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KaTeXify struct docs for internal point types

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Henry de Valence 2017-11-29 12:30:51 -08:00
parent b2a85da09d
commit d862912511
1 changed files with 34 additions and 20 deletions
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54
src/curve_models/mod.rs
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@ -138,8 +138,13 @@ use traits::ValidityCheck;
// Internal point representations
// ------------------------------------------------------------------------
/// A `ProjectivePoint` is a point on the curve in 𝗣²(𝔽ₚ).
/// A point (x,y) in the affine model corresponds to (x:y:1).
/// A `ProjectivePoint` is a point \\((X:Y:Z)\\) on the \\(\mathbb
/// P\^2\\) model of the curve.
/// A point \\((x,y)\\) in the affine model corresponds to
/// \\((x:y:1)\\).
///
/// More details on the relationships between the different curve models
/// can be found in the module-level documentation.
#[derive(Copy, Clone)]
pub struct ProjectivePoint {
pub X: FieldElement,
@ -147,8 +152,13 @@ pub struct ProjectivePoint {
pub Z: FieldElement,
}
/// A `CompletedPoint` is a point ((X:Z), (Y:T)) in 𝗣¹(𝔽ₚ)×𝗣¹(𝔽ₚ).
/// A point (x,y) in the affine model corresponds to ((x:1),(y:1)).
/// A `CompletedPoint` is a point \\(((X:Z), (Y:T))\\) on the \\(\mathbb
/// P\^1 \times \mathbb P\^1 \\) model of the curve.
/// A point (x,y) in the affine model corresponds to \\( ((x:1),(y:1))
/// \\).
///
/// More details on the relationships between the different curve models
/// can be found in the module-level documentation.
#[derive(Copy, Clone)]
#[allow(missing_docs)]
pub struct CompletedPoint {
@ -159,9 +169,10 @@ pub struct CompletedPoint {
}
/// A pre-computed point in the affine model for the curve, represented as
/// (y+x, y-x, 2dxy). These precomputations accelerate addition and
/// subtraction, and were introduced by Niels Duif in the ed25519 paper
/// ["High-Speed High-Security Signatures"](https://ed25519.cr.yp.to/ed25519-20110926.pdf).
/// \\((y+x, y-x, 2dxy)\\) in "Niels coordinates".
///
/// More details on the relationships between the different curve models
/// can be found in the module-level documentation.
// Safe to derive Eq because affine coordinates.
#[derive(Copy, Clone, Eq, PartialEq)]
#[allow(missing_docs)]
@ -171,10 +182,11 @@ pub struct AffineNielsPoint {
pub xy2d: FieldElement,
}
/// A pre-computed point in the P³(𝔽ₚ) model for the curve, represented as
/// (Y+X, Y-X, Z, 2dXY). These precomputations accelerate addition and
/// subtraction, and were introduced by Niels Duif in the ed25519 paper
/// ["High-Speed High-Security Signatures"](https://ed25519.cr.yp.to/ed25519-20110926.pdf).
/// A pre-computed point on the \\( \mathbb P\^3 \\) model for the
/// curve, represented as \\((Y+X, Y-X, Z, 2dXY)\\) in "Niels coordinates".
///
/// More details on the relationships between the different curve models
/// can be found in the module-level documentation.
#[derive(Copy, Clone)]
pub struct ProjectiveNielsPoint {
pub Y_plus_X: FieldElement,
@ -266,14 +278,10 @@ impl ConditionallyAssignable for AffineNielsPoint {
// ------------------------------------------------------------------------
impl ProjectivePoint {
/// Convert to the extended twisted Edwards representation of this
/// point.
/// Convert this point from the \\( \mathbb P\^2 \\) model to the
/// \\( \mathbb P\^3 \\) model.
///
/// From §3 in [0]:
///
/// Given (X:Y:Z) in Ɛ, passing to Ɛₑ can be performed in 3M+1S by
/// computing (XZ,YZ,XY,Z²). (Note that in that paper, points are
/// (X:Y:T:Z) so this really does match the code below).
/// This costs \\(3 \mathrm M + 1 \mathrm S\\).
pub fn to_extended(&self) -> ExtendedPoint {
ExtendedPoint{
X: &self.X * &self.Z,
@ -285,7 +293,10 @@ impl ProjectivePoint {
}
impl CompletedPoint {
/// Convert to a ProjectivePoint
/// Convert this point from the \\( \mathbb P\^1 \times \mathbb P\^1
/// \\) model to the \\( \mathbb P\^2 \\) model.
///
/// This costs \\(3 \mathrm M \\).
pub fn to_projective(&self) -> ProjectivePoint {
ProjectivePoint{
X: &self.X * &self.T,
@ -294,7 +305,10 @@ impl CompletedPoint {
}
}
/// Convert to an ExtendedPoint
/// Convert this point from the \\( \mathbb P\^1 \times \mathbb P\^1
/// \\) model to the \\( \mathbb P\^3 \\) model.
///
/// This costs \\(4 \mathrm M \\).
pub fn to_extended(&self) -> ExtendedPoint {
ExtendedPoint{
X: &self.X * &self.T,