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

Dynamic Residue #2

Merged
merged 3 commits into from
Nov 23, 2023
Merged

Dynamic Residue #2

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
c102545
feat: dyn residue algebra
0xWOLAND Nov 22, 2023
37b065d
fix: dyn residue fft
0xWOLAND Nov 23, 2023
7bfc92f
bench: residue math
0xWOLAND Nov 23, 2023
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
40 changes: 20 additions & 20 deletions BENCHMARKS.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -27,31 +27,31 @@ Socket(s): 1

| | `NTT` |
|:------------|:-------------------------- |
| **`64`** | `202.26 us` (✅ **1.00x**) |
| **`128`** | `354.08 us` (✅ **1.00x**) |
| **`256`** | `665.54 us` (✅ **1.00x**) |
| **`512`** | `1.12 ms` (✅ **1.00x**) |
| **`1024`** | `2.00 ms` (✅ **1.00x**) |
| **`2048`** | `3.94 ms` (✅ **1.00x**) |
| **`4096`** | `7.69 ms` (✅ **1.00x**) |
| **`8192`** | `16.13 ms` (✅ **1.00x**) |
| **`16384`** | `34.01 ms` (✅ **1.00x**) |
| **`32768`** | `74.65 ms` (✅ **1.00x**) |
| **`64`** | `187.17 us` (✅ **1.00x**) |
| **`128`** | `231.50 us` (✅ **1.00x**) |
| **`256`** | `333.26 us` (✅ **1.00x**) |
| **`512`** | `623.88 us` (✅ **1.00x**) |
| **`1024`** | `951.62 us` (✅ **1.00x**) |
| **`2048`** | `1.48 ms` (✅ **1.00x**) |
| **`4096`** | `2.78 ms` (✅ **1.00x**) |
| **`8192`** | `5.48 ms` (✅ **1.00x**) |
| **`16384`** | `11.09 ms` (✅ **1.00x**) |
| **`32768`** | `23.08 ms` (✅ **1.00x**) |

### Polynomial Multiplication Benchmarks

| | `NTT-Based` | `Brute-Force` |
|:------------|:--------------------------|:---------------------------------- |
| **`64`** | `1.18 ms` (✅ **1.00x**) | `48.62 us` (🚀 **24.21x faster**) |
| **`128`** | `2.30 ms` (✅ **1.00x**) | `198.30 us` (🚀 **11.59x faster**) |
| **`256`** | `3.54 ms` (✅ **1.00x**) | `766.71 us` (🚀 **4.62x faster**) |
| **`512`** | `6.50 ms` (✅ **1.00x**) | `3.11 ms` (🚀 **2.09x faster**) |
| **`1024`** | `12.43 ms` (✅ **1.00x**) | `12.34 ms` (✅ **1.01x faster**) |
| **`2048`** | `24.68 ms` (✅ **1.00x**) | `49.90 ms` (❌ *2.02x slower*) |
| **`4096`** | `51.36 ms` (✅ **1.00x**) | `200.91 ms` (❌ *3.91x slower*) |
| **`8192`** | `106.21 ms` (✅ **1.00x**) | `803.87 ms` (❌ *7.57x slower*) |
| **`16384`** | `226.19 ms` (✅ **1.00x**) | `3.24 s` (❌ *14.31x slower*) |
| **`32768`** | `467.75 ms` (✅ **1.00x**) | `12.75 s` (❌ *27.25x slower*) |
| **`64`** | `818.69 us` (✅ **1.00x**) | `494.52 us` (✅ **1.66x faster**) |
| **`128`** | `1.12 ms` (✅ **1.00x**) | `1.93 ms` (❌ *1.72x slower*) |
| **`256`** | `1.74 ms` (✅ **1.00x**) | `7.78 ms` (❌ *4.48x slower*) |
| **`512`** | `2.69 ms` (✅ **1.00x**) | `30.35 ms` (❌ *11.30x slower*) |
| **`1024`** | `4.33 ms` (✅ **1.00x**) | `121.49 ms` (❌ *28.05x slower*) |
| **`2048`** | `7.47 ms` (✅ **1.00x**) | `493.59 ms` (❌ *66.07x slower*) |
| **`4096`** | `14.23 ms` (✅ **1.00x**) | `1.98 s` (❌ *139.11x slower*) |
| **`8192`** | `31.60 ms` (✅ **1.00x**) | `7.88 s` (❌ *249.28x slower*) |
| **`16384`** | `65.51 ms` (✅ **1.00x**) | `31.46 s` (❌ *480.32x slower*) |
| **`32768`** | `141.24 ms` (✅ **1.00x**) | `126.02 s` (❌ *892.30x slower*) |

---
Made with [criterion-table](https://github.com/nu11ptr/criterion-table)
Expand Down
3 changes: 3 additions & 0 deletions Cargo.toml
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -2,6 +2,9 @@
name = "fast-ntt"
version = "0.1.0"
edition = "2021"
license = "MIT OR Apache-2.0"
keywords = ["ntt", "number-theoretic-transform", "fft"]
categories = ["cryptography", "data-structures"]

# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html

Expand Down
84 changes: 23 additions & 61 deletions src/ntt.rs
View file
Open in desktop
Original file line number Diff line number Diff line change
@@ -1,6 +1,7 @@
use std::ops::Add;

use crate::{numbers::BigInt, prime::is_prime};
use crypto_bigint::Invert;
use itertools::Itertools;
use rayon::prelude::*;

Expand All @@ -10,44 +11,10 @@ pub struct Constants {
pub w: BigInt,
}

fn extended_gcd(a: BigInt, b: BigInt) -> BigInt {
let mut a = a;
let mut b = b;
let n = b;
let ZERO = BigInt::from(0);
let ONE = BigInt::from(1);

let mut q = ZERO;
let mut r = ONE;
let mut s1 = ONE;
let mut s2 = ZERO;
let mut s3 = ONE;
let mut t1 = ZERO;
let mut t2 = ONE;
let mut t3 = ZERO;

while r > ZERO {
q = b / a;
r = b - q * a;
s3 = s1 - q * s2;
t3 = t1 - q * t2;

if r > ZERO {
b = a;
a = r;
s1 = s2;
s2 = s3;
t1 = t2;
t2 = t3;
}
}
(t2 + n).rem(n)
}

fn prime_factors(a: BigInt) -> Vec<BigInt> {
let mut ans: Vec<BigInt> = Vec::new();
let mut x = BigInt::from(2);
while x <= a.sqrt() {
while x * x <= a {
if a.rem(x) == 0 {
ans.push(x);
}
Expand All @@ -57,11 +24,13 @@ fn prime_factors(a: BigInt) -> Vec<BigInt> {
}

fn is_primitive_root(a: BigInt, deg: BigInt, N: BigInt) -> bool {
a.mod_exp(deg, N) == 1
&& prime_factors(deg)
.iter()
.map(|&x| a.mod_exp(deg / x, N) != 1)
.all(|x| x)
let lhs = a.mod_exp(deg, N);
let lhs = lhs == 1;
let rhs = prime_factors(deg)
.iter()
.map(|&x| a.mod_exp(deg / x, N) != 1)
.all(|x| x);
lhs && rhs
}

pub fn working_modulus(n: BigInt, M: BigInt) -> Constants {
Expand Down Expand Up @@ -135,7 +104,7 @@ fn fft(inp: Vec<BigInt>, c: &Constants, w: BigInt) -> Vec<BigInt> {
.zip(hi)
.enumerate()
.for_each(|(idx, (lo, hi))| {
*hi = (*hi).mul_mod(pre[nchunks * idx], MOD);
*hi = (*hi * pre[nchunks * idx]).rem(MOD);
let neg = if *lo < *hi {
(MOD + *lo) - *hi
} else {
Expand All @@ -159,9 +128,10 @@ pub fn forward(inp: Vec<BigInt>, c: &Constants) -> Vec<BigInt> {
}

pub fn inverse(inp: Vec<BigInt>, c: &Constants) -> Vec<BigInt> {
let inv = extended_gcd(BigInt::from(inp.len()), BigInt::from(c.N));
let w = extended_gcd(c.w, c.N);

let mut inv = BigInt::from(inp.len());
let _ = inv.set_mod(c.N);
let inv = inv.invert();
let w = c.w.invert();
let mut res = fft(inp, c, w);
res.par_iter_mut().for_each(|x| *x = (inv * (*x)).rem(c.N));
res
Expand All @@ -173,34 +143,26 @@ mod tests {
use rayon::{iter::ParallelIterator, slice::ParallelSliceMut};

use crate::{
ntt::{extended_gcd, forward, inverse, working_modulus},
ntt::{forward, inverse, working_modulus},
numbers::BigInt,
};

#[test]
fn test_forward() {
let n = 1 << rand::thread_rng().gen::<u32>() % 8;
let v: Vec<BigInt> = (0..n)
.map(|_| BigInt::from(rand::thread_rng().gen::<u32>() % (1 << 6)))
.collect();
let M = (*v.iter().max().unwrap() << 1) * BigInt::from(n) + 1;
// let n = 1 << rand::thread_rng().gen::<u32>() % 8;
// let v: Vec<BigInt> = (0..n)
// .map(|_| BigInt::from(rand::thread_rng().gen::<u32>() % (1 << 6)))
// .collect();
// let M = (*v.iter().max().unwrap() << 1) * BigInt::from(n) + 1;
let n = 8;
let v: Vec<BigInt> = (0..n).map(|x| BigInt::from(x)).collect();
let M = BigInt::from(n) * BigInt::from(n) + 1;
let c = working_modulus(BigInt::from(n), BigInt::from(M));
let forward = forward(v.clone(), &c);
let inverse = inverse(forward, &c);
v.iter().zip(inverse).for_each(|(&a, b)| assert_eq!(a, b));
}

#[test]
fn test_extended_gcd() {
(2..11).for_each(|x: u64| {
let inv = extended_gcd(BigInt::from(x), BigInt::from(11));
assert_eq!(
(BigInt::from(x) * inv).rem(BigInt::from(11)),
BigInt::from(1)
);
});
}

#[test]
fn test_roots_of_unity() {
let N = 10;
Expand Down
Loading