Big number calculator

How it works

Ordinary calculators and spreadsheets work with floating point numbers of about 16 significant digits, so $2^{64} + 1$ or $30!$ come out rounded. This calculator works with exact whole numbers of any size (up to 200000 bits), the way cryptographic software does with keys of thousands of bits.

The expression is evaluated in the usual order: brackets and functions, then factorials, then powers (from the right, so $2^{3^2} = 2^9$), then multiplication, division and $\bmod$ from left to right, then addition and subtraction. Division of whole numbers gives the quotient rounded down and notes the remainder; mod (or %) gives the remainder, never negative. powmod(a, e, n) computes $a^e \bmod n$ by square and multiply, without ever writing out the huge power.

For the result the calculator counts the decimal digits and the bits ($b$ bits means $2^{b-1} \le |x| < 2^b$), writes it in scientific form and adds up its digits. The digit sum has the same remainder modulo 9 as the number itself, the old trick of casting out nines.