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e_acos.c
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e_acos.c
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/* @(#)e_acos.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, 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
*/
#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif
#ifndef __have_fpu_acos
double __ieee754_acos(double x)
{
double z, p, q, r, w, s, c, df;
int32_t hx, ix;
static const double one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */
static const double pi = 3.14159265358979311600e+00; /* 0x400921FB, 0x54442D18 */
static const double pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */
static const double pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */
static const double pS0 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */
static const double pS1 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */
static const double pS2 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */
static const double pS3 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */
static const double pS4 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */
static const double pS5 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */
static const double qS1 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */
static const double qS2 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */
static const double qS3 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */
static const double qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
GET_HIGH_WORD(hx, x);
ix = hx & IC(0x7fffffff);
if (ix >= IC(0x3ff00000))
{ /* |x| >= 1 */
uint32_t lx;
GET_LOW_WORD(lx, x);
if (((ix - IC(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 < IC(0x3fe00000))
{ /* |x| < 0.5 */
if (ix <= IC(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);
}
}
#endif
/* wrapper acos */
double __acos(double x)
{
if (_LIB_VERSION != _IEEE_ && isgreater(__ieee754_fabs(x), 1.0))
{
/* acos(|x|>1) */
feraiseexcept(FE_INVALID);
return __kernel_standard(x, x, __builtin_nan(""), KMATHERR_ACOS);
}
return __ieee754_acos(x);
}
__typeof(__acos) acos __attribute__((weak, alias("__acos")));
#ifdef __NO_LONG_DOUBLE_MATH
__typeof(__acosl) __acosl __attribute__((alias("__acos")));
__typeof(__acosl) acosl __attribute__((weak, alias("__acos")));
#endif