Add Bitwise.aes to stdlib

CHANGELOG.md

@@ -6,6 +6,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ## [Unreleased]
 ### Added
+- `Bitwise` stdlib
 - `Set` stdlib
 - `Option.force_msg`
 - Loading namespaces into the current scope (e.g. `using Pair`)

docs/sophia_stdlib.md

@@ -37,6 +37,7 @@ include "List.aes"
 - [Func](#func)
 - [Pair](#pair)
 - [Triple](#triple)
+- [Bitwise](#bitwise)
 - [BLS12_381](bls12_381)
 - [Frac](#frac)
 - [Set](#set-stdlib)
@@ -1294,7 +1295,7 @@ Escapes `option` wrapping by providing default value for `None`.
 Option.force(o : option('a)) : 'a
 ```
 
-Forcefully escapes the `option` wrapping assuming it is `Some`. 
+Forcefully escapes the `option` wrapping assuming it is `Some`.
 Aborts on `None`.
 
 
@@ -1817,6 +1818,90 @@ Triple.rotl(t : ('a * 'b * 'c)) : ('b * 'c * 'a)
 
 Cyclic rotation of the elements to the left.
 
+### Bitwise
+
+Bitwise operations on arbitary precision integers.
+
+#### bsr
+```
+Bitwise.bsr(n : int, x : int) : int
+```
+
+Logical bit shift `x` right `n` positions.
+
+
+#### bsl
+```
+Bitwise.bsl(n : int, x : int) : int
+```
+
+Logical bit shift `x` left `n` positions.
+
+
+#### bsli
+```
+Bitwise.bsli(n : int, x : int, lim : int) : int
+```
+
+Logical bit shift `x` left `n` positions, limit to `lim` bits.
+
+
+#### band
+```
+Bitwise.band(x : int, y : int) : int
+```
+
+Bitwise `and` of `x` and `y`.
+
+
+#### bor
+```
+Bitwise.bor(x : int, y : int) : int
+```
+
+Bitwise `or` of `x` and `y`.
+
+
+#### bxor
+```
+Bitwise.bxor(x : int, y : int) : int
+```
+
+Bitwise `xor` of `x` and `y`.
+
+
+#### bnot
+```
+Bitwise.bnot(x : int) : int
+```
+
+Bitwise `not` of `x`. Defined and implemented as `bnot(x) = bxor(x, -1)`.
+
+
+#### uband
+```
+Bitwise.uband(x : int, y : int) : int
+```
+
+Bitwise `and` of _non-negative_ numbers `x` and `y`.
+
+
+#### ubor
+```
+Bitwise.ubor(x : int, y : int) : int
+```
+
+Bitwise `or` of _non-negative_ `x` and `y`.
+
+
+#### ubxor
+```
+Bitwise.ubxor(x : int, y : int) : int
+```
+
+Bitwise `xor` of _non-negative_ `x` and `y`.
+
+
 ### BLS12\_381
 
 #### Types

priv/stdlib/Bitwise.aes

@@ -0,0 +1,136 @@
+@compiler >= 4.3
+
+namespace Bitwise =
+
+  // bit shift 'x' right 'n' postions
+  function bsr(n : int, x : int) : int =
+    let step = 2^n
+    let res  = x / step
+    if (x >= 0 || x mod step == 0)
+      res
+    else
+      res - 1
+
+  // bit shift 'x' left 'n' positions
+  function bsl(n : int, x : int) : int =
+    x * 2^n
+
+  // bit shift 'x' left 'n' positions, limit at 'lim' bits
+  function bsli(n : int, x : int, lim : int) : int =
+    (x * 2^n) mod (2^lim)
+
+  // bitwise 'and' for arbitrary precision integers
+  function band(a : int, b : int) : int =
+      if (a >= 0 && b >= 0)
+        uband_(a, b)
+      elif (b >= 0)
+        ubnand_(b, -1 - a)
+      elif (a >= 0)
+        ubnand_(a, -1 - b)
+      else
+        -1 - ubor_(-1 - a, -1 - b)
+
+  // bitwise 'or' for arbitrary precision integers
+  function
+    bor : (int, int) => int
+    bor(0, b) = b
+    bor(a, 0) = a
+    bor(a : int, b : int) : int =
+      if (a >= 0 && b >= 0)
+        ubor_(a, b)
+      elif (b >= 0)
+        -1 - ubnand_(-1 - a, b)
+      elif (a >= 0)
+        -1 - ubnand_(-1 - b, a)
+      else
+        -1 - uband_(-1 - a, -1 - b)
+
+  // bitwise 'xor' for arbitrary precision integers
+  function
+    bxor : (int, int) => int
+    bxor(0, b) = b
+    bxor(a, 0) = a
+    bxor(a, b) =
+      if (a >= 0 && b >= 0)
+        ubxor_(a, b)
+      elif (b >= 0)
+        -1 - ubxor_(-1 - a, b)
+      elif (a >= 0)
+        -1 - ubxor_(a, -1 - b)
+      else
+        ubxor_(-1 - a, -1 - b)
+
+  // bitwise 'not' for arbitrary precision integers
+  function bnot(a : int) = bxor(a, -1)
+
+  // Bitwise 'and' for positive integers
+  function uband(a : int, b : int) : int =
+    require(a >= 0 && b >= 0, "uband is only defined for non-negative integers")
+    switch((a, b))
+      (0, _) => 0
+      (_, 0) => 0
+      _      => uband__(a, b, 1, 0)
+
+  private function uband_(a, b) = uband__(a, b, 1, 0)
+
+  private function
+    uband__(0, b, val, acc) = acc
+    uband__(a, 0, val, acc) = acc
+    uband__(a, b, val, acc) =
+      switch (a mod 2 + b mod 2)
+        2 => uband__(a / 2, b / 2, val * 2, acc + val)
+        _ => uband__(a / 2, b / 2, val * 2, acc)
+
+  // Bitwise or for positive integers
+  function ubor(a, b) =
+    require(a >= 0 && b >= 0, "ubor is only defined for non-negative integers")
+    switch((a, b))
+      (0, _) => b
+      (_, 0) => a
+      _      => ubor__(a, b, 1, 0)
+
+  private function ubor_(a, b) = ubor__(a, b, 1, 0)
+
+  private function
+    ubor__(0, 0, val, acc) = acc
+    ubor__(a, b, val, acc) =
+      switch (a mod 2 + b mod 2)
+        0 => ubor__(a / 2, b / 2, val * 2, acc)
+        _ => ubor__(a / 2, b / 2, val * 2, acc + val)
+
+  //Bitwise xor for positive integers
+  function
+    ubxor : (int, int) => int
+    ubxor(0, b) = b
+    ubxor(a, 0) = a
+    ubxor(a, b) =
+      require(a >= 0 && b >= 0, "ubxor is only defined for non-negative integers")
+      ubxor__(a, b, 1, 0)
+
+  private function ubxor_(a, b) = ubxor__(a, b, 1, 0)
+
+  private function
+    ubxor__(0, 0, val, acc) = acc
+    ubxor__(a, b, val, acc) =
+      switch(a mod 2 + b mod 2)
+        1 => ubxor__(a / 2, b / 2, val * 2, acc + val)
+        _ => ubxor__(a / 2, b / 2, val * 2, acc)
+
+  // Bitwise combined 'and' and 'not' of second argument for positive integers
+  // x 'bnand' y = x 'band' ('bnot' y)
+  // The tricky bit is that after negation the second argument has an infinite number of 1's
+  // use as many as needed!
+  //
+  // NOTE: this function is not symmetric!
+  private function ubnand(a, b) =
+    require(a >= 0 && b >= 0, "ubxor is only defined for non-negative integers")
+    ubnand__(a, b, 1, 0)
+
+  private function ubnand_(a, b) = ubnand__(a, b, 1, 0)
+
+  private function
+    ubnand__(0, b, val, acc) = acc
+    ubnand__(a, b, val, acc) =
+      switch((a mod 2, b mod 2))
+        (1, 0) => ubnand__(a / 2, b / 2, val * 2, acc + val)
+        _      => ubnand__(a / 2, b / 2, val * 2, acc)