{-# LANGUAGE ForeignFunctionInterface, GeneralizedNewtypeDeriving #-}

module Numerical.HBLAS.BLAS.FFI  where

import Foreign.Ptr
import Foreign()
import Foreign.C.Types
import Data.Complex

-- /*Set the number of threads on runtime.*/
--foreign import ccall unsafe "openblas_set_num_threads" openblas_set_num_threads_unsafe :: CInt -> IO ()

--foreign import ccall unsafe "goto_set_num_threads" goto_set_num_threads_unsafe :: CInt -> IO ()

{- | For All of the BlAS FFI operations,

-}
{-

typedef enum CBLAS_ORDER     {CblasRowMajor=101, CblasColMajor=102} CBLAS_ORDER;
typedef enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113, CblasConjNoTrans=114} CBLAS_TRANSPOSE;
typedef enum CBLAS_UPLO      {CblasUpper=121, CblasLower=122} CBLAS_UPLO;
typedef enum CBLAS_DIAG      {CblasNonUnit=131, CblasUnit=132} CBLAS_DIAG;
typedef enum CBLAS_SIDE      {CblasLeft=141, CblasRight=142} CBLAS_SIDE;

-}

newtype CBLAS_INDEX = CBIndex CSize
        deriving (Eq,Show)
newtype CBLAS_ORDERT = CBOInt CInt
    deriving (Eq,Show)
data BLASOrder = BLASRowMajor | BLASColMajor
    deriving (Eq,Show)

encodeOrder :: BLASOrder -> CBLAS_ORDERT
encodeOrder BLASRowMajor = CBOInt 101
encodeOrder BLASColMajor = CBOInt 102

newtype CBLAS_TRANSPOSET = CBLAS_TransposeT{ unCBLAS_TransposeT :: CInt } deriving (Eq, Show)

data BLAS_Transpose = BlasNoTranspose | BlasTranspose | BlasConjTranspose | BlasConjNoTranspose

encodeTranspose :: BLAS_Transpose -> CBLAS_TRANSPOSET
encodeTranspose  BlasNoTranspose = CBLAS_TransposeT 111
encodeTranspose  BlasTranspose = CBLAS_TransposeT 112
encodeTranspose  BlasConjTranspose =  CBLAS_TransposeT 113
encodeTranspose  BlasConjNoTranspose = CBLAS_TransposeT 114

newtype CBLAS_UPLOT = CBlasUPLO CInt
    deriving (Eq,Show)
data BLASUplo = BUpper | BLower
    deriving (Eq,Show)

encodeUPLO :: BLASUplo -> CBLAS_UPLOT
encodeUPLO BUpper = CBlasUPLO 121
encodeUPLO BLower = CBlasUPLO 122

newtype CBLAS_DIAGT = CBLAS_DiagT CUChar
    deriving (Show,Eq)

data BlasDiag = BlasNonUnit   | BlasUnit
    deriving (Eq,Show )

encodeDiag :: BlasDiag -> CBLAS_DIAGT
encodeDiag BlasNonUnit = CBLAS_DiagT 131
encodeDiag BlasUnit = CBLAS_DiagT 132

newtype CBLAS_SIDET = CBLAS_SideT { unCBLAS_SideT :: CUChar }
    deriving (Eq, Show)
data BlasSide = BlasLeft | BlasRight
    deriving (Eq,Show)
encodeSide :: BlasSide -> CBLAS_SIDET
encodeSide BlasLeft = CBLAS_SideT 141
encodeSide BlasRight = CBLAS_SideT 142

--typedef enum CBLAS_ORDER     {CblasRowMajor=101, CblasColMajor=102} CBLAS_ORDER;
--typedef enum CBLAS_TRANSPOSE {CblasNoTrans=111, CblasTrans=112, CblasConjTrans=113, CblasConjNoTrans=114} CBLAS_TRANSPOSE;
--typedef enum CBLAS_UPLO      {CblasUpper=121, CblasLower=122} CBLAS_UPLO;
--typedef enum CBLAS_DIAG      {CblasNonUnit=131, CblasUnit=132} CBLAS_DIAG;
--typedef enum CBLAS_SIDE      {CblasLeft=141, CblasRight=142} CBLAS_SIDE;

--dot products
foreign import ccall unsafe "cblas_sdsdot" cblas_sdsdot_unsafe :: CInt -> Float -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO Float
foreign import ccall unsafe "cblas_dsdot" cblas_dsdot_unsafe :: CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO Double
foreign import ccall unsafe "cblas_sdot" cblas_sdot_unsafe :: CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO Float
foreign import ccall unsafe "cblas_ddot" cblas_ddot_unsafe :: CInt -> Ptr Double -> CInt -> Ptr Double -> CInt -> IO Double
--Float  cblas_sdsdot(  CInt n,   Float alpha,   Float *x,   CInt incx,   Float *y,   CInt incy);
--Double cblas_dsdot (  CInt n,   Float *x,   CInt incx,   Float *y,   CInt incy);
--Float  cblas_sdot(  CInt n,   Float  *x,   CInt incx,   Float  *y,   CInt incy);
--Double cblas_ddot(  CInt n,   Double *x,   CInt incx,   Double *y,   CInt incy);

{-
not doing these right now, because requires handling return value as a complex number,
we can only handle pointers to complex numbers right now
-}
--openblas_complex_Float  cblas_cdotu(  CInt n,   Float  *x,   CInt incx,   Float  *y,   CInt incy);
--openblas_complex_Float  cblas_cdotc(  CInt n,   Float  *x,   CInt incx,   Float  *y,   CInt incy);
--openblas_complex_Double cblas_zdotu(  CInt n,   Double *x,   CInt incx,   Double *y,   CInt incy);
--openblas_complex_Double cblas_zdotc(  CInt n,   Double *x,   CInt incx,   Double *y,   CInt incy);

--- not sure what to do for these complex
--void  cblas_cdotu_sub(  CInt n,   Float  *x,   CInt incx,   Float  *y,   CInt incy, openblas_complex_Float  *ret);
--void  cblas_cdotc_sub(  CInt n,   Float  *x,   CInt incx,   Float  *y,   CInt incy, openblas_complex_Float  *ret);
--void  cblas_zdotu_sub(  CInt n,   Double *x,   CInt incx,   Double *y,   CInt incy, openblas_complex_Double *ret);
--void  cblas_zdotc_sub(  CInt n,   Double *x,   CInt incx,   Double *y,   CInt incy, openblas_complex_Double *ret);

---- absolute value
foreign import ccall unsafe "cblas_sasum" cblas_sasum_unsafe::
    CInt -> Ptr Float -> CInt -> IO Float
foreign import ccall unsafe "cblas_dasum" cblas_dasum_unsafe ::
    CInt -> Ptr Double -> CInt -> IO Double
foreign import ccall unsafe "cblas_scasum" cblas_casum_unsafe ::
    CInt -> Ptr (Complex Float)-> CInt -> IO Float
foreign import ccall unsafe "cblas_dzasum" cblas_zasum_unsafe ::
    CInt -> Ptr (Complex Double) -> CInt -> IO Double
--Float  cblas_sasum (  CInt n,   Float  *x,   CInt incx);
--Double cblas_dasum (  CInt n,   Double *x,   CInt incx);
--Float  cblas_scasum(  CInt n,   Float  *x,   CInt incx);
--Double cblas_dzasum(  CInt n,   Double *x,   CInt incx);

foreign import ccall unsafe "cblas_snrm2" cblas_snrm2_unsafe ::
    CInt -> Ptr Float -> CInt -> IO Float
foreign import ccall unsafe "cblas_dnrm2" cblas_dnrm2_unsafe ::
    CInt -> Ptr Double -> CInt -> IO Double
foreign import ccall unsafe "cblas_scnrm2" cblas_scnrm2_unsafe ::
    CInt -> Ptr (Complex Float)-> CInt -> IO Float
foreign import ccall unsafe "cblas_dznrm2" cblas_dznrm2_unsafe ::
    CInt -> Ptr (Complex Double) -> CInt -> IO Double

--Float  cblas_snrm2 (  CInt N,   Float  *X,   CInt incX);
--Double cblas_dnrm2 (  CInt N,   Double *X,   CInt incX);
--Float  cblas_scnrm2(  CInt N,   Float  *X,   CInt incX);
--Double cblas_dznrm2(  CInt N,   Double *X,   CInt incX);

foreign import ccall unsafe "cblas_isamax" cblas_isamax_unsafe ::
    CInt -> Ptr Float -> CInt -> IO CInt
foreign import ccall unsafe "cblas_idamax" cblas_idamax_unsafe ::
    CInt -> Ptr Float -> CInt -> IO CInt
foreign import ccall unsafe "cblas_icamax" cblas_icamax_unsafe ::
    CInt -> Ptr (Complex Float) -> CInt -> IO CInt
foreign import ccall unsafe "cblas_izamax" cblas_izamax_unsafe ::
    CInt -> Ptr (Complex Double) -> CInt -> IO CInt
--CBLAS_INDEX cblas_isamax(  CInt n,   Float  *x,   CInt incx);
--CBLAS_INDEX cblas_idamax(  CInt n,   Double *x,   CInt incx);
--CBLAS_INDEX cblas_icamax(  CInt n,   Float  *x,   CInt incx);
--CBLAS_INDEX cblas_izamax(  CInt n,   Double *x,   CInt incx);

--void cblas_saxpy(  CInt n,   Float alpha,   Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_daxpy(  CInt n,   Double alpha,   Double *x,   CInt incx, Double *y,   CInt incy);
--void cblas_caxpy(  CInt n,   Float *alpha,   Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_zaxpy(  CInt n,   Double *alpha,   Double *x,   CInt incx, Double *y,   CInt incy);

foreign import ccall unsafe "cblas_scopy" cblas_scopy_unsafe ::
    CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO ()
foreign import ccall unsafe "cblas_dcopy" cblas_dcopy_unsafe ::
    CInt -> Ptr Double-> CInt -> Ptr Double -> CInt -> IO ()
foreign import ccall unsafe "cblas_ccopy" cblas_ccopy_unsafe ::
    CInt -> Ptr (Complex Float) -> CInt -> Ptr (Complex Float) -> CInt -> IO ()
foreign import ccall unsafe "cblas_zcopy" cblas_zcopy_unsafe ::
    CInt -> Ptr (Complex Double)-> CInt -> Ptr (Complex Double) -> CInt -> IO ()

--void cblas_scopy(  CInt n,   Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_dcopy(  CInt n,   Double *x,   CInt incx, Double *y,   CInt incy);
--void cblas_ccopy(  CInt n,   Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_zcopy(  CInt n,   Double *x,   CInt incx, Double *y,   CInt incy);

foreign import ccall unsafe "cblas_sswap" cblas_sswap_unsafe ::
    CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO ()
foreign import ccall unsafe "cblas_dswap" cblas_dswap_unsafe ::
    CInt -> Ptr Double-> CInt -> Ptr Double -> CInt -> IO ()
foreign import ccall unsafe "cblas_cswap" cblas_cswap_unsafe ::
    CInt -> Ptr (Complex Float) -> CInt -> Ptr (Complex Float) -> CInt -> IO ()
foreign import ccall unsafe "cblas_zswap" cblas_zswap_unsafe ::
    CInt -> Ptr (Complex Double)-> CInt -> Ptr (Complex Double) -> CInt -> IO ()

--void cblas_sswap(  CInt n, Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_dswap(  CInt n, Double *x,   CInt incx, Double *y,   CInt incy);
--void cblas_cswap(  CInt n, Float *x,   CInt incx, Float *y,   CInt incy);
--void cblas_zswap(  CInt n, Double *x,   CInt incx, Double *y,   CInt incy);

--void cblas_srot(  CInt N, Float *X,   CInt incX, Float *Y,   CInt incY,   Float c,   Float s);
--void cblas_drot(  CInt N, Double *X,   CInt incX, Double *Y,   CInt incY,   Double c,   Double  s);

--void cblas_srotg(Float *a, Float *b, Float *c, Float *s);
--void cblas_drotg(Double *a, Double *b, Double *c, Double *s);

--void cblas_srotm(  CInt N, Float *X,   CInt incX, Float *Y,   CInt incY,   Float *P);
--void cblas_drotm(  CInt N, Double *X,   CInt incX, Double *Y,   CInt incY,   Double *P);

--void cblas_srotmg(Float *d1, Float *d2, Float *b1,   Float b2, Float *P);
--void cblas_drotmg(Double *d1, Double *d2, Double *b1,   Double b2, Double *P);

--void cblas_sscal(  CInt N,   Float alpha, Float *X,   CInt incX);
--void cblas_dscal(  CInt N,   Double alpha, Double *X,   CInt incX);
--void cblas_cscal(  CInt N,   Float *alpha, Float *X,   CInt incX);
--void cblas_zscal(  CInt N,   Double *alpha, Double *X,   CInt incX);
--void cblas_csscal(  CInt N,   Float alpha, Float *X,   CInt incX);
--void cblas_zdscal(  CInt N,   Double alpha, Double *X,   CInt incX);

---------------------
----- BLAS LEVEL 2
---------------------

{-
matrix vector product for general matrices
 perform one of the matrix-vector operations   y :=
      alpha*A*x + beta*y, or y := alpha*A'*x + beta*y,
-}

type GemvFunFFI sc el =
       CBLAS_ORDERT -> CBLAS_TRANSPOSET -> CInt -> CInt
    -> sc -> Ptr el -> CInt -> Ptr el -> CInt -> sc -> Ptr el -> CInt -> IO ()

foreign import ccall unsafe "cblas_sgemv"
    cblas_sgemv_unsafe :: GemvFunFFI Float Float
foreign import ccall safe   "cblas_sgemv"
    cblas_sgemv_safe   :: GemvFunFFI Float Float

foreign import ccall unsafe "cblas_dgemv"
    cblas_dgemv_unsafe :: GemvFunFFI Double Double
foreign import ccall safe   "cblas_dgemv"
    cblas_dgemv_safe   :: GemvFunFFI Double Double

foreign import ccall unsafe "cblas_cgemv"
    cblas_cgemv_unsafe :: GemvFunFFI (Ptr (Complex Float)) (Complex Float)
foreign import ccall safe   "cblas_cgemv"
    cblas_cgemv_safe   :: GemvFunFFI (Ptr (Complex Float)) (Complex Float)

foreign import ccall unsafe "cblas_zgemv"
    cblas_zgemv_unsafe :: GemvFunFFI (Ptr (Complex Double)) (Complex Double)
foreign import ccall safe   "cblas_zgemv"
    cblas_zgemv_safe   :: GemvFunFFI (Ptr (Complex Double)) (Complex Double)

--void cblas_sgemv(  enum CBLAS_ORDER order,    enum CBLAS_TRANSPOSE trans,    CInt m,   CInt n,
--           Float alpha,   Float  *a,   CInt lda,    Float  *x,   CInt incx,    Float beta,  Float  *y,   CInt incy);
--void cblas_dgemv(  enum CBLAS_ORDER order,    enum CBLAS_TRANSPOSE trans,    CInt m,   CInt n,
--           Double alpha,   Double  *a,   CInt lda,    Double  *x,   CInt incx,    Double beta,  Double  *y,   CInt incy);
--void cblas_cgemv(  enum CBLAS_ORDER order,    enum CBLAS_TRANSPOSE trans,    CInt m,   CInt n,
--           Float *alpha,   Float  *a,   CInt lda,    Float  *x,   CInt incx,    Float *beta,  Float  *y,   CInt incy);
--void cblas_zgemv(  enum CBLAS_ORDER order,    enum CBLAS_TRANSPOSE trans,    CInt m,   CInt n,
--           Double *alpha,   Double  *a,   CInt lda,    Double  *x,   CInt incx,    Double *beta,  Double  *y,   CInt incy);

-- perform the rank 1 operation   A := alpha*x*y' + A,

type GerFunFFI el = CBLAS_ORDERT -> CInt -> CInt -> el -> Ptr el -> CInt -> Ptr el -> CInt -> Ptr el -> CInt -> IO ()

foreign import ccall unsafe "cblas_sger" cblas_sger_unsafe ::
        CBLAS_ORDERT -> CInt -> CInt -> Float -> Ptr Float -> CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO ()
foreign import ccall safe   "cblas_sger" cblas_sger_safe   ::
        CBLAS_ORDERT -> CInt -> CInt -> Float -> Ptr Float -> CInt -> Ptr Float -> CInt -> Ptr Float -> CInt -> IO ()
foreign import ccall unsafe "cblas_dger" cblas_dger_unsafe ::
        CBLAS_ORDERT -> CInt -> CInt -> Double -> Ptr Double -> CInt -> Ptr Double -> CInt -> Ptr Double -> CInt -> IO ()
foreign import ccall safe   "cblas_dger" cblas_dger_safe   ::
        CBLAS_ORDERT -> CInt -> CInt -> Double -> Ptr Double -> CInt -> Ptr Double -> CInt -> Ptr Double -> CInt -> IO ()

--void cblas_sger (  enum CBLAS_ORDER order,   CInt M,   CInt N,   Float   alpha,   Float  *X,   CInt incX,   Float  *Y,   CInt incY, Float  *A,   CInt lda);
--void cblas_dger (  enum CBLAS_ORDER order,   CInt M,   CInt N,   Double  alpha,   Double *X,   CInt incX,   Double *Y,   CInt incY, Double *A,   CInt lda);
--void cblas_cgeru(  enum CBLAS_ORDER order,   CInt M,   CInt N,   Float  *alpha,   Float  *X,   CInt incX,   Float  *Y,   CInt incY, Float  *A,   CInt lda);
--void cblas_cgerc(  enum CBLAS_ORDER order,   CInt M,   CInt N,   Float  *alpha,   Float  *X,   CInt incX,   Float  *Y,   CInt incY, Float  *A,   CInt lda);
--void cblas_zgeru(  enum CBLAS_ORDER order,   CInt M,   CInt N,   Double *alpha,   Double *X,   CInt incX,   Double *Y,   CInt incY, Double *A,   CInt lda);
--void cblas_zgerc(  enum CBLAS_ORDER order,   CInt M,   CInt N,   Double *alpha,   Double *X,   CInt incX,   Double *Y,   CInt incY, Double *A,   CInt lda);

--STRSV - solve one of the systems of equations   A*x = b, or A'*x = b, where A is a (non)unit upper(/lower) triangular matrix

--STRSV - solve one of the systems of equations   A*x = b, or A'*x = b, where A is a (non)unit upper(/lower) triangular matrix

type TrsvFunFFI el =
       CBLAS_ORDERT -> CBLAS_UPLOT -> CBLAS_TRANSPOSET -> CBLAS_DIAGT
    -> CInt -> Ptr el -> CInt -> Ptr el -> CInt -> IO ()

foreign import ccall unsafe "cblas_strsv"
  cblas_strsv_unsafe :: TrsvFunFFI Float
foreign import ccall safe   "cblas_strsv"
  cblas_strsv_safe   :: TrsvFunFFI Float

foreign import ccall unsafe "cblas_dtrsv"
  cblas_dtrsv_unsafe :: TrsvFunFFI Double
foreign import ccall safe   "cblas_dtrsv"
  cblas_dtrsv_safe   :: TrsvFunFFI Double

foreign import ccall unsafe "cblas_ctrsv"
  cblas_ctrsv_unsafe :: TrsvFunFFI (Complex Float)
foreign import ccall safe   "cblas_ctrsv"
  cblas_ctrsv_safe   :: TrsvFunFFI (Complex Float)

foreign import ccall unsafe "cblas_ztrsv"
  cblas_ztrsv_unsafe :: TrsvFunFFI (Complex Double)
foreign import ccall safe   "cblas_ztrsv"
  cblas_ztrsv_safe   :: TrsvFunFFI (Complex Double)

--void cblas_strsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_dtrsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Double *A,   CInt lda, Double *X,   CInt incX);
--void cblas_ctrsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_ztrsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Double *A,   CInt lda, Double *X,   CInt incX);

--void cblas_strmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_dtrmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Double *A,   CInt lda, Double *X,   CInt incX);
--void cblas_ctrmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_ztrmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,   CInt N,   Double *A,   CInt lda, Double *X,   CInt incX);

--void cblas_ssyr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *X,   CInt incX, Float *A,   CInt lda);
--void cblas_dsyr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,   CInt incX, Double *A,   CInt lda);
--void cblas_cher(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *X,   CInt incX, Float *A,   CInt lda);
--void cblas_zher(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,   CInt incX, Double *A,   CInt lda);

--void cblas_ssyr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,  CInt N,   Float alpha,   Float *X,
--                  CInt incX,   Float *Y,   CInt incY, Float *A,   CInt lda);
--void cblas_dsyr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,
--                  CInt incX,   Double *Y,   CInt incY, Double *A,   CInt lda);
--void cblas_cher2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float *alpha,   Float *X,   CInt incX,
--                  Float *Y,   CInt incY, Float *A,   CInt lda);
--void cblas_zher2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double *alpha,   Double *X,   CInt incX,
--                  Double *Y,   CInt incY, Double *A,   CInt lda);

--void cblas_sgbmv(  enum CBLAS_ORDER order,   enum CBLAS_TRANSPOSE TransA,   CInt M,   CInt N,
--                   CInt KL,   CInt KU,   Float alpha,   Float *A,   CInt lda,   Float *X,   CInt incX,   Float beta, Float *Y,   CInt incY);
--void cblas_dgbmv(  enum CBLAS_ORDER order,   enum CBLAS_TRANSPOSE TransA,   CInt M,   CInt N,
--                   CInt KL,   CInt KU,   Double alpha,   Double *A,   CInt lda,   Double *X,   CInt incX,   Double beta, Double *Y,   CInt incY);
--void cblas_cgbmv(  enum CBLAS_ORDER order,   enum CBLAS_TRANSPOSE TransA,   CInt M,   CInt N,
--                   CInt KL,   CInt KU,   Float *alpha,   Float *A,   CInt lda,   Float *X,   CInt incX,   Float *beta, Float *Y,   CInt incY);
--void cblas_zgbmv(  enum CBLAS_ORDER order,   enum CBLAS_TRANSPOSE TransA,   CInt M,   CInt N,
--                   CInt KL,   CInt KU,   Double *alpha,   Double *A,   CInt lda,   Double *X,   CInt incX,   Double *beta, Double *Y,   CInt incY);

--void cblas_ssbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   CInt K,   Float alpha,   Float *A,
--                   CInt lda,   Float *X,   CInt incX,   Float beta, Float *Y,   CInt incY);
--void cblas_dsbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   CInt K,   Double alpha,   Double *A,
--                   CInt lda,   Double *X,   CInt incX,   Double beta, Double *Y,   CInt incY);

--void cblas_stbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_dtbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Double *A,   CInt lda, Double *X,   CInt incX);
--void cblas_ctbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_ztbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Double *A,   CInt lda, Double *X,   CInt incX);

----------------
--- | solves  Ax=v where A is k+1 banded triangular matrix, and x and
----------------
--void cblas_stbsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_dtbsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Double *A,   CInt lda, Double *X,   CInt incX);
--void cblas_ctbsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Float *A,   CInt lda, Float *X,   CInt incX);
--void cblas_ztbsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   CInt K,   Double *A,   CInt lda, Double *X,   CInt incX);

-------------------------------------------------------------------------
-- | matrix vector product Av, writes result into v, where A is a packed triangular nxn matrix
-------------------------------------------------------------------------
--void cblas_stpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Float *Ap, Float *X,   CInt incX);
--void cblas_dtpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Double *Ap, Double *X,   CInt incX);
--void cblas_ctpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Float *Ap, Float *X,   CInt incX);
--void cblas_ztpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Double *Ap, Double *X,   CInt incX);

--------------------------------------------------
---  | solve  Ax=v where A is a nxn packed triangular matrix, v vector input, writes the solution into x.
--------------------------------------------------
--void cblas_stpsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Float *Ap, Float *X,   CInt incX);
--void cblas_dtpsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Double *Ap, Double *X,   CInt incX);
--void cblas_ctpsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Float *Ap, Float *X,   CInt incX);
--void cblas_ztpsv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,   enum CBLAS_DIAG Diag,
--                   CInt N,   Double *Ap, Double *X,   CInt incX);

----------------------------------
---- |  (unpacked) symmetric matrix vector product    x:=Av, writes result x into v
---------------------------------

type SymvFunFFI el = CBLAS_ORDERT -> CBLAS_UPLOT -> CInt -> el -> Ptr el ->  CInt ->
                        Ptr el -> CInt -> el -> Ptr el -> CInt -> IO ()

--void cblas_ssymv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *A,
--                   CInt lda,   Float *X,   CInt incX,   Float beta, Float *Y,   CInt incY);
--void cblas_dsymv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *A,
--                   CInt lda,   Double *X,   CInt incX,   Double beta, Double *Y,   CInt incY);

--------------------------------
---- | hermitian matrix vector product   x:=Av, writes result x into v
--------------------------------
--void cblas_chemv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float *alpha,   Float *A,
--                   CInt lda,   Float *X,   CInt incX,   Float *beta, Float *Y,   CInt incY);
--void cblas_zhemv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double *alpha,   Double *A,
--                   CInt lda,   Double *X,   CInt incX,   Double *beta, Double *Y,   CInt incY);

---------------
--- | packed symmetric matrix * vector product  y:= alpha * Av  + beta * y
---------------

--void cblas_sspmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *Ap,
--                   Float *X,   CInt incX,   Float beta, Float *Y,   CInt incY);
--void cblas_dspmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *Ap,
--                   Double *X,   CInt incX,   Double beta, Double *Y,   CInt incY);

--void cblas_sspr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *X,   CInt incX, Float *Ap);
--void cblas_dspr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,   CInt incX, Double *Ap);

--void cblas_chpr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *X,   CInt incX, Float *A);
--void cblas_zhpr(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,  CInt incX, Double *A);

--void cblas_sspr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float alpha,   Float *X,   CInt incX,   Float *Y,   CInt incY, Float *A);
--void cblas_dspr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double alpha,   Double *X,   CInt incX,   Double *Y,   CInt incY, Double *A);
--void cblas_chpr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Float *alpha,   Float *X,   CInt incX,   Float *Y,   CInt incY, Float *Ap);
--void cblas_zhpr2(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   Double *alpha,   Double *X,   CInt incX,   Double *Y,   CInt incY, Double *Ap);

--void cblas_chbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   CInt K,
--           Float *alpha,   Float *A,   CInt lda,   Float *X,   CInt incX,   Float *beta, Float *Y,   CInt incY);
--void cblas_zhbmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,   CInt K,
--           Double *alpha,   Double *A,   CInt lda,   Double *X,   CInt incX,   Double *beta, Double *Y,   CInt incY);

--void cblas_chpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,
--           Float *alpha,   Float *Ap,   Float *X,   CInt incX,   Float *beta, Float *Y,   CInt incY);
--void cblas_zhpmv(  enum CBLAS_ORDER order,   enum CBLAS_UPLO Uplo,   CInt N,
--           Double *alpha,   Double *Ap,   Double *X,   CInt incX,   Double *beta, Double *Y,   CInt incY);

{-

-}

--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
------------------------------ | BLAS LEVEL 3 ROUTINES
--------------------------------------------------------------------------------
-----------------------  |  Level 3 ops are faster than Levels 1 or 2
--------------------------------------------------------------------------------

--void cblas_sgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const blasint M, const blasint N, const blasint K,
--         const float alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float beta, float *C, const blasint ldc);

--void cblas_dgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const blasint M, const blasint N, const blasint K,
--         const double alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double beta, double *C, const blasint ldc);
--void cblas_cgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const blasint M, const blasint N, const blasint K,
--         const float *alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float *beta, float *C, const blasint ldc);
--void cblas_zgemm(const enum CBLAS_ORDER Order, const enum CBLAS_TRANSPOSE TransA, const enum CBLAS_TRANSPOSE TransB, const blasint M, const blasint N, const blasint K,
--         const double *alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double *beta, double *C, const blasint ldc);

-- |  Matrix mult for general dense matrices
type GemmFunFFI scale el = CBLAS_ORDERT ->   CBLAS_TRANSPOSET -> CBLAS_TRANSPOSET->
        CInt -> CInt -> CInt -> {- scal A * B -} scale  -> {- Matrix A-} Ptr el  -> CInt -> {- B -}  Ptr el -> CInt->
            scale -> {- C -}  Ptr el -> CInt -> IO ()

{- C := alpha*op( A )*op( B ) + beta*C ,  -}

-- matrix mult!
foreign import ccall unsafe "cblas_sgemm"
    cblas_sgemm_unsafe :: GemmFunFFI Float Float

foreign import ccall unsafe "cblas_dgemm"
    cblas_dgemm_unsafe :: GemmFunFFI Double Double

foreign import ccall unsafe "cblas_cgemm"
    cblas_cgemm_unsafe :: GemmFunFFI (Ptr(Complex Float)) (Complex Float)

foreign import ccall unsafe "cblas_zgemm"
    cblas_zgemm_unsafe :: GemmFunFFI (Ptr (Complex Double)) (Complex Double)

-- safe ffi variant for large inputs
foreign import ccall "cblas_sgemm"
    cblas_sgemm_safe :: GemmFunFFI Float Float

foreign import ccall "cblas_dgemm"
    cblas_dgemm_safe :: GemmFunFFI Double Double

foreign import ccall "cblas_cgemm"
    cblas_cgemm_safe :: GemmFunFFI (Ptr(Complex Float)) (Complex Float)

foreign import ccall "cblas_zgemm"
    cblas_zgemm_safe :: GemmFunFFI (Ptr (Complex Double)) (Complex Double)

-----------------------------------------
----- |  Matrix mult for Symmetric Matrices
-----------------------------------------

--void cblas_ssymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const blasint M, const blasint N,
--                 const float alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float beta, float *C, const blasint ldc);
--void cblas_dsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const blasint M, const blasint N,
--                 const double alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double beta, double *C, const blasint ldc);
--void cblas_csymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const blasint M, const blasint N,
--                 const float *alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float *beta, float *C, const blasint ldc);
--void cblas_zsymm(const enum CBLAS_ORDER Order, const enum CBLAS_SIDE Side, const enum CBLAS_UPLO Uplo, const blasint M, const blasint N,
--                 const double *alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double *beta, double *C, const blasint ldc);

type SymmFunFFI scale el = CBLAS_ORDERT -> CBLAS_SIDET -> CBLAS_UPLOT ->
     CInt->CInt -> scale -> Ptr el -> CInt -> Ptr el -> CInt -> scale ->Ptr el -> CInt -> IO ()

foreign import ccall unsafe "cblas_ssymm"
    cblas_ssymm_unsafe :: SymmFunFFI Float Float

foreign import ccall unsafe "cblas_dsymm"
    cblas_dsymm_unsafe :: SymmFunFFI Double Double

foreign import ccall unsafe "cblas_csymm"
    cblas_csymm_unsafe :: SymmFunFFI (Ptr (Complex Float )) (Complex Float)

foreign import ccall unsafe "cblas_zsymm"
    cblas_zsymm_unsafe :: SymmFunFFI (Ptr (Complex Double)) (Complex Double)

-- safe ffi variant,
foreign import ccall  "cblas_ssymm"
    cblas_ssymm_safe :: SymmFunFFI Float Float

foreign import ccall  "cblas_dsymm"
    cblas_dsymm_safe :: SymmFunFFI Double Double

foreign import ccall  "cblas_csymm"
    cblas_csymm_safe :: SymmFunFFI (Ptr (Complex Float )) (Complex Float)

foreign import ccall  "cblas_zsymm"
    cblas_zsymm_safe :: SymmFunFFI (Ptr (Complex Double)) (Complex Double)

-----------------------------------
--- |  symmetric rank k  matrix update, C := alpha*A*A' + beta*C
--- or C = alpha*A'*A + beta*C
------------------------------------

--void cblas_ssyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--         const blasint N, const blasint K, const float alpha, const float *A, const blasint lda, const float beta, float *C, const blasint ldc);
--void cblas_dsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--         const blasint N, const blasint K, const double alpha, const double *A, const blasint lda, const double beta, double *C, const blasint ldc);
--void cblas_csyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--         const blasint N, const blasint K, const float *alpha, const float *A, const blasint lda, const float *beta, float *C, const blasint ldc);
--void cblas_zsyrk(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--         const blasint N, const blasint K, const double *alpha, const double *A, const blasint lda, const double *beta, double *C, const blasint ldc);

type SyrkFunFFI scale el = CBLAS_ORDERT -> CBLAS_UPLOT -> CBLAS_TRANSPOSET ->
     CInt->CInt  -> scale -> Ptr el -> CInt -> Ptr el -> CInt ->scale -> Ptr el -> CInt -> IO ()
foreign import ccall unsafe "cblas_ssyrk"
    cblas_ssyrk_unsafe :: SyrkFunFFI Float Float
foreign import ccall unsafe "cblas_dsyrk"
    cblas_dsyrk_unsafe :: SyrkFunFFI Double Double
foreign import ccall unsafe "cblas_csyrk"
    cblas_csyrk_unsafe :: SyrkFunFFI (Ptr(Complex Float)) (Complex Float)
foreign import ccall unsafe "cblas_zsyrk"
    cblas_zsyrk_unsafe :: SyrkFunFFI (Ptr(Complex Double)) (Complex Double)

----------------------
----- | Symmetric Rank 2k matrix update, C= alpha* A*B' + alpha* B*A' + beta * C
----- or C= alpha* A'*B + alpha* B'*A + beta * C
-------------------

--void cblas_ssyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--          const blasint N, const blasint K, const float alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float beta, float *C, const blasint ldc);
--void cblas_dsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--          const blasint N, const blasint K, const double alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double beta, double *C, const blasint ldc);
--void cblas_csyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
--          const blasint N, const blasint K, const float *alpha, const float *A, const blasint lda, const float *B, const blasint ldb, const float *beta, float *C, const blasint ldc);
--void cblas_zsyr2k(const enum CBLAS_ORDER Order, const enum CBLAS_UPLO Uplo, const enum CBLAS_TRANSPOSE Trans,
         --const blasint N, const blasint K, const double *alpha, const double *A, const blasint lda, const double *B, const blasint ldb, const double *beta, double *C, const blasint ldc);

type Syr2kFunFFI scale el = CBLAS_ORDERT -> CBLAS_UPLOT -> CBLAS_TRANSPOSET  ->
     CInt->CInt -> scale -> Ptr el -> CInt -> Ptr el -> CInt ->
     scale ->Ptr el -> CInt -> IO ()

foreign  import ccall unsafe "cblas_ssyr2k"
    cblas_ssyr2k_unsafe :: Syr2kFunFFI Float Float
foreign import ccall unsafe "cblas_dsyr2k"
    cblas_dsyr2k_unsafe :: Syr2kFunFFI Double Double
foreign  import ccall unsafe "cblas_csyr2k"
    cblas_csyr2k_unsafe :: Syr2kFunFFI (Ptr (Complex Float)) Float
foreign  import ccall unsafe "cblas_zsyr2k"
    cblas_zsyr2k_unsafe :: Syr2kFunFFI (Ptr (Complex Double)) Double

-------------------------------
--------  |  matrix matrix product for triangular matrices
------------------------------

type TrmmFunFFI scale el = CBLAS_ORDERT -> CBLAS_SIDET -> CBLAS_UPLOT -> CBLAS_TRANSPOSET -> CBLAS_DIAGT ->
     CInt->CInt -> scale -> Ptr el -> CInt -> Ptr el -> CInt -> Ptr el -> CInt -> IO ()
foreign  import ccall unsafe "cblas_strmm"
    cblas_strmm_unsafe :: TrmmFunFFI Float Float
foreign  import ccall unsafe "cblas_dtrmm"
    cblas_dtrmm_unsafe :: TrmmFunFFI Double Double
foreign  import ccall unsafe "cblas_ctrmm"
    cblas_ctrmm_unsafe :: TrmmFunFFI (Ptr (Complex Float )) (Complex Float)
foreign  import ccall unsafe "cblas_ztrmm"
    cblas_ztrmm_unsafe :: TrmmFunFFI (Ptr (Complex Double )) (Complex Double)

--void cblas_strmm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Float alpha,   Float *A,   CInt lda, Float *B,   CInt ldb);
--void cblas_dtrmm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Double alpha,   Double *A,   CInt lda, Double *B,   CInt ldb);
--void cblas_ctrmm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Float *alpha,   Float *A,   CInt lda, Float *B,   CInt ldb);
--void cblas_ztrmm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Double *alpha,   Double *A,   CInt lda, Double *B,   CInt ldb);

------------------------
--  |  triangular solvers
-----------------------

--
--TRSM solves  op(A)*X = alpha*B or  X*op(A) = alpha*B
--op(A) is one of op(A) = A, or op(A) = A', or op(A) = conjg(A').
-- A is a unit, or non-unit, upper or lower triangular matrix
----
type TrsmFunFFI scale el = CBLAS_ORDERT -> CBLAS_SIDET -> CBLAS_UPLOT -> CBLAS_TRANSPOSET -> CBLAS_DIAGT ->
     CInt->CInt -> scale -> Ptr el -> CInt -> Ptr el -> CInt -> Ptr el -> CInt -> IO ()
foreign  import ccall unsafe "cblas_strsm"
    cblas_strsm_unsafe :: TrmmFunFFI Float Float
foreign  import ccall unsafe "cblas_dtrsm"
    cblas_dtrsm_unsafe :: TrmmFunFFI Double Double
foreign  import ccall unsafe "cblas_ctrsm"
    cblas_ctrsm_unsafe :: TrmmFunFFI (Ptr (Complex Float )) (Complex Float)
foreign  import ccall unsafe "cblas_ztrsm"
    cblas_ztrsm_unsafe :: TrmmFunFFI (Ptr (Complex Double )) (Complex Double)

--void cblas_strsm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Float alpha,   Float *A,   CInt lda, Float *B,   CInt ldb);
--void cblas_dtrsm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Double alpha,   Double *A,   CInt lda, Double *B,   CInt ldb);
--void cblas_ctrsm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Float *alpha,   Float *A,   CInt lda, Float *B,   CInt ldb);
--void cblas_ztrsm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE TransA,
--                   enum CBLAS_DIAG Diag,   CInt M,   CInt N,   Double *alpha,   Double *A,   CInt lda, Double *B,   CInt ldb);

-------------------------
-- | hermitian matrix mult
------------------------

type HemmFunFFI  el = CBLAS_ORDERT -> CBLAS_SIDET -> CBLAS_UPLOT ->
     CInt->CInt -> Ptr el -> Ptr el -> CInt -> Ptr el -> CInt -> Ptr el -> CInt -> IO ()

foreign  import ccall unsafe "cblas_chemm"
    cblas_chemm_unsafe :: HemmFunFFI (Complex Float)
foreign  import ccall unsafe "cblas_zhemm"
    cblas_zhemm_unsafe :: HemmFunFFI  (Complex Double)

--void cblas_chemm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   CInt M,   CInt N,
--                   Float *alpha,   Float *A,   CInt lda,   Float *B,   CInt ldb,   Float *beta, Float *C,   CInt ldc);
--void cblas_zhemm(  enum CBLAS_ORDER Order,   enum CBLAS_SIDE Side,   enum CBLAS_UPLO Uplo,   CInt M,   CInt N,
--                   Double *alpha,   Double *A,   CInt lda,   Double *B,   CInt ldb,   Double *beta, Double *C,   CInt ldc);

type HerkFun scale el = CBLAS_ORDERT -> CBLAS_SIDET-> CBLAS_TRANSPOSET ->
     CInt->CInt ->  scale -> Ptr el -> CInt -> Ptr el -> CInt ->scale ->Ptr el -> CInt -> IO ()

foreign  import ccall unsafe "cblas_cherk"
    cblas_cherk_unsafe :: HerkFun  Float  (Complex Float)
foreign  import ccall unsafe "cblas_zherk"
    cblas_zherk_unsafe :: HerkFun  Double  (Complex Double)
--void cblas_cherk(  enum CBLAS_ORDER Order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE Trans,   CInt N,   CInt K,
--                   Float alpha,   Float *A,   CInt lda,   Float beta, Float *C,   CInt ldc);
--void cblas_zherk(  enum CBLAS_ORDER Order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE Trans,   CInt N,   CInt K,
--                   Double alpha,   Double *A,   CInt lda,   Double beta, Double *C,   CInt ldc);

type Her2kFunFFI scale el = CBLAS_ORDERT -> CBLAS_SIDET -> CBLAS_TRANSPOSET ->
     CInt->CInt -> Ptr el  -> Ptr el -> CInt -> Ptr el -> CInt ->scale ->Ptr el -> CInt -> IO ()

foreign  import ccall unsafe "cblas_cher2k"
    cblas_cher2k_unsafe :: Her2kFunFFI  Float  (Complex Float)
foreign  import ccall unsafe "cblas_zher2k"
    cblas_zher2k_unsafe :: Her2kFunFFI  Double  (Complex Double)

--void cblas_cher2k(  enum CBLAS_ORDER Order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE Trans,   CInt N,   CInt K,
--                    Float *alpha,   Float *A,   CInt lda,   Float *B,   CInt ldb,   Float beta, Float *C,   CInt ldc);
--void cblas_zher2k(  enum CBLAS_ORDER Order,   enum CBLAS_UPLO Uplo,   enum CBLAS_TRANSPOSE Trans,   CInt N,   CInt K,
--                    Double *alpha,   Double *A,   CInt lda,   Double *B,   CInt ldb,   Double beta, Double *C,   CInt ldc);

----void cblas_xerbla(CInt p, char *rout, char *form, ...);


-- | Type classes for random generation of values.
--
-- __Note__: the contents of this module are re-exported by
-- "Test.QuickCheck". You do not need to import it directly.
{-# LANGUAGE CPP #-}
{-# LANGUAGE FlexibleContexts #-}
#ifndef NO_GENERICS
{-# LANGUAGE DefaultSignatures, FlexibleContexts, TypeOperators #-}
{-# LANGUAGE FlexibleInstances, KindSignatures, ScopedTypeVariables #-}
{-# LANGUAGE MultiParamTypeClasses #-}
#if __GLASGOW_HASKELL__ >= 710
#define OVERLAPPING_ {-# OVERLAPPING #-}
#else
{-# LANGUAGE OverlappingInstances  #-}
#define OVERLAPPING_
#endif
#endif
#ifndef NO_POLYKINDS
{-# LANGUAGE PolyKinds #-}
#endif
#ifndef NO_SAFE_HASKELL
{-# LANGUAGE Trustworthy #-}
#endif
#ifndef NO_NEWTYPE_DERIVING
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
#endif
module Test.QuickCheck.Arbitrary
  (
  -- * Arbitrary and CoArbitrary classes
    Arbitrary(..)
  , CoArbitrary(..)

  -- ** Unary and Binary classes
  , Arbitrary1(..)
  , arbitrary1
  , shrink1
  , Arbitrary2(..)
  , arbitrary2
  , shrink2

  -- ** Helper functions for implementing arbitrary
  , applyArbitrary2
  , applyArbitrary3
  , applyArbitrary4
  , arbitrarySizedIntegral        -- :: Integral a => Gen a
  , arbitrarySizedNatural         -- :: Integral a => Gen a
  , arbitraryBoundedIntegral      -- :: (Bounded a, Integral a) => Gen a
  , arbitrarySizedBoundedIntegral -- :: (Bounded a, Integral a) => Gen a
  , arbitrarySizedFractional      -- :: Fractional a => Gen a
  , arbitraryBoundedRandom        -- :: (Bounded a, Random a) => Gen a
  , arbitraryBoundedEnum          -- :: (Bounded a, Enum a) => Gen a
  -- ** Generators for various kinds of character
  , arbitraryUnicodeChar   -- :: Gen Char
  , arbitraryASCIIChar     -- :: Gen Char
  , arbitraryPrintableChar -- :: Gen Char
  -- ** Helper functions for implementing shrink
#ifndef NO_GENERICS
  , RecursivelyShrink
  , GSubterms
  , genericShrink      -- :: (Generic a, Arbitrary a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a]
  , subterms           -- :: (Generic a, Arbitrary a, GSubterms (Rep a) a) => a -> [a]
  , recursivelyShrink  -- :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a]
  , genericCoarbitrary -- :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b
#endif
  , shrinkNothing            -- :: a -> [a]
  , shrinkList               -- :: (a -> [a]) -> [a] -> [[a]]
  , shrinkMap                -- :: Arbitrary a -> (a -> b) -> (b -> a) -> b -> [b]
  , shrinkMapBy              -- :: (a -> b) -> (b -> a) -> (a -> [a]) -> b -> [b]
  , shrinkIntegral           -- :: Integral a => a -> [a]
  , shrinkRealFrac           -- :: RealFrac a => a -> [a]
  , shrinkDecimal            -- :: RealFrac a => a -> [a]
  -- ** Helper functions for implementing coarbitrary
  , coarbitraryIntegral      -- :: Integral a => a -> Gen b -> Gen b
  , coarbitraryReal          -- :: Real a => a -> Gen b -> Gen b
  , coarbitraryShow          -- :: Show a => a -> Gen b -> Gen b
  , coarbitraryEnum          -- :: Enum a => a -> Gen b -> Gen b
  , (><)

  -- ** Generators which use arbitrary
  , vector       -- :: Arbitrary a => Int -> Gen [a]
  , orderedList  -- :: (Ord a, Arbitrary a) => Gen [a]
  , infiniteList -- :: Arbitrary a => Gen [a]
  )
 where

--------------------------------------------------------------------------
-- imports

import Control.Applicative
import Data.Foldable(toList)
import System.Random(Random)
import Test.QuickCheck.Gen
import Test.QuickCheck.Random
import Test.QuickCheck.Gen.Unsafe

{-
import Data.Generics
  ( (:*:)(..)
  , (:+:)(..)
  , Unit(..)
  )
-}

import Data.Char
  ( ord
  , isLower
  , isUpper
  , toLower
  , isDigit
  , isSpace
  , isPrint
  , generalCategory
  , GeneralCategory(..)
  )

#ifndef NO_FIXED
import Data.Fixed
  ( Fixed
  , HasResolution
  )
#endif

import Data.Ratio
  ( Ratio
  , (%)
  , numerator
  , denominator
  )

import Data.Complex
  ( Complex((:+)) )

import Data.List
  ( sort
  , nub
  )

import Data.Version (Version (..))

#if defined(MIN_VERSION_base)
#if MIN_VERSION_base(4,2,0)
import System.IO
  ( Newline(..)
  , NewlineMode(..)
  )
#endif
#endif

import Control.Monad
  ( liftM
  , liftM2
  , liftM3
  , liftM4
  , liftM5
  )

import Data.Int(Int8, Int16, Int32, Int64)
import Data.Word(Word, Word8, Word16, Word32, Word64)
import System.Exit (ExitCode(..))
import Foreign.C.Types

#ifndef NO_GENERICS
import GHC.Generics
#endif

import qualified Data.Set as Set
import qualified Data.Map as Map
import qualified Data.IntSet as IntSet
import qualified Data.IntMap as IntMap
import qualified Data.Sequence as Sequence
import qualified Data.Tree as Tree
import Data.Bits

import qualified Data.Monoid as Monoid

#ifndef NO_TRANSFORMERS
import Data.Functor.Identity
import Data.Functor.Constant
import Data.Functor.Compose
import Data.Functor.Product
#endif

--------------------------------------------------------------------------
-- ** class Arbitrary

-- | Random generation and shrinking of values.
--
-- QuickCheck provides @Arbitrary@ instances for most types in @base@,
-- except those which incur extra dependencies.
-- For a wider range of @Arbitrary@ instances see the
-- <http://hackage.haskell.org/package/quickcheck-instances quickcheck-instances>
-- package.
class Arbitrary a where
  -- | A generator for values of the given type.
  --
  -- It is worth spending time thinking about what sort of test data
  -- you want - good generators are often the difference between
  -- finding bugs and not finding them. You can use 'sample',
  -- 'label' and 'classify' to check the quality of your test data.
  --
  -- There is no generic @arbitrary@ implementation included because we don't
  -- know how to make a high-quality one. If you want one, consider using the
  -- <http://hackage.haskell.org/package/testing-feat testing-feat> or
  -- <http://hackage.haskell.org/package/generic-random generic-random> packages.
  --
  -- The <http://www.cse.chalmers.se/~rjmh/QuickCheck/manual.html QuickCheck manual>
  -- goes into detail on how to write good generators. Make sure to look at it,
  -- especially if your type is recursive!
  arbitrary :: Gen a

  -- | Produces a (possibly) empty list of all the possible
  -- immediate shrinks of the given value.
  --
  -- The default implementation returns the empty list, so will not try to
  -- shrink the value. If your data type has no special invariants, you can
  -- enable shrinking by defining @shrink = 'genericShrink'@, but by customising
  -- the behaviour of @shrink@ you can often get simpler counterexamples.
  --
  -- Most implementations of 'shrink' should try at least three things:
  --
  -- 1. Shrink a term to any of its immediate subterms.
  --    You can use 'subterms' to do this.
  --
  -- 2. Recursively apply 'shrink' to all immediate subterms.
  --    You can use 'recursivelyShrink' to do this.
  --
  -- 3. Type-specific shrinkings such as replacing a constructor by a
  --    simpler constructor.
  --
  -- For example, suppose we have the following implementation of binary trees:
  --
  -- > data Tree a = Nil | Branch a (Tree a) (Tree a)
  --
  -- We can then define 'shrink' as follows:
  --
  -- > shrink Nil = []
  -- > shrink (Branch x l r) =
  -- >   -- shrink Branch to Nil
  -- >   [Nil] ++
  -- >   -- shrink to subterms
  -- >   [l, r] ++
  -- >   -- recursively shrink subterms
  -- >   [Branch x' l' r' | (x', l', r') <- shrink (x, l, r)]
  --
  -- There are a couple of subtleties here:
  --
  -- * QuickCheck tries the shrinking candidates in the order they
  --   appear in the list, so we put more aggressive shrinking steps
  --   (such as replacing the whole tree by @Nil@) before smaller
  --   ones (such as recursively shrinking the subtrees).
  --
  -- * It is tempting to write the last line as
  --   @[Branch x' l' r' | x' <- shrink x, l' <- shrink l, r' <- shrink r]@
  --   but this is the /wrong thing/! It will force QuickCheck to shrink
  --   @x@, @l@ and @r@ in tandem, and shrinking will stop once /one/ of
  --   the three is fully shrunk.
  --
  -- There is a fair bit of boilerplate in the code above.
  -- We can avoid it with the help of some generic functions.
  -- The function 'genericShrink' tries shrinking a term to all of its
  -- subterms and, failing that, recursively shrinks the subterms.
  -- Using it, we can define 'shrink' as:
  --
  -- > shrink x = shrinkToNil x ++ genericShrink x
  -- >   where
  -- >     shrinkToNil Nil = []
  -- >     shrinkToNil (Branch _ l r) = [Nil]
  --
  -- 'genericShrink' is a combination of 'subterms', which shrinks
  -- a term to any of its subterms, and 'recursivelyShrink', which shrinks
  -- all subterms of a term. These may be useful if you need a bit more
  -- control over shrinking than 'genericShrink' gives you.
  --
  -- A final gotcha: we cannot define 'shrink' as simply @'shrink' x = Nil:'genericShrink' x@
  -- as this shrinks @Nil@ to @Nil@, and shrinking will go into an
  -- infinite loop.
  --
  -- If all this leaves you bewildered, you might try @'shrink' = 'genericShrink'@ to begin with,
  -- after deriving @Generic@ for your type. However, if your data type has any
  -- special invariants, you will need to check that 'genericShrink' can't break those invariants.
  shrink :: a -> [a]
  shrink _ = []

-- | Lifting of the 'Arbitrary' class to unary type constructors.
class Arbitrary1 f where
  liftArbitrary :: Gen a -> Gen (f a)
  liftShrink    :: (a -> [a]) -> f a -> [f a]
  liftShrink _ _ = []

arbitrary1 :: (Arbitrary1 f, Arbitrary a) => Gen (f a)
arbitrary1 = liftArbitrary arbitrary

shrink1 :: (Arbitrary1 f, Arbitrary a) => f a -> [f a]
shrink1 = liftShrink shrink

-- | Lifting of the 'Arbitrary' class to binary type constructors.
class Arbitrary2 f where
  liftArbitrary2 :: Gen a -> Gen b -> Gen (f a b)
  liftShrink2    :: (a -> [a]) -> (b -> [b]) -> f a b -> [f a b]
  liftShrink2 _ _ _ = []

arbitrary2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => Gen (f a b)
arbitrary2 = liftArbitrary2 arbitrary arbitrary

shrink2 :: (Arbitrary2 f, Arbitrary a, Arbitrary b) => f a b -> [f a b]
shrink2 = liftShrink2 shrink shrink

#ifndef NO_GENERICS
-- | Shrink a term to any of its immediate subterms,
-- and also recursively shrink all subterms.
genericShrink :: (Generic a, RecursivelyShrink (Rep a), GSubterms (Rep a) a) => a -> [a]
genericShrink x = subterms x ++ recursivelyShrink x

-- | Recursively shrink all immediate subterms.
recursivelyShrink :: (Generic a, RecursivelyShrink (Rep a)) => a -> [a]
recursivelyShrink = map to . grecursivelyShrink . from

class RecursivelyShrink f where
  grecursivelyShrink :: f a -> [f a]

instance (RecursivelyShrink f, RecursivelyShrink g) => RecursivelyShrink (f :*: g) where
  grecursivelyShrink (x :*: y) =
    [x' :*: y | x' <- grecursivelyShrink x] ++
    [x :*: y' | y' <- grecursivelyShrink y]

instance (RecursivelyShrink f, RecursivelyShrink g) => RecursivelyShrink (f :+: g) where
  grecursivelyShrink (L1 x) = map L1 (grecursivelyShrink x)
  grecursivelyShrink (R1 x) = map R1 (grecursivelyShrink x)

instance RecursivelyShrink f => RecursivelyShrink (M1 i c f) where
  grecursivelyShrink (M1 x) = map M1 (grecursivelyShrink x)

instance Arbitrary a => RecursivelyShrink (K1 i a) where
  grecursivelyShrink (K1 x) = map K1 (shrink x)

instance RecursivelyShrink U1 where
  grecursivelyShrink U1 = []

instance RecursivelyShrink V1 where
  -- The empty type can't be shrunk to anything.
  grecursivelyShrink _ = []

-- | All immediate subterms of a term.
subterms :: (Generic a, GSubterms (Rep a) a) => a -> [a]
subterms = gSubterms . from

class GSubterms f a where
  -- | Provides the immediate subterms of a term that are of the same type
  -- as the term itself.
  --
  -- Requires a constructor to be stripped off; this means it skips through
  -- @M1@ wrappers and returns @[]@ on everything that's not `(:*:)` or `(:+:)`.
  --
  -- Once a `(:*:)` or `(:+:)` constructor has been reached, this function
  -- delegates to `gSubtermsIncl` to return the immediately next constructor
  -- available.
  gSubterms :: f a -> [a]

instance GSubterms V1 a where
  -- The empty type can't be shrunk to anything.
  gSubterms _ = []

instance GSubterms U1 a where
  gSubterms U1 = []

instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubterms (f :*: g) a where
  gSubterms (l :*: r) = gSubtermsIncl l ++ gSubtermsIncl r

instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubterms (f :+: g) a where
  gSubterms (L1 x) = gSubtermsIncl x
  gSubterms (R1 x) = gSubtermsIncl x

instance GSubterms f a => GSubterms (M1 i c f) a where
  gSubterms (M1 x) = gSubterms x

instance GSubterms (K1 i a) b where
  gSubterms (K1 _) = []

class GSubtermsIncl f a where
  -- | Provides the immediate subterms of a term that are of the same type
  -- as the term itself.
  --
  -- In contrast to `gSubterms`, this returns the immediate next constructor
  -- available.
  gSubtermsIncl :: f a -> [a]

instance GSubtermsIncl V1 a where
  -- The empty type can't be shrunk to anything.
  gSubtermsIncl _ = []

instance GSubtermsIncl U1 a where
  gSubtermsIncl U1 = []

instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubtermsIncl (f :*: g) a where
  gSubtermsIncl (l :*: r) = gSubtermsIncl l ++ gSubtermsIncl r

instance (GSubtermsIncl f a, GSubtermsIncl g a) => GSubtermsIncl (f :+: g) a where
  gSubtermsIncl (L1 x) = gSubtermsIncl x
  gSubtermsIncl (R1 x) = gSubtermsIncl x

instance GSubtermsIncl f a => GSubtermsIncl (M1 i c f) a where
  gSubtermsIncl (M1 x) = gSubtermsIncl x

-- This is the important case: We've found a term of the same type.
instance OVERLAPPING_ GSubtermsIncl (K1 i a) a where
  gSubtermsIncl (K1 x) = [x]

instance OVERLAPPING_ GSubtermsIncl (K1 i a) b where
  gSubtermsIncl (K1 _) = []

#endif

-- instances

instance (CoArbitrary a) => Arbitrary1 ((->) a) where
  liftArbitrary arbB = promote (`coarbitrary` arbB)

instance (CoArbitrary a, Arbitrary b) => Arbitrary (a -> b) where
  arbitrary = arbitrary1

instance Arbitrary () where
  arbitrary = return ()

instance Arbitrary Bool where
  arbitrary = chooseEnum (False,True)
  shrink True = [False]
  shrink False = []

instance Arbitrary Ordering where
  arbitrary = elements [LT, EQ, GT]
  shrink GT = [EQ, LT]
  shrink LT = [EQ]
  shrink EQ = []

instance Arbitrary1 Maybe where
  liftArbitrary arb = frequency [(1, return Nothing), (3, liftM Just arb)]

  liftShrink shr (Just x) = Nothing : [ Just x' | x' <- shr x ]
  liftShrink _   Nothing  = []

instance Arbitrary a => Arbitrary (Maybe a) where
  arbitrary = arbitrary1
  shrink = shrink1

instance Arbitrary2 Either where
  liftArbitrary2 arbA arbB = oneof [liftM Left arbA, liftM Right arbB]

  liftShrink2 shrA _ (Left x)  = [ Left  x' | x' <- shrA x ]
  liftShrink2 _ shrB (Right y) = [ Right y' | y' <- shrB y ]

instance Arbitrary a => Arbitrary1 (Either a) where
  liftArbitrary = liftArbitrary2 arbitrary
  liftShrink = liftShrink2 shrink

instance (Arbitrary a, Arbitrary b) => Arbitrary (Either a b) where
  arbitrary = arbitrary2
  shrink = shrink2

instance Arbitrary1 [] where
  liftArbitrary = listOf
  liftShrink = shrinkList

instance Arbitrary a => Arbitrary [a] where
  arbitrary = arbitrary1
  shrink = shrink1

-- | Shrink a list of values given a shrinking function for individual values.
shrinkList :: (a -> [a]) -> [a] -> [[a]]
shrinkList shr xs = concat [ removes k n xs | k <- takeWhile (>0) (iterate (`div`2) n) ]
                 ++ shrinkOne xs
 where
  n = length xs

  shrinkOne []     = []
  shrinkOne (x:xs) = [ x':xs | x'  <- shr x ]
                  ++ [ x:xs' | xs' <- shrinkOne xs ]

  removes k n xs
    | k > n     = []
    | null xs2  = [[]]
    | otherwise = xs2 : map (xs1 ++) (removes k (n-k) xs2)
   where
    xs1 = take k xs
    xs2 = drop k xs

{-
  -- "standard" definition for lists:
  shrink []     = []
  shrink (x:xs) = [ xs ]
               ++ [ x:xs' | xs' <- shrink xs ]
               ++ [ x':xs | x'  <- shrink x ]
-}

instance Integral a => Arbitrary (Ratio a) where
  arbitrary = arbitrarySizedFractional
  shrink    = shrinkRealFrac

#if defined(MIN_VERSION_base) && MIN_VERSION_base(4,4,0)
instance Arbitrary a => Arbitrary (Complex a) where
#else
instance (RealFloat a, Arbitrary a) => Arbitrary (Complex a) where
#endif
  arbitrary = liftM2 (:+) arbitrary arbitrary
  shrink (x :+ y) = [ x' :+ y | x' <- shrink x ] ++
                    [ x :+ y' | y' <- shrink y ]

#ifndef NO_FIXED
instance HasResolution a => Arbitrary (Fixed a) where
  arbitrary = arbitrarySizedFractional
  shrink    = shrinkDecimal
#endif

instance Arbitrary2 (,) where
  liftArbitrary2 = liftM2 (,)
  liftShrink2 shrA shrB (x, y) =
       [ (x', y) | x' <- shrA x ]
    ++ [ (x, y') | y' <- shrB y ]

instance (Arbitrary a) => Arbitrary1 ((,) a) where
  liftArbitrary = liftArbitrary2 arbitrary
  liftShrink = liftShrink2 shrink

instance (Arbitrary a, Arbitrary b) => Arbitrary (a,b) where
  arbitrary = arbitrary2
  shrink = shrink2

instance (Arbitrary a, Arbitrary b, Arbitrary c)
      => Arbitrary (a,b,c)
 where
  arbitrary = liftM3 (,,) arbitrary arbitrary arbitrary

  shrink (x, y, z) =
    [ (x', y', z')
    | (x', (y', z')) <- shrink (x, (y, z)) ]

instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d)
      => Arbitrary (a,b,c,d)
 where
  arbitrary = liftM4 (,,,) arbitrary arbitrary arbitrary arbitrary

  shrink (w, x, y, z) =
    [ (w', x', y', z')
    | (w', (x', (y', z'))) <- shrink (w, (x, (y, z))) ]

instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e)
      => Arbitrary (a,b,c,d,e)
 where
  arbitrary = liftM5 (,,,,) arbitrary arbitrary arbitrary arbitrary arbitrary

  shrink (v, w, x, y, z) =
    [ (v', w', x', y', z')
    | (v', (w', (x', (y', z')))) <- shrink (v, (w, (x, (y, z)))) ]

instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e
         , Arbitrary f
         )
      => Arbitrary (a,b,c,d,e,f)
 where
  arbitrary = return (,,,,,)
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary

  shrink (u, v, w, x, y, z) =
    [ (u', v', w', x', y', z')
    | (u', (v', (w', (x', (y', z'))))) <- shrink (u, (v, (w, (x, (y, z))))) ]

instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e
         , Arbitrary f, Arbitrary g
         )
      => Arbitrary (a,b,c,d,e,f,g)
 where
  arbitrary = return (,,,,,,)
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary <*> arbitrary

  shrink (t, u, v, w, x, y, z) =
    [ (t', u', v', w', x', y', z')
    | (t', (u', (v', (w', (x', (y', z')))))) <- shrink (t, (u, (v, (w, (x, (y, z)))))) ]

instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e
         , Arbitrary f, Arbitrary g, Arbitrary h
         )
      => Arbitrary (a,b,c,d,e,f,g,h)
 where
  arbitrary = return (,,,,,,,)
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary

  shrink (s, t, u, v, w, x, y, z) =
    [ (s', t', u', v', w', x', y', z')
    | (s', (t', (u', (v', (w', (x', (y', z')))))))
      <- shrink (s, (t, (u, (v, (w, (x, (y, z))))))) ]

instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e
         , Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i
         )
      => Arbitrary (a,b,c,d,e,f,g,h,i)
 where
  arbitrary = return (,,,,,,,,)
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary

  shrink (r, s, t, u, v, w, x, y, z) =
    [ (r', s', t', u', v', w', x', y', z')
    | (r', (s', (t', (u', (v', (w', (x', (y', z'))))))))
      <- shrink (r, (s, (t, (u, (v, (w, (x, (y, z)))))))) ]

instance ( Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d, Arbitrary e
         , Arbitrary f, Arbitrary g, Arbitrary h, Arbitrary i, Arbitrary j
         )
      => Arbitrary (a,b,c,d,e,f,g,h,i,j)
 where
  arbitrary = return (,,,,,,,,,)
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary <*> arbitrary <*> arbitrary
          <*> arbitrary <*> arbitrary

  shrink (q, r, s, t, u, v, w, x, y, z) =
    [ (q', r', s', t', u', v', w', x', y', z')
    | (q', (r', (s', (t', (u', (v', (w', (x', (y', z')))))))))
      <- shrink (q, (r, (s, (t, (u, (v, (w, (x, (y, z))))))))) ]

-- typical instance for primitive (numerical) types

instance Arbitrary Integer where
  arbitrary = arbitrarySizedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Int where
  arbitrary = arbitrarySizedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Int8 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Int16 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Int32 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Int64 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Word where
  arbitrary = arbitrarySizedNatural
  shrink    = shrinkIntegral

instance Arbitrary Word8 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Word16 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Word32 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Word64 where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink    = shrinkIntegral

instance Arbitrary Char where
  arbitrary =
    frequency
      [(3, arbitraryASCIIChar),
       (1, arbitraryUnicodeChar)]

  shrink c = filter (<. c) $ nub
            $ ['a','b','c']
            ++ [ toLower c | isUpper c ]
            ++ ['A','B','C']
            ++ ['1','2','3']
            ++ [' ','\n']
     where
      a <. b  = stamp a < stamp b
      stamp a = ( (not (isLower a)
                , not (isUpper a)
                , not (isDigit a))
                , (not (a==' ')
                , not (isSpace a)
                , a)
                )

instance Arbitrary Float where
  arbitrary = oneof
    -- generate 0..1 numbers with full precision
    [ genFloat
    -- generate integral numbers
    , fromIntegral <$> (arbitrary :: Gen Int)
    -- generate fractions with small denominators
    , smallDenominators
    -- uniform -size..size with with denominators ~ size
    , uniform
    -- and uniform -size..size with higher precision
    , arbitrarySizedFractional
    ]
    where
      smallDenominators = sized $ \n -> do
        i <- chooseInt (0, n)
        pure (fromRational (streamNth i rationalUniverse))

      uniform = sized $ \n -> do
        let n' = toInteger n
        b <- chooseInteger (1, max 1 n')
        a <- chooseInteger ((-n') * b, n' * b)
        return (fromRational (a % b))

  shrink    = shrinkDecimal

instance Arbitrary Double where
  arbitrary = oneof
    -- generate 0..1 numbers with full precision
    [ genDouble
    -- generate integral numbers
    , fromIntegral <$> (arbitrary :: Gen Int)
    -- generate fractions with small denominators
    , smallDenominators
    -- uniform -size..size with with denominators ~ size
    , uniform
    -- and uniform -size..size with higher precision
    , arbitrarySizedFractional
    ]
    where
      smallDenominators = sized $ \n -> do
        i <- chooseInt (0, n)
        pure (fromRational (streamNth i rationalUniverse))

      uniform = sized $ \n -> do
        let n' = toInteger n
        b <- chooseInteger (1, max 1 n')
        a <- chooseInteger ((-n') * b, n' * b)
        return (fromRational (a % b))

  shrink    = shrinkDecimal

instance Arbitrary CChar where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CSChar where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CUChar where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CShort where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CUShort where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CInt where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CUInt where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CLong where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CULong where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CPtrdiff where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CSize where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CWchar where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CSigAtomic where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CLLong where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CULLong where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CIntPtr where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CUIntPtr where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CIntMax where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

instance Arbitrary CUIntMax where
  arbitrary = arbitrarySizedBoundedIntegral
  shrink = shrinkIntegral

#ifndef NO_CTYPES_CONSTRUCTORS
-- The following four types have no Bounded instance,
-- so we fake it by discovering the bounds at runtime.
instance Arbitrary CClock where
  arbitrary = fmap CClock arbitrary
  shrink (CClock x) = map CClock (shrink x)

instance Arbitrary CTime where
  arbitrary = fmap CTime arbitrary
  shrink (CTime x) = map CTime (shrink x)

#ifndef NO_FOREIGN_C_USECONDS
instance Arbitrary CUSeconds where
  arbitrary = fmap CUSeconds arbitrary
  shrink (CUSeconds x) = map CUSeconds (shrink x)

instance Arbitrary CSUSeconds where
  arbitrary = fmap CSUSeconds arbitrary
  shrink (CSUSeconds x) = map CSUSeconds (shrink x)
#endif
#endif

instance Arbitrary CFloat where
  arbitrary = arbitrarySizedFractional
  shrink = shrinkDecimal

instance Arbitrary CDouble where
  arbitrary = arbitrarySizedFractional
  shrink = shrinkDecimal

-- Arbitrary instances for container types
instance (Ord a, Arbitrary a) => Arbitrary (Set.Set a) where
  arbitrary = fmap Set.fromList arbitrary
  shrink = map Set.fromList . shrink . Set.toList
instance (Ord k, Arbitrary k) => Arbitrary1 (Map.Map k) where
  liftArbitrary = fmap Map.fromList . liftArbitrary . liftArbitrary
  liftShrink shr = map Map.fromList . liftShrink (liftShrink shr) . Map.toList
instance (Ord k, Arbitrary k, Arbitrary v) => Arbitrary (Map.Map k v) where
  arbitrary = arbitrary1
  shrink = shrink1
instance Arbitrary IntSet.IntSet where
  arbitrary = fmap IntSet.fromList arbitrary
  shrink = map IntSet.fromList . shrink . IntSet.toList
instance Arbitrary1 IntMap.IntMap where
  liftArbitrary = fmap IntMap.fromList . liftArbitrary . liftArbitrary
  liftShrink shr = map IntMap.fromList . liftShrink (liftShrink shr) . IntMap.toList
instance Arbitrary a => Arbitrary (IntMap.IntMap a) where
  arbitrary = arbitrary1
  shrink = shrink1
instance Arbitrary1 Sequence.Seq where
  liftArbitrary = fmap Sequence.fromList . liftArbitrary
  liftShrink shr = map Sequence.fromList . liftShrink shr . toList
instance Arbitrary a => Arbitrary (Sequence.Seq a) where
  arbitrary = arbitrary1
  shrink = shrink1
instance Arbitrary1 Tree.Tree where
    liftArbitrary arb = sized $ \n -> do
        k <- chooseInt (0, n)
        go k
      where
        go n = do -- n is the size of the trees.
            value <- arb
            pars <- arbPartition (n - 1) -- can go negative!
            forest <- mapM go pars
            return $ Tree.Node value forest

        arbPartition :: Int -> Gen [Int]
        arbPartition k = case compare k 1 of
            LT -> pure []
            EQ -> pure [1]
            GT -> do
                first <- chooseInt (1, k)
                rest <- arbPartition $ k - first
                shuffle (first : rest)

    liftShrink shr = go
      where
        go (Tree.Node val forest) = forest ++
            [ Tree.Node e fs
            | (e, fs) <- liftShrink2 shr (liftShrink go) (val, forest)
            ]
instance Arbitrary a => Arbitrary (Tree.Tree a) where
  arbitrary = arbitrary1
  shrink = shrink1

-- Arbitrary instance for Ziplist
instance Arbitrary1 ZipList where
  liftArbitrary = fmap ZipList . liftArbitrary
  liftShrink shr = map ZipList . liftShrink shr . getZipList
instance Arbitrary a => Arbitrary (ZipList a) where
  arbitrary = arbitrary1
  shrink = shrink1

#ifndef NO_TRANSFORMERS
-- Arbitrary instance for transformers' Functors
instance Arbitrary1 Identity where
  liftArbitrary = fmap Identity
  liftShrink shr = map Identity . shr . runIdentity
instance Arbitrary a => Arbitrary (Identity a) where
  arbitrary = arbitrary1
  shrink = shrink1

instance Arbitrary2 Constant where
  liftArbitrary2 arbA _ = fmap Constant arbA
  liftShrink2 shrA _ = fmap Constant . shrA . getConstant
instance Arbitrary a => Arbitrary1 (Constant a) where
  liftArbitrary = liftArbitrary2 arbitrary
  liftShrink = liftShrink2 shrink
-- Have to be defined explicitly, as Constant is kind polymorphic
instance Arbitrary a => Arbitrary (Constant a b) where
  arbitrary = fmap Constant arbitrary
  shrink = map Constant . shrink . getConstant

instance (Arbitrary1 f, Arbitrary1 g) => Arbitrary1 (Product f g) where
  liftArbitrary arb = liftM2 Pair (liftArbitrary arb) (liftArbitrary arb)
  liftShrink shr (Pair f g) =
    [ Pair f' g | f' <- liftShrink shr f ] ++
    [ Pair f g' | g' <- liftShrink shr g ]
instance (Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Product f g a) where
  arbitrary = arbitrary1
  shrink = shrink1

instance (Arbitrary1 f, Arbitrary1 g) => Arbitrary1 (Compose f g) where
  liftArbitrary = fmap Compose . liftArbitrary . liftArbitrary
  liftShrink shr = map Compose . liftShrink (liftShrink shr) . getCompose
instance (Arbitrary1 f, Arbitrary1 g, Arbitrary a) => Arbitrary (Compose f g a) where
  arbitrary = arbitrary1
  shrink = shrink1
#endif

-- Arbitrary instance for Const
instance Arbitrary2 Const where
  liftArbitrary2 arbA _ = fmap Const arbA
  liftShrink2 shrA _ = fmap Const . shrA . getConst
instance Arbitrary a => Arbitrary1 (Const a) where
  liftArbitrary = liftArbitrary2 arbitrary
  liftShrink = liftShrink2 shrink
-- Have to be defined explicitly, as Const is kind polymorphic
instance Arbitrary a => Arbitrary (Const a b) where
  arbitrary = fmap Const arbitrary
  shrink = map Const . shrink . getConst

instance Arbitrary (m a) => Arbitrary (WrappedMonad m a) where
  arbitrary = WrapMonad <$> arbitrary
  shrink (WrapMonad a) = map WrapMonad (shrink a)

instance Arbitrary (a b c) => Arbitrary (WrappedArrow a b c) where
  arbitrary = WrapArrow <$> arbitrary
  shrink (WrapArrow a) = map WrapArrow (shrink a)

-- Arbitrary instances for Monoid
instance Arbitrary a => Arbitrary (Monoid.Dual a) where
  arbitrary = fmap Monoid.Dual arbitrary
  shrink = map Monoid.Dual . shrink . Monoid.getDual

instance (Arbitrary a, CoArbitrary a) => Arbitrary (Monoid.Endo a) where
  arbitrary = fmap Monoid.Endo arbitrary
  shrink = map Monoid.Endo . shrink . Monoid.appEndo

instance Arbitrary Monoid.All where
  arbitrary = fmap Monoid.All arbitrary
  shrink = map Monoid.All . shrink . Monoid.getAll

instance Arbitrary Monoid.Any where
  arbitrary = fmap Monoid.Any arbitrary
  shrink = map Monoid.Any . shrink . Monoid.getAny

instance Arbitrary a => Arbitrary (Monoid.Sum a) where
  arbitrary = fmap Monoid.Sum arbitrary
  shrink = map Monoid.Sum . shrink . Monoid.getSum

instance Arbitrary a => Arbitrary (Monoid.Product a) where
  arbitrary = fmap Monoid.Product  arbitrary
  shrink = map Monoid.Product  . shrink . Monoid.getProduct

#if defined(MIN_VERSION_base)
#if MIN_VERSION_base(3,0,0)
instance Arbitrary a => Arbitrary (Monoid.First a) where
  arbitrary = fmap Monoid.First arbitrary
  shrink = map Monoid.First . shrink . Monoid.getFirst

instance Arbitrary a => Arbitrary (Monoid.Last a) where
  arbitrary = fmap Monoid.Last arbitrary
  shrink = map Monoid.Last . shrink . Monoid.getLast
#endif

#if MIN_VERSION_base(4,8,0)
instance Arbitrary (f a) => Arbitrary (Monoid.Alt f a) where
  arbitrary = fmap Monoid.Alt arbitrary
  shrink = map Monoid.Alt . shrink . Monoid.getAlt
#endif
#endif

-- | Generates 'Version' with non-empty non-negative @versionBranch@, and empty @versionTags@
instance Arbitrary Version where
  arbitrary = sized $ \n ->
    do k <- chooseInt (0, log2 n)
       xs <- vectorOf (k+1) arbitrarySizedNatural
       return (Version xs [])
    where
      log2 :: Int -> Int
      log2 n | n <= 1 = 0
             | otherwise = 1 + log2 (n `div` 2)

  shrink (Version xs _) =
    [ Version xs' []
    | xs' <- shrink xs
    , length xs' > 0
    , all (>=0) xs'
    ]

instance Arbitrary QCGen where
  arbitrary = MkGen (\g _ -> g)

instance Arbitrary ExitCode where
  arbitrary = frequency [(1, return ExitSuccess), (3, liftM ExitFailure arbitrary)]

  shrink (ExitFailure x) = ExitSuccess : [ ExitFailure x' | x' <- shrink x ]
  shrink _        = []

#if defined(MIN_VERSION_base)
#if MIN_VERSION_base(4,2,0)
instance Arbitrary Newline where
  arbitrary = elements [LF, CRLF]

  -- The behavior of code for LF is generally simpler than for CRLF
  -- See the documentation for this type, which states that Haskell
  -- Internally always assumes newlines are \n and this type represents
  -- how to translate that to and from the outside world, where LF means
  -- no translation.
  shrink LF = []
  shrink CRLF = [LF]

instance Arbitrary NewlineMode where
  arbitrary = NewlineMode <$> arbitrary <*> arbitrary

  shrink (NewlineMode inNL outNL) = [NewlineMode inNL' outNL' | (inNL', outNL') <- shrink (inNL, outNL)]
#endif
#endif

-- ** Helper functions for implementing arbitrary

-- | Apply a binary function to random arguments.
applyArbitrary2 :: (Arbitrary a, Arbitrary b) => (a -> b -> r) -> Gen r
applyArbitrary2 f = liftA2 f arbitrary arbitrary

-- | Apply a ternary function to random arguments.
applyArbitrary3
  :: (Arbitrary a, Arbitrary b, Arbitrary c)
  => (a -> b -> c -> r) -> Gen r
applyArbitrary3 f = liftA3 f arbitrary arbitrary arbitrary

-- | Apply a function of arity 4 to random arguments.
applyArbitrary4
  :: (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d)
  => (a -> b -> c -> d -> r) -> Gen r
applyArbitrary4 f = applyArbitrary3 (uncurry f)

-- | Generates an integral number. The number can be positive or negative
-- and its maximum absolute value depends on the size parameter.
arbitrarySizedIntegral :: Integral a => Gen a
arbitrarySizedIntegral =
  sized $ \n ->
  inBounds fromIntegral (chooseInt (-n, n))

-- | Generates a natural number. The number's maximum value depends on
-- the size parameter.
arbitrarySizedNatural :: Integral a => Gen a
arbitrarySizedNatural =
  sized $ \n ->
  inBounds fromIntegral (chooseInt (0, n))

inBounds :: Integral a => (Int -> a) -> Gen Int -> Gen a
inBounds fi g = fmap fi (g `suchThat` (\x -> toInteger x == toInteger (fi x)))

-- | Uniformly generates a fractional number. The number can be positive or negative
-- and its maximum absolute value depends on the size parameter.
arbitrarySizedFractional :: Fractional a => Gen a
arbitrarySizedFractional =
  sized $ \n -> do
    denom <- chooseInt (1, max 1 n)
    numer <- chooseInt (-n*denom, n*denom)
    pure $ fromIntegral numer / fromIntegral denom

-- Useful for getting at minBound and maxBound without having to
-- fiddle around with asTypeOf.
{-# INLINE withBounds #-}
withBounds :: Bounded a => (a -> a -> Gen a) -> Gen a
withBounds k = k minBound maxBound

-- | Generates an integral number. The number is chosen uniformly from
-- the entire range of the type. You may want to use
-- 'arbitrarySizedBoundedIntegral' instead.
arbitraryBoundedIntegral :: (Bounded a, Integral a) => Gen a
arbitraryBoundedIntegral = chooseBoundedIntegral (minBound, maxBound)

-- | Generates an element of a bounded type. The element is
-- chosen from the entire range of the type.
arbitraryBoundedRandom :: (Bounded a, Random a) => Gen a
arbitraryBoundedRandom = choose (minBound,maxBound)

-- | Generates an element of a bounded enumeration.
arbitraryBoundedEnum :: (Bounded a, Enum a) => Gen a
arbitraryBoundedEnum = chooseEnum (minBound, maxBound)

-- | Generates an integral number from a bounded domain. The number is
-- chosen from the entire range of the type, but small numbers are
-- generated more often than big numbers. Inspired by demands from
-- Phil Wadler.
arbitrarySizedBoundedIntegral :: (Bounded a, Integral a) => Gen a
-- INLINEABLE so that this combinator gets specialised at each type,
-- which means that the constant 'bits' in the let-block below will
-- only be computed once.
{-# INLINEABLE arbitrarySizedBoundedIntegral #-}
arbitrarySizedBoundedIntegral =
  withBounds $ \mn mx ->
  let ilog2 1 = 0
      ilog2 n | n > 0 = 1 + ilog2 (n `div` 2)

      -- How many bits are needed to represent this type?
      -- (This number is an upper bound, not exact.)
      bits = ilog2 (toInteger mx - toInteger mn + 1) in
  sized $ \k ->
    let
      -- Reach maximum size by k=80, or quicker for small integer types
      power = ((bits `max` 40) * k) `div` 80

      -- Bounds should be 2^power, but:
      --   * clamp the result to minBound/maxBound
      --   * clamp power to 'bits', in case k is a huge number
      lo = toInteger mn `max` (-1 `shiftL` (power `min` bits))
      hi = toInteger mx `min` (1 `shiftL` (power `min` bits)) in
    fmap fromInteger (chooseInteger (lo, hi))

-- ** Generators for various kinds of character

-- | Generates any Unicode character (but not a surrogate)
arbitraryUnicodeChar :: Gen Char
arbitraryUnicodeChar =
  arbitraryBoundedEnum `suchThat` isValidUnicode
  where
    isValidUnicode c = case generalCategory c of
      Surrogate -> False
      NotAssigned -> False
      _ -> True

-- | Generates a random ASCII character (0-127).
arbitraryASCIIChar :: Gen Char
arbitraryASCIIChar = chooseEnum ('\0', '\127')

-- | Generates a printable Unicode character.
arbitraryPrintableChar :: Gen Char
arbitraryPrintableChar = arbitrary `suchThat` isPrint

-- ** Helper functions for implementing shrink

-- | Returns no shrinking alternatives.
shrinkNothing :: a -> [a]
shrinkNothing _ = []

-- | Map a shrink function to another domain. This is handy if your data type
-- has special invariants, but is /almost/ isomorphic to some other type.
--
-- @
-- shrinkOrderedList :: (Ord a, Arbitrary a) => [a] -> [[a]]
-- shrinkOrderedList = shrinkMap sort id
--
-- shrinkSet :: (Ord a, Arbitrary a) => Set a -> [Set a]
-- shrinkSet = shrinkMap fromList toList
-- @
shrinkMap :: Arbitrary a => (a -> b) -> (b -> a) -> b -> [b]
shrinkMap f g = shrinkMapBy f g shrink

-- | Non-overloaded version of `shrinkMap`.
shrinkMapBy :: (a -> b) -> (b -> a) -> (a -> [a]) -> b -> [b]
shrinkMapBy f g shr = map f . shr . g

-- | Shrink an integral number.
shrinkIntegral :: Integral a => a -> [a]
shrinkIntegral x =
  nub $
  [ -x
  | x < 0, -x > x
  ] ++
  [ x'
  | x' <- takeWhile (<< x) (0:[ x - i | i <- tail (iterate (`quot` 2) x) ])
  ]
 where
   -- a << b is "morally" abs a < abs b, but taking care of overflow.
   a << b = case (a >= 0, b >= 0) of
            (True,  True)  -> a < b
            (False, False) -> a > b
            (True,  False) -> a + b < 0
            (False, True)  -> a + b > 0

-- | Shrink a fraction, preferring numbers with smaller
-- numerators or denominators. See also 'shrinkDecimal'.
shrinkRealFrac :: RealFrac a => a -> [a]
shrinkRealFrac x
  | not (x == x)  = 0 : take 10 (iterate (*2) 0) -- NaN
  | not (2*x+1>x) = 0 : takeWhile (<x) (iterate (*2) 0) -- infinity
  | x < 0 = negate x:map negate (shrinkRealFrac (negate x))
  | otherwise =
    -- To ensure termination
    filter (\y -> abs y < abs x) $
      -- Try shrinking to an integer first
      map fromInteger (shrink (truncate x) ++ [truncate x]) ++
      -- Shrink the numerator
      [fromRational (num' % denom) | num' <- shrink num] ++
      -- Shrink the denominator, and keep the fraction as close
      -- to the original as possible, rounding towards zero
      [fromRational (truncate (num * denom' % denom) % denom')
      | denom' <- shrink denom, denom' /= 0 ]
  where
    num = numerator (toRational x)
    denom = denominator (toRational x)

-- | Shrink a real number, preferring numbers with shorter
-- decimal representations. See also 'shrinkRealFrac'.
shrinkDecimal :: RealFrac a => a -> [a]
shrinkDecimal x
  | not (x == x)  = 0 : take 10 (iterate (*2) 0)        -- NaN
  | not (2*abs x+1>abs x) = 0 : takeWhile (<x) (iterate (*2) 0) -- infinity
  | otherwise =
    -- e.g. shrink pi =
    --   shrink 3 ++ map (/ 10) (shrink 31) ++
    --   map (/ 100) (shrink 314) + ...,
    -- where the inner calls to shrink use integer shrinking.
    [ y
    | precision <- take 6 (iterate (*10) 1),
      let m = round (toRational x * precision),
      precision == 1 || m `mod` 10 /= 0, -- don't allow shrinking to increase digits
      n <- m:shrink m,
      let y = fromRational (fromInteger n / precision),
      abs y < abs x ]

--------------------------------------------------------------------------
-- ** CoArbitrary

#ifndef NO_GENERICS
-- | Used for random generation of functions.
-- You should consider using 'Test.QuickCheck.Fun' instead, which
-- can show the generated functions as strings.
--
-- If you are using a recent GHC, there is a default definition of
-- 'coarbitrary' using 'genericCoarbitrary', so if your type has a
-- 'Generic' instance it's enough to say
--
-- > instance CoArbitrary MyType
--
-- You should only use 'genericCoarbitrary' for data types where
-- equality is structural, i.e. if you can't have two different
-- representations of the same value. An example where it's not
-- safe is sets implemented using binary search trees: the same
-- set can be represented as several different trees.
-- Here you would have to explicitly define
-- @coarbitrary s = coarbitrary (toList s)@.
#else
-- | Used for random generation of functions.
#endif
class CoArbitrary a where
  -- | Used to generate a function of type @a -> b@.
  -- The first argument is a value, the second a generator.
  -- You should use 'variant' to perturb the random generator;
  -- the goal is that different values for the first argument will
  -- lead to different calls to 'variant'. An example will help:
  --
  -- @
  -- instance CoArbitrary a => CoArbitrary [a] where
  --   coarbitrary []     = 'variant' 0
  --   coarbitrary (x:xs) = 'variant' 1 . coarbitrary (x,xs)
  -- @
  coarbitrary :: a -> Gen b -> Gen b
#ifndef NO_GENERICS
  default coarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b
  coarbitrary = genericCoarbitrary

-- | Generic CoArbitrary implementation.
genericCoarbitrary :: (Generic a, GCoArbitrary (Rep a)) => a -> Gen b -> Gen b
genericCoarbitrary = gCoarbitrary . from

class GCoArbitrary f where
  gCoarbitrary :: f a -> Gen b -> Gen b

instance GCoArbitrary U1 where
  gCoarbitrary U1 = id

instance (GCoArbitrary f, GCoArbitrary g) => GCoArbitrary (f :*: g) where
  -- Like the instance for tuples.
  gCoarbitrary (l :*: r) = gCoarbitrary l . gCoarbitrary r

instance (GCoArbitrary f, GCoArbitrary g) => GCoArbitrary (f :+: g) where
  -- Like the instance for Either.
  gCoarbitrary (L1 x) = variant 0 . gCoarbitrary x
  gCoarbitrary (R1 x) = variant 1 . gCoarbitrary x

instance GCoArbitrary f => GCoArbitrary (M1 i c f) where
  gCoarbitrary (M1 x) = gCoarbitrary x

instance CoArbitrary a => GCoArbitrary (K1 i a) where
  gCoarbitrary (K1 x) = coarbitrary x
#endif

{-# DEPRECATED (><) "Use ordinary function composition instead" #-}
-- | Combine two generator perturbing functions, for example the
-- results of calls to 'variant' or 'coarbitrary'.
(><) :: (Gen a -> Gen a) -> (Gen a -> Gen a) -> (Gen a -> Gen a)
(><) = (.)

instance (Arbitrary a, CoArbitrary b) => CoArbitrary (a -> b) where
  coarbitrary f gen =
    do xs <- arbitrary
       coarbitrary (map f xs) gen

instance CoArbitrary () where
  coarbitrary _ = id

instance CoArbitrary Bool where
  coarbitrary False = variant 0
  coarbitrary True  = variant 1

instance CoArbitrary Ordering where
  coarbitrary GT = variant 0
  coarbitrary EQ = variant 1
  coarbitrary LT = variant 2

instance CoArbitrary a => CoArbitrary (Maybe a) where
  coarbitrary Nothing  = variant 0
  coarbitrary (Just x) = variant 1 . coarbitrary x

instance (CoArbitrary a, CoArbitrary b) => CoArbitrary (Either a b) where
  coarbitrary (Left x)  = variant 0 . coarbitrary x
  coarbitrary (Right y) = variant 1 . coarbitrary y

instance CoArbitrary a => CoArbitrary [a] where
  coarbitrary []     = variant 0
  coarbitrary (x:xs) = variant 1 . coarbitrary (x,xs)

instance (Integral a, CoArbitrary a) => CoArbitrary (Ratio a) where
  coarbitrary r = coarbitrary (numerator r,denominator r)

#ifndef NO_FIXED
instance HasResolution a => CoArbitrary (Fixed a) where
  coarbitrary = coarbitraryReal
#endif

#if defined(MIN_VERSION_base) && MIN_VERSION_base(4,4,0)
instance CoArbitrary a => CoArbitrary (Complex a) where
#else
instance (RealFloat a, CoArbitrary a) => CoArbitrary (Complex a) where
#endif
  coarbitrary (x :+ y) = coarbitrary x . coarbitrary y

instance (CoArbitrary a, CoArbitrary b)
      => CoArbitrary (a,b)
 where
  coarbitrary (x,y) = coarbitrary x
                    . coarbitrary y

instance (CoArbitrary a, CoArbitrary b, CoArbitrary c)
      => CoArbitrary (a,b,c)
 where
  coarbitrary (x,y,z) = coarbitrary x
                      . coarbitrary y
                      . coarbitrary z

instance (CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d)
      => CoArbitrary (a,b,c,d)
 where
  coarbitrary (x,y,z,v) = coarbitrary x
                        . coarbitrary y
                        . coarbitrary z
                        . coarbitrary v

instance (CoArbitrary a, CoArbitrary b, CoArbitrary c, CoArbitrary d, CoArbitrary e)
      => CoArbitrary (a,b,c,d,e)
 where
  coarbitrary (x,y,z,v,w) = coarbitrary x
                          . coarbitrary y
                          . coarbitrary z
                          . coarbitrary v
                          . coarbitrary w

-- typical instance for primitive (numerical) types

instance CoArbitrary Integer where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Int where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Int8 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Int16 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Int32 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Int64 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Word where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Word8 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Word16 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Word32 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Word64 where
  coarbitrary = coarbitraryIntegral

instance CoArbitrary Char where
  coarbitrary = coarbitrary . ord

instance CoArbitrary Float where
  coarbitrary = coarbitraryReal

instance CoArbitrary Double where
  coarbitrary = coarbitraryReal

-- Coarbitrary instances for container types
instance CoArbitrary a => CoArbitrary (Set.Set a) where
  coarbitrary = coarbitrary. Set.toList
instance (CoArbitrary k, CoArbitrary v) => CoArbitrary (Map.Map k v) where
  coarbitrary = coarbitrary . Map.toList
instance CoArbitrary IntSet.IntSet where
  coarbitrary = coarbitrary . IntSet.toList
instance CoArbitrary a => CoArbitrary (IntMap.IntMap a) where
  coarbitrary = coarbitrary . IntMap.toList
instance CoArbitrary a => CoArbitrary (Sequence.Seq a) where
  coarbitrary = coarbitrary . toList
instance CoArbitrary a => CoArbitrary (Tree.Tree a) where
  coarbitrary (Tree.Node val forest) = coarbitrary val . coarbitrary forest

-- CoArbitrary instance for Ziplist
instance CoArbitrary a => CoArbitrary (ZipList a) where
  coarbitrary = coarbitrary . getZipList

#ifndef NO_TRANSFORMERS
-- CoArbitrary instance for transformers' Functors
instance CoArbitrary a => CoArbitrary (Identity a) where
  coarbitrary = coarbitrary . runIdentity

instance CoArbitrary a => CoArbitrary (Constant a b) where
  coarbitrary = coarbitrary . getConstant
#endif

-- CoArbitrary instance for Const
instance CoArbitrary a => CoArbitrary (Const a b) where
  coarbitrary = coarbitrary . getConst

-- CoArbitrary instances for Monoid
instance CoArbitrary a => CoArbitrary (Monoid.Dual a) where
  coarbitrary = coarbitrary . Monoid.getDual

instance (Arbitrary a, CoArbitrary a) => CoArbitrary (Monoid.Endo a) where
  coarbitrary = coarbitrary . Monoid.appEndo

instance CoArbitrary Monoid.All where
  coarbitrary = coarbitrary . Monoid.getAll

instance CoArbitrary Monoid.Any where
  coarbitrary = coarbitrary . Monoid.getAny

instance CoArbitrary a => CoArbitrary (Monoid.Sum a) where
  coarbitrary = coarbitrary . Monoid.getSum

instance CoArbitrary a => CoArbitrary (Monoid.Product a) where
  coarbitrary = coarbitrary . Monoid.getProduct

#if defined(MIN_VERSION_base)
#if MIN_VERSION_base(3,0,0)
instance CoArbitrary a => CoArbitrary (Monoid.First a) where
  coarbitrary = coarbitrary . Monoid.getFirst

instance CoArbitrary a => CoArbitrary (Monoid.Last a) where
  coarbitrary = coarbitrary . Monoid.getLast
#endif

#if MIN_VERSION_base(4,8,0)
instance CoArbitrary (f a) => CoArbitrary (Monoid.Alt f a) where
  coarbitrary = coarbitrary . Monoid.getAlt
#endif
#endif

instance CoArbitrary Version where
  coarbitrary (Version a b) = coarbitrary (a, b)

#if defined(MIN_VERSION_base)
#if MIN_VERSION_base(4,2,0)
instance CoArbitrary Newline where
  coarbitrary LF = variant 0
  coarbitrary CRLF = variant 1

instance CoArbitrary NewlineMode where
  coarbitrary (NewlineMode inNL outNL) = coarbitrary inNL . coarbitrary outNL
#endif
#endif

-- ** Helpers for implementing coarbitrary

-- | A 'coarbitrary' implementation for integral numbers.
coarbitraryIntegral :: Integral a => a -> Gen b -> Gen b
coarbitraryIntegral = variant

-- | A 'coarbitrary' implementation for real numbers.
coarbitraryReal :: Real a => a -> Gen b -> Gen b
coarbitraryReal x = coarbitrary (toRational x)

-- | 'coarbitrary' helper for lazy people :-).
coarbitraryShow :: Show a => a -> Gen b -> Gen b
coarbitraryShow x = coarbitrary (show x)

-- | A 'coarbitrary' implementation for enums.
coarbitraryEnum :: Enum a => a -> Gen b -> Gen b
coarbitraryEnum = variant . fromEnum

--------------------------------------------------------------------------
-- ** arbitrary generators

-- these are here and not in Gen because of the Arbitrary class constraint

-- | Generates a list of a given length.
vector :: Arbitrary a => Int -> Gen [a]
vector k = vectorOf k arbitrary

-- | Generates an ordered list.
orderedList :: (Ord a, Arbitrary a) => Gen [a]
orderedList = sort `fmap` arbitrary

-- | Generates an infinite list.
infiniteList :: Arbitrary a => Gen [a]
infiniteList = infiniteListOf arbitrary

--------------------------------------------------------------------------
-- ** Rational helper

infixr 5 :<
data Stream a = !a :< Stream a

streamNth :: Int -> Stream a -> a
streamNth n (x :< xs) | n <= 0    = x
                      | otherwise = streamNth (n - 1) xs

-- We read into this stream only with ~size argument,
-- so it's ok to have it as CAF.
--
rationalUniverse :: Stream Rational
rationalUniverse = 0 :< 1 :< (-1) :< go leftSideStream
  where
    go (x :< xs) =
      let nx = -x
          rx = recip x
          nrx = -rx
      in nx `seq` rx `seq` nrx `seq` (x :< rx :< nx :< nrx :< go xs)

-- All the rational numbers on the left side of the Calkin-Wilf tree,
-- in breadth-first order.
leftSideStream :: Stream Rational
leftSideStream = (1 % 2) :< go leftSideStream
  where
    go (x :< xs) =
        lChild `seq` rChild `seq`
        (lChild :< rChild :< go xs)
      where
        nd = numerator x + denominator x
        lChild = numerator x % nd
        rChild = nd % denominator x

--------------------------------------------------------------------------
-- the end.


{-# LANGUAGE TemplateHaskell, QuasiQuotes #-}

module Main where

import Language.Rust.Quote    ( ty )
import Language.Rust.Inline
import Foreign.Marshal.Unsafe ( unsafeLocalState )
import Foreign.Ptr            ( Ptr )
import Foreign.Storable       ( peek )
import Foreign.Marshal        ( with )

import Data.Complex           ( Complex(..) )

-- We add to our context the knowledge that a Rust pointer to a 'Complex' is
-- the same as a Haskell 'Ptr' to a 'Complex Float'.
extendContext basic
extendContext (singleton [ty| *mut Complex |] [t| Ptr (Complex Float) |])

setCrateRoot []

-- Rust representation of Haskell's 'Complex'
[rust|
#[repr(C)]
pub struct Complex {
  re: f32,
  im: f32,
}
|]

-- | Add two complex numbers in Rust
add :: Complex Float -> Complex Float -> Complex Float
add z1 z2 = unsafeLocalState $
  with z1 $ \ptr1 ->
    with z2 $ \ptr2 -> do
      ptr3 <- [rustIO| *mut Complex {
        let z1: *mut Complex = $(ptr1: *mut Complex);
        let z2: *mut Complex = $(ptr2: *mut Complex);

        let z3: Box<Complex> = Box::new(unsafe {
          Complex {
            re: (*z1).re + (*z2).re,
            im: (*z1).im + (*z2).im,
          }
        });
        Box::into_raw(z3)
      } |]
      z3 <- peek ptr3
      [rustIO| () {
        unsafe { Box::from_raw($(ptr3: *mut Complex)) };
      } |]
      pure z3

main = let z1 = 1.3 :+ 2.4
           z2 = 7.1 :+ 3.9
           z3 = add z1 z2
       in putStrLn $ unwords [ show z1, "+", show z2, "=", show z3 ]