approxmath is a Python library of fast, approximate math functions for operations on NumPy arrays. On average it is 4-5x faster than NumPy and has drop-in replacement functions for log, exp, cos, and sin.
The approximations were originally made by Jacques-Henri Jourdan and are explained on Cambium's blog.
If your program doesn't depend on the full precision of floating point operations, the performance-accuracy trade-off will probably be worth it, increasing FLOPS throughput 4-5x. However, in some instances numerical instability will result: for example, approxmath.log(1.0) is nearly, but not exactly 0.0.
| Function | Relative Accuracy | ops / second |
|---|---|---|
| exp | 3e-9 |
647 M/sec |
| log | 5e-9 |
896 M/sec |
| cos | 2e-10 |
470 M/sec |
| sin | 2e-9 |
463 M/sec |
Benchmarks were run on a 2019 MacBook Pro (1.4 GHz Quad-Core Intel Core i5), with Python 3.9.9 and NumPy 1.21.4.
import approxmath.np as npa
import numpy as np
npa.sin(np.array([-np.pi/2, 0.0, np.pi/2]))
# array([-1., 0., 1.])
npa.log(np.array([1.0, np.e, np.e**2]))
# array([4.53119942e-09, 1.00000000e+00, 2.00000000e+00])
npa.cos(np.array([-2*np.pi/3, 0.0, 2*np.pi/3]))
# array([-0.5, 1. , -0.5])
npa.exp(np.array([-1., 0., 1.]))
# array([0.36787944, 1. , 2.71828183])import approxmath.aesara as att
import aesara.tensor as ttFunctional equivalents:
| Aesara | Approxmath | Relative Speed-Up |
|---|---|---|
tt.exp |
att.exp |
15x |
tt.log |
att.log |
15x |
tt.cos |
att.cos |
13x |
tt.sin |
att.sin |
13x |
$ pip install approxmathapproxmath is released under the MIT license.