feat: mul-by-base api

src/field.rs

@@ -26,6 +26,14 @@ pub trait SmallField: PrimeField + Serialize + SerdeObject {
     fn from_limbs(limbs: &[Self::BaseField]) -> Self;
     /// Sample a random over the base field
     fn sample_base(rng: impl RngCore) -> Self;
+    /// Mul-assign self by a base field element
+    fn mul_assign_base(&mut self, rhs: &Self::BaseField);
+    /// Multiply self by a base field element
+    fn mul_base(&self, rhs: &Self::BaseField) -> Self {
+        let mut res = self.clone();
+        res.mul_assign_base(rhs);
+        res
+    }
 }
 
 impl SmallField for Goldilocks {
@@ -56,6 +64,11 @@ impl SmallField for Goldilocks {
     fn sample_base(mut rng: impl RngCore) -> Self {
         Self::random(&mut rng)
     }
+
+    /// Mul-assign self by a base field element
+    fn mul_assign_base(&mut self, rhs: &Self::BaseField) {
+        *self *= rhs;
+    }
 }
 impl SmallField for GoldilocksExt2 {
     type BaseField = Goldilocks;
@@ -90,6 +103,12 @@ impl SmallField for GoldilocksExt2 {
     fn sample_base(mut rng: impl RngCore) -> Self {
         Self::BaseField::random(&mut rng).into()
     }
+
+    /// Mul-assign self by a base field element
+    fn mul_assign_base(&mut self, rhs: &Self::BaseField) {
+        self.0[0] *= rhs;
+        self.0[1] *= rhs;
+    }
 }
 impl SmallField for GoldilocksExt3 {
     type BaseField = Goldilocks;
@@ -124,4 +143,11 @@ impl SmallField for GoldilocksExt3 {
     fn sample_base(mut rng: impl RngCore) -> Self {
         Self::BaseField::random(&mut rng).into()
     }
+
+    /// Mul-assign self by a base field element
+    fn mul_assign_base(&mut self, rhs: &Self::BaseField) {
+        self.0[0] *= rhs;
+        self.0[1] *= rhs;
+        self.0[2] *= rhs;
+    }
 }

src/tests.rs

@@ -9,6 +9,41 @@ use rand_core::RngCore;
 use rand_core::SeedableRng;
 use rand_xorshift::XorShiftRng;
 
+use crate::SmallField;
+
+
+pub fn random_small_field_tests<F: SmallField>(type_name: String) {
+    let mut rng = XorShiftRng::from_seed([
+        0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,
+        0xe5,
+    ]);
+
+    let message = format!("multiplication {}", type_name);
+    let start = start_timer!(|| message);
+    for _ in 0..1000000 {
+        let a = F::random(&mut rng);
+        let b = F::sample_base(&mut rng);
+        let c = F::random(&mut rng);
+
+        let mut t0 = a; // (a * b) * c
+        t0.mul_assign(&b);
+        t0.mul_assign(&c);
+
+        let mut t1 = a; // (a * c) * b
+        t1.mul_assign(&c);
+        t1.mul_assign(&b);
+
+        let mut t2 = b; // (b * c) * a
+        t2.mul_assign(&c);
+        t2.mul_assign(&a);
+
+        assert_eq!(t0, t1);
+        assert_eq!(t1, t2);
+    }
+    end_timer!(start);
+
+}
+
 pub fn random_field_tests<F: Field>(type_name: String) {
     let mut rng = XorShiftRng::from_seed([
         0x59, 0x62, 0xbe, 0x5d, 0x76, 0x3d, 0x31, 0x8d, 0x17, 0xdb, 0x37, 0x32, 0x54, 0x06, 0xbc,

src/tests/fp.rs

@@ -7,6 +7,7 @@ use rand_xorshift::XorShiftRng;
 use super::random_field_tests;
 use super::random_inversion_tests;
 use super::random_prime_field_tests;
+use super::random_small_field_tests;
 use crate::fp::Goldilocks;
 use crate::fp::LegendreSymbol;
 
@@ -56,4 +57,5 @@ fn test_field() {
     random_field_tests::<Goldilocks>("Goldilocks".to_string());
     random_prime_field_tests::<Goldilocks>("Goldilocks".to_string());
     random_inversion_tests::<Goldilocks>("Goldilocks".to_string());
+    random_small_field_tests::<Goldilocks>("Goldilocks".to_string());
 }

src/tests/fp2.rs

@@ -1,6 +1,7 @@
 use super::random_field_tests;
 use super::random_inversion_tests;
 use super::random_prime_field_tests;
+use super::random_small_field_tests;
 use crate::fp::Goldilocks;
 use crate::fp2::GoldilocksExt2;
 
@@ -9,6 +10,7 @@ fn test_field() {
     random_field_tests::<GoldilocksExt2>("GoldilocksExt2".to_string());
     random_prime_field_tests::<GoldilocksExt2>("GoldilocksExt2".to_string());
     random_inversion_tests::<GoldilocksExt2>("GoldilocksExt2".to_string());
+    random_small_field_tests::<GoldilocksExt2>("GoldilocksExt2".to_string());
 }
 
 #[test]

src/tests/fp3.rs

@@ -1,5 +1,6 @@
 use super::random_field_tests;
 use super::random_prime_field_tests;
+use super::random_small_field_tests;
 use crate::fp::Goldilocks;
 use crate::fp3::GoldilocksExt3;
 
@@ -7,6 +8,7 @@ use crate::fp3::GoldilocksExt3;
 fn test_field() {
     random_field_tests::<GoldilocksExt3>("GoldilocksExt3".to_string());
     random_prime_field_tests::<GoldilocksExt3>("GoldilocksExt3".to_string());
+    random_small_field_tests::<GoldilocksExt3>("GoldilocksExt3".to_string());
 }
 
 #[test]