{-# OPTIONS_GHC -Wno-orphans #-}
{-# Language TypeFamilies, FlexibleInstances, FlexibleContexts, ScopedTypeVariables, Rank2Types, CPP #-}
module Csound.Typed.Types.Prim(
    Sig(..), unSig, D(..), unD, Tab(..), unTab, Str(..), Spec(..), Wspec(..), renderTab,
    BoolSig(..), unBoolSig, BoolD(..), unBoolD, Unit(..), unit, Val(..), hideGE, SigOrD,
    Sig2, Sig3, Sig4, Sig5, Sig6, Sig7, Sig8,
    Sig2_2, Sig2_3, Sig2_4, Sig2_5, Sig2_6, Sig2_7, Sig2_8,
    D2, D3, D4, D5, D6,

    -- ** Tables
    preTab, preStringTab, TabSize(..), TabArgs(..), updateTabSize,
    fromPreTab, getPreTabUnsafe, skipNorm, forceNorm,
    nsamp, ftlen, ftchnls, ftsr, ftcps,
    TabList, tabList, fromTabList, fromTabListD,

    -- ** constructors
    double, int, text,

    -- ** constants
    idur, getSampleRate, getControlRate, getBlockSize, getZeroDbfs,
    getBpm, setBpm,

    -- ** converters
    ar, kr, ir, sig,

    -- ** lifters
    on0, on1, on2, on3,

    -- ** numeric funs
    quot', rem', div', mod', ceil', floor', round', int', frac',

    -- ** logic funs
    when1, whens, untilDo, whileDo, boolSig,
    equalsTo, notEqualsTo, lessThan, greaterThan, lessThanEquals, greaterThanEquals,
    whenD1, whenDs, untilDoD, whileDoD, untilBeginD,
) where

import Prelude hiding ((<*))

import Control.Applicative hiding ((<*))
import Control.Monad
import Control.Monad.Trans.Class
import qualified Data.IntMap    as IM
import qualified Data.Map       as M


import Control.Monad.Trans.Reader

import Data.Default
import Data.Boolean
import Data.String

import Csound.Dynamic hiding (genId, double, int, str, when1, whens, ifBegin, ifEnd, elseBegin, untilBegin, untilEnd, untilDo, whileBegin, whileEnd, whileDo)
import qualified Csound.Dynamic as D(double, int, str, ifBegin, ifEnd, elseBegin, untilBegin, untilEnd, whileBegin, whileEnd)
import Csound.Typed.GlobalState.GE
import Csound.Typed.GlobalState.SE
import Csound.Typed.GlobalState.Options
import Csound.Typed.GlobalState.Opcodes(tableK, tableI)

-- | Signals
data Sig
    = Sig  (GE E)
    | PrimSig Double

unSig :: Sig -> GE E
unSig :: Sig -> GE E
unSig = Sig -> GE E
forall a. Val a => a -> GE E
toGE

-- | Constant numbers
data D
    = D  (GE E)
    | PrimD Double

unD :: D -> GE E
unD :: D -> GE E
unD = D -> GE E
forall a. Val a => a -> GE E
toGE

-- | Strings
newtype Str  = Str  { Str -> GE E
unStr :: GE E }

-- | Spectrum. It's @fsig@ in the Csound.
newtype Spec  = Spec  { Spec -> GE E
unSpec  :: GE E }

-- | Another type for spectrum. It's @wsig@ in the Csound.
newtype Wspec = Wspec { Wspec -> GE E
unWspec :: GE E }

type D2 = (D, D)
type D3 = (D, D, D)
type D4 = (D, D, D, D)
type D5 = (D, D, D, D, D)
type D6 = (D, D, D, D, D, D)

type Sig2 = (Sig, Sig)
type Sig3 = (Sig, Sig, Sig)
type Sig4 = (Sig, Sig, Sig, Sig)
type Sig5 = (Sig, Sig, Sig, Sig, Sig)
type Sig6 = (Sig, Sig, Sig, Sig, Sig, Sig)
type Sig7 = (Sig, Sig, Sig, Sig, Sig, Sig, Sig)
type Sig8 = (Sig, Sig, Sig, Sig, Sig, Sig, Sig, Sig)

type Sig2_2 = (Sig2, Sig2)
type Sig2_3 = (Sig2, Sig2, Sig2)
type Sig2_4 = (Sig2, Sig2, Sig2, Sig2)
type Sig2_5 = (Sig2, Sig2, Sig2, Sig2, Sig2)
type Sig2_6 = (Sig2, Sig2, Sig2, Sig2, Sig2, Sig2)
type Sig2_7 = (Sig2, Sig2, Sig2, Sig2, Sig2, Sig2, Sig2)
type Sig2_8 = (Sig2, Sig2, Sig2, Sig2, Sig2, Sig2, Sig2, Sig2)

-- Booleans

-- | A signal of booleans.
data BoolSig
    = BoolSig (GE E)
    | PrimBoolSig Bool

unBoolSig :: BoolSig -> GE E
unBoolSig :: BoolSig -> GE E
unBoolSig = BoolSig -> GE E
forall a. Val a => a -> GE E
toGE

-- | A constant boolean value.
data BoolD
    = BoolD (GE E)
    | PrimBoolD Bool

unBoolD :: BoolD -> GE E
unBoolD :: BoolD -> GE E
unBoolD = BoolD -> GE E
forall a. Val a => a -> GE E
toGE

type instance BooleanOf Sig  = BoolSig

type instance BooleanOf D    = BoolD
type instance BooleanOf Str  = BoolD
type instance BooleanOf Tab  = BoolD
type instance BooleanOf Spec = BoolD

-- Procedures

-- | Csound's empty tuple.
newtype Unit = Unit { Unit -> GE ()
unUnit :: GE () }

-- | Constructs Csound's empty tuple.
unit :: Unit
unit :: Unit
unit = GE () -> Unit
Unit (GE () -> Unit) -> GE () -> Unit
forall a b. (a -> b) -> a -> b
$ () -> GE ()
forall (m :: * -> *) a. Monad m => a -> m a
return ()

#if MIN_VERSION_base(4,11,0)
instance Semigroup Unit where
    <> :: Unit -> Unit -> Unit
(<>) = Unit -> Unit -> Unit
mappendUnit

instance Monoid Unit where
    mempty :: Unit
mempty  = Unit
forall a. Default a => a
def

#else

instance Monoid Unit where
    mempty  = def
    mappend = mappendUnit

#endif

mappendUnit :: Unit -> Unit -> Unit
mappendUnit :: Unit -> Unit -> Unit
mappendUnit Unit
a Unit
b = GE () -> Unit
Unit (GE () -> Unit) -> GE () -> Unit
forall a b. (a -> b) -> a -> b
$ (Unit -> GE ()
unUnit Unit
a) GE () -> GE () -> GE ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> (Unit -> GE ()
unUnit Unit
b)

instance Default Unit where
    def :: Unit
def = Unit
unit

-- tables

-- | Tables (or arrays)
data Tab
    = Tab (GE E)
    | TabPre PreTab

preTab :: TabSize -> Int -> TabArgs -> Tab
preTab :: TabSize -> Int -> TabArgs -> Tab
preTab TabSize
size Int
gen TabArgs
args = PreTab -> Tab
TabPre (PreTab -> Tab) -> PreTab -> Tab
forall a b. (a -> b) -> a -> b
$ TabSize -> GenId -> TabArgs -> PreTab
PreTab TabSize
size (Int -> GenId
IntGenId Int
gen) TabArgs
args

preStringTab :: TabSize -> String -> TabArgs -> Tab
preStringTab :: TabSize -> String -> TabArgs -> Tab
preStringTab TabSize
size String
gen TabArgs
args = PreTab -> Tab
TabPre (PreTab -> Tab) -> PreTab -> Tab
forall a b. (a -> b) -> a -> b
$ TabSize -> GenId -> TabArgs -> PreTab
PreTab TabSize
size (String -> GenId
StringGenId String
gen) TabArgs
args

data PreTab = PreTab
    { PreTab -> TabSize
preTabSize    :: TabSize
    , PreTab -> GenId
preTabGen     :: GenId
    , PreTab -> TabArgs
preTabArgs    :: TabArgs }

-- Table size.
data TabSize
    -- Size is fixed by the user.
    = SizePlain Int
    -- Size is relative to the renderer settings.
    | SizeDegree
    { TabSize -> Bool
hasGuardPoint :: Bool
    , TabSize -> Int
sizeDegree    :: Int      -- is the power of two
    }

instance Default TabSize where
    def :: TabSize
def = SizeDegree :: Bool -> Int -> TabSize
SizeDegree
        { hasGuardPoint :: Bool
hasGuardPoint = Bool
False
        , sizeDegree :: Int
sizeDegree = Int
0 }

-- Table arguments can be
data TabArgs
    -- absolute
    = ArgsPlain (Reader Int [Double])
{-    -- or relative to the table size (used for tables that implement interpolation)
    | ArgsRelative [Double]
    -- GEN 16 uses unusual interpolation scheme, so we need a special case
    | ArgsGen16 [Double] -}
    | FileAccess String [Double]

renderPreTab :: PreTab -> GE E
renderPreTab :: PreTab -> GE E
renderPreTab PreTab
a = ((Int -> E) -> GE Int -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Int -> E
D.int (GE Int -> GE E) -> (Gen -> GE Int) -> Gen -> GE E
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Gen -> GE Int
saveGen) (Gen -> GE E) -> GE Gen -> GE E
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< PreTab -> GE Gen
fromPreTab PreTab
a

getPreTabUnsafe :: String -> Tab -> PreTab
getPreTabUnsafe :: String -> Tab -> PreTab
getPreTabUnsafe String
msg Tab
x = case Tab
x of
    TabPre PreTab
a    -> PreTab
a
    Tab
_           -> String -> PreTab
forall a. HasCallStack => String -> a
error String
msg

fromPreTab :: PreTab -> GE Gen
fromPreTab :: PreTab -> GE Gen
fromPreTab PreTab
a = (Options -> Gen) -> GE Gen
forall a. (Options -> a) -> GE a
withOptions ((Options -> Gen) -> GE Gen) -> (Options -> Gen) -> GE Gen
forall a b. (a -> b) -> a -> b
$ \Options
opt -> TabFi -> PreTab -> Gen
go (Options -> TabFi
defTabFi Options
opt) PreTab
a
    where
        go :: TabFi -> PreTab -> Gen
        go :: TabFi -> PreTab -> Gen
go TabFi
tabFi PreTab
tab = Int -> GenId -> [Double] -> Maybe String -> Gen
Gen Int
size (PreTab -> GenId
preTabGen PreTab
tab) [Double]
args Maybe String
file
            where size :: Int
size = Int -> TabSize -> Int
defineTabSize (TabFi -> PreTab -> Int
getTabSizeBase TabFi
tabFi PreTab
tab) (PreTab -> TabSize
preTabSize PreTab
tab)
                  ([Double]
args, Maybe String
file) = Int -> TabArgs -> ([Double], Maybe String)
defineTabArgs Int
size (PreTab -> TabArgs
preTabArgs PreTab
tab)

getTabSizeBase :: TabFi -> PreTab -> Int
getTabSizeBase :: TabFi -> PreTab -> Int
getTabSizeBase TabFi
tf PreTab
tab = case PreTab -> GenId
preTabGen PreTab
tab of
    IntGenId Int
intId -> Int -> Int -> IntMap Int -> Int
forall a. a -> Int -> IntMap a -> a
IM.findWithDefault (TabFi -> Int
tabFiBase TabFi
tf) Int
intId (TabFi -> IntMap Int
tabFiGens TabFi
tf)
    StringGenId String
stringId -> Int -> String -> Map String Int -> Int
forall k a. Ord k => a -> k -> Map k a -> a
M.findWithDefault (TabFi -> Int
tabFiBase TabFi
tf) String
stringId (TabFi -> Map String Int
tabNamedFiGens TabFi
tf)

defineTabSize :: Int -> TabSize -> Int
defineTabSize :: Int -> TabSize -> Int
defineTabSize Int
base TabSize
x = case TabSize
x of
       SizePlain Int
n -> Int
n
       SizeDegree Bool
guardPoint Int
degree ->
                Bool -> Int -> Int
forall a. Num a => Bool -> a -> a
byGuardPoint Bool
guardPoint (Int -> Int) -> Int -> Int
forall a b. (a -> b) -> a -> b
$
                Int -> Int -> Int
forall b a. (Integral b, Num a) => b -> b -> a
byDegree Int
base Int
degree
    where byGuardPoint :: Bool -> a -> a
byGuardPoint Bool
guardPoint
            | Bool
guardPoint = (a -> a -> a
forall a. Num a => a -> a -> a
+ a
1)
            | Bool
otherwise  = a -> a
forall a. a -> a
id

          byDegree :: b -> b -> a
byDegree b
zero b
n = a
2 a -> b -> a
forall a b. (Num a, Integral b) => a -> b -> a
^ b -> b -> b
forall a. Ord a => a -> a -> a
max b
0 (b
zero b -> b -> b
forall a. Num a => a -> a -> a
+ b
n)

defineTabArgs :: Int -> TabArgs -> ([Double], Maybe String)
defineTabArgs :: Int -> TabArgs -> ([Double], Maybe String)
defineTabArgs Int
size TabArgs
args = case TabArgs
args of
    ArgsPlain Reader Int [Double]
as -> (Reader Int [Double] -> Int -> [Double]
forall r a. Reader r a -> r -> a
runReader Reader Int [Double]
as Int
size, Maybe String
forall a. Maybe a
Nothing)
    FileAccess String
filename [Double]
as -> ([Double]
as, String -> Maybe String
forall a. a -> Maybe a
Just String
filename)

-- | Skips normalization (sets table size to negative value)
skipNorm :: Tab -> Tab
skipNorm :: Tab -> Tab
skipNorm Tab
x = case Tab
x of
    Tab GE E
_ -> String -> Tab
forall a. HasCallStack => String -> a
error String
"you can skip normalization only for primitive tables (made with gen-routines)"
    TabPre PreTab
a -> PreTab -> Tab
TabPre (PreTab -> Tab) -> PreTab -> Tab
forall a b. (a -> b) -> a -> b
$ PreTab
a{ preTabGen :: GenId
preTabGen = GenId -> GenId
skipNormGenId (GenId -> GenId) -> GenId -> GenId
forall a b. (a -> b) -> a -> b
$ PreTab -> GenId
preTabGen PreTab
a }

skipNormGenId :: GenId -> GenId
skipNormGenId :: GenId -> GenId
skipNormGenId = (Int -> Int) -> GenId -> GenId
mapIntGenId (Int -> Int
forall a. Num a => a -> a
negate (Int -> Int) -> (Int -> Int) -> Int -> Int
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> Int
forall a. Num a => a -> a
abs)

-- | Force normalization (sets table size to positive value).
-- Might be useful to restore normalization for table 'Csound.Tab.doubles'.
forceNorm :: Tab -> Tab
forceNorm :: Tab -> Tab
forceNorm Tab
x = case Tab
x of
    Tab GE E
_ -> String -> Tab
forall a. HasCallStack => String -> a
error String
"you can force normalization only for primitive tables (made with gen-routines)"
    TabPre PreTab
a -> PreTab -> Tab
TabPre (PreTab -> Tab) -> PreTab -> Tab
forall a b. (a -> b) -> a -> b
$ PreTab
a{ preTabGen :: GenId
preTabGen = GenId -> GenId
normGenId (GenId -> GenId) -> GenId -> GenId
forall a b. (a -> b) -> a -> b
$ PreTab -> GenId
preTabGen PreTab
a }

normGenId :: GenId -> GenId
normGenId :: GenId -> GenId
normGenId = (Int -> Int) -> GenId -> GenId
mapIntGenId Int -> Int
forall a. Num a => a -> a
abs

mapIntGenId :: (Int -> Int) -> GenId -> GenId
mapIntGenId :: (Int -> Int) -> GenId -> GenId
mapIntGenId Int -> Int
f GenId
genId = case GenId
genId of
    IntGenId Int
intId -> Int -> GenId
IntGenId (Int -> Int
f Int
intId)
    GenId
_              -> GenId
genId

----------------------------------------------------------------------------
-- change table size

updateTabSize :: (TabSize -> TabSize) -> Tab -> Tab
updateTabSize :: (TabSize -> TabSize) -> Tab -> Tab
updateTabSize TabSize -> TabSize
phi Tab
x = case Tab
x of
    Tab GE E
_ -> String -> Tab
forall a. HasCallStack => String -> a
error String
"you can change size only for primitive tables (made with gen-routines)"
    TabPre PreTab
a -> PreTab -> Tab
TabPre (PreTab -> Tab) -> PreTab -> Tab
forall a b. (a -> b) -> a -> b
$ PreTab
a{ preTabSize :: TabSize
preTabSize = TabSize -> TabSize
phi (TabSize -> TabSize) -> TabSize -> TabSize
forall a b. (a -> b) -> a -> b
$ PreTab -> TabSize
preTabSize PreTab
a }

----------------------------------------------------------------------------
-- Tab of tabs

-- | Container list of tables
data TabList = TabList { TabList -> GE E
unTabList :: GE E }

tabList :: [Tab] -> TabList
tabList :: [Tab] -> TabList
tabList [Tab]
xs = GE E -> TabList
TabList (GE E -> TabList) -> GE E -> TabList
forall a b. (a -> b) -> a -> b
$ [Gen] -> GE E
saveTabs ([Gen] -> GE E) -> GE [Gen] -> GE E
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< (PreTab -> GE Gen) -> [PreTab] -> GE [Gen]
forall (t :: * -> *) (m :: * -> *) a b.
(Traversable t, Monad m) =>
(a -> m b) -> t a -> m (t b)
mapM PreTab -> GE Gen
fromPreTab ([Tab] -> [PreTab]
getPreTabs [Tab]
xs)
    where
        getPreTabs :: [Tab] -> [PreTab]
getPreTabs = \case
            []            -> []
            Tab    GE E
_ : [Tab]
as -> [Tab] -> [PreTab]
getPreTabs [Tab]
as
            TabPre PreTab
a : [Tab]
as -> PreTab
a PreTab -> [PreTab] -> [PreTab]
forall a. a -> [a] -> [a]
: [Tab] -> [PreTab]
getPreTabs [Tab]
as

fromTabList :: TabList -> Sig -> Tab
fromTabList :: TabList -> Sig -> Tab
fromTabList TabList
ts Sig
knd = GE E -> Tab
Tab (GE E -> Tab) -> GE E -> Tab
forall a b. (a -> b) -> a -> b
$ do
    E
ets  <- TabList -> GE E
forall a. Val a => a -> GE E
toGE TabList
ts
    E
eknd <- Sig -> GE E
forall a. Val a => a -> GE E
toGE Sig
knd
    E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ E -> E -> E
tableK E
eknd E
ets

fromTabListD :: TabList -> D -> Tab
fromTabListD :: TabList -> D -> Tab
fromTabListD TabList
ts D
ind = GE E -> Tab
Tab (GE E -> Tab) -> GE E -> Tab
forall a b. (a -> b) -> a -> b
$ do
    E
ets  <- TabList -> GE E
forall a. Val a => a -> GE E
toGE TabList
ts
    E
eind <- D -> GE E
forall a. Val a => a -> GE E
toGE D
ind
    E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ E -> E -> E
tableI E
eind E
ets

-------------------------------------------------------------------------------
-- constructors

-- | Constructs a number.
double :: Double -> D
double :: Double -> D
double = Double -> D
PrimD

-- | Constructs an integer.
int :: Int -> D
int :: Int -> D
int =  Double -> D
PrimD (Double -> D) -> (Int -> Double) -> Int -> D
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Int -> Double
forall a b. (Integral a, Num b) => a -> b
fromIntegral

-- | Constructs a string.
text :: String -> Str
text :: String -> Str
text = E -> Str
forall a. Val a => E -> a
fromE (E -> Str) -> (String -> E) -> String -> Str
forall b c a. (b -> c) -> (a -> b) -> a -> c
. String -> E
D.str

instance IsString Str where
    fromString :: String -> Str
fromString = String -> Str
text

-------------------------------------------------------------------------------
-- constants

-- | Querries a total duration of the note. It's equivallent to Csound's @p3@ field.
idur :: D
idur :: D
idur = E -> D
forall a. Val a => E -> a
fromE (E -> D) -> E -> D
forall a b. (a -> b) -> a -> b
$ Int -> E
pn Int
3

getSampleRate :: D
getSampleRate :: D
getSampleRate = E -> D
forall a. Val a => E -> a
fromE (E -> D) -> E -> D
forall a b. (a -> b) -> a -> b
$ Var -> E
readOnlyVar (Rate -> String -> Var
VarVerbatim Rate
Ir String
"sr")

getControlRate :: D
getControlRate :: D
getControlRate = E -> D
forall a. Val a => E -> a
fromE (E -> D) -> E -> D
forall a b. (a -> b) -> a -> b
$ Var -> E
readOnlyVar (Rate -> String -> Var
VarVerbatim Rate
Ir String
"kr")

getBlockSize :: D
getBlockSize :: D
getBlockSize = E -> D
forall a. Val a => E -> a
fromE (E -> D) -> E -> D
forall a b. (a -> b) -> a -> b
$ Var -> E
readOnlyVar (Rate -> String -> Var
VarVerbatim Rate
Ir String
"ksmps")

getZeroDbfs :: D
getZeroDbfs :: D
getZeroDbfs = E -> D
forall a. Val a => E -> a
fromE (E -> D) -> E -> D
forall a b. (a -> b) -> a -> b
$ Var -> E
readOnlyVar (Rate -> String -> Var
VarVerbatim Rate
Ir String
"0dbfs")

-- | Gets the global BPM value.
getBpm :: Sig
getBpm :: Sig
getBpm = E -> Sig
forall a. Val a => E -> a
fromE (E -> Sig) -> E -> Sig
forall a b. (a -> b) -> a -> b
$ Var -> E
readOnlyVar Var
bpmVar

-- | Sets the global BPM value.
setBpm :: Sig -> SE ()
setBpm :: Sig -> SE ()
setBpm Sig
x = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ GE (Dep ()) -> Dep ()
forall a. GE (Dep a) -> Dep a
hideGEinDep (GE (Dep ()) -> Dep ()) -> GE (Dep ()) -> Dep ()
forall a b. (a -> b) -> a -> b
$ (E -> Dep ()) -> GE E -> GE (Dep ())
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Var -> E -> Dep ()
forall (m :: * -> *). Monad m => Var -> E -> DepT m ()
writeVar Var
bpmVar) (Sig -> GE E
forall a. Val a => a -> GE E
toGE Sig
x)

-------------------------------------------------------------------------------
-- converters

-- | Sets a rate of the signal to audio rate.
ar :: Sig -> Sig
ar :: Sig -> Sig
ar Sig
x = case Sig
x of
    PrimSig Double
a -> Double -> Sig
PrimSig Double
a
    Sig GE E
expr  -> GE E -> Sig
Sig (GE E -> Sig) -> GE E -> Sig
forall a b. (a -> b) -> a -> b
$ (E -> E) -> GE E -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Rate -> E -> E
setRate Rate
Ar) GE E
expr

-- | Sets a rate of the signal to control rate.
kr :: Sig -> Sig
kr :: Sig -> Sig
kr Sig
x = case Sig
x of
    PrimSig Double
a -> Double -> Sig
PrimSig Double
a
    Sig GE E
expr  -> GE E -> Sig
Sig (GE E -> Sig) -> GE E -> Sig
forall a b. (a -> b) -> a -> b
$ (E -> E) -> GE E -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Rate -> E -> E
setRate Rate
Kr) GE E
expr

-- | Converts a signal to the number (initial value of the signal).
ir :: Sig -> D
ir :: Sig -> D
ir Sig
x = case Sig
x of
    PrimSig Double
a -> Double -> D
PrimD Double
a
    Sig GE E
a -> GE E -> D
D (GE E -> D) -> GE E -> D
forall a b. (a -> b) -> a -> b
$ (E -> E) -> GE E -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Rate -> E -> E
setRate Rate
Ir) GE E
a

-- | Makes a constant signal from the number.
sig :: D -> Sig
sig :: D -> Sig
sig D
x = case D
x of
    PrimD Double
a -> Double -> Sig
PrimSig Double
a
    D GE E
expr  -> GE E -> Sig
Sig (GE E -> Sig) -> GE E -> Sig
forall a b. (a -> b) -> a -> b
$ (E -> E) -> GE E -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap (Rate -> E -> E
setRate Rate
Kr) GE E
expr

-------------------------------------------------------------------------------
-- single wrapper

-- | Contains all Csound values.
class Val a where
    fromGE  :: GE E -> a
    toGE    :: a -> GE E

    fromE   :: E -> a
    fromE = GE E -> a
forall a. Val a => GE E -> a
fromGE (GE E -> a) -> (E -> GE E) -> E -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return

hideGE :: Val a => GE a -> a
hideGE :: GE a -> a
hideGE = GE E -> a
forall a. Val a => GE E -> a
fromGE (GE E -> a) -> (GE a -> GE E) -> GE a -> a
forall b c a. (b -> c) -> (a -> b) -> a -> c
. GE (GE E) -> GE E
forall (m :: * -> *) a. Monad m => m (m a) -> m a
join (GE (GE E) -> GE E) -> (GE a -> GE (GE E)) -> GE a -> GE E
forall b c a. (b -> c) -> (a -> b) -> a -> c
. (a -> GE E) -> GE a -> GE (GE E)
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap a -> GE E
forall a. Val a => a -> GE E
toGE

instance Val Sig    where
    fromGE :: GE E -> Sig
fromGE = GE E -> Sig
Sig

    toGE :: Sig -> GE E
toGE Sig
x = case Sig
x of
        Sig GE E
a       -> GE E
a
        PrimSig Double
d   -> E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ Double -> E
D.double Double
d

instance Val D      where
    fromGE :: GE E -> D
fromGE  = GE E -> D
D
    toGE :: D -> GE E
toGE D
x  = case D
x of
        D GE E
a     -> GE E
a
        PrimD Double
d -> E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ Double -> E
D.double Double
d

instance Val Str    where { fromGE :: GE E -> Str
fromGE = GE E -> Str
Str    ; toGE :: Str -> GE E
toGE = Str -> GE E
unStr  }
instance Val Spec   where { fromGE :: GE E -> Spec
fromGE = GE E -> Spec
Spec   ; toGE :: Spec -> GE E
toGE = Spec -> GE E
unSpec }
instance Val Wspec  where { fromGE :: GE E -> Wspec
fromGE = GE E -> Wspec
Wspec  ; toGE :: Wspec -> GE E
toGE = Wspec -> GE E
unWspec}

instance Val TabList where { fromGE :: GE E -> TabList
fromGE = GE E -> TabList
TabList; toGE :: TabList -> GE E
toGE = TabList -> GE E
unTabList }

instance Val Tab where
    fromGE :: GE E -> Tab
fromGE = GE E -> Tab
Tab
    toGE :: Tab -> GE E
toGE = Tab -> GE E
unTab

unTab :: Tab -> GE E
unTab :: Tab -> GE E
unTab Tab
x = case Tab
x of
        Tab GE E
a -> GE E
a
        TabPre PreTab
a -> PreTab -> GE E
renderPreTab PreTab
a

renderTab :: Tab -> GE Int
renderTab :: Tab -> GE Int
renderTab Tab
x = case Tab
x of
    TabPre PreTab
a -> Gen -> GE Int
saveGen (Gen -> GE Int) -> GE Gen -> GE Int
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< PreTab -> GE Gen
fromPreTab PreTab
a
    Tab GE E
_    -> String -> GE Int
forall a. HasCallStack => String -> a
error String
"table should be primitive"

instance Val BoolSig where
    fromGE :: GE E -> BoolSig
fromGE = GE E -> BoolSig
BoolSig
    toGE :: BoolSig -> GE E
toGE BoolSig
x = case BoolSig
x of
        BoolSig GE E
a -> GE E
a
        PrimBoolSig Bool
b -> E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ if Bool
b then E
forall b. Boolean b => b
true else E
forall b. Boolean b => b
false

instance Val BoolD   where
    fromGE :: GE E -> BoolD
fromGE = GE E -> BoolD
BoolD
    toGE :: BoolD -> GE E
toGE BoolD
x = case BoolD
x of
        BoolD GE E
a -> GE E
a
        PrimBoolD Bool
b -> E -> GE E
forall (m :: * -> *) a. Monad m => a -> m a
return (E -> GE E) -> E -> GE E
forall a b. (a -> b) -> a -> b
$ if Bool
b then E
forall b. Boolean b => b
true else E
forall b. Boolean b => b
false


class (IsPrim a, RealFrac (PrimOf a), Val a) => SigOrD a where

instance SigOrD Sig where
instance SigOrD D   where

on0 :: Val a => E -> a
on0 :: E -> a
on0 = E -> a
forall a. Val a => E -> a
fromE

on1 :: (Val a, Val b) => (E -> E) -> (a -> b)
on1 :: (E -> E) -> a -> b
on1 E -> E
f a
a = GE E -> b
forall a. Val a => GE E -> a
fromGE (GE E -> b) -> GE E -> b
forall a b. (a -> b) -> a -> b
$ (E -> E) -> GE E -> GE E
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap E -> E
f (GE E -> GE E) -> GE E -> GE E
forall a b. (a -> b) -> a -> b
$ a -> GE E
forall a. Val a => a -> GE E
toGE a
a

on2 :: (Val a, Val b, Val c) => (E -> E -> E) -> (a -> b -> c)
on2 :: (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
f a
a b
b = GE E -> c
forall a. Val a => GE E -> a
fromGE (GE E -> c) -> GE E -> c
forall a b. (a -> b) -> a -> b
$ (E -> E -> E) -> GE E -> GE E -> GE E
forall (f :: * -> *) a b c.
Applicative f =>
(a -> b -> c) -> f a -> f b -> f c
liftA2 E -> E -> E
f (a -> GE E
forall a. Val a => a -> GE E
toGE a
a) (b -> GE E
forall a. Val a => a -> GE E
toGE b
b)

on3 :: (Val a, Val b, Val c, Val d) => (E -> E -> E -> E) -> (a -> b -> c -> d)
on3 :: (E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
f a
a b
b c
c = GE E -> d
forall a. Val a => GE E -> a
fromGE (GE E -> d) -> GE E -> d
forall a b. (a -> b) -> a -> b
$ (E -> E -> E -> E) -> GE E -> GE E -> GE E -> GE E
forall (f :: * -> *) a b c d.
Applicative f =>
(a -> b -> c -> d) -> f a -> f b -> f c -> f d
liftA3 E -> E -> E -> E
f (a -> GE E
forall a. Val a => a -> GE E
toGE a
a) (b -> GE E
forall a. Val a => a -> GE E
toGE b
b) (c -> GE E
forall a. Val a => a -> GE E
toGE c
c)

op1 :: (Val a, Val b, IsPrim a, IsPrim b) => (PrimOf a -> PrimOf b) -> (E -> E) -> (a -> b)
op1 :: (PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 PrimOf a -> PrimOf b
primFun E -> E
exprFun a
x = b -> (PrimOf a -> b) -> Maybe (PrimOf a) -> b
forall b a. b -> (a -> b) -> Maybe a -> b
maybe ((E -> E) -> a -> b
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 E -> E
exprFun a
x) (PrimOf b -> b
forall a. IsPrim a => PrimOf a -> a
fromPrim (PrimOf b -> b) -> (PrimOf a -> PrimOf b) -> PrimOf a -> b
forall b c a. (b -> c) -> (a -> b) -> a -> c
. PrimOf a -> PrimOf b
primFun) (a -> Maybe (PrimOf a)
forall a. IsPrim a => a -> Maybe (PrimOf a)
getPrim a
x)

op2 :: (Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) => (PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> (a -> b -> c)
op2 :: (PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf a -> PrimOf b -> PrimOf c
primFun E -> E -> E
exprFun a
xa b
xb = case (a -> Maybe (PrimOf a)
forall a. IsPrim a => a -> Maybe (PrimOf a)
getPrim a
xa, b -> Maybe (PrimOf b)
forall a. IsPrim a => a -> Maybe (PrimOf a)
getPrim b
xb) of
    (Just PrimOf a
a, Just PrimOf b
b) -> PrimOf c -> c
forall a. IsPrim a => PrimOf a -> a
fromPrim (PrimOf c -> c) -> PrimOf c -> c
forall a b. (a -> b) -> a -> b
$ PrimOf a -> PrimOf b -> PrimOf c
primFun PrimOf a
a PrimOf b
b
    (Maybe (PrimOf a), Maybe (PrimOf b))
_                -> (E -> E -> E) -> a -> b -> c
forall a b c. (Val a, Val b, Val c) => (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
exprFun a
xa b
xb

-------------------------------------------------------------------------------
-- defaults

instance Default Sig    where def :: Sig
def = Sig
0
instance Default D      where def :: D
def = D
0
instance Default Tab    where def :: Tab
def = E -> Tab
forall a. Val a => E -> a
fromE E
0
instance Default Str    where def :: Str
def = String -> Str
text String
""
instance Default Spec   where def :: Spec
def = E -> Spec
forall a. Val a => E -> a
fromE E
0

instance Default TabList where def :: TabList
def = E -> TabList
forall a. Val a => E -> a
fromE E
0

-------------------------------------------------------------------------------
-- monoid

#if MIN_VERSION_base(4,11,0)
instance Semigroup Sig where
    <> :: Sig -> Sig -> Sig
(<>) = (E -> E -> E) -> Sig -> Sig -> Sig
forall a b c. (Val a, Val b, Val c) => (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
forall a. Monoid a => a -> a -> a
mappend

instance Monoid Sig where
    mempty :: Sig
mempty = E -> Sig
forall a. Val a => E -> a
on0 E
forall a. Monoid a => a
mempty

#else

instance Monoid Sig where
    mempty  = on0 mempty
    mappend = on2 mappend

#endif


#if MIN_VERSION_base(4,11,0)
instance Semigroup D where
    <> :: D -> D -> D
(<>) = (E -> E -> E) -> D -> D -> D
forall a b c. (Val a, Val b, Val c) => (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
forall a. Monoid a => a -> a -> a
mappend

instance Monoid D where
    mempty :: D
mempty = E -> D
forall a. Val a => E -> a
on0 E
forall a. Monoid a => a
mempty

#else

instance Monoid D where
    mempty  = on0 mempty
    mappend = on2 mappend

#endif

-------------------------------------------------------------------------------
-- numeric

sigOn1 :: (Double -> Double) -> (E -> E) -> (Sig -> Sig)
sigOn1 :: (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
numFun E -> E
exprFun Sig
x = case Sig
x of
    PrimSig Double
a -> Double -> Sig
PrimSig (Double -> Sig) -> Double -> Sig
forall a b. (a -> b) -> a -> b
$ Double -> Double
numFun Double
a
    Sig
_         -> (E -> E) -> Sig -> Sig
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 E -> E
exprFun Sig
x

sigOn2 :: (Double -> Double -> Double) -> (E -> E -> E) -> (Sig -> Sig -> Sig)
sigOn2 :: (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
numFun E -> E -> E
exprFun Sig
xa Sig
xb = case (Sig
xa, Sig
xb) of
    (PrimSig Double
a, PrimSig Double
b) -> Double -> Sig
PrimSig (Double -> Sig) -> Double -> Sig
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double
numFun Double
a Double
b
    (Sig, Sig)
_                      -> (E -> E -> E) -> Sig -> Sig -> Sig
forall a b c. (Val a, Val b, Val c) => (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
exprFun Sig
xa Sig
xb


instance Num Sig where
    { + :: Sig -> Sig -> Sig
(+) = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
forall a. Num a => a -> a -> a
(+) E -> E -> E
forall a. Num a => a -> a -> a
(+); * :: Sig -> Sig -> Sig
(*) = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
forall a. Num a => a -> a -> a
(*) E -> E -> E
forall a. Num a => a -> a -> a
(*); negate :: Sig -> Sig
negate = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Num a => a -> a
negate E -> E
forall a. Num a => a -> a
negate
    ; (-) = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 (\Double
a Double
b -> Double
a Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
b) (\E
a E
b -> E
a E -> E -> E
forall a. Num a => a -> a -> a
- E
b)
    ; fromInteger :: Integer -> Sig
fromInteger = Double -> Sig
PrimSig (Double -> Sig) -> (Integer -> Double) -> Integer -> Sig
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> Double
forall a. Num a => Integer -> a
fromInteger; abs :: Sig -> Sig
abs = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Num a => a -> a
abs E -> E
forall a. Num a => a -> a
abs; signum :: Sig -> Sig
signum = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Num a => a -> a
signum E -> E
forall a. Num a => a -> a
signum }

dOn1 :: (Double -> Double) -> (E -> E) -> (D -> D)
dOn1 :: (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
numFun E -> E
exprFun D
x = case D
x of
    PrimD Double
a -> Double -> D
PrimD (Double -> D) -> Double -> D
forall a b. (a -> b) -> a -> b
$ Double -> Double
numFun Double
a
    D
_         -> (E -> E) -> D -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 E -> E
exprFun D
x

dOn2 :: (Double -> Double -> Double) -> (E -> E -> E) -> (D -> D -> D)
dOn2 :: (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
numFun E -> E -> E
exprFun D
xa D
xb = case (D
xa, D
xb) of
    (PrimD Double
a, PrimD Double
b) -> Double -> D
PrimD (Double -> D) -> Double -> D
forall a b. (a -> b) -> a -> b
$ Double -> Double -> Double
numFun Double
a Double
b
    (D, D)
_                      -> (E -> E -> E) -> D -> D -> D
forall a b c. (Val a, Val b, Val c) => (E -> E -> E) -> a -> b -> c
on2 E -> E -> E
exprFun D
xa D
xb

instance Num D where
    { + :: D -> D -> D
(+) = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
forall a. Num a => a -> a -> a
(+) E -> E -> E
forall a. Num a => a -> a -> a
(+); * :: D -> D -> D
(*) = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
forall a. Num a => a -> a -> a
(*) E -> E -> E
forall a. Num a => a -> a -> a
(*); negate :: D -> D
negate = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Num a => a -> a
negate E -> E
forall a. Num a => a -> a
negate
    ; (-) = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 (\Double
a Double
b -> Double
a Double -> Double -> Double
forall a. Num a => a -> a -> a
- Double
b) (\E
a E
b -> E
a E -> E -> E
forall a. Num a => a -> a -> a
- E
b)
    ; fromInteger :: Integer -> D
fromInteger = Double -> D
PrimD (Double -> D) -> (Integer -> Double) -> Integer -> D
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Integer -> Double
forall a. Num a => Integer -> a
fromInteger; abs :: D -> D
abs = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Num a => a -> a
abs E -> E
forall a. Num a => a -> a
abs; signum :: D -> D
signum = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Num a => a -> a
signum E -> E
forall a. Num a => a -> a
signum }

instance Fractional Sig  where { / :: Sig -> Sig -> Sig
(/) = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
(/) E -> E -> E
forall a. Fractional a => a -> a -> a
(/);  fromRational :: Rational -> Sig
fromRational = Double -> Sig
PrimSig (Double -> Sig) -> (Rational -> Double) -> Rational -> Sig
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> Double
forall a. Fractional a => Rational -> a
fromRational }
instance Fractional D    where { / :: D -> D -> D
(/) = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
forall a. Fractional a => a -> a -> a
(/) E -> E -> E
forall a. Fractional a => a -> a -> a
(/);    fromRational :: Rational -> D
fromRational = Double -> D
PrimD (Double -> D) -> (Rational -> Double) -> Rational -> D
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Rational -> Double
forall a. Fractional a => Rational -> a
fromRational }

instance Floating Sig where
    { pi :: Sig
pi = Double -> Sig
PrimSig Double
forall a. Floating a => a
pi;  exp :: Sig -> Sig
exp = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
exp E -> E
forall a. Floating a => a -> a
exp;  sqrt :: Sig -> Sig
sqrt = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
sqrt E -> E
forall a. Floating a => a -> a
sqrt; log :: Sig -> Sig
log = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
log E -> E
forall a. Floating a => a -> a
log; logBase :: Sig -> Sig -> Sig
logBase = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
forall a. Floating a => a -> a -> a
logBase E -> E -> E
forall a. Floating a => a -> a -> a
logBase; ** :: Sig -> Sig -> Sig
(**) = (Double -> Double -> Double) -> (E -> E -> E) -> Sig -> Sig -> Sig
sigOn2 Double -> Double -> Double
forall a. Floating a => a -> a -> a
(**) E -> E -> E
forall a. Floating a => a -> a -> a
(**)
    ; sin :: Sig -> Sig
sin = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
sin E -> E
forall a. Floating a => a -> a
sin;  tan :: Sig -> Sig
tan = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
tan E -> E
forall a. Floating a => a -> a
tan;  cos :: Sig -> Sig
cos = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
cos E -> E
forall a. Floating a => a -> a
cos; sinh :: Sig -> Sig
sinh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
sinh E -> E
forall a. Floating a => a -> a
sinh; tanh :: Sig -> Sig
tanh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
tanh E -> E
forall a. Floating a => a -> a
tanh; cosh :: Sig -> Sig
cosh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
cosh E -> E
forall a. Floating a => a -> a
cosh
    ; asin :: Sig -> Sig
asin = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
asin E -> E
forall a. Floating a => a -> a
asin; atan :: Sig -> Sig
atan = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
atan E -> E
forall a. Floating a => a -> a
atan;  acos :: Sig -> Sig
acos = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
acos E -> E
forall a. Floating a => a -> a
acos ; asinh :: Sig -> Sig
asinh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
asinh E -> E
forall a. Floating a => a -> a
asinh; acosh :: Sig -> Sig
acosh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
acosh E -> E
forall a. Floating a => a -> a
acosh; atanh :: Sig -> Sig
atanh = (Double -> Double) -> (E -> E) -> Sig -> Sig
sigOn1 Double -> Double
forall a. Floating a => a -> a
atanh E -> E
forall a. Floating a => a -> a
atanh }

instance Floating D where
    { pi :: D
pi = Double -> D
PrimD Double
forall a. Floating a => a
pi;  exp :: D -> D
exp = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
exp E -> E
forall a. Floating a => a -> a
exp;  sqrt :: D -> D
sqrt = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
sqrt E -> E
forall a. Floating a => a -> a
sqrt; log :: D -> D
log = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
log E -> E
forall a. Floating a => a -> a
log;  logBase :: D -> D -> D
logBase = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
forall a. Floating a => a -> a -> a
logBase E -> E -> E
forall a. Floating a => a -> a -> a
logBase; ** :: D -> D -> D
(**) = (Double -> Double -> Double) -> (E -> E -> E) -> D -> D -> D
dOn2 Double -> Double -> Double
forall a. Floating a => a -> a -> a
(**) E -> E -> E
forall a. Floating a => a -> a -> a
(**)
    ; sin :: D -> D
sin = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
sin E -> E
forall a. Floating a => a -> a
sin;  tan :: D -> D
tan = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
tan E -> E
forall a. Floating a => a -> a
tan;  cos :: D -> D
cos = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
cos E -> E
forall a. Floating a => a -> a
cos; sinh :: D -> D
sinh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
sinh E -> E
forall a. Floating a => a -> a
sinh; tanh :: D -> D
tanh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
tanh E -> E
forall a. Floating a => a -> a
tanh; cosh :: D -> D
cosh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
cosh E -> E
forall a. Floating a => a -> a
cosh
    ; asin :: D -> D
asin = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
asin E -> E
forall a. Floating a => a -> a
asin; atan :: D -> D
atan = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
atan E -> E
forall a. Floating a => a -> a
atan;  acos :: D -> D
acos = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
acos E -> E
forall a. Floating a => a -> a
acos ; asinh :: D -> D
asinh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
asinh E -> E
forall a. Floating a => a -> a
asinh; acosh :: D -> D
acosh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
acosh E -> E
forall a. Floating a => a -> a
acosh; atanh :: D -> D
atanh = (Double -> Double) -> (E -> E) -> D -> D
dOn1 Double -> Double
forall a. Floating a => a -> a
atanh E -> E
forall a. Floating a => a -> a
atanh }

class IsPrim a where
    type PrimOf a :: *
    getPrim :: a -> Maybe (PrimOf a)
    fromPrim :: PrimOf a -> a

instance IsPrim Sig where
    type PrimOf Sig = Double

    getPrim :: Sig -> Maybe (PrimOf Sig)
getPrim Sig
x = case Sig
x of
        PrimSig Double
a -> Double -> Maybe Double
forall a. a -> Maybe a
Just Double
a
        Sig
_         -> Maybe (PrimOf Sig)
forall a. Maybe a
Nothing

    fromPrim :: PrimOf Sig -> Sig
fromPrim = Double -> Sig
PrimOf Sig -> Sig
PrimSig

instance IsPrim D where
    type PrimOf D = Double

    getPrim :: D -> Maybe (PrimOf D)
getPrim D
x = case D
x of
        PrimD Double
a -> Double -> Maybe Double
forall a. a -> Maybe a
Just Double
a
        D
_         -> Maybe (PrimOf D)
forall a. Maybe a
Nothing

    fromPrim :: PrimOf D -> D
fromPrim = Double -> D
PrimOf D -> D
PrimD

instance IsPrim BoolSig where
    type PrimOf BoolSig = Bool

    getPrim :: BoolSig -> Maybe (PrimOf BoolSig)
getPrim BoolSig
x = case BoolSig
x of
        PrimBoolSig Bool
a -> Bool -> Maybe Bool
forall a. a -> Maybe a
Just Bool
a
        BoolSig
_         -> Maybe (PrimOf BoolSig)
forall a. Maybe a
Nothing

    fromPrim :: PrimOf BoolSig -> BoolSig
fromPrim = Bool -> BoolSig
PrimOf BoolSig -> BoolSig
PrimBoolSig

instance IsPrim BoolD where
    type PrimOf BoolD = Bool

    getPrim :: BoolD -> Maybe (PrimOf BoolD)
getPrim BoolD
x = case BoolD
x of
        PrimBoolD Bool
a -> Bool -> Maybe Bool
forall a. a -> Maybe a
Just Bool
a
        BoolD
_         -> Maybe (PrimOf BoolD)
forall a. Maybe a
Nothing

    fromPrim :: PrimOf BoolD -> BoolD
fromPrim = Bool -> BoolD
PrimOf BoolD -> BoolD
PrimBoolD


ceil', floor', int', round' :: SigOrD a => a -> a
quot', rem', div', mod' :: SigOrD a => a -> a -> a

frac' :: (SigOrD a) => a -> a
frac' :: a -> a
frac' a
a = (PrimOf a -> PrimOf a) -> (E -> E) -> a -> a
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 (\PrimOf a
x -> a -> (Int, PrimOf a) -> PrimOf a
forall a. SigOrD a => a -> (Int, PrimOf a) -> PrimOf a
proxySnd a
a (PrimOf a -> (Int, PrimOf a)
forall a b. (RealFrac a, Integral b) => a -> (b, a)
properFraction PrimOf a
x)) E -> E
fracE a
a
    where
        proxySnd :: SigOrD a => a -> (Int, PrimOf a) -> PrimOf a
        proxySnd :: a -> (Int, PrimOf a) -> PrimOf a
proxySnd a
_ (Int, PrimOf a)
x = (Int, PrimOf a) -> PrimOf a
forall a b. (a, b) -> b
snd (Int, PrimOf a)
x

ceil' :: a -> a
ceil' = (PrimOf a -> PrimOf a) -> (E -> E) -> a -> a
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 (\PrimOf a
x -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
ceiling PrimOf a
x) :: Int)) E -> E
ceilE
floor' :: a -> a
floor' = (PrimOf a -> PrimOf a) -> (E -> E) -> a -> a
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 (\PrimOf a
x -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
floor PrimOf a
x) :: Int)) E -> E
floorE
int' :: a -> a
int' = (PrimOf a -> PrimOf a) -> (E -> E) -> a -> a
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 (\PrimOf a
x -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
x) :: Int)) E -> E
intE
round' :: a -> a
round' = (PrimOf a -> PrimOf a) -> (E -> E) -> a -> a
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1 (\PrimOf a
x -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
round PrimOf a
x) :: Int)) E -> E
roundE
quot' :: a -> a -> a
quot' = (PrimOf a -> PrimOf a -> PrimOf a) -> (E -> E -> E) -> a -> a -> a
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 (\PrimOf a
a PrimOf a
b -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> PrimOf a) -> Int -> PrimOf a
forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int
forall a. Integral a => a -> a -> a
quot ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
a) :: Int) ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
b):: Int)) E -> E -> E
forall a. Integral a => a -> a -> a
quot
rem' :: a -> a -> a
rem' = (PrimOf a -> PrimOf a -> PrimOf a) -> (E -> E -> E) -> a -> a -> a
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 (\PrimOf a
a PrimOf a
b -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> PrimOf a) -> Int -> PrimOf a
forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int
forall a. Integral a => a -> a -> a
rem ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
a) :: Int) ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
b):: Int)) E -> E -> E
forall a. Integral a => a -> a -> a
rem
div' :: a -> a -> a
div' = (PrimOf a -> PrimOf a -> PrimOf a) -> (E -> E -> E) -> a -> a -> a
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 (\PrimOf a
a PrimOf a
b -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> PrimOf a) -> Int -> PrimOf a
forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int
forall a. Integral a => a -> a -> a
div ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
a) :: Int) ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
b):: Int)) E -> E -> E
forall a. Integral a => a -> a -> a
div
mod' :: a -> a -> a
mod' = (PrimOf a -> PrimOf a -> PrimOf a) -> (E -> E -> E) -> a -> a -> a
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 (\PrimOf a
a PrimOf a
b -> Int -> PrimOf a
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int -> PrimOf a) -> Int -> PrimOf a
forall a b. (a -> b) -> a -> b
$ Int -> Int -> Int
forall a. Integral a => a -> a -> a
mod ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
a) :: Int) ((PrimOf a -> Int
forall a b. (RealFrac a, Integral b) => a -> b
truncate PrimOf a
b):: Int)) E -> E -> E
forall a. Integral a => a -> a -> a
mod

-------------------------------------------------------------------------------
-- logic

boolSigOn1 :: (Bool -> Bool) -> (E -> E) -> BoolSig -> BoolSig
boolSigOn1 :: (Bool -> Bool) -> (E -> E) -> BoolSig -> BoolSig
boolSigOn1 = (Bool -> Bool) -> (E -> E) -> BoolSig -> BoolSig
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1

boolSigOn2 :: (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolSig -> BoolSig -> BoolSig
boolSigOn2 :: (Bool -> Bool -> Bool)
-> (E -> E -> E) -> BoolSig -> BoolSig -> BoolSig
boolSigOn2 = (Bool -> Bool -> Bool)
-> (E -> E -> E) -> BoolSig -> BoolSig -> BoolSig
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2

boolDOn1 :: (Bool -> Bool) -> (E -> E) -> BoolD -> BoolD
boolDOn1 :: (Bool -> Bool) -> (E -> E) -> BoolD -> BoolD
boolDOn1 = (Bool -> Bool) -> (E -> E) -> BoolD -> BoolD
forall a b.
(Val a, Val b, IsPrim a, IsPrim b) =>
(PrimOf a -> PrimOf b) -> (E -> E) -> a -> b
op1

boolDOn2 :: (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolD -> BoolD -> BoolD
boolDOn2 :: (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolD -> BoolD -> BoolD
boolDOn2 = (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolD -> BoolD -> BoolD
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2

instance Boolean BoolSig  where { true :: BoolSig
true = Bool -> BoolSig
PrimBoolSig Bool
True;  false :: BoolSig
false = Bool -> BoolSig
PrimBoolSig Bool
False;  notB :: BoolSig -> BoolSig
notB = (Bool -> Bool) -> (E -> E) -> BoolSig -> BoolSig
boolSigOn1 Bool -> Bool
not E -> E
forall b. Boolean b => b -> b
notB;  &&* :: BoolSig -> BoolSig -> BoolSig
(&&*) = (Bool -> Bool -> Bool)
-> (E -> E -> E) -> BoolSig -> BoolSig -> BoolSig
boolSigOn2 Bool -> Bool -> Bool
(&&) E -> E -> E
forall b. Boolean b => b -> b -> b
(&&*);  ||* :: BoolSig -> BoolSig -> BoolSig
(||*) = (Bool -> Bool -> Bool)
-> (E -> E -> E) -> BoolSig -> BoolSig -> BoolSig
boolSigOn2 Bool -> Bool -> Bool
(||) E -> E -> E
forall b. Boolean b => b -> b -> b
(||*) }
instance Boolean BoolD    where { true :: BoolD
true = Bool -> BoolD
PrimBoolD   Bool
True;  false :: BoolD
false = Bool -> BoolD
PrimBoolD   Bool
False;  notB :: BoolD -> BoolD
notB = (Bool -> Bool) -> (E -> E) -> BoolD -> BoolD
boolDOn1   Bool -> Bool
not E -> E
forall b. Boolean b => b -> b
notB;  &&* :: BoolD -> BoolD -> BoolD
(&&*) = (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolD -> BoolD -> BoolD
boolDOn2   Bool -> Bool -> Bool
(&&) E -> E -> E
forall b. Boolean b => b -> b -> b
(&&*);  ||* :: BoolD -> BoolD -> BoolD
(||*) = (Bool -> Bool -> Bool) -> (E -> E -> E) -> BoolD -> BoolD -> BoolD
boolDOn2   Bool -> Bool -> Bool
(||) E -> E -> E
forall b. Boolean b => b -> b -> b
(||*) }

instance IfB Sig  where
    ifB :: bool -> Sig -> Sig -> Sig
ifB bool
x Sig
a Sig
b = case bool
x of
        PrimBoolSig c -> if Bool
c then Sig
a else Sig
b
        bool
_                -> (E -> E -> E -> E) -> bool -> Sig -> Sig -> Sig
forall a b c d.
(Val a, Val b, Val c, Val d) =>
(E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
forall a bool. (IfB a, bool ~ BooleanOf a) => bool -> a -> a -> a
ifB bool
x Sig
a Sig
b

instance IfB D    where
    ifB :: bool -> D -> D -> D
ifB bool
x D
a D
b = case bool
x of
        PrimBoolD c -> if Bool
c then D
a else D
b
        bool
_              -> (E -> E -> E -> E) -> bool -> D -> D -> D
forall a b c d.
(Val a, Val b, Val c, Val d) =>
(E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
forall a bool. (IfB a, bool ~ BooleanOf a) => bool -> a -> a -> a
ifB bool
x D
a D
b

instance IfB Tab  where
    ifB :: bool -> Tab -> Tab -> Tab
ifB bool
x Tab
a Tab
b = case bool
x of
        PrimBoolD c -> if Bool
c then Tab
a else Tab
b
        bool
_              -> (E -> E -> E -> E) -> bool -> Tab -> Tab -> Tab
forall a b c d.
(Val a, Val b, Val c, Val d) =>
(E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
forall a bool. (IfB a, bool ~ BooleanOf a) => bool -> a -> a -> a
ifB bool
x Tab
a Tab
b

instance IfB Str  where
    ifB :: bool -> Str -> Str -> Str
ifB bool
x Str
a Str
b = case bool
x of
        PrimBoolD c -> if Bool
c then Str
a else Str
b
        bool
_              -> (E -> E -> E -> E) -> bool -> Str -> Str -> Str
forall a b c d.
(Val a, Val b, Val c, Val d) =>
(E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
forall a bool. (IfB a, bool ~ BooleanOf a) => bool -> a -> a -> a
ifB bool
x Str
a Str
b

instance IfB Spec where
    ifB :: bool -> Spec -> Spec -> Spec
ifB bool
x Spec
a Spec
b = case bool
x of
        PrimBoolD c -> if Bool
c then Spec
a else Spec
b
        bool
_           -> (E -> E -> E -> E) -> bool -> Spec -> Spec -> Spec
forall a b c d.
(Val a, Val b, Val c, Val d) =>
(E -> E -> E -> E) -> a -> b -> c -> d
on3 E -> E -> E -> E
forall a bool. (IfB a, bool ~ BooleanOf a) => bool -> a -> a -> a
ifB bool
x Spec
a Spec
b

instance EqB Sig  where { ==* :: Sig -> Sig -> bool
(==*) = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Eq a => a -> a -> Bool
(==) E -> E -> E
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(==*);    /=* :: Sig -> Sig -> bool
(/=*) = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Eq a => a -> a -> Bool
(/=) E -> E -> E
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(/=*) }
instance EqB D    where { ==* :: D -> D -> bool
(==*) = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Eq a => a -> a -> Bool
(==) E -> E -> E
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(==*);    /=* :: D -> D -> bool
(/=*) = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Eq a => a -> a -> Bool
(/=) E -> E -> E
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(/=*) }

instance OrdB Sig where { <* :: Sig -> Sig -> bool
(<*)  = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(<) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<*) ;    >* :: Sig -> Sig -> bool
(>*)  = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(>) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>*);     <=* :: Sig -> Sig -> bool
(<=*) = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(<=) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<=*);    >=* :: Sig -> Sig -> bool
(>=*) = (PrimOf Sig -> PrimOf Sig -> PrimOf bool)
-> (E -> E -> E) -> Sig -> Sig -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf Sig -> PrimOf Sig -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(>=) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>=*) }
instance OrdB D   where { <* :: D -> D -> bool
(<*)  = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(<) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<*) ;    >* :: D -> D -> bool
(>*)  = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(>) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>*);     <=* :: D -> D -> bool
(<=*) = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(<=) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<=*);    >=* :: D -> D -> bool
(>=*) = (PrimOf D -> PrimOf D -> PrimOf bool)
-> (E -> E -> E) -> D -> D -> bool
forall a b c.
(Val a, Val b, Val c, IsPrim a, IsPrim b, IsPrim c) =>
(PrimOf a -> PrimOf b -> PrimOf c) -> (E -> E -> E) -> a -> b -> c
op2 PrimOf D -> PrimOf D -> PrimOf bool
forall a. Ord a => a -> a -> Bool
(>=) E -> E -> E
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>=*) }

-- | Invokes the given procedure if the boolean signal is true.
when1 :: BoolSig -> SE () -> SE ()
when1 :: BoolSig -> SE () -> SE ()
when1 BoolSig
xp SE ()
body = case BoolSig
xp of
    PrimBoolSig Bool
p -> if Bool
p then SE ()
body else () -> SE ()
forall (m :: * -> *) a. Monad m => a -> m a
return ()
    BoolSig
_             -> do
        BoolSig -> SE ()
ifBegin BoolSig
xp
        SE ()
body
        SE ()
ifEnd

-- | The chain of @when1@s. Tests all the conditions in sequence
-- if everything is false it invokes the procedure given in the second argument.
whens :: [(BoolSig, SE ())] -> SE () -> SE ()
whens :: [(BoolSig, SE ())] -> SE () -> SE ()
whens [(BoolSig, SE ())]
bodies SE ()
el = case [(BoolSig, SE ())]
bodies of
    []   -> SE ()
el
    (BoolSig, SE ())
a:[(BoolSig, SE ())]
as -> do
        BoolSig -> SE ()
ifBegin ((BoolSig, SE ()) -> BoolSig
forall a b. (a, b) -> a
fst (BoolSig, SE ())
a)
        (BoolSig, SE ()) -> SE ()
forall a b. (a, b) -> b
snd (BoolSig, SE ())
a
        [(BoolSig, SE ())] -> SE ()
forall b. [(BoolSig, SE b)] -> SE ()
elseIfs [(BoolSig, SE ())]
as
        SE ()
elseBegin
        SE ()
el
        (SE () -> SE () -> SE ()) -> [SE ()] -> SE ()
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
foldl1 SE () -> SE () -> SE ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
(>>) ([SE ()] -> SE ()) -> [SE ()] -> SE ()
forall a b. (a -> b) -> a -> b
$ Int -> SE () -> [SE ()]
forall a. Int -> a -> [a]
replicate ([(BoolSig, SE ())] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [(BoolSig, SE ())]
bodies) SE ()
ifEnd
    where elseIfs :: [(BoolSig, SE b)] -> SE ()
elseIfs = ((BoolSig, SE b) -> SE b) -> [(BoolSig, SE b)] -> SE ()
forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
(a -> m b) -> t a -> m ()
mapM_ (\(BoolSig
p, SE b
body) -> SE ()
elseBegin SE () -> SE () -> SE ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> BoolSig -> SE ()
ifBegin BoolSig
p SE () -> SE b -> SE b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> SE b
body)

ifBegin :: BoolSig -> SE ()
ifBegin :: BoolSig -> SE ()
ifBegin BoolSig
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ Rate -> E -> Dep ()
forall (m :: * -> *). Monad m => Rate -> E -> DepT m ()
D.ifBegin Rate
Kr (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolSig -> GE E
forall a. Val a => a -> GE E
toGE BoolSig
a)

ifEnd :: SE ()
ifEnd :: SE ()
ifEnd = Dep () -> SE ()
fromDep_ Dep ()
forall (m :: * -> *). Monad m => DepT m ()
D.ifEnd

elseBegin :: SE ()
elseBegin :: SE ()
elseBegin = Dep () -> SE ()
fromDep_ Dep ()
forall (m :: * -> *). Monad m => DepT m ()
D.elseBegin

-- | Invokes the given procedure if the boolean signal is true.
whenD1 :: BoolD -> SE () -> SE ()
whenD1 :: BoolD -> SE () -> SE ()
whenD1 BoolD
xp SE ()
body = case BoolD
xp of
    PrimBoolD Bool
p -> if Bool
p then SE ()
body else () -> SE ()
forall (m :: * -> *) a. Monad m => a -> m a
return ()
    BoolD
_             -> do
        BoolD -> SE ()
ifBeginD BoolD
xp
        SE ()
body
        SE ()
ifEnd

-- | The chain of @when1@s. Tests all the conditions in sequence
-- if everything is false it invokes the procedure given in the second argument.
whenDs :: [(BoolD, SE ())] -> SE () -> SE ()
whenDs :: [(BoolD, SE ())] -> SE () -> SE ()
whenDs [(BoolD, SE ())]
bodies SE ()
el = case [(BoolD, SE ())]
bodies of
    []   -> SE ()
el
    (BoolD, SE ())
a:[(BoolD, SE ())]
as -> do
        BoolD -> SE ()
ifBeginD ((BoolD, SE ()) -> BoolD
forall a b. (a, b) -> a
fst (BoolD, SE ())
a)
        (BoolD, SE ()) -> SE ()
forall a b. (a, b) -> b
snd (BoolD, SE ())
a
        [(BoolD, SE ())] -> SE ()
forall b. [(BoolD, SE b)] -> SE ()
elseIfs [(BoolD, SE ())]
as
        SE ()
elseBegin
        SE ()
el
        (SE () -> SE () -> SE ()) -> [SE ()] -> SE ()
forall (t :: * -> *) a. Foldable t => (a -> a -> a) -> t a -> a
foldl1 SE () -> SE () -> SE ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
(>>) ([SE ()] -> SE ()) -> [SE ()] -> SE ()
forall a b. (a -> b) -> a -> b
$ Int -> SE () -> [SE ()]
forall a. Int -> a -> [a]
replicate ([(BoolD, SE ())] -> Int
forall (t :: * -> *) a. Foldable t => t a -> Int
length [(BoolD, SE ())]
bodies) SE ()
ifEnd
    where elseIfs :: [(BoolD, SE b)] -> SE ()
elseIfs = ((BoolD, SE b) -> SE b) -> [(BoolD, SE b)] -> SE ()
forall (t :: * -> *) (m :: * -> *) a b.
(Foldable t, Monad m) =>
(a -> m b) -> t a -> m ()
mapM_ (\(BoolD
p, SE b
body) -> SE ()
elseBegin SE () -> SE () -> SE ()
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> BoolD -> SE ()
ifBeginD BoolD
p SE () -> SE b -> SE b
forall (m :: * -> *) a b. Monad m => m a -> m b -> m b
>> SE b
body)

ifBeginD :: BoolD -> SE ()
ifBeginD :: BoolD -> SE ()
ifBeginD BoolD
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ Rate -> E -> Dep ()
forall (m :: * -> *). Monad m => Rate -> E -> DepT m ()
D.ifBegin Rate
Ir (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolD -> GE E
forall a. Val a => a -> GE E
toGE BoolD
a)

-- elseIfBegin :: BoolSig -> SE ()
-- elseIfBegin a = fromDep_ $ D.elseIfBegin =<< lift (toGE a)

untilDo :: BoolSig -> SE () -> SE ()
untilDo :: BoolSig -> SE () -> SE ()
untilDo BoolSig
p SE ()
body = do
    BoolSig -> SE ()
untilBegin BoolSig
p
    SE ()
body
    SE ()
untilEnd

whileDo :: BoolSig -> SE () -> SE ()
whileDo :: BoolSig -> SE () -> SE ()
whileDo BoolSig
p SE ()
body = do
    BoolSig -> SE ()
whileBegin BoolSig
p
    SE ()
body
    SE ()
whileEnd

whileBegin :: BoolSig -> SE ()
whileBegin :: BoolSig -> SE ()
whileBegin BoolSig
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ E -> Dep ()
forall (m :: * -> *). Monad m => E -> DepT m ()
D.whileBegin (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolSig -> GE E
forall a. Val a => a -> GE E
toGE BoolSig
a)

whileEnd :: SE ()
whileEnd :: SE ()
whileEnd = Dep () -> SE ()
fromDep_ Dep ()
forall (m :: * -> *). Monad m => DepT m ()
D.whileEnd

untilBegin :: BoolSig -> SE ()
untilBegin :: BoolSig -> SE ()
untilBegin BoolSig
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ E -> Dep ()
forall (m :: * -> *). Monad m => E -> DepT m ()
D.untilBegin (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolSig -> GE E
forall a. Val a => a -> GE E
toGE BoolSig
a)

untilEnd :: SE ()
untilEnd :: SE ()
untilEnd = Dep () -> SE ()
fromDep_ Dep ()
forall (m :: * -> *). Monad m => DepT m ()
D.untilEnd

untilDoD :: BoolD -> SE () -> SE ()
untilDoD :: BoolD -> SE () -> SE ()
untilDoD BoolD
p SE ()
body = do
    BoolD -> SE ()
untilBeginD BoolD
p
    SE ()
body
    SE ()
untilEnd

whileDoD :: BoolD -> SE () -> SE ()
whileDoD :: BoolD -> SE () -> SE ()
whileDoD BoolD
p SE ()
body = do
    BoolD -> SE ()
whileBeginD BoolD
p
    SE ()
body
    SE ()
whileEnd

whileBeginD :: BoolD -> SE ()
whileBeginD :: BoolD -> SE ()
whileBeginD BoolD
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ E -> Dep ()
forall (m :: * -> *). Monad m => E -> DepT m ()
D.whileBegin (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolD -> GE E
forall a. Val a => a -> GE E
toGE BoolD
a)

untilBeginD :: BoolD -> SE ()
untilBeginD :: BoolD -> SE ()
untilBeginD BoolD
a = Dep () -> SE ()
fromDep_ (Dep () -> SE ()) -> Dep () -> SE ()
forall a b. (a -> b) -> a -> b
$ E -> Dep ()
forall (m :: * -> *). Monad m => E -> DepT m ()
D.untilBegin (E -> Dep ()) -> DepT GE E -> Dep ()
forall (m :: * -> *) a b. Monad m => (a -> m b) -> m a -> m b
=<< GE E -> DepT GE E
forall (t :: (* -> *) -> * -> *) (m :: * -> *) a.
(MonadTrans t, Monad m) =>
m a -> t m a
lift (BoolD -> GE E
forall a. Val a => a -> GE E
toGE BoolD
a)

-- | Creates a constant boolean signal.
boolSig :: BoolD -> BoolSig
boolSig :: BoolD -> BoolSig
boolSig BoolD
x = case BoolD
x of
    PrimBoolD Bool
b -> Bool -> BoolSig
PrimBoolSig Bool
b
    BoolD GE E
a     -> GE E -> BoolSig
BoolSig GE E
a

infix  4  `equalsTo`, `notEqualsTo`, `lessThan`, `lessThanEquals`, `greaterThanEquals`, `greaterThan`

equalsTo :: EqB a => a -> a -> BooleanOf a
equalsTo :: a -> a -> BooleanOf a
equalsTo = a -> a -> BooleanOf a
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(==*)

notEqualsTo :: EqB a => a -> a -> BooleanOf a
notEqualsTo :: a -> a -> BooleanOf a
notEqualsTo = a -> a -> BooleanOf a
forall a bool. (EqB a, bool ~ BooleanOf a) => a -> a -> bool
(/=*)

lessThan :: OrdB a => a -> a -> BooleanOf a
lessThan :: a -> a -> BooleanOf a
lessThan = a -> a -> BooleanOf a
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<*)

greaterThan :: OrdB a => a -> a -> BooleanOf a
greaterThan :: a -> a -> BooleanOf a
greaterThan = a -> a -> BooleanOf a
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>*)

lessThanEquals :: OrdB a => a -> a -> BooleanOf a
lessThanEquals :: a -> a -> BooleanOf a
lessThanEquals = a -> a -> BooleanOf a
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(<=*)

greaterThanEquals :: OrdB a => a -> a -> BooleanOf a
greaterThanEquals :: a -> a -> BooleanOf a
greaterThanEquals = a -> a -> BooleanOf a
forall a bool. (OrdB a, bool ~ BooleanOf a) => a -> a -> bool
(>=*)

----------------------------------------------

-- | nsamp — Returns the number of samples loaded into a stored function table number.
--
-- > nsamp(x) (init-rate args only)
--
-- csound doc: <http://www.csounds.com/manual/html/nsamp.html>
nsamp :: Tab -> D
nsamp :: Tab -> D
nsamp = (E -> E) -> Tab -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 ((E -> E) -> Tab -> D) -> (E -> E) -> Tab -> D
forall a b. (a -> b) -> a -> b
$ String -> E -> E
opr1 String
"nsamp"

-- | Returns a length of the table.
ftlen :: Tab -> D
ftlen :: Tab -> D
ftlen = (E -> E) -> Tab -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 ((E -> E) -> Tab -> D) -> (E -> E) -> Tab -> D
forall a b. (a -> b) -> a -> b
$ String -> E -> E
opr1 String
"ftlen"

-- | Returns the number of channels for a table that stores wav files
ftchnls :: Tab -> D
ftchnls :: Tab -> D
ftchnls = (E -> E) -> Tab -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 ((E -> E) -> Tab -> D) -> (E -> E) -> Tab -> D
forall a b. (a -> b) -> a -> b
$ String -> E -> E
opr1 String
"ftchnls"

-- | Returns the sample rate for a table that stores wav files
ftsr :: Tab -> D
ftsr :: Tab -> D
ftsr = (E -> E) -> Tab -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 ((E -> E) -> Tab -> D) -> (E -> E) -> Tab -> D
forall a b. (a -> b) -> a -> b
$ String -> E -> E
opr1 String
"ftsr"

-- | Returns the base frequency for a table that stores wav files
ftcps :: Tab -> D
ftcps :: Tab -> D
ftcps = (E -> E) -> Tab -> D
forall a b. (Val a, Val b) => (E -> E) -> a -> b
on1 ((E -> E) -> Tab -> D) -> (E -> E) -> Tab -> D
forall a b. (a -> b) -> a -> b
$ String -> E -> E
opr1 String
"ftcps"


-------------------------------------------------
-- numeric instances

instance (Num a1, Num a2, Num a3, Num a4, Num a5, Num a6, Num a7, Num a8) => Num (a1, a2, a3, a4, a5, a6, a7, a8) where
    (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) + :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
+ (a1
b1, a2
b2, a3
b3, a4
b4, a5
b5, a6
b6, a7
b7, a8
b8) = (a1
a1 a1 -> a1 -> a1
forall a. Num a => a -> a -> a
+ a1
b1, a2
a2 a2 -> a2 -> a2
forall a. Num a => a -> a -> a
+ a2
b2, a3
a3 a3 -> a3 -> a3
forall a. Num a => a -> a -> a
+ a3
b3, a4
a4 a4 -> a4 -> a4
forall a. Num a => a -> a -> a
+ a4
b4, a5
a5 a5 -> a5 -> a5
forall a. Num a => a -> a -> a
+ a5
b5, a6
a6 a6 -> a6 -> a6
forall a. Num a => a -> a -> a
+ a6
b6, a7
a7 a7 -> a7 -> a7
forall a. Num a => a -> a -> a
+ a7
b7, a8
a8 a8 -> a8 -> a8
forall a. Num a => a -> a -> a
+ a8
b8)
    (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) * :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
* (a1
b1, a2
b2, a3
b3, a4
b4, a5
b5, a6
b6, a7
b7, a8
b8) = (a1
a1 a1 -> a1 -> a1
forall a. Num a => a -> a -> a
* a1
b1, a2
a2 a2 -> a2 -> a2
forall a. Num a => a -> a -> a
* a2
b2, a3
a3 a3 -> a3 -> a3
forall a. Num a => a -> a -> a
* a3
b3, a4
a4 a4 -> a4 -> a4
forall a. Num a => a -> a -> a
* a4
b4, a5
a5 a5 -> a5 -> a5
forall a. Num a => a -> a -> a
* a5
b5, a6
a6 a6 -> a6 -> a6
forall a. Num a => a -> a -> a
* a6
b6, a7
a7 a7 -> a7 -> a7
forall a. Num a => a -> a -> a
+ a7
b7, a8
a8 a8 -> a8 -> a8
forall a. Num a => a -> a -> a
+ a8
b8)
    negate :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
negate (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) = (a1 -> a1
forall a. Num a => a -> a
negate a1
a1, a2 -> a2
forall a. Num a => a -> a
negate a2
a2, a3 -> a3
forall a. Num a => a -> a
negate a3
a3, a4 -> a4
forall a. Num a => a -> a
negate a4
a4, a5 -> a5
forall a. Num a => a -> a
negate a5
a5, a6 -> a6
forall a. Num a => a -> a
negate a6
a6, a7 -> a7
forall a. Num a => a -> a
negate a7
a7, a8 -> a8
forall a. Num a => a -> a
negate a8
a8)

    fromInteger :: Integer -> (a1, a2, a3, a4, a5, a6, a7, a8)
fromInteger Integer
n = (Integer -> a1
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a2
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a3
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a4
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a5
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a6
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a7
forall a. Num a => Integer -> a
fromInteger Integer
n, Integer -> a8
forall a. Num a => Integer -> a
fromInteger Integer
n)
    signum :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
signum (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) = (a1 -> a1
forall a. Num a => a -> a
signum a1
a1, a2 -> a2
forall a. Num a => a -> a
signum a2
a2, a3 -> a3
forall a. Num a => a -> a
signum a3
a3, a4 -> a4
forall a. Num a => a -> a
signum a4
a4, a5 -> a5
forall a. Num a => a -> a
signum a5
a5, a6 -> a6
forall a. Num a => a -> a
signum a6
a6, a7 -> a7
forall a. Num a => a -> a
signum a7
a7, a8 -> a8
forall a. Num a => a -> a
signum a8
a8)
    abs :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
abs (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) = (a1 -> a1
forall a. Num a => a -> a
abs a1
a1, a2 -> a2
forall a. Num a => a -> a
abs a2
a2, a3 -> a3
forall a. Num a => a -> a
abs a3
a3, a4 -> a4
forall a. Num a => a -> a
abs a4
a4, a5 -> a5
forall a. Num a => a -> a
abs a5
a5, a6 -> a6
forall a. Num a => a -> a
abs a6
a6, a7 -> a7
forall a. Num a => a -> a
abs a7
a7, a8 -> a8
forall a. Num a => a -> a
abs a8
a8)

instance (Fractional a1, Fractional a2, Fractional a3, Fractional a4, Fractional a5, Fractional a6, Fractional a7, Fractional a8) => Fractional (a1, a2, a3, a4, a5, a6, a7, a8) where
    recip :: (a1, a2, a3, a4, a5, a6, a7, a8)
-> (a1, a2, a3, a4, a5, a6, a7, a8)
recip (a1
a1, a2
a2, a3
a3, a4
a4, a5
a5, a6
a6, a7
a7, a8
a8) = (a1 -> a1
forall a. Fractional a => a -> a
recip a1
a1, a2 -> a2
forall a. Fractional a => a -> a
recip a2
a2, a3 -> a3
forall a. Fractional a => a -> a
recip a3
a3, a4 -> a4
forall a. Fractional a => a -> a
recip a4
a4, a5 -> a5
forall a. Fractional a => a -> a
recip a5
a5, a6 -> a6
forall a. Fractional a => a -> a
recip a6
a6, a7 -> a7
forall a. Fractional a => a -> a
recip a7
a7, a8 -> a8
forall a. Fractional a => a -> a
recip a8
a8)
    fromRational :: Rational -> (a1, a2, a3, a4, a5, a6, a7, a8)
fromRational Rational
n = (Rational -> a1
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a2
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a3
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a4
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a5
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a6
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a7
forall a. Fractional a => Rational -> a
fromRational Rational
n, Rational -> a8
forall a. Fractional a => Rational -> a
fromRational Rational
n)