| Index: fusl/src/math/acos.c
|
| diff --git a/fusl/src/math/acos.c b/fusl/src/math/acos.c
|
| new file mode 100644
|
| index 0000000000000000000000000000000000000000..ea9c87bf087809f9a6b1fa6a2ed2f065d8184f72
|
| --- /dev/null
|
| +++ b/fusl/src/math/acos.c
|
| @@ -0,0 +1,101 @@
|
| +/* 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"
|
| +
|
| +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);
|
| +}
|
|
|