maph 0.8.1

Maths package for use with personal stuff, but like, you can totally use it! If you want! There's even some light documentation now!
Documentation 
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use std::f32::consts::PI;

use crate::{geom::{vector::*, matrix::*, quaternion::{Quaternion, DualQuaternion}}, RotationOrder};
use crate::num::Magnitude;

fn equal_ish(a: f32, b: f32, d: f32) -> bool {
    (a - b).abs() < d
}
fn vec_equal_ish<const L: usize>(a: Vector<L>, b: Vector<L>, d: f32) -> bool {
    for i in 0..L {
        if !equal_ish(a[i], b[i], d) { return false; }
    }
    true
}
fn mat_equal_ish<const R: usize, const C: usize>(a: Matrix<R, C>, b: Matrix<R, C>, d: f32) -> bool {
    for i in 0..R {
        if !vec_equal_ish(a.row(i), b.row(i), d) { return false; }
    }
    true
}
#[test]
fn rational_test() {
    use crate::num::rational::*;

    let n = r32::from(1234.923456);
    eprintln!("{}", n);

    let a = (Vector::<3>::new([0.1, 0.2, 0.3]), Vector::<3>::new([0.4, 0.5, 0.6]), Vector::<3>::new([0.7, 0.8, 0.9]));
    let b = (VectorPrecise::<3>::new([r32::from(0.1), r32::from(0.2), r32::from(0.3)]), VectorPrecise::<3>::new([r32::from(0.4), r32::from(0.5), r32::from(0.6)]), VectorPrecise::<3>::new([r32::from(0.7), r32::from(0.8), r32::from(0.9)]));
    //eprintln!("{}", b.1 + b.2);
    //eprintln!("{}, {}", a.0*(a.1 + a.2)/a.1, b.0*(b.1 + b.2)/b.1);
    assert!(vec_equal_ish(a.0*(a.1 + a.2)/a.1, Vector::<3>::from(b.0*(b.1 + b.2)/b.1), 0.0001));
}
#[test]
fn gcd_test() {
    assert!(crate::num::factors::gcd32(35, 10) == 5);
    assert!(crate::num::factors::gcd32(156, 36) == 12);
}
#[test]
fn factor_test() {
    assert!(crate::num::factors::fac32(24) == vec!(2, 2, 2, 3))
}
#[test]
fn sqrt_test() {
    use crate::num::rational::*;
    eprintln!("{}", r32::new_unchecked(25, 7).surd_sqrt());
    assert!(r32::new_unchecked(25, 7).surd_sqrt().squared() == r32::new_unchecked(25, 7));
}
#[test]
fn quaternion_composition() {
    let a = Quaternion::new(0.4, 0.3, 0.2, 0.5);
    let b = Quaternion::new(0.5, 0.4, 0.3, 0.6);
    let c = Quaternion::new(0.5, 0.36, 0.28, -0.08);
    eprintln!("{}", Vector::<4>::from(a*b));
    assert!(vec_equal_ish(Vector::<4>::from(a*b), Vector::<4>::from(c), 0.001));
}

//Vector Dot
#[test]
fn matrix_dot() {
    assert!(equal_ish(Vector::<2>::new([2.0, 3.0]).dot(Vector::<2>::new([4.0, 5.0])), 23.0, 0.001));
    assert!(equal_ish(Vector::<3>::new([2.0, 3.0, 4.0]).dot(Vector::<3>::new([4.0, 5.0, 6.0])), 47.0, 0.001));
    assert!(equal_ish(Vector::<4>::new([2.0, 3.0, 4.0, 5.0]).dot(Vector::<4>::new([4.0, 5.0, 6.0, 7.0])), 82.0, 0.001));
}
//Vector Cross
#[test]
fn matrix_cross() {
    assert!(vec_equal_ish(crate::geom::cross(Vector::<3>::new([0.0, 1.0, 0.0]), Vector::<3>::new([1.0, 0.0, 0.0])), Vector::<3>::new([0.0, 0.0, -1.0]), 0.001));
}
//Vector Mag
#[test]
fn matrix_mag() {
    assert!(equal_ish(Vector::<2>::new([2.0_f32, 3.0_f32]).mag(), (13.0_f32).sqrt(), 0.001));
    assert!(equal_ish(Vector::<3>::new([2.0_f32, 3.0_f32, 4.0_f32]).mag(), (29.0_f32).sqrt(), 0.001));
    assert!(equal_ish(Vector::<4>::new([2.0_f32, 3.0_f32, 4.0_f32, 5.0_f32]).mag(), (54.0_f32).sqrt(), 0.001));
}
//Matrix Math Tests

//Matrix Mul
#[test]
fn matrix_mul() {
    let mat1 = Matrix::<3, 3>::new([[0.0, 1.0, 2.0], [3.0, 4.0, 5.0], [6.0, 7.0, 8.0]]);
    let mat2 = Matrix::<3, 3>::new([[9.0, 8.0, 7.0], [6.0, 5.0, 4.0], [3.0, 2.0, 1.0]]);
    let mat3 = Matrix::<3, 3>::new([[12.0, 9.0, 6.0], [66.0, 54.0, 42.0], [120.0, 99.0, 78.0]]);
    assert!(mat_equal_ish(mat1 * mat2, mat3, 0.001));
}

//Matrix LU
#[test]
fn matrix_lu() {
    {
        let lu = Matrix::<4, 4>::new([
            [1.0, 1.0, 1.0, -5.0], 
            [-2.0, -6.0, 1.0, 13.0], 
            [3.0, -17.0, 16.0, -2.0], 
            [5.0, -3.0, 9.0, -25.0]
        ]).lu();
        let lu0 = Matrix::<4, 4>::new([
            [1.0, 0.0, 0.0, 0.0], 
            [-2.0, 1.0, 0.0, 0.0], 
            [3.0, 5.0, 1.0, 0.0],
            [5.0, 2.0, 1.0, 1.0]]);
        let lu1 = Matrix::<4, 4>::new([
            [1.0, 1.0, 1.0, -5.0], 
            [0.0, -4.0, 3.0, 3.0], 
            [0.0, 0.0, -2.0, -2.0],
            [0.0, 0.0, 0.0, -4.0]]);
        assert!(mat_equal_ish(lu0, lu.unwrap().0, 0.001));
        assert!(mat_equal_ish(lu1, lu.unwrap().1, 0.001));
    }
}
#[test]
fn back_sub_test() {
    let u = Matrix::<3, 3>::new([
        [1.0, -2.0, 1.0],
        [0.0, 1.0, 6.0],
        [0.0, 0.0, 1.0],
    ]);
    let d = Vector::<3>::new([4.0, -1.0, 2.0]);
    let x = Vector::<3>::new([-24.0, -13.0, 2.0]);
    eprintln!("{}", u.back_sub(d));
    assert!(vec_equal_ish(u.back_sub(d), x, 0.001));
}
#[test]
fn sub_test() {
    let a = Matrix::<4, 4>::new([
        [1.0, 1.0, 1.0, -5.0], 
        [-2.0, -6.0, 1.0, 13.0], 
        [3.0, -17.0, 16.0, -2.0], 
        [5.0, -3.0, 9.0, -25.0]
    ]);
    let b = Vector::<4>::new([-14.0, 41.0, 9.0, -74.0]);
    let x = Vector::<4>::new([1.0, 2.0, 3.0, 4.0]);
    eprintln!("{}", a.lup_sub(b).unwrap());
    assert!(vec_equal_ish(a.lup_sub(b).unwrap(), x, 0.001));
}
#[test]
fn inverse_test() {
    let m = Matrix::<4, 4>::new([
        [1.0, 4.0, 5.0, -1.0],
        [-2.0, 3.0, -1.0, 0.0],
        [2.0, 1.0, 1.0, 0.0],
        [3.0, -1.0, 2.0, 1.0]
    ]);
    let m2 = Matrix::<4, 4>::new([
        [-0.1, -0.1, 0.6, -0.1],
        [0.0, 0.25, 0.25, 0.0],
        [0.2, -0.05, -0.45, 0.2],
        [-0.1, 0.65, -0.65, 0.9]
    ]);
    //eprintln!("{}", m.lu().unwrap().0);
    //eprintln!("{}", m.inverse().unwrap());
    assert!(mat_equal_ish(m.inverse().unwrap(), m2, 0.001));
    let dq = DualQuaternion::from_translate_rotate(Vector::<3>::new([2.0, 3.0, 5.0]), Quaternion::from_euler(0.5, 0.4, 0.3, RotationOrder::xyz())).normalise();
    let point = Vector::<4>::new([5.0, 4.0, 3.0, 1.0]);
    eprintln!("{:?}\n{:?}", dq, dq * dq.inverse() * dq);
    assert!(vec_equal_ish(point, dq.inverse().transform(dq.transform(point)), 0.0001));
}

//Matrix Det
#[test]
fn matrix_det() {
    let mat = Matrix::<3, 3>::new([
        [22.0, 15.0, 5.0],
        [2.0, 45.0, 3.0],
        [42.0, 0.0, 10.0]
    ]);
    assert!((mat.det().unwrap() - 2040.0_f32).abs() < 0.001);
    let mat2 = Matrix::<4, 4>::new([
        [1.0, 1.0, 1.0, -5.0], 
        [-2.0, -6.0, 1.0, 13.0], 
        [3.0, -17.0, 16.0, -2.0], 
        [5.0, -3.0, 9.0, -25.0]
    ]);
    assert!((mat2.det().unwrap() + 32.0_f32).abs() < 0.001);
}

//Matrix Vector Tests

//Matrix Vector Mul
#[test]
fn matrix_vec_mul() {
    let vec = Vector::<4>::new([1.0, 2.0, 3.0, 4.0]);
    let mat = Matrix::<4, 4>::new([
        [1.0, 2.0, 3.0, 4.0],
        [5.0, 6.0, 7.0, 8.0],
        [9.0, 8.0, 7.0, 6.0],
        [5.0, 4.0, 3.0, 2.0]
    ]);
    assert!(vec_equal_ish(mat*vec, Vector::<4>::new([30.0, 70.0, 70.0, 30.0]), 0.001)); 
}

//Vector Matrix Mul
#[test]
fn vec_matrix_mul() {
    let vec = Vector::<4>::new([1.0, 2.0, 3.0, 4.0]);
    let mat = Matrix::<4, 4>::new([
        [1.0, 2.0, 3.0, 4.0],
        [5.0, 6.0, 7.0, 8.0],
        [9.0, 8.0, 7.0, 6.0],
        [5.0, 4.0, 3.0, 2.0]
    ]);
    assert!(vec_equal_ish(vec*mat, Vector::<4>::new([58.0, 54.0, 50.0, 46.0]), 0.001)); 
}
//Axis Angle
#[test]
fn axis_angle() {
    let axis = Vector::<3>::new([0.5, 0.6, 0.7]).normalised();
    let angle = 0.53;
    let quat = Quaternion::from_axis_angle(axis, angle);
    let aa_rev = quat.to_axis_angle();
    assert!(vec_equal_ish(aa_rev.0, axis, 0.001));
    assert!(equal_ish(aa_rev.1, angle, 0.001));
}

//TRS
#[test]
fn transformation_test() {
    let point = Vector::<4>::new([1.0, 0.0, 0.0, 1.0]);
    let scale = Vector::<3>::new([2.0, 2.0, 2.0]);
    let rotation = Vector::<3>::new([0.0, 0.0, PI/2.0]);
    let translation = Vector::<3>::new([0.0, 2.0, 0.0]);
    let trs = crate::geom::transforms::transform_mat::from_trs(translation, Quaternion::from_euler(rotation[0], rotation[1], rotation[2], crate::geom::transforms::RotationOrder::xyz()), scale);
    let new_point = trs * point;
    //eprintln!("{}, {}", new_point, trs);
    assert!(Vector::<3>::new([new_point[0], new_point[1], new_point[2]]).mag() < 0.001);
    let scaled_point = Vector::<4>::new([2.0, 0.0, 0.0, 1.0]);
    let dual_quat = DualQuaternion::from_rotate_translate(Quaternion::from_euler(rotation[0], rotation[1], rotation[2], crate::geom::transforms::RotationOrder::xyz()), translation);
    //let dual_rot = DualQuaternion::from_quat(Quaternion::from_euler(rotation[0], rotation[1], rotation[2], crate::geom::transforms::RotationOrder::xyz()));
    //let dual_trans = DualQuaternion::from_translate(translation);
    let dual_point = dual_quat.transform(scaled_point);
    assert!(Vector::<3>::new([dual_point[0], dual_point[1], dual_point[2]]).mag() < 0.001);
}

//Projection

//Orthographic

//CG Tests

#[test]
fn matrix_identity() {
    let mat1 = Matrix::<3, 3>::new([[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0 , 0.0, 1.0]]);
    let mat2 = Matrix::<3, 1>::new([[4.0], [5.0], [6.0]]);
    assert!(mat1.multiply(mat2) == mat2);
}

//Bit Tests
#[test]
fn bit_test() {
    let f = crate::bit::sesp(-125.24);
    eprintln!("{}, {}, {}", f.0, f.1, f.2);
    assert!(!f.0);
    assert!(f.1 == 133);
    assert!(f.2 == 8026849);
}