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/* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */
/*
* ====================================================
* 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.
* ====================================================
*/
/* 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 "libm.h" // for GET_HIGH_WORD, GET_LOW_WORD, SET_LOW_WORD
#include <math.h> // for sqrt, acos, double_t
#include <stdint.h> // for uint32_t
static const double 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 */
static double R(double z)
{
double_t p, q;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 + z * (pS4 + z * pS5)))));
q = 1.0 + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
return p / q;
}
double acos(double x)
{
double z, w, s, c, df;
uint32_t hx, ix;
GET_HIGH_WORD(hx, x);
ix = hx & 0x7fffffff;
/* |x| >= 1 or nan */
if (ix >= 0x3ff00000) {
uint32_t lx;
GET_LOW_WORD(lx, x);
if ((ix - 0x3ff00000 | lx) == 0) {
/* acos(1)=0, acos(-1)=pi */
if (hx >> 31)
return 2 * pio2_hi + 0x1p-120f;
return 0;
}
return 0 / (x - x);
}
/* |x| < 0.5 */
if (ix < 0x3fe00000) {
if (ix <= 0x3c600000) /* |x| < 2**-57 */
return pio2_hi + 0x1p-120f;
return pio2_hi - (x - (pio2_lo - x * R(x * x)));
}
/* x < -0.5 */
if (hx >> 31) {
z = (1.0 + x) * 0.5;
s = sqrt(z);
w = R(z) * s - pio2_lo;
return 2 * (pio2_hi - (s + w));
}
/* x > 0.5 */
z = (1.0 - x) * 0.5;
s = sqrt(z);
df = s;
SET_LOW_WORD(df, 0);
c = (z - df * df) / (s + df);
w = R(z) * s + c;
return 2 * (df + w);
}
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