-- |
-- Module: Numeric.Optics
-- Description: Optics for working with numeric types.
--
module Numeric.Optics
  ( base
  , integral
    -- * Predefined bases
  , binary
  , octal
  , decimal
  , hex
    -- * Arithmetic lenses
  , adding
  , subtracting
  , multiplying
  , dividing
  , exponentiating
  , negated
  , pattern Integral
  ) where

import Data.Char (chr, ord, isAsciiLower, isAsciiUpper, isDigit)
import Data.Maybe (fromMaybe)
import GHC.Stack
import Numeric (readInt, showIntAtBase)

import Data.Tuple.Optics
import Optics.AffineFold
import Optics.Iso
import Optics.Optic
import Optics.Prism
import Optics.Review
import Optics.Setter

-- | This 'Prism' can be used to model the fact that every 'Prelude.Integral'
-- type is a subset of 'Integer'.
--
-- Embedding through the 'Prism' only succeeds if the 'Integer' would pass
-- through unmodified when re-extracted.
integral :: (Integral a, Integral b) => Prism Integer Integer a b
integral :: forall a b. (Integral a, Integral b) => Prism Integer Integer a b
integral = forall b t s a. (b -> t) -> (s -> Either t a) -> Prism s t a b
prism forall a. Integral a => a -> Integer
toInteger forall a b. (a -> b) -> a -> b
$ \Integer
i -> let a :: a
a = forall a. Num a => Integer -> a
fromInteger Integer
i in
  if forall a. Integral a => a -> Integer
toInteger a
a forall a. Eq a => a -> a -> Bool
== Integer
i
  then forall a b. b -> Either a b
Right a
a
  else forall a b. a -> Either a b
Left Integer
i
{-# INLINE integral #-}

-- | Pattern synonym that can be used to construct or pattern match on an
-- 'Integer' as if it were of any 'Prelude.Integral' type.
pattern Integral :: forall a. Integral a => a -> Integer
pattern $bIntegral :: forall a. Integral a => a -> Integer
$mIntegral :: forall {r} {a}.
Integral a =>
Integer -> (a -> r) -> ((# #) -> r) -> r
Integral a <- (preview integral -> Just a) where
  Integral a
a = forall k (is :: IxList) t b.
Is k A_Review =>
Optic' k is t b -> b -> t
review forall a b. (Integral a, Integral b) => Prism Integer Integer a b
integral a
a

-- | A prism that shows and reads integers in base-2 through base-36
--
-- Note: This is an improper prism, since leading 0s are stripped when reading.
--
-- >>> "100" ^? base 16
-- Just 256
--
-- >>> 1767707668033969 ^. re (base 36)
-- "helloworld"
base :: (HasCallStack, Integral a) => Int -> Prism' String a
base :: forall a. (HasCallStack, Integral a) => Int -> Prism' String a
base Int
b
  | Int
b forall a. Ord a => a -> a -> Bool
< Int
2 Bool -> Bool -> Bool
|| Int
b forall a. Ord a => a -> a -> Bool
> Int
36 = forall a. HasCallStack => String -> a
error (String
"base: Invalid base " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> String
show Int
b)
  | Bool
otherwise       = forall b t s a. (b -> t) -> (s -> Either t a) -> Prism s t a b
prism a -> String
intShow String -> Either String a
intRead
  where
    intShow :: a -> String
intShow a
n = forall a. Real a => (a -> ShowS) -> a -> ShowS
showSigned' (forall a. (Integral a, Show a) => a -> (Int -> Char) -> a -> ShowS
showIntAtBase (forall a. Integral a => a -> Integer
toInteger Int
b) HasCallStack => Int -> Char
intToDigit') (forall a. Integral a => a -> Integer
toInteger a
n) String
""

    intRead :: String -> Either String a
intRead String
s =
      case forall a. Real a => ReadS a -> ReadS a
readSigned' (forall a. Num a => a -> (Char -> Bool) -> (Char -> Int) -> ReadS a
readInt (forall a b. (Integral a, Num b) => a -> b
fromIntegral Int
b) (Int -> Char -> Bool
isDigit' Int
b) HasCallStack => Char -> Int
digitToInt') String
s of
        [(a
n,String
"")] -> forall a b. b -> Either a b
Right a
n
        [(a, String)]
_ -> forall a b. a -> Either a b
Left String
s
{-# INLINE base #-}

-- | Like 'Data.Char.intToDigit', but handles up to base-36
intToDigit' :: HasCallStack => Int -> Char
intToDigit' :: HasCallStack => Int -> Char
intToDigit' Int
i
  | Int
i forall a. Ord a => a -> a -> Bool
>= Int
0  Bool -> Bool -> Bool
&& Int
i forall a. Ord a => a -> a -> Bool
< Int
10 = Int -> Char
chr (Char -> Int
ord Char
'0' forall a. Num a => a -> a -> a
+ Int
i)
  | Int
i forall a. Ord a => a -> a -> Bool
>= Int
10 Bool -> Bool -> Bool
&& Int
i forall a. Ord a => a -> a -> Bool
< Int
36 = Int -> Char
chr (Char -> Int
ord Char
'a' forall a. Num a => a -> a -> a
+ Int
i forall a. Num a => a -> a -> a
- Int
10)
  | Bool
otherwise = forall a. HasCallStack => String -> a
error (String
"intToDigit': Invalid int " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> String
show Int
i)
{-# INLINE intToDigit' #-}

-- | Like 'Data.Char.digitToInt', but handles up to base-36
digitToInt' :: HasCallStack => Char -> Int
digitToInt' :: HasCallStack => Char -> Int
digitToInt' Char
c = forall a. a -> Maybe a -> a
fromMaybe (forall a. HasCallStack => String -> a
error (String
"digitToInt': Invalid digit " forall a. [a] -> [a] -> [a]
++ forall a. Show a => a -> String
show Char
c))
                          (Char -> Maybe Int
digitToIntMay Char
c)
{-# INLINE digitToInt' #-}

-- | A safe variant of 'digitToInt''
digitToIntMay :: Char -> Maybe Int
digitToIntMay :: Char -> Maybe Int
digitToIntMay Char
c
  | Char -> Bool
isDigit Char
c      = forall a. a -> Maybe a
Just (Char -> Int
ord Char
c forall a. Num a => a -> a -> a
- Char -> Int
ord Char
'0')
  | Char -> Bool
isAsciiLower Char
c = forall a. a -> Maybe a
Just (Char -> Int
ord Char
c forall a. Num a => a -> a -> a
- Char -> Int
ord Char
'a' forall a. Num a => a -> a -> a
+ Int
10)
  | Char -> Bool
isAsciiUpper Char
c = forall a. a -> Maybe a
Just (Char -> Int
ord Char
c forall a. Num a => a -> a -> a
- Char -> Int
ord Char
'A' forall a. Num a => a -> a -> a
+ Int
10)
  | Bool
otherwise = forall a. Maybe a
Nothing
{-# INLINE digitToIntMay #-}

-- | Select digits that fall into the given base
isDigit' :: Int -> Char -> Bool
isDigit' :: Int -> Char -> Bool
isDigit' Int
b Char
c = case Char -> Maybe Int
digitToIntMay Char
c of
  Just Int
i -> Int
i forall a. Ord a => a -> a -> Bool
< Int
b
  Maybe Int
_ -> Bool
False
{-# INLINE isDigit' #-}

-- | A simpler variant of 'Numeric.showSigned' that only prepends a dash and
-- doesn't know about parentheses
showSigned' :: Real a => (a -> ShowS) -> a -> ShowS
showSigned' :: forall a. Real a => (a -> ShowS) -> a -> ShowS
showSigned' a -> ShowS
f a
n
  | a
n forall a. Ord a => a -> a -> Bool
< a
0     = Char -> ShowS
showChar Char
'-' forall b c a. (b -> c) -> (a -> b) -> a -> c
. a -> ShowS
f (forall a. Num a => a -> a
negate a
n)
  | Bool
otherwise = a -> ShowS
f a
n
{-# INLINE showSigned' #-}

-- | A simpler variant of 'Numeric.readSigned' that supports any base, only
-- recognizes an initial dash and doesn't know about parentheses
readSigned' :: Real a => ReadS a -> ReadS a
readSigned' :: forall a. Real a => ReadS a -> ReadS a
readSigned' ReadS a
f (Char
'-':String
xs) = ReadS a
f String
xs forall (f :: * -> *) a b. Functor f => f a -> (a -> b) -> f b
<&> forall k (is :: IxList) s t a b.
Is k A_Setter =>
Optic k is s t a b -> (a -> b) -> s -> t
over forall s t a b. Field1 s t a b => Lens s t a b
_1 forall a. Num a => a -> a
negate
readSigned' ReadS a
f String
xs       = ReadS a
f String
xs
{-# INLINE readSigned' #-}

-- | @'binary' = 'base' 2@
binary :: Integral a => Prism' String a
binary :: forall a. Integral a => Prism' String a
binary = forall a. (HasCallStack, Integral a) => Int -> Prism' String a
base Int
2
{-# INLINE binary #-}

-- | @'octal' = 'base' 8@
octal :: Integral a => Prism' String a
octal :: forall a. Integral a => Prism' String a
octal = forall a. (HasCallStack, Integral a) => Int -> Prism' String a
base Int
8
{-# INLINE octal #-}

-- | @'decimal' = 'base' 10@
decimal :: Integral a => Prism' String a
decimal :: forall a. Integral a => Prism' String a
decimal = forall a. (HasCallStack, Integral a) => Int -> Prism' String a
base Int
10
{-# INLINE decimal #-}

-- | @'hex' = 'base' 16@
hex :: Integral a => Prism' String a
hex :: forall a. Integral a => Prism' String a
hex = forall a. (HasCallStack, Integral a) => Int -> Prism' String a
base Int
16
{-# INLINE hex #-}

-- | @'adding' n = 'iso' (+n) (subtract n)@
--
-- >>> [1..3] ^.. traversed % adding 1000
-- [1001,1002,1003]
adding :: Num a => a -> Iso' a a
adding :: forall a. Num a => a -> Iso' a a
adding a
n = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (forall a. Num a => a -> a -> a
+a
n) (forall a. Num a => a -> a -> a
subtract a
n)
{-# INLINE adding #-}

-- | @
-- 'subtracting' n = 'iso' (subtract n) ((+n)
-- 'subtracting' n = 'Optics.Re.re' ('adding' n)
-- @
subtracting :: Num a => a -> Iso' a a
subtracting :: forall a. Num a => a -> Iso' a a
subtracting a
n = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (forall a. Num a => a -> a -> a
subtract a
n) (forall a. Num a => a -> a -> a
+a
n)
{-# INLINE subtracting #-}

-- | @'multiplying' n = iso (*n) (/n)@
--
-- Note: This errors for n = 0
--
-- >>> 5 & multiplying 1000 %~ (+3)
-- 5.003
--
-- >>> let fahrenheit = multiplying (9/5) % adding 32 in 230 ^. re fahrenheit
-- 110.0
multiplying :: (Fractional a, Eq a) => a -> Iso' a a
multiplying :: forall a. (Fractional a, Eq a) => a -> Iso' a a
multiplying a
0 = forall a. HasCallStack => String -> a
error String
"Numeric.Optics.multiplying: factor 0"
multiplying a
n = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (forall a. Num a => a -> a -> a
*a
n) (forall a. Fractional a => a -> a -> a
/a
n)
{-# INLINE multiplying #-}

-- | @
-- 'dividing' n = 'iso' (/n) (*n)
-- 'dividing' n = 'Optics.Re.re' ('multiplying' n)@
--
-- Note: This errors for n = 0
dividing :: (Fractional a, Eq a) => a -> Iso' a a
dividing :: forall a. (Fractional a, Eq a) => a -> Iso' a a
dividing a
0 = forall a. HasCallStack => String -> a
error String
"Numeric.Optics.dividing: divisor 0"
dividing a
n = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (forall a. Fractional a => a -> a -> a
/a
n) (forall a. Num a => a -> a -> a
*a
n)
{-# INLINE dividing #-}

-- | @'exponentiating' n = 'iso' (**n) (**recip n)@
--
-- Note: This errors for n = 0
--
-- >>> au (coerced1 @Sum % re (exponentiating 2)) (foldMapOf each) (3,4) == 5
-- True
exponentiating :: (Floating a, Eq a) => a -> Iso' a a
exponentiating :: forall a. (Floating a, Eq a) => a -> Iso' a a
exponentiating a
0 = forall a. HasCallStack => String -> a
error String
"Numeric.Optics.exponentiating: exponent 0"
exponentiating a
n = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso (forall a. Floating a => a -> a -> a
**a
n) (forall a. Floating a => a -> a -> a
**forall a. Fractional a => a -> a
recip a
n)
{-# INLINE exponentiating #-}

-- | @'negated' = 'iso' 'negate' 'negate'@
--
-- >>> au (coerced1 @Sum % negated) (foldMapOf each) (3,4) == 7
-- True
--
-- >>> au (coerced1 @Sum) (foldMapOf (each % negated)) (3,4) == -7
-- True
negated :: Num a => Iso' a a
negated :: forall a. Num a => Iso' a a
negated = forall s a b t. (s -> a) -> (b -> t) -> Iso s t a b
iso forall a. Num a => a -> a
negate forall a. Num a => a -> a
negate
{-# INLINE negated #-}

-- $setup
-- >>> import Data.Monoid
-- >>> import Optics.Core