## Accounting for FLOPS

Marketing literature for GPUs stresses their high FLOPS. An A100 is advertised as capable of achieving $19.5$ FP32 TFLOPS. The code below performs a number of numerical operations on tensors: addition, scalar multiplication, transcendental functions, and matrix multiplications etc.

```
import torch
from torch.profiler import ProfilerActivity, profile, tensorboard_trace_handler
def flop_ops():
SIZE = 2**12
ones = torch.ones((SIZE, SIZE), device=torch.device('cuda:0'))
torch.matmul(ones, ones, out=ones) # matrix multiplication
ones.mul_(0.5) # in place multiplication
result_mul = ones.mul(0.5) # out of place multiplication
total = ones + result_mul # adding tensors
result_sum = torch.sum(ones) # adding elements of a tensor
result_sqrt = torch.sqrt(ones) # sqrt takes 7 ops
result_sin = torch.sin(ones) # sin takes 17 ops (14 fp64, 3 fp32)
result_sigmoid = torch.sigmoid(ones) # sigmoid takes 24 ops
result = torch.log10(ones) # log10 takes 24 ops
result = torch.pow(ones, 3.14159) # pow takes 142 ops
# warmup
flop_ops()
trace_handler = tensorboard_trace_handler(dir_name="./flops_trace", use_gzip=True)
with profile(activities = [ProfilerActivity.CPU, ProfilerActivity.CUDA],
on_trace_ready = trace_handler,
record_shapes = True,
with_stack = True
) as prof:
flop_ops()
```

The trace shown below indicates that other than matrix multiplication, all of the other operations are a tiny fraction (~$1\%$) of the advertised flops. Furthermore, simple operations like addition take exactly as long as complex ones like sine and log. Why?