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(.module:
[library
[lux (#- and or not false true)
[abstract
[equivalence (#+ Equivalence)]
[hash (#+ Hash)]
[monoid (#+ Monoid)]]
[control
["." try]]]]
[//
["n" nat]])
(def: .public bits_per_byte
8)
(def: .public bytes_per_i64
8)
(def: .public width
Nat
(n.* ..bits_per_byte
..bytes_per_i64))
(template [<parameter_type> <name> <op> <doc>]
[(def: .public (<name> parameter subject)
{#.doc <doc>}
(All [s] (-> <parameter_type> (I64 s) (I64 s)))
(<op> parameter subject))]
[(I64 Any) or "lux i64 or" "Bitwise or."]
[(I64 Any) xor "lux i64 xor" "Bitwise xor."]
[(I64 Any) and "lux i64 and" "Bitwise and."]
[Nat left_shifted "lux i64 left-shift" "Bitwise left-shift."]
[Nat right_shifted "lux i64 right-shift" "Unsigned/logic bitwise right-shift."]
)
... https://en.wikipedia.org/wiki/Mask_(computing)
(type: .public Mask
{#.doc (example "A pattern of bits that can be imposed on I64 values.")}
I64)
(def: .public (bit position)
{#.doc (example "A mask with only a specific bit set.")}
(-> Nat Mask)
(|> 1 .i64 (..left_shifted (n.% ..width position))))
(def: .public sign
{#.doc (example "A mask for the sign bit of ints.")}
Mask
(..bit (dec ..width)))
(def: .public not
{#.doc "Bitwise negation."}
(All [s] (-> (I64 s) (I64 s)))
(..xor (.i64 (dec 0))))
(def: .public false
Mask
(.i64 0))
(def: .public true
Mask
(..not ..false))
(def: .public (mask amount_of_bits)
{#.doc (example "Mask a block of bits of the specified size.")}
(-> Nat Mask)
(case amount_of_bits
0 ..false
bits (case (n.% ..width bits)
0 ..true
bits (|> 1 .i64 (..left_shifted (n.% ..width bits)) .dec))))
(def: (with_shift shift value)
(-> Nat Nat Nat)
(|> value (right_shifted shift) (n.+ value)))
(def: .public (ones subject)
{#.doc "Count the number of 1s in a bit-map."}
(-> (I64 Any) Nat)
(let [ones' (n.- (|> subject (right_shifted 1) (..and 6148914691236517205) i64)
(i64 subject))]
(|> ones'
(right_shifted 2) (..and 3689348814741910323) (n.+ (..and 3689348814741910323 ones'))
(with_shift 4) (..and 1085102592571150095)
(with_shift 8)
(with_shift 16)
(with_shift 32)
(..and 127))))
(def: .public (zero index input)
{#.doc "Clear bit at the given index."}
(All [s] (-> Nat (I64 s) (I64 s)))
(|> index ..bit ..not (..and input)))
(template [<name> <op> <doc>]
[(def: .public (<name> index input)
{#.doc <doc>}
(All [s] (-> Nat (I64 s) (I64 s)))
(|> index ..bit (<op> input)))]
[one ..or "Set bit at given index."]
[flipped ..xor "Flip bit at given index."]
)
(def: .public (one? index input)
(-> Nat (I64 Any) Bit)
(|> input (:as I64) (..and (..bit index)) (n.= 0) .not))
(def: .public (zero? index input)
(-> Nat (I64 Any) Bit)
(.not (..one? index input)))
(template [<name> <forward> <backward>]
[(def: .public (<name> distance input)
(All [s] (-> Nat (I64 s) (I64 s)))
(..or (<forward> distance input)
(<backward> (n.- (n.% ..width distance) ..width) input)))]
[left_rotated ..left_shifted ..right_shifted]
[right_rotated ..right_shifted ..left_shifted]
)
(def: .public (region offset size)
{#.doc (example "A mask for a block of bits of the given size, starting at the given offset.")}
(-> Nat Nat Mask)
(..left_rotated offset (..mask size)))
(implementation: .public equivalence
(All [a] (Equivalence (I64 a)))
(def: (= reference sample)
("lux i64 =" reference sample)))
(implementation: .public hash
(All [a] (Hash (I64 a)))
(def: &equivalence ..equivalence)
(def: hash .nat))
(template [<monoid> <identity> <compose>]
[(implementation: .public <monoid>
(All [a] (Monoid (I64 a)))
(def: identity <identity>)
(def: compose <compose>))]
[disjunction ..false ..or]
[conjunction ..true ..and]
)
(def: .public reversed
(All [a] (-> (I64 a) (I64 a)))
(let [swapper (: (-> Nat (All [a] (-> (I64 a) (I64 a))))
(function (_ power)
(let [size (..left_shifted power 1)
repetitions (: (-> Nat Text Text)
(function (_ times char)
(loop [iterations 1
output char]
(if (n.< times iterations)
(recur (inc iterations)
("lux text concat" char output))
output))))
pattern (repetitions (n./ (n.+ size size) ..width)
("lux text concat"
(repetitions size "1")
(repetitions size "0")))
high (try.assumed (\ n.binary decode pattern))
low (..right_rotated size high)]
(function (_ value)
(..or (..right_shifted size (..and high value))
(..left_shifted size (..and low value)))))))
swap/01 (swapper 0)
swap/02 (swapper 1)
swap/04 (swapper 2)
swap/08 (swapper 3)
swap/16 (swapper 4)
swap/32 (swapper 5)]
(|>> swap/32
swap/16
swap/08
swap/04
swap/02
swap/01)))
(interface: .public (Sub size)
{#.doc (example "A sub-space of I64 with a reduce amount of bits.")}
(: (Equivalence (I64 size))
&equivalence)
(: Nat
width)
(: (-> I64 (I64 size))
narrow)
(: (-> (I64 size) I64)
widen))
(def: .public (sub width)
{#.doc (example "Given a width in the interval (0,64), yields an implementation for integers of that width.")}
(Ex [size] (-> Nat (Maybe (Sub size))))
(if (.and (n.> 0 width)
(n.< ..width width))
(let [sign_shift (n.- width ..width)
sign (..bit (dec width))
mantissa (..mask (dec width))
co_mantissa (..xor (.i64 -1) mantissa)]
(#.Some (: Sub
(implementation
(def: &equivalence ..equivalence)
(def: width width)
(def: (narrow value)
(..or (|> value (..and ..sign) (..right_shifted sign_shift))
(|> value (..and mantissa))))
(def: (widen value)
(.i64 (case (.nat (..and sign value))
0 value
_ (..or co_mantissa value))))))))
#.None))
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