morton 0.2.0

morton iterator for rust
Documentation 
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#![allow(unused_features)]
#![feature(test)]
#[cfg(test)] extern crate rand;
#[cfg(test)] extern crate test;

// http://graphics.stanford.edu/~seander/bithacks.html#InterleaveBMN
#[inline]
pub fn interleave_morton(x: u16, y: u16) -> u32 {
    if cfg!(target_pointer_width = "64") {
        let x = x as u64;
        let y = y as u64;

        let z = y << 32 | x;
        let z = (z | (z << 8)) & 0x00FF00FF_00FF00FF;
        let z = (z | (z << 4)) & 0x0F0F0F0F_0F0F0F0F;
        let z = (z | (z << 2)) & 0x33333333_33333333;
        let z = (z | (z << 1)) & 0x55555555_55555555;

        let z = z | ((z >> 32) << 1);
        z as u32
    } else {
        let x = x as u32;
        let x = (x | (x << 8)) & 0x00FF00FF;
        let x = (x | (x << 4)) & 0x0F0F0F0F;
        let x = (x | (x << 2)) & 0x33333333;
        let x = (x | (x << 1)) & 0x55555555;

        let y = y as u32;
        let y = (y | (y << 8)) & 0x00FF00FF;
        let y = (y | (y << 4)) & 0x0F0F0F0F;
        let y = (y | (y << 2)) & 0x33333333;
        let y = (y | (y << 1)) & 0x55555555;

        let z = x | (y << 1);
        z
    }
}

// http://stackoverflow.com/questions/4909263/how-to-efficiently-de-interleave-bits-inverse-morton
#[inline]
pub fn deinterleave_morton(z: u32) -> (u16, u16) {
      if cfg!(target_pointer_width = "64") {
        let z = z as u64;

        let z = (z | ((z >> 1) << 32)) & 0x55555555_55555555;
        let z = (z | (z >> 1)) & 0x33333333_33333333;
        let z = (z | (z >> 2)) & 0x0F0F0F0F_0F0F0F0F;
        let z = (z | (z >> 4)) & 0x00FF00FF_00FF00FF;
        let z = (z | (z >> 8)) & 0x0000FFFF_0000FFFF;

        let x = (z & 0x00000000_0000FFFF) as u16;
        let y = ((z >> 32) & 0x00000000_0000FFFF) as u16;

        (x,y)
      } else {
        let x = z & 0x55555555;
        let x = (x | (x >> 1)) & 0x33333333;
        let x = (x | (x >> 2)) & 0x0F0F0F0F;
        let x = (x | (x >> 4)) & 0x00FF00FF;
        let x = ((x | (x >> 8)) & 0x0000FFFF) as u16;

        let y = (z >> 1) & 0x55555555;
        let y = (y | (y >> 1)) & 0x33333333;
        let y = (y | (y >> 2)) & 0x0F0F0F0F;
        let y = (y | (y >> 4)) & 0x00FF00FF;
        let y = ((y | (y >> 8)) & 0x0000FFFF) as u16;

        (x,y)
      }
}

#[cfg(test)]
mod tests {
    use super::*;
    use rand::Rng;
    use rand::thread_rng;

    use test::Bencher;

    fn idx_tile(x: usize, y: usize, stride: usize) -> usize { stride * y + x }
    fn idx_tile_tuple(xy: (u16,u16), stride: usize) -> usize { let (x,y) = xy; stride * y as usize + x as usize }

    #[test]
    fn test_interleave() {
        let mut tile_morton = [0;32*32]; // 1024 locations
        let mut tile_normal = [0;32*32]; // 1024 locations
        // fill tiles with same random numbers
        for x in 0..32 {
            for y in 0..32 {
                let random = thread_rng().gen::<u32>();
                tile_morton[interleave_morton(x as u16, y as u16) as usize] = random;
                tile_normal[idx_tile(x, y, 32)] = random;
            }
        }
        // check that the same random numbers are stored there
        // (morton curve did not override it's own elements)
        for x in 0..32 {
            for y in 0..32 {
                let morton = tile_morton[interleave_morton(x as u16, y as u16) as usize];
                let normal = tile_normal[idx_tile(x, y, 32)];
                assert!(morton == normal);
            }
        }
    }
    #[test]
    fn test_deinterleave() {
        let mut tile_morton = [0;32*32]; // 1024 locations
        let mut tile_normal = [0;32*32]; // 1024 locations
        // fill tiles with same random numbers
        for x in 0..32 {
            for y in 0..32 {
                let random = thread_rng().gen::<u32>();
                tile_morton[interleave_morton(x as u16, y as u16) as usize] = random;
                tile_normal[idx_tile(x, y, 32)] = random;
            }
        }
        // check that the same random numbers are stored there
        // (morton curve did not override it's own elements)
        for z in 0..1024 {
            let morton = tile_morton[z];
            let normal = tile_normal[idx_tile_tuple(deinterleave_morton(z as u32), 32) as usize];
            assert!(morton == normal);
        }
    }
    #[test]
    fn deinterleave_interleave() {
        for z in 0..65536 {
            let (x,y) = deinterleave_morton(z);
            let morton = interleave_morton(x,y);
            assert!(morton == z);
        }
    }
    #[test]
    fn interleave_deinterleave() {
        for x in 0..1024 {
            for y in 0..1024 {
                let morton = interleave_morton(x,y);
                let (d_x,d_y) = deinterleave_morton(morton);
                assert!(d_x == x && d_y == y);
            }
        }
    }

    // tests with random input
    #[test]
    fn rand_interleave_deinterleave_1000() {
        for _ in 0..1024 {
            let x = thread_rng().gen::<u16>();
            let y = thread_rng().gen::<u16>();
            let morton = interleave_morton(x,y);
            let (d_x,d_y) = deinterleave_morton(morton);
            assert!(d_x == x && d_y == y);
        }
    }
    #[test]
    fn rand_deinterleave_interleave_1000() {
        for _ in 0..1024 {
            let z = thread_rng().gen::<u32>();
            let (x,y) = deinterleave_morton(z);
            let morton = interleave_morton(x,y);
            assert!(morton == z);
        }
    }

    // benchmarks
    #[bench]
    fn bench_interleave_1000(b: &mut Bencher) {
        let x = thread_rng().gen::<u16>();
        let y = thread_rng().gen::<u16>();
        b.iter(|| for _ in 0..1000 { test::black_box(interleave_morton(x, y)); });
    }
    #[bench]
    fn bench_deinterleave_1000(b: &mut Bencher) {
        let morton = thread_rng().gen::<u32>();
        b.iter(|| for _ in 0..1000 { test::black_box(deinterleave_morton(morton)); });
    }
    #[bench]
    fn bench_interleave_deinterleave_1000(b: &mut Bencher) {
        let x = thread_rng().gen::<u16>();
        let y = thread_rng().gen::<u16>();
        b.iter(|| for _ in 0..1000 { test::black_box(deinterleave_morton(interleave_morton(x, y))); });
    }
    #[bench]
    fn bench_deinterleave_interleave_1000(b: &mut Bencher) {
        let morton = thread_rng().gen::<u32>();
        b.iter(|| for _ in 0..1000 {
            let (x,y) = deinterleave_morton(morton);
            test::black_box(interleave_morton(x,y));
        });
    }
    #[bench]
    fn bench_horizontal_access_normal(b: &mut Bencher) {
        let mut tile_normal = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for y in 0..2048 {
            for x in 0..2048 {
                let random = thread_rng().gen::<u32>();
                tile_normal[idx_tile(x, y, 2048)] = random;
            }
        }
        // bench horizontal access (x direction)
        b.iter(|| {
            for y in 0..2048 {
                for x in 0..2048 {
                    test::black_box(tile_normal[idx_tile(x, y, 2048)]);
                }
            }
        });
    }
    #[bench]
    fn bench_vertical_access_normal(b: &mut Bencher) {
        let mut tile_normal = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for x in 0..2048 {
            for y in 0..2048 {
                let random = thread_rng().gen::<u32>();
                tile_normal[idx_tile(x, y, 2048)] = random;
            }
        }
        // bench vertical access (y direction)
        b.iter(|| {
            for x in 0..2048 {
                for y in 0..2048 {
                    test::black_box(tile_normal[idx_tile(x, y, 2048) as usize]);
                }
            }
        });
    }
    #[bench]
    fn bench_morton_access_normal(b: &mut Bencher) {
        let mut tile_morton = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for z in 0..2048*2048 {
            let random = thread_rng().gen::<u32>();
            tile_morton[idx_tile_tuple(deinterleave_morton(z), 2048) as usize] = random;
        }
        // bench horizontal access (x direction)
        b.iter(|| {
            for z in 0..2048*2048 {
                test::black_box(tile_morton[idx_tile_tuple(deinterleave_morton(z), 2048) as usize]);
            }
        });
    }
    #[bench]
    fn bench_horizontal_access_morton(b: &mut Bencher) {
        let mut tile_morton = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for y in 0..2048 {
            for x in 0..2048 {
                let random = thread_rng().gen::<u32>();
                tile_morton[interleave_morton(x, y) as usize] = random;
            }
        }
        // bench horizontal access (x direction)
        b.iter(|| {
            for y in 0..2048 {
                for x in 0..2048 {
                    test::black_box(tile_morton[interleave_morton(x,y) as usize]);
                }
            }
        });
    }
    #[bench]
    fn bench_vertical_access_morton(b: &mut Bencher) {
        let mut tile_morton = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for x in 0..2048 {
            for y in 0..2048 {
                let random = thread_rng().gen::<u32>();
                tile_morton[interleave_morton(x, y) as usize] = random;
            }
        }
        // bench vertical access (y direction)
        b.iter(|| {
            for x in 0..2048 {
                for y in 0..2048 {
                    test::black_box(tile_morton[interleave_morton(x,y) as usize]);
                }
            }
        });
    }
    #[bench]
    fn bench_morton_access_morton(b: &mut Bencher) {
        let mut tile_morton = vec![0;2048*2048]; // 16MB allocate more then largest cache
        // fill tiles with some random numbers
        for z in 0..2048*2048 {
            let random = thread_rng().gen::<u32>();
            tile_morton[z] = random;
        }
        // bench horizontal access (x direction)
        b.iter(|| {
            for z in 0..2048*2048 {
                test::black_box(tile_morton[z]);
            }
        });
    }
}