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Add a carry-reduction during subtraction.

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Henry de Valence 2017-03-12 23:18:51 -07:00
parent b75a88458a
commit d2a51197d7
1 changed files with 34 additions and 19 deletions
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53
src/field.rs
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@ -144,29 +144,41 @@ impl<'b> SubAssign<&'b FieldElement> for FieldElement {
}
#[cfg(feature="radix_51")]
fn sub_assign(&mut self, _rhs: &'b FieldElement) {
// To avoid underflow, first add p
// XXX how many copies should we add to preserve headroom?
self.0[0] += 2*constants::p.0[0];
self.0[1] += 2*constants::p.0[1];
self.0[2] += 2*constants::p.0[2];
self.0[3] += 2*constants::p.0[3];
self.0[4] += 2*constants::p.0[4];
// then subtract _rhs
self.0[0] -= _rhs.0[0];
self.0[1] -= _rhs.0[1];
self.0[2] -= _rhs.0[2];
self.0[3] -= _rhs.0[3];
self.0[4] -= _rhs.0[4];
let result = (self as &FieldElement) - _rhs;
for i in 0..5 {
self.0[i] = result.0[i];
}
}
}
impl<'a, 'b> Sub<&'b FieldElement> for &'a FieldElement {
type Output = FieldElement;
#[cfg(feature="radix_25_5")]
fn sub(self, _rhs: &'b FieldElement) -> FieldElement {
let mut output = self.clone();
output -= _rhs;
output
}
#[cfg(feature="radix_51")]
fn sub(self, _rhs: &'b FieldElement) -> FieldElement {
// To avoid underflow, first add a multiple of p.
// Choose 16*p = p << 4 to be larger than 54-bit _rhs.
//
// If we could statically track the bitlengths of the limbs
// of every FieldElement, we could choose a multiple of p
// just bigger than _rhs and avoid having to do a reduction.
//
// Since we don't yet have type-level integers to do this, we
// have to add an explicit reduction call here, which is a
// significant cost.
FieldElement::reduce([
(self.0[0] + 36028797018963664u64) - _rhs.0[0],
(self.0[1] + 36028797018963952u64) - _rhs.0[1],
(self.0[2] + 36028797018963952u64) - _rhs.0[2],
(self.0[3] + 36028797018963952u64) - _rhs.0[3],
(self.0[4] + 36028797018963952u64) - _rhs.0[4],
])
}
}
impl<'b> MulAssign<&'b FieldElement> for FieldElement {
@ -251,12 +263,15 @@ impl FieldElement {
/// Invert the sign of this field element
#[cfg(feature="radix_51")]
pub fn negate(&mut self) {
// XXX how many copies of p
self.0[0] = constants::p.0[0] - self.0[0];
self.0[1] = constants::p.0[1] - self.0[1];
self.0[2] = constants::p.0[2] - self.0[2];
self.0[3] = constants::p.0[3] - self.0[3];
self.0[4] = constants::p.0[4] - self.0[4];
// See commentary in the Sub impl
let neg = FieldElement::reduce([
36028797018963664u64 - self.0[0],
36028797018963952u64 - self.0[1],
36028797018963952u64 - self.0[2],
36028797018963952u64 - self.0[3],
36028797018963952u64 - self.0[4],
]);
self.0 = neg.0;
}
/// Construct zero.