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 #[inline]
r(z: f64) -> f6452 fn r(z: f64) -> f64 {
53 let p: f64 = z * (PS0 + z * (PS1 + z * (PS2 + z * (PS3 + z * (PS4 + z * PS5)))));
54 let q: f64 = 1.0 + z * (QS1 + z * (QS2 + z * (QS3 + z * QS4)));
55 p / q
56 }
57
58 /// Arccosine (f64)
59 ///
60 /// Computes the inverse cosine (arc cosine) of the input value.
61 /// Arguments must be in the range -1 to 1.
62 /// Returns values in radians, in the range of 0 to pi.
63 #[inline]
64 #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
acos(x: f64) -> f6465 pub fn acos(x: f64) -> f64 {
66 let x1p_120f = f64::from_bits(0x3870000000000000); // 0x1p-120 === 2 ^ -120
67 let z: f64;
68 let w: f64;
69 let s: f64;
70 let c: f64;
71 let df: f64;
72 let hx: u32;
73 let ix: u32;
74
75 hx = (x.to_bits() >> 32) as u32;
76 ix = hx & 0x7fffffff;
77 /* |x| >= 1 or nan */
78 if ix >= 0x3ff00000 {
79 let lx: u32 = x.to_bits() as u32;
80
81 if ((ix - 0x3ff00000) | lx) == 0 {
82 /* acos(1)=0, acos(-1)=pi */
83 if (hx >> 31) != 0 {
84 return 2. * PIO2_HI + x1p_120f;
85 }
86 return 0.;
87 }
88 return 0. / (x - x);
89 }
90 /* |x| < 0.5 */
91 if ix < 0x3fe00000 {
92 if ix <= 0x3c600000 {
93 /* |x| < 2**-57 */
94 return PIO2_HI + x1p_120f;
95 }
96 return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
97 }
98 /* x < -0.5 */
99 if (hx >> 31) != 0 {
100 z = (1.0 + x) * 0.5;
101 s = sqrt(z);
102 w = r(z) * s - PIO2_LO;
103 return 2. * (PIO2_HI - (s + w));
104 }
105 /* x > 0.5 */
106 z = (1.0 - x) * 0.5;
107 s = sqrt(z);
108 // Set the low 4 bytes to zero
109 df = f64::from_bits(s.to_bits() & 0xff_ff_ff_ff_00_00_00_00);
110
111 c = (z - df * df) / (s + df);
112 w = r(z) * s + c;
113 2. * (df + w)
114 }
115