libm/math/
sqrtf.rs

1/* origin: FreeBSD /usr/src/lib/msun/src/e_sqrtf.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
16/// The square root of `x` (f32).
17#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
18pub fn sqrtf(x: f32) -> f32 {
19    // On wasm32 we know that LLVM's intrinsic will compile to an optimized
20    // `f32.sqrt` native instruction, so we can leverage this for both code size
21    // and speed.
22    llvm_intrinsically_optimized! {
23        #[cfg(target_arch = "wasm32")] {
24            return if x < 0.0 {
25                ::core::f32::NAN
26            } else {
27                unsafe { ::core::intrinsics::sqrtf32(x) }
28            }
29        }
30    }
31    #[cfg(all(target_feature = "sse", not(feature = "force-soft-floats")))]
32    {
33        // Note: This path is unlikely since LLVM will usually have already
34        // optimized sqrt calls into hardware instructions if sse is available,
35        // but if someone does end up here they'll appreciate the speed increase.
36        #[cfg(target_arch = "x86")]
37        use core::arch::x86::*;
38        #[cfg(target_arch = "x86_64")]
39        use core::arch::x86_64::*;
40        unsafe {
41            let m = _mm_set_ss(x);
42            let m_sqrt = _mm_sqrt_ss(m);
43            _mm_cvtss_f32(m_sqrt)
44        }
45    }
46    #[cfg(any(not(target_feature = "sse"), feature = "force-soft-floats"))]
47    {
48        const TINY: f32 = 1.0e-30;
49
50        let mut z: f32;
51        let sign: i32 = 0x80000000u32 as i32;
52        let mut ix: i32;
53        let mut s: i32;
54        let mut q: i32;
55        let mut m: i32;
56        let mut t: i32;
57        let mut i: i32;
58        let mut r: u32;
59
60        ix = x.to_bits() as i32;
61
62        /* take care of Inf and NaN */
63        if (ix as u32 & 0x7f800000) == 0x7f800000 {
64            return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
65        }
66
67        /* take care of zero */
68        if ix <= 0 {
69            if (ix & !sign) == 0 {
70                return x; /* sqrt(+-0) = +-0 */
71            }
72            if ix < 0 {
73                return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
74            }
75        }
76
77        /* normalize x */
78        m = ix >> 23;
79        if m == 0 {
80            /* subnormal x */
81            i = 0;
82            while ix & 0x00800000 == 0 {
83                ix <<= 1;
84                i = i + 1;
85            }
86            m -= i - 1;
87        }
88        m -= 127; /* unbias exponent */
89        ix = (ix & 0x007fffff) | 0x00800000;
90        if m & 1 == 1 {
91            /* odd m, double x to make it even */
92            ix += ix;
93        }
94        m >>= 1; /* m = [m/2] */
95
96        /* generate sqrt(x) bit by bit */
97        ix += ix;
98        q = 0;
99        s = 0;
100        r = 0x01000000; /* r = moving bit from right to left */
101
102        while r != 0 {
103            t = s + r as i32;
104            if t <= ix {
105                s = t + r as i32;
106                ix -= t;
107                q += r as i32;
108            }
109            ix += ix;
110            r >>= 1;
111        }
112
113        /* use floating add to find out rounding direction */
114        if ix != 0 {
115            z = 1.0 - TINY; /* raise inexact flag */
116            if z >= 1.0 {
117                z = 1.0 + TINY;
118                if z > 1.0 {
119                    q += 2;
120                } else {
121                    q += q & 1;
122                }
123            }
124        }
125
126        ix = (q >> 1) + 0x3f000000;
127        ix += m << 23;
128        f32::from_bits(ix as u32)
129    }
130}
131
132// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
133#[cfg(not(target_arch = "powerpc64"))]
134#[cfg(test)]
135mod tests {
136    use core::f32::*;
137
138    use super::*;
139
140    #[test]
141    fn sanity_check() {
142        assert_eq!(sqrtf(100.0), 10.0);
143        assert_eq!(sqrtf(4.0), 2.0);
144    }
145
146    /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
147    #[test]
148    fn spec_tests() {
149        // Not Asserted: FE_INVALID exception is raised if argument is negative.
150        assert!(sqrtf(-1.0).is_nan());
151        assert!(sqrtf(NAN).is_nan());
152        for f in [0.0, -0.0, INFINITY].iter().copied() {
153            assert_eq!(sqrtf(f), f);
154        }
155    }
156
157    #[test]
158    fn conformance_tests() {
159        let values = [3.14159265359f32, 10000.0f32, f32::from_bits(0x0000000f), INFINITY];
160        let results = [1071833029u32, 1120403456u32, 456082799u32, 2139095040u32];
161
162        for i in 0..values.len() {
163            let bits = f32::to_bits(sqrtf(values[i]));
164            assert_eq!(results[i], bits);
165        }
166    }
167}
libm/math/sqrtf.rs

libm/math/
sqrtf.rs
