forked from xuos/xiuos
145 lines
4.4 KiB
C
145 lines
4.4 KiB
C
/* Copyright JS Foundation and other contributors, http://js.foundation
|
|
*
|
|
* Licensed under the Apache License, Version 2.0 (the "License");
|
|
* you may not use this file except in compliance with the License.
|
|
* You may obtain a copy of the License at
|
|
*
|
|
* http://www.apache.org/licenses/LICENSE-2.0
|
|
*
|
|
* Unless required by applicable law or agreed to in writing, software
|
|
* distributed under the License is distributed on an "AS IS" BASIS
|
|
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
|
|
* See the License for the specific language governing permissions and
|
|
* limitations under the License.
|
|
*
|
|
* This file is based on work under the following copyright and permission
|
|
* notice:
|
|
*
|
|
* 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.
|
|
*
|
|
* @(#)e_acos.c 1.3 95/01/18
|
|
*/
|
|
|
|
#include "jerry-math-internal.h"
|
|
|
|
/* 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
|
|
*/
|
|
|
|
#define one 1.00000000000000000000e+00 /* 0x3FF00000, 0x00000000 */
|
|
#define pi 3.14159265358979311600e+00 /* 0x400921FB, 0x54442D18 */
|
|
#define pio2_hi 1.57079632679489655800e+00 /* 0x3FF921FB, 0x54442D18 */
|
|
#define pio2_lo 6.12323399573676603587e-17 /* 0x3C91A626, 0x33145C07 */
|
|
#define pS0 1.66666666666666657415e-01 /* 0x3FC55555, 0x55555555 */
|
|
#define pS1 -3.25565818622400915405e-01 /* 0xBFD4D612, 0x03EB6F7D */
|
|
#define pS2 2.01212532134862925881e-01 /* 0x3FC9C155, 0x0E884455 */
|
|
#define pS3 -4.00555345006794114027e-02 /* 0xBFA48228, 0xB5688F3B */
|
|
#define pS4 7.91534994289814532176e-04 /* 0x3F49EFE0, 0x7501B288 */
|
|
#define pS5 3.47933107596021167570e-05 /* 0x3F023DE1, 0x0DFDF709 */
|
|
#define qS1 -2.40339491173441421878e+00 /* 0xC0033A27, 0x1C8A2D4B */
|
|
#define qS2 2.02094576023350569471e+00 /* 0x40002AE5, 0x9C598AC8 */
|
|
#define qS3 -6.88283971605453293030e-01 /* 0xBFE6066C, 0x1B8D0159 */
|
|
#define qS4 7.70381505559019352791e-02 /* 0x3FB3B8C5, 0xB12E9282 */
|
|
|
|
double
|
|
acos (double x)
|
|
{
|
|
double z, p, q, r, w, s, c;
|
|
int hx, ix;
|
|
|
|
hx = __HI (x);
|
|
ix = hx & 0x7fffffff;
|
|
if (ix >= 0x3ff00000) /* |x| >= 1 */
|
|
{
|
|
if (((ix - 0x3ff00000) | __LO (x)) == 0) /* |x| == 1 */
|
|
{
|
|
if (hx > 0) /* acos(1) = 0 */
|
|
{
|
|
return 0.0;
|
|
}
|
|
else /* acos(-1) = pi */
|
|
{
|
|
return pi + 2.0 * pio2_lo;
|
|
}
|
|
}
|
|
return NAN; /* acos(|x|>1) is NaN */
|
|
}
|
|
if (ix < 0x3fe00000) /* |x| < 0.5 */
|
|
{
|
|
if (ix <= 0x3c600000) /* if |x| < 2**-57 */
|
|
{
|
|
return pio2_hi + pio2_lo;
|
|
}
|
|
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 */
|
|
{
|
|
double_accessor df;
|
|
z = (one - x) * 0.5;
|
|
s = sqrt (z);
|
|
df.dbl = s;
|
|
df.as_int.lo = 0;
|
|
c = (z - df.dbl * df.dbl) / (s + df.dbl);
|
|
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.dbl + w);
|
|
}
|
|
} /* acos */
|
|
|
|
#undef one
|
|
#undef pi
|
|
#undef pio2_hi
|
|
#undef pio2_lo
|
|
#undef pS0
|
|
#undef pS1
|
|
#undef pS2
|
|
#undef pS3
|
|
#undef pS4
|
|
#undef pS5
|
|
#undef qS1
|
|
#undef qS2
|
|
#undef qS3
|
|
#undef qS4
|