A Simple Ruby CLI for the Hyperfactorial

What is the hyperfactorial?

At a high level, the hyperfactorial of a non‑negative integer n is the product of each integer from 1 to n, raised to its own power:

[ H(n) = \prod\limits_{k=1}^n k^k,\quad\text{with } H(0)=1. ]

For more background, see the MathWorld entry: Hyperfactorial.

Small examples

• H(0) = 1
• H(1) = 1
• H(2) = 4
• H(3) = 108
• H(4) = 27,648
• H(5) = 86,400,000
• H(6) = 4,031,078,400,000
• H(7) = 3,319,766,398,771,200,000
• H(8) exceeds signed 64‑bit integer range

Ruby CLI: straightforward, no flags

This standalone script accepts exactly one non‑negative integer argument (0 allowed). It prints the exact hyperfactorial if it fits in a signed 64‑bit integer; otherwise it prints out of bounds. Invalid input prints invalid input to STDERR and exits with code 1.

#!/usr/bin/env ruby
# hyperfactorial

SIGNED_64_MAX = (2**63 - 1)

def invalid!
  $stderr.puts "invalid input"
  exit 1
end

# Validate arity
invalid! unless ARGV.length == 1

arg = ARGV[0]
# Validate non-negative integer (no signs, no decimals)
invalid! unless arg.match?(/\A\d+\z/)

n = arg.to_i

# H(0) = 1 by convention
result = 1

(1..n).each do |k|
  term = k ** k

  # Early overflow check for 64-bit signed integer
  # If term alone exceeds the limit, or result * term would exceed it -> out of bounds
  if term > SIGNED_64_MAX || result > SIGNED_64_MAX / term
    puts "out of bounds"
    exit 0
  end

  result *= term
end

puts result

Usage

Make it executable and run with a single integer:

chmod +x hyperfactorial
./hyperfactorial 5
# 86400000

Notes

• Valid input: 0, 1, 2, …
• Error behavior: invalid input to STDERR, exit code 1.
• Range guard: prints out of bounds once the exact value would overflow a signed 64‑bit integer (H(8) and above).