{-# LANGUAGE FlexibleInstances     #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE ScopedTypeVariables   #-}
{-# LANGUAGE TypeFamilies          #-}

module HaskellWorks.Data.Bits.Broadword.Word64
  ( h
  , l
  , kBitDiff
  , kBitDiffPos
  , kBitDiffUnsafe
  ) where

import Data.Word
import HaskellWorks.Data.Bits.BitWise

-- | Initialise all sub-words of size k where 'k' ∈ { 2, 4, 8, 16, 32, 64 } such that the lowest bit is set to 1 and all other bits are cleared.
--
-- >>> import Numeric(showHex)
-- >>> showHex (l 2) ""
-- "5555555555555555"
-- >>> showHex (l 4) ""
-- "1111111111111111"
-- >>> showHex (l 8) ""
-- "101010101010101"
-- >>> showHex (l 16) ""
-- "1000100010001"
-- >>> showHex (l 32) ""
-- "100000001"
-- >>> showHex (l 64) ""
-- "1"
l :: Int -> Word64
l :: Int -> Word64
l Int
2  = Word64
0x5555555555555555
l Int
4  = Word64
0x1111111111111111
l Int
8  = Word64
0x0101010101010101
l Int
16 = Word64
0x0001000100010001
l Int
32 = Word64
0x0000000100000001
l Int
64 = Word64
0x0000000000000001
l Int
k  = [Char] -> Word64
forall a. HasCallStack => [Char] -> a
error ([Char]
"Invalid h k where k = " [Char] -> [Char] -> [Char]
forall a. [a] -> [a] -> [a]
++ Int -> [Char]
forall a. Show a => a -> [Char]
show Int
k)
{-# INLINE l #-}

-- | Initialise all sub-words of size k where 'k' ∈ { 2, 4, 8, 16, 32, 64 } such that the highest bit is set to 1 and all other bits are cleared.
--
-- >>> import Numeric(showHex)
-- >>> showHex (h 2) ""
-- "aaaaaaaaaaaaaaaa"
-- >>> showHex (h 4) ""
-- "8888888888888888"
-- >>> showHex (h 8) ""
-- "8080808080808080"
-- >>> showHex (h 16) ""
-- "8000800080008000"
-- >>> showHex (h 32) ""
-- "8000000080000000"
-- >>> showHex (h 64) ""
-- "8000000000000000"
h :: Int -> Word64
h :: Int -> Word64
h Int
2  = Word64
0xaaaaaaaaaaaaaaaa
h Int
4  = Word64
0x8888888888888888
h Int
8  = Word64
0x8080808080808080
h Int
16 = Word64
0x8000800080008000
h Int
32 = Word64
0x8000000080000000
h Int
64 = Word64
0x8000000000000000
h Int
k  = [Char] -> Word64
forall a. HasCallStack => [Char] -> a
error ([Char]
"Invalid h k where k = " [Char] -> [Char] -> [Char]
forall a. [a] -> [a] -> [a]
++ Int -> [Char]
forall a. Show a => a -> [Char]
show Int
k)
{-# INLINE h #-}

-- | Broadword subtraction of sub-words of size 'k' where 'k' ∈ { 2, 4, 8, 16, 32, 64 }.
--
-- The subtraction respects 2's complement so sub-words may be regarded as signed or unsigned words.
--
-- >>> import Numeric(showHex)
-- >>> showHex (kBitDiff 8 0x0807060504030201 0x0404030302020101) ""
-- "403030202010100"
-- >>> showHex (kBitDiff 8 0x0807060504030201 0x0102030405060708) ""
-- "7050301fffdfbf9"
-- >>> showHex (kBitDiff 8 0x20000000000000ff 0x10000000000000ff) ""
-- "1000000000000000"
kBitDiff :: Int -> Word64 -> Word64 -> Word64
kBitDiff :: Int -> Word64 -> Word64 -> Word64
kBitDiff Int
k Word64
x Word64
y = ((Word64
x Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.|. Int -> Word64
h Int
k) Word64 -> Word64 -> Word64
forall a. Num a => a -> a -> a
- (Word64
y Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.&. Word64 -> Word64
forall a. BitWise a => a -> a
comp (Int -> Word64
h Int
k))) Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.^. ((Word64
x Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.^. Word64 -> Word64
forall a. BitWise a => a -> a
comp Word64
y) Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.&. Int -> Word64
h Int
k)
{-# INLINE kBitDiff #-}

-- | Broadword subtraction of sub-words of size 'k' where 'k' ∈ { 2, 4, 8, 16, 32, 64 } where results are bounded from below by 0.
--
-- >>> import Numeric(showHex)
-- >>> showHex (kBitDiffPos 8 0x0807060504030201 0x0404030302020101) ""
-- "403030202010100"
-- >>> showHex (kBitDiffPos 8 0x0807060504030201 0x0102030405060708) ""
-- "705030100000000"
-- >>> showHex (kBitDiffPos 8 0x20000000000000ff 0x10000000000000ff) ""
-- "1000000000000000"
kBitDiffPos :: Int -> Word64 -> Word64 -> Word64
kBitDiffPos :: Int -> Word64 -> Word64 -> Word64
kBitDiffPos Int
k Word64
x Word64
y =
                                                                        -- let !_ = trace (">> x = " <> bitShow x) x in
                                                                        -- let !_ = trace (">> y = " <> bitShow y) y in
  let d :: Word64
d = Int -> Word64 -> Word64 -> Word64
kBitDiff Int
k Word64
x Word64
y                                            in  -- let !_ = trace (">> d = " <> bitShow d) d in
  let s :: Word64
s = Int -> Word64 -> Word64 -> Word64
kBitDiff Int
k Word64
0 ((Word64 -> Word64
forall a. BitWise a => a -> a
comp Word64
d Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.&. Int -> Word64
h Int
k) Word64 -> Word64 -> Word64
forall a. Shift a => a -> Word64 -> a
.>. Int -> Word64
forall a b. (Integral a, Num b) => a -> b
fromIntegral (Int
k Int -> Int -> Int
forall a. Num a => a -> a -> a
- Int
1))  in  -- let !_ = trace (">> s = " <> bitShow s) s in
  let r :: Word64
r = Word64
d Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.&. Word64
s                                                   in  -- let !_ = trace (">> r = " <> bitShow r) r in
  Word64
r
{-# INLINE kBitDiffPos #-}

-- | Broadword subtraction of sub-words of size 'k' where 'k' ∈ { 2, 4, 8, 16, 32, 64 } where all the sub-words of 'x' and 'y' must
-- not have the signed bit set for the result to be meaningful.
--
-- >>> import Numeric(showHex)
-- >>> showHex (kBitDiffUnsafe 8 0x0807060504030201 0x0404030302020101) ""
-- "403030202010100"
-- >>> showHex (kBitDiffUnsafe 8 0x0807060504030201 0x0102030405060708) ""
-- "7050301fffdfbf9"
-- >>> showHex (kBitDiffUnsafe 8 0x20000000000000ff 0x10000000000000ff) "" -- produces nonsense in the last sub-word
-- "1000000000000080"
kBitDiffUnsafe :: Int -> Word64 -> Word64 -> Word64
kBitDiffUnsafe :: Int -> Word64 -> Word64 -> Word64
kBitDiffUnsafe Int
k Word64
x Word64
y = ((Word64
x Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.|. Int -> Word64
h Int
k) Word64 -> Word64 -> Word64
forall a. Num a => a -> a -> a
- Word64
y) Word64 -> Word64 -> Word64
forall a. BitWise a => a -> a -> a
.^. Int -> Word64
h Int
k
{-# INLINE kBitDiffUnsafe #-}