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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 acos = __acos
/* INDENT OFF */
/*
* acos(x)
* Method :
* acos(x) = pi/2 - asin(x)
* acos(-x) = pi/2 + asin(x)
* For |x|<=0.5
* acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c)
* For x>0.5
* acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2)))
* = 2asin(sqrt((1-x)/2))
* = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z)
* = 2f + (2c + 2s*z*R(z))
* where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term
* for f so that f+c ~ sqrt(z).
* For x<-0.5
* acos(x) = pi - 2asin(sqrt((1-|x|)/2))
* = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z)
*
* Special cases:
* if x is NaN, return x itself;
* if |x|>1, return NaN with invalid signal.
*
* Function needed: sqrt
*/
/* INDENT ON */
#include "libm_synonyms.h" /* __acos, __sqrt, __isnan */
#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 */
/* pi */ 3.14159265358979311600e+00, /* 400921FB, 54442D18 */
/* pio2_hi */ 1.57079632679489655800e+00, /* 3FF921FB, 54442D18 */
/* pio2_lo */ 6.12323399573676603587e-17, /* 3C91A626, 33145C07 */
/* 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 pi xxx[1]
#define pio2_hi xxx[2]
#define pio2_lo xxx[3]
#define pS0 xxx[4]
#define pS1 xxx[5]
#define pS2 xxx[6]
#define pS3 xxx[7]
#define pS4 xxx[8]
#define pS5 xxx[9]
#define qS1 xxx[10]
#define qS2 xxx[11]
#define qS3 xxx[12]
#define qS4 xxx[13]
/* INDENT ON */
double
acos(double x) {
double z, p, q, r, w, s, c, df;
int hx, ix;
hx = ((int *) &x)[HIWORD];
ix = hx & 0x7fffffff;
if (ix >= 0x3ff00000) { /* |x| >= 1 */
if (((ix - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) {
/* |x| == 1 */
if (hx > 0) /* acos(1) = 0 */
return (0.0);
else /* acos(-1) = pi */
return (pi + 2.0 * 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); /* acos(|x|>1) is NaN */
#endif
else
return (_SVID_libm_err(x, x, 1));
}
if (ix < 0x3fe00000) { /* |x| < 0.5 */
if (ix <= 0x3c600000)
return (pio2_hi + pio2_lo); /* if |x| < 2**-57 */
z = x * x;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
return (pio2_hi - (x - (pio2_lo - x * r)));
} else if (hx < 0) {
/* x < -0.5 */
z = (one + x) * 0.5;
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
s = sqrt(z);
r = p / q;
w = r * s - pio2_lo;
return (pi - 2.0 * (s + w));
} else {
/* x > 0.5 */
z = (one - x) * 0.5;
s = sqrt(z);
df = s;
((int *) &df)[LOWORD] = 0;
c = (z - df * df) / (s + df);
p = z * (pS0 + z * (pS1 + z * (pS2 + z * (pS3 +
z * (pS4 + z * pS5)))));
q = one + z * (qS1 + z * (qS2 + z * (qS3 + z * qS4)));
r = p / q;
w = r * s + c;
return (2.0 * (df + w));
}
}
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