diff options
Diffstat (limited to 'lib/mlibc/options/ansi/musl-generic-math/asin.c')
| -rw-r--r-- | lib/mlibc/options/ansi/musl-generic-math/asin.c | 107 |
1 files changed, 0 insertions, 107 deletions
diff --git a/lib/mlibc/options/ansi/musl-generic-math/asin.c b/lib/mlibc/options/ansi/musl-generic-math/asin.c deleted file mode 100644 index c926b18..0000000 --- a/lib/mlibc/options/ansi/musl-generic-math/asin.c +++ /dev/null @@ -1,107 +0,0 @@ -/* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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. - * ==================================================== - */ -/* asin(x) - * Method : - * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... - * we approximate asin(x) on [0,0.5] by - * asin(x) = x + x*x^2*R(x^2) - * where - * R(x^2) is a rational approximation of (asin(x)-x)/x^3 - * and its remez error is bounded by - * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) - * - * For x in [0.5,1] - * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) - * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; - * then for x>0.98 - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) - * For x<=0.98, let pio4_hi = pio2_hi/2, then - * f = hi part of s; - * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) - * and - * asin(x) = pi/2 - 2*(s+s*z*R(z)) - * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) - * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) - * - * Special cases: - * if x is NaN, return x itself; - * if |x|>1, return NaN with invalid signal. - * - */ - -#include "libm.h" - -static const double -pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ -pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ -/* coefficients for R(x^2) */ -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 asin(double x) -{ - double z,r,s; - 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) - /* asin(1) = +-pi/2 with inexact */ - return x*pio2_hi + 0x1p-120f; - return 0/(x-x); - } - /* |x| < 0.5 */ - if (ix < 0x3fe00000) { - /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ - if (ix < 0x3e500000 && ix >= 0x00100000) - return x; - return x + x*R(x*x); - } - /* 1 > |x| >= 0.5 */ - z = (1 - fabs(x))*0.5; - s = sqrt(z); - r = R(z); - if (ix >= 0x3fef3333) { /* if |x| > 0.975 */ - x = pio2_hi-(2*(s+s*r)-pio2_lo); - } else { - double f,c; - /* f+c = sqrt(z) */ - f = s; - SET_LOW_WORD(f,0); - c = (z-f*f)/(s+f); - x = 0.5*pio2_hi - (2*s*r - (pio2_lo-2*c) - (0.5*pio2_hi-2*f)); - } - if (hx >> 31) - return -x; - return x; -} |