Precision Multiplication Calculator (BigInt)

Standard digital calculators and spreadsheet software rely on floating-point arithmetic (IEEE 754), which sacrifices accuracy for speed. This often results in rounding errors when handling numbers with more than 15-17 significant digits. For fields like cryptography, astrophysics, or high-frequency trading, a loss of precision in the 20th decimal place can propagate into catastrophic errors.

This tool utilizes arbitrary-precision arithmetic to multiply numbers of virtually infinite length. It treats numbers as strings of digits rather than binary approximations, ensuring that 10⁵⁰ × 10^-50 equals exactly 1, not 0.99999999. The "History Tape" interface allows users to chain multiple factors, edit individual entries, and instantly verify the cascading impact on the final product without re-entering the entire sequence.

The core logic bypasses standard CPU multiplication instructions. Instead, it implements a schoolbook long-multiplication algorithm or Karatsuba algorithm logic optimized for strings. If we define two numbers x and y as:

The product is computed by summing partial products, preserving every digit. Decimal placement is handled separately by tracking the scale:

This ensures that multiplying 0.1 (1×10^-1) by 0.2 (2×10^-1) results in exactly 0.02 (2×10^-2).