Returns the absolute value and true if the value was negative

generateRandomPoints is a similar version of the one that exist in the ipa package but we're pulling it here for tests to avoid an import cycle and ou

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BytesLE returns the little-endian byte representation of a field element.

BytesUncompressedTrusted returns the uncompressed serialized version of the element. The returned bytes can only be used with SetBytesUncompressed wit

DivideOnDomain computes f(x) - f(x_i) / x - x_i where x_i is an element in the domain

ExtendedAddNormalized computes p = p1 + p2. https://hyperelliptic.org/EFD/g1p/auto-twisted-extended.html#addition-madd-2008-hwcd

GenerateRandomPoints generates numPoints random points on the curve using hardcoded seed.

Legendre returns the Legendre symbol of z (either +1, -1, or 0.)

MapToScalarField maps a group element to the scalar field.

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Neg computes p = -p1

NewIPASettings generates the SRS, Q and precomputed weights for the barycentric formula. The SRS is generated as common.VectorLength random points whe

PointExtendedFromProj converts a point in projective coordinates to extended coordinates.

Read deserializes a multi-proof from a reader.

Read deserializes the IPA proof from the given reader.

ScalarMul multiplies the point by the given scalar using the precomputed points. It applies a trick to push a carry between windows since our precompu

SetRawBytes reads up to Bytes (bytes needed to represent Element) from reader and interpret it as big endian uint64 used for fuzzing purposes only

ToRegular returns z in regular form (doesn't mutate z)

Computes c[i] =a[i] + b[i] * x returns c

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Taken from https://rosettacode.org/wiki/Polynomial_long_division#Go

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setBigInt assumes 0 <= v < q

Splits a slice of scalars into two slices of equal length Eg [S1,S2,S3,S4] becomes [S1,S2] , [S3,S4]

sqrtAlg_GetPrecomputedRootOfUnity sets target to g^(multiplier << (order * sqrtParam_BlockSize)), where g is the fixed primitive 2^32th root of unity.

sqrtAlg_NegDlogInSmallDyadicSubgroup takes a (not necessarily primitive) root of unity x of order 2^sqrtParam_BlockSize. x has the form sqrtPrecomp_Re

BatchMapToScalarField maps a slice of group elements to the scalar field.

Bit returns the i'th bit, with lsb == bit 0. It is the responsability of the caller to convert from Montgomery to Regular form if needed

BitLen returns the minimum number of bits needed to represent z returns 0 if z == 0

ElementsToBytes serialises a slice of group elements in compressed form.

Equal checks if two multi-proofs are equal.

GenFr generates an Fr element

IsOnCurve returns true if p is on the curve.

MinusOne returns the field element -1.

MultiExp calculates the multi exponentiation of points and scalars.

NewPrecompPoint creates a new PrecompPoint for the given point and window size.

Reads an uncompressed affine point Point is not guaranteed to be in the prime subgroup

SetIdentity sets p to the identity element.

Write serializes a multi-proof to a writer.

Writes an uncompressed affine point to an io.Writer

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batchProjToAffine converts a slice of points in projective coordinates to affine coordinates. This code was pulled from gnark-crypto which unfortunate

computes A'(x_j) where x_j must be an element in the domain This is computed as the product of x_j - x_i where x_i is an element in the domain and x_i

This function does log2(vector_size) Since we do not allow for 0 size vectors, this is checked since we also do not allow for vectors which are not p

ax^2 + y^2 = 1 + dx^2y^2 ax^2 -1 = dx^2y^2 - y^2 ax^2 -1 = y^2(dx^2 -1) ax^2 - 1 / (dx^2 - 1) = y^2

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another way to evaluate a point outside of the domain TODO, we can probably remove this and just interpolate and evaluate in tests

Computes c[i] =a[i] + b[i] * x returns c

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computes X/Y

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Splits a slice of points into two slices of equal length Eg [P1,P2,P3,P4,P5,P6] becomes [P1,P2,P3] , [P4,P5,P6]

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