{-# LANGUAGE TemplateHaskell #-}
{-|
    Module      :  Numeric.MixedType.Complex
    Description :  Instances for Data.Complex
    Copyright   :  (c) Michal Konecny
    License     :  BSD3

    Maintainer  :  mikkonecny@gmail.com
    Stability   :  experimental
    Portability :  portable

    Instances for "Data.Complex".
-}

{-# OPTIONS_GHC -Wno-orphans #-}
module Numeric.MixedTypes.Complex
(
  tComplex
)
where

import Numeric.MixedTypes.PreludeHiding
-- import qualified Prelude as P
-- import Text.Printf

import Utils.TH.DeclForTypes

import Data.Complex

import Numeric.MixedTypes.Literals
import Numeric.MixedTypes.Bool
import Numeric.MixedTypes.Eq
import Numeric.MixedTypes.MinMaxAbs
import Numeric.MixedTypes.AddSub
import Numeric.MixedTypes.Mul
import Numeric.MixedTypes.Div
-- import Numeric.MixedTypes.Power
-- import Numeric.MixedTypes.Field
import Numeric.MixedTypes.Elementary

tComplex :: T t -> T (Complex t)
tComplex :: T t -> T (Complex t)
tComplex (T String
tName) = String -> T (Complex t)
forall t. String -> T t
T (String
"(Complex " String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
tName String -> String -> String
forall a. [a] -> [a] -> [a]
++ String
")")

instance (ConvertibleExactly Integer t) => (ConvertibleExactly Integer (Complex t))
  where
  safeConvertExactly :: Integer -> ConvertResult (Complex t)
safeConvertExactly Integer
n =
    do
    t
nT <- Integer -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly Integer
n
    t
zT <- Integer -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly Integer
0
    Complex t -> ConvertResult (Complex t)
forall (m :: * -> *) a. Monad m => a -> m a
return (Complex t -> ConvertResult (Complex t))
-> Complex t -> ConvertResult (Complex t)
forall a b. (a -> b) -> a -> b
$ t
nT t -> t -> Complex t
forall a. a -> a -> Complex a
:+ t
zT

instance (ConvertibleExactly Int t) => (ConvertibleExactly Int (Complex t))
  where
  safeConvertExactly :: Int -> ConvertResult (Complex t)
safeConvertExactly Int
n =
    do
    t
nT <- Int -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly Int
n
    t
zT <- Int -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly (Integer -> Int
forall t. CanBeInt t => t -> Int
int Integer
0)
    Complex t -> ConvertResult (Complex t)
forall (m :: * -> *) a. Monad m => a -> m a
return (Complex t -> ConvertResult (Complex t))
-> Complex t -> ConvertResult (Complex t)
forall a b. (a -> b) -> a -> b
$ t
nT t -> t -> Complex t
forall a. a -> a -> Complex a
:+ t
zT

instance (ConvertibleExactly Rational t) => (ConvertibleExactly Rational (Complex t))
  where
  safeConvertExactly :: Rational -> ConvertResult (Complex t)
safeConvertExactly Rational
r =
    do
    t
rT <- Rational -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly Rational
r
    t
zT <- Rational -> ConvertResult t
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly Rational
0.0
    Complex t -> ConvertResult (Complex t)
forall (m :: * -> *) a. Monad m => a -> m a
return (Complex t -> ConvertResult (Complex t))
-> Complex t -> ConvertResult (Complex t)
forall a b. (a -> b) -> a -> b
$ t
rT t -> t -> Complex t
forall a. a -> a -> Complex a
:+ t
zT

instance (ConvertibleExactly t1 t2) => (ConvertibleExactly (Complex t1) (Complex t2))
  where
  safeConvertExactly :: Complex t1 -> ConvertResult (Complex t2)
safeConvertExactly (t1
a1 :+ t1
i1) =
    do
    t2
a2 <- t1 -> ConvertResult t2
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly t1
a1
    t2
i2 <- t1 -> ConvertResult t2
forall t1 t2. ConvertibleExactly t1 t2 => t1 -> ConvertResult t2
safeConvertExactly t1
i1
    Complex t2 -> ConvertResult (Complex t2)
forall (m :: * -> *) a. Monad m => a -> m a
return (Complex t2 -> ConvertResult (Complex t2))
-> Complex t2 -> ConvertResult (Complex t2)
forall a b. (a -> b) -> a -> b
$ t2
a2 t2 -> t2 -> Complex t2
forall a. a -> a -> Complex a
:+ t2
i2

instance (HasEqAsymmetric a b) => HasEqAsymmetric (Complex a) (Complex b) where
  type EqCompareType (Complex a) (Complex b) = EqCompareType a b
  equalTo :: Complex a -> Complex b -> EqCompareType (Complex a) (Complex b)
equalTo (a
a1 :+ a
i1) (b
a2 :+ b
i2) = (a
a1 a -> b -> EqCompareType a b
forall a b. HasEqAsymmetric a b => a -> b -> EqCompareType a b
== b
a2) EqCompareType a b
-> EqCompareType a b
-> AndOrType (EqCompareType a b) (EqCompareType a b)
forall a b. CanAndOrAsymmetric a b => a -> b -> AndOrType a b
&& (a
i1 a -> b -> EqCompareType a b
forall a b. HasEqAsymmetric a b => a -> b -> EqCompareType a b
== b
i2)

instance (CanTestInteger t, CanTestZero t) => CanTestInteger (Complex t) where
  certainlyNotInteger :: Complex t -> Bool
certainlyNotInteger (t
a :+ t
i) =
    t -> Bool
forall t. CanTestInteger t => t -> Bool
certainlyNotInteger t
a Bool -> Bool -> AndOrType Bool Bool
forall a b. CanAndOrAsymmetric a b => a -> b -> AndOrType a b
|| t -> Bool
forall t. CanTestZero t => t -> Bool
isCertainlyNonZero t
i
  certainlyIntegerGetIt :: Complex t -> Maybe Integer
certainlyIntegerGetIt (t
a :+ t
i) =
    case (t -> Maybe Integer
forall t. CanTestInteger t => t -> Maybe Integer
certainlyIntegerGetIt t
a, t -> Maybe Integer
forall t. CanTestInteger t => t -> Maybe Integer
certainlyIntegerGetIt t
i) of
      (Just Integer
aN, Just Integer
iN) | Integer
iN Integer -> Integer -> EqCompareType Integer Integer
forall a b. HasEqAsymmetric a b => a -> b -> EqCompareType a b
== Integer
0 -> Integer -> Maybe Integer
forall a. a -> Maybe a
Just Integer
aN
      (Maybe Integer, Maybe Integer)
_ -> Maybe Integer
forall a. Maybe a
Nothing

instance CanNeg t => CanNeg (Complex t) where
  type NegType (Complex t) = Complex (NegType t)
  negate :: Complex t -> NegType (Complex t)
negate (t
a :+ t
i) = (t -> NegType t
forall t. CanNeg t => t -> NegType t
negate t
a) NegType t -> NegType t -> Complex (NegType t)
forall a. a -> a -> Complex a
:+ (t -> NegType t
forall t. CanNeg t => t -> NegType t
negate t
i)

instance (CanAddAsymmetric a b) => CanAddAsymmetric (Complex a) (Complex b) where
  type AddType (Complex a) (Complex b) = Complex (AddType a b)
  add :: Complex a -> Complex b -> AddType (Complex a) (Complex b)
add (a
a1 :+ a
i1) (b
a2 :+ b
i2) = (a
a1 a -> b -> AddType a b
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ b
a2) AddType a b -> AddType a b -> Complex (AddType a b)
forall a. a -> a -> Complex a
:+ (a
i1 a -> b -> AddType a b
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ b
i2)

instance (CanSub a b) => CanSub (Complex a) (Complex b) where
  type SubType (Complex a) (Complex b) = Complex (SubType a b)
  sub :: Complex a -> Complex b -> SubType (Complex a) (Complex b)
sub (a
a1 :+ a
i1) (b
a2 :+ b
i2) = (a
a1 a -> b -> SubType a b
forall t1 t2. CanSub t1 t2 => t1 -> t2 -> SubType t1 t2
- b
a2) SubType a b -> SubType a b -> Complex (SubType a b)
forall a. a -> a -> Complex a
:+ (a
i1 a -> b -> SubType a b
forall t1 t2. CanSub t1 t2 => t1 -> t2 -> SubType t1 t2
- b
i2)

instance
  (CanMulAsymmetric a b
  , CanAddSameType (MulType a b), CanSubSameType (MulType a b))
  =>
  CanMulAsymmetric (Complex a) (Complex b)
  where
  type MulType (Complex a) (Complex b) = Complex (MulType a b)
  mul :: Complex a -> Complex b -> MulType (Complex a) (Complex b)
mul (a
a1 :+ a
i1) (b
a2 :+ b
i2) =
    (a
a1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
a2 MulType a b -> MulType a b -> SubType (MulType a b) (MulType a b)
forall t1 t2. CanSub t1 t2 => t1 -> t2 -> SubType t1 t2
- a
i1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
i2) MulType a b -> MulType a b -> Complex (MulType a b)
forall a. a -> a -> Complex a
:+ (a
a1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
i2 MulType a b -> MulType a b -> AddType (MulType a b) (MulType a b)
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ a
i1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
a2)

instance
  (CanMulAsymmetric a b
  , CanAddSameType (MulType a b), CanSubSameType (MulType a b)
  , CanMulAsymmetric b b, CanAddSameType (MulType b b)
  , CanDiv (MulType a b) (MulType b b))
  =>
  CanDiv (Complex a) (Complex b)
  where
  type DivType (Complex a) (Complex b) = Complex (DivType (MulType a b) (MulType b b))
  divide :: Complex a -> Complex b -> DivType (Complex a) (Complex b)
divide (a
a1 :+ a
i1) (b
a2 :+ b
i2) =
    let d :: AddType (MulType b b) (MulType b b)
d = b
a2b -> b -> MulType b b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
a2 MulType b b -> MulType b b -> AddType (MulType b b) (MulType b b)
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ b
i2b -> b -> MulType b b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
i2 in
    ((a
a1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
a2 MulType a b -> MulType a b -> AddType (MulType a b) (MulType a b)
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ a
i1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
i2)MulType a b -> MulType b b -> DivType (MulType a b) (MulType b b)
forall t1 t2. CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2
/AddType (MulType b b) (MulType b b)
MulType b b
d) DivType (MulType a b) (MulType b b)
-> DivType (MulType a b) (MulType b b)
-> Complex (DivType (MulType a b) (MulType b b))
forall a. a -> a -> Complex a
:+ ((a
i1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
a2MulType a b -> MulType a b -> SubType (MulType a b) (MulType a b)
forall t1 t2. CanSub t1 t2 => t1 -> t2 -> SubType t1 t2
-a
a1a -> b -> MulType a b
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*b
i2)MulType a b -> MulType b b -> DivType (MulType a b) (MulType b b)
forall t1 t2. CanDiv t1 t2 => t1 -> t2 -> DivType t1 t2
/AddType (MulType b b) (MulType b b)
MulType b b
d)

instance
  (CanMulAsymmetric t t
  , CanAddSameType (MulType t t)
  , CanSqrt (MulType t t))
  =>
  CanAbs (Complex t)
  where
  type AbsType (Complex t) = SqrtType (MulType t t)
  abs :: Complex t -> AbsType (Complex t)
abs (t
a :+ t
i) = MulType t t -> SqrtType (MulType t t)
forall t. CanSqrt t => t -> SqrtType t
sqrt (t
at -> t -> MulType t t
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*t
a MulType t t -> MulType t t -> AddType (MulType t t) (MulType t t)
forall t1 t2. CanAddAsymmetric t1 t2 => t1 -> t2 -> AddType t1 t2
+ t
it -> t -> MulType t t
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
*t
i)

instance
  (CanExp t
  , CanSinCos t
  , CanMulAsymmetric (ExpType t) (SinCosType t))
  =>
  CanExp (Complex t)
  where
  type ExpType (Complex t) = Complex (MulType (ExpType t) (SinCosType t))
  exp :: Complex t -> ExpType (Complex t)
exp (t
a :+ t
i) =
    let ea :: ExpType t
ea = t -> ExpType t
forall t. CanExp t => t -> ExpType t
exp t
a in
    (ExpType t
ea ExpType t -> SinCosType t -> MulType (ExpType t) (SinCosType t)
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
* t -> SinCosType t
forall t. CanSinCos t => t -> SinCosType t
cos t
i) MulType (ExpType t) (SinCosType t)
-> MulType (ExpType t) (SinCosType t)
-> Complex (MulType (ExpType t) (SinCosType t))
forall a. a -> a -> Complex a
:+ (ExpType t
ea ExpType t -> SinCosType t -> MulType (ExpType t) (SinCosType t)
forall t1 t2. CanMulAsymmetric t1 t2 => t1 -> t2 -> MulType t1 t2
* t -> SinCosType t
forall t. CanSinCos t => t -> SinCosType t
sin t
i)

$(declForTypes
  [[t| Integer |], [t| Int |], [t| Rational |], [t| Double |]]
  (\ t -> [d|

    instance (HasEqAsymmetric $t b) => HasEqAsymmetric $t (Complex b) where
      type EqCompareType $t (Complex b) = EqCompareType $t b
      equalTo n (a2 :+ i2) = (n == a2) && (convertExactlyTargetSample n 0 == i2)

    instance (HasEqAsymmetric a $t) => HasEqAsymmetric (Complex a) $t where
      type EqCompareType (Complex a) $t = EqCompareType a $t
      equalTo (a1 :+ i1) n = (a1 == n) && (i1 == convertExactlyTargetSample n 0)

    instance (CanAddAsymmetric $t b) => CanAddAsymmetric $t (Complex b) where
      type AddType $t (Complex b) = Complex (AddType $t b)
      add n (a2 :+ i2) = (n + a2) :+ (convertExactlyTargetSample n 0 + i2)

    instance (CanAddAsymmetric a $t) => CanAddAsymmetric (Complex a) $t where
      type AddType (Complex a) $t = Complex (AddType a $t)
      add (a1 :+ i1) n = (a1 + n) :+ (i1 + (convertExactlyTargetSample n 0))

    instance (CanSub $t b) => CanSub $t (Complex b) where
      type SubType $t (Complex b) = Complex (SubType $t b)
      sub n (a2 :+ i2) = (n - a2) :+ (convertExactlyTargetSample n 0 - i2)

    instance (CanSub a $t) => CanSub (Complex a) $t where
      type SubType (Complex a) $t = Complex (SubType a $t)
      sub (a1 :+ i1) n = (a1 - n) :+ (i1 - (convertExactlyTargetSample n 0))

    instance
      (CanMulAsymmetric $t b) => CanMulAsymmetric $t (Complex b)
      where
      type MulType $t (Complex b) = Complex (MulType $t b)
      mul n (a2 :+ i2) = (n*a2) :+ (n*i2)

    instance
      (CanMulAsymmetric a $t) => CanMulAsymmetric (Complex a) $t
      where
      type MulType (Complex a) $t = Complex (MulType a $t)
      mul (a1 :+ i1) n = (a1*n) :+ (i1*n)

    instance
      (CanMulAsymmetric $t b
      , CanMulAsymmetric b b, CanAddSameType (MulType b b)
      , CanDiv (MulType $t b) (MulType b b))
      =>
      CanDiv $t (Complex b)
      where
      type DivType $t (Complex b) = Complex (DivType (MulType $t b) (MulType b b))
      divide n (a2 :+ i2) =
        let d = a2*a2 + i2*i2 in
        ((n*a2)/d) :+ (((-n)*i2)/d)

    instance
      (CanDiv a $t) => CanDiv (Complex a) $t
      where
      type DivType (Complex a) $t = Complex (DivType a $t)
      divide (a1 :+ i1) n = (a1/n) :+ (i1/n)
  |]))