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Fix an issue in Barrett reduction.

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This commit is contained in:
Adam Wick
2018-10-04 20:00:46 -07:00
parent 78750598a5
commit fe43949684
2 changed files with 46 additions and 43 deletions
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85
src/unsigned/barrett.rs
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@@ -8,51 +8,52 @@ macro_rules! barrett_impl {
impl $bar {
pub fn new(m: $name) -> $bar {
// Step #1: Figure out k
let mut k = 0;
for i in 0..m.value.len() {
if m.value[i] != 0 {
k = i;
}
}
k += 1;
// Step #2: Compute b
let mut b = $dbl64::zero();
b.value[2*k] = 1;
// Step #3: Divide b by m.
let bigm = $dbl64::from(&m);
let quot = b / &bigm;
let resm = $name64::from(&m);
let mu = $name64::from(&quot);
// Done!
$bar { k: k, m: resm, mu: mu }
// Step #1: Figure out k
let mut k = 0;
for i in 0..m.value.len() {
if m.value[i] != 0 {
k = i;
}
}
k += 1;
// Step #2: Compute b
let mut b = $dbl64::zero();
b.value[2*k] = 1;
// Step #3: Divide b by m.
let bigm = $dbl64::from(&m);
let quot = b / &bigm;
let resm = $name64::from(&m);
let mu = $name64::from(&quot);
// Done!
$bar { k: k, m: resm, mu: mu }
}
pub fn reduce(&self, x: &$dbl) -> $name {
let m2: $dbl64 = $dbl64::from(&self.m);
// 1. q1←⌊x/bk−1⌋, q2←q1 · μ, q3←⌊q2/bk+1⌋.
let q1: $name64 = $name64::from(x >> ((self.k - 1) * 64));
let q2: $dbl64 = $dbl64::from(q1 * &self.mu);
let q3: $name64 = $name64::from(q2 >> ((self.k + 1) * 64));
// 2. r1←x mod bk+1, r2←q3 · m mod bk+1, r←r1 − r2.
let mut r: $dbl64 = $dbl64::from(x);
r.mask(self.k + 1);
let mut r2: $dbl64 = $dbl64::from(q3 * &self.m);
r2.mask(self.k + 1);
let went_negative = &r < &r2;
r -= &r2;
// 3. If r<0 then r←r+bk+1.
if went_negative {
let mut bk1 = $dbl64::zero();
bk1.value[self.k+1] = 1;
r += &bk1;
}
// 4. While r≥m do: r←r−m.
while &r > &m2 {
r -= &m2;
}
// Done!
$name::from(&r)
// 1. q1←⌊x/bk−1⌋, q2←q1 · μ, q3←⌊q2/bk+1⌋.
let q1: $name64 = $name64::from(x >> ((self.k - 1) * 64));
let q2 = q1 * &self.mu;
let q3: $name64 = $name64::from(q2 >> ((self.k + 1) * 64));
// 2. r1←x mod bk+1, r2←q3 · m mod bk+1, r←r1 − r2.
let mut r: $dbl64 = $dbl64::from(x);
r.mask(self.k + 1);
let mut r2: $dbl64 = $dbl64::from(q3 * &self.m);
r2.mask(self.k + 1);
let went_negative = &r < &r2;
r -= &r2;
// 3. If r<0 then r←r+bk+1.
if went_negative {
let mut bk1 = $dbl64::zero();
bk1.value[self.k+1] = 1;
// this may overflow, and we should probably be OK with it.
r += &bk1;
}
// 4. While r≥m do: r←r−m.
let m2 = $dbl64::from(&self.m);
while &r > &m2 {
r -= &m2;
}
// Done!
$name::from(&r)
}
}