Can I use the AVX FMA units to do bit-exact 52 bit integer multiplications?

Question

AXV2 doesn\'t have any integer multiplications with sources larger than 32-bit. It does offer 32 x 32 -> 32 multiplies, as well as 32 x 32 -> 64 multiplies¹, but

Answer 1

Well, you certainly can do FP-lane operations on things that are integers. And they will always be exact: While there are SSE instructions that do not guarantee proper IEEE-754 precision and rounding, without exception they are the ones which do not have an integer range, so not the ones you're looking at anyway. Bottom line: Addition/subtraction/multiplication will always be exact in the integer domain, even if you're doing them on packed floats.

As for quad-precision floats (>52 bit mantissa), no, those aren't supported, and likely won't be in the foreseeable future. Just not much call for them. They showed up in a few SPARC-era workstation architectures, but honestly they were just a bandage over developers' incomplete understanding of how to write numerically stable algorithms, and over time they faded out.

Wide-integer operations turn out to be a really bad fit for SSE. I really tried to leverage it recently when I was implementing a big-integer library, and honestly it did me no good. x86 was designed for multi-word arithmetic; you can see it in operations such as ADC (which produces and consumes a carry bit) and IDIV (which allows the divisor to be twice as wide as the dividend as long as the quotient is no wider than the dividend, a constraint that makes it useless for anything but multiword division). But multiword arithmetic is by nature sequential, and SSE is by nature parallel. If you're lucky enough that your numbers have just enough bits to fit into a FP mantissa, congratulations. But if you have big integers in general, SSE is probably not going to be your friend.