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//! Rust functions for mapping between 1D and 2D space using the Hilbert curve, and its approximations.
//!
//! When working with images and matrices, use the `h2xy_discrete` and `xy2h_discrete` functions:
//!
//! ```rust
//! use hilbert_2d::{h2xy_discrete, xy2h_discrete, Variant};
//!
//! let (x, y) = h2xy_discrete(7, 2, Variant::Hilbert); // (1, 2)
//! let h = xy2h_discrete(2, 1, 2, Variant::Hilbert); // 13
//! ```
//!
//! When performing real-valued calculations, use the continuous functions instead:
//!
//! ```rust
//! use hilbert_2d::{h2xy_continuous_f64, Variant};
//!
//! // Approaches the bottom-left corner
//! let (x1, y1) = h2xy_continuous_f64(0.0, Variant::Hilbert);
//! // Approaches the bottom-right corner
//! let (x2, y2) = h2xy_continuous_f64(1.0, Variant::Hilbert);
//! ```
//!
//! Some of the pattern variants of the Hilbert curve have also been implemented:
//!
//! ```rust
//! use hilbert_2d::{h2xy_continuous_f64, Variant};
//!
//! // In the Liu L1 variant, both ends of the curve approach the center of the square
//! let (x1, y1) = h2xy_continuous_f64(0.0, Variant::Liu1); // (~0.5, ~0.5)
//! let (x2, y2) = h2xy_continuous_f64(1.0, Variant::Liu1); // (~0.5, ~0.5)
//! ```
#![doc(html_root_url = "https://docs.rs/hilbert_2d/1.1.0")]
#[macro_use]
mod hilbert_macros;
hilbert_impl! { "8-bit", u8, U8_BITS }
hilbert_impl! { "16-bit", u16, U16_BITS }
hilbert_impl! { "32-bit", u32, U32_BITS }
hilbert_impl! { "64-bit", u64, U64_BITS }
hilbert_impl! { "128-bit", u128, U128_BITS }
hilbert_impl! { "pointer-sized", usize, USIZE_BITS }
pub use crate::usize::{h2xy_discrete, xy2h_discrete};
use crate::usize::{ORDER_MAX, USIZE_BITS};
/// Indicates the pattern variant of the Hilbert curve to be constructed.
///
/// Different patterns of the Hilbert curve have been demonstrated, and they can also be constructed by the methods
/// present in this library.
#[derive(Copy, Clone, PartialEq, Eq, Debug, Hash)]
pub enum Variant {
/// The traditional pattern, as presented by David Hilbert. [(Hilbert, D., 1935)](https://doi.org/10.1007/BF01199431)
Hilbert,
/// The pattern variant introduced by E. H. Moore. [(Moore, E.H., 1900)](https://doi.org/10.1090/S0002-9947-1900-1500526-4)
Moore,
/// The pattern L1, as presented by Xian Liu. [(Liu, X., 2004)](https://doi.org/10.1016/S0096-3003(02)00808-1)
Liu1,
/// The pattern L2, as presented by Xian Liu. [(Liu, X., 2004)](https://doi.org/10.1016/S0096-3003(02)00808-1)
Liu2,
/// The pattern L3, as presented by Xian Liu. [(Liu, X., 2004)](https://doi.org/10.1016/S0096-3003(02)00808-1)
Liu3,
/// The pattern L4, as presented by Xian Liu. [(Liu, X., 2004)](https://doi.org/10.1016/S0096-3003(02)00808-1)
Liu4,
}
/// Determines the index of the next lookup table to be used.
///
/// The conversion from/to the Hilbert curve is done using a matrix, that is transformed after each subsequent order,
/// based on the curve quadrant for that transition. We, instead, use a set of lookup tables containing all possible
/// transition matrices, and simply change the lookup index to indicate which matrix to use next.
const fn next_lut_index(lut_index: usize, quadrant: usize) -> usize {
match quadrant {
0 => lut_index ^ 0b001,
3 => lut_index ^ 0b010,
_ => lut_index,
}
}
/// Determines the index of the lookup table to be used in the transition from order 1 to order 2.
///
/// See [`next_lut_index`](fn.next_lut_index.html) for more details.
const fn next_lut_index_variant(
lut_index: usize,
cur_quadrant: usize,
variant: Variant,
) -> usize {
match variant {
Variant::Moore => match cur_quadrant {
0 | 1 => (lut_index ^ 0b10) ^ 0b111,
_ => (lut_index ^ 0b01) ^ 0b111,
},
Variant::Liu1 => match cur_quadrant {
0 | 3 => (lut_index ^ 0b01) ^ 0b10,
_ => lut_index,
},
Variant::Liu2 => match cur_quadrant {
1 => (lut_index ^ 0b10) ^ 0b111,
2 => (lut_index ^ 0b01) ^ 0b111,
_ => lut_index ^ 0b111,
},
Variant::Liu3 => match cur_quadrant {
0 => lut_index ^ 0b01,
3 => (lut_index ^ 0b01) ^ 0b10,
_ => lut_index,
},
Variant::Liu4 => match cur_quadrant {
0 => lut_index ^ 0b111,
1 => (lut_index ^ 0b10) ^ 0b111,
_ => (lut_index ^ 0b01) ^ 0b111,
},
_ => next_lut_index(lut_index, cur_quadrant),
}
}
/// Maps from a 1D value to an approximate 2D coordinate, using the closest approachable limit of the Hilbert curve.
/// Recommended for real-valued calculations.
///
/// Given a value `h`, this method calculates an approximation of it's corresponding limit point `(x, y)`, in the
/// Hilbert curve of the highest achievable order for the target platform.
///
/// The value of `h` must be in the range `0.0 <= h < 1.0`. A value `h >= 1.0` can be given, but functionally, it will
/// be clipped to the closest value to one possible. The coordinates returned will be in the range `0.0 <= x/y < 1.0`.
///
/// The pattern of the Hilbert curve to be constructed must be indicated by the `variant` parameter. See [`Variant`]
/// for more details.
///
/// Internally, this method uses [`h2xy_discrete`] for the calculation, coupled with a trick using the fractional parts
/// of binary/quaternary numbers. In short, the precision of the calculation, as well as the closest approximation
/// possible, both depend on the number of bits in a `usize` for the target platform. See [`h2xy_discrete`] for more
/// details.
///
/// # Examples
///
/// Basic usage:
///
/// ```rust
/// use hilbert_2d::{h2xy_continuous_f32, Variant};
///
/// // In the traditional pattern, the edges of the Hilbert curve are horizontally distant...
/// let (x_a, _) = h2xy_continuous_f32(0.0, Variant::Hilbert);
/// let (x_b, _) = h2xy_continuous_f32(1.0, Variant::Hilbert);
/// assert!(x_b - x_a > 0.999);
///
/// // ...but in the Moore pattern, the edges of the curve close up.
/// let (x_a, _) = h2xy_continuous_f32(0.0, Variant::Moore);
/// let (x_b, _) = h2xy_continuous_f32(1.0, Variant::Moore);
/// assert!(x_b - x_a < 0.001);
/// ```
///
/// [`h2xy_discrete`]: fn.h2xy_discrete.html
/// [`Variant`]: enum.Variant.html
///
pub fn h2xy_continuous_f32(h: f32, variant: Variant) -> (f32, f32) {
// Convert decimal `h` into fractional representation, and calculate the square position
let (square_x, square_y) = h2xy_discrete(f32_to_binfrac(h), ORDER_MAX as usize, variant);
// Convert the fractional result to decimal and return
(
binfrac_to_f32(square_x << ORDER_MAX),
binfrac_to_f32(square_y << ORDER_MAX),
)
}
/// Maps from a 1D value to an approximate 2D coordinate, using the closest approachable limit of the Hilbert curve.
/// Recommended for real-valued calculations.
///
/// Given a value `h`, this method calculates an approximation of it's corresponding limit point `(x, y)`, in the
/// Hilbert curve of the highest achievable order for the target platform.
///
/// The value of `h` must be in the range `0.0 <= h < 1.0`. A value `h >= 1.0` can be given, but functionally, it will
/// be clipped to the closest value to one possible. The coordinates returned will be in the range `0.0 <= x/y < 1.0`.
///
/// The pattern of the Hilbert curve to be constructed must be indicated by the `variant` parameter. See [`Variant`]
/// for more details.
///
/// Internally, this method uses [`h2xy_discrete`] for the calculation, coupled with a trick using the fractional parts
/// of binary/quaternary numbers. In short, the precision of the calculation, as well as the closest approximation
/// possible, both depend on the number of bits in a `usize` for the target platform. See [`h2xy_discrete`] for more
/// details.
///
/// # Examples
///
/// Basic usage:
///
/// ```rust
/// use hilbert_2d::{h2xy_continuous_f64, Variant};
///
/// // In the traditional pattern, the edges of the Hilbert curve are horizontally distant...
/// let (x_a, _) = h2xy_continuous_f64(0.0, Variant::Hilbert);
/// let (x_b, _) = h2xy_continuous_f64(1.0, Variant::Hilbert);
/// assert!(x_b - x_a > 0.999);
///
/// // ...but in the Moore pattern, the edges of the curve close up.
/// let (x_a, _) = h2xy_continuous_f64(0.0, Variant::Moore);
/// let (x_b, _) = h2xy_continuous_f64(1.0, Variant::Moore);
/// assert!(x_b - x_a < 0.001);
/// ```
///
/// [`h2xy_discrete`]: fn.h2xy_discrete.html
/// [`Variant`]: enum.Variant.html
///
pub fn h2xy_continuous_f64(h: f64, variant: Variant) -> (f64, f64) {
// Convert decimal `h` into fractional representation, and calculate the square position
let (square_x, square_y) = h2xy_discrete(f64_to_binfrac(h), ORDER_MAX as usize, variant);
// Convert the fractional result to decimal and return
(
binfrac_to_f64(square_x << ORDER_MAX),
binfrac_to_f64(square_y << ORDER_MAX),
)
}
/// Maps from a 2D coordinate to an approximate 1D value, using the closest approachable limit of the Hilbert curve.
/// Recommended for real-valued calculations.
///
/// Given `x` and `y`, this method calculates an approximation of it's corresponding limit `h`, in the Hilbert curve
/// of the highest achievable order for the target platform.
///
/// The value of `x` and `y` must be in the range `0.0 <= x/y < 1.0`. A value `x/y >= 1.0` can be given, but
/// functionally, it will be clipped to the closest value to one possible. The value returned will be in the range
/// `0.0 <= h <= 1.0`.
///
/// The pattern of the Hilbert curve to be constructed must be indicated by the `variant` parameter. See [`Variant`]
/// for more details.
///
/// Internally, this method uses [`xy2h_discrete`] for the calculation, coupled with a trick using the fractional parts
/// of binary/quaternary numbers. In short, the precision of the calculation, as well as the closest approximation
/// possible, both depend on the number of bits in a `usize` for the target platform. See [`xy2h_discrete`] for more
/// details.
///
/// # Examples
///
/// Basic usage:
///
/// ```rust
/// use hilbert_2d::{xy2h_continuous_f32, Variant};
///
/// // In the third pattern presented by Liu, the curve begins at the lower left corner...
/// let h = xy2h_continuous_f32(0.0, 0.0, Variant::Liu3);
/// assert!(h < 0.001);
///
/// // ...but ends near the center of the square.
/// let h = xy2h_continuous_f32(0.5001, 0.4999, Variant::Liu3);
/// assert!(h > 0.999);
/// ```
///
/// [`xy2h_discrete`]: fn.xy2h_discrete.html
/// [`Variant`]: enum.Variant.html
///
pub fn xy2h_continuous_f32(x: f32, y: f32, variant: Variant) -> f32 {
// Convert the x/y coordinates into a factional representation, and calculate the index
let h = xy2h_discrete(
f32_to_binfrac(x) >> ORDER_MAX,
f32_to_binfrac(y) >> ORDER_MAX,
ORDER_MAX as usize,
variant,
);
// Convert the fractional result back into decimal, and return
binfrac_to_f32(h)
}
/// Maps from a 2D coordinate to an approximate 1D value, using the closest approachable limit of the Hilbert curve.
/// Recommended for real-valued calculations.
///
/// Given `x` and `y`, this method calculates an approximation of it's corresponding limit `h`, in the Hilbert curve
/// of the highest achievable order for the target platform.
///
/// The value of `x` and `y` must be in the range `0.0 <= x/y < 1.0`. A value `x/y >= 1.0` can be given, but
/// functionally, it will be clipped to the closest value to one possible. The value returned will be in the range
/// `0.0 <= h <= 1.0`.
///
/// The pattern of the Hilbert curve to be constructed must be indicated by the `variant` parameter. See [`Variant`]
/// for more details.
///
/// Internally, this method uses [`xy2h_discrete`] for the calculation, coupled with a trick using the fractional parts
/// of binary/quaternary numbers. In short, the precision of the calculation, as well as the closest approximation
/// possible, both depend on the number of bits in a `usize` for the target platform. See [`xy2h_discrete`] for more
/// details.
///
/// # Examples
///
/// Basic usage:
///
/// ```rust
/// use hilbert_2d::{xy2h_continuous_f64, Variant};
///
/// // In the third pattern presented by Liu, the curve begins at the lower left corner...
/// let h = xy2h_continuous_f64(0.0, 0.0, Variant::Liu3);
/// assert!(h < 0.001);
///
/// // ...but ends near the center of the square.
/// let h = xy2h_continuous_f64(0.5001, 0.4999, Variant::Liu3);
/// assert!(h > 0.999);
/// ```
///
/// [`xy2h_discrete`]: fn.xy2h_discrete.html
/// [`Variant`]: enum.Variant.html
///
pub fn xy2h_continuous_f64(x: f64, y: f64, variant: Variant) -> f64 {
// Convert the x/y coordinates into a factional representation, and calculate the index
let h = xy2h_discrete(
f64_to_binfrac(x) >> ORDER_MAX,
f64_to_binfrac(y) >> ORDER_MAX,
ORDER_MAX as usize,
variant,
);
// Convert the fractional result back into decimal, and return
binfrac_to_f64(h)
}
/// Calculates the lowest decimal number that could be represented in a binary fraction with N decimal places, where N
/// is the number of bits in `usize`.
fn lowest_decimal_f32() -> f32 {
2.0f32.powi(-(USIZE_BITS as i32))
}
/// Calculates the lowest decimal number that could be represented in a binary fraction with N decimal places, where N
/// is the number of bits in `usize`.
fn lowest_decimal_f64() -> f64 {
2.0f64.powi(-(USIZE_BITS as i32))
}
/// Convert the fractional part of a binary decimal number to a 32-bit floating point number.
fn binfrac_to_f32(frac: usize) -> f32 {
lowest_decimal_f32() * (frac as f32)
}
/// Convert the fractional part of a binary decimal number to a 64-bit floating point number.
fn binfrac_to_f64(frac: usize) -> f64 {
lowest_decimal_f64() * (frac as f64)
}
/// Extracts the fractional part, in binary, of a 32-bit floating point number.
fn f32_to_binfrac(dec: f32) -> usize {
(dec / lowest_decimal_f32()) as usize
}
/// Extracts the fractional part, in binary, of a 64-bit floating point number.
fn f64_to_binfrac(dec: f64) -> usize {
(dec / lowest_decimal_f64()) as usize
}
#[cfg(test)]
mod tests {
use super::*;
use assert_approx_eq::assert_approx_eq;
#[test]
fn lut_transition_standard() {
// LUT transition for the Hilbert variant, with the curve 0b011 as the seed
assert_eq!(next_lut_index(0b011, 0), 0b010);
assert_eq!(next_lut_index(0b011, 1), 0b011);
assert_eq!(next_lut_index(0b011, 2), 0b011);
assert_eq!(next_lut_index(0b011, 3), 0b001);
}
#[test]
fn lut_transition_variant() {
// LUT transition for the Moore variant, with the curve 0b111 as the seed
assert_eq!(next_lut_index_variant(0b111, 0, Variant::Moore), 0b010);
assert_eq!(next_lut_index_variant(0b111, 1, Variant::Moore), 0b010);
assert_eq!(next_lut_index_variant(0b111, 2, Variant::Moore), 0b001);
assert_eq!(next_lut_index_variant(0b111, 3, Variant::Moore), 0b001);
// LUT transition for the Liu1 variant, with the curve 0b111 as the seed
assert_eq!(next_lut_index_variant(0b111, 0, Variant::Liu1), 0b100);
assert_eq!(next_lut_index_variant(0b111, 1, Variant::Liu1), 0b111);
assert_eq!(next_lut_index_variant(0b111, 2, Variant::Liu1), 0b111);
assert_eq!(next_lut_index_variant(0b111, 3, Variant::Liu1), 0b100);
// LUT transition for the Liu2 variant, with the curve 0b111 as the seed
assert_eq!(next_lut_index_variant(0b111, 0, Variant::Liu2), 0b000);
assert_eq!(next_lut_index_variant(0b111, 1, Variant::Liu2), 0b010);
assert_eq!(next_lut_index_variant(0b111, 2, Variant::Liu2), 0b001);
assert_eq!(next_lut_index_variant(0b111, 3, Variant::Liu2), 0b000);
// LUT transition for the Liu3 variant, with the curve 0b111 as the seed
assert_eq!(next_lut_index_variant(0b111, 0, Variant::Liu3), 0b110);
assert_eq!(next_lut_index_variant(0b111, 1, Variant::Liu3), 0b111);
assert_eq!(next_lut_index_variant(0b111, 2, Variant::Liu3), 0b111);
assert_eq!(next_lut_index_variant(0b111, 3, Variant::Liu3), 0b100);
// LUT transition for the Liu4 variant, with the curve 0b111 as the seed
assert_eq!(next_lut_index_variant(0b111, 0, Variant::Liu4), 0b000);
assert_eq!(next_lut_index_variant(0b111, 1, Variant::Liu4), 0b010);
assert_eq!(next_lut_index_variant(0b111, 2, Variant::Liu4), 0b001);
assert_eq!(next_lut_index_variant(0b111, 3, Variant::Liu4), 0b001);
}
#[test]
fn map_continuous_hilbert() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.33333334, 0.33333334, 0.13333334);
let h = xy2h_continuous_f32(tx, ty, Variant::Hilbert);
let (x, y) = h2xy_continuous_f32(th, Variant::Hilbert);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.33333334, 0.6666667, 0.46666667);
let h = xy2h_continuous_f32(tx, ty, Variant::Hilbert);
let (x, y) = h2xy_continuous_f32(th, Variant::Hilbert);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.6666666666666666, 0.3333333333333333, 0.8666666666666667);
let h = xy2h_continuous_f64(tx, ty, Variant::Hilbert);
let (x, y) = h2xy_continuous_f64(th, Variant::Hilbert);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.6666666666666666, 0.6666666666666666, 0.5333333333333333);
let h = xy2h_continuous_f64(tx, ty, Variant::Hilbert);
let (x, y) = h2xy_continuous_f64(th, Variant::Hilbert);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn map_continuous_moore() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.33333334, 0.33333334, 0.21666667);
let h = xy2h_continuous_f32(tx, ty, Variant::Moore);
let (x, y) = h2xy_continuous_f32(th, Variant::Moore);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.33333334, 0.6666667, 0.28333333);
let h = xy2h_continuous_f32(tx, ty, Variant::Moore);
let (x, y) = h2xy_continuous_f32(th, Variant::Moore);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.6666666666666666, 0.3333333333333333, 0.7833333333333333);
let h = xy2h_continuous_f64(tx, ty, Variant::Moore);
let (x, y) = h2xy_continuous_f64(th, Variant::Moore);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.6666666666666666, 0.6666666666666666, 0.7166666666666667);
let h = xy2h_continuous_f64(tx, ty, Variant::Moore);
let (x, y) = h2xy_continuous_f64(th, Variant::Moore);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn map_continuous_liu1() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.22222222, 0.22222222, 0.12564103);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu1);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu1);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.22222222, 0.44444445, 0.22758524);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu1);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu1);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.4444444444444444, 0.2222222222222222, 0.06545535120101877);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu1);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu1);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.4444444444444444, 0.4444444444444444, 0.002564102564102564);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu1);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu1);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn map_continuous_liu2() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.22222222, 0.22222222, 0.124358974);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu2);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu2);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.22222222, 0.44444445, 0.02241476);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu2);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu2);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.4444444444444444, 0.2222222222222222, 0.18454464879898125);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu2);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu2);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.4444444444444444, 0.4444444444444444, 0.24743589743589745);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu2);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu2);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn map_continuous_liu3() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.22222222, 0.22222222, 0.041025642);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu3);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu3);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.22222222, 0.44444445, 0.18914248);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu3);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu3);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.4444444444444444, 0.2222222222222222, 0.10511851937285181);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu3);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu3);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.4444444444444444, 0.4444444444444444, 0.1641025641025641);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu3);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu3);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn map_continuous_liu4() {
// Max acceptable error, based on a couple of naive tests of my own
// A proper analysis of the precision loss in the `continuous` methods is still required
let err32 = 0.000163;
let err64 = 0.00000000722;
let (tx, ty, th) = (0.22222222, 0.22222222, 0.124358974);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu4);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu4);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.22222222, 0.44444445, 0.02241476);
let h = xy2h_continuous_f32(tx, ty, Variant::Liu4);
let (x, y) = h2xy_continuous_f32(th, Variant::Liu4);
assert_approx_eq!(h, th, err32);
assert_approx_eq!(x, tx, err32);
assert_approx_eq!(y, ty, err32);
let (tx, ty, th) = (0.4444444444444444, 0.2222222222222222, 0.18454464879898125);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu4);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu4);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
let (tx, ty, th) = (0.4444444444444444, 0.4444444444444444, 0.24743589743589745);
let h = xy2h_continuous_f64(tx, ty, Variant::Liu4);
let (x, y) = h2xy_continuous_f64(th, Variant::Liu4);
assert_approx_eq!(h, th, err64);
assert_approx_eq!(x, tx, err64);
assert_approx_eq!(y, ty, err64);
}
#[test]
fn extract_binary_fractional_f32() {
// Test conversion for every single decimal place able to be represented.
// The conversion is not completely precise, but it's imprecision should match that of the f32 multiplication.
let mut frac = 0b1usize.reverse_bits();
let mut dec = 0.5f32;
while frac != 0 {
assert_eq!(frac, f32_to_binfrac(dec));
assert_approx_eq!(dec, binfrac_to_f32(frac));
frac >>= 1;
dec *= 0.5;
}
}
#[test]
fn extract_binary_fractional_f64() {
// Test conversion for every single decimal place able to be represented.
// The conversion is not completely precise, but it's imprecision should match that of the f64 multiplication.
let mut frac = 0b1usize.reverse_bits();
let mut dec = 0.5f64;
while frac != 0 {
assert_eq!(frac, f64_to_binfrac(dec));
assert_approx_eq!(dec, binfrac_to_f64(frac));
frac >>= 1;
dec *= 0.5;
}
}
}