DXR is a code search and navigation tool aimed at making sense of large projects. It supports full-text and regex searches as well as structural queries.

#### Mercurial (d38398e5144e)

Line Code
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112
``````
``````/* @(#)e_asin.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.
`````` * ====================================================
`````` */
``````
``````//#include <sys/cdefs.h>
``````//__FBSDID("\$FreeBSD\$");
``````
``````/* __ieee754_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 <float.h>
``````
``````#include "math_private.h"
``````
``````static const double
``````one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
``````huge =  1.000e+300,
``````pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
``````pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
``````pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
``````	/* coefficient 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 */
``````
``````double
``````__ieee754_asin(double x)
``````{
``````	double t=0.0,w,p,q,c,r,s;
``````	int32_t hx,ix;
``````	GET_HIGH_WORD(hx,x);
``````	ix = hx&0x7fffffff;
``````	if(ix>= 0x3ff00000) {		/* |x|>= 1 */
``````	    u_int32_t lx;
``````	    GET_LOW_WORD(lx,x);
``````	    if(((ix-0x3ff00000)|lx)==0)
``````		    /* asin(1)=+-pi/2 with inexact */
``````		return x*pio2_hi+x*pio2_lo;
``````	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
``````	} else if (ix<0x3fe00000) {	/* |x|<0.5 */
``````	    if(ix<0x3e500000) {		/* if |x| < 2**-26 */
``````		if(huge+x>one) return x;/* return x with inexact if x!=0*/
``````	    }
``````	    t = x*x;
``````	    p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
``````	    q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
``````	    w = p/q;
``````	    return x+x*w;
``````	}
``````	/* 1> |x|>= 0.5 */
``````	w = one-fabs(x);
``````	t = w*0.5;
``````	p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
``````	q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
``````	s = sqrt(t);
``````	if(ix>=0x3FEF3333) { 	/* if |x| > 0.975 */
``````	    w = p/q;
``````	    t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
``````	} else {
``````	    w  = s;
``````	    SET_LOW_WORD(w,0);
``````	    c  = (t-w*w)/(s+w);
``````	    r  = p/q;
``````	    p  = 2.0*s*r-(pio2_lo-2.0*c);
``````	    q  = pio4_hi-2.0*w;
``````	    t  = pio4_hi-(p-q);
``````	}
``````	if(hx>0) return t; else return -t;
``````}
``````