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|
//! [`Uint`] square root operations.
use super::Uint;
use crate::{Limb, Word};
use subtle::{ConstantTimeEq, CtOption};
impl<const LIMBS: usize> Uint<LIMBS> {
/// See [`Self::sqrt_vartime`].
#[deprecated(
since = "0.5.3",
note = "This functionality will be moved to `sqrt_vartime` in a future release."
)]
pub const fn sqrt(&self) -> Self {
self.sqrt_vartime()
}
/// Computes √(`self`)
/// Uses Brent & Zimmermann, Modern Computer Arithmetic, v0.5.9, Algorithm 1.13
///
/// Callers can check if `self` is a square by squaring the result
pub const fn sqrt_vartime(&self) -> Self {
let max_bits = (self.bits_vartime() + 1) >> 1;
let cap = Self::ONE.shl_vartime(max_bits);
let mut guess = cap; // ≥ √(`self`)
let mut xn = {
let q = self.wrapping_div(&guess);
let t = guess.wrapping_add(&q);
t.shr_vartime(1)
};
// If guess increased, the initial guess was low.
// Repeat until reverse course.
while Uint::ct_lt(&guess, &xn).is_true_vartime() {
// Sometimes an increase is too far, especially with large
// powers, and then takes a long time to walk back. The upper
// bound is based on bit size, so saturate on that.
let le = Limb::ct_le(Limb(xn.bits_vartime() as Word), Limb(max_bits as Word));
guess = Self::ct_select(&cap, &xn, le);
xn = {
let q = self.wrapping_div(&guess);
let t = guess.wrapping_add(&q);
t.shr_vartime(1)
};
}
// Repeat while guess decreases.
while Uint::ct_gt(&guess, &xn).is_true_vartime() && xn.ct_is_nonzero().is_true_vartime() {
guess = xn;
xn = {
let q = self.wrapping_div(&guess);
let t = guess.wrapping_add(&q);
t.shr_vartime(1)
};
}
Self::ct_select(&Self::ZERO, &guess, self.ct_is_nonzero())
}
/// See [`Self::wrapping_sqrt_vartime`].
#[deprecated(
since = "0.5.3",
note = "This functionality will be moved to `wrapping_sqrt_vartime` in a future release."
)]
pub const fn wrapping_sqrt(&self) -> Self {
self.wrapping_sqrt_vartime()
}
/// Wrapped sqrt is just normal √(`self`)
/// There’s no way wrapping could ever happen.
/// This function exists, so that all operations are accounted for in the wrapping operations.
pub const fn wrapping_sqrt_vartime(&self) -> Self {
self.sqrt_vartime()
}
/// See [`Self::checked_sqrt_vartime`].
#[deprecated(
since = "0.5.3",
note = "This functionality will be moved to `checked_sqrt_vartime` in a future release."
)]
pub fn checked_sqrt(&self) -> CtOption<Self> {
self.checked_sqrt_vartime()
}
/// Perform checked sqrt, returning a [`CtOption`] which `is_some`
/// only if the √(`self`)² == self
pub fn checked_sqrt_vartime(&self) -> CtOption<Self> {
let r = self.sqrt_vartime();
let s = r.wrapping_mul(&r);
CtOption::new(r, ConstantTimeEq::ct_eq(self, &s))
}
}
#[cfg(test)]
mod tests {
use crate::{Limb, U256};
#[cfg(feature = "rand")]
use {
crate::{CheckedMul, Random, U512},
rand_chacha::ChaChaRng,
rand_core::{RngCore, SeedableRng},
};
#[test]
fn edge() {
assert_eq!(U256::ZERO.sqrt_vartime(), U256::ZERO);
assert_eq!(U256::ONE.sqrt_vartime(), U256::ONE);
let mut half = U256::ZERO;
for i in 0..half.limbs.len() / 2 {
half.limbs[i] = Limb::MAX;
}
assert_eq!(U256::MAX.sqrt_vartime(), half,);
}
#[test]
fn simple() {
let tests = [
(4u8, 2u8),
(9, 3),
(16, 4),
(25, 5),
(36, 6),
(49, 7),
(64, 8),
(81, 9),
(100, 10),
(121, 11),
(144, 12),
(169, 13),
];
for (a, e) in &tests {
let l = U256::from(*a);
let r = U256::from(*e);
assert_eq!(l.sqrt_vartime(), r);
assert_eq!(l.checked_sqrt_vartime().is_some().unwrap_u8(), 1u8);
}
}
#[test]
fn nonsquares() {
assert_eq!(U256::from(2u8).sqrt_vartime(), U256::from(1u8));
assert_eq!(
U256::from(2u8).checked_sqrt_vartime().is_some().unwrap_u8(),
0
);
assert_eq!(U256::from(3u8).sqrt_vartime(), U256::from(1u8));
assert_eq!(
U256::from(3u8).checked_sqrt_vartime().is_some().unwrap_u8(),
0
);
assert_eq!(U256::from(5u8).sqrt_vartime(), U256::from(2u8));
assert_eq!(U256::from(6u8).sqrt_vartime(), U256::from(2u8));
assert_eq!(U256::from(7u8).sqrt_vartime(), U256::from(2u8));
assert_eq!(U256::from(8u8).sqrt_vartime(), U256::from(2u8));
assert_eq!(U256::from(10u8).sqrt_vartime(), U256::from(3u8));
}
#[cfg(feature = "rand")]
#[test]
fn fuzz() {
let mut rng = ChaChaRng::from_seed([7u8; 32]);
for _ in 0..50 {
let t = rng.next_u32() as u64;
let s = U256::from(t);
let s2 = s.checked_mul(&s).unwrap();
assert_eq!(s2.sqrt_vartime(), s);
assert_eq!(s2.checked_sqrt_vartime().is_some().unwrap_u8(), 1);
}
for _ in 0..50 {
let s = U256::random(&mut rng);
let mut s2 = U512::ZERO;
s2.limbs[..s.limbs.len()].copy_from_slice(&s.limbs);
assert_eq!(s.square().sqrt_vartime(), s2);
}
}
}
|
