/*

 * Copyright (c) 1998, 2001, Oracle and/or its affiliates. All rights reserved.

 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

 *

 * This code is free software; you can redistribute it and/or modify it

 * under the terms of the GNU General Public License version 2 only, as

 * published by the Free Software Foundation.  Oracle designates this

 * particular file as subject to the "Classpath" exception as provided

 * by Oracle in the LICENSE file that accompanied this code.

 *

 * This code is distributed in the hope that it will be useful, but WITHOUT

 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or

 * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

 * version 2 for more details (a copy is included in the LICENSE file that

 * accompanied this code).

 *

 * You should have received a copy of the GNU General Public License version

 * 2 along with this work; if not, write to the Free Software Foundation,

 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.

 *

 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA

 * or visit www.oracle.com if you need additional information or have any

 * questions.

 */

/* __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=0,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;

}