Flint2-0.1.0.5: Haskell bindings for the flint library for number theory
Safe HaskellSafe-Inferred
LanguageHaskell2010

Data.Number.Flint.NMod

Description

 
Synopsis

Integers mod n (word-size n)

data NMod Source #

Constructors

NMod !(ForeignPtr CNMod) 

data CNMod Source #

Constructors

CNMod CMpLimb CMpLimb CFBitCnt 

Instances

Instances details
Storable CNMod Source # 
Instance details

Defined in Data.Number.Flint.NMod.FFI

Methods

sizeOf :: CNMod -> Int #

alignment :: CNMod -> Int #

peekElemOff :: Ptr CNMod -> Int -> IO CNMod #

pokeElemOff :: Ptr CNMod -> Int -> CNMod -> IO () #

peekByteOff :: Ptr b -> Int -> IO CNMod #

pokeByteOff :: Ptr b -> Int -> CNMod -> IO () #

peek :: Ptr CNMod -> IO CNMod #

poke :: Ptr CNMod -> CNMod -> IO () #

Show CNMod Source # 
Instance details

Defined in Data.Number.Flint.NMod.FFI

Methods

showsPrec :: Int -> CNMod -> ShowS #

show :: CNMod -> String #

showList :: [CNMod] -> ShowS #

Memory management

newNMod :: CMpLimb -> IO NMod Source #

Create a new NMod structure

withNMod :: NMod -> (Ptr CNMod -> IO a) -> IO (NMod, a) Source #

Use NMod structure

withNewNMod :: CMpLimb -> (Ptr CNMod -> IO a) -> IO (NMod, a) Source #

nmod_init :: Ptr CNMod -> CMpLimb -> IO () Source #

nmod_init mod n

Initialises the given nmod_t structure for reduction modulo \(n\) with a precomputed inverse.

Modular reduction and arithmetic

_nmod_add :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

_nmod_add a b mod

Returns \(a + b\) modulo mod.n. It is assumed that mod is no more than FLINT_BITS - 1 bits. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

nmod_add :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_add a b mod

Returns \(a + b\) modulo mod.n. No assumptions are made about mod.n. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

_nmod_sub :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

_nmod_sub a b mod

Returns \(a - b\) modulo mod.n. It is assumed that mod is no more than FLINT_BITS - 1 bits. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

nmod_sub :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_sub a b mod

Returns \(a - b\) modulo mod.n. No assumptions are made about mod.n. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

nmod_neg :: CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_neg a mod

Returns \(-a\) modulo mod.n. It is assumed that \(a\) is already reduced modulo mod.n, but no assumptions are made about the latter.

nmod_mul :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_mul a b mod

Returns \(ab\) modulo mod.n. No assumptions are made about mod.n. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

_nmod_mul_fullword :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

_nmod_mul_fullword a b mod

Returns \(ab\) modulo mod.n. Requires that mod.n is exactly FLINT_BITS large. It is assumed that \(a\) and \(b\) are already reduced modulo mod.n.

nmod_inv :: CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_inv a mod

Returns \(a^{-1}\) modulo mod.n. The inverse is assumed to exist.

nmod_div :: CMpLimb -> CMpLimb -> Ptr CNMod -> IO CMpLimb Source #

nmod_div a b mod

Returns \(ab^{-1}\) modulo mod.n. The inverse of \(b\) is assumed to exist. It is assumed that \(a\) is already reduced modulo mod.n.

nmod_pow_ui :: CMpLimb -> CULong -> Ptr CNMod -> IO CMpLimb Source #

nmod_pow_ui a e mod

Returns \(a^e\) modulo mod.n. No assumptions are made about mod.n. It is assumed that \(a\) is already reduced modulo mod.n.

Discrete Logarithms via Pohlig-Hellman

data NModDiscreteLogPohligHellman Source #

Constructors

NModDiscreteLogPohligHellman !(ForeignPtr CNModDiscreteLogPohligHellman) 

Instances

Instances details
Storable CNModDiscreteLogPohligHellman Source # 
Instance details

Defined in Data.Number.Flint.NMod.FFI

Methods

sizeOf :: CNModDiscreteLogPohligHellman -> Int #

alignment :: CNModDiscreteLogPohligHellman -> Int #

peekElemOff :: Ptr CNModDiscreteLogPohligHellman -> Int -> IO CNModDiscreteLogPohligHellman #

pokeElemOff :: Ptr CNModDiscreteLogPohligHellman -> Int -> CNModDiscreteLogPohligHellman -> IO () #

peekByteOff :: Ptr b -> Int -> IO CNModDiscreteLogPohligHellman #

pokeByteOff :: Ptr b -> Int -> CNModDiscreteLogPohligHellman -> IO () #

peek :: Ptr CNModDiscreteLogPohligHellman -> IO CNModDiscreteLogPohligHellman #

poke :: Ptr CNModDiscreteLogPohligHellman -> CNModDiscreteLogPohligHellman -> IO () #

type CNModDiscreteLogPohligHellman = CFlint NModDiscreteLogPohligHellman Source #

nmod_discrete_log_pohlig_hellman_init :: Ptr CNModDiscreteLogPohligHellman -> IO () Source #

nmod_discrete_log_pohlig_hellman_init L

Initialize L. Upon initialization L is not ready for computation.

nmod_discrete_log_pohlig_hellman_clear :: Ptr CNModDiscreteLogPohligHellman -> IO () Source #

nmod_discrete_log_pohlig_hellman_clear L

Free any space used by L.

nmod_discrete_log_pohlig_hellman_precompute_prime :: Ptr CNModDiscreteLogPohligHellman -> CMpLimb -> IO CDouble Source #

nmod_discrete_log_pohlig_hellman_precompute_prime L p

Configure L for discrete logarithms modulo p to an internally chosen base. It is assumed that p is prime. The return is an estimate on the number of multiplications needed for one run.

nmod_discrete_log_pohlig_hellman_primitive_root :: Ptr CNModDiscreteLogPohligHellman -> IO CMpLimb Source #

nmod_discrete_log_pohlig_hellman_primitive_root L

Return the internally stored base.

nmod_discrete_log_pohlig_hellman_run :: Ptr CNModDiscreteLogPohligHellman -> CMpLimb -> IO CULong Source #

nmod_discrete_log_pohlig_hellman_run L y

Return the logarithm of y with respect to the internally stored base. y is expected to be reduced modulo the p. The function is undefined if the logarithm does not exist.