1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180

/* origin: FreeBSD /usr/src/lib/msun/src/s_sinf.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
 * Optimized by Bruce D. Evans.
 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

use super::{k_cosf, k_sinf, rem_pio2f};

/* Small multiples of pi/2 rounded to double precision. */
const PI_2: f64 = 0.5 * 3.1415926535897931160E+00;
const S1PIO2: f64 = 1.0 * PI_2; /* 0x3FF921FB, 0x54442D18 */
const S2PIO2: f64 = 2.0 * PI_2; /* 0x400921FB, 0x54442D18 */
const S3PIO2: f64 = 3.0 * PI_2; /* 0x4012D97C, 0x7F3321D2 */
const S4PIO2: f64 = 4.0 * PI_2; /* 0x401921FB, 0x54442D18 */

/// Both the sine and cosine of `x` (f32).
///
/// `x` is specified in radians and the return value is (sin(x), cos(x)).
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn sincosf(x: f32) -> (f32, f32) {
    let s: f32;
    let c: f32;
    let mut ix: u32;
    let sign: bool;

    ix = x.to_bits();
    sign = (ix >> 31) != 0;
    ix &= 0x7fffffff;

    /* |x| ~<= pi/4 */
    if ix <= 0x3f490fda {
        /* |x| < 2**-12 */
        if ix < 0x39800000 {
            /* raise inexact if x!=0 and underflow if subnormal */

            let x1p120 = f32::from_bits(0x7b800000); // 0x1p120 == 2^120
            if ix < 0x00100000 {
                force_eval!(x / x1p120);
            } else {
                force_eval!(x + x1p120);
            }
            return (x, 1.0);
        }
        return (k_sinf(x as f64), k_cosf(x as f64));
    }

    /* |x| ~<= 5*pi/4 */
    if ix <= 0x407b53d1 {
        if ix <= 0x4016cbe3 {
            /* |x| ~<= 3pi/4 */
            if sign {
                s = -k_cosf(x as f64 + S1PIO2);
                c = k_sinf(x as f64 + S1PIO2);
            } else {
                s = k_cosf(S1PIO2 - x as f64);
                c = k_sinf(S1PIO2 - x as f64);
            }
        }
        /* -sin(x+c) is not correct if x+c could be 0: -0 vs +0 */
        else {
            if sign {
                s = -k_sinf(x as f64 + S2PIO2);
                c = -k_cosf(x as f64 + S2PIO2);
            } else {
                s = -k_sinf(x as f64 - S2PIO2);
                c = -k_cosf(x as f64 - S2PIO2);
            }
        }

        return (s, c);
    }

    /* |x| ~<= 9*pi/4 */
    if ix <= 0x40e231d5 {
        if ix <= 0x40afeddf {
            /* |x| ~<= 7*pi/4 */
            if sign {
                s = k_cosf(x as f64 + S3PIO2);
                c = -k_sinf(x as f64 + S3PIO2);
            } else {
                s = -k_cosf(x as f64 - S3PIO2);
                c = k_sinf(x as f64 - S3PIO2);
            }
        } else {
            if sign {
                s = k_sinf(x as f64 + S4PIO2);
                c = k_cosf(x as f64 + S4PIO2);
            } else {
                s = k_sinf(x as f64 - S4PIO2);
                c = k_cosf(x as f64 - S4PIO2);
            }
        }

        return (s, c);
    }

    /* sin(Inf or NaN) is NaN */
    if ix >= 0x7f800000 {
        let rv = x - x;
        return (rv, rv);
    }

    /* general argument reduction needed */
    let (n, y) = rem_pio2f(x);
    s = k_sinf(y);
    c = k_cosf(y);
    match n & 3 {
        0 => (s, c),
        1 => (c, -s),
        2 => (-s, -c),
        3 => (-c, s),
        #[cfg(debug_assertions)]
        _ => unreachable!(),
        #[cfg(not(debug_assertions))]
        _ => (0.0, 1.0),
    }
}

// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
#[cfg(not(target_arch = "powerpc64"))]
#[cfg(test)]
mod tests {
    use super::sincosf;

    #[test]
    fn rotational_symmetry() {
        use core::f32::consts::PI;
        const N: usize = 24;
        for n in 0..N {
            let theta = 2. * PI * (n as f32) / (N as f32);
            let (s, c) = sincosf(theta);
            let (s_plus, c_plus) = sincosf(theta + 2. * PI);
            let (s_minus, c_minus) = sincosf(theta - 2. * PI);

            const TOLERANCE: f32 = 1e-6;
            assert!(
                (s - s_plus).abs() < TOLERANCE,
                "|{} - {}| = {} >= {}",
                s,
                s_plus,
                (s - s_plus).abs(),
                TOLERANCE
            );
            assert!(
                (s - s_minus).abs() < TOLERANCE,
                "|{} - {}| = {} >= {}",
                s,
                s_minus,
                (s - s_minus).abs(),
                TOLERANCE
            );
            assert!(
                (c - c_plus).abs() < TOLERANCE,
                "|{} - {}| = {} >= {}",
                c,
                c_plus,
                (c - c_plus).abs(),
                TOLERANCE
            );
            assert!(
                (c - c_minus).abs() < TOLERANCE,
                "|{} - {}| = {} >= {}",
                c,
                c_minus,
                (c - c_minus).abs(),
                TOLERANCE
            );
        }
    }
}