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Implement GCD for Gaussian integers

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This commit is contained in:
Kiëd Llaentenn 2021-10-04 03:40:50 +00:00
parent b26bced8fe
commit 6480d3ba0e
1 changed files with 46 additions and 19 deletions
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65
kalk/src/prelude/mod.rs
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@ -513,33 +513,60 @@ pub mod funcs {
}
pub fn gcd(x: KalkNum, y: KalkNum) -> KalkNum {
// Find the norm of a Gaussian integer
fn norm(x: KalkNum) -> KalkNum {
KalkNum::new((x.value.clone() * x.value) + (x.imaginary_value.clone() * x.imaginary_value), &x.unit)
}
if x.has_imaginary() || y.has_imaginary() {
if x.imaginary_value.fract() != 0 || y.imaginary_value.fract() != 0 {
if x.value.clone().fract() != 0 || y.value.clone().fract() != 0
|| x.imaginary_value.clone().fract() != 0 || y.imaginary_value.clone().fract() != 0 {
// Not a Gaussian integer!
// TODO: throw an actual error instead of returning NaN
return KalkNum::from(NaNf64);
return KalkNum::from(f64::NAN);
}
// TODO
todo!();
}
// Partially derived from:
// https://stackoverflow.com/a/52692832
if x.value < 0f64 || y.value < 0f64 {
return gcd(KalkNum::new(x.value.abs(), &x.unit), KalkNum::new(y.value.abs(), &y.unit));
}
let a;
let b;
// Euclidean GCD algorithm
let mut x_a = x.clone();
let mut y_a = y.clone();
while !y_a.value.eq(&0) {
let t = y_a.value.clone();
y_a.value = x_a.value % y_a.value;
x_a.value = t;
}
// Ensure a > b
if norm(x.clone()).value < norm(y.clone()).value {
a = y;
b = x;
} else {
a = x;
b = y;
}
// Usually we'd need to return max(x, -x), but since we've handled negative
// values above, that is unnecessary.
return x_a;
let mut c = a.clone().div_without_unit(b.clone());
if c.imaginary_value.clone().fract() == 0 {
KalkNum::new_with_imaginary(b.value.abs(), &b.unit, b.imaginary_value)
} else {
c.value = c.value.round();
c.imaginary_value = c.imaginary_value.round();
gcd(a.sub_without_unit(b.clone().mul_without_unit(c)), b)
}
} else {
if x.value < 0f64 || y.value < 0f64 {
return gcd(KalkNum::new(x.value.abs(), &x.unit), KalkNum::new(y.value.abs(), &y.unit));
}
// Euclidean GCD algorithm, but with modulus
let mut x_a = x.clone();
let mut y_a = y.clone();
while !y_a.value.eq(&0) {
let t = y_a.value.clone();
y_a.value = x_a.value % y_a.value;
x_a.value = t;
}
// Usually we'd need to return max(x, -x), but since we've handled negative
// values above, that is unnecessary.
x_a
}
}
pub fn im(x: KalkNum) -> KalkNum {