/src/moddable/xs/tools/fdlibm/e_acos.c
Line | Count | Source |
1 | | |
2 | | /* |
3 | | * ==================================================== |
4 | | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | * |
6 | | * Developed at SunSoft, 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 | | */ |
12 | | |
13 | | /* acos(x) |
14 | | * Method : |
15 | | * acos(x) = pi/2 - asin(x) |
16 | | * acos(-x) = pi/2 + asin(x) |
17 | | * For |x|<=0.5 |
18 | | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
19 | | * For x>0.5 |
20 | | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
21 | | * = 2asin(sqrt((1-x)/2)) |
22 | | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
23 | | * = 2f + (2c + 2s*z*R(z)) |
24 | | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
25 | | * for f so that f+c ~ sqrt(z). |
26 | | * For x<-0.5 |
27 | | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
28 | | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
29 | | * |
30 | | * Special cases: |
31 | | * if x is NaN, return x itself; |
32 | | * if |x|>1, return NaN with invalid signal. |
33 | | * |
34 | | * Function needed: sqrt |
35 | | */ |
36 | | |
37 | | #include "math_private.h" |
38 | | |
39 | | static const double |
40 | | one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ |
41 | | pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ |
42 | | pio2_hi = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
43 | | static volatile double |
44 | | pio2_lo = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
45 | | static const double |
46 | | pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ |
47 | | pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ |
48 | | pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ |
49 | | pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ |
50 | | pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ |
51 | | pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ |
52 | | qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ |
53 | | qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ |
54 | | qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ |
55 | | qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
56 | | |
57 | | double |
58 | | __ieee754_acos(double x) |
59 | 11.4k | { |
60 | 11.4k | double z,p,q,r,w,s,c,df; |
61 | 11.4k | int32_t hx,ix; |
62 | 11.4k | GET_HIGH_WORD(hx,x); |
63 | 11.4k | ix = hx&0x7fffffff; |
64 | 11.4k | if(ix>=0x3ff00000) { /* |x| >= 1 */ |
65 | 5.55k | u_int32_t lx; |
66 | 5.55k | GET_LOW_WORD(lx,x); |
67 | 5.55k | if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ |
68 | 2.58k | if(hx>0) return 0.0; /* acos(1) = 0 */ |
69 | 200 | else return pi+2.0*pio2_lo; /* acos(-1)= pi */ |
70 | 2.58k | } |
71 | 2.97k | return (x-x)/(x-x); /* acos(|x|>1) is NaN */ |
72 | 5.55k | } |
73 | 5.89k | if(ix<0x3fe00000) { /* |x| < 0.5 */ |
74 | 1.95k | if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ |
75 | 1.42k | z = x*x; |
76 | 1.42k | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
77 | 1.42k | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
78 | 1.42k | r = p/q; |
79 | 1.42k | return pio2_hi - (x - (pio2_lo-x*r)); |
80 | 3.93k | } else if (hx<0) { /* x < -0.5 */ |
81 | 3.66k | z = (one+x)*0.5; |
82 | 3.66k | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
83 | 3.66k | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
84 | 3.66k | s = sqrt(z); |
85 | 3.66k | r = p/q; |
86 | 3.66k | w = r*s-pio2_lo; |
87 | 3.66k | return pi - 2.0*(s+w); |
88 | 3.66k | } else { /* x > 0.5 */ |
89 | 271 | z = (one-x)*0.5; |
90 | 271 | s = sqrt(z); |
91 | 271 | df = s; |
92 | 271 | SET_LOW_WORD(df,0); |
93 | 271 | c = (z-df*df)/(s+df); |
94 | 271 | p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); |
95 | 271 | q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); |
96 | 271 | r = p/q; |
97 | 271 | w = r*s+c; |
98 | 271 | return 2.0*(df+w); |
99 | 271 | } |
100 | 5.89k | } |