How I Calculate An x86 CPU FLOPs

My friend and I have been taking some performance engineering courses. One thing we’ve come to realize is how important calculating the maximum Floating-point Operations per second (FLOPs) of a CPU is. It turns out this is a little trickier than it looks.

This is a formula I use to calculate this value. The formula is number of cores * peak cpu speed * (max SIMD register size/32) * (fma throughput * 2). Let me break it down.

• Number of cores: The amount of cores in its CPU.

• Peak CPU speed: The highest speed the CPU can achieve. On Intel, it’s Turbo Boost. On AMD, it’s Max. Boost Clock.

• Max SIMD register size: Single Instruction Multiple Data (SIMD) allows a program to carry out vectorized operations using special registers. Some of the extensions are SSE, AVX, AVX2, and AVX-512. There are other extensions on Wikipedia. You can find a CPU’s supported extension on its web page. CPUs that only support SSE have a max SIMD register size of 128 bits. Those that support AVX or AVX2 have a max SIMD register size of 256 bits. Those that support AVX-512 have a max SIMD register size of 512 bits.

  The size of a single-precision float type is 4 bytes. To check the maximum number of floats a SIMD register can support, the formula is register size / 4 bytes * 8 bits in a byte.

• FMA throughput: This is the tricky one. Fused Multiply Add (FMA) allows a program to carry out this operation A*B + C in a single instruction (VFMADD…). Getting a CPU’s microarchitecture is the first step in figuring out its FMA throughput. Once that’s done, we can get its throughput of the FMA instruction in the Reciprocal throughput column of the Arithmetic subsection within the Floating point XMM and YMM instructions table of the CPU’s microarchitecture chapter in the excellent Agner Fog’s Instruction Tables doc. We divide 1 by this reciprocal throughput to get the throughput. This throughput defines the number of FMA operations that the CPU can execute in a single cycle.

Finally, we multiply this number by 2 because FMA contains 2 operations. We should note that the FMA instruction was only introduced in 2012. Processors made before that year will not support it. In their case, we use the VMULPS instruction and multiply by 1 instead of 2 in the equation.

A Simple Example

The cheapest AMD dedicated server on Hetzner is the AX42. This has an AMD Ryzen™ 7 PRO 8700GE CPU. From its page, we can see it’s a Zen 4 microarchitecture CPU. Let’s calculate its FLOPs.

Number of cores: 8
Peak CPU speed: 5.1 GHz
Max SIMD register size: 512 bits (It supports AVX-512). This means we can do vectorized operations on 16 floats at a time.
FMA throughput: 1 (For smaller vector register sizes, it's 2). 
Its peak FLOPs: 8 * 5.1 * 10^9 * 16 * 1 * 2 = 1305.6 GFLOPs.

It’s surreal that we can get all that power for just €46.00/month.