prime/src/Runtime/e_acos.c

/* @(#)e_acos.c 1.2 95/01/04 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

/* __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: sqrt
 */

#include "fdlibm.h"

#ifdef __STDC__
static const double
#else
static double
#endif
    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 */

#ifdef __STDC__
double __ieee754_acos(double x)
#else
double __ieee754_acos(x)
double x;
#endif
{
  double z, p, q, r, w, s, c, df;
  _INT32 hx, ix;
  hx = __HI(x);
  ix = hx & 0x7fffffff;
  if (ix >= 0x3ff00000) {                     /* |x| >= 1 */
    if (((ix - 0x3ff00000) | __LO(x)) == 0) { /* |x|==1 */
      if (hx > 0)
        return 0.0; /* acos(1) = 0  */
      else
        return pi + 2.0 * pio2_lo; /* acos(-1)= pi */
    }
    return NAN; /* 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 = 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 = sqrt(z);
    df = s;
    __LO(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);
  }
}