addition in gallois field with char 2
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@ -18,7 +18,7 @@
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use crate::{math::modexp, cplex::printing::seperator, math::modred::modred};
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use core::fmt;
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use std::fmt::Debug;
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use std::{fmt::Debug, ops::BitXor};
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use num::{Integer, NumCast};
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@ -186,6 +186,30 @@ impl GalloisField {
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return Ok(egcd);
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}
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/// addition in the field
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///
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/// in case of a prime base, addition works as normal,
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/// if the base is a prime power, all elements are treated as polynomials, so the
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/// operations are changed too.
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pub fn add<T>(&self, a: T, b: T) -> T
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where
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T: Integer,
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T: Debug,
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T: NumCast,
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{
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let a: u128 = self.reduce(num::cast::<_, u128>(a).unwrap());
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let b: u128 = self.reduce(num::cast::<_, u128>(b).unwrap());
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let r: u128;
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if self.prime_base {
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r = a + b;
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}
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else {
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r = a ^ b;
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println!("r = a ^ b = {a:b} ^ {b:b} = {r:b}");
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}
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num::cast(self.reduce::<_, T>(r)).unwrap()
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}
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pub fn divide(self, a: u128, b: u128) -> Result<u128, DivisionByZeroError> {
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let b = self.inverse(b);
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match b {
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@ -382,8 +406,8 @@ impl GalloisField {
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println!("calculating characteristic of F_{}", self.base);
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}
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let mut i = 1u128;
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while self.reduce::<_, u128>(i) > 0 {
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i += 1;
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while self.reduce::<_, u128>(i) != 0 {
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i = self.add(i, 1);
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}
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if self.verbose {
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println!("{i} = {} (mod {})", self.reduce::<_, u128>(i), self.base);
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@ -548,10 +572,36 @@ pub mod test {
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}
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}
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#[test]
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fn test_gallois_add() {
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let field = GalloisField::new(977, true, None);
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let ns = [132,1232,121,424];
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for i in 0..976 {
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for n in ns {
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assert_eq!(field.add(i, n), field.reduce(i+n));
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}
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}
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let field = GalloisField::new(8, true, None);
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assert_eq!(field.add(0b1, 0b10), field.reduce(0b11));
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assert_eq!(field.add(0b11, 0b10), field.reduce(0b01));
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assert_eq!(field.add(0b101, 0b1010), field.reduce(0b1111));
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assert_eq!(field.add(0b1010101, 0b10101010), field.reduce(0b11111111));
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let field = GalloisField::new(16, true, None);
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assert_eq!(field.add(0b1, 0b10), field.reduce(0b11));
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assert_eq!(field.add(0b11, 0b10), field.reduce(0b01));
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assert_eq!(field.add(0b1111, 0b1011), field.reduce(0b0100));
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assert_eq!(field.add(0b101, 0b1010), field.reduce(0b1111));
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assert_eq!(field.add(0b1000, 0b111), field.reduce(0b1111));
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assert_eq!(field.add(0b1010101, 0b10101010), field.reduce(0b11111111));
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}
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#[test]
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fn test_gallois_reduce_c2() {
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let field = GalloisField::new(16, true, None);
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for i in 0..976 {
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for i in 0..0xf {
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assert_eq!(field.reduce::<_, u128>(i), i);
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assert_eq!(field.reduce::<_, u128>(i), i);
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}
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}
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