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Operation: modulo

Interface Signature

modulo: Number, Number -> Number

Behavioral Semantics

Purpose: Computes the remainder of division of two numbers.

Parameters:

  • a: The dividend (number to be divided)
  • b: The divisor (number by which to divide)

Return Value: The remainder when a is divided by b.

Properties:

  • Non-commutative: modulo(a, b) ≠ modulo(b, a) (in general)
  • modulo(a, b) has the same sign as the divisor in most implementations
  • For positive integers: 0 ≤ modulo(a, b) < b when b > 0

Preconditions:

  • b ≠ 0 (modulo by zero behavior is implementation-defined)

Edge Cases:

  • Modulo by zero is implementation-defined (Standard Library concern)
  • Sign of result with negative operands is implementation-defined
    • Some languages use truncated division (result has sign of dividend)
    • Others use floored division (result has sign of divisor)
  • Behavior with floating-point numbers is implementation-defined

Executable Test Cases

test_cases:
  - input: [7, 3]
    output: 1
    description: "Basic modulo with positive integers"

  - input: [10, 5]
    output: 0
    description: "Modulo with no remainder"

  - input: [15, 4]
    output: 3
    description: "Modulo returning non-zero remainder"

  - input: [0, 5]
    output: 0
    description: "Zero modulo non-zero"

  - input: [100, 7]
    output: 2
    description: "Modulo with larger numbers"

Note: Test cases with negative numbers are omitted due to implementation-defined behavior across languages.