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#![allow(unused)]
type Fraction = ( i64, u64);
#[derive(PartialEq, Debug)]
pub struct Dec2FracError {
num_iter: u64,
decimal_error: f64,
}
impl std::fmt::Display for Dec2FracError {
fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
write!(
f,
"Failed to find an exact fraction representation after {} iterations.\
The error at this precision is {}.",
self.num_iter, self.decimal_error,
)
}
}
pub fn dec2frac(mut num: f64, max_iter: u64) -> Result<Fraction, Dec2FracError> {
let coeff = if num < 0. { -1 } else { 1 };
let num = num.abs();
let whole_part = num.floor() as u64;
let decimal = num - num.floor();
let mut lo = (0, 1);
let mut hi = (1, 1);
fn mediant(lo: (u64, u64), hi: (u64, u64)) -> (u64, u64) {
(lo.0 + hi.0, lo.1 + hi.1)
}
let frac = {
|| {
if decimal == 0. {
return Ok(lo);
}
let mut med = mediant(lo, hi);
let mut med_dec = (med.0 as f64) / (med.1 as f64);
for _ in 0..max_iter {
med = mediant(lo, hi);
med_dec = (med.0 as f64) / (med.1 as f64);
if (med_dec - decimal).abs() <= std::f64::EPSILON {
return Ok(med);
} else if decimal < med_dec {
hi = med;
} else {
lo = med;
}
}
Err(Dec2FracError {
num_iter: max_iter,
decimal_error: (decimal - (med.0 as f64) / (med.1 as f64)).abs(),
})
}
}()?;
let (numerator, denominator) = frac;
let combined_numerator = (numerator + whole_part * denominator) as i64;
Ok((coeff * combined_numerator, denominator))
}
#[cfg(test)]
mod tests {
use super::*;
type Dec2FracCase = (f64, Result<(i64, u64), Dec2FracError>);
#[allow(clippy::excessive_precision)]
const CASES: [Dec2FracCase; 7] = [
(0., Ok((0 , 1))),
(1., Ok((1 , 1))),
(0.5, Ok((1 , 2))),
(
0.318181818181818181818181818181818181818181818181818181818,
Ok((7 , 22)),
),
(
3.142857142857142857142857142857142857142857142857142857142,
Ok((22 , 7)),
),
(
3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128,
Ok((245_850_922, 78_256_779)),
),
(
-3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128,
Ok((-245_850_922, 78_256_779)),
),
];
#[test]
fn test_dec2frac() {
for (dec, frac) in CASES.iter() {
assert_eq!(dec2frac(*dec, 1_000_000), *frac, "{} != {:?}", dec, frac);
}
}
}