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}
168