brendanashworth / approxmath

Fast, approximate math functions for numpy (log, exp, sin, cos)

Fast, Approximate Math Functions for NumPy

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The approximations were originally made by Jacques-Henri Jourdan and are explained on Cambium's blog.

Performance & Accuracy

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.

Drop-in Replacement for NumPy

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])

Drop-in Replacement for Aesara Tensor

import approxmath.aesara as att
import aesara.tensor as tt

Functional 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

Installation

$ pip install approxmath

approxmath is released under the MIT license.