CPU Theoretical Peak (Rpeak) Calculation in Practice

Abstract: Rpeak is the first number every HPL acceptance, capacity bid, and TOP500 submission needs. No theory dump here — three steps, real machine specs, and a ready-to-use lookup table.

1. Definition in One Line

Rpeak (theoretical peak) = max double-precision FLOPs per second per core × total physical cores.

Units: GFlops (10⁹ FLOP/s); large clusters use TFlops / PFlops.

2. Core Formula

On Intel Skylake and newer (AVX-512), each core completes 16 FMA = 32 double-precision FLOPs per clock cycle:

$$\text{Rpeak}_{\text{node}} = \text{Clock (GHz)} \times \text{Cores} \times 32 \quad (\text{GFlops})$$

Full cluster:

$$\text{Rpeak}_{\text{cluster}} = \text{Clock (GHz)} \times \text{Cores} \times 32 \times \text{Nodes} \quad (\text{GFlops})$$

Why 32: one FMA instruction = 1 multiply + 1 add; a 512-bit ZMM register holds 8 doubles; 8 × 2 = 16 per FMA unit; × 2 FMA pipelines = 32.

Architecture quick reference

Architecture	ISA	DP FLOPs / cycle
Sandy Bridge and earlier	AVX	16
Haswell / Broadwell	AVX2	16
Skylake+ (Xeon Scalable)	AVX-512	32
Ice Lake / Sapphire Rapids	AVX-512	32
AMD EPYC Zen4	AVX-512	32

3. Worked Examples (Real Production Specs)

3.1 Single node, 104 cores @ 2.0 GHz

Dual-socket, 52 physical cores per socket, hyper-threading off:

$$\text{Rpeak} = 32 \times 104 \times 2.0 = 6656 \text{ GFlops} \approx 6.66 \text{ TFlops}$$

3.2 Single node, 56 cores @ 2.7 GHz

$$\text{Rpeak} = 32 \times 56 \times 2.7 = 4838.4 \text{ GFlops} \approx 4.84 \text{ TFlops}$$

3.3 80-node cluster (spec of 3.1)

$$\text{Rpeak} = 6656 \times 80 = 532480 \text{ GFlops} \approx 532.5 \text{ TFlops}$$

3.4 36-node cluster

$$\text{Rpeak} = 6656 \times 36 = 239616 \text{ GFlops} \approx 239.6 \text{ TFlops}$$

4. Three Traps: Cores and Clock

4.1 Use physical cores × sockets, not logical cores

With hyper-threading on, lscpu shows 208 logical CPUs for a 104-core box. HPL runs physical cores; use physical for Rpeak:

lscpu | grep -E "^(CPU\(s\)|Core|Socket|Model name)"
# CPU(s):                208      <- logical, includes HT
# Core(s) per socket:    52
# Socket(s):             2        <- physical = 52 × 2 = 104

4.2 Use the nominal base clock, not boost

• Base 2.0 GHz: use for Rpeak
• Turbostat during a run typically shows ~2.1 GHz (boost, 100% busy)

cpupower frequency-info | grep -E "hardware limits|current CPU frequency"
# hardware limits: 800 MHz - 3.80 GHz
# current CPU frequency: 2.12 GHz (asserted by call to hardware)

Acceptance uses the nominal base clock so both sides agree; measured results above base are normal headroom.

4.3 Don't use lscpu "CPU max MHz"

That is the turbo ceiling (e.g., 3.8 GHz), not the base clock. Confirm the vendor base frequency for the Model name.

5. Lookup Table (32 FLOP/cycle)

Per-node Rpeak in GFlops:

Clock \ Cores	56	64	96	104
1.8 GHz	3225.6	3686.4	5529.6	5990.4
2.0 GHz	3584.0	4096.0	6144.0	6656.0
2.3 GHz	4121.6	4710.4	7065.6	7654.4
2.7 GHz	4838.4	5529.6	8294.4	8985.6
3.0 GHz	5376.0	6144.0	9216.0	9984.0

6. Verification

python3 -c "print(32 * 104 * 2.0, 'GFlops per node')"
# 6656.0 GFlops per node

The Intel Linpack N_calculator.calculator also prints Rpeak plus an efficiency table:

How Many Nodes :       1
How much memory on per node (GB) :   1536
How many cores per node :  104
What is your CPU speed per core (Ghz) :  2.0
--------------------------------------------------
The System's theoretical performance (Rpeak) in Gflops is <<<< 6656.0 Gflops >>>>
*** 80% --> 5324.80    *** 90% --> 5990.40    ***
*** 100%--> 6656.0     ***

7. Takeaway

• Rpeak depends only on clock, physical cores, FLOPs/cycle (32 for AVX-512), and node count.
• Rpeak ≠ measured. Next: Estimating HPL Performance: from Theoretical Peak to Deliverable Efficiency — single-node HPL efficiency ~93%, 80-node ~78%.