Bignums

How omega handles integers that don't fit in 64 bits. For the basics, read numbers first.

Small and big

A number that fits in 64 bits is kept as a plain machine integer. When a result gets bigger than that, it becomes a bignum by itself, and when a result fits again, it goes back to being a plain integer. 2 64 ^ 2 64 ^ - is a plain 0. Code that only uses small numbers never pays for bignums.

The limit

A bignum can have up to 65,536 bits, so the biggest number is just under 2^65536. A result that would be bigger fails with that number is too big, the limit is 2^65536 before any work is done, so 2 100000 ^ fails straight away instead of hanging.

Printing a very big number takes a moment. 2 65536 ^ . prints about 19,700 digits.

Where they work

Arithmetic, comparisons, str, >num, conditions and saving all take bignums. / rounds toward zero and mod takes the sign of the left number, the same as with small numbers.

Words that need a machine number, like times, at, peek and the bitwise words, fail with foo needs a number that fits in 64 bits.

With ordinals, a bignum works on the left, where it disappears anyway: 2 100 ^ omega + is omega. On the right it fails with that number is too big to mix with an ordinal that way.

Bignums and the JIT

Compiled code does +, -, * and neg in registers. When a result overflows, it falls back to the normal word, which makes the bignum, so compiled code gives the same answers as the interpreter. See the JIT page.