```{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE TypeFamilies #-}
module Data.Fixed.Binary.VectorSpace () where

import Data.Bits

import Data.AffineSpace
import Data.Basis
import Data.VectorSpace

import Data.Fixed.Binary

instance ( HasResolution r, Bits a, Bits (Super a), Integral a
, Integral (Super a), SuperTypeable a) =>
AdditiveGroup (Fixed r a) where
{-# INLINE zeroV #-}
zeroV = 0
{-# INLINE (^+^) #-}
(^+^) = (+)
{-# INLINE negateV #-}
negateV = negate

instance ( HasResolution r, Bits a, Bits (Super a), Integral a
, Integral (Super a), SuperTypeable a) =>
AffineSpace (Fixed r a) where
type Diff (Fixed r a) = Fixed r a
{-# INLINE (.-.) #-}
(.-.) = (-)
{-# INLINE (.+^) #-}
(.+^) = (+)

instance ( HasResolution r, Bits a, Bits (Super a), Integral a
, Integral (Super a), SuperTypeable a) =>
HasBasis (Fixed r a) where
type Basis (Fixed r a) = ()
{-# INLINE basisValue #-}
basisValue ~() = 1
{-# INLINE decompose #-}
decompose s = [((), s)]
{-# INLINE decompose' #-}
decompose' s = const s

instance ( HasResolution r, Bits a, Bits (Super a), Integral a
, Integral (Super a), SuperTypeable a) =>
VectorSpace (Fixed r a) where
type Scalar (Fixed r a) = Fixed r a
{-# INLINE (*^) #-}
(*^) = (*)

instance ( HasResolution r, Bits a, Bits (Super a), Integral a
, Integral (Super a), SuperTypeable a) =>
InnerSpace (Fixed r a) where
{-# INLINE (<.>) #-}
(<.>) = (*)
```