# [Numpy-discussion] Different results from repeated calculation

Keith Goodman kwgoodman at gmail.com
Mon Jan 29 13:52:00 CST 2007

```On 1/29/07, Keith Goodman <kwgoodman at gmail.com> wrote:
> On 1/29/07, Keith Goodman <kwgoodman at gmail.com> wrote:
> > On 1/29/07, Charles R Harris <charlesr.harris at gmail.com> wrote:
> >
> > > That's odd, the LSB bit of the  double precision mantissa is only about
> > > 2.2e-16, so  you can't *get* differences as  small as 8.4e-22 without about
> > > 70 bit mantissa's. Hmmm, and extended double precision only has 63 bit
> > > mantissa's. Are you sure you are computing the error correctly?
> >
> > That is odd.
> >
> > 8.4e-22 is just the output of the test script: abs(z - z0).max(). That
> > abs is from python.
>
> By playing around with x and y I can get all sorts of values for abs(z
> - z0).max(). I can get down to the e-23 range and to 2.2e-16. I've
> also seen e-18 and e-22.

Here is a setting for x and y that gives me a difference (using the
unit test in this thread) of 4.54747e-13! That is huge---and a serious
problem. I am sure I can get bigger.

# x data
x = M.zeros((3,3))
x[0,0] =  9.0030140479499
x[0,1] =  9.0026474226671
x[0,2] = -9.0011270502873
x[1,0] =  9.0228605377994
x[1,1] =  9.0033715311274
x[1,2] = -9.0082367491299
x[2,0] =  9.0044783987583
x[2,1] =  0.0027488028057
x[2,2] = -9.0036113393360

# y data
y = M.zeros((3,1))
y[0,0] =10.00088539878978
y[1,0] = 0.00667193234012
y[2,0] = 0.00032472712345
```