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/*
* 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);
}
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