[Numpy-discussion] Products of small float32 values.

Matthew Brett matthew.brett at gmail.com
Wed Oct 2 21:06:08 EDT 2013

```Hi,

On Wed, Oct 2, 2013 at 6:00 PM, Dave Cook <daverz at gmail.com> wrote:
> Can someone explain what is going on here?
>
> In [153]:
>
> small = ones(1, dtype='float32')
>
> In [154]:
>
> small
>
> Out[154]:
>
> array([ 1.], dtype=float32)
>
> In [155]:
>
> small*1e-45
>
> Out[155]:
>
> array([  1.40129846e-45], dtype=float32)
>
> In [156]:
>
> small*1e-46
>
> Out[156]:
>
> array([ 0.], dtype=float32)
>
> I would expect float32 to be able to represent
> numbers with exponents as small as -127.

Is it possible you are thinking of 2**-126 rather than 10**-126?

In [3]: print np.finfo(np.float32)
Machine parameters for float32
---------------------------------------------------------------------
precision=  6   resolution= 1.0000000e-06
machep=   -23   eps=        1.1920929e-07
negep =   -24   epsneg=     5.9604645e-08
minexp=  -126   tiny=       1.1754944e-38
maxexp=   128   max=        3.4028235e+38
nexp  =     8   min=        -max
---------------------------------------------------------------------

In [4]: 2**-126
Out[4]: 1.1754943508222875e-38

So I think your 10**-45 was already 'subnormal' and then 10**-46 went
down to 0...

Cheers,

Matthew

```