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Numeric protocols

These protocols describe the operations available on built-in numeric types.

Protocol hierarchy

  • Number (Times[Self], Minus): core numeric behavior such as +, -, *, **, unary + and -, abs, real, imag, and conjugate
  • Real (Number): float-style conversion and rounding operations such as __float__, trunc, floor, ceil, and round
  • RealFloat (Real): floating-point real numbers
  • Rational (Real): values with numerator and denominator
  • Integral (Rational, Logical): integer-style operations such as //, %, shifts, bit operations, and indexing

Built-in implementations

  • int, bigint, and the fixed-width signed and unsigned integer types implement Integral
  • float implements RealFloat
  • complex implements Number

Use the narrowest constraint that matches the operations you need:

Choose Number when you need ordinary arithmetic. Choose Integral when you need integer-only operations such as floor division, modulo, or bit shifts.

def square[A(Number)](x: A) -> A:
    return x * x

def bucket[A(Integral)](x: A, size: A) -> A:
    return x // size

Numeric constraints affect both operator availability and result types. For example, Div[A] separates the type of the result from the type of the operands, which is why integer division through / can return a different type than floor division through //.