refactoring for specific implementations

src/modulus/impl_u64/montgomery.rs

@@ -0,0 +1,267 @@
+
+use crate::modulus::ReduceOnce;
+use crate::modulus::montgomery::{MontgomeryPrecomp, Montgomery};
+use crate::modulus::barrett::{BarrettPrecomp};
+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, 
+            barrett: BarrettPrecomp::new(q), 
+            q_inv: q_inv,
+            one: Montgomery(0),
+            minus_one: Montgomery(0),
+        };
+
+        precomp.one = precomp.prepare(1);
+        precomp.minus_one = Montgomery(q-precomp.one.value());
+
+        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
+    }
+
+    /// Returns lhs * 2^64 mod q as a Montgomery<u64>.
+    #[inline(always)]
+    pub fn prepare(&self, lhs: u64) -> Montgomery<u64>{
+        let mut rhs = Montgomery(0);
+        self.prepare_assign(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * 2^64 mod q to rhs.
+    #[inline(always)]
+    pub fn prepare_assign(&self, lhs: u64, rhs: &mut Montgomery<u64>){
+        self.prepare_lazy_assign(lhs, rhs);
+        rhs.value_mut().reduce_once_assign(self.q);
+    }
+
+    /// Returns lhs * 2^64 mod q in range [0, 2q-1] as a Montgomery<u64>.
+    #[inline(always)]
+    pub fn prepare_lazy(&self, lhs: u64) -> Montgomery<u64>{
+        let mut rhs = Montgomery(0);
+        self.prepare_lazy_assign(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * 2^64 mod q in range [0, 2q-1] to rhs.
+    #[inline(always)]
+    pub fn prepare_lazy_assign(&self, lhs: u64, rhs: &mut Montgomery<u64>){
+        let (_, mhi) = lhs.widening_mul(*self.barrett.value_lo());
+        *rhs = Montgomery((lhs.wrapping_mul(*self.barrett.value_hi()).wrapping_add(mhi)).wrapping_mul(self.q).wrapping_neg());
+    }
+
+    /// Returns lhs * (2^64)^-1 mod q as a u64.
+    #[inline(always)]
+    pub fn unprepare(&self, lhs: Montgomery<u64>) -> u64{
+        let mut rhs = 0u64;
+        self.unprepare_assign(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * (2^64)^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn unprepare_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        self.unprepare_lazy_assign(lhs, rhs);
+        rhs.reduce_once_assign(self.q);
+        
+    }
+
+    /// Returns lhs * (2^64)^-1 mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn unprepare_lazy(&self, lhs: Montgomery<u64>) -> u64{
+        let mut rhs = 0u64;
+        self.unprepare_lazy_assign(lhs, &mut rhs);
+        rhs
+    }
+
+    /// Assigns lhs * (2^64)^-1 mod q in range [0, 2q-1] to rhs.
+    #[inline(always)]
+    pub fn unprepare_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        let (_, r) = self.q.widening_mul(lhs.value().wrapping_mul(self.q_inv));
+        *rhs = self.q - r
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q.
+    #[inline(always)]
+    pub fn mul_external(&self, lhs: Montgomery<u64>, rhs: u64) -> u64{
+        let mut r = self.mul_external_lazy(lhs, rhs);
+        r.reduce_once_assign(self.q);
+        r
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn mul_external_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        self.mul_external_lazy_assign(lhs, rhs);
+        rhs.reduce_once_assign(self.q);
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn mul_external_lazy(&self, lhs: Montgomery<u64>, rhs: u64) -> u64{
+        let mut result: u64 = rhs;
+        self.mul_external_lazy_assign(lhs, &mut result);
+        result
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1] to rhs.
+    #[inline(always)]
+    pub fn mul_external_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut u64){
+        let (mlo, mhi) = lhs.value().widening_mul(*rhs);
+        let (_, hhi) = self.q.widening_mul(mlo.wrapping_mul(self.q_inv));
+        *rhs = mhi.wrapping_add(self.q - hhi)
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn mul_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
+        Montgomery(self.mul_external(lhs, *rhs.value()))
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q to rhs.
+    #[inline(always)]
+    pub fn mul_internal_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        self.mul_external_assign(lhs, rhs.value_mut());
+    }
+
+    /// Returns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn mul_internal_lazy(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
+        Montgomery(self.mul_external_lazy(lhs, *rhs.value()))
+    }
+
+    /// Assigns lhs * rhs * (2^{64})^-1 mod q in range [0, 2q-1] to rhs.
+    #[inline(always)]
+    pub fn mul_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        self.mul_external_lazy_assign(lhs, rhs.value_mut());
+    }
+
+    #[inline(always)]
+    pub fn add_internal(&self, lhs: Montgomery<u64>, rhs: Montgomery<u64>) -> Montgomery<u64>{
+        Montgomery(self.barrett.reduce(rhs.value() + lhs.value()))
+    }
+
+    /// Assigns lhs + rhs to rhs.
+    #[inline(always)]
+    pub fn add_internal_lazy_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        *rhs.value_mut() += lhs.value()
+    }
+
+    /// Assigns lhs + rhs - q if (lhs + rhs) >= q to rhs.
+    #[inline(always)]
+    pub fn add_internal_reduce_once_assign(&self, lhs: Montgomery<u64>, rhs: &mut Montgomery<u64>){
+        self.add_internal_lazy_assign(lhs, rhs);
+        rhs.value_mut().reduce_once_assign(self.q);
+    }
+
+    #[inline(always)]
+    pub fn reduce(&self, lhs: u64) -> u64{
+        self.barrett.reduce(lhs)
+    }
+
+    /// Returns lhs mod q in range [0, 2q-1].
+    #[inline(always)]
+    pub fn reduce_lazy(&self, lhs: u64) -> u64{
+        self.barrett.reduce_lazy(lhs)
+    }
+
+    #[inline(always)]
+    pub fn reduce_assign(&self, lhs: &mut u64){
+        self.barrett.reduce_assign(lhs)
+    }
+
+    /// 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(x_mut, &mut y);
+            }
+            self.mul_internal_assign(x_mut, &mut x_mut);
+            i >>= 1;
+        }
+
+        y.value_mut().reduce_once_assign(self.q);
+        y
+    }
+}
+
+/// Returns x^exponent mod q.
+/// This function internally instantiate a new MontgomeryPrecomp<u64>
+/// To be used when called only a few times and if there 
+/// is no Prime instantiated with q.
+fn pow(x:u64, exponent:u64, q:u64) -> u64{
+    let montgomery: MontgomeryPrecomp<u64> = MontgomeryPrecomp::<u64>::new(q);
+    let mut y_mont: Montgomery<u64> = montgomery.one();
+    let mut x_mont: Montgomery<u64> = montgomery.prepare(x);
+    while exponent > 0{
+        if exponent & 1 == 1{
+            montgomery.mul_internal_assign(x_mont, &mut y_mont);
+        }
+
+        montgomery.mul_internal_assign(x_mont, &mut x_mont);
+    }
+    
+    montgomery.unprepare(y_mont)
+}
+
+#[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(y);
+    	assert!(m_precomp.mul_external(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(y);
+        b.iter(|| m_precomp.mul_external_assign(y_mont, &mut x));
+    }
+}