/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */

/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak __asin = asin

/* INDENT OFF */
/*
 * 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.
 *
 */
/* INDENT ON */

#include "libm_protos.h"        /* _SVID_libm_error */
#include "libm_macros.h"
#include <math.h>

/* INDENT OFF */
static const double xxx[] = {
/* one */        1.00000000000000000000e+00,    /* 3FF00000, 00000000 */
/* huge */       1.000e+300,
/* pio2_hi */    1.57079632679489655800e+00,    /* 3FF921FB, 54442D18 */
/* pio2_lo */    6.12323399573676603587e-17,    /* 3C91A626, 33145C07 */
/* pio4_hi */    7.85398163397448278999e-01,    /* 3FE921FB, 54442D18 */
/* coefficient for R(x^2) */
/* pS0 */        1.66666666666666657415e-01,    /* 3FC55555, 55555555 */
/* pS1 */       -3.25565818622400915405e-01,    /* BFD4D612, 03EB6F7D */
/* pS2 */        2.01212532134862925881e-01,    /* 3FC9C155, 0E884455 */
/* pS3 */       -4.00555345006794114027e-02,    /* BFA48228, B5688F3B */
/* pS4 */        7.91534994289814532176e-04,    /* 3F49EFE0, 7501B288 */
/* pS5 */        3.47933107596021167570e-05,    /* 3F023DE1, 0DFDF709 */
/* qS1 */       -2.40339491173441421878e+00,    /* C0033A27, 1C8A2D4B */
/* qS2 */        2.02094576023350569471e+00,    /* 40002AE5, 9C598AC8 */
/* qS3 */       -6.88283971605453293030e-01,    /* BFE6066C, 1B8D0159 */
/* qS4 */        7.70381505559019352791e-02     /* 3FB3B8C5, B12E9282 */
};
#define one     xxx[0]
#define huge    xxx[1]
#define pio2_hi xxx[2]
#define pio2_lo xxx[3]
#define pio4_hi xxx[4]
#define pS0     xxx[5]
#define pS1     xxx[6]
#define pS2     xxx[7]
#define pS3     xxx[8]
#define pS4     xxx[9]
#define pS5     xxx[10]
#define qS1     xxx[11]
#define qS2     xxx[12]
#define qS3     xxx[13]
#define qS4     xxx[14]
/* INDENT ON */

double
asin(double x) {
        double t, w, p, q, c, r, s;
        int hx, ix, i;

        hx = ((int *) &x)[HIWORD];
        ix = hx & 0x7fffffff;
        if (ix >= 0x3ff00000) { /* |x| >= 1 */
                if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0)
                        /* asin(1)=+-pi/2 with inexact */
                        return (x * pio2_hi + x * pio2_lo);
                else if (isnan(x))
#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
                        return (ix >= 0x7ff80000 ? x : (x - x) / (x - x));
                        /* assumes sparc-like QNaN */
#else
                        return (x - x) / (x - x);       /* asin(|x|>1) is NaN */
#endif
                else
                        return (_SVID_libm_err(x, x, 2));
        } else if (ix < 0x3fe00000) {   /* |x| < 0.5 */
                if (ix < 0x3e400000) {  /* if |x| < 2**-27 */
                        if ((i = (int) x) == 0)
                                /* return x with inexact if x != 0 */
                                return (x);
                }
                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;
                ((int *) &w)[LOWORD] = 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);
        }
        return (hx > 0 ? t : -t);
}