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factor::numeric::Arithmetic: Rename associated type I to ModInt

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This commit is contained in:
nicoo 2020-07-01 13:15:50 +02:00
parent caa79a1261
commit 19a8231fb2
1 changed files with 15 additions and 14 deletions
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29
src/uu/factor/src/numeric.rs
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@ -27,16 +27,17 @@ pub(crate) fn gcd(mut a: u64, mut b: u64) -> u64 {
} }
pub(crate) trait Arithmetic: Copy + Sized { pub(crate) trait Arithmetic: Copy + Sized {
type I: Copy + Sized + Eq; // The type of integers mod m, in some opaque representation
type ModInt: Copy + Sized + Eq;
fn new(m: u64) -> Self; fn new(m: u64) -> Self;
fn modulus(&self) -> u64; fn modulus(&self) -> u64;
fn from_u64(&self, n: u64) -> Self::I; fn from_u64(&self, n: u64) -> Self::ModInt;
fn to_u64(&self, n: Self::I) -> u64; fn to_u64(&self, n: Self::ModInt) -> u64;
fn add(&self, a: Self::I, b: Self::I) -> Self::I; fn add(&self, a: Self::ModInt, b: Self::ModInt) -> Self::ModInt;
fn mul(&self, a: Self::I, b: Self::I) -> Self::I; fn mul(&self, a: Self::ModInt, b: Self::ModInt) -> Self::ModInt;
fn pow(&self, mut a: Self::I, mut b: u64) -> Self::I { fn pow(&self, mut a: Self::ModInt, mut b: u64) -> Self::ModInt {
let (_a, _b) = (a, b); let (_a, _b) = (a, b);
let mut result = self.one(); let mut result = self.one();
while b > 0 { while b > 0 {
@ -61,13 +62,13 @@ pub(crate) trait Arithmetic: Copy + Sized {
result result
} }
fn one(&self) -> Self::I { fn one(&self) -> Self::ModInt {
self.from_u64(1) self.from_u64(1)
} }
fn minus_one(&self) -> Self::I { fn minus_one(&self) -> Self::ModInt {
self.from_u64(self.modulus() - 1) self.from_u64(self.modulus() - 1)
} }
fn zero(&self) -> Self::I { fn zero(&self) -> Self::ModInt {
self.from_u64(0) self.from_u64(0)
} }
} }
@ -114,7 +115,7 @@ impl<T: DoubleInt> Montgomery<T> {
impl<T: DoubleInt> Arithmetic for Montgomery<T> { impl<T: DoubleInt> Arithmetic for Montgomery<T> {
// Montgomery transform, R=2⁶⁴ // Montgomery transform, R=2⁶⁴
// Provides fast arithmetic mod n (n odd, u64) // Provides fast arithmetic mod n (n odd, u64)
type I = T; type ModInt = T;
fn new(n: u64) -> Self { fn new(n: u64) -> Self {
debug_assert!(T::zero().count_zeros() >= 64 || n < (1 << T::zero().count_zeros() as usize)); debug_assert!(T::zero().count_zeros() >= 64 || n < (1 << T::zero().count_zeros() as usize));
@ -128,7 +129,7 @@ impl<T: DoubleInt> Arithmetic for Montgomery<T> {
self.n.as_() self.n.as_()
} }
fn from_u64(&self, x: u64) -> Self::I { fn from_u64(&self, x: u64) -> Self::ModInt {
// TODO: optimise! // TODO: optimise!
debug_assert!(x < self.n.as_()); debug_assert!(x < self.n.as_());
let r = T::from_double( let r = T::from_double(
@ -138,11 +139,11 @@ impl<T: DoubleInt> Arithmetic for Montgomery<T> {
r r
} }
fn to_u64(&self, n: Self::I) -> u64 { fn to_u64(&self, n: Self::ModInt) -> u64 {
self.reduce(n.as_double()).as_() self.reduce(n.as_double()).as_()
} }
fn add(&self, a: Self::I, b: Self::I) -> Self::I { fn add(&self, a: Self::ModInt, b: Self::ModInt) -> Self::ModInt {
let (r, overflow) = a.overflowing_add_(b); let (r, overflow) = a.overflowing_add_(b);
// In case of overflow, a+b = 2⁶⁴ + r = (2⁶⁴ - n) + r (working mod n) // In case of overflow, a+b = 2⁶⁴ + r = (2⁶⁴ - n) + r (working mod n)
@ -173,7 +174,7 @@ impl<T: DoubleInt> Arithmetic for Montgomery<T> {
r r
} }
fn mul(&self, a: Self::I, b: Self::I) -> Self::I { fn mul(&self, a: Self::ModInt, b: Self::ModInt) -> Self::ModInt {
let r = self.reduce(a.as_double() * b.as_double()); let r = self.reduce(a.as_double() * b.as_double());
// Check that r (reduced back to the usual representation) equals // Check that r (reduced back to the usual representation) equals