/* @(#)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.
 *
 */


#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif

#ifndef __have_fpu_asin

double __ieee754_asin(double x)
{
	double t, w, p, q, c, r, s;
	int32_t hx, ix;

	static const double one = 1.00000000000000000000e+00;		/* 0x3FF00000, 0x00000000 */
	static const double hugeval = 1.000e+300;
	static const double pio2_hi = 1.57079632679489655800e+00;	/* 0x3FF921FB, 0x54442D18 */
	static const double pio2_lo = 6.12323399573676603587e-17;	/* 0x3C91A626, 0x33145C07 */
	static const double pio4_hi = 7.85398163397448278999e-01;	/* 0x3FE921FB, 0x54442D18 */
	/* coefficient for R(x^2) */
	static const double pS0 = 1.66666666666666657415e-01;	/* 0x3FC55555, 0x55555555 */
	static const double pS1 = -3.25565818622400915405e-01;	/* 0xBFD4D612, 0x03EB6F7D */
	static const double pS2 = 2.01212532134862925881e-01;	/* 0x3FC9C155, 0x0E884455 */
	static const double pS3 = -4.00555345006794114027e-02;	/* 0xBFA48228, 0xB5688F3B */
	static const double pS4 = 7.91534994289814532176e-04;	/* 0x3F49EFE0, 0x7501B288 */
	static const double pS5 = 3.47933107596021167570e-05;	/* 0x3F023DE1, 0x0DFDF709 */
	static const double qS1 = -2.40339491173441421878e+00;	/* 0xC0033A27, 0x1C8A2D4B */
	static const double qS2 = 2.02094576023350569471e+00;	/* 0x40002AE5, 0x9C598AC8 */
	static const double qS3 = -6.88283971605453293030e-01;	/* 0xBFE6066C, 0x1B8D0159 */
	static const double qS4 = 7.70381505559019352791e-02;	/* 0x3FB3B8C5, 0xB12E9282 */

	GET_HIGH_WORD(hx, x);
	ix = hx & IC(0x7fffffff);
	if (ix >= IC(0x3ff00000))
	{									/* |x|>= 1 */
		uint32_t lx;

		GET_LOW_WORD(lx, x);
		if (((ix - IC(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 < IC(0x3fe00000))
	{									/* |x|<0.5 */
		if (ix < IC(0x3e400000))
		{								/* if |x| < 2**-27 */
			if (hugeval + 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 - __ieee754_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 = __ieee754_sqrt(t);
	if (ix >= IC(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;
	return -t;
}

#endif

/* wrapper asin */
double __asin(double x)
{
	if (_LIB_VERSION != _IEEE_ && isgreater(__ieee754_fabs(x), 1.0))
	{
		/* asin(|x|>1) */
		feraiseexcept(FE_INVALID);
		return __kernel_standard(x, x, __builtin_nan(""), KMATHERR_ASIN);
	}

	return __ieee754_asin(x);
}

__typeof(__asin) asin __attribute__((weak, alias("__asin")));
#ifdef __NO_LONG_DOUBLE_MATH
__typeof(__asinl) __asinl __attribute__((alias("__asin")));
__typeof(__asinl) asinl __attribute__((weak, alias("__asin")));
#endif
