Just for reference, this is the current results on the numpy main branch at special points:
In [1]: import numpy as np In [2]: np.sin(0.0) Out[2]: 0.0 In [3]: np.cos(0.0) Out[3]: 0.9999999999999999 In [4]: np.cos(2*np.pi) Out[4]: 0.9999999999999998 In [5]: np.sin(2*np.pi) Out[5]: -2.4492935982947064e-16 In [6]: np.sin(np.pi) Out[6]: 1.2246467991473532e-16 In [7]: np.cos(np.pi) Out[7]: -0.9999999999999998 In [8]: np.cos(np.pi/2) Out[8]: 6.123233995736766e-17 In [9]: np.sin(np.pi/2) Out[9]: 0.9999999999999998 In [10]: np.__version__ Out[10]: '2.0.0.dev0+60.g174dfae62' On Wed, May 31, 2023 at 6:20 PM Robert Kern <[email protected]> wrote: > On Wed, May 31, 2023 at 5:51 PM Benjamin Root <[email protected]> > wrote: > >> I think it is the special values aspect that is most concerning. Math is >> just littered with all sorts of identities, especially with trig functions. >> While I know that floating point calculations are imprecise, there are >> certain properties of these functions that still held, such as going from >> -1 to 1. >> >> As a reference point on an M1 Mac using conda-forge: >> ``` >> >>> import numpy as np >> >>> np.__version__ >> '1.24.3' >> >>> np.sin(0.0) >> 0.0 >> >>> np.cos(0.0) >> 1.0 >> >>> np.sin(np.pi) >> 1.2246467991473532e-16 >> >>> np.cos(np.pi) >> -1.0 >> >>> np.sin(2*np.pi) >> -2.4492935982947064e-16 >> >>> np.cos(2*np.pi) >> 1.0 >> ``` >> >> Not perfect, but still right in most places. >> > > FWIW, those ~0 answers are actually closer to the correct answers than 0 > would be because `np.pi` is not actually π. Those aren't problems in the > implementations of np.sin/np.cos, just the intrinsic problems with floating > point representations and the choice of radians which places particularly > special values at places in between adjacent representable floating point > numbers. > > >> I'm ambivalent about reverting. I know I would love speed improvements >> because transformation calculations in GIS is slow using numpy, but also >> some coordinate transformations might break because of these changes. >> > > Good to know. Do you have any concrete example that might be worth taking > a look at in more detail? Either for performance or accuracy. > > -- > Robert Kern > _______________________________________________ > NumPy-Discussion mailing list -- [email protected] > To unsubscribe send an email to [email protected] > https://mail.python.org/mailman3/lists/numpy-discussion.python.org/ > Member address: [email protected] > -- Thomas Caswell [email protected]
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