[Numpy-discussion] IEEE 754-2008 decimal floating point support

[Robert Kern]

On Wed, Sep 8, 2010 at 15:10, Michael Gilbert
<michael.s.gilbert at gmail.com> wrote:
> On Wed, 8 Sep 2010 15:04:17 -0500, Robert Kern wrote:
>> On Wed, Sep 8, 2010 at 14:44, Michael Gilbert
>> <michael.s.gilbert at gmail.com> wrote:

>> > Just wanted to say that numpy object arrays + decimal solved all of my
>> > problems, which were all caused by the disconnect between decimal and
>> > binary representation of floating point numbers.
>>
>> Are you sure? Unless if I'm failing to think through this properly,
>> catastrophic cancellation for large numbers is an intrinsic property
>> of fixed-precision floating point regardless of the base. decimal and
>> mpmath both help with that problem because they have arbitrary
>> precision.
>
> Here is an example:
>
>   >>> 0.3/3.0 - 0.1
>   -1.3877787807814457e-17
>
>   >>> mpmath.mpf( '0.3' )/mpmath.mpf( '3.0' ) - mpmath.mpf( '0.1' )
>   mpf('-1.3877787807814457e-17')
>
>   >>> decimal.Decimal( '0.3' )/decimal.Decimal( '3.0' ) - decimal.Decimal ( '0.1' )
>   Decimal("0.0")
>
> Decimal solves the problem; whereas mpmath doesn't.

Okay, that's not an example of catastrophic cancellation, just a
representation issue.

-- 
Robert Kern

"I have come to believe that the whole world is an enigma, a harmless
enigma that is made terrible by our own mad attempt to interpret it as
though it had an underlying truth."
  -- Umberto Eco