Simple, fast linearization of 2D, 3D, and 4D coordinates.
The canonical choice of linearization function is row-major, i.e. stepping linearly through an N dimensional array would
step by X first, then Y, then Z, etc, assuming that [T; N] coordinates are provided as [X, Y, Z, ...]. More explicitly:
linearize([x, y, z, ...]) = x + X_SIZE * y + X_SIZE * Y_SIZE * z + ...
Of course, to achieve a different layout, one only needs to choose a different permutation of coordinates. For example,
column-major layout would require coordinates specified as [..., Z, Y, X]. For a 3D layout where each Y level set is
contiguous in memory, either layout [X, Z, Y] or [Z, X, Y] would work.
```rust use ndshape::{Shape, ConstShape3u32, ConstShape4u32, ConstPow2Shape3u32, Shape3u32};
// An arbitrary shape. let shape = ConstShape3u32::<5, 6, 7>; let index = shape.linearize([1, 2, 3]); asserteq!(index, 101); asserteq!(shape.delinearize(index), [1, 2, 3]);
// A shape with power-of-two dimensions // This allows us to use bit shifting and masking for linearization. let shape = ConstPow2Shape3u32::<1, 2, 3>; // These are number of bits per dimension. let index = shape.linearize([1, 2, 3]); asserteq!(index, 0b011101); asserteq!(shape.delinearize(index), [1, 2, 3]);
// A runtime shape. let shape = Shape3u32::new([5, 6, 7]); let index = shape.linearize([1, 2, 3]); asserteq!(index, 101); asserteq!(shape.delinearize(index), [1, 2, 3]);
// Use a shape for indexing an array in 4D.
// Step X, then Y, then Z, since that results in monotonic increasing indices.
// (Believe it or not, Rust's N-dimensional array (e.g. [[T; N]; M])
// indexing is significantly slower than this).
let shape = ConstShape4u32::<5, 6, 7, 8>;
let data = [0; 5 * 6 * 7 * 8];
for w in 0..8 {
for z in 0..7 {
for y in 0..6 {
for x in 0..5 {
let i = shape.linearize([x, y, z, w]);
assert_eq!(0, data[i as usize]);
}
}
}
}
```
It is often beneficial to linearize a negative vector that results in a negative linear "stride." But when using unsigned
linear indices, a negative stride would require a modular arithmetic representation, where e.g. -1 maps to u32::MAX.
This works fine with any Shape. You just need to be sure to use modular arithmetic with the resulting
linear strides, e.g. u32::wrapping_add and u32::wrapping_mul. Also, it is not
possible to delinearize a negative stride with modular arithmetic. For that, you must use signed integer coordinates.
```rust use ndshape::{Shape, ConstShape3u32, ConstShape3i32};
let shape = ConstShape3u32::<10, 10, 10>; let stride = shape.linearize([0, -1i32 as u32, 0]); assert_eq!(stride, -10i32 as u32);
// Delinearize does not work with unsigned coordinates! assertne!(shape.delinearize(stride), [0, -1i32 as u32, 0]); asserteq!(shape.delinearize(stride), [6, 8, 42949672]);
let shape = ConstShape3i32::<10, 10, 10>; let stride = shape.linearize([0, -1, 0]); assert_eq!(stride, -10);
// Delinearize works with signed coordinates. assert_eq!(shape.delinearize(stride), [0, -1, 0]); ```
License: MIT OR Apache-2.0