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|
//! [`UInt`] division operations.
use super::UInt;
use crate::limb::Word;
use crate::{Integer, Limb, NonZero, Wrapping};
use core::ops::{Div, DivAssign, Rem, RemAssign};
use subtle::{Choice, CtOption};
impl<const LIMBS: usize> UInt<LIMBS> {
/// Computes `self` / `rhs`, returns the quotient (q), remainder (r)
/// and 1 for is_some or 0 for is_none. The results can be wrapped in [`CtOption`].
/// NOTE: Use only if you need to access const fn. Otherwise use `div_rem` because
/// the value for is_some needs to be checked before using `q` and `r`.
///
/// This is variable only with respect to `rhs`.
///
/// When used with a fixed `rhs`, this function is constant-time with respect
/// to `self`.
pub(crate) const fn ct_div_rem(&self, rhs: &Self) -> (Self, Self, u8) {
let mb = rhs.bits_vartime();
let mut bd = (LIMBS * Limb::BIT_SIZE) - mb;
let mut rem = *self;
let mut quo = Self::ZERO;
let mut c = rhs.shl_vartime(bd);
loop {
let (mut r, borrow) = rem.sbb(&c, Limb::ZERO);
rem = Self::ct_select(r, rem, borrow.0);
r = quo.bitor(&Self::ONE);
quo = Self::ct_select(r, quo, borrow.0);
if bd == 0 {
break;
}
bd -= 1;
c = c.shr_vartime(1);
quo = quo.shl_vartime(1);
}
let is_some = Limb(mb as Word).is_nonzero();
quo = Self::ct_select(Self::ZERO, quo, is_some);
(quo, rem, (is_some & 1) as u8)
}
/// Computes `self` % `rhs`, returns the remainder and
/// and 1 for is_some or 0 for is_none. The results can be wrapped in [`CtOption`].
/// NOTE: Use only if you need to access const fn. Otherwise use `reduce`
/// This is variable only with respect to `rhs`.
///
/// When used with a fixed `rhs`, this function is constant-time with respect
/// to `self`.
pub(crate) const fn ct_reduce(&self, rhs: &Self) -> (Self, u8) {
let mb = rhs.bits_vartime();
let mut bd = (LIMBS * Limb::BIT_SIZE) - mb;
let mut rem = *self;
let mut c = rhs.shl_vartime(bd);
loop {
let (r, borrow) = rem.sbb(&c, Limb::ZERO);
rem = Self::ct_select(r, rem, borrow.0);
if bd == 0 {
break;
}
bd -= 1;
c = c.shr_vartime(1);
}
let is_some = Limb(mb as Word).is_nonzero();
(rem, (is_some & 1) as u8)
}
/// Computes `self` % 2^k. Faster than reduce since its a power of 2.
/// Limited to 2^16-1 since UInt doesn't support higher.
pub const fn reduce2k(&self, k: usize) -> Self {
let highest = (LIMBS - 1) as u32;
let index = k as u32 / (Limb::BIT_SIZE as u32);
let res = Limb::ct_cmp(Limb::from_u32(index), Limb::from_u32(highest)) - 1;
let le = Limb::is_nonzero(Limb(res as Word));
let word = Limb::ct_select(Limb::from_u32(highest), Limb::from_u32(index), le).0 as usize;
let base = k % Limb::BIT_SIZE;
let mask = (1 << base) - 1;
let mut out = *self;
let outmask = Limb(out.limbs[word].0 & mask);
out.limbs[word] = Limb::ct_select(out.limbs[word], outmask, le);
let mut i = word + 1;
while i < LIMBS {
out.limbs[i] = Limb::ZERO;
i += 1;
}
out
}
/// Computes self / rhs, returns the quotient, remainder
/// if rhs != 0
pub fn div_rem(&self, rhs: &Self) -> CtOption<(Self, Self)> {
let (q, r, c) = self.ct_div_rem(rhs);
CtOption::new((q, r), Choice::from(c))
}
/// Computes self % rhs, returns the remainder
/// if rhs != 0
pub fn reduce(&self, rhs: &Self) -> CtOption<Self> {
let (r, c) = self.ct_reduce(rhs);
CtOption::new(r, Choice::from(c))
}
/// Wrapped division is just normal division i.e. `self` / `rhs`
/// 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_div(&self, rhs: &Self) -> Self {
let (q, _, c) = self.ct_div_rem(rhs);
assert!(c == 1, "divide by zero");
q
}
/// Perform checked division, returning a [`CtOption`] which `is_some`
/// only if the rhs != 0
pub fn checked_div(&self, rhs: &Self) -> CtOption<Self> {
let (q, _, c) = self.ct_div_rem(rhs);
CtOption::new(q, Choice::from(c))
}
/// Wrapped (modular) remainder calculation is just `self` % `rhs`.
/// 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_rem(&self, rhs: &Self) -> Self {
let (r, c) = self.ct_reduce(rhs);
assert!(c == 1, "modulo zero");
r
}
/// Perform checked reduction, returning a [`CtOption`] which `is_some`
/// only if the rhs != 0
pub fn checked_rem(&self, rhs: &Self) -> CtOption<Self> {
let (r, c) = self.ct_reduce(rhs);
CtOption::new(r, Choice::from(c))
}
}
impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
*self / *rhs
}
}
impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
self / *rhs
}
}
impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
*self / rhs
}
}
impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
let (q, _, _) = self.ct_div_rem(&rhs);
q
}
}
impl<const LIMBS: usize> DivAssign<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
fn div_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
let (q, _, _) = self.ct_div_rem(rhs);
*self = q
}
}
impl<const LIMBS: usize> DivAssign<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
fn div_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
*self /= &rhs;
}
}
impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
Wrapping(self.0.wrapping_div(rhs.as_ref()))
}
}
impl<const LIMBS: usize> Div<NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn div(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
*self / rhs
}
}
impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
*self / *rhs
}
}
impl<const LIMBS: usize> Div<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn div(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
self / *rhs
}
}
impl<const LIMBS: usize> DivAssign<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
fn div_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
*self = Wrapping(self.0.wrapping_div(rhs.as_ref()))
}
}
impl<const LIMBS: usize> DivAssign<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
fn div_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
*self /= &rhs;
}
}
impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
*self % *rhs
}
}
impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
self % *rhs
}
}
impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for &UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
*self % rhs
}
}
impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
type Output = UInt<LIMBS>;
fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
let (r, _) = self.ct_reduce(&rhs);
r
}
}
impl<const LIMBS: usize> RemAssign<&NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
fn rem_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
let (r, _) = self.ct_reduce(rhs);
*self = r
}
}
impl<const LIMBS: usize> RemAssign<NonZero<UInt<LIMBS>>> for UInt<LIMBS>
where
UInt<LIMBS>: Integer,
{
fn rem_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
*self %= &rhs;
}
}
impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
Wrapping(self.0.wrapping_rem(rhs.as_ref()))
}
}
impl<const LIMBS: usize> Rem<NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn rem(self, rhs: NonZero<UInt<LIMBS>>) -> Self::Output {
*self % rhs
}
}
impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for &Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
*self % *rhs
}
}
impl<const LIMBS: usize> Rem<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
type Output = Wrapping<UInt<LIMBS>>;
fn rem(self, rhs: &NonZero<UInt<LIMBS>>) -> Self::Output {
self % *rhs
}
}
impl<const LIMBS: usize> RemAssign<NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
fn rem_assign(&mut self, rhs: NonZero<UInt<LIMBS>>) {
*self %= &rhs;
}
}
impl<const LIMBS: usize> RemAssign<&NonZero<UInt<LIMBS>>> for Wrapping<UInt<LIMBS>> {
fn rem_assign(&mut self, rhs: &NonZero<UInt<LIMBS>>) {
*self = Wrapping(self.0.wrapping_rem(rhs.as_ref()))
}
}
#[cfg(test)]
mod tests {
use super::*;
use crate::{limb::HI_BIT, Limb, U256};
#[cfg(feature = "rand")]
use {
crate::{CheckedMul, Random},
rand_chacha::ChaChaRng,
rand_core::RngCore,
rand_core::SeedableRng,
};
#[test]
fn div_word() {
for (n, d, e, ee) in &[
(200u64, 2u64, 100u64, 0),
(100u64, 25u64, 4u64, 0),
(100u64, 10u64, 10u64, 0),
(1024u64, 8u64, 128u64, 0),
(27u64, 13u64, 2u64, 1u64),
(26u64, 13u64, 2u64, 0u64),
(14u64, 13u64, 1u64, 1u64),
(13u64, 13u64, 1u64, 0u64),
(12u64, 13u64, 0u64, 12u64),
(1u64, 13u64, 0u64, 1u64),
] {
let lhs = U256::from(*n);
let rhs = U256::from(*d);
let (q, r, is_some) = lhs.ct_div_rem(&rhs);
assert_eq!(is_some, 1);
assert_eq!(U256::from(*e), q);
assert_eq!(U256::from(*ee), r);
}
}
#[cfg(feature = "rand")]
#[test]
fn div() {
let mut rng = ChaChaRng::from_seed([7u8; 32]);
for _ in 0..25 {
let num = U256::random(&mut rng).shr_vartime(128);
let den = U256::random(&mut rng).shr_vartime(128);
let n = num.checked_mul(&den);
if n.is_some().unwrap_u8() == 1 {
let (q, _, is_some) = n.unwrap().ct_div_rem(&den);
assert_eq!(is_some, 1);
assert_eq!(q, num);
}
}
}
#[test]
fn div_max() {
let mut a = U256::ZERO;
let mut b = U256::ZERO;
b.limbs[b.limbs.len() - 1] = Limb(Word::MAX);
let q = a.wrapping_div(&b);
assert_eq!(q, UInt::ZERO);
a.limbs[a.limbs.len() - 1] = Limb(1 << (HI_BIT - 7));
b.limbs[b.limbs.len() - 1] = Limb(0x82 << (HI_BIT - 7));
let q = a.wrapping_div(&b);
assert_eq!(q, UInt::ZERO);
}
#[test]
fn div_zero() {
let (q, r, is_some) = U256::ONE.ct_div_rem(&U256::ZERO);
assert_eq!(is_some, 0);
assert_eq!(q, U256::ZERO);
assert_eq!(r, U256::ONE);
}
#[test]
fn div_one() {
let (q, r, is_some) = U256::from(10u8).ct_div_rem(&U256::ONE);
assert_eq!(is_some, 1);
assert_eq!(q, U256::from(10u8));
assert_eq!(r, U256::ZERO);
}
#[test]
fn reduce_one() {
let (r, is_some) = U256::from(10u8).ct_reduce(&U256::ONE);
assert_eq!(is_some, 1);
assert_eq!(r, U256::ZERO);
}
#[test]
fn reduce_zero() {
let u = U256::from(10u8);
let (r, is_some) = u.ct_reduce(&U256::ZERO);
assert_eq!(is_some, 0);
assert_eq!(r, u);
}
#[test]
fn reduce_tests() {
let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(2u8));
assert_eq!(is_some, 1);
assert_eq!(r, U256::ZERO);
let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(3u8));
assert_eq!(is_some, 1);
assert_eq!(r, U256::ONE);
let (r, is_some) = U256::from(10u8).ct_reduce(&U256::from(7u8));
assert_eq!(is_some, 1);
assert_eq!(r, U256::from(3u8));
}
#[test]
fn reduce_max() {
let mut a = U256::ZERO;
let mut b = U256::ZERO;
b.limbs[b.limbs.len() - 1] = Limb(Word::MAX);
let r = a.wrapping_rem(&b);
assert_eq!(r, UInt::ZERO);
a.limbs[a.limbs.len() - 1] = Limb(1 << (HI_BIT - 7));
b.limbs[b.limbs.len() - 1] = Limb(0x82 << (HI_BIT - 7));
let r = a.wrapping_rem(&b);
assert_eq!(r, a);
}
#[cfg(feature = "rand")]
#[test]
fn reduce2krand() {
let mut rng = ChaChaRng::from_seed([7u8; 32]);
for _ in 0..25 {
let num = U256::random(&mut rng);
let k = (rng.next_u32() % 256) as usize;
let den = U256::ONE.shl_vartime(k);
let a = num.reduce2k(k);
let e = num.wrapping_rem(&den);
assert_eq!(a, e);
}
}
}
|