Multiplication of very long integers

Question

Is there an algorithm for accurately multiplying two arbitrarily long integers together? The language I am working with is limited to 64-bit unsigned integer length (maximum int

Answer 1

The simplest way would be to use the schoolbook mechanism, splitting your arbitrarily sized numbers into chunks of 32-bit each.

Given A B C D * E F G H (each chunk 32-bit, for a total 128 bit)
You need an output array 9 dwords wide. Set Out[0..8] to 0

You'd start by doing: H * D + out[8] => 64 bit result.
Store the low 32-bits in out[8] and take the high 32-bits as carry
Next: (H * C) + out[7] + carry
Again, store low 32-bit in out[7], use the high 32-bits as carry
after doing H*A + out[4] + carry, you need to continue looping until you have no carry.

Then repeat with G, F, E.
For G, you'd start at out[7] instead of out[8], and so forth.

Finally, walk through and convert the large integer into digits (which will require a "divide large number by a single word" routine)