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2005-03-05 Andreas Tobler <a.tobler@schweiz.ch>
[pf3gnuchains/gcc-fork.git] / libjava / java / lang / e_asin.c
1
2 /* @(#)e_asin.c 5.1 93/09/24 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunPro, a Sun Microsystems, Inc. business.
8  * Permission to use, copy, modify, and distribute this
9  * software is freely granted, provided that this notice 
10  * is preserved.
11  * ====================================================
12  */
13
14 /* __ieee754_asin(x)
15  * Method :                  
16  *      Since  asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
17  *      we approximate asin(x) on [0,0.5] by
18  *              asin(x) = x + x*x^2*R(x^2)
19  *      where
20  *              R(x^2) is a rational approximation of (asin(x)-x)/x^3 
21  *      and its remez error is bounded by
22  *              |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
23  *
24  *      For x in [0.5,1]
25  *              asin(x) = pi/2-2*asin(sqrt((1-x)/2))
26  *      Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
27  *      then for x>0.98
28  *              asin(x) = pi/2 - 2*(s+s*z*R(z))
29  *                      = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
30  *      For x<=0.98, let pio4_hi = pio2_hi/2, then
31  *              f = hi part of s;
32  *              c = sqrt(z) - f = (z-f*f)/(s+f)         ...f+c=sqrt(z)
33  *      and
34  *              asin(x) = pi/2 - 2*(s+s*z*R(z))
35  *                      = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
36  *                      = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
37  *
38  * Special cases:
39  *      if x is NaN, return x itself;
40  *      if |x|>1, return NaN with invalid signal.
41  *
42  */
43
44
45 #include "fdlibm.h"
46
47 #ifndef _DOUBLE_IS_32BITS
48
49 #ifdef __STDC__
50 static const double 
51 #else
52 static double 
53 #endif
54 one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
55 huge =  1.000e+300,
56 pio2_hi =  1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
57 pio2_lo =  6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
58 pio4_hi =  7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
59         /* coefficient for R(x^2) */
60 pS0 =  1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
61 pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
62 pS2 =  2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
63 pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
64 pS4 =  7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
65 pS5 =  3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
66 qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
67 qS2 =  2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
68 qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
69 qS4 =  7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
70
71 #ifdef __STDC__
72         double __ieee754_asin(double x)
73 #else
74         double __ieee754_asin(x)
75         double x;
76 #endif
77 {
78         double t = 0., w, p, q, c, r, s;
79         int32_t hx,ix;
80         GET_HIGH_WORD(hx,x);
81         ix = hx&0x7fffffff;
82         if(ix>= 0x3ff00000) {           /* |x|>= 1 */
83             uint32_t lx;
84             GET_LOW_WORD(lx,x);
85             if(((ix-0x3ff00000)|lx)==0)
86                     /* asin(1)=+-pi/2 with inexact */
87                 return x*pio2_hi+x*pio2_lo;     
88             return (x-x)/(x-x);         /* asin(|x|>1) is NaN */   
89         } else if (ix<0x3fe00000) {     /* |x|<0.5 */
90             if(ix<0x3e400000) {         /* if |x| < 2**-27 */
91                 if(huge+x>one) return x;/* return x with inexact if x!=0*/
92             } else 
93                 t = x*x;
94                 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
95                 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
96                 w = p/q;
97                 return x+x*w;
98         }
99         /* 1> |x|>= 0.5 */
100         w = one-fabs(x);
101         t = w*0.5;
102         p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
103         q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
104         s = __ieee754_sqrt(t);
105         if(ix>=0x3FEF3333) {    /* if |x| > 0.975 */
106             w = p/q;
107             t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
108         } else {
109             w  = s;
110             SET_LOW_WORD(w,0);
111             c  = (t-w*w)/(s+w);
112             r  = p/q;
113             p  = 2.0*s*r-(pio2_lo-2.0*c);
114             q  = pio4_hi-2.0*w;
115             t  = pio4_hi-(p-q);
116         }    
117         if(hx>0) return t; else return -t;    
118 }
119
120 #endif /* defined(_DOUBLE_IS_32BITS) */