readdition-snippet.rs

impl<'a, 'b> Add<&'b CachedPoint> for &'a ExtendedPoint {
    type Output = ExtendedPoint;

    fn add(self, other: &'b CachedPoint) -> ExtendedPoint {
        // The coefficients of an `ExtendedPoint` are reduced after
        // every operation.  If the `CachedPoint` was negated, its
        // coefficients grow by one bit.  So on input, `self` is
        // bounded with `b < 0.007` and `other` is bounded with
        // `b < 1.0`.
        let mut tmp = self.0;

        tmp = tmp.blend(tmp.diff_sum(), Lanes::AB);
        // tmp = (Y1-X1 Y1+X1 Z1 T1) = (S0 S1 Z1 T1) with b < 1.6

        // (tmp, other) bounded with b < (1.6, 1.0) < (2.5, 1.75).
        tmp = &tmp * &other.0;
        // tmp = (S0*S2' S1*S3' Z1*Z2' T1*T2') = (S8 S9 S10 S11)

        tmp = tmp.shuffle(Shuffle::ABDC);
        // tmp = (S8 S9 S11 S10)

        tmp = tmp.diff_sum();
        // tmp = (S9-S8 S9+S8 S10-S11 S10+S11) = (S12 S13 S14 S15)

        let t0 = tmp.shuffle(Shuffle::ADDA);
        // t0 = (S12 S15 S15 S12)
        let t1 = tmp.shuffle(Shuffle::CBCB);
        // t1 = (S14 S13 S14 S13)

        // All coefficients of t0, t1 are bounded with b < 1.6.
        // Return (S12*S14 S15*S13 S15*S14 S12*S13) = (X3 Y3 Z3 T3)
        ExtendedPoint(&t0 * &t1)
    }
}