Why are trigonometric functions of Pytorch and Numpy when evaluated at integer multiples of Pi result in such huge discrepancy in the orders of magnitude?
>>> torch.sin(torch.ones(1)*2*np.pi)
tensor([1.7485e-07])
>>> np.sin(np.ones(1)*2*np.pi)
array([-2.4492936e-16])
Expanding on the answer you got, but using plain Python:
>>> import math
>>> math.sin(2 * math.pi)
-2.4492935982947064e-16
Python uses 64-bit floats, and that's a close match to the numpy result.
IEEE-754 64-bit floats have 53 bits of precision, but 32-bit floats only 24. So let's round the input back to 24 significant bits and see what happens:
>>> x = 2 * math.pi
>>> m, e = math.frexp(x)
>>> m *= 2**24
>>> m = round(m)
>>> y = math.ldexp(m, e - 24)
>>> math.sin(y)
1.7484556000744883e-07
And that's a close match to the torch result.
Torch defaults to 32-bit floats, while NumPy defaults to 64-bit. The rounding error you're getting in Torch is around the expected scale for 32-bit floats. Specify a different dtype if you want a different dtype.