`fft` dramatic slowdown upon multiplying by `scipy.signal` window

Question

import numpy as np
import scipy.signal as sig
from scipy.fft import fft
from timeit import default_timer as dtime

dtype = 'float32'
n_fft = 598
A = np.random.randn(n_fft, 160000).astype(dtype)
v0 = sig.windows.dpss(n_fft, 4).astype(dtype)
v1 = sig.windows.dpss(n_fft, n_fft // 8).astype(dtype)
v = v1

#%%###############################################################
t0 = dtime()
fft(A)
print(dtime() - t0)

A *= v.reshape(-1, 1)
#%%###############################################################
t0 = dtime()
fft(A)
print(dtime() - t0)

>>> 1.3161122000001342
>>> 4.751361799999813

Equal if using v = v0 or dtype = 'float64' instead. Why does this happen? (more times)

Note: a workaround is v = v1 + 1, v -= 1, but this shouldn't be necessary... filed Issue.

Win 10 x64, numpy 1.18.5, scipy 1.6.1, Python 3.7.9.

Answer 1

This is caused by denormals (extremely small non-zero numbers) which make some CPU instructions run much slower; details. Workaround is to zero them manually, as in +1/-1, or 'safely' via e.g. ftz (and after type casting):

from ftz import ftz

ftz(v)
A *= v.reshape(-1, 1)

t0 = dtime()
fft(A)
print(dtime() - t0)

>>> 1.4638332999998056
>>> 1.4597183999999288