# [Numpy-discussion] float128 casting rounding as if it were float64

Matthew Brett matthew.brett@gmail....
Sat Oct 15 13:54:33 CDT 2011

```Hi,

On Wed, Oct 12, 2011 at 11:24 AM, Charles R Harris
<charlesr.harris@gmail.com> wrote:
>
>
> On Tue, Oct 11, 2011 at 12:17 PM, Matthew Brett <matthew.brett@gmail.com>
> wrote:
>>
>> Hi,
>>
>> While struggling with floating point precision, I ran into this:
>>
>> In [52]: a = 2**54+3
>>
>> In [53]: a
>> Out[53]: 18014398509481987L
>>
>> In [54]: np.float128(a)
>> Out[54]: 18014398509481988.0
>>
>> In [55]: np.float128(a)-1
>> Out[55]: 18014398509481987.0
>>
>> The line above tells us that float128 can exactly represent 2**54+3,
>> but the line above that says that np.float128(2**54+3) rounds upwards
>> as if it were a float64:
>>
>> In [59]: np.float64(a)
>> Out[59]: 18014398509481988.0
>>
>> In [60]: np.float64(a)-1
>> Out[60]: 18014398509481988.0
>>
>> Similarly:
>>
>> In [66]: np.float128('1e308')
>> Out[66]: 1.000000000000000011e+308
>>
>> In [67]: np.float128('1e309')
>> Out[67]: inf
>>
>> Is it possible that float64 is being used somewhere in float128 casting?
>>
>
> The problem is probably in specifying the values. Python doesn't support
> long double and I expect python integers to be converted to doubles, then
> cast to long double.

Presumably our (numpy) casting function receives the python integer,
and therefore its
us who are doing the conversion?  If so, surely that is a bug?

> The only way to get around this is probably using
> string representations of the numbers,  and I don't know how
> well/consistently numpy does that at the moment. If it calls python to do
> the job, then double is probably what is returned. It doesn't help on my
> system:
>
> In [1]: float128("18014398509481987.0")
> Out[1]: 18014398509481988.0

Note though that:

>> In [66]: np.float128('1e308')
>> Out[66]: 1.000000000000000011e+308
>>
>> In [67]: np.float128('1e309')
>> Out[67]: inf

and I infer that we (numpy) are using float64 for converting the
strings; that seems to me to be the likely explanation of both
phenomena - do you agree?

See you,

Matthew
```

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