Finished the Vector definition.

This complete what is needed for the definition of Vector2, Vector3, and Vector4.

This required a trigonometry section, fleshing out the rest of the Number, ToNumber,
and FromNumber section, correctly defining all the available function for the Real
trait, and defining several constants.

tests/constants.rs

@@ -0,0 +1,97 @@
+extern crate sigils;
+
+use std::{f32, f64};
+use sigils::Constants;
+
+
+#[test]
+fn constant_check_f32()
+{
+   let val: f32 = Constants::SQRT_2;
+   assert_eq!(val, f32::consts::SQRT_2);
+   let val: f32 = Constants::SQRT_3;
+   assert_eq!(val, 1.73205080756887729352f32);
+   let val: f32 = Constants::INVERSE_SQRT_2;
+   assert_eq!(val, 1.0f32 / f32::consts::SQRT_2);
+   let val: f32 = Constants::INVERSE_SQRT_3;
+   assert_eq!(val, 1.0f32 / 1.73205080756887729352f32);
+
+   let val: f32 = Constants::E;
+   assert_eq!(val, f32::consts::E);
+
+   let val: f32 = Constants::LOG2_E;
+   assert_eq!(val, f32::consts::LOG2_E);
+   let val: f32 = Constants::LOG10_E;
+   assert_eq!(val, f32::consts::LOG10_E);
+   let val: f32 = Constants::LOGE_2;
+   assert_eq!(val, 2f32.ln());
+   let val: f32 = Constants::LOGE_10;
+   assert_eq!(val, 10f32.ln());
+
+   let val: f32 = Constants::TWO_PI;
+   assert_eq!(val, 2f32 * f32::consts::PI);
+   let val: f32 = Constants::PI;
+   assert_eq!(val, f32::consts::PI);
+   let val: f32 = Constants::HALF_PI;
+   assert_eq!(val, f32::consts::PI / 2f32);
+   let val: f32 = Constants::THIRD_PI;
+   assert_eq!(val, f32::consts::PI / 3f32);
+   let val: f32 = Constants::QUARTER_PI;
+   assert_eq!(val, f32::consts::PI / 4f32);
+   let val: f32 = Constants::SIXTH_PI;
+   assert_eq!(val, f32::consts::PI / 6f32);
+   let val: f32 = Constants::EIGHTH_PI;
+   assert_eq!(val, f32::consts::PI / 8f32);
+   let val: f32 = Constants::INVERSE_PI;
+   assert_eq!(val, 1.0f32 / f32::consts::PI);
+   let val: f32 = Constants::TWO_INVERSE_PI;
+   assert_eq!(val, 2.0f32 / f32::consts::PI);
+   let val: f32 = Constants::TWO_INVERSE_SQRT_PI;
+   assert_eq!(val, 2.0f32 / (f32::consts::PI).sqrt());
+}
+
+#[test]
+fn constant_check_f64()
+{
+   let val: f64 = Constants::SQRT_2;
+   assert_eq!(val, f64::consts::SQRT_2);
+   let val: f64 = Constants::SQRT_3;
+   assert_eq!(val, 1.73205080756887729352f64);
+   let val: f64 = Constants::INVERSE_SQRT_2;
+   assert_eq!(val, 1.0f64 / f64::consts::SQRT_2);
+   let val: f64 = Constants::INVERSE_SQRT_3;
+   assert_eq!(val, 1.0f64 / 1.73205080756887729352f64);
+
+   let val: f64 = Constants::E;
+   assert_eq!(val, f64::consts::E);
+
+   let val: f64 = Constants::LOG2_E;
+   assert_eq!(val, f64::consts::LOG2_E);
+   let val: f64 = Constants::LOG10_E;
+   assert_eq!(val, f64::consts::LOG10_E);
+   let val: f64 = Constants::LOGE_2;
+   assert_eq!(val, 2f64.ln());
+   let val: f64 = Constants::LOGE_10;
+   assert_eq!(val, 10f64.ln());
+
+   let val: f64 = Constants::TWO_PI;
+   assert_eq!(val, 2f64 * f64::consts::PI);
+   let val: f64 = Constants::PI;
+   assert_eq!(val, f64::consts::PI);
+   let val: f64 = Constants::HALF_PI;
+   assert_eq!(val, f64::consts::PI / 2f64);
+   let val: f64 = Constants::THIRD_PI;
+   assert_eq!(val, f64::consts::PI / 3f64);
+   let val: f64 = Constants::QUARTER_PI;
+   assert_eq!(val, f64::consts::PI / 4f64);
+   let val: f64 = Constants::SIXTH_PI;
+   assert_eq!(val, f64::consts::PI / 6f64);
+   let val: f64 = Constants::EIGHTH_PI;
+   assert_eq!(val, f64::consts::PI / 8f64);
+   let val: f64 = Constants::INVERSE_PI;
+   assert_eq!(val, 1.0f64 / f64::consts::PI);
+   let val: f64 = Constants::TWO_INVERSE_PI;
+   assert_eq!(val, 2.0f64 / f64::consts::PI);
+   let val: f64 = Constants::TWO_INVERSE_SQRT_PI;
+   assert_eq!(val, 2.0f64 / (f64::consts::PI).sqrt());
+}