Skip to content
New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Jump to bottom

mod optimisations #239

Merged
merged 1 commit into from
Jan 12, 2024
Merged

mod optimisations #239

Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
17 changes: 13 additions & 4 deletions src/math/src/mod_arithmetics.cairo
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -7,6 +7,7 @@ use integer::u512;
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - result of modular addition
#[inline(always)]
fn add_mod(a: u256, b: u256, modulo: u256) -> u256 {
let mod_non_zero: NonZero<u256> = integer::u256_try_as_non_zero(modulo).unwrap();
let low: u256 = a.low.into() + b.low.into();
Expand All @@ -25,10 +26,12 @@ fn add_mod(a: u256, b: u256, modulo: u256) -> u256 {
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - modular multiplicative inverse
#[inline(always)]
fn mult_inverse(b: u256, modulo: u256) -> u256 {
// From Fermat's little theorem, a ^ (p - 1) = 1 when p is prime and a != 0. Since a ^ (p - 1) = a · a ^ (p - 2) we have that
// a ^ (p - 2) is the multiplicative inverse of a modulo p.
pow_mod(b, modulo - 2, modulo)
match math::u256_guarantee_inv_mod_n(b, modulo.try_into().expect('inverse non zero')) {
Result::Ok((inv_a, _, _, _, _, _, _, _, _)) => inv_a.into(),
Result::Err(_) => 0
}
}

/// Function that return the modular additive inverse.
Expand All @@ -37,6 +40,7 @@ fn mult_inverse(b: u256, modulo: u256) -> u256 {
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - modular additive inverse
#[inline(always)]
fn add_inverse_mod(b: u256, modulo: u256) -> u256 {
modulo - b
}
Expand All @@ -48,6 +52,7 @@ fn add_inverse_mod(b: u256, modulo: u256) -> u256 {
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - result of modular substraction
#[inline(always)]
fn sub_mod(mut a: u256, mut b: u256, modulo: u256) -> u256 {
// reduce values
a = a % modulo;
Expand All @@ -65,6 +70,7 @@ fn sub_mod(mut a: u256, mut b: u256, modulo: u256) -> u256 {
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - result of modular multiplication
#[inline(always)]
fn mult_mod(a: u256, b: u256, modulo: u256) -> u256 {
let mult: u512 = integer::u256_wide_mul(a, b);
let mod_non_zero: NonZero<u256> = integer::u256_try_as_non_zero(modulo).unwrap();
Expand All @@ -79,8 +85,11 @@ fn mult_mod(a: u256, b: u256, modulo: u256) -> u256 {
/// * `modulo` - modulo.
/// # Returns
/// * `u256` - result of modular division
#[inline(always)]
fn div_mod(a: u256, b: u256, modulo: u256) -> u256 {
mult_mod(a, mult_inverse(b, modulo), modulo)
let modulo_nz = modulo.try_into().expect('0 modulo');
let inv = math::u256_inv_mod(b, modulo_nz).unwrap().into();
math::u256_mul_mod_n(a, inv, modulo_nz)
}

/// Function that performs modular exponentiation.
Expand Down