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2aa62f2b 1/* @(#)e_asin.c 5.1 93/09/24 */\r
2/*\r
3 * ====================================================\r
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.\r
5 *\r
6 * Developed at SunPro, a Sun Microsystems, Inc. business.\r
7 * Permission to use, copy, modify, and distribute this\r
8 * software is freely granted, provided that this notice\r
9 * is preserved.\r
10 * ====================================================\r
11 */\r
12#include <LibConfig.h>\r
13#include <sys/EfiCdefs.h>\r
14#if defined(LIBM_SCCS) && !defined(lint)\r
15__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $");\r
16#endif\r
17\r
18#if defined(_MSC_VER) /* Handle Microsoft VC++ compiler specifics. */\r
19// C4723: potential divide by zero.\r
20#pragma warning ( disable : 4723 )\r
21#endif\r
22\r
23/* __ieee754_asin(x)\r
24 * Method :\r
25 * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ...\r
26 * we approximate asin(x) on [0,0.5] by\r
27 * asin(x) = x + x*x^2*R(x^2)\r
28 * where\r
29 * R(x^2) is a rational approximation of (asin(x)-x)/x^3\r
30 * and its remez error is bounded by\r
31 * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75)\r
32 *\r
33 * For x in [0.5,1]\r
34 * asin(x) = pi/2-2*asin(sqrt((1-x)/2))\r
35 * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2;\r
36 * then for x>0.98\r
37 * asin(x) = pi/2 - 2*(s+s*z*R(z))\r
38 * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo)\r
39 * For x<=0.98, let pio4_hi = pio2_hi/2, then\r
40 * f = hi part of s;\r
41 * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z)\r
42 * and\r
43 * asin(x) = pi/2 - 2*(s+s*z*R(z))\r
44 * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo)\r
45 * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c))\r
46 *\r
47 * Special cases:\r
48 * if x is NaN, return x itself;\r
49 * if |x|>1, return NaN with invalid signal.\r
50 *\r
51 */\r
52\r
53\r
54#include "math.h"\r
55#include "math_private.h"\r
56\r
57static const double\r
58one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */\r
59huge = 1.000e+300,\r
60pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */\r
61pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */\r
62pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */\r
63 /* coefficient for R(x^2) */\r
64pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */\r
65pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */\r
66pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */\r
67pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */\r
68pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */\r
69pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */\r
70qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */\r
71qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */\r
72qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */\r
73qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */\r
74\r
75double\r
76__ieee754_asin(double x)\r
77{\r
78 double t,w,p,q,c,r,s;\r
79 int32_t hx,ix;\r
80\r
81 t = 0;\r
82 GET_HIGH_WORD(hx,x);\r
83 ix = hx&0x7fffffff;\r
84 if(ix>= 0x3ff00000) { /* |x|>= 1 */\r
85 u_int32_t lx;\r
86 GET_LOW_WORD(lx,x);\r
87 if(((ix-0x3ff00000)|lx)==0)\r
88 /* asin(1)=+-pi/2 with inexact */\r
89 return x*pio2_hi+x*pio2_lo;\r
90 return (x-x)/(x-x); /* asin(|x|>1) is NaN */\r
91 } else if (ix<0x3fe00000) { /* |x|<0.5 */\r
92 if(ix<0x3e400000) { /* if |x| < 2**-27 */\r
93 if(huge+x>one) return x;/* return x with inexact if x!=0*/\r
94 } else\r
95 t = x*x;\r
96 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));\r
97 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));\r
98 w = p/q;\r
99 return x+x*w;\r
100 }\r
101 /* 1> |x|>= 0.5 */\r
102 w = one-fabs(x);\r
103 t = w*0.5;\r
104 p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5)))));\r
105 q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4)));\r
106 s = __ieee754_sqrt(t);\r
107 if(ix>=0x3FEF3333) { /* if |x| > 0.975 */\r
108 w = p/q;\r
109 t = pio2_hi-(2.0*(s+s*w)-pio2_lo);\r
110 } else {\r
111 w = s;\r
112 SET_LOW_WORD(w,0);\r
113 c = (t-w*w)/(s+w);\r
114 r = p/q;\r
115 p = 2.0*s*r-(pio2_lo-2.0*c);\r
116 q = pio4_hi-2.0*w;\r
117 t = pio4_hi-(p-q);\r
118 }\r
119 if(hx>0) return t; else return -t;\r
120}\r