switch to sobol sampling
This commit is contained in:
parent
726dded047
commit
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SSH key fingerprint:
SHA256:9GtP+M3O2IivPDlw1UY872UPUuJH2gI0yG6ExBxaaiM
6 changed files with 263 additions and 208 deletions
117
Cargo.lock
generated
117
Cargo.lock
generated
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@ -14,6 +14,12 @@ version = "1.22.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "b6b1fc10dbac614ebc03540c9dbd60e83887fda27794998c6528f1782047d540"
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[[package]]
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name = "cfg-if"
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version = "0.1.10"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "4785bdd1c96b2a846b2bd7cc02e86b6b3dbf14e7e53446c4f54c92a361040822"
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[[package]]
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name = "cfg-if"
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version = "1.0.0"
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@ -32,6 +38,40 @@ dependencies = [
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"syn",
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]
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[[package]]
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name = "fasthash"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "032213946b4eaae09117ec63f020322b78ca7a31d8aa2cf64df3032e1579690f"
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dependencies = [
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"cfg-if 0.1.10",
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"fasthash-sys",
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"num-traits",
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"seahash",
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"xoroshiro128",
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]
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[[package]]
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name = "fasthash-sys"
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version = "0.3.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "b6de941abfe2e715cdd34009d90546f850597eb69ca628ddfbf616e53dda28f8"
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dependencies = [
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"gcc",
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]
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[[package]]
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name = "fuchsia-cprng"
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version = "0.1.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "a06f77d526c1a601b7c4cdd98f54b5eaabffc14d5f2f0296febdc7f357c6d3ba"
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[[package]]
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name = "gcc"
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version = "0.3.55"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "8f5f3913fa0bfe7ee1fd8248b6b9f42a5af4b9d65ec2dd2c3c26132b950ecfc2"
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[[package]]
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name = "glam"
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version = "0.30.2"
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@ -71,6 +111,7 @@ version = "0.1.0"
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dependencies = [
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"bytemuck",
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"enum_dispatch",
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"fasthash",
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"glam",
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"primal",
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]
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@ -184,7 +225,7 @@ version = "0.24.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "e5203598f366b11a02b13aa20cab591229ff0a89fd121a308a5df751d5fc9219"
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dependencies = [
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"cfg-if",
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"cfg-if 1.0.0",
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"indoc",
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"libc",
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"memoffset",
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@ -250,6 +291,49 @@ dependencies = [
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"proc-macro2",
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]
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[[package]]
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name = "rand"
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version = "0.4.6"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "552840b97013b1a26992c11eac34bdd778e464601a4c2054b5f0bff7c6761293"
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dependencies = [
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"fuchsia-cprng",
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"libc",
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"rand_core 0.3.1",
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"rdrand",
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"winapi",
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]
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[[package]]
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name = "rand_core"
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version = "0.3.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "7a6fdeb83b075e8266dcc8762c22776f6877a63111121f5f8c7411e5be7eed4b"
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dependencies = [
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"rand_core 0.4.2",
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]
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[[package]]
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name = "rand_core"
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version = "0.4.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "9c33a3c44ca05fa6f1807d8e6743f3824e8509beca625669633be0acbdf509dc"
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[[package]]
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name = "rdrand"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "678054eb77286b51581ba43620cc911abf02758c91f93f479767aed0f90458b2"
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dependencies = [
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"rand_core 0.3.1",
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]
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[[package]]
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name = "seahash"
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version = "3.0.7"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "58f57ca1d128a43733fd71d583e837b1f22239a37ebea09cde11d8d9a9080f47"
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[[package]]
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name = "smallvec"
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version = "1.15.0"
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@ -284,3 +368,34 @@ name = "unindent"
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version = "0.2.4"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "7264e107f553ccae879d21fbea1d6724ac785e8c3bfc762137959b5802826ef3"
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[[package]]
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name = "winapi"
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version = "0.3.9"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
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dependencies = [
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"winapi-i686-pc-windows-gnu",
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"winapi-x86_64-pc-windows-gnu",
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]
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[[package]]
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name = "winapi-i686-pc-windows-gnu"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
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[[package]]
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name = "winapi-x86_64-pc-windows-gnu"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
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[[package]]
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name = "xoroshiro128"
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version = "0.3.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "e0eeda34baec49c4f1eb2c04d59b761582fd6330010f9330ca696ca1a355dfcd"
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dependencies = [
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"rand",
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]
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@ -9,6 +9,7 @@ repository.workspace = true
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[dependencies]
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bytemuck = { version = "1.22.0", optional = true }
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enum_dispatch = "0.3.13"
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fasthash = "0.4.0"
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glam = "0.30.2"
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[features]
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@ -1,17 +0,0 @@
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use std::{env, fs::File, io::Write, path::PathBuf};
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fn main() {
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let dest: PathBuf = env::var("OUT_DIR").unwrap().into();
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let mut file = File::create(dest.join("primes.rs")).unwrap();
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write_primes(&mut file).unwrap();
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}
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fn write_primes(file: &mut File) -> std::io::Result<()> {
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write!(file, "[")?;
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let sieve = primal::Sieve::new(7919);
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for p in sieve.primes_from(2).take_while(|x| *x <= 7919) {
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write!(file, "{p},")?;
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}
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write!(file, "]")
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}
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@ -30,7 +30,7 @@ impl Scene {
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}
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pub fn render(&self, width: u32, height: u32, samples: u32) -> Box<[Rgba]> {
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let mut sampler = Sampler::new(width, height);
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let mut sampler = Sampler::new(width, height, samples, 0);
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let mut data = Box::new_uninit_slice(width as usize * height as usize);
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let w = width as f32;
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let h = height as f32;
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@ -42,9 +42,10 @@ impl Scene {
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let mut rgb = Vector::ZERO;
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for (offset_x, offset_y, _) in sampler.pixel(bx, by, samples) {
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let x = bx as f32 + offset_x;
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let y = by as f32 + offset_y;
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for mut pixel_samples in sampler.pixel(bx, by) {
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let (x_offset, y_offset) = pixel_samples.get_2d();
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let x = bx as f32 + x_offset;
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let y = by as f32 + y_offset;
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let cx = 2.0 * x / w - 1.0;
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let cy = (1.0 - 2.0 * y / h) * aspect_ratio;
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@ -1,220 +1,175 @@
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//! Halton sampling
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use core::f32;
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const PRIMES: [u32; 1000] = include!(concat!(env!("OUT_DIR"), "/primes.rs"));
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const MAX_HALTON_RESOLUTION: u32 = 128;
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use fasthash::murmur2::hash64_with_seed;
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// rust needs to add hex literals. this is 0x1p-32
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const ONE_OVER_MAX: f32 = 2.3283064e-10;
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const SOBOL_MATRIX: [u32; 32] = [
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0x80000000, 0xc0000000, 0xa0000000, 0xf0000000, 0x88000000, 0xcc000000, 0xaa000000, 0xff000000,
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0x80800000, 0xc0c00000, 0xa0a00000, 0xf0f00000, 0x88880000, 0xcccc0000, 0xaaaa0000, 0xffff0000,
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0x80008000, 0xc000c000, 0xa000a000, 0xf000f000, 0x88008800, 0xcc00cc00, 0xaa00aa00, 0xff00ff00,
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0x80808080, 0xc0c0c0c0, 0xa0a0a0a0, 0xf0f0f0f0, 0x88888888, 0xcccccccc, 0xaaaaaaaa, 0xffffffff,
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];
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#[rustfmt::skip]
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const PERMUTATIONS: [[u8; 4]; 24] = [
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[0, 1, 2, 3], [0, 1, 3, 2], [0, 2, 1, 3], [0, 2, 3, 1], [0, 3, 1, 2], [0, 3, 2, 1],
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[1, 0, 2, 3], [1, 0, 3, 2], [1, 2, 0, 3], [1, 2, 3, 0], [1, 3, 0, 2], [1, 3, 2, 0],
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[2, 0, 1, 3], [2, 0, 3, 1], [2, 1, 0, 3], [2, 1, 3, 0], [2, 3, 0, 1], [2, 3, 1, 0],
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[3, 0, 1, 2], [3, 0, 2, 1], [3, 1, 0, 2], [3, 1, 2, 0], [3, 2, 0, 1], [3, 2, 1, 0],
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];
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pub struct Sampler {
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x_scale: u8,
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x_exponent: u8,
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x_inverse: u8,
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y_scale: u8,
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y_exponent: u8,
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y_inverse: u8,
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index: u32,
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dimension: u16,
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seed: u32,
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samples: u32,
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log2_samples: u32,
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base4_digits: u32,
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}
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impl Sampler {
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pub fn new(width: u32, height: u32) -> Self {
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let mut x_scale = 1u8;
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let mut x_exponent = 0u8;
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let x_res = u32::min(width, MAX_HALTON_RESOLUTION) as u8;
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while x_scale < x_res {
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x_scale *= 2;
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x_exponent += 1;
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}
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let mut y_scale = 1u8;
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let mut y_exponent = 0u8;
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let y_res = u32::min(height, MAX_HALTON_RESOLUTION) as u8;
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while y_scale < y_res {
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y_scale *= 3;
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y_exponent += 1;
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}
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let x_inverse = mod_inverse(y_scale, x_scale);
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let y_inverse = mod_inverse(x_scale, y_scale);
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pub fn new(width: u32, height: u32, samples: u32, seed: u32) -> Self {
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let res = u32::next_power_of_two(u32::max(width, height));
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let log2_samples = u32::ilog2(samples);
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let base4_digits = u32::ilog2(res) + log2_samples.div_ceil(2);
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Self {
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dimension: 2,
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index: 0,
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x_scale,
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x_exponent,
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x_inverse,
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y_scale,
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y_exponent,
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y_inverse,
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seed,
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samples,
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log2_samples,
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base4_digits,
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}
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}
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pub fn pixel(
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&mut self,
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x: u32,
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y: u32,
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samples: u32,
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) -> impl Iterator<Item = (f32, f32, Sample)> {
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let mut base = 0;
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let sample_stride = self.y_scale as u32 * self.x_scale as u32;
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if sample_stride > 1 {
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let mx = x % MAX_HALTON_RESOLUTION;
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let my = y % MAX_HALTON_RESOLUTION;
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let x_offset = inverse_radical_inverse(mx, 2, self.x_exponent as u32);
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let y_offset = inverse_radical_inverse(my, 3, self.y_exponent as u32);
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base += x_offset * (sample_stride / self.x_scale as u32) * self.x_inverse as u32;
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base += y_offset * (sample_stride / self.y_scale as u32) * self.y_inverse as u32;
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base %= sample_stride;
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}
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pub fn pixel(&mut self, x: u32, y: u32) -> impl Iterator<Item = PixelSample> {
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let &mut Self {
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seed,
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samples,
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log2_samples,
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base4_digits,
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..
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} = self;
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(0..samples).map(move |i| {
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let index = base + i * sample_stride;
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let x_offset = radical_inverse(0, index >> self.x_exponent);
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let y_offset = radical_inverse(1, index / self.y_scale as u32);
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(x_offset, y_offset, Sample::new(index))
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let morton_index = (morton_2d(x, y) << log2_samples) | i;
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PixelSample {
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seed,
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log2_samples,
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base4_digits,
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morton_index,
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dimension: 0,
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}
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})
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}
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}
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pub struct Sample {
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index: u32,
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pub struct PixelSample {
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seed: u32,
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log2_samples: u32,
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base4_digits: u32,
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morton_index: u32,
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dimension: u32,
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}
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impl Sample {
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fn new(index: u32) -> Self {
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Self {
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index,
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dimension: 2,
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}
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}
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impl PixelSample {
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pub fn get_1d(&mut self) -> f32 {
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if self.dimension as usize >= PRIMES.len() {
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self.dimension = 2;
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}
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let dim = self.dimension as u64;
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let index = self.get_sample_index();
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self.dimension += 1;
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scrambled_radical_inverse(dim as usize, self.index, mix_bits(1 + (dim << 4)))
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let hash = hash64_with_seed(self.dimension.to_ne_bytes(), self.seed as u64);
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let seed = hash as u32;
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sobol_sample0(index, seed)
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}
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pub fn get_2d(&mut self) -> (f32, f32) {
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if self.dimension as usize + 1 >= PRIMES.len() {
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self.dimension = 2;
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}
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let mut dim = self.dimension as u64;
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let index = self.get_sample_index();
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self.dimension += 2;
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let x = scrambled_radical_inverse(dim as usize, self.index, mix_bits(1 + (dim << 4)));
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dim += 1;
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let y = scrambled_radical_inverse(dim as usize, self.index, mix_bits(1 + (dim << 4)));
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(x, y)
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let hash = hash64_with_seed(self.dimension.to_ne_bytes(), self.seed as u64);
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let lo = hash as u32;
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let hi = (hash >> 32) as u32;
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(sobol_sample0(index, lo), sobol_sample1(index, hi))
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}
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fn get_sample_index(&self) -> u32 {
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let mut index: u32 = 0;
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let last_digit = self.log2_samples & 1;
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for i in (last_digit..self.base4_digits).rev() {
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let digit_shift = 2 * i - last_digit;
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let digit = (self.morton_index >> digit_shift) & 3;
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let higher_bits = self.morton_index >> (digit_shift + 2);
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let mixed = mix_bits((higher_bits ^ (0x55555555 * self.dimension)) as u64);
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let p = (mixed >> 24) as usize % PERMUTATIONS.len();
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let digit = PERMUTATIONS[p][digit as usize];
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index |= (digit as u32) << digit_shift;
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}
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if last_digit != 0 {
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let digit = self.morton_index & 1;
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let higher_bits = self.morton_index >> 1;
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let mixed = mix_bits((higher_bits ^ (0x55555555 * self.dimension)) as u64) as u32;
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index |= (digit ^ mixed) & 1;
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}
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index
|
||||
}
|
||||
}
|
||||
|
||||
fn egcd(a: i16, b: i16) -> (i16, i16) {
|
||||
if a == 0 {
|
||||
(0, 1)
|
||||
} else {
|
||||
let (x, y) = egcd(b % a, a);
|
||||
(y - (b / a) * x, x)
|
||||
}
|
||||
fn sobol_sample0(a: u32, seed: u32) -> f32 {
|
||||
let v = a.reverse_bits();
|
||||
f32::min(fast_owen(v, seed) as f32 * ONE_OVER_MAX, 1.0 - f32::EPSILON)
|
||||
}
|
||||
|
||||
fn mod_inverse(a: u8, m: u8) -> u8 {
|
||||
let m = m as i16;
|
||||
let (x, _) = egcd(a as i16, m);
|
||||
((x % m + m) % m) as u8
|
||||
}
|
||||
|
||||
fn radical_inverse(base_index: usize, mut i: u32) -> f32 {
|
||||
let base = PRIMES[base_index];
|
||||
let inv_base = 1.0 / base as f32;
|
||||
let mut inv_base_m = 1.0;
|
||||
let mut reversed = 0;
|
||||
|
||||
while i > 0 {
|
||||
let next = i / base;
|
||||
let digit = i - next * base;
|
||||
reversed = reversed * base + digit;
|
||||
inv_base_m *= inv_base;
|
||||
i = next
|
||||
}
|
||||
|
||||
f32::min(reversed as f32 * inv_base_m, 1.0 - f32::EPSILON)
|
||||
}
|
||||
|
||||
fn inverse_radical_inverse(mut inverse: u32, base: u32, digits: u32) -> u32 {
|
||||
let mut i = 0;
|
||||
for _ in 0..digits {
|
||||
let digit = inverse % base;
|
||||
inverse /= base;
|
||||
i = i * base + digit;
|
||||
}
|
||||
i
|
||||
}
|
||||
|
||||
fn scrambled_radical_inverse(base_index: usize, mut i: u32, hash: u64) -> f32 {
|
||||
let base = PRIMES[base_index];
|
||||
let inv_base = 1.0 / base as f32;
|
||||
let mut inv_base_m = 1.0;
|
||||
let mut reversed = 0;
|
||||
|
||||
while 1.0 - inv_base_m < 1.0 {
|
||||
let next = i / base;
|
||||
let digit_value = i - next * base;
|
||||
let digit_hash = mix_bits(hash ^ digit_value as u64);
|
||||
let digit = permutation_element(digit_value, base, digit_hash as u32);
|
||||
reversed = reversed * base + digit;
|
||||
inv_base_m *= inv_base;
|
||||
i = next;
|
||||
}
|
||||
|
||||
f32::min(reversed as f32 * inv_base_m, 1.0 - f32::EPSILON)
|
||||
}
|
||||
|
||||
// magic. Taken from pbrt/util/hash.h in pbrt
|
||||
#[inline(always)]
|
||||
fn mix_bits(mut val: u64) -> u64 {
|
||||
val ^= val >> 31;
|
||||
val *= 0x7fb5d329728ea185;
|
||||
val ^= val >> 27;
|
||||
val *= 0x81dadef4bc2dd44d;
|
||||
val ^ (val >> 33)
|
||||
}
|
||||
|
||||
// more magic. Taken from pbrt/util/math.h in pbrt
|
||||
#[inline(always)]
|
||||
fn permutation_element(mut i: u32, n: u32, seed: u32) -> u32 {
|
||||
let mut w = n - 1;
|
||||
w |= w >> 1;
|
||||
w |= w >> 2;
|
||||
w |= w >> 4;
|
||||
w |= w >> 8;
|
||||
w |= w >> 16;
|
||||
loop {
|
||||
i ^= seed;
|
||||
i *= 0xe170893d;
|
||||
i ^= seed >> 16;
|
||||
i ^= (i & w) >> 4;
|
||||
i ^= seed >> 8;
|
||||
i *= 0x0929eb3f;
|
||||
i ^= seed >> 23;
|
||||
i ^= (i & w) >> 1;
|
||||
i *= 1 | seed >> 27;
|
||||
i *= 0x6935fa69;
|
||||
i ^= (i & w) >> 11;
|
||||
i *= 0x74dcb303;
|
||||
i ^= (i & w) >> 2;
|
||||
i *= 0x9e501cc3;
|
||||
i ^= (i & w) >> 2;
|
||||
i *= 0xc860a3df;
|
||||
i &= w;
|
||||
i ^= i >> 5;
|
||||
if i < n {
|
||||
fn sobol_sample1(mut a: u32, seed: u32) -> f32 {
|
||||
let mut v: u32 = 0;
|
||||
for m in SOBOL_MATRIX {
|
||||
if a & 1 != 0 {
|
||||
v ^= m;
|
||||
}
|
||||
a >>= 1;
|
||||
if a == 0 {
|
||||
break;
|
||||
}
|
||||
}
|
||||
(i + seed) % n
|
||||
f32::min(fast_owen(v, seed) as f32 * ONE_OVER_MAX, 1.0 - f32::EPSILON)
|
||||
}
|
||||
|
||||
// magic. taken from pbrt.
|
||||
#[inline(always)]
|
||||
fn fast_owen(mut v: u32, seed: u32) -> u32 {
|
||||
v = v.reverse_bits();
|
||||
v ^= v.wrapping_mul(0x3d20adea);
|
||||
v = v.wrapping_add(seed);
|
||||
v = v.wrapping_mul((seed >> 16) | 1);
|
||||
v ^= v.wrapping_mul(0x05526c56);
|
||||
v ^= v.wrapping_mul(0x53a22864);
|
||||
v.reverse_bits()
|
||||
}
|
||||
|
||||
// more magic. also taken from pbrt.
|
||||
#[inline(always)]
|
||||
fn mix_bits(mut v: u64) -> u64 {
|
||||
v ^= v >> 31;
|
||||
v = v.wrapping_mul(0x7fb5d329728ea185);
|
||||
v ^= v >> 27;
|
||||
v = v.wrapping_mul(0x81dadef4bc2dd44d);
|
||||
v ^ (v >> 33)
|
||||
}
|
||||
|
||||
fn separate(mut v: u32) -> u32 {
|
||||
v &= 0x0000ffff;
|
||||
v = (v | (v << 8)) & 0x00ff00ff;
|
||||
v = (v | (v << 4)) & 0x0f0f0f0f;
|
||||
v = (v | (v << 2)) & 0x33333333;
|
||||
v = (v | (v << 1)) & 0x55555555;
|
||||
v
|
||||
}
|
||||
|
||||
fn morton_2d(x: u32, y: u32) -> u32 {
|
||||
(separate(y) << 1) | separate(x)
|
||||
}
|
||||
|
|
|
|||
|
|
@ -4,7 +4,7 @@ from mechthild import Scene, Shape, Camera
|
|||
|
||||
WIDTH = 800
|
||||
HEIGHT = 600
|
||||
SAMPLES = 20
|
||||
SAMPLES = 32
|
||||
|
||||
s1 = Shape.sphere((0.75, 1.0, 1.0), 1.0)
|
||||
s2 = Shape.sphere((-1.5, 2.0, -2.0), 2.0)
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue