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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 | |
57 | static const double\r | |
58 | one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */\r | |
59 | huge = 1.000e+300,\r | |
60 | pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */\r | |
61 | pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */\r | |
62 | pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */\r | |
63 | /* coefficient for R(x^2) */\r | |
64 | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */\r | |
65 | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */\r | |
66 | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */\r | |
67 | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */\r | |
68 | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */\r | |
69 | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */\r | |
70 | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */\r | |
71 | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */\r | |
72 | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */\r | |
73 | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */\r | |
74 | \r | |
75 | double\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 |