# [Numpy-tickets] [NumPy] #924: problem with summing large array of float32

NumPy numpy-tickets@scipy....
Fri Oct 3 00:40:24 CDT 2008

```#924: problem with summing large array of float32
-------------------------------+--------------------------------------------
Reporter:  emil               |        Owner:  somebody
Type:  defect             |       Status:  closed
Priority:  high               |    Milestone:
Component:  numpy.core         |      Version:  1.0.1
Severity:  critical           |   Resolution:  wontfix
Keywords:  sum, dot, float32  |
-------------------------------+--------------------------------------------
Changes (by rkern):

* status:  new => closed
* resolution:  => wontfix

Comment:

Yup, that's floating point arithmetic for you. At 32-bit precision, adding
1 to 16777216 gives you 16777216 back again because 16777217 cannot be
represented at 32-bit precision.

{{{

In [1]: from numpy import *

In [2]: x = float32(16777216)

In [3]: one = float32(1.0)

In [4]: x
Out[4]: 16777216.0

In [5]: x + one
Out[5]: 16777216.0

}}}

With the multiple sums across each axis, you are accumulating separate
larger numbers *then* adding them together. Fortunately, the intermediates
and the final result are multiples of reasonable powers of 2, so you can
afford to drop off some of the low bits. If the final result were
something like 110880003, that number cannot even be represented in 32-bit
precision.

You can use {{{sum(a, dtype=float64)}}} to use a double-precision
accumulator for the sum and thus be able to be more accurate for larger
inputs.

--
Ticket URL: <http://scipy.org/scipy/numpy/ticket/924#comment:1>
NumPy <http://projects.scipy.org/scipy/numpy>
The fundamental package needed for scientific computing with Python.
```