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|
//! [`Uint`] subtraction modulus operations.
use crate::{Limb, SubMod, Uint};
impl<const LIMBS: usize> Uint<LIMBS> {
/// Computes `self - rhs mod p` in constant time.
///
/// Assumes `self - rhs` as unbounded signed integer is in `[-p, p)`.
pub const fn sub_mod(&self, rhs: &Uint<LIMBS>, p: &Uint<LIMBS>) -> Uint<LIMBS> {
let (mut out, borrow) = self.sbb(rhs, Limb::ZERO);
// If underflow occurred on the final limb, borrow = 0xfff...fff, otherwise
// borrow = 0x000...000. Thus, we use it as a mask to conditionally add the modulus.
let mut carry = Limb::ZERO;
let mut i = 0;
while i < LIMBS {
let (l, c) = out.limbs[i].adc(p.limbs[i].bitand(borrow), carry);
out.limbs[i] = l;
carry = c;
i += 1;
}
out
}
/// Computes `self - rhs mod p` in constant time for the special modulus
/// `p = MAX+1-c` where `c` is small enough to fit in a single [`Limb`].
///
/// Assumes `self - rhs` as unbounded signed integer is in `[-p, p)`.
pub const fn sub_mod_special(&self, rhs: &Self, c: Limb) -> Self {
let (out, borrow) = self.sbb(rhs, Limb::ZERO);
// If underflow occurred, then we need to subtract `c` to account for
// the underflow. This cannot underflow due to the assumption
// `self - rhs >= -p`.
let l = borrow.0 & c.0;
let (out, _) = out.sbb(&Uint::from_word(l), Limb::ZERO);
out
}
}
impl<const LIMBS: usize> SubMod for Uint<LIMBS> {
type Output = Self;
fn sub_mod(&self, rhs: &Self, p: &Self) -> Self {
debug_assert!(self < p);
debug_assert!(rhs < p);
self.sub_mod(rhs, p)
}
}
#[cfg(all(test, feature = "rand"))]
mod tests {
use crate::{Limb, NonZero, Random, RandomMod, Uint};
use rand_core::SeedableRng;
macro_rules! test_sub_mod {
($size:expr, $test_name:ident) => {
#[test]
fn $test_name() {
let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
let moduli = [
NonZero::<Uint<$size>>::random(&mut rng),
NonZero::<Uint<$size>>::random(&mut rng),
];
for p in &moduli {
let base_cases = [
(1u64, 0u64, 1u64.into()),
(0, 1, p.wrapping_sub(&1u64.into())),
(0, 0, 0u64.into()),
];
for (a, b, c) in &base_cases {
let a: Uint<$size> = (*a).into();
let b: Uint<$size> = (*b).into();
let x = a.sub_mod(&b, p);
assert_eq!(*c, x, "{} - {} mod {} = {} != {}", a, b, p, x, c);
}
if $size > 1 {
for _i in 0..100 {
let a: Uint<$size> = Limb::random(&mut rng).into();
let b: Uint<$size> = Limb::random(&mut rng).into();
let (a, b) = if a < b { (b, a) } else { (a, b) };
let c = a.sub_mod(&b, p);
assert!(c < **p, "not reduced");
assert_eq!(c, a.wrapping_sub(&b), "result incorrect");
}
}
for _i in 0..100 {
let a = Uint::<$size>::random_mod(&mut rng, p);
let b = Uint::<$size>::random_mod(&mut rng, p);
let c = a.sub_mod(&b, p);
assert!(c < **p, "not reduced: {} >= {} ", c, p);
let x = a.wrapping_sub(&b);
if a >= b && x < **p {
assert_eq!(c, x, "incorrect result");
}
}
}
}
};
}
macro_rules! test_sub_mod_special {
($size:expr, $test_name:ident) => {
#[test]
fn $test_name() {
let mut rng = rand_chacha::ChaCha8Rng::seed_from_u64(1);
let moduli = [
NonZero::<Limb>::random(&mut rng),
NonZero::<Limb>::random(&mut rng),
];
for special in &moduli {
let p = &NonZero::new(Uint::ZERO.wrapping_sub(&Uint::from_word(special.0)))
.unwrap();
let minus_one = p.wrapping_sub(&Uint::ONE);
let base_cases = [
(Uint::ZERO, Uint::ZERO, Uint::ZERO),
(Uint::ONE, Uint::ZERO, Uint::ONE),
(Uint::ZERO, Uint::ONE, minus_one),
(minus_one, minus_one, Uint::ZERO),
(Uint::ZERO, minus_one, Uint::ONE),
];
for (a, b, c) in &base_cases {
let x = a.sub_mod_special(&b, *special.as_ref());
assert_eq!(*c, x, "{} - {} mod {} = {} != {}", a, b, p, x, c);
}
for _i in 0..100 {
let a = Uint::<$size>::random_mod(&mut rng, p);
let b = Uint::<$size>::random_mod(&mut rng, p);
let c = a.sub_mod_special(&b, *special.as_ref());
assert!(c < **p, "not reduced: {} >= {} ", c, p);
let expected = a.sub_mod(&b, p);
assert_eq!(c, expected, "incorrect result");
}
}
}
};
}
// Test requires 1-limb is capable of representing a 64-bit integer
#[cfg(target_pointer_width = "64")]
test_sub_mod!(1, sub1);
test_sub_mod!(2, sub2);
test_sub_mod!(3, sub3);
test_sub_mod!(4, sub4);
test_sub_mod!(5, sub5);
test_sub_mod!(6, sub6);
test_sub_mod!(7, sub7);
test_sub_mod!(8, sub8);
test_sub_mod!(9, sub9);
test_sub_mod!(10, sub10);
test_sub_mod!(11, sub11);
test_sub_mod!(12, sub12);
test_sub_mod_special!(1, sub_mod_special_1);
test_sub_mod_special!(2, sub_mod_special_2);
test_sub_mod_special!(3, sub_mod_special_3);
test_sub_mod_special!(4, sub_mod_special_4);
test_sub_mod_special!(5, sub_mod_special_5);
test_sub_mod_special!(6, sub_mod_special_6);
test_sub_mod_special!(7, sub_mod_special_7);
test_sub_mod_special!(8, sub_mod_special_8);
test_sub_mod_special!(9, sub_mod_special_9);
test_sub_mod_special!(10, sub_mod_special_10);
test_sub_mod_special!(11, sub_mod_special_11);
test_sub_mod_special!(12, sub_mod_special_12);
}
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