# Why does numpy.power return 0 for small exponents while math.pow returns the correct answer?

PythonNumpyExponentiation## Python Problem Overview

```
In [25]: np.power(10,-100)
Out[25]: 0
In [26]: math.pow(10,-100)
Out[26]: 1e-100
```

I would expect both the commands to return 1e-100. This is not a precision issue either, since the issue persists even after increasing precision to 500. Is there some setting which I can change to get the correct answer?

## Python Solutions

## Solution 1 - Python

Oh, it's much "worse" than that:

```
In [2]: numpy.power(10,-1)
Out[2]: 0
```

But this is a hint to what's going on: `10`

is an integer, and `numpy.power`

doesn't coerce the numbers to floats. But this works:

```
In [3]: numpy.power(10.,-1)
Out[3]: 0.10000000000000001
In [4]: numpy.power(10.,-100)
Out[4]: 1e-100
```

Note, however, that the power operator, `**`

, *does* convert to float:

```
In [5]: 10**-1
Out[5]: 0.1
```

## Solution 2 - Python

numpy method assumes you want integer returned since you supplied an integer.

```
np.power(10.0,-100)
```

works as you would expect.

## Solution 3 - Python

(Just a footnote to the two other answers on this page.)

Given input two input values, you can check the datatype of the object that `np.power`

will return by inspecting the `types`

attribute:

```
>>> np.power.types
['bb->b', 'BB->B', 'hh->h', 'HH->H', 'ii->i', 'II->I', 'll->l', 'LL->L', 'qq->q',
'QQ->Q', 'ee->e', 'ff->f', 'dd->d', 'gg->g', 'FF->F', 'DD->D', 'GG->G', 'OO->O']
```

Python-compatible integer types are denoted by `l`

, compatible-compatible Python floats by `d`

(documents).

`np.power`

effectively decides what to return by checking the types of the arguments passed and using the first matching signature from this list.

So given 10 and -100, `np.power`

matches the `integer integer -> integer`

signature and returns the integer `0`

.

On the other hand, if one of the arguments is a float then the integer argument will also be cast to a float, and the `float float -> float`

signature is used (and the correct float value is returned).