From e4a79af68b2542bec5cd30237869cef0fc911f77 Mon Sep 17 00:00:00 2001
From: Justin Worthe <justin.worthe@gmail.com>
Date: Sat, 26 Nov 2016 22:56:37 +0200
Subject: Adding constructors from polar coordinates

---
 src/complex.rs    | 68 +++++++++++++++++++++++++++++++++++++++++++---
 src/lib.rs        |  1 +
 src/num_traits.rs | 80 +++++++++++++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 146 insertions(+), 3 deletions(-)
 create mode 100644 src/num_traits.rs

(limited to 'src')

diff --git a/src/complex.rs b/src/complex.rs
index 0919564..1a8bc20 100644
--- a/src/complex.rs
+++ b/src/complex.rs
@@ -1,4 +1,5 @@
-use std::ops::Add;
+use std::ops::{Add, Sub, Mul};
+use ::num_traits::{Trig, Pow};
 
 #[derive(Debug, Clone, Copy, PartialEq, Eq)]
 pub struct Complex<T> {
@@ -6,12 +7,27 @@ pub struct Complex<T> {
     imag: T
 }
 
-impl<T: Clone> Complex<T> {
-    fn new(real: T, imag: T) -> Complex<T> {
+impl<T> Complex<T> {
+    pub fn new(real: T, imag: T) -> Complex<T> {
         Complex{real: real, imag: imag}
     }
 }
 
+impl<T> Complex<T> where T: Trig<T> + Mul<Output=T> + Copy {
+    pub fn from_polar(r: T, theta: T) -> Complex<T> {
+        let real = r*theta.cos();
+        let imag = r*theta.sin();
+        Complex::new(real, imag)
+    }
+}
+impl<T> Complex<T> where T: Trig<T> + Pow<T> + Add<Output=T> + Copy  {
+    pub fn to_polar(self) -> (T, T) {
+        let r = (self.real.powi(2) + self.imag.powi(2)).sqrt();
+        let theta = self.imag.atan2(self.real);
+        (r, theta)
+    }
+}
+
 impl<T> Add for Complex<T> where T: Add<Output=T> + Copy {
     type Output = Complex<T>;
 
@@ -22,14 +38,60 @@ impl<T> Add for Complex<T> where T: Add<Output=T> + Copy {
     }
 }
 
+impl<T> Sub for Complex<T> where T: Sub<Output=T> + Copy {
+    type Output = Complex<T>;
+
+    fn sub(self, other: Self) -> Self {
+        let real = self.real - other.real;
+        let imag = self.imag - other.imag;
+        Complex::new(real, imag)
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use super::*;
+    use std::f32;
+    
     #[test]
     fn addition() {
         let a = Complex::new(1, 5);
         let b = Complex::new(-3, 2);
         assert_eq!(a+b, Complex::new(-2, 7));
     }
+
+    #[test]
+    fn subtraction() {
+        let a = Complex::new(1, 5);
+        let b = Complex::new(-3, 2);
+        assert_eq!(a-b, Complex::new(4, 3));
+    }
+
+
+    #[test]
+    fn from_polar() {
+        let right = Complex::from_polar(1.0 as f32, 0.0 as f32);
+        assert!((right.real-1.0).abs() < f32::EPSILON);
+        assert!((right.imag-0.0).abs() < f32::EPSILON);
+
+        let up = Complex::from_polar(1.0 as f32, f32::consts::PI/2.0);
+        assert!((up.real-0.0).abs() < f32::EPSILON/2.0);
+        assert!((up.imag-1.0).abs() < f32::EPSILON/2.0);
+
+        let left = Complex::from_polar(1.0 as f32, f32::consts::PI);
+        assert!((left.real+1.0).abs() < f32::EPSILON);
+        assert!((left.imag-0.0).abs() < f32::EPSILON);
+
+        let down = Complex::from_polar(1.0 as f32, f32::consts::PI*3.0/2.0);
+        assert!((down.real-0.0).abs() < f32::EPSILON);
+        assert!((down.imag+1.0).abs() < f32::EPSILON);
+
+        //not sure why the error here is more than epsilon. My guess
+        // is that it's the 2.0*PI, meaning that the value for PI has
+        // twice the normal error.
+        let rev = Complex::from_polar(1.0 as f32, f32::consts::PI*2.0);
+        assert!((rev.real-1.0).abs() < f32::EPSILON*2.0);
+        assert!((rev.imag-0.0).abs() < f32::EPSILON*2.0);
+    }
 }
 
diff --git a/src/lib.rs b/src/lib.rs
index 3987f3d..818890f 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1 +1,2 @@
 pub mod complex;
+pub mod num_traits;
diff --git a/src/num_traits.rs b/src/num_traits.rs
new file mode 100644
index 0000000..3e18a4b
--- /dev/null
+++ b/src/num_traits.rs
@@ -0,0 +1,80 @@
+pub trait Trig<T> {
+    fn sin(self) -> Self;
+    fn cos(self) -> Self;
+    fn tan(self) -> Self;
+
+    fn asin(self) -> Self;
+    fn acos(self) -> Self;
+    fn atan2(self, other: Self) -> Self;
+}
+
+impl Trig<f32> for f32 {
+    fn sin(self) -> Self {
+        self.sin()
+    }
+    fn cos(self) -> Self {
+        self.cos()
+    }
+    fn tan(self) -> Self {
+        self.tan()
+    }
+    fn asin(self) -> Self {
+        self.asin()
+    }
+    fn acos(self) -> Self {
+        self.acos()
+    }
+    fn atan2(self, other: Self) -> Self {
+        self.atan2(other)
+    }
+}
+impl Trig<f64> for f64 {
+    fn sin(self) -> Self {
+        self.sin()
+    }
+    fn cos(self) -> Self {
+        self.cos()
+    }
+    fn tan(self) -> Self {
+        self.tan()
+    }
+    fn asin(self) -> Self {
+        self.asin()
+    }
+    fn acos(self) -> Self {
+        self.acos()
+    }
+    fn atan2(self, other: Self) -> Self {
+        self.atan2(other)
+    }
+}
+
+
+pub trait Pow<T> {
+    fn powi(self, n: i32) -> Self;
+    fn powf(self, n: T) -> Self;
+    fn sqrt(self) -> Self;
+}
+
+impl Pow<f32> for f32 {
+    fn powi(self, n: i32) -> Self {
+        self.powi(n)
+    }
+    fn powf(self, n: Self) -> Self {
+        self.powf(n)
+    }
+    fn sqrt(self) -> Self {
+        self.sqrt()
+    }
+}
+impl Pow<f64> for f64 {
+    fn powi(self, n: i32) -> Self {
+        self.powi(n)
+    }
+    fn powf(self, n: Self) -> Self {
+        self.powf(n)
+    }
+    fn sqrt(self) -> Self {
+        self.sqrt()
+    }
+}
-- 
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