{-|
module      :  Data.Number.Flint.Acb.Modular.Instances
copyright   :  (c) 2022 Hartmut Monien
license     :  GNU GPL, version 2 or above (see LICENSE)
maintainer  :  hmonien@uni-bonn.de
-}

module Data.Number.Flint.Acb.Modular.Instances where

import System.IO.Unsafe

import Foreign.C.String
import Foreign.Marshal.Alloc (free)

import Data.Group

import Data.Number.Flint.Acb.Modular

instance Show PSL2Z where
  show :: PSL2Z -> String
show PSL2Z
x = forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    (PSL2Z
_, CString
cs) <- forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
x Ptr CPSL2Z -> IO CString
psl2z_get_str
    String
s <- CString -> IO String
peekCString CString
cs
    forall a. Ptr a -> IO ()
free CString
cs
    forall (m :: * -> *) a. Monad m => a -> m a
return String
s

instance Eq PSL2Z where
  == :: PSL2Z -> PSL2Z -> Bool
(==) PSL2Z
x PSL2Z
y =  forall a b. (a, b) -> b
snd forall a b. (a -> b) -> a -> b
$ forall a b. (a, b) -> b
snd forall a b. (a -> b) -> a -> b
$ forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
x forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
x -> do
      forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
y forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
y -> do
        CInt
flag <- Ptr CPSL2Z -> Ptr CPSL2Z -> IO CInt
psl2z_equal Ptr CPSL2Z
x Ptr CPSL2Z
y
        forall (m :: * -> *) a. Monad m => a -> m a
return forall a b. (a -> b) -> a -> b
$ CInt
flag forall a. Eq a => a -> a -> Bool
== CInt
1
        
instance Monoid PSL2Z where
  mempty :: PSL2Z
mempty = forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    PSL2Z
result <- IO PSL2Z
newPSL2Z
    forall (m :: * -> *) a. Monad m => a -> m a
return PSL2Z
result
  
instance Semigroup PSL2Z where
  <> :: PSL2Z -> PSL2Z -> PSL2Z
(<>) PSL2Z
x PSL2Z
y = forall a b. (a, b) -> a
fst forall a b. (a -> b) -> a -> b
$ forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    forall {a}. (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withNewPSL2Z forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
result -> do 
      forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
x forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
x -> do
        forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
y forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
y -> do
          Ptr CPSL2Z -> Ptr CPSL2Z -> Ptr CPSL2Z -> IO ()
psl2z_mul Ptr CPSL2Z
result Ptr CPSL2Z
x Ptr CPSL2Z
y
          
instance Group PSL2Z where
  invert :: PSL2Z -> PSL2Z
invert PSL2Z
x = forall a b. (a, b) -> a
fst forall a b. (a -> b) -> a -> b
$ forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    forall {a}. (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withNewPSL2Z forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
result -> do
      forall {a}. PSL2Z -> (Ptr CPSL2Z -> IO a) -> IO (PSL2Z, a)
withPSL2Z PSL2Z
x forall a b. (a -> b) -> a -> b
$ \Ptr CPSL2Z
x -> do
        Ptr CPSL2Z -> Ptr CPSL2Z -> IO ()
psl2z_inv Ptr CPSL2Z
result Ptr CPSL2Z
x

instance Show PSL2ZWord where
  show :: PSL2ZWord -> String
show PSL2ZWord
x = forall a. IO a -> a
unsafePerformIO forall a b. (a -> b) -> a -> b
$ do
    (PSL2ZWord
_, CString
cs) <- forall {a}.
PSL2ZWord -> (Ptr CPSL2ZWord -> IO a) -> IO (PSL2ZWord, a)
withPSL2ZWord PSL2ZWord
x Ptr CPSL2ZWord -> IO CString
psl2z_word_get_str_pretty
    String
s <- CString -> IO String
peekCString CString
cs
    forall a. Ptr a -> IO ()
free CString
cs
    forall (m :: * -> *) a. Monad m => a -> m a
return String
s