Question

Hints and allegations abound that arithmetic with NaNs can be ‘slow’ in hardware FPUs. Specifically in the modern x64 FPU, e.g on a Nehalem i7, is that still true? Do FPU multiplies get churned out at the same speed regardless of the values of the operands?

I have some interpolation code that can wander off the edge of our defined data, and I’m trying to determine whether it’s faster to check for NaNs (or some other sentinel value) here there and everywhere, or just at convenient points.

Yes, I will benchmark my particular case (it could be dominated by something else entirely, like memory bandwidth), but I was surprised not to see a concise summary somewhere to help with my intuition.

I’ll be doing this from the CLR, if it makes a difference as to the flavor of NaNs generated.

Answer 1

For what it’s worth, using the SSE instruction mulsd with NaN is pretty much exactly as fast as with the constant 4.0 (chosen by a fair dice roll, guaranteed to be random).

This code:

for (unsigned i = 0; i < 2000000000; i++)
{
    double j = doubleValue * i;
}

generates this machine code (inside the loop) with clang (I assume the .NET virtual machine uses SSE instructions when it can too):

movsd     -16(%rbp), %xmm0    ; gets the constant (NaN or 4.0) into xmm0
movl      -20(%rbp), %eax     ; puts i into a register
cvtsi2sdq %rax, %xmm1         ; converts i to a double and puts it in xmm1
mulsd     %xmm0, %xmm1        ; multiplies xmm0 (the constant) with xmm1 (i)
movsd     %xmm1, -32(%rbp)    ; puts the result somewhere on the stack

And with two billion iterations, the NaN (as defined by the C macro NAN from <math.h>) version took about 0.017 less seconds to execute on my i7. The difference was probably caused by the task scheduler.

So to be fair, they’re exactly as fast.