ᵇ — Bitwise

Monadic operator. Keys: Alt-6 b. Hanzi: 按

fᵇ applies the Boolean function f separately to each bit of its integer arguments. Negative integers use infinite two’s complement.

6∧ᵇ3               ⍝ 2ₓ
6∨ᵇ3               ⍝ 7ₓ
6≠ᵇ3               ⍝ 5ₓ
~ᵇ6                ⍝ ¯7ₓ

Arguments follow the usual integer conversion, including whole-valued floats such as bare 6. Results are exact integers, or Booleans when every argument is Boolean. Agreement is pervasive.

6 3∧ᵇ5             ⍝ [4 1]ₓ
$t∧ᵇ$f             ⍝ $f

For a monadic call, f is evaluated on $f and $t. For a dyadic call, it is evaluated on all four Boolean pairs. Each evaluation must return one Boolean value. The operand can be any function or composition that satisfies this rule.

ᵇ is an ordinary monadic operator. It requires a function operand. Differentiation is unsupported.

In Python, f.bitwise constructs fᵇ. Array and Function &, | and ~ use ∧ᵇ, ∨ᵇ and ~ᵇ. Plain BPL ∧ and ∨ retain LCM and GCD.