/src/mozilla-central/modules/fdlibm/src/e_acos.cpp
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1 | | |
2 | | /* @(#)e_acos.c 1.3 95/01/18 */ |
3 | | /* |
4 | | * ==================================================== |
5 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
6 | | * |
7 | | * Developed at SunSoft, 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 | | //#include <sys/cdefs.h> |
15 | | //__FBSDID("$FreeBSD$"); |
16 | | |
17 | | /* __ieee754_acos(x) |
18 | | * Method : |
19 | | * acos(x) = pi/2 - asin(x) |
20 | | * acos(-x) = pi/2 + asin(x) |
21 | | * For |x|<=0.5 |
22 | | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
23 | | * For x>0.5 |
24 | | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
25 | | * = 2asin(sqrt((1-x)/2)) |
26 | | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
27 | | * = 2f + (2c + 2s*z*R(z)) |
28 | | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
29 | | * for f so that f+c ~ sqrt(z). |
30 | | * For x<-0.5 |
31 | | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
32 | | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
33 | | * |
34 | | * Special cases: |
35 | | * if x is NaN, return x itself; |
36 | | * if |x|>1, return NaN with invalid signal. |
37 | | * |
38 | | * Function needed: sqrt |
39 | | */ |
40 | | |
41 | | #include <float.h> |
42 | | |
43 | | #include "math_private.h" |
44 | | |
45 | | static const double |
46 | | one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
47 | | pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
48 | | pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
49 | | static volatile double |
50 | | pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
51 | | static const double |
52 | | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
53 | | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
54 | | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
55 | | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
56 | | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
57 | | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
58 | | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
59 | | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
60 | | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
61 | | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
62 | | |
63 | | double |
64 | | __ieee754_acos(double x) |
65 | 0 | { |
66 | 0 | double z,p,q,r,w,s,c,df; |
67 | 0 | int32_t hx,ix; |
68 | 0 | GET_HIGH_WORD(hx,x); |
69 | 0 | ix = hx&0x7fffffff; |
70 | 0 | if(ix>=0x3ff00000) { /* |x| >= 1 */ |
71 | 0 | u_int32_t lx; |
72 | 0 | GET_LOW_WORD(lx,x); |
73 | 0 | if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ |
74 | 0 | if(hx>0) return 0.0; /* acos(1) = 0 */ |
75 | 0 | else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
76 | 0 | } |
77 | 0 | return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
78 | 0 | } |
79 | 0 | if(ix<0x3fe00000) { /* |x| < 0.5 */ |
80 | 0 | if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
81 | 0 | z = x*x; |
82 | 0 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
83 | 0 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
84 | 0 | r = p/q; |
85 | 0 | return pio2_hi - (x - (pio2_lo-x*r)); |
86 | 0 | } else if (hx<0) { /* x < -0.5 */ |
87 | 0 | z = (one+x)*0.5; |
88 | 0 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
89 | 0 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
90 | 0 | s = sqrt(z); |
91 | 0 | r = p/q; |
92 | 0 | w = r*s-pio2_lo; |
93 | 0 | return pi - 2.0*(s+w); |
94 | 0 | } else { /* x > 0.5 */ |
95 | 0 | z = (one-x)*0.5; |
96 | 0 | s = sqrt(z); |
97 | 0 | df = s; |
98 | 0 | SET_LOW_WORD(df,0); |
99 | 0 | c = (z-df*df)/(s+df); |
100 | 0 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
101 | 0 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
102 | 0 | r = p/q; |
103 | 0 | w = r*s+c; |
104 | 0 | return 2.0*(df+w); |
105 | 0 | } |
106 | 0 | } |