2 files changed, 78 insertions, 1 deletions

diff --git a/libmu/src/maths/complex.rs b/libmu/src/maths/complex.rs
index 79212b6..931b030 100644
--- a/libmu/src/maths/complex.rs
+++ b/libmu/src/maths/complex.rs
@@ -1,7 +1,7 @@
 use crate::numeric_types::Float;
 use core::{fmt, ops};
 
-#[derive(Copy, Clone)]
+#[derive(Copy, Clone, PartialOrd, PartialEq)]
 pub struct Complex<T: Float> {
     pub real: T,
     pub imaginary: T,
@@ -49,6 +49,17 @@ impl<T: Float> Complex<T> {
     }
 }
 
+impl<T: Float> ops::Neg for Complex<T> {
+    type Output = Complex<T>;
+
+    fn neg(self) -> Complex<T> {
+        Complex {
+            real: -self.real,
+            imaginary: -self.imaginary,
+        }
+    }
+}
+
 impl<T: Float> ops::Add for Complex<T> {
     type Output = Complex<T>;
 
diff --git a/libmu/src/maths/numeric_types.rs b/libmu/src/maths/numeric_types.rs
index 42e2fb7..f9833dc 100644
--- a/libmu/src/maths/numeric_types.rs
+++ b/libmu/src/maths/numeric_types.rs
@@ -1,5 +1,7 @@
 use core::ops;
 
+use super::Complex;
+
 pub trait Numeric:
     Copy
     + PartialOrd
@@ -43,6 +45,50 @@ impl Float for f64 {
     }
 }
 
+impl Float for Complex<f32> {
+    fn sqrt(self) -> Self {
+        let r = self.abs();
+        let theta = self.phase();
+
+        let sqrt_r = libm::sqrtf(r);
+        let sqrt_theta = theta / 2.0;
+
+        Complex::new(
+            sqrt_r * libm::cosf(sqrt_theta),
+            sqrt_r * libm::sinf(sqrt_theta),
+        )
+    }
+
+    fn atan2(y: Self, x: Self) -> Self {
+        Complex::new(
+            libm::atan2f(y.real, x.real),
+            libm::atan2f(y.imaginary, x.imaginary),
+        )
+    }
+}
+
+impl Float for Complex<f64> {
+    fn sqrt(self) -> Self {
+        let r = self.abs();
+        let theta = self.phase();
+
+        let sqrt_r = libm::sqrt(r);
+        let sqrt_theta = theta / 2.0;
+
+        Complex::new(
+            sqrt_r * libm::cos(sqrt_theta),
+            sqrt_r * libm::sin(sqrt_theta),
+        )
+    }
+
+    fn atan2(y: Self, x: Self) -> Self {
+        Complex::new(
+            libm::atan2(y.real, x.real),
+            libm::atan2(y.imaginary, x.imaginary),
+        )
+    }
+}
+
 impl Integer for i64 {}
 impl Integer for i32 {}
 
@@ -85,3 +131,23 @@ impl Numeric for f64 {
         1.0
     }
 }
+
+impl Numeric for Complex<f32> {
+    fn zero() -> Self {
+        Complex::new(0.0, 0.0)
+    }
+
+    fn one() -> Self {
+        Complex::new(1.0, 0.0)
+    }
+}
+
+impl Numeric for Complex<f64> {
+    fn zero() -> Self {
+        Complex::new(0.0, 0.0)
+    }
+
+    fn one() -> Self {
+        Complex::new(1.0, 0.0)
+    }
+}