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  • Raymond Toy's avatar
    3b4f3977
    Fix compiler warning about else · 3b4f3977
    Raymond Toy authored
    Add braces around the else clause that's indented as if it were part
    of the else clause.  Inspection of the algorithm indicates that this
    is probably the intended code and in this case doesn't change what
    gets executed because the following statements would have been anyway.
    
    Also verified a few random values that `(asin x)` and `(asin (float x
    1w0))` produce the same values.  Only need to test 2^-27 <= x < 0.5.
    3b4f3977
    History
    Fix compiler warning about else
    Raymond Toy authored
    Add braces around the else clause that's indented as if it were part
    of the else clause.  Inspection of the algorithm indicates that this
    is probably the intended code and in this case doesn't change what
    gets executed because the following statements would have been anyway.
    
    Also verified a few random values that `(asin x)` and `(asin (float x
    1w0))` produce the same values.  Only need to test 2^-27 <= x < 0.5.
e_asin.c 3.73 KiB

/* @(#)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.
 * ====================================================
 */

/* __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 "fdlibm.h"

#ifdef __STDC__
static const double 
#else
static double 
#endif
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
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 */

#ifdef __STDC__
	double __ieee754_asin(double x)
#else
	double __ieee754_asin(x)
	double x;
#endif
{
	double t = 0;
        double w,p,q,c,r,s;
	int hx,ix;
	union { int i[2]; double d; } ux;

        ux.d = x;
	hx = ux.i[HIWORD];
	ix = hx&0x7fffffff;
	if(ix>= 0x3ff00000) {		/* |x|>= 1 */
	    if(((ix-0x3ff00000)|ux.i[LOWORD])==0)
		    /* asin(1)=+-pi/2 with inexact */
		return x*pio2_hi+x*pio2_lo;	
            /* asin(|x|>1) is NaN */
	    return fdlibm_setexception(x, FDLIBM_INVALID);
	} else if (ix<0x3fe00000) {	/* |x|<0.5 */
	    if(ix<0x3e400000) {		/* if |x| < 2**-27 */
                /* return x inexact except 0 */
                if (x != 0) {
                    fdlibm_setexception(x, FDLIBM_INEXACT);
                }

                return x;
	    } else {
		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;
            ux.d = w;
	    ux.i[LOWORD] = 0;
            w = ux.d;
	    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;    
}