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#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
17pub fn sqrtf(x: f32) -> f32 {
18 // On wasm32 we know that LLVM's intrinsic will compile to an optimized
19 // `f32.sqrt` native instruction, so we can leverage this for both code size
20 // and speed.
21 llvm_intrinsically_optimized! {
22 #[cfg(target_arch = "wasm32")] {
23 return if x < 0.0 {
24 ::core::f32::NAN
25 } else {
26 unsafe { ::core::intrinsics::sqrtf32(x) }
27 }
28 }
29 }
30 #[cfg(target_feature = "sse")]
31 {
32 // Note: This path is unlikely since LLVM will usually have already
33 // optimized sqrt calls into hardware instructions if sse is available,
34 // but if someone does end up here they'll apprected the speed increase.
35 #[cfg(target_arch = "x86")]
36 use core::arch::x86::*;
37 #[cfg(target_arch = "x86_64")]
38 use core::arch::x86_64::*;
39 unsafe {
40 let m = _mm_set_ss(x);
41 let m_sqrt = _mm_sqrt_ss(m);
42 _mm_cvtss_f32(m_sqrt)
43 }
44 }
45 #[cfg(not(target_feature = "sse"))]
46 {
47 const TINY: f32 = 1.0e-30;
48
49 let mut z: f32;
50 let sign: i32 = 0x80000000u32 as i32;
51 let mut ix: i32;
52 let mut s: i32;
53 let mut q: i32;
54 let mut m: i32;
55 let mut t: i32;
56 let mut i: i32;
57 let mut r: u32;
58
59 ix = x.to_bits() as i32;
60
61 /* take care of Inf and NaN */
62 if (ix as u32 & 0x7f800000) == 0x7f800000 {
63 return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf, sqrt(-inf)=sNaN */
64 }
65
66 /* take care of zero */
67 if ix <= 0 {
68 if (ix & !sign) == 0 {
69 return x; /* sqrt(+-0) = +-0 */
70 }
71 if ix < 0 {
72 return (x - x) / (x - x); /* sqrt(-ve) = sNaN */
73 }
74 }
75
76 /* normalize x */
77 m = ix >> 23;
78 if m == 0 {
79 /* subnormal x */
80 i = 0;
81 while ix & 0x00800000 == 0 {
82 ix <<= 1;
83 i = i + 1;
84 }
85 m -= i - 1;
86 }
87 m -= 127; /* unbias exponent */
88 ix = (ix & 0x007fffff) | 0x00800000;
89 if m & 1 == 1 {
90 /* odd m, double x to make it even */
91 ix += ix;
92 }
93 m >>= 1; /* m = [m/2] */
94
95 /* generate sqrt(x) bit by bit */
96 ix += ix;
97 q = 0;
98 s = 0;
99 r = 0x01000000; /* r = moving bit from right to left */
100
101 while r != 0 {
102 t = s + r as i32;
103 if t <= ix {
104 s = t + r as i32;
105 ix -= t;
106 q += r as i32;
107 }
108 ix += ix;
109 r >>= 1;
110 }
111
112 /* use floating add to find out rounding direction */
113 if ix != 0 {
114 z = 1.0 - TINY; /* raise inexact flag */
115 if z >= 1.0 {
116 z = 1.0 + TINY;
117 if z > 1.0 {
118 q += 2;
119 } else {
120 q += q & 1;
121 }
122 }
123 }
124
125 ix = (q >> 1) + 0x3f000000;
126 ix += m << 23;
127 f32::from_bits(ix as u32)
128 }
129}
130
131// PowerPC tests are failing on LLVM 13: https://github.com/rust-lang/rust/issues/88520
132#[cfg(not(target_arch = "powerpc64"))]
133#[cfg(test)]
134mod tests {
135 use super::*;
136 use core::f32::*;
137
138 #[test]
139 fn sanity_check() {
140 assert_eq!(sqrtf(100.0), 10.0);
141 assert_eq!(sqrtf(4.0), 2.0);
142 }
143
144 /// The spec: https://en.cppreference.com/w/cpp/numeric/math/sqrt
145 #[test]
146 fn spec_tests() {
147 // Not Asserted: FE_INVALID exception is raised if argument is negative.
148 assert!(sqrtf(-1.0).is_nan());
149 assert!(sqrtf(NAN).is_nan());
150 for f in [0.0, -0.0, INFINITY].iter().copied() {
151 assert_eq!(sqrtf(f), f);
152 }
153 }
154
155 #[test]
156 fn conformance_tests() {
157 let values = [
158 3.14159265359f32,
159 10000.0f32,
160 f32::from_bits(0x0000000f),
161 INFINITY,
162 ];
163 let results = [1071833029u32, 1120403456u32, 456082799u32, 2139095040u32];
164
165 for i in 0..values.len() {
166 let bits = f32::to_bits(sqrtf(values[i]));
167 assert_eq!(results[i], bits);
168 }
169 }
170}
171