libm/math/
sincosf.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */
2/*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
4 * Optimized by Bruce D. Evans.
5 */
6/*
7 * ====================================================
8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9 *
10 * Developed at SunPro, a Sun Microsystems, Inc. business.
11 * Permission to use, copy, modify, and distribute this
12 * software is freely granted, provided that this notice
13 * is preserved.
14 * ====================================================
15 */
16
17use super::{k_cosf, k_sinf, rem_pio2f};
18
19/* Small multiples of pi/2 rounded to double precision. */
20const PI_2: f32 = 0.5 * 3.1415926535897931160E+00;
21const S1PIO2: f32 = 1.0 * PI_2; /* 0x3FF921FB, 0x54442D18 */
22const S2PIO2: f32 = 2.0 * PI_2; /* 0x400921FB, 0x54442D18 */
23const S3PIO2: f32 = 3.0 * PI_2; /* 0x4012D97C, 0x7F3321D2 */
24const S4PIO2: f32 = 4.0 * PI_2; /* 0x401921FB, 0x54442D18 */
25
26#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
27pub fn sincosf(x: f32) -> (f32, f32) {
28    let s: f32;
29    let c: f32;
30    let mut ix: u32;
31    let sign: bool;
32
33    ix = x.to_bits();
34    sign = (ix >> 31) != 0;
35    ix &= 0x7fffffff;
36
37    /* |x| ~<= pi/4 */
38    if ix <= 0x3f490fda {
39        /* |x| < 2**-12 */
40        if ix < 0x39800000 {
41            /* raise inexact if x!=0 and underflow if subnormal */
42
43            let x1p120 = f32::from_bits(0x7b800000); // 0x1p120 == 2^120
44            if ix < 0x00100000 {
45                force_eval!(x / x1p120);
46            } else {
47                force_eval!(x + x1p120);
48            }
49            return (x, 1.0);
50        }
51        return (k_sinf(x as f64), k_cosf(x as f64));
52    }
53
54    /* |x| ~<= 5*pi/4 */
55    if ix <= 0x407b53d1 {
56        if ix <= 0x4016cbe3 {
57            /* |x| ~<= 3pi/4 */
58            if sign {
59                s = -k_cosf((x + S1PIO2) as f64);
60                c = k_sinf((x + S1PIO2) as f64);
61            } else {
62                s = k_cosf((S1PIO2 - x) as f64);
63                c = k_sinf((S1PIO2 - x) as f64);
64            }
65        }
66        /* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */
67        else {
68            if sign {
69                s = -k_sinf((x + S2PIO2) as f64);
70                c = -k_cosf((x + S2PIO2) as f64);
71            } else {
72                s = -k_sinf((x - S2PIO2) as f64);
73                c = -k_cosf((x - S2PIO2) as f64);
74            }
75        }
76
77        return (s, c);
78    }
79
80    /* |x| ~<= 9*pi/4 */
81    if ix <= 0x40e231d5 {
82        if ix <= 0x40afeddf {
83            /* |x| ~<= 7*pi/4 */
84            if sign {
85                s = k_cosf((x + S3PIO2) as f64);
86                c = -k_sinf((x + S3PIO2) as f64);
87            } else {
88                s = -k_cosf((x - S3PIO2) as f64);
89                c = k_sinf((x - S3PIO2) as f64);
90            }
91        } else {
92            if sign {
93                s = k_sinf((x + S4PIO2) as f64);
94                c = k_cosf((x + S4PIO2) as f64);
95            } else {
96                s = k_sinf((x - S4PIO2) as f64);
97                c = k_cosf((x - S4PIO2) as f64);
98            }
99        }
100
101        return (s, c);
102    }
103
104    /* sin(Inf or NaN) is NaN */
105    if ix >= 0x7f800000 {
106        let rv = x - x;
107        return (rv, rv);
108    }
109
110    /* general argument reduction needed */
111    let (n, y) = rem_pio2f(x);
112    s = k_sinf(y);
113    c = k_cosf(y);
114    match n & 3 {
115        0 => (s, c),
116        1 => (c, -s),
117        2 => (-s, -c),
118        3 => (-c, s),
119        #[cfg(debug_assertions)]
120        _ => unreachable!(),
121        #[cfg(not(debug_assertions))]
122        _ => (0.0, 1.0),
123    }
124}
125
126// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
127#[cfg(not(target_arch = "powerpc64"))]
128#[cfg(test)]
129mod tests {
130    use super::sincosf;
131    use crate::_eqf;
132
133    #[test]
134    fn with_pi() {
135        let (s, c) = sincosf(core::f32::consts::PI);
136        _eqf(s.abs(), 0.0).unwrap();
137        _eqf(c, -1.0).unwrap();
138    }
139
140    #[test]
141    fn rotational_symmetry() {
142        use core::f32::consts::PI;
143        const N: usize = 24;
144        for n in 0..N {
145            let theta = 2. * PI * (n as f32) / (N as f32);
146            let (s, c) = sincosf(theta);
147            let (s_plus, c_plus) = sincosf(theta + 2. * PI);
148            let (s_minus, c_minus) = sincosf(theta - 2. * PI);
149
150            const TOLERANCE: f32 = 1e-6;
151            assert!(
152                (s - s_plus).abs() < TOLERANCE,
153                "|{} - {}| = {} >= {}",
154                s,
155                s_plus,
156                (s - s_plus).abs(),
157                TOLERANCE
158            );
159            assert!(
160                (s - s_minus).abs() < TOLERANCE,
161                "|{} - {}| = {} >= {}",
162                s,
163                s_minus,
164                (s - s_minus).abs(),
165                TOLERANCE
166            );
167            assert!(
168                (c - c_plus).abs() < TOLERANCE,
169                "|{} - {}| = {} >= {}",
170                c,
171                c_plus,
172                (c - c_plus).abs(),
173                TOLERANCE
174            );
175            assert!(
176                (c - c_minus).abs() < TOLERANCE,
177                "|{} - {}| = {} >= {}",
178                c,
179                c_minus,
180                (c - c_minus).abs(),
181                TOLERANCE
182            );
183        }
184    }
185}