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//! Limb comparisons
use super::HI_BIT;
use crate::{CtChoice, Limb};
use core::cmp::Ordering;
use subtle::{Choice, ConstantTimeEq, ConstantTimeGreater, ConstantTimeLess};
impl Limb {
/// Is this limb an odd number?
#[inline]
pub fn is_odd(&self) -> Choice {
Choice::from(self.0 as u8 & 1)
}
/// Perform a comparison of the inner value in variable-time.
///
/// Note that the [`PartialOrd`] and [`Ord`] impls wrap constant-time
/// comparisons using the `subtle` crate.
pub fn cmp_vartime(&self, other: &Self) -> Ordering {
self.0.cmp(&other.0)
}
/// Performs an equality check in variable-time.
pub const fn eq_vartime(&self, other: &Self) -> bool {
self.0 == other.0
}
/// Return `b` if `c` is truthy, otherwise return `a`.
#[inline]
pub(crate) const fn ct_select(a: Self, b: Self, c: CtChoice) -> Self {
Self(c.select(a.0, b.0))
}
/// Returns the truthy value if `self != 0` and the falsy value otherwise.
#[inline]
pub(crate) const fn ct_is_nonzero(&self) -> CtChoice {
let inner = self.0;
CtChoice::from_lsb((inner | inner.wrapping_neg()) >> HI_BIT)
}
/// Returns the truthy value if `lhs == rhs` and the falsy value otherwise.
#[inline]
pub(crate) const fn ct_eq(lhs: Self, rhs: Self) -> CtChoice {
let x = lhs.0;
let y = rhs.0;
// x ^ y == 0 if and only if x == y
Self(x ^ y).ct_is_nonzero().not()
}
/// Returns the truthy value if `lhs < rhs` and the falsy value otherwise.
#[inline]
pub(crate) const fn ct_lt(lhs: Self, rhs: Self) -> CtChoice {
let x = lhs.0;
let y = rhs.0;
let bit = (((!x) & y) | (((!x) | y) & (x.wrapping_sub(y)))) >> (Limb::BITS - 1);
CtChoice::from_lsb(bit)
}
/// Returns the truthy value if `lhs <= rhs` and the falsy value otherwise.
#[inline]
pub(crate) const fn ct_le(lhs: Self, rhs: Self) -> CtChoice {
let x = lhs.0;
let y = rhs.0;
let bit = (((!x) | y) & ((x ^ y) | !(y.wrapping_sub(x)))) >> (Limb::BITS - 1);
CtChoice::from_lsb(bit)
}
}
impl ConstantTimeEq for Limb {
#[inline]
fn ct_eq(&self, other: &Self) -> Choice {
self.0.ct_eq(&other.0)
}
}
impl ConstantTimeGreater for Limb {
#[inline]
fn ct_gt(&self, other: &Self) -> Choice {
self.0.ct_gt(&other.0)
}
}
impl ConstantTimeLess for Limb {
#[inline]
fn ct_lt(&self, other: &Self) -> Choice {
self.0.ct_lt(&other.0)
}
}
impl Eq for Limb {}
impl Ord for Limb {
fn cmp(&self, other: &Self) -> Ordering {
let mut n = 0i8;
n -= self.ct_lt(other).unwrap_u8() as i8;
n += self.ct_gt(other).unwrap_u8() as i8;
match n {
-1 => Ordering::Less,
1 => Ordering::Greater,
_ => {
debug_assert_eq!(n, 0);
debug_assert!(bool::from(self.ct_eq(other)));
Ordering::Equal
}
}
}
}
impl PartialOrd for Limb {
#[inline]
fn partial_cmp(&self, other: &Self) -> Option<Ordering> {
Some(self.cmp(other))
}
}
impl PartialEq for Limb {
#[inline]
fn eq(&self, other: &Self) -> bool {
self.ct_eq(other).into()
}
}
#[cfg(test)]
mod tests {
use crate::{Limb, Zero};
use core::cmp::Ordering;
use subtle::{ConstantTimeEq, ConstantTimeGreater, ConstantTimeLess};
#[test]
fn is_zero() {
assert!(bool::from(Limb::ZERO.is_zero()));
assert!(!bool::from(Limb::ONE.is_zero()));
assert!(!bool::from(Limb::MAX.is_zero()));
}
#[test]
fn is_odd() {
assert!(!bool::from(Limb::ZERO.is_odd()));
assert!(bool::from(Limb::ONE.is_odd()));
assert!(bool::from(Limb::MAX.is_odd()));
}
#[test]
fn ct_eq() {
let a = Limb::ZERO;
let b = Limb::MAX;
assert!(bool::from(a.ct_eq(&a)));
assert!(!bool::from(a.ct_eq(&b)));
assert!(!bool::from(b.ct_eq(&a)));
assert!(bool::from(b.ct_eq(&b)));
}
#[test]
fn ct_gt() {
let a = Limb::ZERO;
let b = Limb::ONE;
let c = Limb::MAX;
assert!(bool::from(b.ct_gt(&a)));
assert!(bool::from(c.ct_gt(&a)));
assert!(bool::from(c.ct_gt(&b)));
assert!(!bool::from(a.ct_gt(&a)));
assert!(!bool::from(b.ct_gt(&b)));
assert!(!bool::from(c.ct_gt(&c)));
assert!(!bool::from(a.ct_gt(&b)));
assert!(!bool::from(a.ct_gt(&c)));
assert!(!bool::from(b.ct_gt(&c)));
}
#[test]
fn ct_lt() {
let a = Limb::ZERO;
let b = Limb::ONE;
let c = Limb::MAX;
assert!(bool::from(a.ct_lt(&b)));
assert!(bool::from(a.ct_lt(&c)));
assert!(bool::from(b.ct_lt(&c)));
assert!(!bool::from(a.ct_lt(&a)));
assert!(!bool::from(b.ct_lt(&b)));
assert!(!bool::from(c.ct_lt(&c)));
assert!(!bool::from(b.ct_lt(&a)));
assert!(!bool::from(c.ct_lt(&a)));
assert!(!bool::from(c.ct_lt(&b)));
}
#[test]
fn cmp() {
assert_eq!(Limb::ZERO.cmp(&Limb::ONE), Ordering::Less);
assert_eq!(Limb::ONE.cmp(&Limb::ONE), Ordering::Equal);
assert_eq!(Limb::MAX.cmp(&Limb::ONE), Ordering::Greater);
}
}
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