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// devela::num::lin::vector::array::methods
//
//! impl methods for Vector
//
#[allow(unused_imports)]
#[cfg(not(feature = "std"))]
use crate::FloatExt;
#[cfg(feature = "int")]
use crate::{Int, unwrap};
use crate::{Vector, concat as cc, stringify as fy};
/* common methods */
impl<T, const D: usize> Vector<T, D> {
/// Returns a new `Vector` from the given `coords` array.
pub const fn new(coords: [T; D]) -> Self {
Self { coords }
}
}
/* compile-time ops for primitives */
/// helper for implementing methods on `Vector`.
///
/// $t: the inner integer primitive type
macro_rules! impl_vector {
() => {
#[cfg(feature = "int")]
impl_vector![sint i8, i16, i32, i64, i128, isize];
#[cfg(feature = "int")]
impl_vector![uint u8, u16, u32, u64, u128, usize];
impl_vector![float f32, f64];
};
// integers common methods
(int $($t:ty),+ $(,)?) => {
$( impl_vector![@int $t]; )+
};
(@int $t:ty) => {
#[doc = cc!("# Methods for vectors represented using `", fy!($t), "`.")]
impl<const D: usize> Vector<$t, D> {
/// A `Vector` with all ones.
pub const ONE: Self = Self::new([1; D]);
/// A `Vector` with all zeros.
pub const ZERO: Self = Self::new([0; D]);
/* ops with vector */
/// Returns the normalized vector, using the given vector `magnitude`.
///
/// $$
/// \bm{n} = \widehat{\bm{a}} = \frac{1}{d}\thinspace\bm{a} =
/// \frac{\bm{a}}{|\bm{a}|}
/// $$
pub const fn c_normalize_with(self, magnitude: $t) -> Self {
let mut normalized = [0; D];
let mut i = 0;
while i < D {
normalized[i] = self.coords[i] / magnitude;
i += 1;
}
Vector { coords: normalized }
}
/// Calculates the magnitude of the vector (squared).
///
/// This is faster than calculating the magnitude,
/// which is useful for comparisons.
///
/// # Formula
/// $$ \large |\vec{V}|^2 = V_0^2 + ... + V_n^2 $$
pub const fn c_magnitude_sq(self) -> $t { self.c_dot(self) }
/// Adds two vectors together, in compile-time.
pub const fn c_add(self, other: Self) -> Self {
let mut result = [0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] + other.coords[i];
i += 1;
}
Vector::new(result)
}
/// Subtracts another vector from this vector, in compile-time.
pub const fn c_sub(self, other: Self) -> Self {
let mut result = [0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] - other.coords[i];
i += 1;
}
Vector::new(result)
}
/// Computes the dot product of two vectors, in compile-time.
pub const fn c_dot(self, other: Self) -> $t {
let mut result = 0;
let mut i = 0;
while i < D {
result += self.coords[i] * other.coords[i];
i += 1;
}
result
}
/* ops with scalar */
/// Multiplies each element of the vector by a scalar, in compile-time.
pub const fn c_scalar_mul(self, scalar: $t) -> Self {
let mut result = [0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] * scalar;
i += 1;
}
Vector::new(result)
}
/// Divides each element of the vector by a scalar, in compile-time.
pub const fn c_scalar_div(self, scalar: $t) -> Self {
let mut result = [0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] / scalar;
i += 1;
}
Vector::new(result)
}
}
#[doc = cc!("# Methods for 3d vectors represented using `", fy!($t), "`.")]
impl Vector<$t, 3> {
/// Computes the cross product of two vectors.
///
/// That is the vector orthogonal to both vectors.
///
/// Also known as the *exterior product* or the *vector product*.
///
/// It is only defined for 3-dimensional vectors, and it is not
/// commutative: $\vec{a}\times\vec{b} = -(\vec{b}\times\vec{a})$.
///
/// # Formula
/// $$
/// \bm{a} \times \bm{b} =
/// \begin{bmatrix} a_x \cr a_y \cr a_z \end{bmatrix} \times
/// \begin{bmatrix} b_x \cr b_y \cr b_z \end{bmatrix} =
/// \begin{bmatrix}
/// a_y b_z - a_z b_y \cr
/// a_z b_x - a_x b_z \cr
/// a_x b_y - a_y b_x
/// \end{bmatrix}
/// $$
pub const fn c_cross(self, other: Self) -> Self {
let cross_product = [
self.coords[1] * other.coords[2] - self.coords[2] * other.coords[1], // i
self.coords[2] * other.coords[0] - self.coords[0] * other.coords[2], // j
self.coords[0] * other.coords[1] - self.coords[1] * other.coords[0], // k
];
Vector::new(cross_product)
}
}
};
// signed integers specific methods
(sint $($t:ty),+ $(,)?) => {
$( impl_vector![@sint $t]; )+
};
(@sint $t:ty) => {
impl_vector![int $t];
#[doc = cc!("# Methods for vectors represented using `", fy!($t), "`, signed.")]
impl<const D: usize> Vector<$t, D> {
/// A `Vector` with all negative ones.
pub const NEG_ONE: Self = Self::new([-1; D]);
/// Calculates the floored magnitude of the vector.
///
/// It could underestimate the true magnitude.
pub const fn c_magnitude_floor(self) -> $t {
unwrap![ok Int(self.c_dot(self).abs()).sqrt_floor()].0
}
/// Calculates the ceiled magnitude of the vector.
///
/// It could overestimate the true magnitude.
pub const fn c_magnitude_ceil(self) -> $t {
unwrap![ok Int(self.c_dot(self).abs()).sqrt_ceil()].0
}
/// Calculates the rounded magnitude of the vector.
/// # Panics
/// Can panic if we reach a `i128` value close to its maximum during operations.
pub const fn c_magnitude_round(self) -> $t {
unwrap![ok Int(self.c_dot(self).abs()).sqrt_round()].0
}
}
};
// unsigned integers specific methods
(uint $($t:ty),+ $(,)?) => {
$( impl_vector![@uint $t]; )+
};
(@uint $t:ty) => {
impl_vector![int $t];
#[doc = cc!("# Methods for vectors represented using `", fy!($t), "`, unsigned.")]
impl<const D: usize> Vector<$t, D> {
/// Calculates the floored magnitude of the vector.
///
/// It could underestimate the true magnitude.
pub const fn c_magnitude_floor(self) -> $t {
Int(self.c_dot(self)).sqrt_floor().0
}
/// Calculates the ceiled magnitude of the vector.
///
/// It could overestimate the true magnitude.
pub const fn c_magnitude_ceil(self) -> $t {
Int(self.c_dot(self)).sqrt_ceil().0
}
/// Calculates the rounded magnitude of the vector.
/// # Panics
/// Can panic if we reach a `u128` value close to its maximum during operations.
pub const fn c_magnitude_round(self) -> $t {
unwrap![ok Int(self.c_dot(self)).sqrt_round()].0
}
}
};
// $f: the inner floating-point primitive type
(float $($f:ty),+ $(,)?) => {
$( impl_vector![@float $f]; )+
};
(@float $f:ty) => {
#[doc = cc!("# Methods for vectors represented using `", fy!($f), "`.")]
impl<const D: usize> Vector<$f, D> {
/// A `Vector` with all ones.
pub const ONE: Self = Self::new([1.0; D]);
/// A `Vector` with all zeros.
pub const ZERO: Self = Self::new([0.0; D]);
/// A `Vector` with all negative ones.
pub const NEG_ONE: Self = Self::new([-1.0; D]);
/// Returns the normalized vector, as a *unit vector*.
///
/// $$
/// \bm{n} = \widehat{\bm{a}} = \frac{1}{d}\thinspace\bm{a} =
/// \frac{\bm{a}}{|\bm{a}|}
/// $$
pub fn normalize(&self) -> Self {
let mag = self.magnitude();
let mut normalized = [0.0; D];
for i in 0..D {
normalized[i] = self.coords[i] / mag;
}
Vector { coords: normalized }
}
/// Calculates the magnitude of the vector.
///
/// # Formula
/// $$ \large |\vec{V}| = \sqrt{V_0^2 + ... + V_n^2} $$
pub fn magnitude(self) -> $f { self.dot(self).sqrt() }
/// Calculates the squared magnitude of the vector.
///
/// This is faster than calculating the magnitude,
/// which is useful for comparisons.
///
/// # Formula
/// $$ \large |\vec{V}|^2 = V_0^2 + ... + V_n^2 $$
pub fn magnitude_sq(self) -> $f { self.dot(self) }
/// Adds two vectors together.
#[allow(clippy::should_implement_trait)]
pub fn add(self, other: Self) -> Self {
let mut result = [0.0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] + other.coords[i];
i += 1;
}
Vector::new(result)
}
/// Subtracts another vector from this vector.
#[allow(clippy::should_implement_trait)]
pub fn sub(self, other: Self) -> Self {
let mut result = [0.0; D];
let mut i = 0;
while i < D {
result[i] = self.coords[i] - other.coords[i];
i += 1;
}
Vector::new(result)
}
/// Computes the dot product of two vectors.
///
/// That is the magnitude of one vector in the direction of another.
///
/// Also known as the *inner produc* or the *scalar product*.
///
/// # Formula
/// $$
/// \large \vec{a}\cdot\vec{b} =
/// \begin{bmatrix} a_0 \cr ... \cr a_n \end{bmatrix} \cdot
/// \begin{bmatrix} b_0 \cr ... \cr b_n \end{bmatrix} =
/// a_0 b_0 + ... + a_n b_n
/// $$
pub fn dot(self, other: Self) -> $f {
let mut result = 0.0;
let mut i = 0;
while i < D {
result += self.coords[i] * other.coords[i];
i += 1;
}
result
}
}
#[doc = cc!("# Methods for 3d vectors represented using `", fy!($f), "`.")]
impl Vector<$f, 3> {
/// Computes the cross product of two vectors.
///
/// That is the vector orthogonal to both vectors.
///
/// Also known as the *exterior product* or the *vector product*.
///
/// It is only defined for 3-dimensional vectors, and it is not
/// commutative: $\vec{a}\times\vec{b} = -(\vec{b}\times\vec{a})$.
///
/// # Formula
/// $$
/// \bm{a} \times \bm{b} =
/// \begin{bmatrix} a_x \cr a_y \cr a_z \end{bmatrix} \times
/// \begin{bmatrix} b_x \cr b_y \cr b_z \end{bmatrix} =
/// \begin{bmatrix}
/// a_y b_z - a_z b_y \cr
/// a_z b_x - a_x b_z \cr
/// a_x b_y - a_y b_x
/// \end{bmatrix}
/// $$
pub fn cross(self, other: Self) -> Self {
let cross_product = [
self.coords[1] * other.coords[2] - self.coords[2] * other.coords[1], // i
self.coords[2] * other.coords[0] - self.coords[0] * other.coords[2], // j
self.coords[0] * other.coords[1] - self.coords[1] * other.coords[0], // k
];
Vector::new(cross_product)
}
}
};
}
impl_vector!();