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```
```/// Macro to test that two values are approximately equal. It checks that the relative difference between
/// the two values is less than some epsilon value.
///
/// ```ignore
/// use approx_eq::assert_approx_eq;
/// fn main() {
///   assert_approx_eq!(1., 0.99999999999); // should pass
///   assert_approx_eq!(1., 0.99999999999, 1e-5); // should pass
///   assert_approx_eq!(1., 0.99999999999, 1e-20); // should fail
///   assert_approx_eq!(0., 0.); // should pass
///   assert_approx_eq!(1., 2.); // should fail
/// }
/// ```
#[macro_use]
pub mod approx_eq {
#[macro_export]
/// Epsilon takes a default value of 1e-6.
/// It is also possible to specify the error level to use.
macro_rules! assert_approx_eq {
(\$x: expr, \$y: expr) => {
let eps = 1e-6;
let (x, y): (f64, f64) = (\$x, \$y);
if x == 0. {
assert!(y.abs() < eps, "x = {}, y = {}", x, y);
} else if y == 0. {
assert!(x.abs() < eps, "x = {}, y = {}", x, y);
} else {
assert!(&x.signum() == &y.signum(), "x = {}, y = {}", x, y);
let (x, y): (f64, f64) = (x.abs(), y.abs());
assert!(
(&x - &y).abs() / [x, y].iter().cloned().fold(f64::NAN, f64::min) < eps,
"x = {}, y = {}",
x,
y
);
}
};
(\$x: expr, \$y: expr, \$e: expr) => {
let (x, y): (f64, f64) = (\$x, \$y);
if x == 0. {
assert!(y.abs() < \$e, "x = {}, y = {}", x, y);
} else if y == 0. {
assert!(x.abs() < \$e, "x = {}, y = {}", x, y);
} else {
assert!(&x.signum() == &y.signum(), "x = {}, y = {}", x, y);
let (x, y): (f64, f64) = (x.abs(), y.abs());
assert!(
(&x - &y).abs() / [x, y].iter().cloned().fold(f64::NAN, f64::min) < \$e,
"x = {}, y = {}",
x,
y
);
}
};
}
}

/// Function to find the relative difference between two values.
pub fn rel_diff(x: f64, y: f64) -> f64 {
if x == 0. {
return y.abs();
} else if y == 0. {
return x.abs();
} else {
let (ax, ay) = (x.abs(), y.abs());
return (&ax - &ay).abs() / [ax, ay].iter().cloned().fold(f64::NAN, f64::min);
}
}

#[cfg(test)]
mod tests {
use super::*;

#[test]
fn test_noeps() {
assert_approx_eq!(1., 1.);
assert_approx_eq!(1., 1.000001);
}

#[test]
fn test_witheps() {
assert_approx_eq!(1.0000000001, 1., 1e-5);
}

#[test]
fn test_nearzero() {
assert_approx_eq!(0., -0.0000000000245);
}

#[test]
fn test_zero() {
assert_approx_eq!(0., 0.);
}

#[test]
#[should_panic]
fn test_invalid() {
assert_approx_eq!(1.0000000001, 1., 1e-10);
}

#[test]
#[should_panic]
fn test_sign() {
assert_approx_eq!(1., -1.);
}
}
```