package tezos-bls12-381-polynomial

degree p n returns the degree of a polynomial p

• requires: size p = n

of_sparse res p n converts the sparse representation of a polynomial p to the dense representation, from an OCaml array p of size n to a C array res of size degree p + 1

requires:

• degree of each coeff d_i >= 0 and d_i are unique
• the result must be initialized with zero (as done by Carray.allocate)
• size res = degree p + 1
• size p = n

add res a b size_a size_b writes the result of polynomial addition of a and b in res

requires:

• size a = size_a
• size b = size_b
• size res = max (size_a, size_b)
• res, a and b are either pairwise disjoint or equal

sub res a b size_a size_b writes the result of polynomial subtraction of b from a in res

requires:

• size a = size_a
• size b = size_b
• size res = max (size_a, size_b)
• res, a and b are either pairwise disjoint or equal

mul res a b size_a size_b writes the result of polynomial multiplication of a by b in res

requires:

• the result must be initialized with zero (as done by Carray.allocate)
• size a = size_a
• size b = size_b
• size res = size_a + size_b - 1

mul_by_scalar res b a size_a writes the result of multiplying a polynomial a by a blst_fr element b in res

requires:

• size a = size_a
• size res = size_a
• res and a either disjoint or equal

linear res poly_polylen_coeff nb_polys writes the result of computing λ₁·p₁(x) + λ₂·p₂(x) + … + λₖ·pₖ(x) in res, where

• poly_polylen_coeff.[i] = (pᵢ, size_p_i, λᵢ)
• nb_polys is a number of polynomials, i.e., i = 1..nb_polys

requires:

• the result must be initialized with zero (as done by Carray.allocate)
• size res = max (size_p_i)
• size poly_polylen_coeff = nb_polys
• size p_i = size_p_i

negate res p n writes the result of negating a polynomial p in res

requires:

• size p = n
• size res = n
• res and p either disjoint or equal

is_zero p n checks whether a polynomial p is the zero polynomial

• requires: size p = n

evaluate res p n x writes the result of evaluating a polynomial p at x in res

• requires: size p = n and n > 0

division_x_z res p n z writes the quotient of the division of a polynomial p by (X - z) in res

requires:

• size p = n and n > 1
• size res = n - 1

division_zs res p n s writes the quotient of the division of a polynomial p by (X^s - 1) in res

requires:

• size p = n and n >= 2s
• size res = n - s

mul_zs res p n s writes the result of multiplying a polynomial p by (X^s - 1) in res

requires:

• size p = n and n >= s
• size res = n + s