clash-prelude-0.11: CAES Language for Synchronous Hardware - Prelude library

Copyright (C) 2013-2016 University of Twente BSD2 (see the file LICENSE) Christiaan Baaij Trustworthy Haskell2010 MonoLocalBindsTemplateHaskellTemplateHaskellQuotesGADTsGADTSyntaxDataKindsMagicHashKindSignaturesTypeOperatorsExplicitNamespaces

CLaSH.Promoted.Nat

Description

Synopsis

# Singleton natural numbers

## Data type

data SNat n where Source #

Singleton value for a type-level natural number n

Constructors

 SNat :: KnownNat n => SNat n

Instances

 Show (SNat n) Source # MethodsshowsPrec :: Int -> SNat n -> ShowS #show :: SNat n -> String #showList :: [SNat n] -> ShowS # Lift (SNat n) Source # Methodslift :: SNat n -> Q Exp # ShowX (SNat n) Source # MethodsshowsPrecX :: Int -> SNat n -> ShowS Source #showX :: SNat n -> String Source #showListX :: [SNat n] -> ShowS Source #

## Construction

snatProxy :: KnownNat n => proxy n -> SNat n Source #

Create an SNat n from a proxy for n

withSNat :: KnownNat n => (SNat n -> a) -> a Source #

Supply a function with a singleton natural n according to the context

snat :: KnownNat n => SNat n Source #

Deprecated: Use SNat instead of snat

Create a singleton literal for a type-level natural number

## Conversion

Reify the type-level Nat n to it's term-level Integer representation.

snatToNum :: Num a => SNat n -> a Source #

Reify the type-level Nat n to it's term-level Number.

## Arithmetic

addSNat :: SNat a -> SNat b -> SNat (a + b) Source #

Add two singleton natural numbers

mulSNat :: SNat a -> SNat b -> SNat (a * b) Source #

Multiply two singleton natural numbers

powSNat :: SNat a -> SNat b -> SNat (a ^ b) Source #

Power of two singleton natural numbers

### Partial

subSNat :: SNat (a + b) -> SNat b -> SNat a Source #

Subtract two singleton natural numbers

divSNat :: 1 <= b => SNat a -> SNat b -> SNat (Div a b) Source #

Division of two singleton natural numbers

modSNat :: 1 <= b => SNat a -> SNat b -> SNat (Mod a b) Source #

Modulo of two singleton natural numbers

Arguments

 :: (2 <= base, 1 <= x) => SNat base Base -> SNat x -> SNat (FLog base x)

Floor of the logarithm of a natural number

Arguments

 :: (2 <= base, 1 <= x) => SNat base Base -> SNat x -> SNat (CLog base x)

Ceiling of the logarithm of a natural number

Arguments

 :: FLog base x ~ CLog base x => SNat base Base -> SNat x -> SNat (Log base x)

Exact integer logarithm of a natural number

NB: Only works when the argument is a power of the base

### Specialised

pow2SNat :: SNat a -> SNat (2 ^ a) Source #

Power of two of a singleton natural number

# Unary/Peano-encoded natural numbers

## Data type

data UNat :: Nat -> * where Source #

Unary representation of a type-level natural

NB: Not synthesisable

Constructors

 UZero :: UNat 0 USucc :: UNat n -> UNat (n + 1)

Instances

 KnownNat n => Show (UNat n) Source # MethodsshowsPrec :: Int -> UNat n -> ShowS #show :: UNat n -> String #showList :: [UNat n] -> ShowS # KnownNat n => ShowX (UNat n) Source # MethodsshowsPrecX :: Int -> UNat n -> ShowS Source #showX :: UNat n -> String Source #showListX :: [UNat n] -> ShowS Source #

## Construction

toUNat :: SNat n -> UNat n Source #

Convert a singleton natural number to its unary representation

NB: Not synthesisable

## Conversion

fromUNat :: UNat n -> SNat n Source #

Convert a unary-encoded natural number to its singleton representation

NB: Not synthesisable

## Arithmetic

addUNat :: UNat n -> UNat m -> UNat (n + m) Source #

Add two unary-encoded natural numbers

NB: Not synthesisable

mulUNat :: UNat n -> UNat m -> UNat (n * m) Source #

Multiply two unary-encoded natural numbers

NB: Not synthesisable

powUNat :: UNat n -> UNat m -> UNat (n ^ m) Source #

Power of two unary-encoded natural numbers

NB: Not synthesisable

### Partial

predUNat :: UNat (n + 1) -> UNat n Source #

Predecessor of a unary-encoded natural number

NB: Not synthesisable

subUNat :: UNat (m + n) -> UNat n -> UNat m Source #

Subtract two unary-encoded natural numbers

NB: Not synthesisable

# Base-2 encoded natural numbers

## Data type

data BNat :: Nat -> * where Source #

Base-2 encoded natural number

• NB: The LSB is the left/outer-most constructor:
• NB: Not synthesisable
>>> B0 (B1 (B1 BT))
b6


## Constructors

• Starting/Terminating element:

BT :: BNat 0

• Append a zero (0):

B0 :: BNat n -> BNat (2 * n)

• Append a one (1):

B1 :: BNat n -> BNat ((2 * n) + 1)


Constructors

 BT :: BNat 0 B0 :: BNat n -> BNat (2 * n) B1 :: BNat n -> BNat ((2 * n) + 1)

Instances

 KnownNat n => Show (BNat n) Source # MethodsshowsPrec :: Int -> BNat n -> ShowS #show :: BNat n -> String #showList :: [BNat n] -> ShowS # KnownNat n => ShowX (BNat n) Source # MethodsshowsPrecX :: Int -> BNat n -> ShowS Source #showX :: BNat n -> String Source #showListX :: [BNat n] -> ShowS Source #

## Construction

toBNat :: SNat n -> BNat n Source #

Convert a singleton natural number to its base-2 representation

NB: Not synthesisable

## Conversion

fromBNat :: BNat n -> SNat n Source #

Convert a base-2 encoded natural number to its singleton representation

NB: Not synthesisable

## Pretty printing base-2 encoded natural numbers

Show a base-2 encoded natural as a binary literal

NB: The LSB is shown as the right-most bit

>>> d789
d789
>>> toBNat d789
b789
>>> showBNat (toBNat d789)
"0b1100010101"
>>> 0b1100010101 :: Integer
789


## Arithmetic

succBNat :: BNat n -> BNat (n + 1) Source #

Successor of a base-2 encoded natural number

NB: Not synthesisable

addBNat :: BNat n -> BNat m -> BNat (n + m) Source #

Add two base-2 encoded natural numbers

NB: Not synthesisable

mulBNat :: BNat n -> BNat m -> BNat (n * m) Source #

Multiply two base-2 encoded natural numbers

NB: Not synthesisable

powBNat :: BNat n -> BNat m -> BNat (n ^ m) Source #

Power of two base-2 encoded natural numbers

NB: Not synthesisable

### Partial

predBNat :: BNat (n + 1) -> BNat n Source #

Predecessor of a base-2 encoded natural number

NB: Not synthesisable

div2BNat :: BNat (2 * n) -> BNat n Source #

Divide a base-2 encoded natural number by 2

NB: Not synthesisable

div2Sub1BNat :: BNat ((2 * n) + 1) -> BNat n Source #

Subtract 1 and divide a base-2 encoded natural number by 2

NB: Not synthesisable

log2BNat :: BNat (2 ^ n) -> BNat n Source #

Get the log2 of a base-2 encoded natural number

NB: Not synthesisable

## Normalisation

stripZeros :: BNat n -> BNat n Source #

Strip non-contributing zero's from a base-2 encoded natural number

>>> B1 (B0 (B0 (B0 BT)))
b1
>>> showBNat (B1 (B0 (B0 (B0 BT))))
"0b0001"
>>> showBNat (stripZeros (B1 (B0 (B0 (B0 BT)))))
"0b1"
>>> stripZeros (B1 (B0 (B0 (B0 BT))))
b1


NB: Not synthesisable