wip

math/src/modulus/impl_u64/montgomery.rs

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+
+use crate::modulus::ReduceOnce;
+use crate::modulus::montgomery::{MontgomeryPrecomp, Montgomery};
+use crate::modulus::barrett::BarrettPrecomp;
+use crate::modulus::{REDUCEMOD, NONE, ONCE, TWICE, FOURTIMES, BARRETT, BARRETTLAZY};
+extern crate test;
+
+/// MontgomeryPrecomp is a set of methods implemented for MontgomeryPrecomp<u64>
+/// enabling Montgomery arithmetic over u64 values.
+impl MontgomeryPrecomp<u64>{
+
+    /// Returns an new instance of MontgomeryPrecomp<u64>.
+    /// This method will fail if gcd(q, 2^64) != 1.
+    #[inline(always)]
+    pub fn new(q: u64) -> MontgomeryPrecomp<u64>{
+        assert!(q & 1 != 0, "Invalid argument: gcd(q={}, radix=2^64) != 1", q);
+        let mut q_inv: u64 = 1;
+        let mut q_pow = q;
+        for _i in 0..63{
+            q_inv = q_inv.wrapping_mul(q_pow);
+            q_pow = q_pow.wrapping_mul(q_pow);
+        }
+        let mut precomp = Self{ 
+            q: q,
+            two_q: q<<1,
+            four_q: q<<2,
+            barrett: BarrettPrecomp::new(q), 
+            q_inv: q_inv,
+            one: 0,
+            minus_one:0,
+        };
+
+        precomp.one = precomp.prepare::<ONCE>(1);
+        precomp.minus_one = q-precomp.one;
+
+        precomp
+    }
+
+    /// Returns 2^64 mod q as a Montgomery<u64>.
+    #[inline(always)]
+    pub fn one(&self) -> Montgomery<u64>{
+        self.one
+    }
+
+    /// Returns (q-1) * 2^64 mod q as a Montgomery<u64>.
+    #[inline(always)]
+    pub fn minus_one(&self) -> Montgomery<u64>{
+        self.minus_one
+    }
+
+    /// Applies a modular reduction on x based on REDUCE:
+    /// - LAZY: no modular reduction.
+    /// - ONCE: subtracts q if x >= q.
+    /// - FULL: maps x to x mod q using Barrett reduction.
+    #[inline(always)]
+    pub fn reduce<const REDUCE:REDUCEMOD>(&self, x: u64) -> u64{
+        let mut r: u64 = x;
+        self.reduce_assign::<REDUCE>(&mut r);
+        r
+    }
+
+    /// Applies a modular reduction on x based on REDUCE:
+    /// - LAZY: no modular reduction.
+    /// - ONCE: subtracts q if x >= q.
+    /// - FULL: maps x to x mod q using Barrett reduction.
+    #[inline(always)]
+    pub fn reduce_assign<const REDUCE:REDUCEMOD>(&self, x: &mut u64){
+        match REDUCE {
+            NONE =>{},
+            ONCE =>{x.reduce_once_assign(self.q)},
+            TWICE=>{x.reduce_once_assign(self.two_q)},
+            FOURTIMES =>{x.reduce_once_assign(self.four_q)},
+            BARRETT =>{self.barrett.reduce_assign(x)},
+            BARRETTLAZY =>{self.barrett.reduce_lazy_assign(x)},
+            _ => unreachable!("invalid REDUCE argument")
+        }
+    }
+
+    /// Returns lhs * 2^64 mod q as a Montgomery<u64>.
+    #[inline(always)]
+    pub fn prepare<const REDUCE:REDUCEMOD>(&self, lhs: u64) -> Montgomery<u64>{
+        let mut rhs: u64 = 0;
+        self.prepare_assign::<REDUCE>(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * 2^64 mod q to rhs.
+    #[inline(always)]
+    pub fn prepare_assign<const REDUCE:REDUCEMOD>(&self, lhs: u64, rhs: &mut Montgomery<u64>){
+        let (_, mhi) = lhs.widening_mul(*self.barrett.value_lo());
+        *rhs = (lhs.wrapping_mul(*self.barrett.value_hi()).wrapping_add(mhi)).wrapping_mul(self.q).wrapping_neg();
+        self.reduce_assign::<REDUCE>(rhs); 
+    }
+
+    /// Returns lhs * (2^64)^-1 mod q as a u64.
+    #[inline(always)]
+    pub fn unprepare<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>) -> u64{
+        let mut rhs = 0u64;
+        self.unprepare_assign::<REDUCE>(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * (2^64)^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn unprepare_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        let (_, r) = self.q.widening_mul(lhs.wrapping_mul(self.q_inv));
+        *rhs = self.reduce::<REDUCE>(self.q.wrapping_sub(r));        
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q.
+    #[inline(always)]
+    pub fn mul_external<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: u64) -> u64{
+        let mut r: u64 = rhs;
+        self.mul_external_assign::<REDUCE>(lhs, &mut r);
+        r
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn mul_external_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        let (mlo, mhi) = lhs.widening_mul(*rhs);
+        let (_, hhi) = self.q.widening_mul(mlo.wrapping_mul(self.q_inv));
+        *rhs = self.reduce::<REDUCE>(mhi.wrapping_sub(hhi).wrapping_add(self.q));
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn mul_internal<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
+        self.mul_external::<REDUCE>(lhs, rhs)
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn mul_internal_assign<const REDUCE:REDUCEMOD>(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        self.mul_external_assign::<REDUCE>(lhs, rhs);
+    }
+
+    #[inline(always)]
+    pub fn add_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
+        self.barrett.reduce(rhs + lhs)
+    }
+
+    /// Assigns lhs + rhs to rhs.
+    #[inline(always)]
+    pub fn add_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        *rhs += lhs
+    }
+
+    /// Assigns lhs + rhs - q if (lhs + rhs) >= q to rhs.
+    #[inline(always)]
+    pub fn add_internal_reduce_once_assign<const LAZY:bool>(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        self.add_internal_lazy_assign(lhs, rhs);
+        rhs.reduce_once_assign(self.q);
+    }
+
+    /// Returns lhs mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn reduce_lazy_assign(&self, lhs: &mut u64){
+        self.barrett.reduce_lazy_assign(lhs)
+    }
+
+    /// Returns (x^exponent) * 2^64 mod q.
+    #[inline(always)]
+    pub fn pow(&self, x: Montgomery<u64>, exponent:u64) -> Montgomery<u64>{
+        let mut y: Montgomery<u64> = self.one();
+        let mut x_mut: Montgomery<u64> = x;
+        let mut i: u64 = exponent;
+        while i > 0{
+            if i & 1 == 1{
+                self.mul_internal_assign::<ONCE>(x_mut, &mut y);
+            }
+            self.mul_internal_assign::<ONCE>(x_mut, &mut x_mut);
+            i >>= 1;
+        }
+
+        y.reduce_once_assign(self.q);
+        y
+    }
+}
+
+#[cfg(test)]
+mod tests {
+    use crate::modulus::montgomery;
+    use super::*;
+    use test::Bencher;
+
+    #[test]
+    fn test_mul_external() {
+        let q: u64 = 0x1fffffffffe00001;
+    	let m_precomp = montgomery::MontgomeryPrecomp::new(q);
+        let x: u64 = 0x5f876e514845cc8b;
+        let y: u64 = 0xad726f98f24a761a;
+        let y_mont = m_precomp.prepare::<ONCE>(y);
+    	assert!(m_precomp.mul_external::<ONCE>(y_mont, x) == (x as u128 * y as u128 % q as u128) as u64);
+    }
+
+    #[bench]
+    fn bench_mul_external(b: &mut Bencher){
+        let q: u64 = 0x1fffffffffe00001;
+    	let m_precomp = montgomery::MontgomeryPrecomp::new(q);
+        let mut x: u64 = 0x5f876e514845cc8b;
+        let y: u64 = 0xad726f98f24a761a;
+        let y_mont = m_precomp.prepare::<ONCE>(y);
+        b.iter(|| m_precomp.mul_external_assign::<ONCE>(y_mont, &mut x));
+    }
+}