DoxigAlpha

llsquareBasecase

r MUST NOT alias x.

Function parameters

Parameters

#
r:[]Limb
x:[]const Limb

Used to indicate either limit of a 2s-complement integer.

Types

#
TwosCompIntLimit
Used to indicate either limit of a 2s-complement integer.
Mutable
A arbitrary-precision big integer, with a fixed set of mutable limbs.
Const
A arbitrary-precision big integer, with a fixed set of immutable limbs.
Managed
An arbitrary-precision big integer along with an allocator which manages the memory.

Returns the number of limbs needed to store `scalar`, which must be a

Functions

#
calcLimbLen
Returns the number of limbs needed to store `scalar`, which must be a
calcSetStringLimbCount
Assumes `string_len` doesn't account for minus signs if the number is negative.
calcNonZeroTwosCompLimbCount
Compute the number of limbs required to store a 2s-complement number of `bit_count` bits.
calcTwosCompLimbCount
Compute the number of limbs required to store a 2s-complement number of `bit_count` bits.
addMulLimbWithCarry
a + b * c + *carry, sets carry to the overflow bits
llcmp
Returns -1, 0, 1 if |a| < |b|, |a| == |b| or |a| > |b| respectively for limbs.

Source

Implementation

#
fn llsquareBasecase(r: []Limb, x: []const Limb) void {
    const x_norm = x;
    assert(r.len >= 2 * x_norm.len + 1);
    assert(!slicesOverlap(r, x));

    // Compute the square of a N-limb bigint with only (N^2 + N)/2
    // multiplications by exploiting the symmetry of the coefficients around the
    // diagonal:
    //
    //           a   b   c *
    //           a   b   c =
    // -------------------
    //          ca  cb  cc +
    //      ba  bb  bc     +
    //  aa  ab  ac
    //
    // Note that:
    //  - Each mixed-product term appears twice for each column,
    //  - Squares are always in the 2k (0 <= k < N) column

    for (x_norm, 0..) |v, i| {
        // Accumulate all the x[i]*x[j] (with x!=j) products
        const overflow = llmulLimb(.add, r[2 * i + 1 ..], x_norm[i + 1 ..], v);
        assert(!overflow);
    }

    // Each product appears twice, multiply by 2
    _ = llshl(r, r[0 .. 2 * x_norm.len], 1);

    for (x_norm, 0..) |v, i| {
        // Compute and add the squares
        const overflow = llmulLimb(.add, r[2 * i ..], x[i..][0..1], v);
        assert(!overflow);
    }
}