1 | /* origin: FreeBSD /usr/src/lib/msun/src/e_acos.c */ |
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 | /* acos(x) |
13 | * Method : |
14 | * acos(x) = pi/2 - asin(x) |
15 | * acos(-x) = pi/2 + asin(x) |
16 | * For |x|<=0.5 |
17 | * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) |
18 | * For x>0.5 |
19 | * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) |
20 | * = 2asin(sqrt((1-x)/2)) |
21 | * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) |
22 | * = 2f + (2c + 2s*z*R(z)) |
23 | * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term |
24 | * for f so that f+c ~ sqrt(z). |
25 | * For x<-0.5 |
26 | * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) |
27 | * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) |
28 | * |
29 | * Special cases: |
30 | * if x is NaN, return x itself; |
31 | * if |x|>1, return NaN with invalid signal. |
32 | * |
33 | * Function needed: sqrt |
34 | */ |
35 | |
36 | use super::sqrt; |
37 | |
38 | const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
39 | const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
40 | const PS0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */ |
41 | const PS1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */ |
42 | const PS2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */ |
43 | const PS3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */ |
44 | const PS4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */ |
45 | const PS5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */ |
46 | const QS1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */ |
47 | const QS2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */ |
48 | const QS3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */ |
49 | const QS4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
50 | |
51 | fn r(z: f64) -> f64 { |
52 | let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5))))); |
53 | let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4))); |
54 | p / q |
55 | } |
56 | |
57 | /// Arccosine (f64) |
58 | /// |
59 | /// Computes the inverse cosine (arc cosine) of the input value. |
60 | /// Arguments must be in the range -1 to 1. |
61 | /// Returns values in radians, in the range of 0 to pi. |
62 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
63 | pub fn acos(x: f64) -> f64 { |
64 | let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120 |
65 | let z: f64; |
66 | let w: f64; |
67 | let s: f64; |
68 | let c: f64; |
69 | let df: f64; |
70 | let hx: u32; |
71 | let ix: u32; |
72 | |
73 | hx = (x.to_bits() >> 32) as u32; |
74 | ix = hx & 0x7fffffff; |
75 | /* |x| >= 1 or nan */ |
76 | if ix >= 0x3ff00000 { |
77 | let lx: u32 = x.to_bits() as u32; |
78 | |
79 | if ((ix - 0x3ff00000) | lx) == 0 { |
80 | /* acos(1)=0, acos(-1)=pi */ |
81 | if (hx >> 31) != 0 { |
82 | return 2. * PIO2_HI + x1p_120f; |
83 | } |
84 | return 0.; |
85 | } |
86 | return 0. / (x - x); |
87 | } |
88 | /* |x| < 0.5 */ |
89 | if ix < 0x3fe00000 { |
90 | if ix <= 0x3c600000 { |
91 | /* |x| < 2**-57 */ |
92 | return PIO2_HI + x1p_120f; |
93 | } |
94 | return PIO2_HI - (x - (PIO2_LO - x * r(x * x))); |
95 | } |
96 | /* x < -0.5 */ |
97 | if (hx >> 31) != 0 { |
98 | z = (1.0 + x) * 0.5; |
99 | s = sqrt(z); |
100 | w = r(z) * s - PIO2_LO; |
101 | return 2. * (PIO2_HI - (s + w)); |
102 | } |
103 | /* x > 0.5 */ |
104 | z = (1.0 - x) * 0.5; |
105 | s = sqrt(z); |
106 | // Set the low 4 bytes to zero |
107 | df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00); |
108 | |
109 | c = (z - df * df) / (s + df); |
110 | w = r(z) * s + c; |
111 | 2. * (df + w) |
112 | } |
113 | |