/* @(#)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 */

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 */

#ifdef __STDC__

	double __ieee754_asin(double x)

#else

	double __ieee754_asin(x)

	double x;

#endif

{

	double t,w,p,q,c,r,s;

	int hx,ix;

	hx = __HI(x);

	ix = hx&0x7fffffff;

	if(ix>= 0x3ff00000) {		/* |x|>= 1 */

	    if(((ix-0x3ff00000)|__LO(x))==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<0x3e400000) {		/* if |x| < 2**-27 */

		if(huge+x>one) return x;/* return x with inexact if x!=0*/

	    } 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;

	    __LO(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;    

}