/rust/registry/src/index.crates.io-1949cf8c6b5b557f/libm-0.2.11/src/math/asin.rs
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1 | | /* origin: FreeBSD /usr/src/lib/msun/src/e_asin.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 | | /* asin(x) |
13 | | * Method : |
14 | | * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... |
15 | | * we approximate asin(x) on [0,0.5] by |
16 | | * asin(x) = x + x*x^2*R(x^2) |
17 | | * where |
18 | | * R(x^2) is a rational approximation of (asin(x)-x)/x^3 |
19 | | * and its remez error is bounded by |
20 | | * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) |
21 | | * |
22 | | * For x in [0.5,1] |
23 | | * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) |
24 | | * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; |
25 | | * then for x>0.98 |
26 | | * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
27 | | * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) |
28 | | * For x<=0.98, let pio4_hi = pio2_hi/2, then |
29 | | * f = hi part of s; |
30 | | * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) |
31 | | * and |
32 | | * asin(x) = pi/2 - 2*(s+s*z*R(z)) |
33 | | * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) |
34 | | * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) |
35 | | * |
36 | | * Special cases: |
37 | | * if x is NaN, return x itself; |
38 | | * if |x|>1, return NaN with invalid signal. |
39 | | * |
40 | | */ |
41 | | |
42 | | use super::{fabs, get_high_word, get_low_word, sqrt, with_set_low_word}; |
43 | | |
44 | | const PIO2_HI: f64 = 1.57079632679489655800e+00; /* 0x3FF921FB, 0x54442D18 */ |
45 | | const PIO2_LO: f64 = 6.12323399573676603587e-17; /* 0x3C91A626, 0x33145C07 */ |
46 | | /* coefficients for R(x^2) */ |
47 | | const P_S0: f64 = 1.66666666666666657415e-01; /* 0x3FC55555, 0x55555555 */ |
48 | | const P_S1: f64 = -3.25565818622400915405e-01; /* 0xBFD4D612, 0x03EB6F7D */ |
49 | | const P_S2: f64 = 2.01212532134862925881e-01; /* 0x3FC9C155, 0x0E884455 */ |
50 | | const P_S3: f64 = -4.00555345006794114027e-02; /* 0xBFA48228, 0xB5688F3B */ |
51 | | const P_S4: f64 = 7.91534994289814532176e-04; /* 0x3F49EFE0, 0x7501B288 */ |
52 | | const P_S5: f64 = 3.47933107596021167570e-05; /* 0x3F023DE1, 0x0DFDF709 */ |
53 | | const Q_S1: f64 = -2.40339491173441421878e+00; /* 0xC0033A27, 0x1C8A2D4B */ |
54 | | const Q_S2: f64 = 2.02094576023350569471e+00; /* 0x40002AE5, 0x9C598AC8 */ |
55 | | const Q_S3: f64 = -6.88283971605453293030e-01; /* 0xBFE6066C, 0x1B8D0159 */ |
56 | | const Q_S4: f64 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ |
57 | | |
58 | 0 | fn comp_r(z: f64) -> f64 { |
59 | 0 | let p = z * (P_S0 + z * (P_S1 + z * (P_S2 + z * (P_S3 + z * (P_S4 + z * P_S5))))); |
60 | 0 | let q = 1.0 + z * (Q_S1 + z * (Q_S2 + z * (Q_S3 + z * Q_S4))); |
61 | 0 | p / q |
62 | 0 | } |
63 | | |
64 | | /// Arcsine (f64) |
65 | | /// |
66 | | /// Computes the inverse sine (arc sine) of the argument `x`. |
67 | | /// Arguments to asin must be in the range -1 to 1. |
68 | | /// Returns values in radians, in the range of -pi/2 to pi/2. |
69 | | #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
70 | 0 | pub fn asin(mut x: f64) -> f64 { |
71 | | let z: f64; |
72 | | let r: f64; |
73 | | let s: f64; |
74 | | let hx: u32; |
75 | | let ix: u32; |
76 | | |
77 | 0 | hx = get_high_word(x); |
78 | 0 | ix = hx & 0x7fffffff; |
79 | | /* |x| >= 1 or nan */ |
80 | 0 | if ix >= 0x3ff00000 { |
81 | | let lx: u32; |
82 | 0 | lx = get_low_word(x); |
83 | 0 | if ((ix - 0x3ff00000) | lx) == 0 { |
84 | | /* asin(1) = +-pi/2 with inexact */ |
85 | 0 | return x * PIO2_HI + f64::from_bits(0x3870000000000000); |
86 | | } else { |
87 | 0 | return 0.0 / (x - x); |
88 | | } |
89 | 0 | } |
90 | | /* |x| < 0.5 */ |
91 | 0 | if ix < 0x3fe00000 { |
92 | | /* if 0x1p-1022 <= |x| < 0x1p-26, avoid raising underflow */ |
93 | 0 | if ix < 0x3e500000 && ix >= 0x00100000 { |
94 | 0 | return x; |
95 | | } else { |
96 | 0 | return x + x * comp_r(x * x); |
97 | | } |
98 | 0 | } |
99 | | /* 1 > |x| >= 0.5 */ |
100 | 0 | z = (1.0 - fabs(x)) * 0.5; |
101 | 0 | s = sqrt(z); |
102 | 0 | r = comp_r(z); |
103 | 0 | if ix >= 0x3fef3333 { |
104 | 0 | /* if |x| > 0.975 */ |
105 | 0 | x = PIO2_HI - (2. * (s + s * r) - PIO2_LO); |
106 | 0 | } else { |
107 | 0 | let f: f64; |
108 | 0 | let c: f64; |
109 | 0 | /* f+c = sqrt(z) */ |
110 | 0 | f = with_set_low_word(s, 0); |
111 | 0 | c = (z - f * f) / (s + f); |
112 | 0 | x = 0.5 * PIO2_HI - (2.0 * s * r - (PIO2_LO - 2.0 * c) - (0.5 * PIO2_HI - 2.0 * f)); |
113 | 0 | } |
114 | 0 | if hx >> 31 != 0 { -x } else { x } |
115 | 0 | } |