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+
+// calculations inspired by
+// https://github.com/AcademySoftwareFoundation/openexr/blob/master/OpenEXR/IlmImf/ImfTiledMisc.cpp
+
+//! Simple math utilities.
+
+use std::convert::TryFrom;
+use crate::error::{i32_to_usize};
+use crate::error::Result;
+use std::ops::{Add, Sub, Div, Mul};
+use std::fmt::Debug;
+
+/// Simple two-dimensional vector of any numerical type.
+/// Supports only few mathematical operations
+/// as this is used mainly as data struct.
+#[derive(Clone, Copy, Debug, PartialEq, Eq, Hash, Default)]
+pub struct Vec2<T> (pub T, pub T);
+
+impl<T> Vec2<T> {
+
+ /// Returns the vector with the maximum of either coordinates.
+ pub fn max(self, other: Self) -> Self where T: Ord {
+ Vec2(self.0.max(other.0), self.1.max(other.1))
+ }
+
+ /// Returns the vector with the minimum of either coordinates.
+ pub fn min(self, other: Self) -> Self where T: Ord {
+ Vec2(self.0.min(other.0), self.1.min(other.1))
+ }
+
+ /// Try to convert all components of this vector to a new type,
+ /// yielding either a vector of that new type, or an error.
+ pub fn try_from<S>(value: Vec2<S>) -> std::result::Result<Self, T::Error> where T: TryFrom<S> {
+ let x = T::try_from(value.0)?;
+ let y = T::try_from(value.1)?;
+ Ok(Vec2(x, y))
+ }
+
+
+
+ /// Seeing this vector as a dimension or size (width and height),
+ /// this returns the area that this dimensions contains (`width * height`).
+ #[inline] pub fn area(self) -> T where T: std::ops::Mul<T, Output = T> {
+ self.0 * self.1
+ }
+
+ /// The first component of this 2D vector.
+ #[inline] pub fn x(self) -> T { self.0 }
+
+ /// The second component of this 2D vector.
+ #[inline] pub fn y(self) -> T { self.1 }
+
+ /// The first component of this 2D vector.
+ #[inline] pub fn width(self) -> T { self.0 }
+
+ /// The second component of this 2D vector.
+ #[inline] pub fn height(self) -> T { self.1 }
+
+ // TODO use this!
+ /// Convert this two-dimensional coordinate to an index suited for one-dimensional flattened image arrays.
+ /// Works for images that store the pixels row by row, one after another, in a single array.
+ /// In debug mode, panics for an index out of bounds.
+ #[inline] pub fn flat_index_for_size(self, resolution: Vec2<T>) -> T
+ where T: Copy + Debug + Ord + Mul<Output=T> + Add<Output=T>
+ {
+ debug_assert!(
+ self.x() < resolution.width() && self.y() < resolution.height(),
+ "Vec2 index {:?} is invalid for resolution {:?}", self, resolution
+ );
+
+ let Vec2(x, y) = self;
+ y * resolution.width() + x
+ }
+}
+
+
+
+impl Vec2<i32> {
+
+ /// Try to convert to [`Vec2<usize>`], returning an error on negative numbers.
+ pub fn to_usize(self, error_message: &'static str) -> Result<Vec2<usize>> {
+ let x = i32_to_usize(self.0, error_message)?;
+ let y = i32_to_usize(self.1, error_message)?;
+ Ok(Vec2(x, y))
+ }
+
+}
+
+impl Vec2<usize> {
+
+ /// Panics for too large values
+ pub fn to_i32(self) -> Vec2<i32> {
+ let x = i32::try_from(self.0).expect("vector x coordinate too large");
+ let y = i32::try_from(self.1).expect("vector y coordinate too large");
+ Vec2(x, y)
+ }
+
+}
+
+
+impl<T: std::ops::Add<T>> std::ops::Add<Vec2<T>> for Vec2<T> {
+ type Output = Vec2<T::Output>;
+ fn add(self, other: Vec2<T>) -> Self::Output {
+ Vec2(self.0 + other.0, self.1 + other.1)
+ }
+}
+
+impl<T: std::ops::Sub<T>> std::ops::Sub<Vec2<T>> for Vec2<T> {
+ type Output = Vec2<T::Output>;
+ fn sub(self, other: Vec2<T>) -> Self::Output {
+ Vec2(self.0 - other.0, self.1 - other.1)
+ }
+}
+
+impl<T: std::ops::Div<T>> std::ops::Div<Vec2<T>> for Vec2<T> {
+ type Output = Vec2<T::Output>;
+ fn div(self, other: Vec2<T>) -> Self::Output {
+ Vec2(self.0 / other.0, self.1 / other.1)
+ }
+}
+
+impl<T: std::ops::Mul<T>> std::ops::Mul<Vec2<T>> for Vec2<T> {
+ type Output = Vec2<T::Output>;
+ fn mul(self, other: Vec2<T>) -> Self::Output {
+ Vec2(self.0 * other.0, self.1 * other.1)
+ }
+}
+
+impl<T> std::ops::Neg for Vec2<T> where T: std::ops::Neg<Output=T> {
+ type Output = Vec2<T>;
+ fn neg(self) -> Self::Output { Vec2(-self.0, -self.1) }
+}
+
+impl<T> From<(T, T)> for Vec2<T> {
+ fn from((x, y): (T, T)) -> Self { Vec2(x, y) }
+}
+
+impl<T> From<Vec2<T>> for (T, T) {
+ fn from(vec2: Vec2<T>) -> Self { (vec2.0, vec2.1) }
+}
+
+/// Computes `floor(log(x)/log(2))`. Returns 0 where argument is 0.
+// TODO does rust std not provide this?
+pub(crate) fn floor_log_2(mut number: u32) -> u32 {
+ let mut log = 0;
+
+ // TODO check if this unrolls properly?
+ while number > 1 {
+ log += 1;
+ number >>= 1;
+ }
+
+ log
+}
+
+
+/// Computes `ceil(log(x)/log(2))`. Returns 0 where argument is 0.
+// taken from https://github.com/openexr/openexr/blob/master/OpenEXR/IlmImf/ImfTiledMisc.cpp
+// TODO does rust std not provide this?
+pub(crate) fn ceil_log_2(mut number: u32) -> u32 {
+ let mut log = 0;
+ let mut round_up = 0;
+
+ // TODO check if this unrolls properly
+ while number > 1 {
+ if number & 1 != 0 {
+ round_up = 1;
+ }
+
+ log += 1;
+ number >>= 1;
+ }
+
+ log + round_up
+}
+
+
+/// Round up or down in specific calculations.
+#[derive(Debug, Clone, Copy, Eq, PartialEq, Hash)]
+pub enum RoundingMode {
+
+ /// Round down.
+ Down,
+
+ /// Round up.
+ Up,
+}
+
+impl RoundingMode {
+ pub(crate) fn log2(self, number: u32) -> u32 {
+ match self {
+ RoundingMode::Down => self::floor_log_2(number),
+ RoundingMode::Up => self::ceil_log_2(number),
+ }
+ }
+
+ /// Only works for positive numbers.
+ pub(crate) fn divide<T>(self, dividend: T, divisor: T) -> T
+ where T: Copy + Add<Output = T> + Sub<Output = T> + Div<Output = T> + From<u8> + std::cmp::PartialOrd
+ {
+ assert!(
+ dividend >= T::from(0) && divisor >= T::from(1),
+ "division with rounding up only works for positive numbers"
+ );
+
+ match self {
+ RoundingMode::Up => (dividend + divisor - T::from(1_u8)) / divisor, // only works for positive numbers
+ RoundingMode::Down => dividend / divisor,
+ }
+ }
+}
+
+// TODO log2 tests