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

/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.c */
/*
 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
 */
/*
 * ====================================================
 * 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.
 * ====================================================
 */

#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub fn sqrtf(x: f32) -> f32 {
    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
    // `f32.sqrt` native instruction, so we can leverage this for both code size
    // and speed.
    llvm_intrinsically_optimized! {
        #[cfg(target_arch = "wasm32")] {
            return if x < 0.0 {
                ::core::f32::NAN
            } else {
                unsafe { ::core::intrinsics::sqrtf32(x) }
            }
        }
    }
    #[cfg(target_feature = "sse")]
    {
        // Note: This path is unlikely since LLVM will usually have already
        // optimized sqrt calls into hardware instructions if sse is available,
        // but if someone does end up here they'll apprected the speed increase.
        #[cfg(target_arch = "x86")]
        use core::arch::x86::*;
        #[cfg(target_arch = "x86_64")]
        use core::arch::x86_64::*;
        unsafe {
            let m = _mm_set_ss(x);
            let m_sqrt = _mm_sqrt_ss(m);
            _mm_cvtss_f32(m_sqrt)
        }
    }
    #[cfg(not(target_feature = "sse"))]
    {
        const TINY: f32 = 1.0e-30;

        let mut z: f32;
        let sign: i32 = 0x80000000u32 as i32;
        let mut ix: i32;
        let mut s: i32;
        let mut q: i32;
        let mut m: i32;
        let mut t: i32;
        let mut i: i32;
        let mut r: u32;

        ix = x.to_bits() as i32;

        /* take care of Inf and NaN */
        if (ix as u32 & 0x7f800000) == 0x7f800000 {
            return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
        }

        /* take care of zero */
        if ix <= 0 {
            if (ix & !sign) == 0 {
                return x; /* sqrt(+-0) = +-0 */
            }
            if ix < 0 {
                return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
            }
        }

        /* normalize x */
        m = ix >> 23;
        if m == 0 {
            /* subnormal x */
            i = 0;
            while ix & 0x00800000 == 0 {
                ix <<= 1;
                i = i + 1;
            }
            m -= i - 1;
        }
        m -= 127; /* unbias exponent */
        ix = (ix & 0x007fffff) | 0x00800000;
        if m & 1 == 1 {
            /* odd m, double x to make it even */
            ix += ix;
        }
        m >>= 1; /* m = [m/2] */

        /* generate sqrt(x) bit by bit */
        ix += ix;
        q = 0;
        s = 0;
        r = 0x01000000; /* r = moving bit from right to left */

        while r != 0 {
            t = s + r as i32;
            if t <= ix {
                s = t + r as i32;
                ix -= t;
                q += r as i32;
            }
            ix += ix;
            r >>= 1;
        }

        /* use floating add to find out rounding direction */
        if ix != 0 {
            z = 1.0 - TINY; /* raise inexact flag */
            if z >= 1.0 {
                z = 1.0 + TINY;
                if z > 1.0 {
                    q += 2;
                } else {
                    q += q & 1;
                }
            }
        }

        ix = (q >> 1) + 0x3f000000;
        ix += m << 23;
        f32::from_bits(ix as u32)
    }
}

// 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::*;
    use core::f32::*;

    #[test]
    fn sanity_check() {
        assert_eq!(sqrtf(100.0), 10.0);
        assert_eq!(sqrtf(4.0), 2.0);
    }

    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
    #[test]
    fn spec_tests() {
        // Not Asserted: FE_INVALID exception is raised if argument is negative.
        assert!(sqrtf(-1.0).is_nan());
        assert!(sqrtf(NAN).is_nan());
        for f in [0.0, -0.0, INFINITY].iter().copied() {
            assert_eq!(sqrtf(f), f);
        }
    }

    #[test]
    fn conformance_tests() {
        let values = [
            3.14159265359f32,
            10000.0f32,
            f32::from_bits(0x0000000f),
            INFINITY,
        ];
        let results = [1071833029u32, 1120403456u32, 456082799u32, 2139095040u32];

        for i in 0..values.len() {
            let bits = f32::to_bits(sqrtf(values[i]));
            assert_eq!(results[i], bits);
        }
    }
}