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Merged
rivy merged 3 commits into from
Jul 25, 2020
Merged

factor::miller_rabin: Minor improvements #1562

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e415b17
factor::miller_rabin: Remove duplicated work
nicoonoclaste Jun 25, 2020
ecc3e2d
factor::miller_rabin::test: Minor readability improvement
nicoonoclaste Jul 17, 2020
3e55139
factor::miller_rabbin::Result: Mark as #[must_use]
nicoonoclaste Jul 17, 2020
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23 changes: 7 additions & 16 deletions src/uu/factor/src/miller_rabin.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,7 @@ impl Basis for Montgomery<u32> {
}

#[derive(Eq, PartialEq)]
#[must_use = "Ignoring the output of a primality test."]
pub(crate) enum Result {
Prime,
Pseudoprime,
Expand Down Expand Up @@ -54,7 +55,7 @@ pub(crate) fn test<A: Arithmetic + Basis>(m: A) -> Result {
let one = m.one();
let minus_one = m.minus_one();

for _a in A::BASIS.iter() {
'witness: for _a in A::BASIS.iter() {
let _a = _a % n;
if _a == 0 {
continue;
Expand All @@ -65,33 +66,23 @@ pub(crate) fn test<A: Arithmetic + Basis>(m: A) -> Result {
// x = a^r mod n
let mut x = m.pow(a, r);

{
// y = ((x²)²...)² i times = x ^ (2ⁱ) = a ^ (r 2ⁱ) = x ^ (n - 1)
let mut y = x;
for _ in 0..i {
y = m.mul(y, y)
}
if y != one {
return Pseudoprime;
};
}

if x == one || x == minus_one {
continue;
}

loop {
for _ in 1..i {
let y = m.mul(x, x);
if y == one {
return Composite(gcd(m.to_u64(x) - 1, m.modulus()));
}
if y == minus_one {
} else if y == minus_one {
// This basis element is not a witness of `n` being composite.
// Keep looking.
break;
continue 'witness;
}
x = y;
}

return Pseudoprime;
}

Prime
Expand Down