1
/* -*- Mode: C; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 4 -*-
3
* ***** BEGIN LICENSE BLOCK *****
4
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
6
* The contents of this file are subject to the Mozilla Public License Version
7
* 1.1 (the "License"); you may not use this file except in compliance with
8
* the License. You may obtain a copy of the License at
9
* http://www.mozilla.org/MPL/
11
* Software distributed under the License is distributed on an "AS IS" basis,
12
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
13
* for the specific language governing rights and limitations under the
16
* The Original Code is Mozilla Communicator client code, released
19
* The Initial Developer of the Original Code is
20
* Sun Microsystems, Inc.
21
* Portions created by the Initial Developer are Copyright (C) 1998
22
* the Initial Developer. All Rights Reserved.
26
* Alternatively, the contents of this file may be used under the terms of
27
* either of the GNU General Public License Version 2 or later (the "GPL"),
28
* or the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
29
* in which case the provisions of the GPL or the LGPL are applicable instead
30
* of those above. If you wish to allow use of your version of this file only
31
* under the terms of either the GPL or the LGPL, and not to allow others to
32
* use your version of this file under the terms of the MPL, indicate your
33
* decision by deleting the provisions above and replace them with the notice
34
* and other provisions required by the GPL or the LGPL. If you do not delete
35
* the provisions above, a recipient may use your version of this file under
36
* the terms of any one of the MPL, the GPL or the LGPL.
38
* ***** END LICENSE BLOCK ***** */
40
/* @(#)e_asin.c 1.3 95/01/18 */
42
* ====================================================
43
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
45
* Developed at SunSoft, a Sun Microsystems, Inc. business.
46
* Permission to use, copy, modify, and distribute this
47
* software is freely granted, provided that this notice
49
* ====================================================
54
* Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
55
* we approximate asin(x) on [0,0.5] by
56
* asin(x) = x + x*x^2*R(x^2)
58
* R(x^2) is a rational approximation of (asin(x)-x)/x^3
59
* and its remez error is bounded by
60
* |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
63
* asin(x) = pi/2-2*asin(sqrt((1-x)/2))
64
* Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
66
* asin(x) = pi/2 - 2*(s+s*z*R(z))
67
* = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
68
* For x<=0.98, let pio4_hi = pio2_hi/2, then
70
* c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
72
* asin(x) = pi/2 - 2*(s+s*z*R(z))
73
* = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
74
* = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
77
* if x is NaN, return x itself;
78
* if |x|>1, return NaN with invalid signal.
90
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
91
really_big = 1.000e+300,
92
pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
93
pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
94
pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
95
/* coefficient for R(x^2) */
96
pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
97
pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
98
pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
99
pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
100
pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
101
pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
102
qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
103
qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
104
qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
105
qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
108
double __ieee754_asin(double x)
110
double __ieee754_asin(x)
115
double w,t,p,q,c,r,s;
121
if(ix>= 0x3ff00000) { /* |x|>= 1 */
122
if(((ix-0x3ff00000)|__LO(u))==0)
123
/* asin(1)=+-pi/2 with inexact */
124
return x*pio2_hi+x*pio2_lo;
125
return (x-x)/(x-x); /* asin(|x|>1) is NaN */
126
} else if (ix<0x3fe00000) { /* |x|<0.5 */
127
if(ix<0x3e400000) { /* if |x| < 2**-27 */
128
if(really_big+x>one) return x;/* return x with inexact if x!=0*/
131
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
132
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
139
p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
140
q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
142
if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
144
t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
151
p = 2.0*s*r-(pio2_lo-2.0*c);
155
if(hx>0) return t; else return -t;
added
removed
src/extension/script/js/fdlibm/e_asin.c
