D(0x3fa747e4, 0xa38c190b)},
{D(0x3f98c283, 0xc04a0db6)},
{D(0x3fa596d2, 0x8a9d07d2)},
};

/* coefficients for polynomial approximation of asin on +/- sqrt(2 - sqrt(3))/2 */

static const du P2[] =
{
{D(0x3ff00000, 0x00000000)},
{D(0x3fc55564, 0xfd6bdcbc)},
{D(0x3fb32843, 0xb5c74590)},
{D(0x3fa90146, 0xd5d24e0c)},
};

static const du half =
{D(0x3fe00000, 0x00000000)};

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

static const du piby4 =
{D(0x3fe921fb, 0x54442d18)};

static const du piby2 =
{D(0x3ff921fb, 0x54442d18)};

static const du threepiby4 =
{D(0x4002d97c, 0x7f3321d2)};

static const du pi =
{D(0x400921fb, 0x54442d18)};

static const  fu  Qnan = {QNANF};

static const fu f_half = {0x3f000000};

static const fu f_one = {0x3f800000};

static const fu f_m_one = {0xbf800000};

static const fu f_piby2 = {0x3fc90fdb};

static const fu f_pi = {0x40490fdb};

static const int root3by2 = 0x3f5db3d7;

#ifndef _HDW_SQRT

#define MAGIC 0x5fe6eb3b

#endif


/* ====================================================================
 *
 * FunctionName   acosf
 *
 * Description    computes arccosine of arg
 *
 * ====================================================================
 */

float
__acosf( float x )
{
int n;
int ix, xpt;
unsigned int  iabsx;
float absx;
double  dx, xsq, poly;
double  result;
double  y, ysq;
double  w;
double  q, Q;
double  ysqby2;
#ifdef _CALL_MATHERR
struct exception  exstruct;
#endif

  FLT2INT(x, ix);   /* copy arg to an integer */
  iabsx = (ix << 1);
  iabsx >>= 1;
  xpt = (iabsx >> MANTWIDTH);

  if ( xpt < 0x7e ) 
  {
    /* |x| < 0.5 */

    if ( xpt >= 0x65 )
    {
      /* |x| >= 2^(-26) */

      dx = x;

      xsq = dx*dx;

      poly = ((((P[5].d*xsq + P[4].d)*xsq + P[3].d)*xsq +
             P[2].d)*xsq + P[1].d)*(xsq*dx) + dx;

      result = piby2.d - poly;

      return ( (float)result );
    }

    return ( f_piby2.f );
  }

  if ( xpt < 0x7f ) 
  {
    /* |x| < 1.0 */

    if ( iabsx < root3by2 )
    {
      /* |x| < sqrt(3)/2 */
  
      dx = x;

      xsq = dx*dx;
      y = xsq + xsq - one.d;
      ysq = y*y;

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

      poly = y + (y*ysq)*poly;

      if ( ix > 0 )
        return ( (float)(piby4.d - half.d*poly) );
      else
        return ( (float)(threepiby4.d + half.d*poly) );
    }

    absx = fabsf(x);

    ysq = f_half.f*(f_one.f - absx);

#ifdef  _HDW_SQRT

    y = sqrt(ysq);
#else

    /* Compute y = sqrt(ysq) using Newton-Raphson method.
    */

    /* First, approximate 1/sqrt(ysq) using a "magic"
       constant.
    */

    y = 0.0;
    DBLHI2INT(ysq, n);
    n >>= 1;
    n = MAGIC - n;
    INT2DBLHI(n, y);
    ysqby2 = half.d*ysq;
  
    /* Improve estimate by iterating twice. */

    y = y*(1.5 - ysqby2*y*y);
    y = y*(1.5 - ysqby2*y*y);

    /* Do one final iteration, multiplying by ysq. */

    q = ysqby2*y;
    Q = q + q;
    y = Q*(1.5 - q*y);
#endif

    /* Now compute asin(y) using a polynomial approximation. */

    poly = ((P2[3].d*ysq + P2[2].d)*ysq + P2[1].d);

    w = y + (y*ysq)*poly;

    if ( ix > 0 )
      return ( (float)(w + w) );
    else
      return ( (float)(pi.d - (w + w)) );
  }

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

#ifdef _CALL_MATHERR

                exstruct.type = DOMAIN;
                exstruct.name = "acosf";
                exstruct.arg1 = x;
                exstruct.retval = Qnan.f;

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

                return ( exstruct.retval );
#else
    NAN_SETERRNO(EDOM);
    
    return ( Qnan.f );
#endif
  }

  if ( x == f_one.f )
    return ( 0.0f );

  if ( x == f_m_one.f )
    return ( f_pi.f );

  /*  |x| > 1.0; return a NaN */

#ifdef _CALL_MATHERR

        exstruct.type = DOMAIN;
        exstruct.name = "acosf";
        exstruct.arg1 = x;
        exstruct.retval = Qnan.f;

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

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

  return ( Qnan.f );
#endif
}

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