StdLib/LibC/Math/e_acos.c

/** @file
  Compute acos(x) using ieee FP math.

  Copyright (c) 2010 - 2011, Intel Corporation. All rights reserved.<BR>
  This program and the accompanying materials are licensed and made available under
  the terms and conditions of the BSD License that accompanies this distribution.
  The full text of the license may be found at
  http://opensource.org/licenses/bsd-license.

  THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
  WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.

 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================

  e_acos.c 5.1 93/09/24
  NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp
 */
#if defined(_MSC_VER)           /* Handle Microsoft VC++ compiler specifics. */
  // Keep older compilers quiet about floating-point divide-by-zero
  #pragma warning ( disable : 4723 )
#endif

#include  <LibConfig.h>
#include  <sys/EfiCdefs.h>

/* __ieee754_acos(x)
 * Method :
 *  acos(x)  = pi/2 - asin(x)
 *  acos(-x) = pi/2 + asin(x)
 * For |x|<=0.5
 *  acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
 * For x>0.5
 *  acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
 *    = 2asin(sqrt((1-x)/2))
 *    = 2s + 2s*z*R(z)  ...z=(1-x)/2, s=sqrt(z)
 *    = 2f + (2c + 2s*z*R(z))
 *     where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
 *     for f so that f+c ~ sqrt(z).
 * For x<-0.5
 *  acos(x) = pi - 2asin(sqrt((1-|x|)/2))
 *    = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
 *
 * Special cases:
 *  if x is NaN, return x itself;
 *  if |x|>1, return NaN with invalid signal.
 *
 * Function needed: __ieee754_sqrt
 */

#include "math.h"
#include "math_private.h"

static const double
one     =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi      =  3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
pS0     =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
pS1     = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
pS2     =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
pS3     = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
pS4     =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
pS5     =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
qS1     = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
qS2     =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
qS3     = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
qS4     =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */

double
__ieee754_acos(double x)
{
  double z,p,q,r,w,s,c,df;
  int32_t hx,ix;
  GET_HIGH_WORD(hx,x);
  ix = hx&0x7fffffff;
  if(ix>=0x3ff00000) {  /* |x| >= 1 */
    u_int32_t lx;

    GET_LOW_WORD(lx,x);
    if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */
      if(hx>0)  return 0.0;             /* acos(1) = 0  */
      else      return pi+2.0*pio2_lo;  /* acos(-1)= pi */
    }
    return (x-x)/(x-x);   /* acos(|x|>1) is NaN */
  }
  if(ix<0x3fe00000) { /* |x| < 0.5 */
    if(ix<=0x3c600000) return pio2_hi+pio2_lo;  /*if|x|<2**-57*/
    z = x*x;
    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
    r = p/q;
    return pio2_hi - (x - (pio2_lo-x*r));
  }
  else  if (hx<0) {   /* x < -0.5 */
    z = (one+x)*0.5;
    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
    s = __ieee754_sqrt(z);
    r = p/q;
    w = r*s-pio2_lo;
    return pi - 2.0*(s+w);
  }
  else {      /* x > 0.5 */
    z = (one-x)*0.5;
    s = __ieee754_sqrt(z);
    df = s;
    SET_LOW_WORD(df,0);
    c  = (z-df*df)/(s+df);
    p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5)))));
    q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4)));
    r = p/q;
    w = r*s+c;
    return 2.0*(df+w);
  }
}