Annotation of src/lib/libm/src/e_asin.c, Revision 1.6
1.1 jtc 1: /* @(#)e_asin.c 5.1 93/09/24 */
2: /*
3: * ====================================================
4: * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5: *
6: * Developed at SunPro, a Sun Microsystems, Inc. business.
7: * Permission to use, copy, modify, and distribute this
8: * software is freely granted, provided that this notice
9: * is preserved.
10: * ====================================================
11: */
1.3 jtc 12:
13: #ifndef lint
1.6 ! jtc 14: static char rcsid[] = "$Id: e_asin.c,v 1.5 1994/08/10 20:30:33 jtc Exp $";
1.3 jtc 15: #endif
1.1 jtc 16:
17: /* __ieee754_asin(x)
18: * Method :
19: * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...
20: * we approximate asin(x) on [0,0.5] by
21: * asin(x) = x + x*x^2*R(x^2)
22: * where
23: * R(x^2) is a rational approximation of (asin(x)-x)/x^3
24: * and its remez error is bounded by
25: * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)
26: *
27: * For x in [0.5,1]
28: * asin(x) = pi/2-2*asin(sqrt((1-x)/2))
29: * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;
30: * then for x>0.98
31: * asin(x) = pi/2 - 2*(s+s*z*R(z))
32: * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)
33: * For x<=0.98, let pio4_hi = pio2_hi/2, then
34: * f = hi part of s;
35: * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)
36: * and
37: * asin(x) = pi/2 - 2*(s+s*z*R(z))
38: * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)
39: * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))
40: *
41: * Special cases:
42: * if x is NaN, return x itself;
43: * if |x|>1, return NaN with invalid signal.
44: *
45: */
46:
47:
1.5 jtc 48: #include "math.h"
49: #include "math_private.h"
1.1 jtc 50:
51: #ifdef __STDC__
52: static const double
53: #else
54: static double
55: #endif
56: one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
57: huge = 1.000e+300,
58: pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */
59: pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */
60: pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */
61: /* coefficient for R(x^2) */
62: pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */
63: pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */
64: pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */
65: pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */
66: pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */
67: pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */
68: qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */
69: qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */
70: qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */
71: qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */
72:
73: #ifdef __STDC__
74: double __ieee754_asin(double x)
75: #else
76: double __ieee754_asin(x)
77: double x;
78: #endif
79: {
80: double t,w,p,q,c,r,s;
1.6 ! jtc 81: int32_t hx,ix;
1.5 jtc 82: GET_HIGH_WORD(hx,x);
1.1 jtc 83: ix = hx&0x7fffffff;
84: if(ix>= 0x3ff00000) { /* |x|>= 1 */
1.6 ! jtc 85: u_int32_t lx;
1.5 jtc 86: GET_LOW_WORD(lx,x);
87: if(((ix-0x3ff00000)|lx)==0)
1.1 jtc 88: /* asin(1)=+-pi/2 with inexact */
89: return x*pio2_hi+x*pio2_lo;
90: return (x-x)/(x-x); /* asin(|x|>1) is NaN */
91: } else if (ix<0x3fe00000) { /* |x|<0.5 */
92: if(ix<0x3e400000) { /* if |x| < 2**-27 */
93: if(huge+x>one) return x;/* return x with inexact if x!=0*/
94: } else
95: t = x*x;
96: p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
97: q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
98: w = p/q;
99: return x+x*w;
100: }
101: /* 1> |x|>= 0.5 */
102: w = one-fabs(x);
103: t = w*0.5;
104: p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));
105: q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));
106: s = sqrt(t);
107: if(ix>=0x3FEF3333) { /* if |x| > 0.975 */
108: w = p/q;
109: t = pio2_hi-(2.0*(s+s*w)-pio2_lo);
110: } else {
111: w = s;
1.5 jtc 112: SET_LOW_WORD(w,0);
1.1 jtc 113: c = (t-w*w)/(s+w);
114: r = p/q;
115: p = 2.0*s*r-(pio2_lo-2.0*c);
116: q = pio4_hi-2.0*w;
117: t = pio4_hi-(p-q);
118: }
119: if(hx>0) return t; else return -t;
120: }
CVSweb <webmaster@jp.NetBSD.org>