libm/math/
acosf.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/e_acosf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 */
5/*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 */
15
16use super::sqrtf::sqrtf;
17
18const PIO2_HI: f32 = 1.5707962513e+00; /* 0x3fc90fda */
19const PIO2_LO: f32 = 7.5497894159e-08; /* 0x33a22168 */
20const P_S0: f32 = 1.6666586697e-01;
21const P_S1: f32 = -4.2743422091e-02;
22const P_S2: f32 = -8.6563630030e-03;
23const Q_S1: f32 = -7.0662963390e-01;
24
25fn r(z: f32) -> f32 {
26    let p = z * (P_S0 + z * (P_S1 + z * P_S2));
27    let q = 1. + z * Q_S1;
28    p / q
29}
30
31/// Arccosine (f32)
32///
33/// Computes the inverse cosine (arc cosine) of the input value.
34/// Arguments must be in the range -1 to 1.
35/// Returns values in radians, in the range of 0 to pi.
36#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
37pub fn acosf(x: f32) -> f32 {
38    let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120)
39
40    let z: f32;
41    let w: f32;
42    let s: f32;
43
44    let mut hx = x.to_bits();
45    let ix = hx & 0x7fffffff;
46    /* |x| >= 1 or nan */
47    if ix >= 0x3f800000 {
48        if ix == 0x3f800000 {
49            if (hx >> 31) != 0 {
50                return 2. * PIO2_HI + x1p_120;
51            }
52            return 0.;
53        }
54        return 0. / (x - x);
55    }
56    /* |x| < 0.5 */
57    if ix < 0x3f000000 {
58        if ix <= 0x32800000 {
59            /* |x| < 2**-26 */
60            return PIO2_HI + x1p_120;
61        }
62        return PIO2_HI - (x - (PIO2_LO - x * r(x * x)));
63    }
64    /* x < -0.5 */
65    if (hx >> 31) != 0 {
66        z = (1. + x) * 0.5;
67        s = sqrtf(z);
68        w = r(z) * s - PIO2_LO;
69        return 2. * (PIO2_HI - (s + w));
70    }
71    /* x > 0.5 */
72    z = (1. - x) * 0.5;
73    s = sqrtf(z);
74    hx = s.to_bits();
75    let df = f32::from_bits(hx & 0xfffff000);
76    let c = (z - df * df) / (s + df);
77    w = r(z) * s + c;
78    2. * (df + w)
79}