feat: use Zac's quicksort algorithm in stdlib sorting

docs/docs/noir/concepts/data_types/arrays.md

@@ -128,7 +128,7 @@ fn main() {
 
 ### sort_via
 
-Sorts the array with a custom comparison function
+Sorts the array with a custom comparison function. The ordering function must return true if the first argument should be sorted to be before the second argument, otherwise it should return false.
 
 ```rust
 fn sort_via(self, ordering: fn(T, T) -> bool) -> [T; N]

noir_stdlib/src/array/check_shuffle.nr

@@ -0,0 +1,116 @@
+use crate::cmp::Eq;
+
+unconstrained fn __get_shuffle_indices<T, let N: u32>(lhs: [T; N], rhs: [T; N]) -> [Field; N] where T: Eq {
+    let mut shuffle_indices: [Field;N ] = [0; N];
+
+    let mut shuffle_mask: [bool; N] = [false; N];
+    for i in 0..N {
+        let mut found = false;
+        for j in 0..N {
+            if ((shuffle_mask[j] == false) & (!found)) {
+                if (lhs[i] == rhs[j]) {
+                    found = true;
+                    shuffle_indices[i] = j as Field;
+                    shuffle_mask[j] = true;
+                }
+            }
+            if (found) {
+                continue;
+            }
+        }
+        assert(found == true, "check_shuffle, lhs and rhs arrays do not contain equivalent values");
+    }
+
+    shuffle_indices
+}
+
+unconstrained fn __get_index<let N: u32>(indices: [Field; N], idx: Field) -> Field {
+    let mut result = 0;
+    for i in 0..N {
+        if (indices[i] == idx) {
+            result = i as Field;
+            break;
+        }
+    }
+    result
+}
+
+pub(crate) fn check_shuffle<T, let N: u32>(lhs: [T; N], rhs: [T; N]) where T: Eq {
+    unsafe {
+        let shuffle_indices = __get_shuffle_indices(lhs, rhs);
+
+        for i in 0..N {
+            let idx = __get_index(shuffle_indices, i as Field);
+            assert_eq(shuffle_indices[idx], i as Field);
+        }
+        for i in 0..N {
+            let idx = shuffle_indices[i];
+            let expected = rhs[idx];
+            let result = lhs[i];
+            assert_eq(expected, result);
+        }
+    }
+}
+
+mod test {
+    use super::check_shuffle;
+    use crate::cmp::Eq;
+
+    struct CompoundStruct {
+        a: bool,
+        b: Field,
+        c: u64
+    }
+    impl Eq for CompoundStruct {
+        fn eq(self, other: Self) -> bool {
+            (self.a == other.a) & (self.b == other.b) & (self.c == other.c)
+        }
+    }
+
+    #[test]
+    fn test_shuffle() {
+        let lhs: [Field; 5] = [0, 1, 2, 3, 4];
+        let rhs: [Field; 5] = [2, 0, 3, 1, 4];
+        check_shuffle(lhs, rhs);
+    }
+
+    #[test]
+    fn test_shuffle_identity() {
+        let lhs: [Field; 5] = [0, 1, 2, 3, 4];
+        let rhs: [Field; 5] = [0, 1, 2, 3, 4];
+        check_shuffle(lhs, rhs);
+    }
+
+    #[test(should_fail_with = "check_shuffle, lhs and rhs arrays do not contain equivalent values")]
+    fn test_shuffle_fail() {
+        let lhs: [Field; 5] = [0, 1, 2, 3, 4];
+        let rhs: [Field; 5] = [0, 1, 2, 3, 5];
+        check_shuffle(lhs, rhs);
+    }
+
+    #[test(should_fail_with = "check_shuffle, lhs and rhs arrays do not contain equivalent values")]
+    fn test_shuffle_duplicates() {
+        let lhs: [Field; 5] = [0, 1, 2, 3, 4];
+        let rhs: [Field; 5] = [0, 1, 2, 3, 3];
+        check_shuffle(lhs, rhs);
+    }
+
+    #[test]
+    fn test_shuffle_compound_struct() {
+        let lhs: [CompoundStruct; 5] = [
+            CompoundStruct { a: false, b: 0, c: 12345 },
+            CompoundStruct { a: false, b: -100, c: 54321 },
+            CompoundStruct { a: true, b: 5, c: 0xffffffffffffffff },
+            CompoundStruct { a: true, b: 9814, c: 0xeeffee0011001133 },
+            CompoundStruct { a: false, b: 0x155, c: 0 }
+        ];
+        let rhs: [CompoundStruct; 5] = [
+            CompoundStruct { a: false, b: 0x155, c: 0 },
+            CompoundStruct { a: false, b: 0, c: 12345 },
+            CompoundStruct { a: false, b: -100, c: 54321 },
+            CompoundStruct { a: true, b: 9814, c: 0xeeffee0011001133 },
+            CompoundStruct { a: true, b: 5, c: 0xffffffffffffffff }
+        ];
+        check_shuffle(lhs, rhs);
+    }
+}

noir_stdlib/src/array.nr → noir_stdlib/src/array/mod.nr

@@ -1,63 +1,15 @@
-use crate::cmp::Ord;
+use crate::cmp::{Eq, Ord};
 use crate::convert::From;
+use crate::runtime::is_unconstrained;
+
+mod check_shuffle;
+mod quicksort;
 
 impl<T, let N: u32> [T; N] {
     /// Returns the length of the slice.
     #[builtin(array_len)]
     pub fn len(self) -> u32 {}
 
-    pub fn sort(self) -> Self where T: Ord {
-        self.sort_via(|a: T, b: T| a <= b)
-    }
-
-    pub fn sort_via<Env>(self, ordering: fn[Env](T, T) -> bool) -> Self {
-        let sorted_index = unsafe {
-            // Safety: These indices are asserted to be the sorted element indices via `find_index`
-            let sorted_index: [u32; N] = self.get_sorting_index(ordering);
-
-            for i in 0..N {
-                let pos = find_index(sorted_index, i);
-                assert(sorted_index[pos] == i);
-            }
-
-            sorted_index
-        };
-
-        // Sort the array using the indexes
-        let mut result = self;
-        for i in 0..N {
-            result[i] = self[sorted_index[i]];
-        }
-        // Ensure the array is sorted
-        for i in 0..N - 1 {
-            assert(ordering(result[i], result[i + 1]));
-        }
-
-        result
-    }
-
-    /// Returns the index of the elements in the array that would sort it, using the provided custom sorting function.
-    unconstrained fn get_sorting_index<Env>(self, ordering: fn[Env](T, T) -> bool) -> [u32; N] {
-        let mut result = [0; N];
-        let mut a = self;
-        for i in 0..N {
-            result[i] = i;
-        }
-        for i in 1..N {
-            for j in 0..i {
-                if ordering(a[i], a[j]) {
-                    let old_a_j = a[j];
-                    a[j] = a[i];
-                    a[i] = old_a_j;
-                    let old_j = result[j];
-                    result[j] = result[i];
-                    result[i] = old_j;
-                }
-            }
-        }
-        result
-    }
-
     #[builtin(as_slice)]
     pub fn as_slice(self) -> [T] {}
 
@@ -114,25 +66,44 @@ impl<T, let N: u32> [T; N] {
     }
 }
 
+impl<T, let N: u32> [T; N] where T: Ord + Eq {
+    pub fn sort(self) -> Self {
+        self.sort_via(|a: T, b: T| a <= b)
+    }
+}
+
+impl<T, let N: u32> [T; N] where T: Eq {
+
+    /// Sorts the array using a custom predicate function `ordering`.
+    ///
+    /// # Safety
+    /// The `ordering` function must be designed to return `true` for equal valued inputs
+    /// If this is not done, `sort_via` will fail to sort inputs with duplicated elements.
+    pub fn sort_via<Env>(self, ordering: fn[Env](T, T) -> bool) -> Self {
+        unsafe {
+            // Safety: `sorted` array is checked to be:
+            //   a. a permutation of `input`'s elements
+            //   b. satisfying the predicate `ordering`
+            let sorted = quicksort::quicksort(self, ordering);
+
+            if !is_unconstrained() {
+                for i in 0..N - 1 {
+                    assert(ordering(sorted[i], sorted[i + 1]), "Array has not been sorted correctly according to `ordering`.");
+                }
+                check_shuffle::check_shuffle(self, sorted);
+            }
+            sorted
+        }
+    }
+}
+
 impl<let N: u32> [u8; N] {
     /// Convert a sequence of bytes as-is into a string.
     /// This function performs no UTF-8 validation or similar.
     #[builtin(array_as_str_unchecked)]
     pub fn as_str_unchecked(self) -> str<N> {}
 }
 
-// helper function used to look up the position of a value in an array of Field
-// Note that function returns 0 if the value is not found
-unconstrained fn find_index<let N: u32>(a: [u32; N], find: u32) -> u32 {
-    let mut result = 0;
-    for i in 0..a.len() {
-        if a[i] == find {
-            result = i;
-        }
-    }
-    result
-}
-
 impl<let N: u32> From<str<N>> for [u8; N] {
     fn from(s: str<N>) -> Self {
         s.as_bytes()

noir_stdlib/src/array/quicksort.nr

@@ -0,0 +1,39 @@
+unconstrained fn partition<T, Env, let N: u32>(
+    arr: &mut [T; N],
+    low: u32,
+    high: u32,
+    sortfn: fn[Env](T, T) -> bool
+) -> u32 {
+    let pivot = high;
+    let mut i = low;
+    for j in low..high {
+        if (sortfn(arr[j], arr[pivot])) {
+            let temp = arr[i];
+            arr[i] = arr[j];
+            arr[j] = temp;
+            i += 1;
+        }
+    }
+    let temp = arr[i];
+    arr[i] = arr[pivot];
+    arr[pivot] = temp;
+    i
+}
+
+unconstrained fn quicksort_recursive<T, Env, let N: u32>(arr: &mut [T; N], low: u32, high: u32, sortfn: fn[Env](T, T) -> bool) {
+    if low < high {
+        let pivot_index = partition(arr, low, high, sortfn);
+        if pivot_index > 0 {
+            quicksort_recursive(arr, low, pivot_index - 1, sortfn);
+        }
+        quicksort_recursive(arr, pivot_index + 1, high, sortfn);
+    }
+}
+
+unconstrained pub(crate) fn quicksort<T, Env, let N: u32>(_arr: [T; N], sortfn: fn[Env](T, T) -> bool) -> [T; N] {
+    let mut arr: [T; N] = _arr;
+    if arr.len() <= 1 {} else {
+        quicksort_recursive(&mut arr, 0, arr.len() - 1, sortfn);
+    }
+    arr
+}