More improvements to Sobol sampling.

- Added an additional scramble round to the Owen scrambling, with
  new optimized constants.
- Reordered the dimensions of the direction numbers to improve 2d
  projections between adjecent dimensions.  Only did this for
  dimensions under ~40.

src/renderer.rs

@@ -709,10 +709,7 @@ fn get_sample(dimension: u32, i: u32, pixel_co: (u32, u32), seed: u32) -> f32 {
         n if (n - 1) < sobol::MAX_DIMENSION as u32 => {
             let dim = n - 1;
             // Sobol sampling.
-            // We skip the first 32 samples because doing so reduces noise
-            // in some areas when rendering at 64 spp.  Not sure why, but it
-            // works.
-            sobol::sample_owen_cranley(dim, i + 32, hash_u32(dim, scramble))
+            sobol::sample_owen_cranley(dim, i, hash_u32(dim, scramble))
         }
         _ => {
             // Random sampling.

sub_crates/sobol/build.rs

@@ -7,7 +7,7 @@ use std::{env, fs::File, io::Write, path::Path};
 const NUM_DIMENSIONS: usize = 256;
 
 /// What file to generate the numbers from.
-const DIRECTION_NUMBERS_TEXT: &str = include_str!("direction_numbers/joe-kuo-other-3.1024.txt");
+const DIRECTION_NUMBERS_TEXT: &str = include_str!("direction_numbers/joe-kuo-cessen-3.1024.txt");
 
 fn main() {
     let out_dir = env::var("OUT_DIR").unwrap();
@@ -143,7 +143,9 @@ pub fn generate_direction_vectors(dimensions: usize) -> Vec<[u32; SOBOL_BITS]> {
 /// text file.  Returns the `a` and `m` parts.
 fn parse_direction_numbers(text: &str) -> Result<(u32, Vec<u32>), Box<dyn std::error::Error>> {
     let mut numbers = text.split_whitespace();
-    assert!(numbers.clone().count() >= 4);
+    if numbers.clone().count() < 4 || text.starts_with("#") {
+        return Err(Box::new(ParseError(())));
+    }
 
     // Skip the first two numbers, which are just the dimension and the count
     // of direction numbers for this dimension.
@@ -159,3 +161,12 @@ fn parse_direction_numbers(text: &str) -> Result<(u32, Vec<u32>), Box<dyn std::e
 
     Ok((a, m))
 }
+
+#[derive(Debug, Copy, Clone)]
+struct ParseError(());
+impl std::error::Error for ParseError {}
+impl std::fmt::Display for ParseError {
+    fn fmt(&self, _f: &mut std::fmt::Formatter) -> Result<(), std::fmt::Error> {
+        Ok(())
+    }
+}

sub_crates/sobol/src/lib.rs

@@ -125,7 +125,7 @@ fn owen_scramble_u32(mut n: u32, scramble: u32) -> u32 {
 
     n = n.reverse_bits();
     n ^= scramble;
-    let perms = [0x7ed7a4b4, 0xcb95fcb6, 0x4ea13ebc];
+    let perms = [0xa56bb1c6, 0xef577134, 0xd0e5e808, 0x200bd50a];
     for p in perms.iter() {
         n ^= n.wrapping_mul(*p);
     }