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**/*.rs.bk
.#*
/target
/tests
Cargo.lock

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[package]
name = "libm"
version = "0.1.0"
authors = ["Jorge Aparicio <jorge@japaric.io>"]
[workspace]
members = ["test-generator"]

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Copyright (c) 2018 Jorge Aparicio
Permission is hereby granted, free of charge, to any
person obtaining a copy of this software and associated
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DEALINGS IN THE SOFTWARE.

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# `libm`
A port of [MUSL]'s libm to Rust.
[MUSL]: https://www.musl-libc.org/
## Testing
The test suite of this crate can only be run on x86_64 Linux systems.
```
$ # The test suite depends on the `cross` tool so install it if you don't have it
$ cargo install cross
$ # and the `cross` tool requires docker to be running
$ systemctl start docker
$ # execute the test suite for the x86_64 target
$ TARGET=x86_64-unknown-linux-gnu bash ci/script.sh
$ # execute the test suite for the ARMv7 target
$ TARGET=armv7-unknown-linux-gnueabihf bash ci/script.sh
```
## Contributing
- Pick your favorite math function from the list below.
- Look for the C implementation of the function in the [MUSL source code][src].
- Copy paste the C code into a Rust file in the `src` directory and adjust `src/lib.rs` accordingly.
- Run `cargo watch check` and fix the compiler errors.
- If you can, run the test suite locally. If you can't, no problem! Your PR will be tested
automatically.
- Send us a pull request!
- :tada:
### Notes
- To reinterpret a float as an integer use the `to_bits` method. The MUSL code uses the
`GET_FLOAT_WORD` macro, or a union, to do this operation.
- To reinterpret an integer as a float use the `f32::from_bits` constructor. The MUSL code uses the
`SET_FLOAT_WORD` macro, or a union, to do this operation.
- Rust code panics on arithmetic overflows when not optimized. You may need to use the [`Wrapping`]
newtype to avoid this problem.
[src]: https://git.musl-libc.org/cgit/musl/tree/src/math
[`Wrapping`]: https://doc.rust-lang.org/std/num/struct.Wrapping.html
## Progress
### Functions wanted by the wasm WG
cf. [rustwasm/team#84](https://github.com/rustwasm/team/issues/84).
- [ ] acos
- [ ] asin
- [ ] atan
- [ ] atan2
- [ ] cbrt
- [ ] cos
- [ ] cosf
- [ ] cosh
- [ ] exp
- [ ] exp2
- [ ] exp2f
- [ ] expf
- [ ] expm1
- [ ] fma
- [ ] fmaf
- [ ] fmod
- [ ] fmodf
- [ ] hypot
- [ ] log
- [ ] log10
- [ ] log10f
- [ ] log1p
- [ ] log2
- [ ] log2f
- [ ] logf
- [ ] pow
- [x] powf
- [ ] round
- [ ] roundf
- [ ] sin
- [ ] sinf
- [ ] sinh
- [ ] tan
- [ ] tanh
### Other functions
- [x] fabsf
- [x] scalbnf
- [x] sqrtf
## License
Licensed under either of
- Apache License, Version 2.0 ([LICENSE-APACHE](LICENSE-APACHE) or
http://www.apache.org/licenses/LICENSE-2.0)
- MIT license ([LICENSE-MIT](LICENSE-MIT) or http://opensource.org/licenses/MIT)
at your option.
### Contribution
Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the
work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any
additional terms or conditions.

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set -euxo pipefail
main() {
cargo run --package test-generator --target x86_64-unknown-linux-musl
if hash cargo-fmt; then
# nicer syntax error messages (if any)
cargo fmt
fi
cross test --target $TARGET --release
}
main

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pub fn fabsf(x: f32) -> f32 {
f32::from_bits(x.to_bits() & 0x7fffffff)
}

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#![deny(warnings)]
#![no_std]
mod fabsf;
mod powf;
mod scalbnf;
mod sqrtf;
pub use fabsf::fabsf;
pub use powf::powf;
pub use scalbnf::scalbnf;
pub use sqrtf::sqrtf;

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use {scalbnf, sqrtf};
const BP: [f32; 2] = [1.0, 1.5];
const DP_H: [f32; 2] = [0.0, 5.84960938e-01]; /* 0x3f15c000 */
const DP_L: [f32; 2] = [0.0, 1.56322085e-06]; /* 0x35d1cfdc */
const TWO24: f32 = 16777216.0; /* 0x4b800000 */
const HUGE: f32 = 1.0e30;
const TINY: f32 = 1.0e-30;
const L1: f32 = 6.0000002384e-01; /* 0x3f19999a */
const L2: f32 = 4.2857143283e-01; /* 0x3edb6db7 */
const L3: f32 = 3.3333334327e-01; /* 0x3eaaaaab */
const L4: f32 = 2.7272811532e-01; /* 0x3e8ba305 */
const L5: f32 = 2.3066075146e-01; /* 0x3e6c3255 */
const L6: f32 = 2.0697501302e-01; /* 0x3e53f142 */
const P1: f32 = 1.6666667163e-01; /* 0x3e2aaaab */
const P2: f32 = -2.7777778450e-03; /* 0xbb360b61 */
const P3: f32 = 6.6137559770e-05; /* 0x388ab355 */
const P4: f32 = -1.6533901999e-06; /* 0xb5ddea0e */
const P5: f32 = 4.1381369442e-08; /* 0x3331bb4c */
const LG2: f32 = 6.9314718246e-01; /* 0x3f317218 */
const LG2_H: f32 = 6.93145752e-01; /* 0x3f317200 */
const LG2_L: f32 = 1.42860654e-06; /* 0x35bfbe8c */
const OVT: f32 = 4.2995665694e-08; /* -(128-log2(ovfl+.5ulp)) */
const CP: f32 = 9.6179670095e-01; /* 0x3f76384f =2/(3ln2) */
const CP_H: f32 = 9.6191406250e-01; /* 0x3f764000 =12b cp */
const CP_L: f32 = -1.1736857402e-04; /* 0xb8f623c6 =tail of cp_h */
const IVLN2: f32 = 1.4426950216e+00;
const IVLN2_H: f32 = 1.4426879883e+00;
const IVLN2_L: f32 = 7.0526075433e-06;
pub fn powf(x: f32, y: f32) -> f32 {
let mut z: f32;
let mut ax: f32;
let z_h: f32;
let z_l: f32;
let mut p_h: f32;
let mut p_l: f32;
let y1: f32;
let mut t1: f32;
let t2: f32;
let mut r: f32;
let s: f32;
let mut sn: f32;
let mut t: f32;
let mut u: f32;
let mut v: f32;
let mut w: f32;
let i: i32;
let mut j: i32;
let mut k: i32;
let mut yisint: i32;
let mut n: i32;
let hx: i32;
let hy: i32;
let mut ix: i32;
let iy: i32;
let mut is: i32;
hx = x.to_bits() as i32;
hy = y.to_bits() as i32;
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x**0 = 1, even if x is NaN */
if iy == 0 {
return 1.0;
}
/* 1**y = 1, even if y is NaN */
if hx == 0x3f800000 {
return 1.0;
}
/* NaN if either arg is NaN */
if ix > 0x7f800000 || iy > 0x7f800000 {
return x + y;
}
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if hx < 0 {
if iy >= 0x4b800000 {
yisint = 2; /* even integer y */
} else if iy >= 0x3f800000 {
k = (iy >> 23) - 0x7f; /* exponent */
j = iy >> (23 - k);
if (j << (23 - k)) == iy {
yisint = 2 - (j & 1);
}
}
}
/* special value of y */
if iy == 0x7f800000 {
/* y is +-inf */
if ix == 0x3f800000 {
/* (-1)**+-inf is 1 */
return 1.0;
} else if ix > 0x3f800000 {
/* (|x|>1)**+-inf = inf,0 */
return if hy >= 0 { y } else { 0.0 };
} else {
/* (|x|<1)**+-inf = 0,inf */
return if hy >= 0 { 0.0 } else { -y };
}
}
if iy == 0x3f800000 {
/* y is +-1 */
return if hy >= 0 { x } else { 1.0 / x };
}
if hy == 0x40000000 {
/* y is 2 */
return x * x;
}
if hy == 0x3f000000 {
/* y is 0.5 */
if hx >= 0 {
/* x >= +0 */
return sqrtf(x);
}
}
ax = ::fabsf(x);
/* special value of x */
if ix == 0x7f800000 || ix == 0 || ix == 0x3f800000 {
/* x is +-0,+-inf,+-1 */
z = ax;
if hy < 0 {
/* z = (1/|x|) */
z = 1.0 / z;
}
if hx < 0 {
if ((ix - 0x3f800000) | yisint) == 0 {
z = (z - z) / (z - z); /* (-1)**non-int is NaN */
} else if yisint == 1 {
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
}
return z;
}
sn = 1.0; /* sign of result */
if hx < 0 {
if yisint == 0 {
/* (x<0)**(non-int) is NaN */
return (x - x) / (x - x);
}
if yisint == 1 {
/* (x<0)**(odd int) */
sn = -1.0;
}
}
/* |y| is HUGE */
if iy > 0x4d000000 {
/* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if ix < 0x3f7ffff8 {
return if hy < 0 {
sn * HUGE * HUGE
} else {
sn * TINY * TINY
};
}
if ix > 0x3f800007 {
return if hy > 0 {
sn * HUGE * HUGE
} else {
sn * TINY * TINY
};
}
/* now |1-x| is TINY <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax - 1.; /* t has 20 trailing zeros */
w = (t * t) * (0.5 - t * (0.333333333333 - t * 0.25));
u = IVLN2_H * t; /* IVLN2_H has 16 sig. bits */
v = t * IVLN2_L - w * IVLN2;
t1 = u + v;
is = t1.to_bits() as i32;
t1 = f32::from_bits(is as u32 & 0xfffff000);
t2 = v - (t1 - u);
} else {
let mut s2: f32;
let mut s_h: f32;
let s_l: f32;
let mut t_h: f32;
let mut t_l: f32;
n = 0;
/* take care subnormal number */
if ix < 0x00800000 {
ax *= TWO24;
n -= 24;
ix = ax.to_bits() as i32;
}
n += ((ix) >> 23) - 0x7f;
j = ix & 0x007fffff;
/* determine interval */
ix = j | 0x3f800000; /* normalize ix */
if j <= 0x1cc471 {
/* |x|<sqrt(3/2) */
k = 0;
} else if j < 0x5db3d7 {
/* |x|<sqrt(3) */
k = 1;
} else {
k = 0;
n += 1;
ix -= 0x00800000;
}
ax = f32::from_bits(ix as u32);
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - BP[k as usize]; /* bp[0]=1.0, bp[1]=1.5 */
v = 1.0 / (ax + BP[k as usize]);
s = u * v;
s_h = s;
is = s_h.to_bits() as i32;
s_h = f32::from_bits(is as u32 & 0xfffff000);
/* t_h=ax+bp[k] High */
is = (((ix as u32 >> 1) & 0xfffff000) | 0x20000000) as i32;
t_h = f32::from_bits(is as u32 + 0x00400000 + ((k as u32) << 21));
t_l = ax - (t_h - BP[k as usize]);
s_l = v * ((u - s_h * t_h) - s_h * t_l);
/* compute log(ax) */
s2 = s * s;
r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
r += s_l * (s_h + s);
s2 = s_h * s_h;
t_h = 3.0 + s2 + r;
is = t_h.to_bits() as i32;
t_h = f32::from_bits(is as u32 & 0xfffff000);
t_l = r - ((t_h - 3.0) - s2);
/* u+v = s*(1+...) */
u = s_h * t_h;
v = s_l * t_h + t_l * s;
/* 2/(3log2)*(s+...) */
p_h = u + v;
is = p_h.to_bits() as i32;
p_h = f32::from_bits(is as u32 & 0xfffff000);
p_l = v - (p_h - u);
z_h = CP_H * p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = CP_L * p_h + p_l * CP + DP_L[k as usize];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = n as f32;
t1 = ((z_h + z_l) + DP_H[k as usize]) + t;
is = t1.to_bits() as i32;
t1 = f32::from_bits(is as u32 & 0xfffff000);
t2 = z_l - (((t1 - t) - DP_H[k as usize]) - z_h);
};
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
is = y.to_bits() as i32;
y1 = f32::from_bits(is as u32 & 0xfffff000);
p_l = (y - y1) * t1 + y * t2;
p_h = y1 * t1;
z = p_l + p_h;
j = z.to_bits() as i32;
if j > 0x43000000 {
/* if z > 128 */
return sn * HUGE * HUGE; /* overflow */
} else if j == 0x43000000 {
/* if z == 128 */
if p_l + OVT > z - p_h {
return sn * HUGE * HUGE; /* overflow */
}
} else if (j & 0x7fffffff) > 0x43160000 {
/* z < -150 */
// FIXME: check should be (uint32_t)j > 0xc3160000
return sn * TINY * TINY; /* underflow */
} else if j as u32 == 0xc3160000 {
/* z == -150 */
if p_l <= z - p_h {
return sn * TINY * TINY; /* underflow */
}
}
/*
* compute 2**(p_h+p_l)
*/
i = j & 0x7fffffff;
k = (i >> 23) - 0x7f;
n = 0;
if i > 0x3f000000 {
/* if |z| > 0.5, set n = [z+0.5] */
n = j + (0x00800000 >> (k + 1));
k = ((n & 0x7fffffff) >> 23) - 0x7f; /* new k for n */
t = f32::from_bits(n as u32 & !(0x007fffff >> k));
n = ((n & 0x007fffff) | 0x00800000) >> (23 - k);
if j < 0 {
n = -n;
}
p_h -= t;
}
t = p_l + p_h;
is = t.to_bits() as i32;
t = f32::from_bits(is as u32 & 0xffff8000);
u = t * LG2_H;
v = (p_l - (t - p_h)) * LG2 + t * LG2_L;
z = u + v;
w = v - (z - u);
t = z * z;
t1 = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
r = (z * t1) / (t1 - 2.0) - (w + z * w);
z = 1.0 - (r - z);
j = z.to_bits() as i32;
j += n << 23;
if (j >> 23) <= 0 {
/* subnormal output */
z = scalbnf(z, n);
} else {
z = f32::from_bits(j as u32);
}
return sn * z;
}

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pub fn scalbnf(mut x: f32, mut n: i32) -> f32 {
let x1p127 = f32::from_bits(0x7f000000); // 0x1p127f === 2 ^ 127
let x1p_126 = f32::from_bits(0x800000); // 0x1p-126f === 2 ^ -126
let x1p24 = f32::from_bits(0x4b800000); // 0x1p24f === 2 ^ 24
let mut y: f32 = x;
if n > 127 {
y *= x1p127;
n -= 127;
if n > 127 {
y *= x1p127;
n -= 127;
if n > 127 {
n = 127;
}
}
} else if n < -126 {
y *= x1p_126;
y *= x1p24;
n += 126 - 24;
if n < -126 {
y *= x1p_126;
y *= x1p24;
n += 126 - 24;
if n < -126 {
n = -126;
}
}
}
x = y * f32::from_bits((0x7f + n as u32) << 23);
x
}

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const TINY: f32 = 1.0e-30;
pub fn sqrtf(x: f32) -> f32 {
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)
}

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[package]
name = "test-generator"
version = "0.1.0"
authors = ["Jorge Aparicio <jorge@japaric.io>"]
publish = false
[dependencies]
rand = "0.5.3"

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# `test-generator`
This is a tool to generate test cases for the `libm` crate.
The generator randomly creates inputs for each math function, then proceeds to compute the
expected output for the given function by running the MUSL *C implementation* of the function and
finally it packs the test cases as a Cargo test file. For this reason, this generator **must**
always be compiled for the `x86_64-unknown-linux-musl` target.

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// NOTE we intentionally avoid using the `quote` crate here because it doesn't work with the
// `x86_64-unknown-linux-musl` target.
// NOTE usually the only thing you need to do to test a new math function is to add it to one of the
// macro invocations found in the bottom of this file.
extern crate rand;
use std::error::Error;
use std::fmt::Write as _0;
use std::fs::{self, File};
use std::io::Write as _1;
use std::{i16, u32, u8};
use rand::{Rng, SeedableRng, XorShiftRng};
// Number of test cases to generate
const NTESTS: usize = 10_000;
// TODO tweak this function to generate edge cases (zero, infinity, NaN) more often
fn f32(rng: &mut XorShiftRng) -> f32 {
let sign = if rng.gen_bool(0.5) { 1 << 31 } else { 0 };
let exponent = (rng.gen_range(0, u8::MAX) as u32) << 23;
let mantissa = rng.gen_range(0, u32::MAX) & ((1 << 23) - 1);
f32::from_bits(sign + exponent + mantissa)
}
// fn(f32) -> f32
macro_rules! f32_f32 {
($($intr:ident,)+) => {
fn f32_f32(rng: &mut XorShiftRng) -> Result<(), Box<Error>> {
// MUSL C implementation of the function to test
extern "C" {
$(fn $intr(_: f32) -> f32;)+
}
$(
let mut cases = String::new();
for _ in 0..NTESTS {
let inp = f32(rng);
let out = unsafe { $intr(inp) };
let inp = inp.to_bits();
let out = out.to_bits();
write!(cases, "({}, {})", inp, out).unwrap();
cases.push(',');
}
let mut f = File::create(concat!("tests/", stringify!($intr), ".rs"))?;
write!(f, "
extern crate libm;
#[test]
fn {0}() {{
const CASES: &[(u32, u32)] = &[
{1}
];
for case in CASES {{
let (inp, expected) = *case;
let outf = libm::{0}(f32::from_bits(inp));
let outi = outf.to_bits();
if !((outf.is_nan() && f32::from_bits(expected).is_nan()) ||
outi == expected) {{
panic!(
\"input: {{}}, output: {{}}, expected: {{}}\",
inp,
outi,
expected,
);
}}
}}
}}
",
stringify!($intr),
cases)?;
)+
Ok(())
}
}
}
macro_rules! f32f32_f32 {
($($intr:ident,)+) => {
fn f32f32_f32(rng: &mut XorShiftRng) -> Result<(), Box<Error>> {
extern "C" {
$(fn $intr(_: f32, _: f32) -> f32;)+
}
$(
let mut cases = String::new();
for _ in 0..NTESTS {
let i1 = f32(rng);
let i2 = f32(rng);
let out = unsafe { $intr(i1, i2) };
let i1 = i1.to_bits();
let i2 = i2.to_bits();
let out = out.to_bits();
write!(cases, "(({}, {}), {})", i1, i2, out).unwrap();
cases.push(',');
}
let mut f = File::create(concat!("tests/", stringify!($intr), ".rs"))?;
write!(f, "
extern crate libm;
#[test]
fn {0}() {{
const CASES: &[((u32, u32), u32)] = &[
{1}
];
for case in CASES {{
let ((i1, i2), expected) = *case;
let outf = libm::{0}(f32::from_bits(i1), f32::from_bits(i2));
let outi = outf.to_bits();
if !((outf.is_nan() && f32::from_bits(expected).is_nan()) ||
outi == expected) {{
panic!(
\"input: {{:?}}, output: {{}}, expected: {{}}\",
(i1, i2),
outi,
expected,
);
}}
}}
}}
",
stringify!($intr),
cases)?;
)+
Ok(())
}
};
}
macro_rules! f32i32_f32 {
($($intr:ident,)+) => {
fn f32i32_f32(rng: &mut XorShiftRng) -> Result<(), Box<Error>> {
extern "C" {
$(fn $intr(_: f32, _: i32) -> f32;)+
}
$(
let mut cases = String::new();
for _ in 0..NTESTS {
let i1 = f32(rng);
let i2 = rng.gen_range(i16::MIN, i16::MAX);
let out = unsafe { $intr(i1, i2 as i32) };
let i1 = i1.to_bits();
let out = out.to_bits();
write!(cases, "(({}, {}), {})", i1, i2, out).unwrap();
cases.push(',');
}
let mut f = File::create(concat!("tests/", stringify!($intr), ".rs"))?;
write!(f, "
extern crate libm;
#[test]
fn {0}() {{
const CASES: &[((u32, i16), u32)] = &[
{1}
];
for case in CASES {{
let ((i1, i2), expected) = *case;
let outf = libm::{0}(f32::from_bits(i1), i2 as i32);
let outi = outf.to_bits();
if !((outf.is_nan() && f32::from_bits(expected).is_nan()) ||
outi == expected) {{
panic!(
\"input: {{:?}}, output: {{}}, expected: {{}}\",
(i1, i2),
outi,
expected,
);
}}
}}
}}
",
stringify!($intr),
cases)?;
)+
Ok(())
}
};
}
fn main() -> Result<(), Box<Error>> {
fs::remove_dir_all("tests").ok();
fs::create_dir("tests")?;
let mut rng = XorShiftRng::from_rng(&mut rand::thread_rng())?;
f32_f32(&mut rng)?;
f32f32_f32(&mut rng)?;
f32i32_f32(&mut rng)?;
Ok(())
}
/* Functions to test */
// With signature `fn(f32) -> f32`
f32_f32! {
fabsf,
sqrtf,
}
// With signature `fn(f32, f32) -> f32`
f32f32_f32! {
powf,
}
// With signature `fn(f32, i32) -> f32`
f32i32_f32! {
scalbnf,
}