GitHub - sourcekris/goflint: Golang bindings for FLINT2 and FLINT3

goflint

Golang wrapper for FLINT functions that I find useful for use upstream in goRsaTool.

This supports FLINT2 and FLINT3 library versions but due to API changes over time has not been exhaustively integration tested.

Features

Assignments

(z *Fmpz) Set(x *Fmpz) *Fmpz Set z to the Fmpz x and return z
(z *Fmpz) SetUint64(x uint64) *Fmpz Sets Fpmz z to ulong x and returns z
(z *Fmpz) SetInt64(x int64) *Fmpz Sets Fpmz z to slong x and returns z
(z *Mpz) SetMpzInt64(x int64) *Mpz Sets Mpz z to slong x and returns z
NewFmpz(x int64) *Fmpz allocates a new Fpmz and sets it to x
NewMpz(x int64) *Mpz allocates a new GMP Mpz and sets it to x
NewFmpq(p, q int64) *Fmpq allocates and returns a new Fmpq set to p / q
NewFmpqFmpz(p, q *Fmpz) *Fmpq allocates and returns a new Fmpq set to p / q where p and q are Fmpz types.
(q *Fmpq) SetFmpqFraction(num, den *Fmpz) *Fmpq sets the value of q to the fraction num / den and returns q.

Comparisons

(z *Fmpz) Cmp(y *Fmpz) (r int) Compares z to y and returns -1, 0, or 1
(z *Mpz) Cmp(y *Mpz) (r int) Compares z to y and returns -1, 0, or 1 where z is an Mpz type.
(z *Fmpq) CmpRational(y *Fmpq) (r int) Compares rational z to y and returns -1, 0, or 1
(q *Fmpq) Cmp(y *Fmpq) int Compares rationals z and y and returns -1, 0, or 1
(z *Fmpz) Equals(y *Fmpz) bool Compares z and y and returns true if they are equal.
(z *Fmpz) IsZero() bool Returns true if z == 0.

Formatters

(z *Fmpz) String() string Returns a base 10 string representaiton of z
(q *Fmpq) String() string Returns a base 10 string representation of rational q

Helpers

(z *Fmpz) BitLen() int Returns the length of z in bits
(z *Fmpz) Bits() int Returns the number of bits required to store z
(z *Fmpz) Sign() (r int) Returns the sign of z returns -1, 0, or 1
(z *Fmpz) Lsh(bits int) *Fmpz Left shifts an Fmpz z by an arbitrary number of bits and returns it.
(z *Fmpz) Rsh(bits int) *Fmpz Right shifts an Fmpz z by an arbitrary number of bits and returns it.

Primality Testing and Factorization

(z *Fmpz) IsStrongProbabPrime(a *Fmpz) returns 1 if z is a strong probable prime to base a, otherwise it returns 0
(z *Fmpz) IsProbabPrimeLucas() int performs a Lucas probable prime test returns 1 if z is a Lucas probable prime, otherwise return 0
(z *Fmpz) IsProbabPrimeBPSW() int performs a Baillie-PSW probable prime test returns 1 if z is a probable prime, otherwise return 0
(z *Fmpz) IsProbabPrime() int returns 1 if z is a probable prime, otherwise return 0
(z *Fmpz) IsProbabPrimePseudosquare() int returns 0 is z is composite. If z is too large (greater than about 94 bits) the function fails silently and returns −1, otherwise, if z is proven prime by the pseudosquares method, return 1.
(z *Fmpz) LucasChain(v2, a, m, n *Fmpz) Given V0 = 2, V1 = A compute Vm, Vm+1 (mod n) from the recurrences Vj = AVj−1 − Vj−2 (mod n).

Random Number Generation

(z *Fmpz) Randm(state *FlintRandT, m *Fmpz) *Fmpz Sets z to a random number between 0 and m-1 inclusive

Conversions

(f *Fmpz) GetInt() int Lowers f to type int
(f *Fmpz) GetUInt() uint Lowers f to type uint
(z *Fmpz) Int64() (y int64) Lowers z to type int64
(z *Fmpz) Uint64() (y uint64) Lower z to type uint64
(q *Fmpq) GetFmpqFraction() (int, int) gets the numerator and denomenator of the rational q returning them as ints.
(q *Fmpq) NumRef() int returns the numerator of an Fmpq as an integer.
(q *Fmpq) DenRef() int returns the denominator of an Fmpq as an integer.
(z *Fmpz) SetString(s string, base int) (*Fmpz, bool) Sets z to the value in string s using given base
(z *Fmpz) SetMpz(x *Mpz) Set z to the value in Mpz x
(z *Mpz) GetMpz(x *Fmpz) Set Mpz z to the value of the Fmpz x
(z *Fmpz) SetBytes(buf []byte) *Fmpz Set z to the value stored in byte array buf and return z
(z *Fmpz) Bytes() []byte Return the bytes of Fmpz z

Arithmetic

(z *Fmpz) Abs(x *Fmpz) *Fmpz Set z to the absolute value of x and return z
(z *Fmpz) Neg(x *Fmpz) *Fmpz Set z to the negated value of x and return z
(z *Fmpz) Add(x, y *Fmpz) *Fmpz Set z to x + y and return z
(z *Fmpz) AddZ(x *Fmpz) *Fmpz Set z to z + x and return z
(z *Fmpz) AddI(i int) *Fmpz Set z to z + i where i is an int type and return z
(z *Fmpz) Sub(x, y *Fmpz) *Fmpz Set z to x - y and return z
(z *Fmpz) SubZ(x *Fmpz) *Fmpz Set z to z - x and return z
(z *Fmpz) SubI(i int) *Fmpz Set z to z - i where i is an int type and return z
(z *Mpz) SubRMpz(y, n *Mpz) Sets z to z - y in the ring of integers modulo n using Mpz types.
(z *Fmpz) Mul(x, y *Fmpz) *Fmpz Set z to x * y and return z
(z *Fmpz) MulZ(x *Fmpz) *Fmpz Set z to z * x and return z
(z *Fmpz) MulI(i int) *Fmpz Set z to z * i where i is an int type and return z
(z *Mpz) MulRMpz(y, n *Mpz) *Mpz Sets z to z * y in the integer ring modulo n using Mpz types.
(q *Fmpq) MulRational(o *Fmpq, x *Fmpz) *Fmpq Sets q to the product of rational o and Fmpz x and returns q.
(z *Fmpz) DivR(y, n *Fmpz) *Fmpz Sets z to the result of z/y in the ring of integers modulo n. Only works if y fits into the int type
(z *Fmpz) Div(x, y *Fmpz) *Fmpz Set z to x / y and return z
(z *Fmpz) Quo(x, y *Fmpz) *Fmpz
(z *Fmpz) QuoRem(x, y, r *Fmpz) (*Fmpz, *Fmpz)
(z *Fmpz) Mod(x, y *Fmpz) *Fmpz Set z to the value of x % y and return z
(z *Fmpz) ModZ(y *Fmpz) *Fmpz Set z to the value of z % y and return z
(z *Fmpz) ModRational(x *Fmpq, n *Fmpz) int Sets z to the residue of x = n/d (num, den) modulo n and returns 1 if such a modulo exists or 0 if it does not
(z *Fmpz) DivMod(x, y, m *Fmpz) (*Fmpz, *Fmpz)
(z *Fmpz) ModInverse(x, y *Fmpz) *Fmpz
(z *Fmpz) NegMod(x, y *Fmpz) *Fmpz
(a *Fmpz) Jacobi(p *Fmpz) int
(z *Fmpz) Exp(x, y, m *Fmpz) *Fmpz Set z to the value of (x^y)%m and return z
(z *Fmpz) ExpZ(x *Fmpz) *Fmpz Set z to the value of (z^x) and return z
(z *Fmpz) ExpI(x int) *Fmpz Set z to the value of (z^i) where i is an int type and return z
(z *Fmpz) ExpXY(x, y *Fmpz) *Fmpz Set z to the value of (x^y) and return z
(z *Fmpz) ExpXI(x *Fmpz, y int) *Fmpz Set z to the value of (x^y) where y is an int type and return z
(z *Fmpz) ExpXIM(x *Fmpz, i int, m *Fmpz) *Fmpz Set z to the value of (x^y)%m where y is an int type and return z
(z *Fmpz) Pow(x, y, m *Fmpz) *Fmpz Set z to the value of (x^y)%m and return z
(z *Fmpz) Square() *Fmpz raises z to the power of 2 and returns z.
(z *Fmpz) Cube() *Fmpz raises z to the power of 3 and returns z.
(f *Fmpz) GCD(g, h *Fmpz) *Fmpz Set z to the value of the greatest common divisor of g and h and return z
(f *Fmpz) Lcm(g, h *Fmpz) *Fmpz Set z to the value of the lowest common multiple of g and h and return z
(f *Fmpz) GCDInv(g *Fmpz) (*Fmpz, *Fmpz)

Bitwise Operations

(z *Fmpz) And(x, y *Fmpz) *Fmpz Set z to the value of x & y and return z
(z *Fmpz) Xor(a, b *Fmpz) *Fmpz Set z to the bitwise exclusive or of a and b and returns z.
(z *Fmpz) TstBit(i int) int Returns the value of the bit stored at index i where 0 is the least significant bit.

Roots

(z *Fmpz) Sqrt(x *Fmpz) *Fmpz Set z to the value of the square root of x and return z
(z *Fmpz) Root(x *Fmpz, y int32) *Fmpz Set z to the value of then yth root of x and return z

Matrices

NewFmpzMat(rows, cols int) *FmpzMat Creates and allocates a new FmpzMat matrix type of size rows * cols.
(m *FmpzMat) String() string Returns a pretty printed string version of the matrix as a string.
(m *FmpzMat) Zero() *FmpzMat Sets all of the values of the matrix to zero and returns the matrix.
(m *FmpzMat) One() *FmpzMat Sets the diagonal values of the matrix to 1 and returns the matrix.
(m *FmpzMat) NumRows() int Returns the number of rows in the matrix as an integer.
(m *FmpzMat) NumCols() int Returns the number of columns in the matrix.
(m *FmpzMat) Entry(x, y int) *Fmpz Returns the value at coordinates x, y in the matrix m.
(m *FmpzMat) SetPosVal(val *Fmpz, pos int) *FmpzMat Sets the value at offset pos in the matrix m and returns m.
(m *FmpzMat) SetVal(val *Fmpz, x, y int) *FmpzMat Sets the value at coordinates x,y in the matrix and returns m.

Lattice Basis Reduction

NewFmpzLLL() *FmpzLLL Creates and allocates a new FmpzLLL context.
(m *FmpzMat) LLL() *FmpzMat Reduces m in place according to the parameters specified by the default LLL context.

Univariate Polynomials over the integers.

NewFmpzPoly() *FmpzPoly NewFmpzPoly allocates a new FmpzPoly and returns it.
NewFmpzPoly2(a int) *FmpzPoly NewFmpzPoly2 allocates a new FmpzPoly with at least a coefficients and returns it.
NewFmpzPolyFactor() *FmpzPolyFactor allocates a new FmpzPolyFactor and returns it.
FmpzPolySetString(poly string) (*FmpzPoly, error) FmpzPolySetString returns a polynomial using the string representation as the definition.
(z *FmpzPoly) Set(poly *FmpzPoly) *FmpzPoly Set sets z to poly and returns z
(f *FmpzPolyFactor) Set(fac *FmpzPolyFactor) *FmpzPolyFactor Set sets f to FmpzPolyFactor fac and returns f.
(z *FmpzPoly) String() string String returns a string representation of the polynomial.
(z *FmpzPoly) StringSimple() string StringSimple returns a simple string representation of the polynomials length and coefficients.
(f *FmpzPolyFactor) Print() Print prints the FmpzPolyFactor to stdout.
(z *FmpzPoly) Zero() *FmpzPoly Zero sets z to the zero polynomial and returns z.
(z *FmpzPoly) FitLength(l int) FitLength sets the number of coefficiets in z to l.
(z *FmpzPoly) SetCoeff(c int, x *Fmpz) *FmpzPoly SetCoeff sets the c'th coefficient of z to x where x is an Fmpz and returns z.
(z *FmpzPoly) SetCoeffUI(c int, x uint) *FmpzPoly SetCoeffUI sets the c'th coefficient of z to x where x is an uint and returns z.
(z *FmpzPoly) GetCoeff(c int) *Fmpz GetCoeff gets the c'th coefficient of z and returns an Fmpz.
(z *FmpzPoly) GetCoeffs() []*Fmpz GetCoeffs gets all of the coefficient of z and returns a slice of Fmpz.
(z *FmpzPoly) Len() int Len returns the length of the poly z.
(z *FmpzPoly) Neg(p *FmpzPoly) *FmpzPoly Neg sets z to the negative of p and returns z.
(z *FmpzPoly) GCD(a, b *FmpzPoly) *FmpzPoly GCD sets z = gcd(a, b) and returns z.
(z *FmpzPoly) Equal(p *FmpzPoly) bool Equal returns true if z is equal to p otherwise false.
(z *FmpzPoly) Add(a, b *FmpzPoly) *FmpzPoly Add sets z = a + b and returns z.
(z *FmpzPoly) Sub(a, b *FmpzPoly) *FmpzPoly Sub sets z = a - b and returns z.
(z *FmpzPoly) Mul(a, b *FmpzPoly) *FmpzPoly Mul sets z = a * b and returns z.
(z *FmpzPoly) MulScalar(a *FmpzPoly, x *Fmpz) *FmpzPoly MulScalar sets z = a * x where x is an Fmpz.
(z *FmpzPoly) DivScalar(a *FmpzPoly, x *Fmpz) *FmpzPoly DivScalar sets z = a / x where x is an Fmpz. Rounding coefficients down toward -infinity.
(z *FmpzPoly) Pow(m *FmpzPoly, e int) *FmpzPoly Pow sets z to m^e and returns z.
(z *FmpzPoly) DivRem(m *FmpzPoly) (*FmpzPoly, *FmpzPoly) DivRem computes q, r such that z=mq+r and 0 ≤ len(r) < len(m).
(z *FmpzPoly) Factor() *FmpzPolyFactor Factor uses the Zassenhaus factoring algorithm.
(f *FmpzPolyFactor) GetPoly(n int) *FmpzPoly GetPoly gets the nth polynomial factor from a FmpzPolyFactor and returns it.
(f *FmpzPolyFactor) GetExp(n int) int GetExp gets the exponent of the nth polynomial from the FmpzPolyFactor.
(f *FmpzPolyFactor) GetCoeff() *Fmpz GetCoeff gets the coefficient from the FmpzPolyFactor.
(f *FmpzPolyFactor) Len() int Len gets the length of the FmpzPolyFactors list. i.e. the number of factors found.

Univariate Polynomials over the integers modulo n.

NewFmpzModCtx(n *Fmpz) *FmpzModCtx NewFmpzModCtx allocates a new FmpzModCtx with modulus n and returns it.
NewFmpzModPoly(n *FmpzModCtx) *FmpzModPoly NewFmpzModPoly allocates a new FmpzModPoly mod n and returns it.
NewFmpzModPoly2(n *FmpzModCtx, a int) *FmpzModPoly NewFmpzModPoly2 allocates a new FmpzModPoly mod n with at least a coefficients and returns it.
SetString(poly string) (*FmpzModPoly, error) SetString returns a polynomial mod n using the string representation as the definition.
(z *FmpzModPoly) Set(poly *FmpzModPoly) *FmpzModPoly Set sets z to poly and returns z
(z *FmpzModPoly) String() string String returns a string representation of the polynomial.
(z *FmpzModPoly) StringSimple() string StringSimple returns a simple string representation of the polynomials length, modulus and coefficients.
(z *FmpzModPoly) Zero() *FmpzModPoly Zero sets z to the zero polynomial and returns z.
(z *FmpzModPoly) FitLength(l int) FitLength sets the number of coefficiets in z to l.
(z *FmpzModPoly) SetCoeff(c int, x *Fmpz) *FmpzModPoly SetCoeff sets the c'th coefficient of z to x where x is an Fmpz and returns z.
(z *FmpzModPoly) SetCoeffUI(c int, x uint) *FmpzModPoly SetCoeffUI sets the c'th coefficient of z to x where x is an uint and returns z.
(z *FmpzModPoly) GetCoeff(c int) *Fmpz GetCoeff gets the c'th coefficient of z and returns an Fmpz.
(z *FmpzModPoly) GetCoeffs() []*Fmpz GetCoeffs gets all of the coefficient of z and returns a slice of Fmpz.
(z *FmpzModPoly) GetMod() *Fmpz GetMod gets the modulus of z and returns an Fmpz.
(z *FmpzModPoly) Len() int Len returns the length of the poly z.
(z *FmpzModPoly) Neg(p *FmpzModPoly) *FmpzModPoly Neg sets z to the negative of p and returns z.
(z *FmpzModPoly) GCD(a, b *FmpzModPoly) *FmpzModPoly GCD sets z = gcd(a, b) and returns z.
(z *FmpzModPoly) Equal(p *FmpzModPoly) bool Equal returns true if z is equal to p otherwise false.
(z *FmpzModPoly) Add(a, b *FmpzModPoly) *FmpzModPoly Add sets z = a + b and returns z.
(z *FmpzModPoly) Sub(a, b *FmpzModPoly) *FmpzModPoly Sub sets z = a - b and returns z.
(z *FmpzModPoly) Mul(a, b *FmpzModPoly) *FmpzModPoly Mul sets z = a * b and returns z.
(z *FmpzModPoly) MulScalar(a *FmpzModPoly, x *Fmpz) *FmpzModPoly MulScalar sets z = a * x where x is an Fmpz.
(z *FmpzModPoly) DivScalar(a *FmpzModPoly, x *Fmpz) *FmpzModPoly DivScalar sets z = a / x where x is an Fmpz.
(z *FmpzModPoly) Pow(m *FmpzModPoly, e int) *FmpzModPoly Pow sets z to m^e and returns z.
(z *FmpzModPoly) DivRem(m *FmpzModPoly) (*FmpzModPoly, *FmpzModPoly) DivRem computes q, r such that z=mq+r and 0 ≤ len(r) < len(m).

Chinese Remainder Theorem

(z *Fmpz) CRT(r1, m1, r2, m2 *Fmpz, sign int) *Fmpz uses the Chinese Remainder Theorem to set out to the unique value.

Min and Max

(z *Fmpz) Min(a, b *Fmpz) *Fmpz finds the min(a, b) sets z to it and returns it.
(z *Fmpz) Max(a, b *Fmpz) *Fmpz finds the max(a, b) sets z to it and returns it.

Natural Logarithm

(z *Fmpz) DLog() float64 returns log(z) as a float64.

Types

// Fmpz is a arbitrary size integer type.
type Fmpz struct {
  i    C.fmpz_t
  init bool
}

// Mpz is an abitrary size integer type from the Gnu Multiprecision Library.
type Mpz struct {
  i    C.mpz_t
  init bool
}

// Fmpq is an arbitrary precision rational type.
type Fmpq struct {
  i    C.fmpq_t
  init bool
}

// FmpzPoly type represents a univatiate polynomial over the integers.
type FmpzPoly struct {
	i    C.fmpz_poly_t
	init bool
}

// FmpzPolyFactor type represents the factors univariate polynomial over the integers.
type FmpzPolyFactor struct {
	i    C.fmpz_poly_factor_t
	init bool
}

// FmpzModPoly type represents elements of Z/nZ[x] for a fixed modulus n.
type FmpzModPoly struct {
	i    C.fmpz_mod_poly_t
	ctx  *FmpzModCtx
	init bool
}

// FmpzModCtx type represents a context for modular arithmetic.
type FmpzModCtx struct {
	i    C.fmpz_mod_ctx_t
	n    *Fmpz
	init bool
}

// NmodPoly type represents elements of Z/nZ[x] for a fixed modulus n.
type NmodPoly struct {
  i    C.nmod_poly_t
  init bool
}

// MpLimb type is a uint64.
type MpLimb struct {
  i    C.mp_limb_t
}

// FlintRandT keeps state for Fmpz random number generation.
type FlintRandT struct {
	i    C.flint_rand_t
	init bool
}

// FmpzMat is a matrix of Fmpz.
type FmpzMat struct {
	i    C.fmpz_mat_t
	rows int
	cols int
	init bool
}

// FmpzLLL stores a LLL matrix reduction context.
type FmpzLLL struct {
	i    C.fmpz_lll_t
	init bool
}

Examples

a := NewFmpz(1)

fmt.Println(a.String())

Install

Install the golang and the FLINT library.

On Ubuntu (tested on 20.04LTS):
```
$ apt install golang libflint-dev`
```
On MacOS (tested on Monterey 12.1 M1)
```
$ brew install flint
```

Use go to install the library:

go get github.com/sourcekris/goflint

License

Apache 2.0. See the LICENSE file for details.

Note About Prior Art

I found this on the internet, it might help me get going quicker but seems written to do a few tasks only:

https://github.com/faahmed/goflint

I am also heavily influenced to do this by nick [at] craig-wood.com due to this repo:

https://github.com/ncw/gmp

Authors

Kris Hunt

Contributors

https://github.com/x9xhack

Name		Name	Last commit message	Last commit date
Latest commit History 84 Commits
doc		doc
.gitignore		.gitignore
LICENSE		LICENSE
README.md		README.md
flint.go		flint.go
flint_fmpq.go		flint_fmpq.go
flint_fmpq_test.go		flint_fmpq_test.go
flint_fmpz_lll.go		flint_fmpz_lll.go
flint_fmpz_mat.go		flint_fmpz_mat.go
flint_fmpz_mat_test.go		flint_fmpz_mat_test.go
flint_fmpz_mod.go		flint_fmpz_mod.go
flint_fmpz_mod_poly.go		flint_fmpz_mod_poly.go
flint_fmpz_mod_poly_test.go		flint_fmpz_mod_poly_test.go
flint_fmpz_poly.go		flint_fmpz_poly.go
flint_fmpz_poly_test.go		flint_fmpz_poly_test.go
flint_test.go		flint_test.go
go.mod		go.mod

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goflint

Features

Assignments

Comparisons

Formatters

Helpers

Primality Testing and Factorization

Random Number Generation

Conversions

Arithmetic

Bitwise Operations

Roots

Matrices

Lattice Basis Reduction

Univariate Polynomials over the integers.

Univariate Polynomials over the integers modulo n.

Chinese Remainder Theorem

Min and Max

Natural Logarithm

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Formatters

Helpers

Primality Testing and Factorization

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Lattice Basis Reduction

Univariate Polynomials over the integers.

Univariate Polynomials over the integers modulo n.

Chinese Remainder Theorem

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Examples

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