# [Numpy-discussion] Unexpected float96 precision loss

Charles R Harris charlesr.harris@gmail....
Wed Sep 1 20:03:00 CDT 2010

```On Wed, Sep 1, 2010 at 3:30 PM, Michael Gilbert <michael.s.gilbert@gmail.com
> wrote:

> On Wed, 1 Sep 2010 21:15:22 +0000 (UTC), Pauli Virtanen wrote:
> > Wed, 01 Sep 2010 16:26:59 -0400, Michael Gilbert wrote:
> > > I've been using numpy's float96 class lately, and I've run into some
> > > strange precision errors.
> > [clip]
> > >   >>> x = numpy.array( [0.01] , numpy.float96 )
> > [clip]
> > > I would expect the float96 calculation to also produce 0.0 exactly as
> > > found in the float32 and float64 examples.  Why isn't this the case?
> >
> > (i) It is not possible to write long double literals in Python.
> >     "float96(0.0001)" means in fact "float96(float64(0.0001))"
> >
> > (ii) It is not possible to represent numbers 10^-r, r > 1 exactly
> >      in base-2 floating point.
> >
> > So if you write "float96(0.0001)", the result is not the float96 number
> > closest to 0.0001, but the 96-bit representation of the 64-bit number
> > closest to 0.0001. Indeed,
> >
> > >>> float96(0.0001), float96(1.0)/1000
> > (0.00010000000000000000479, 0.00099999999999999999996)
>
> Interesting.  float96( '0.0001' ) also seems to evaluate to the first
> result. I assume that it also does a float64( '0.0001' ) conversion
> first. I understand that you can't change how python passes in floats,
> but wouldn't it be better to exactly handle strings since those can be
> converted exactly, which is what the user wants/expects?
>
>
Well, yes. But then we would need to write our own routines for the
conversions...

Chuck
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mail.scipy.org/pipermail/numpy-discussion/attachments/20100901/18fcb6df/attachment.html
```