{-# LINE 1 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
{-|
module      :  Data.Number.Flint.Fq.NMod.FFI
copyright   :  (c) 2022 Hartmut Monien
license     :  GNU GPL, version 2 or above (see LICENSE)
maintainer  :  hmonien@uni-bonn.de
-}
module Data.Number.Flint.Fq.NMod.FFI (
  -- * Finite fields (word-size characteristic)
    FqNMod (..)
  , CFqNMod (..)
  , newFqNMod
  , withFqNMod
  -- * Context
  , FqNModCtx (..)
  , CFqNModCtx (..)
  , newFqNModCtx
  , newFqNModCtxConway
  , newFqNModCtxModulus
  , withFqNModCtx
  -- * Context Management
  , fq_nmod_ctx_init
  , _fq_nmod_ctx_init_conway
  , fq_nmod_ctx_init_conway
  , fq_nmod_ctx_init_modulus
  , fq_nmod_ctx_clear
  , fq_nmod_ctx_modulus
  , fq_nmod_ctx_degree
  -- , fq_nmod_ctx_prime
  , fq_nmod_ctx_order
  , fq_nmod_ctx_fprint
  , fq_nmod_ctx_print
  , fq_nmod_ctx_randtest
  , fq_nmod_ctx_randtest_reducible
  -- * Memory management
  , fq_nmod_init
  , fq_nmod_init2
  , fq_nmod_clear
  , _fq_nmod_sparse_reduce
  , _fq_nmod_dense_reduce
  , _fq_nmod_reduce
  , fq_nmod_reduce
  -- * Basic arithmetic
  , fq_nmod_add
  , fq_nmod_sub
  , fq_nmod_sub_one
  , fq_nmod_neg
  , fq_nmod_mul
  , fq_nmod_mul_fmpz
  , fq_nmod_mul_si
  , fq_nmod_mul_ui
  , fq_nmod_sqr
  , _fq_nmod_inv
  , fq_nmod_inv
  , fq_nmod_gcdinv
  , _fq_nmod_pow
  , fq_nmod_pow
  , fq_nmod_pow_ui
  -- * Roots
  , fq_nmod_sqrt
  , fq_nmod_pth_root
  , fq_nmod_is_square
  -- * Output
  , fq_nmod_fprint_pretty
  , fq_nmod_print_pretty
  , fq_nmod_fprint
  , fq_nmod_print
  , fq_nmod_get_str
  , fq_nmod_get_str_pretty
  -- * Randomisation
  , fq_nmod_randtest
  , fq_nmod_randtest_not_zero
  , fq_nmod_randtest_dense
  , fq_nmod_rand
  , fq_nmod_rand_not_zero
  -- * Assignments and conversions
  , fq_nmod_set
  , fq_nmod_set_si
  , fq_nmod_set_ui
  , fq_nmod_set_fmpz
  , fq_nmod_swap
  , fq_nmod_zero
  , fq_nmod_one
  , fq_nmod_gen
  , fq_nmod_get_fmpz
  , fq_nmod_get_nmod_poly
  , fq_nmod_set_nmod_poly
  , fq_nmod_get_nmod_mat
  , fq_nmod_set_nmod_mat
  -- * Comparison
  , fq_nmod_is_zero
  , fq_nmod_is_one
  , fq_nmod_equal
  , fq_nmod_is_invertible
  , fq_nmod_is_invertible_f
  , fq_nmod_cmp
  -- * Special functions
  , _fq_nmod_trace
  , fq_nmod_trace
  , _fq_nmod_norm
  , fq_nmod_norm
  , _fq_nmod_frobenius
  , fq_nmod_frobenius
  , fq_nmod_multiplicative_order
  , fq_nmod_is_primitive
  -- * Bit packing
  , fq_nmod_bit_pack
  , fq_nmod_bit_unpack
) where

-- Finite fields (word-size characteristic) ------------------------------------

import Foreign.C.String
import Foreign.C.Types
import qualified Foreign.Concurrent
import Foreign.ForeignPtr
import Foreign.Ptr
import Foreign.Storable
import Foreign.Marshal

import Data.Number.Flint.Flint
import Data.Number.Flint.Fmpz
import Data.Number.Flint.NMod
import Data.Number.Flint.NMod.Types
import Data.Number.Flint.Fq.NMod.Types





-- fq_nmod_t -------------------------------------------------------------------

instance Storable CFqNMod where
  {-# INLINE sizeOf #-}
  sizeOf :: CFqNMod -> Int
sizeOf CFqNMod
_ = (Int
48)
{-# LINE 135 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
  {-# INLINE alignment #-}
  alignment :: CFqNMod -> Int
alignment CFqNMod
_ = Int
8
{-# LINE 137 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
  peek = undefined
  poke :: Ptr CFqNMod -> CFqNMod -> IO ()
poke = Ptr CFqNMod -> CFqNMod -> IO ()
forall a. HasCallStack => a
undefined

newFqNMod :: FqNModCtx -> IO FqNMod
newFqNMod ctx :: FqNModCtx
ctx@(FqNModCtx ForeignPtr CFqNModCtx
ftx) = do
  ForeignPtr CFqNMod
x <- IO (ForeignPtr CFqNMod)
forall a. Storable a => IO (ForeignPtr a)
mallocForeignPtr
  ForeignPtr CFqNMod -> (Ptr CFqNMod -> IO ()) -> IO ()
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNMod
x((Ptr CFqNMod -> IO ()) -> IO ())
-> (Ptr CFqNMod -> IO ()) -> IO ()
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNMod
x -> do
    FqNModCtx -> (Ptr CFqNModCtx -> IO ()) -> IO (FqNModCtx, ())
forall {a}.
FqNModCtx -> (Ptr CFqNModCtx -> IO a) -> IO (FqNModCtx, a)
withFqNModCtx FqNModCtx
ctx ((Ptr CFqNModCtx -> IO ()) -> IO (FqNModCtx, ()))
-> (Ptr CFqNModCtx -> IO ()) -> IO (FqNModCtx, ())
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNModCtx
ctx -> do
      Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()
fq_nmod_init Ptr CFqNMod
x Ptr CFqNModCtx
ctx
    FinalizerEnvPtr CFqNMod CFqNModCtx
-> Ptr CFqNMod -> ForeignPtr CFqNModCtx -> IO ()
forall env a.
FinalizerEnvPtr env a -> Ptr env -> ForeignPtr a -> IO ()
addForeignPtrFinalizerEnv FinalizerEnvPtr CFqNMod CFqNModCtx
p_fq_nmod_clear Ptr CFqNMod
x ForeignPtr CFqNModCtx
ftx
  FqNMod -> IO FqNMod
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (FqNMod -> IO FqNMod) -> FqNMod -> IO FqNMod
forall a b. (a -> b) -> a -> b
$ ForeignPtr CFqNMod -> FqNMod
FqNMod ForeignPtr CFqNMod
x

{-# INLINE withFqNMod #-}
withFqNMod :: FqNMod -> (Ptr CFqNMod -> IO a) -> IO (FqNMod, a)
withFqNMod (FqNMod ForeignPtr CFqNMod
x) Ptr CFqNMod -> IO a
f = do
  ForeignPtr CFqNMod
-> (Ptr CFqNMod -> IO (FqNMod, a)) -> IO (FqNMod, a)
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNMod
x ((Ptr CFqNMod -> IO (FqNMod, a)) -> IO (FqNMod, a))
-> (Ptr CFqNMod -> IO (FqNMod, a)) -> IO (FqNMod, a)
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNMod
px -> Ptr CFqNMod -> IO a
f Ptr CFqNMod
px IO a -> (a -> IO (FqNMod, a)) -> IO (FqNMod, a)
forall a b. IO a -> (a -> IO b) -> IO b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= (FqNMod, a) -> IO (FqNMod, a)
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return ((FqNMod, a) -> IO (FqNMod, a))
-> (a -> (FqNMod, a)) -> a -> IO (FqNMod, a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForeignPtr CFqNMod -> FqNMod
FqNMod ForeignPtr CFqNMod
x,)

-- fq_nmod_ctx_t ---------------------------------------------------------------

instance Storable CFqNModCtx where
  {-# INLINE sizeOf #-}
  sizeOf :: CFqNModCtx -> Int
sizeOf CFqNModCtx
_ = (Int
168)
{-# LINE 157 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
  {-# INLINE alignment #-}
  alignment :: CFqNModCtx -> Int
alignment CFqNModCtx
_ = Int
8
{-# LINE 159 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
  peek ptr = CFqNModCtx
    <$> (return $ castPtr ptr)
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 8) ptr
{-# LINE 162 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 32) ptr
{-# LINE 163 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 36) ptr
{-# LINE 164 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 40) ptr
{-# LINE 165 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 48) ptr
{-# LINE 166 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 56) ptr
{-# LINE 167 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 64) ptr
{-# LINE 168 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 112) ptr
{-# LINE 169 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
    <*> (\hsc_ptr -> peekByteOff hsc_ptr 160) ptr
{-# LINE 170 "src/Data/Number/Flint/Fq/NMod/FFI.hsc" #-}
  poke = undefined

newFqNModCtx :: Fmpz -> CLong -> String -> IO FqNModCtx
newFqNModCtx Fmpz
p CLong
d String
var = do
  ForeignPtr CFqNModCtx
x <- IO (ForeignPtr CFqNModCtx)
forall a. Storable a => IO (ForeignPtr a)
mallocForeignPtr
  ForeignPtr CFqNModCtx
-> (Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ())
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNModCtx
x ((Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ()))
-> (Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ())
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNModCtx
x ->
    Fmpz -> (Ptr CFmpz -> IO ()) -> IO (Fmpz, ())
forall {a}. Fmpz -> (Ptr CFmpz -> IO a) -> IO (Fmpz, a)
withFmpz Fmpz
p ((Ptr CFmpz -> IO ()) -> IO (Fmpz, ()))
-> (Ptr CFmpz -> IO ()) -> IO (Fmpz, ())
forall a b. (a -> b) -> a -> b
$ \Ptr CFmpz
p -> 
      String -> (CString -> IO ()) -> IO ()
forall a. String -> (CString -> IO a) -> IO a
withCString String
var ((CString -> IO ()) -> IO ()) -> (CString -> IO ()) -> IO ()
forall a b. (a -> b) -> a -> b
$ \CString
var -> 
        Ptr CFqNModCtx -> Ptr CFmpz -> CLong -> CString -> IO ()
fq_nmod_ctx_init Ptr CFqNModCtx
x Ptr CFmpz
p CLong
d CString
var
  FinalizerPtr CFqNModCtx -> ForeignPtr CFqNModCtx -> IO ()
forall a. FinalizerPtr a -> ForeignPtr a -> IO ()
addForeignPtrFinalizer FinalizerPtr CFqNModCtx
p_fq_nmod_ctx_clear ForeignPtr CFqNModCtx
x
  FqNModCtx -> IO FqNModCtx
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (FqNModCtx -> IO FqNModCtx) -> FqNModCtx -> IO FqNModCtx
forall a b. (a -> b) -> a -> b
$ ForeignPtr CFqNModCtx -> FqNModCtx
FqNModCtx ForeignPtr CFqNModCtx
x

newFqNModCtxConway :: Fmpz -> CLong -> String -> IO FqNModCtx
newFqNModCtxConway Fmpz
p CLong
d String
var = do
  ForeignPtr CFqNModCtx
x <- IO (ForeignPtr CFqNModCtx)
forall a. Storable a => IO (ForeignPtr a)
mallocForeignPtr
  ForeignPtr CFqNModCtx
-> (Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ())
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNModCtx
x ((Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ()))
-> (Ptr CFqNModCtx -> IO (Fmpz, ())) -> IO (Fmpz, ())
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNModCtx
x ->
    Fmpz -> (Ptr CFmpz -> IO ()) -> IO (Fmpz, ())
forall {a}. Fmpz -> (Ptr CFmpz -> IO a) -> IO (Fmpz, a)
withFmpz Fmpz
p ((Ptr CFmpz -> IO ()) -> IO (Fmpz, ()))
-> (Ptr CFmpz -> IO ()) -> IO (Fmpz, ())
forall a b. (a -> b) -> a -> b
$ \Ptr CFmpz
p -> 
      String -> (CString -> IO ()) -> IO ()
forall a. String -> (CString -> IO a) -> IO a
withCString String
var ((CString -> IO ()) -> IO ()) -> (CString -> IO ()) -> IO ()
forall a b. (a -> b) -> a -> b
$ \CString
var -> 
        Ptr CFqNModCtx -> Ptr CFmpz -> CLong -> CString -> IO ()
fq_nmod_ctx_init_conway Ptr CFqNModCtx
x Ptr CFmpz
p CLong
d CString
var
  FinalizerPtr CFqNModCtx -> ForeignPtr CFqNModCtx -> IO ()
forall a. FinalizerPtr a -> ForeignPtr a -> IO ()
addForeignPtrFinalizer FinalizerPtr CFqNModCtx
p_fq_nmod_ctx_clear ForeignPtr CFqNModCtx
x
  FqNModCtx -> IO FqNModCtx
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (FqNModCtx -> IO FqNModCtx) -> FqNModCtx -> IO FqNModCtx
forall a b. (a -> b) -> a -> b
$ ForeignPtr CFqNModCtx -> FqNModCtx
FqNModCtx ForeignPtr CFqNModCtx
x

newFqNModCtxModulus :: Ptr CNModPoly -> String -> IO FqNModCtx
newFqNModCtxModulus Ptr CNModPoly
modulus String
var = do
  ForeignPtr CFqNModCtx
x <- IO (ForeignPtr CFqNModCtx)
forall a. Storable a => IO (ForeignPtr a)
mallocForeignPtr
  ForeignPtr CFqNModCtx -> (Ptr CFqNModCtx -> IO ()) -> IO ()
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNModCtx
x ((Ptr CFqNModCtx -> IO ()) -> IO ())
-> (Ptr CFqNModCtx -> IO ()) -> IO ()
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNModCtx
x ->
    String -> (CString -> IO ()) -> IO ()
forall a. String -> (CString -> IO a) -> IO a
withCString String
var ((CString -> IO ()) -> IO ()) -> (CString -> IO ()) -> IO ()
forall a b. (a -> b) -> a -> b
$ \CString
var ->
      Ptr CFqNModCtx -> Ptr CNModPoly -> CString -> IO ()
fq_nmod_ctx_init_modulus Ptr CFqNModCtx
x Ptr CNModPoly
modulus CString
var 
  FinalizerPtr CFqNModCtx -> ForeignPtr CFqNModCtx -> IO ()
forall a. FinalizerPtr a -> ForeignPtr a -> IO ()
addForeignPtrFinalizer FinalizerPtr CFqNModCtx
p_fq_nmod_ctx_clear ForeignPtr CFqNModCtx
x
  FqNModCtx -> IO FqNModCtx
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return (FqNModCtx -> IO FqNModCtx) -> FqNModCtx -> IO FqNModCtx
forall a b. (a -> b) -> a -> b
$ ForeignPtr CFqNModCtx -> FqNModCtx
FqNModCtx ForeignPtr CFqNModCtx
x
  
{-# INLINE withFqNModCtx #-}
withFqNModCtx :: FqNModCtx -> (Ptr CFqNModCtx -> IO a) -> IO (FqNModCtx, a)
withFqNModCtx (FqNModCtx ForeignPtr CFqNModCtx
x) Ptr CFqNModCtx -> IO a
f = do
  ForeignPtr CFqNModCtx
-> (Ptr CFqNModCtx -> IO (FqNModCtx, a)) -> IO (FqNModCtx, a)
forall a b. ForeignPtr a -> (Ptr a -> IO b) -> IO b
withForeignPtr ForeignPtr CFqNModCtx
x ((Ptr CFqNModCtx -> IO (FqNModCtx, a)) -> IO (FqNModCtx, a))
-> (Ptr CFqNModCtx -> IO (FqNModCtx, a)) -> IO (FqNModCtx, a)
forall a b. (a -> b) -> a -> b
$ \Ptr CFqNModCtx
px -> Ptr CFqNModCtx -> IO a
f Ptr CFqNModCtx
px IO a -> (a -> IO (FqNModCtx, a)) -> IO (FqNModCtx, a)
forall a b. IO a -> (a -> IO b) -> IO b
forall (m :: * -> *) a b. Monad m => m a -> (a -> m b) -> m b
>>= (FqNModCtx, a) -> IO (FqNModCtx, a)
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return ((FqNModCtx, a) -> IO (FqNModCtx, a))
-> (a -> (FqNModCtx, a)) -> a -> IO (FqNModCtx, a)
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (ForeignPtr CFqNModCtx -> FqNModCtx
FqNModCtx ForeignPtr CFqNModCtx
x,)

-- Context Management ----------------------------------------------------------

-- | /fq_nmod_ctx_init/ /ctx/ /p/ /d/ /var/ 
--
-- Initialises the context for prime \(p\) and extension degree \(d\), with
-- name @var@ for the generator. By default, it will try use a Conway
-- polynomial; if one is not available, a random irreducible polynomial
-- will be used.
-- 
-- Assumes that \(p\) is a prime.
-- 
-- Assumes that the string @var@ is a null-terminated string of length at
-- least one.
foreign import ccall "fq_nmod.h fq_nmod_ctx_init"
  fq_nmod_ctx_init :: Ptr CFqNModCtx -> Ptr CFmpz -> CLong -> CString -> IO ()

-- | /_fq_nmod_ctx_init_conway/ /ctx/ /p/ /d/ /var/ 
--
-- Attempts to initialise the context for prime \(p\) and extension degree
-- \(d\), with name @var@ for the generator using a Conway polynomial for
-- the modulus.
-- 
-- Returns \(1\) if the Conway polynomial is in the database for the given
-- size and the initialization is successful; otherwise, returns \(0\).
-- 
-- Assumes that \(p\) is a prime.
-- 
-- Assumes that the string @var@ is a null-terminated string of length at
-- least one.
foreign import ccall "fq_nmod.h _fq_nmod_ctx_init_conway"
  _fq_nmod_ctx_init_conway :: Ptr CFqNModCtx -> Ptr CFmpz -> CLong -> CString -> IO CInt

-- | /fq_nmod_ctx_init_conway/ /ctx/ /p/ /d/ /var/ 
--
-- Initialises the context for prime \(p\) and extension degree \(d\), with
-- name @var@ for the generator using a Conway polynomial for the modulus.
-- 
-- Assumes that \(p\) is a prime.
-- 
-- Assumes that the string @var@ is a null-terminated string of length at
-- least one.
foreign import ccall "fq_nmod.h fq_nmod_ctx_init_conway"
  fq_nmod_ctx_init_conway :: Ptr CFqNModCtx -> Ptr CFmpz -> CLong -> CString -> IO ()

-- | /fq_nmod_ctx_init_modulus/ /ctx/ /modulus/ /var/ 
--
-- Initialises the context for given @modulus@ with name @var@ for the
-- generator.
-- 
-- Assumes that @modulus@ is an irreducible polynomial over
-- \(\mathbf{F}_{p}\).
-- 
-- Assumes that the string @var@ is a null-terminated string of length at
-- least one.
foreign import ccall "fq_nmod.h fq_nmod_ctx_init_modulus"
  fq_nmod_ctx_init_modulus :: Ptr CFqNModCtx -> Ptr CNModPoly -> CString -> IO ()

-- | /fq_nmod_ctx_clear/ /ctx/ 
--
-- Clears all memory that has been allocated as part of the context.
foreign import ccall "fq_nmod.h fq_nmod_ctx_clear"
  fq_nmod_ctx_clear :: Ptr CFqNModCtx -> IO ()

foreign import ccall "fq_nmod.h &fq_nmod_ctx_clear"
  p_fq_nmod_ctx_clear :: FunPtr (Ptr CFqNModCtx -> IO ())

-- | /fq_nmod_ctx_modulus/ /ctx/ 
--
-- Returns a pointer to the modulus in the context.
foreign import ccall "fq_nmod.h fq_nmod_ctx_modulus"
  fq_nmod_ctx_modulus :: Ptr CFqNModCtx -> IO (Ptr (Ptr CNModPoly))

-- | /fq_nmod_ctx_degree/ /ctx/ 
--
-- Returns the degree of the field extension
-- \([\mathbf{F}_{q} : \mathbf{F}_{p}]\), which is equal to \(\log_{p} q\).
foreign import ccall "fq_nmod.h fq_nmod_ctx_degree"
  fq_nmod_ctx_degree :: Ptr CFqNModCtx -> IO CLong

-- | /fq_nmod_ctx_prime/ /ctx/ 
--
-- Returns a pointer to the prime \(p\) in the context.
-- foreign import ccall "fq_nmod.h fq_nmod_ctx_prime"
fq_nmod_ctx_prime :: Ptr CFqNModCtx -> IO (Ptr CFmpz)
fq_nmod_ctx_prime :: Ptr CFqNModCtx -> IO (Ptr CFmpz)
fq_nmod_ctx_prime Ptr CFqNModCtx
ctx = do
  CFqNModCtx Ptr CFmpz
p Ptr CNMod
_ CInt
_ CInt
_ Ptr CMpLimb
_ Ptr CLong
_ Ptr CLong
_ Ptr CNModPoly
_ Ptr CNModPoly
_ CString
_ <- Ptr CFqNModCtx -> IO CFqNModCtx
forall a. Storable a => Ptr a -> IO a
peek Ptr CFqNModCtx
ctx
  Ptr CFmpz -> IO (Ptr CFmpz)
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return Ptr CFmpz
p
  
-- | /fq_nmod_ctx_order/ /f/ /ctx/ 
--
-- Sets \(f\) to be the size of the finite field.
foreign import ccall "fq_nmod.h fq_nmod_ctx_order"
  fq_nmod_ctx_order :: Ptr CFmpz -> Ptr CFqNModCtx -> IO ()

-- Input and Output ------------------------------------------------------------

-- | /fq_nmod_ctx_get_str/ /ctx/ 
--
-- Return a string representation of the context information. 
foreign import ccall "fq_nmod.h fq_nmod_ctx_get_str"
  fq_nmod_ctx_get_str :: Ptr CFqNModCtx -> IO CString
  
-- | /fq_nmod_ctx_fprint/ /file/ /ctx/ 
--
-- Prints the context information to @file@. Returns 1 for a success and a
-- negative number for an error.
foreign import ccall "fq_nmod.h fq_nmod_ctx_fprint"
  fq_nmod_ctx_fprint :: Ptr CFile -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_ctx_print/ /ctx/ 
--
-- Prints the context information to @stdout@.
fq_nmod_ctx_print :: Ptr CFqNModCtx -> IO ()
fq_nmod_ctx_print :: Ptr CFqNModCtx -> IO ()
fq_nmod_ctx_print Ptr CFqNModCtx
ctx = do
  (Ptr CFqNModCtx -> IO CString) -> Ptr CFqNModCtx -> IO CInt
forall a. (Ptr a -> IO CString) -> Ptr a -> IO CInt
printCStr Ptr CFqNModCtx -> IO CString
fq_nmod_ctx_get_str Ptr CFqNModCtx
ctx
  () -> IO ()
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return ()

-- | /fq_nmod_ctx_randtest/ /ctx/ 
--
-- Initializes @ctx@ to a random finite field. Assumes that
-- @fq_nmod_ctx_init@ has not been called on @ctx@ already.
foreign import ccall "fq_nmod.h fq_nmod_ctx_randtest"
  fq_nmod_ctx_randtest :: Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_ctx_randtest_reducible/ /ctx/ 
--
-- Initializes @ctx@ to a random extension of a word-sized prime field. The
-- modulus may or may not be irreducible. Assumes that @fq_nmod_ctx_init@
-- has not been called on @ctx@ already.
foreign import ccall "fq_nmod.h fq_nmod_ctx_randtest_reducible"
  fq_nmod_ctx_randtest_reducible :: Ptr CFqNModCtx -> IO ()

-- Memory management -----------------------------------------------------------

-- | /fq_nmod_init/ /rop/ /ctx/ 
--
-- Initialises the element @rop@, setting its value to \(0\). Currently,
-- the behaviour is identical to @fq_nmod_init2@, as it also ensures @rop@
-- has enough space for it to be an element of @ctx@, this may change in
-- the future.
foreign import ccall "fq_nmod.h fq_nmod_init"
  fq_nmod_init :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_init2/ /rop/ /ctx/ 
--
-- Initialises @rop@ with at least enough space for it to be an element of
-- @ctx@ and sets it to \(0\).
foreign import ccall "fq_nmod.h fq_nmod_init2"
  fq_nmod_init2 :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_clear/ /rop/ /ctx/ 
--
-- Clears the element @rop@.
foreign import ccall "fq_nmod.h fq_nmod_clear"
  fq_nmod_clear :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

foreign import ccall "fq_nmod.h &fq_nmod_clear"
  p_fq_nmod_clear :: FunPtr (Ptr CFqNMod -> Ptr CFqNModCtx -> IO ())

-- | /_fq_nmod_sparse_reduce/ /R/ /lenR/ /ctx/ 
--
-- Reduces @(R, lenR)@ modulo the polynomial \(f\) given by the modulus of
-- @ctx@.
foreign import ccall "fq_nmod.h _fq_nmod_sparse_reduce"
  _fq_nmod_sparse_reduce :: Ptr CMp -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_dense_reduce/ /R/ /lenR/ /ctx/ 
--
-- Reduces @(R, lenR)@ modulo the polynomial \(f\) given by the modulus of
-- @ctx@ using Newton division.
foreign import ccall "fq_nmod.h _fq_nmod_dense_reduce"
  _fq_nmod_dense_reduce :: Ptr CMp -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_reduce/ /r/ /lenR/ /ctx/ 
--
-- Reduces @(R, lenR)@ modulo the polynomial \(f\) given by the modulus of
-- @ctx@. Does either sparse or dense reduction based on
-- @ctx->sparse_modulus@.
foreign import ccall "fq_nmod.h _fq_nmod_reduce"
  _fq_nmod_reduce :: Ptr CMp -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_reduce/ /rop/ /ctx/ 
--
-- Reduces the polynomial @rop@ as an element of
-- \(\mathbf{F}_p[X] / (f(X))\).
foreign import ccall "fq_nmod.h fq_nmod_reduce"
  fq_nmod_reduce :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- Basic arithmetic ------------------------------------------------------------

-- | /fq_nmod_add/ /rop/ /op1/ /op2/ /ctx/ 
--
-- Sets @rop@ to the sum of @op1@ and @op2@.
foreign import ccall "fq_nmod.h fq_nmod_add"
  fq_nmod_add :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_sub/ /rop/ /op1/ /op2/ /ctx/ 
--
-- Sets @rop@ to the difference of @op1@ and @op2@.
foreign import ccall "fq_nmod.h fq_nmod_sub"
  fq_nmod_sub :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_sub_one/ /rop/ /op1/ /ctx/ 
--
-- Sets @rop@ to the difference of @op1@ and \(1\).
foreign import ccall "fq_nmod.h fq_nmod_sub_one"
  fq_nmod_sub_one :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_neg/ /rop/ /op/ /ctx/ 
--
-- Sets @rop@ to the negative of @op@.
foreign import ccall "fq_nmod.h fq_nmod_neg"
  fq_nmod_neg :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_mul/ /rop/ /op1/ /op2/ /ctx/ 
--
-- Sets @rop@ to the product of @op1@ and @op2@, reducing the output in the
-- given context.
foreign import ccall "fq_nmod.h fq_nmod_mul"
  fq_nmod_mul :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_mul_fmpz/ /rop/ /op/ /x/ /ctx/ 
--
-- Sets @rop@ to the product of @op@ and \(x\), reducing the output in the
-- given context.
foreign import ccall "fq_nmod.h fq_nmod_mul_fmpz"
  fq_nmod_mul_fmpz :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFmpz -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_mul_si/ /rop/ /op/ /x/ /ctx/ 
--
-- Sets @rop@ to the product of @op@ and \(x\), reducing the output in the
-- given context.
foreign import ccall "fq_nmod.h fq_nmod_mul_si"
  fq_nmod_mul_si :: Ptr CFqNMod -> Ptr CFqNMod -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_mul_ui/ /rop/ /op/ /x/ /ctx/ 
--
-- Sets @rop@ to the product of @op@ and \(x\), reducing the output in the
-- given context.
foreign import ccall "fq_nmod.h fq_nmod_mul_ui"
  fq_nmod_mul_ui :: Ptr CFqNMod -> Ptr CFqNMod -> CULong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_sqr/ /rop/ /op/ /ctx/ 
--
-- Sets @rop@ to the square of @op@, reducing the output in the given
-- context.
foreign import ccall "fq_nmod.h fq_nmod_sqr"
  fq_nmod_sqr :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_inv/ /rop/ /op/ /len/ /ctx/ 
--
-- Sets @(rop, d)@ to the inverse of the non-zero element @(op, len)@.
foreign import ccall "fq_nmod.h _fq_nmod_inv"
  _fq_nmod_inv :: Ptr (Ptr CMp) -> Ptr (Ptr CMp) -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_inv/ /rop/ /op/ /ctx/ 
--
-- Sets @rop@ to the inverse of the non-zero element @op@.
foreign import ccall "fq_nmod.h fq_nmod_inv"
  fq_nmod_inv :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_gcdinv/ /f/ /inv/ /op/ /ctx/ 
--
-- Sets @inv@ to be the inverse of @op@ modulo the modulus of @ctx@. If
-- @op@ is not invertible, then @f@ is set to a factor of the modulus;
-- otherwise, it is set to one.
foreign import ccall "fq_nmod.h fq_nmod_gcdinv"
  fq_nmod_gcdinv :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_pow/ /rop/ /op/ /len/ /e/ /ctx/ 
--
-- Sets @(rop, 2*d-1)@ to @(op,len)@ raised to the power \(e\), reduced
-- modulo \(f(X)\), the modulus of @ctx@.
-- 
-- Assumes that \(e \geq 0\) and that @len@ is positive and at most \(d\).
-- 
-- Although we require that @rop@ provides space for \(2d - 1\)
-- coefficients, the output will be reduced modulo \(f(X)\), which is a
-- polynomial of degree \(d\).
-- 
-- Does not support aliasing.
foreign import ccall "fq_nmod.h _fq_nmod_pow"
  _fq_nmod_pow :: Ptr (Ptr CMp) -> Ptr (Ptr CMp) -> CLong -> Ptr CFmpz -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_pow/ /rop/ /op/ /e/ /ctx/ 
--
-- Sets @rop@ to @op@ raised to the power \(e\).
-- 
-- Currently assumes that \(e \geq 0\).
-- 
-- Note that for any input @op@, @rop@ is set to \(1\) whenever \(e = 0\).
foreign import ccall "fq_nmod.h fq_nmod_pow"
  fq_nmod_pow :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFmpz -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_pow_ui/ /rop/ /op/ /e/ /ctx/ 
--
-- Sets @rop@ to @op@ raised to the power \(e\).
-- 
-- Currently assumes that \(e \geq 0\).
-- 
-- Note that for any input @op@, @rop@ is set to \(1\) whenever \(e = 0\).
foreign import ccall "fq_nmod.h fq_nmod_pow_ui"
  fq_nmod_pow_ui :: Ptr CFqNMod -> Ptr CFqNMod -> CULong -> Ptr CFqNModCtx -> IO ()

-- Roots -----------------------------------------------------------------------

-- | /fq_nmod_sqrt/ /rop/ /op1/ /ctx/ 
--
-- Sets @rop@ to the square root of @op1@ if it is a square, and return
-- \(1\), otherwise return \(0\).
foreign import ccall "fq_nmod.h fq_nmod_sqrt"
  fq_nmod_sqrt :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_pth_root/ /rop/ /op1/ /ctx/ 
--
-- Sets @rop@ to a \(p^{\textrm{th}}\) root of @op1@. Currently, this
-- computes the root by raising @op1@ to \(p^{d-1}\) where \(d\) is the
-- degree of the extension.
foreign import ccall "fq_nmod.h fq_nmod_pth_root"
  fq_nmod_pth_root :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_is_square/ /op/ /ctx/ 
--
-- Return @1@ if @op@ is a square.
foreign import ccall "fq_nmod.h fq_nmod_is_square"
  fq_nmod_is_square :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- Output ----------------------------------------------------------------------

-- | /fq_nmod_fprint_pretty/ /file/ /op/ /ctx/ 
--
-- Prints a pretty representation of @op@ to @file@.
-- 
-- In case of success, returns a positive value. In case of failure,
-- returns a non-positive value.
foreign import ccall "fq_nmod.h fq_nmod_fprint_pretty"
  fq_nmod_fprint_pretty :: Ptr CFile -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_print_pretty/ /op/ /ctx/ 
--
-- Prints a pretty representation of @op@ to @stdout@.
-- 
-- In case of success, returns a positive value. In case of failure,
-- returns a non-positive value.
fq_nmod_print_pretty :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt
fq_nmod_print_pretty :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt
fq_nmod_print_pretty Ptr CFqNMod
op Ptr CFqNModCtx
ctx = do
  (Ptr CFqNMod -> IO CString) -> Ptr CFqNMod -> IO CInt
forall a. (Ptr a -> IO CString) -> Ptr a -> IO CInt
printCStr (Ptr CFqNMod -> Ptr CFqNModCtx -> IO CString
`fq_nmod_get_str_pretty` Ptr CFqNModCtx
ctx) Ptr CFqNMod
op

-- | /fq_nmod_fprint/ /file/ /op/ /ctx/ 
--
-- Prints a representation of @op@ to @file@.
-- 
-- For further details on the representation used, see
-- @nmod_poly_fprint()@.
foreign import ccall "fq_nmod.h fq_nmod_fprint"
  fq_nmod_fprint :: Ptr CFile -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_print/ /op/ /ctx/ 
--
-- Prints a representation of @op@ to @stdout@.
-- 
-- For further details on the representation used, see @nmod_poly_print()@.
fq_nmod_print :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()
fq_nmod_print :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()
fq_nmod_print Ptr CFqNMod
op Ptr CFqNModCtx
ctx = do
  (Ptr CFqNMod -> IO CString) -> Ptr CFqNMod -> IO CInt
forall a. (Ptr a -> IO CString) -> Ptr a -> IO CInt
printCStr (Ptr CFqNMod -> Ptr CFqNModCtx -> IO CString
`fq_nmod_get_str` Ptr CFqNModCtx
ctx) Ptr CFqNMod
op
  () -> IO ()
forall a. a -> IO a
forall (m :: * -> *) a. Monad m => a -> m a
return ()

-- | /fq_nmod_get_str/ /op/ /ctx/ 
--
-- Returns the plain FLINT string representation of the element @op@.
foreign import ccall "fq_nmod.h fq_nmod_get_str"
  fq_nmod_get_str :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CString

-- | /fq_nmod_get_str_pretty/ /op/ /ctx/ 
--
-- Returns a pretty representation of the element @op@ using the
-- null-terminated string @x@ as the variable name.
foreign import ccall "fq_nmod.h fq_nmod_get_str_pretty"
  fq_nmod_get_str_pretty :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CString

-- Randomisation ---------------------------------------------------------------

-- | /fq_nmod_randtest/ /rop/ /state/ /ctx/ 
--
-- Generates a random element of \(\mathbf{F}_q\).
foreign import ccall "fq_nmod.h fq_nmod_randtest"
  fq_nmod_randtest :: Ptr CFqNMod -> Ptr CFRandState -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_randtest_not_zero/ /rop/ /state/ /ctx/ 
--
-- Generates a random non-zero element of \(\mathbf{F}_q\).
foreign import ccall "fq_nmod.h fq_nmod_randtest_not_zero"
  fq_nmod_randtest_not_zero :: Ptr CFqNMod -> Ptr CFRandState -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_randtest_dense/ /rop/ /state/ /ctx/ 
--
-- Generates a random element of \(\mathbf{F}_q\) which has an underlying
-- polynomial with dense coefficients.
foreign import ccall "fq_nmod.h fq_nmod_randtest_dense"
  fq_nmod_randtest_dense :: Ptr CFqNMod -> Ptr CFRandState -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_rand/ /rop/ /state/ /ctx/ 
--
-- Generates a high quality random element of \(\mathbf{F}_q\).
foreign import ccall "fq_nmod.h fq_nmod_rand"
  fq_nmod_rand :: Ptr CFqNMod -> Ptr CFRandState -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_rand_not_zero/ /rop/ /state/ /ctx/ 
--
-- Generates a high quality non-zero random element of \(\mathbf{F}_q\).
foreign import ccall "fq_nmod.h fq_nmod_rand_not_zero"
  fq_nmod_rand_not_zero :: Ptr CFqNMod -> Ptr CFRandState -> Ptr CFqNModCtx -> IO ()

-- Assignments and conversions -------------------------------------------------

-- | /fq_nmod_set/ /rop/ /op/ /ctx/ 
--
-- Sets @rop@ to @op@.
foreign import ccall "fq_nmod.h fq_nmod_set"
  fq_nmod_set :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_set_si/ /rop/ /x/ /ctx/ 
--
-- Sets @rop@ to @x@, considered as an element of \(\mathbf{F}_p\).
foreign import ccall "fq_nmod.h fq_nmod_set_si"
  fq_nmod_set_si :: Ptr CFqNMod -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_set_ui/ /rop/ /x/ /ctx/ 
--
-- Sets @rop@ to @x@, considered as an element of \(\mathbf{F}_p\).
foreign import ccall "fq_nmod.h fq_nmod_set_ui"
  fq_nmod_set_ui :: Ptr CFqNMod -> CULong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_set_fmpz/ /rop/ /x/ /ctx/ 
--
-- Sets @rop@ to @x@, considered as an element of \(\mathbf{F}_p\).
foreign import ccall "fq_nmod.h fq_nmod_set_fmpz"
  fq_nmod_set_fmpz :: Ptr CFqNMod -> Ptr CFmpz -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_swap/ /op1/ /op2/ /ctx/ 
--
-- Swaps the two elements @op1@ and @op2@.
foreign import ccall "fq_nmod.h fq_nmod_swap"
  fq_nmod_swap :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_zero/ /rop/ /ctx/ 
--
-- Sets @rop@ to zero.
foreign import ccall "fq_nmod.h fq_nmod_zero"
  fq_nmod_zero :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_one/ /rop/ /ctx/ 
--
-- Sets @rop@ to one, reduced in the given context.
foreign import ccall "fq_nmod.h fq_nmod_one"
  fq_nmod_one :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_gen/ /rop/ /ctx/ 
--
-- Sets @rop@ to a generator for the finite field. There is no guarantee
-- this is a multiplicative generator of the finite field.
foreign import ccall "fq_nmod.h fq_nmod_gen"
  fq_nmod_gen :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_get_fmpz/ /rop/ /op/ /ctx/ 
--
-- If @op@ has a lift to the integers, return \(1\) and set @rop@ to the
-- lift in \([0,p)\). Otherwise, return \(0\) and leave \(rop\) undefined.
foreign import ccall "fq_nmod.h fq_nmod_get_fmpz"
  fq_nmod_get_fmpz :: Ptr CFmpz -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_get_nmod_poly/ /a/ /b/ /ctx/ 
--
-- Set @a@ to a representative of @b@ in @ctx@. The representatives are
-- taken in \((\mathbb{Z}/p\mathbb{Z})[x]/h(x)\) where \(h(x)\) is the
-- defining polynomial in @ctx@.
foreign import ccall "fq_nmod.h fq_nmod_get_nmod_poly"
  fq_nmod_get_nmod_poly :: Ptr CNModPoly -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_set_nmod_poly/ /a/ /b/ /ctx/ 
--
-- Set @a@ to the element in @ctx@ with representative @b@. The
-- representatives are taken in \((\mathbb{Z}/p\mathbb{Z})[x]/h(x)\) where
-- \(h(x)\) is the defining polynomial in @ctx@.
foreign import ccall "fq_nmod.h fq_nmod_set_nmod_poly"
  fq_nmod_set_nmod_poly :: Ptr CFqNMod -> Ptr CNModPoly -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_get_nmod_mat/ /col/ /a/ /ctx/ 
--
-- Convert @a@ to a column vector of length @degree(ctx)@.
foreign import ccall "fq_nmod.h fq_nmod_get_nmod_mat"
  fq_nmod_get_nmod_mat :: Ptr CNModMat -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_set_nmod_mat/ /a/ /col/ /ctx/ 
--
-- Convert a column vector @col@ of length @degree(ctx)@ to an element of
-- @ctx@.
foreign import ccall "fq_nmod.h fq_nmod_set_nmod_mat"
  fq_nmod_set_nmod_mat :: Ptr CFqNMod -> Ptr CNModMat -> Ptr CFqNModCtx -> IO ()

-- Comparison ------------------------------------------------------------------

-- | /fq_nmod_is_zero/ /op/ /ctx/ 
--
-- Returns whether @op@ is equal to zero.
foreign import ccall "fq_nmod.h fq_nmod_is_zero"
  fq_nmod_is_zero :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_is_one/ /op/ /ctx/ 
--
-- Returns whether @op@ is equal to one.
foreign import ccall "fq_nmod.h fq_nmod_is_one"
  fq_nmod_is_one :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_equal/ /op1/ /op2/ /ctx/ 
--
-- Returns whether @op1@ and @op2@ are equal.
foreign import ccall "fq_nmod.h fq_nmod_equal"
  fq_nmod_equal :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_is_invertible/ /op/ /ctx/ 
--
-- Returns whether @op@ is an invertible element.
foreign import ccall "fq_nmod.h fq_nmod_is_invertible"
  fq_nmod_is_invertible :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_is_invertible_f/ /f/ /op/ /ctx/ 
--
-- Returns whether @op@ is an invertible element. If it is not, then @f@ is
-- set to a factor of the modulus.
foreign import ccall "fq_nmod.h fq_nmod_is_invertible_f"
  fq_nmod_is_invertible_f :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_cmp/ /a/ /b/ /ctx/ 
--
-- Return @1@ (resp. @-1@, or @0@) if @a@ is after (resp. before, same as)
-- @b@ in some arbitrary but fixed total ordering of the elements.
foreign import ccall "fq_nmod.h fq_nmod_cmp"
  fq_nmod_cmp :: Ptr CFqNMod -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- Special functions -----------------------------------------------------------

-- | /_fq_nmod_trace/ /rop/ /op/ /len/ /ctx/ 
--
-- Sets @rop@ to the trace of the non-zero element @(op, len)@ in
-- \(\mathbf{F}_{q}\).
foreign import ccall "fq_nmod.h _fq_nmod_trace"
  _fq_nmod_trace :: Ptr CFmpz -> Ptr (Ptr CMp) -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_trace/ /rop/ /op/ /ctx/ 
--
-- Sets @rop@ to the trace of @op@.
-- 
-- For an element \(a \in \mathbf{F}_q\), multiplication by \(a\) defines a
-- \(\mathbf{F}_p\)-linear map on \(\mathbf{F}_q\). We define the trace of
-- \(a\) as the trace of this map. Equivalently, if \(\Sigma\) generates
-- \(\operatorname{Gal}(\mathbf{F}_q / \mathbf{F}_p)\) then the trace of
-- \(a\) is equal to \(\sum_{i=0}^{d-1} \Sigma^i (a)\), where \(d =
-- \log_{p} q\).
foreign import ccall "fq_nmod.h fq_nmod_trace"
  fq_nmod_trace :: Ptr CFmpz -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_norm/ /rop/ /op/ /len/ /ctx/ 
--
-- Sets @rop@ to the norm of the non-zero element @(op, len)@ in
-- \(\mathbf{F}_{q}\).
foreign import ccall "fq_nmod.h _fq_nmod_norm"
  _fq_nmod_norm :: Ptr CFmpz -> Ptr (Ptr CMp) -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_norm/ /rop/ /op/ /ctx/ 
--
-- Computes the norm of @op@.
-- 
-- For an element \(a \in \mathbf{F}_q\), multiplication by \(a\) defines a
-- \(\mathbf{F}_p\)-linear map on \(\mathbf{F}_q\). We define the norm of
-- \(a\) as the determinant of this map. Equivalently, if \(\Sigma\)
-- generates \(\operatorname{Gal}(\mathbf{F}_q / \mathbf{F}_p)\) then the
-- trace of \(a\) is equal to \(\prod_{i=0}^{d-1} \Sigma^i (a)\), where
-- \(d = \text{dim}_{\mathbf{F}_p}(\mathbf{F}_q)\).
-- 
-- Algorithm selection is automatic depending on the input.
foreign import ccall "fq_nmod.h fq_nmod_norm"
  fq_nmod_norm :: Ptr CFmpz -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO ()

-- | /_fq_nmod_frobenius/ /rop/ /op/ /len/ /e/ /ctx/ 
--
-- Sets @(rop, 2d-1)@ to the image of @(op, len)@ under the Frobenius
-- operator raised to the e-th power, assuming that neither @op@ nor @e@
-- are zero.
foreign import ccall "fq_nmod.h _fq_nmod_frobenius"
  _fq_nmod_frobenius :: Ptr (Ptr CMp) -> Ptr (Ptr CMp) -> CLong -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_frobenius/ /rop/ /op/ /e/ /ctx/ 
--
-- Evaluates the homomorphism \(\Sigma^e\) at @op@.
-- 
-- Recall that \(\mathbf{F}_q / \mathbf{F}_p\) is Galois with Galois group
-- \(\langle \sigma \rangle\), which is also isomorphic to
-- \(\mathbf{Z}/d\mathbf{Z}\), where
-- \(\sigma \in \operatorname{Gal}(\mathbf{F}_q/\mathbf{F}_p)\) is the
-- Frobenius element \(\sigma \colon x \mapsto x^p\).
foreign import ccall "fq_nmod.h fq_nmod_frobenius"
  fq_nmod_frobenius :: Ptr CFqNMod -> Ptr CFqNMod -> CLong -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_multiplicative_order/ /ord/ /op/ /ctx/ 
--
-- Computes the order of @op@ as an element of the multiplicative group of
-- @ctx@.
-- 
-- Returns 0 if @op@ is 0, otherwise it returns 1 if @op@ is a generator of
-- the multiplicative group, and -1 if it is not.
-- 
-- This function can also be used to check primitivity of a generator of a
-- finite field whose defining polynomial is not primitive.
foreign import ccall "fq_nmod.h fq_nmod_multiplicative_order"
  fq_nmod_multiplicative_order :: Ptr CFmpz -> Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- | /fq_nmod_is_primitive/ /op/ /ctx/ 
--
-- Returns whether @op@ is primitive, i.e., whether it is a generator of
-- the multiplicative group of @ctx@.
foreign import ccall "fq_nmod.h fq_nmod_is_primitive"
  fq_nmod_is_primitive :: Ptr CFqNMod -> Ptr CFqNModCtx -> IO CInt

-- Bit packing -----------------------------------------------------------------

-- | /fq_nmod_bit_pack/ /f/ /op/ /bit_size/ /ctx/ 
--
-- Packs @op@ into bitfields of size @bit_size@, writing the result to @f@.
foreign import ccall "fq_nmod.h fq_nmod_bit_pack"
  fq_nmod_bit_pack :: Ptr CFmpz -> Ptr CFqNMod -> CFBitCnt -> Ptr CFqNModCtx -> IO ()

-- | /fq_nmod_bit_unpack/ /rop/ /f/ /bit_size/ /ctx/ 
--
-- Unpacks into @rop@ the element with coefficients packed into fields of
-- size @bit_size@ as represented by the integer @f@.
foreign import ccall "fq_nmod.h fq_nmod_bit_unpack"
  fq_nmod_bit_unpack :: Ptr CFqNMod -> Ptr CFmpz -> CFBitCnt -> Ptr CFqNModCtx -> IO ()