feat: initial implementation (#1)

TomAFrench · web-flow · commit 4e5778bd8866 · 2024-10-03T08:37:09.000+01:00
Release-as: 0.1.0
diff --git a/Nargo.toml b/Nargo.toml
@@ -1,7 +1,8 @@
 [package]
-name = "noir_library"
+name = "sparse_array"
 type = "lib"
 authors = [""]
 compiler_version = ">=0.34.0"
 
 [dependencies]
+sort = {tag = "v0.1.0", git = "https://github.com/noir-lang/noir_sort"}
diff --git a/README.md b/README.md
@@ -1,20 +1,7 @@
-# noir-library-starter
+# sparse_array
 
-This repository is a template used by the noir-lang org when creating internally maintained libraries.
+Noir library that implements efficient sparse arrays, both constant (SparseArray) and mutable (MutSparseArray)
 
-This provides out of the box:
-
-- A simple CI setup to test and format the library
-- A canary flagging up compilation failures on nightly releases.
-- A [release-please](https://github.com/googleapis/release-please) setup to ease creating releases for the library.
-
-Feel free to use this template as a starting point to create your own Noir libraries.
-
----
-
-# LIBRARY_NAME
-
-Add a brief description of the library
 
 ## Benchmarks
 
@@ -27,11 +14,40 @@ In your _Nargo.toml_ file, add the version of this library you would like to ins
 
 ```
 [dependencies]
-LIBRARY = { tag = "v0.1.0", git = "https://github.com/noir-lang/LIBRARY_NAME" }
+sparse_array = { tag = "v0.1.0", git = "https://github.com/noir-lang/sparse_array" }
 ```
 
-## `library`
+## `sparse_array`
 
 ### Usage
 
-`PLACEHOLDER`
+```rust
+use dep::sparse_array::{SparseArray, MutSparseArray}
+
+// a sparse array of size 10,000 with 10 nonzero values
+fn example_sparse_array(nonzero_indices: [Field; 10], nonzero_values: [Field; 10]) {
+    let sparse_array_size = 10000;
+    let array: SparseArray<10, Field> = SparseArray::create(nonzero_indices, nonzero_values, sparse_array_size);
+
+    assert(array.get(999) == 12345);
+}
+
+// a mutable sparse array that can contain up to 10 nonzero values
+fn example_mut_sparse_array(initial_nonzero_indices: [Field; 9], initial_nonzero_values: [Field; 9]) {
+    let sparse_array_size = 10000;
+    let mut array: MutSparseArray<10, Field> = MutSparseArray::create(nonzero_indices, nonzero_values, sparse_array_size);
+
+    // update element 1234 to contain value 9999
+    array.set(1234, 9999);
+
+    // error, array can only contain 10 nonzero values
+    array.ser(10, 888);
+}
+```
+
+# Costs
+
+Constructing arrays is proportional to the number of nonzero entries in the array and very small ~10 gates per element (plus the cost of initializing range tables if not already done so)
+
+Reading from `SparseArray` is 14.5 gates
+Reading and writing to `MutSparseArray` is ~30 gates
diff --git a/src/lib.nr b/src/lib.nr
@@ -1,5 +1,273 @@
-/// This doesn't really do anything by ensures that there is a test for CI to run.
-#[test]
-fn smoke_test() {
-    assert(true);
+mod mut_sparse_array;
+use dep::sort::sort_advanced;
+
+unconstrained fn __sort_field_as_u32(lhs: Field, rhs: Field) -> bool {
+    //  lhs.lt(rhs)
+    lhs as u32 < rhs as u32
+}
+
+fn assert_sorted(lhs: Field, rhs: Field) {
+    let result = (rhs - lhs - 1);
+    result.assert_max_bit_size(32);
+}
+
+/**
+ * @brief MutSparseArray, a sparse array of configurable size with `N` nonzero entries.
+ *        Can be read from and written into
+ *
+ * @param keys is size N+2 because we want to always ensure that,
+ *        for any valid index, there is some X where `keys[X] <= index <= keys[X+1]`
+ *        when constructing, we will set keys[0] = 0, and keys[N-1] = maximum - 1
+ * @param values is size N+3 because of the following:
+ *        1. keys[i] maps to values[i+1]
+ *        2. values[0] is an empty object. when calling `get(idx)`, if `idx` is not in `keys` we will return `values[0]`
+ **/
+struct MutSparseArrayBase<let N: u32, T, ComparisonFuncs>
+{
+    values: [T; N + 3],
+    keys: [Field; N + 2],
+    linked_keys: [Field; N + 2],
+    tail_ptr: Field,
+    maximum: Field
+}
+
+struct U32RangeTraits {
+}
+
+struct MutSparseArray<let N: u32, T>
+{
+    inner: MutSparseArrayBase<N, T, U32RangeTraits>
+}
+/**
+ * @brief SparseArray, stores a sparse array of up to size 2^32 with `N` nonzero entries
+ *        SparseArray is constant i.e. values canot be inserted after creation.
+ *        See MutSparseArray for a mutable version (a bit more expensive)
+ * @param keys is size N+2 because we want to always ensure that,
+ *        for any valid index, there is some X where `keys[X] <= index <= keys[X+1]`
+ *        when constructing, we will set keys[0] = 0, and keys[N-1] = maximum - 1
+ * @param values is size N+3 because of the following:
+ *        1. keys[i] maps to values[i+1]
+ *        2. values[0] is an empty object. when calling `get(idx)`, if `idx` is not in `keys` we will return `values[0]`
+ **/
+struct SparseArray<let N: u32, T> {
+    keys: [Field; N + 2],
+    values: [T; N + 3],
+    maximum: Field // can be up to 2^32
+}
+impl<let N: u32, T> SparseArray<N, T> where T : std::default::Default {
+
+    /**
+     * @brief construct a SparseArray
+     **/
+    fn create(_keys: [Field; N], _values: [T; N], size: Field) -> Self {
+        let _maximum = size - 1;
+        let mut r: Self = SparseArray { keys: [0; N + 2], values: [T::default(); N + 3], maximum: _maximum };
+
+        // for any valid index, we want to ensure the following is satified:
+        // self.keys[X] <= index <= self.keys[X+1]
+        // this requires us to sort hte keys, and insert a startpoint and endpoint
+        let sorted_keys = sort_advanced(_keys, __sort_field_as_u32, assert_sorted);
+
+        // insert start and endpoints
+        r.keys[0] = 0;
+        for i in 0..N {
+            r.keys[i+1] = sorted_keys.sorted[i];
+        }
+        r.keys[N+1] = _maximum;
+
+        // populate values based on the sorted keys
+        // note: self.keys[i] maps to self.values[i+1]
+        // self.values[0] does not map to any key. we use it to store the default empty value,
+        // which is returned when `get(idx)` is called and `idx` does not exist in `self.keys`
+        for i in 0..N {
+            r.values[i+2] = _values[sorted_keys.sort_indices[i]];
+        }
+        // insert values that map to our key start and endpoints
+        // if _keys[0] = 0 then values[0] must equal _values[0], so some conditional logic is required
+        // (same for _keys[N-1])
+        let mut initial_value = T::default();
+        if (_keys[0] == 0) {
+            initial_value = _values[0];
+        }
+        let mut final_value = T::default();
+        if (_keys[N - 1] == _maximum) {
+            final_value = _values[N-1];
+        }
+        r.values[1] = initial_value;
+        r.values[N+2] = final_value;
+
+        // perform boundary checks!
+        // the maximum size of the sparse array is 2^32
+        // we need to check that every element in `self.keys` is less than 2^32
+        // because `self.keys` is sorted, we can simply validate that
+        // sorted_keys.sorted[0] < 2^32
+        // sorted_keys.sorted[N-1] < maximum
+        sorted_keys.sorted[0].assert_max_bit_size(32);
+        _maximum.assert_max_bit_size(32);
+        (_maximum - sorted_keys.sorted[N - 1]).assert_max_bit_size(32);
+        r
+    }
+
+    /**
+     * @brief determine whether `target` is present in `self.keys`
+     * @details if `found == false`, `self.keys[found_index] < target < self.keys[found_index + 1]`
+     **/
+    unconstrained fn search_for_key(self, target: Field) -> (Field, Field) {
+        let mut found = false;
+        let mut found_index = 0;
+        let mut previous_less_than_or_equal_to_target = false;
+        for i in 0..N + 2 {
+            // if target = 0xffffffff we need to be able to add 1 here, so use u64
+            let current_less_than_or_equal_to_target = self.keys[i] as u64 <= target as u64;
+            if (self.keys[i] == target) {
+                found = true;
+                found_index = i as Field;
+                break;
+            }
+            if (previous_less_than_or_equal_to_target & !current_less_than_or_equal_to_target) {
+                found_index = i as Field - 1;
+                break;
+            }
+            previous_less_than_or_equal_to_target = current_less_than_or_equal_to_target;
+        }
+        (found as Field, found_index)
+    }
+
+    /**
+     * @brief return element `idx` from the sparse array
+     * @details cost is 14.5 gates per lookup
+     **/
+    fn get(self, idx: Field) -> T {
+        let (found, found_index) = unsafe {
+            self.search_for_key(idx)
+        };
+        // bool check. 0.25 gates cheaper than a raw `bool` type. need to fix at some point
+        assert(found * found == found);
+
+        // OK! So we have the following cases to check
+        // 1. if `found` then `self.keys[found_index] == idx`
+        // 2. if `!found` then `self.keys[found_index] < idx < self.keys[found_index + 1]
+        // how do we simplify these checks?
+        // case 1 can be converted to `self.keys[found_index] <= idx <= self.keys[found_index]
+        // case 2 can be modified to  `self.keys[found_index] + 1 <= idx <= self.keys[found_index + 1] - 1
+        // combine the two into the following single statement:
+        // `self.keys[found_index] + 1 - found <= idx <= self.keys[found_index + 1 - found] - 1 + found
+        let lhs = self.keys[found_index];
+        let rhs = self.keys[found_index + 1 - found];
+        let lhs_condition = idx - lhs - 1 + found;
+        let rhs_condition = rhs - 1 + found - idx;
+        lhs_condition.assert_max_bit_size(32);
+        rhs_condition.assert_max_bit_size(32);
+
+        // self.keys[i] maps to self.values[i+1]
+        // however...if we did not find a non-sparse entry, we want to return self.values[0] (the default value)
+        let value_index = (found_index + 1) * found;
+        self.values[value_index]
+    }
+}
+
+mod test {
+
+    use crate::SparseArray;
+    #[test]
+fn test_sparse_lookup() {
+        let example = SparseArray::create([1, 99, 7, 5], [123, 101112, 789, 456], 100);
+
+        assert(example.get(1) == 123);
+        assert(example.get(5) == 456);
+        assert(example.get(7) == 789);
+        assert(example.get(99) == 101112);
+
+        for i in 0..100 {
+            if ((i != 1) & (i != 5) & (i != 7) & (i != 99)) {
+                assert(example.get(i as Field) == 0);
+            }
+        }
+    }
+
+    #[test]
+fn test_sparse_lookup_boundary_cases() {
+        // what about when keys[0] = 0 and keys[N-1] = 2^32 - 1?
+        let example = SparseArray::create(
+            [0, 99999, 7, 0xffffffff],
+            [123, 101112, 789, 456],
+            0x100000000
+        );
+
+        assert(example.get(0) == 123);
+        assert(example.get(99999) == 101112);
+        assert(example.get(7) == 789);
+        assert(example.get(0xffffffff) == 456);
+        assert(example.get(0xfffffffe) == 0);
+    }
+
+    #[test(should_fail_with = "call to assert_max_bit_size")]
+fn test_sparse_lookup_overflow() {
+        let example = SparseArray::create([1, 5, 7, 99999], [123, 456, 789, 101112], 100000);
+
+        assert(example.get(100000) == 0);
+    }
+
+    #[test(should_fail_with = "call to assert_max_bit_size")]
+fn test_sparse_lookup_boundary_case_overflow() {
+        let example = SparseArray::create([0, 5, 7, 0xffffffff], [123, 456, 789, 101112], 0x100000000);
+
+        assert(example.get(0x100000000) == 0);
+    }
+
+    #[test(should_fail_with = "call to assert_max_bit_size")]
+fn test_sparse_lookup_key_exceeds_maximum() {
+        let example = SparseArray::create([0, 5, 7, 0xffffffff], [123, 456, 789, 101112], 0xffffffff);
+        assert(example.maximum == 0xffffffff);
+    }
+    #[test]
+fn test_sparse_lookup_u32() {
+        let example = SparseArray::create(
+            [1, 99, 7, 5],
+            [123 as u32, 101112 as u32, 789 as u32, 456 as u32],
+            100
+        );
+
+        assert(example.get(1) == 123);
+        assert(example.get(5) == 456);
+        assert(example.get(7) == 789);
+        assert(example.get(99) == 101112);
+
+        for i in 0..100 {
+            if ((i != 1) & (i != 5) & (i != 7) & (i != 99)) {
+                assert(example.get(i as Field) == 0);
+            }
+        }
+    }
+
+    struct F {
+    foo: [Field; 3]
+}
+    impl std::cmp::Eq for F {
+        fn eq(self, other: Self) -> bool {
+            self.foo == other.foo
+        }
+    }
+
+    impl std::default::Default for F {
+        fn default() -> Self {
+            F { foo: [0; 3] }
+        }
+    }
+
+    #[test]
+fn test_sparse_lookup_struct() {
+        let values = [F { foo: [1, 2, 3] }, F { foo: [4, 5, 6] }, F { foo: [7, 8, 9] }, F { foo: [10, 11, 12] }];
+        let example = SparseArray::create([1, 99, 7, 5], values, 100000);
+
+        assert(example.get(1) == values[0]);
+        assert(example.get(5) == values[3]);
+        assert(example.get(7) == values[2]);
+        assert(example.get(99) == values[1]);
+        for i in 0..100 {
+            if ((i != 1) & (i != 5) & (i != 7) & (i != 99)) {
+                assert(example.get(i as Field) == F::default());
+            }
+        }
+    }
 }
diff --git a/src/mut_sparse_array.nr b/src/mut_sparse_array.nr
