What is the difference between math.exp and numpy.exp and why do numpy creators choose to introduce exp again?

Question

exp means exponential function. Why do numpy creators introduce this function again?

• math.exp
• numpy.exp

Answer 1

The math.exp works only for scalars, whereas numpy.exp will work for arrays.

Example:

>>> import math
>>> import numpy as np
>>> x = [1.,2.,3.,4.,5.]
>>> math.exp(x)
Traceback (most recent call last):
  File "<pyshell#10>", line 1, in <module>
    math.exp(x)
TypeError: a float is required
>>> np.exp(x)
array([   2.71828183,    7.3890561 ,   20.08553692,   54.59815003,
        148.4131591 ])

It is the same case for other math functions.

>>> math.sin(x)
Traceback (most recent call last):
  File "<pyshell#12>", line 1, in <module>
    math.sin(x)
TypeError: a float is required
>>> np.sin(x)
array([ 0.84147098,  0.90929743,  0.14112001, -0.7568025 , -0.95892427])

Also refer to this answer to check out how numpy is faster than math.

Answer 2

math.exp works on a single number, the numpy version works on numpy arrays and is tremendously faster due to the benefits of vectorization. The exp function isn't alone in this - several math functions have numpy counterparts, such as sin, pow, etc.

Consider the following:

In [10]: import math

In [11]: import numpy

In [13]: arr = numpy.random.random_integers(0, 500, 100000)

In [14]: %timeit numpy.exp(arr)
100 loops, best of 3: 1.89 ms per loop

In [15]: %timeit [math.exp(i) for i in arr]
100 loops, best of 3: 17.9 ms per loop

The numpy version is ~9x faster (and probably can be made faster still by a careful choice of optimized math libraries)

As @camz states below - the math version will be faster when working on single values (in a quick test, ~7.5x faster).

Answer 3

If you manually vectorize math.exp using map, it is faster than numpy. As far as I tested..

%timeit np.exp(arr)

500 µs ± 3.37 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

%timeit map(math.exp, arr)

148 ns ± 4 ns per loop (mean ± std. dev. of 7 runs, 10000000 loops each)

​