Implement Int::gcd

Author: erik-3milabs

benches/int.rs

@@ -332,13 +332,92 @@ fn bench_sub(c: &mut Criterion) {
     group.finish();
 }
 
+fn bench_gcd(c: &mut Criterion) {
+    let mut group = c.benchmark_group("gcd");
+
+    group.bench_function("gcd, I128-I128", |b| {
+        b.iter_batched(
+            || {
+                let x = I128::random(&mut OsRng);
+                let y = I128::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.bench_function("gcd, I256-I256", |b| {
+        b.iter_batched(
+            || {
+                let x = I256::random(&mut OsRng);
+                let y = I256::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.bench_function("gcd, I512-I512", |b| {
+        b.iter_batched(
+            || {
+                let x = I512::random(&mut OsRng);
+                let y = I512::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.bench_function("gcd, I1024-I1024", |b| {
+        b.iter_batched(
+            || {
+                let x = I1024::random(&mut OsRng);
+                let y = I1024::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.bench_function("gcd, I2048-I2048", |b| {
+        b.iter_batched(
+            || {
+                let x = I2048::random(&mut OsRng);
+                let y = I2048::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.bench_function("gcd, I4096-I4096", |b| {
+        b.iter_batched(
+            || {
+                let x = I4096::random(&mut OsRng);
+                let y = I4096::random(&mut OsRng);
+                (x, y)
+            },
+            |(x, y)| black_box(x.gcd(&y)),
+            BatchSize::SmallInput,
+        )
+    });
+
+    group.finish();
+}
+
 criterion_group!(
     benches,
     bench_mul,
     bench_widening_mul,
     bench_div,
     bench_add,
     bench_sub,
+    bench_gcd,
 );
 
 criterion_main!(benches);

src/int.rs

@@ -23,6 +23,7 @@ mod cmp;
 mod div;
 mod encoding;
 mod from;
+mod gcd;
 mod mul;
 mod neg;
 mod resize;

src/int/gcd.rs

@@ -0,0 +1,77 @@
+//! Support for computing the greatest common divisor of two [`Int`]s.
+
+use crate::modular::SafeGcdInverter;
+use crate::{Int, Odd, PrecomputeInverter, Uint};
+
+impl<const SAT_LIMBS: usize, const UNSAT_LIMBS: usize> Int<SAT_LIMBS>
+where
+    Odd<Uint<SAT_LIMBS>>: PrecomputeInverter<Inverter = SafeGcdInverter<SAT_LIMBS, UNSAT_LIMBS>>,
+{
+    /// Compute the greatest common divisor (`gcd`) of `self` and `rhs`.
+    /// Always returns a non-negative value.
+    pub const fn gcd(&self, rhs: &Self) -> Uint<SAT_LIMBS> {
+        self.abs().gcd(&rhs.abs())
+    }
+}
+
+impl<const SAT_LIMBS: usize, const UNSAT_LIMBS: usize> Odd<Int<SAT_LIMBS>>
+where
+    Odd<Uint<SAT_LIMBS>>: PrecomputeInverter<Inverter = SafeGcdInverter<SAT_LIMBS, UNSAT_LIMBS>>,
+{
+    /// Compute the greatest common divisor (GCD) of this number and another.
+    ///
+    /// Runs in variable time with respect to `rhs`.
+    pub fn gcd_vartime(&self, rhs: &Int<SAT_LIMBS>) -> Uint<SAT_LIMBS> {
+        // safe to unwrap; self is odd
+        self.abs().to_odd().unwrap().gcd_vartime(&rhs.abs())
+    }
+}
+
+// TODO: implement Gcd trait. Depends on Integer trait.
+
+#[cfg(test)]
+mod tests {
+    use crate::{Int, I1024, I128, U1024, U128};
+
+    #[test]
+    fn gcd() {
+        // Odd GCD
+        assert_eq!(I128::from(-77).gcd(&I128::from(14)), U128::from(7u32));
+        assert_eq!(I128::from(-77).gcd(&I128::from(-14)), U128::from(7u32));
+        assert_eq!(I128::from(77).gcd(&I128::from(14)), U128::from(7u32));
+        assert_eq!(I128::from(77).gcd(&I128::from(-14)), U128::from(7u32));
+
+        // Even GCD
+        assert_eq!(I128::from(-144).gcd(&I128::from(28)), U128::from(4u32));
+        assert_eq!(I128::from(-144).gcd(&I128::from(-28)), U128::from(4u32));
+        assert_eq!(I128::from(144).gcd(&I128::from(28)), U128::from(4u32));
+        assert_eq!(I128::from(144).gcd(&I128::from(-28)), U128::from(4u32));
+    }
+
+    #[test]
+    fn gcd_large() {
+        // larger values
+        let x = I1024::from_be_hex("0084A671979467BD329796EF6B55CC555C4B6DE1DA7425F7DF0175C04164A2F1D333D2DD4BCD1BE078E0FC9C1616F8532F3A4AB2CA9102B948B7217955344BF3FBD687F205789E5118FF43B372AE93F131BF6624721518CF73BE04DA1645495B12DDE8032226F1D02E1939631CC5D0B43AC47212CF819447C05F8899EFD13C80");
+        let y = I1024::from_be_hex("6FE1503B3DD76A256360BC23041D2D47D47DA27E2474C1CB8ABCBB0617320996C9319B3DC29FC24F38E2D9B9BE9B48BFB0A7B955B03F784F3DCE963CFD03ED07C0A89583B00BE7EDDFFC229087CF08DADF838B3A65EE5F85BAE06132B1FED2DAB3FF12CCB8E0357AEAF95195E59A0D06E0626B894A20DFDC7B1252A5E1ABF000").neg().unwrap();
+        let target = U1024::from_be_hex("0000000000000000000000000000000000000000000000000000106F3345CEC3099E40DD1CD11AA51AA63D0351C8B83B200CAC0563F10BA25470C66EDE1E1A98FFFD0EBC98641BE024071CC9798D213826A24786FF1A2D26E5C819DFBF3E907112EA34CE9E40A3AB8D59190A361A1AE6E3D9393211621B27EEFB4D5FD3DF5580");
+
+        let res = x.gcd(&y);
+        assert_eq!(res, target);
+
+        // divide out factors
+        let x_on_gcd = x.checked_div(&Int::new_from_uint(res)).unwrap();
+        let y_on_gcd = y.checked_div(&Int::new_from_uint(res)).unwrap();
+
+        assert_eq!(x_on_gcd.gcd(&y_on_gcd), U1024::ONE);
+    }
+
+    #[test]
+    fn gcd_vartime() {
+        let min_77 = I128::from(-77).to_odd().unwrap();
+        assert_eq!(min_77.gcd_vartime(&I128::from(21)), U128::from(7u32));
+        assert_eq!(min_77.gcd_vartime(&I128::from(-21)), U128::from(7u32));
+        let pos_77 = I128::from(77).to_odd().unwrap();
+        assert_eq!(pos_77.gcd_vartime(&I128::from(21)), U128::from(7u32));
+        assert_eq!(pos_77.gcd_vartime(&I128::from(-21)), U128::from(7u32));
+    }
+}