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factor::numeric::Montgomery: Fix overflow bug

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This commit is contained in:
nicoo 2020-06-15 19:00:31 +02:00
parent 2238065c9d
commit cb6051c580
1 changed files with 18 additions and 9 deletions
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21
src/uu/factor/src/numeric.rs
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@ -71,17 +71,26 @@ pub(crate) struct Montgomery {
impl Montgomery {
/// computes x/R mod n efficiently
fn reduce(&self, x: u64) -> u64 {
fn reduce(&self, x: u128) -> u64 {
debug_assert!(x < (self.n as u128) << 64);
// TODO: optimiiiiiiise
let Montgomery { a, n } = self;
let t = x.wrapping_mul(*a);
let nt = (*n as u128) * (t as u128);
let y = ((x as u128 + nt) >> 64) as u64;
let m = (x as u64).wrapping_mul(*a);
let nm = (*n as u128) * (m as u128);
let (xnm, overflow) = (x as u128).overflowing_add(nm); // x + n*m
debug_assert_eq!(xnm % (1 << 64), 0);
if !overflow {
let y = (xnm >> 64) as u64 + overflow as u64; // (x + n*m) / R
if y >= *n {
y - n
} else {
y
}
} else {
// y = (2¹²⁸ + xnm)/2⁶⁴ - n = xnm/2⁶⁴ + (2⁶⁴ - n)
(xnm >> 64) as u64 + n.wrapping_neg()
}
}
}
@ -109,7 +118,7 @@ impl Arithmetic for Montgomery {
}
fn to_u64(&self, n: Self::I) -> u64 {
self.reduce(n)
self.reduce(n as u128)
}
fn add(&self, a: Self::I, b: Self::I) -> Self::I {
@ -133,7 +142,7 @@ impl Arithmetic for Montgomery {
}
fn mul(&self, a: Self::I, b: Self::I) -> Self::I {
let r = self.reduce(a.wrapping_mul(b));
let r = self.reduce((a as u128) * (b as u128));
// Check that r (reduced back to the usual representation) equals
// a*b % n