Robert Bradshaw wrote:
> On Dec 29, 2009, at 9:59 PM, Peter Jeremy wrote:
>
>> On 2009-Dec-29 23:29:42 +0000, "Dr. David Kirkby" <david.kir...@onetel.net
>>> wrote:
>>> There are a few failures, but these couple just came up, and look
>>> rather odd, as this is only an error in the last decimal place, and
>>> so will be subject to rounding errors with different floating point
>>> processors. They do not really seem failures to me.
>> One of the claims for IEEE-754 arithmetic is that basic arithmetic
>> operations (+, -, *, /, sqrt) will give bit-for-bit identical
>> results on different implementations.
>
> I would have expected t2 to be IEEE-754 compliant, but maybe it isn't.
>
>>> **********************************************************************
>>> File "/rootpool2/local/kirkby/sage-4.3/devel/sage/sage/symbolic/
>>> pynac.pyx", line
>>> 1276:
>>> sage: py_exp(float(1))
>>> Expected:
>>> 2.7182818284590451
>>> Got:
>>> 2.7182818284590455
>>> **********************************************************************
>> As a correctly rounded IEEE-754 double precision constant,
>> e=0x4005BF0A8B145769 (0x2.B7E1 5162 8AED 2), this should convert
>> to 2.7182818284590451 (rounded to "sufficient" accuracy).
>>
>> 2.7182818284590455 is 1ULP high - this may reflect a rounding error
>> in either the exp() or double_to_ascii() implementation.
>
> It's probably not double_to_ascii, as (on t2)
>
> >>> float("2.7182818284590452353602874713526625")
> 2.7182818284590451
>
> I bet Solaris has a completely different (and unfortunately not as
> accurate) implementation of exp in its libm. It could also be a bug in
> the compiler, as math.e is defined as
I might be mistaken, but I believe the SPARC processor users 64 bits for
floating point and the Intel chips use 80 internally, so it might be an issue
with the processor. I've got no idea how that fits in with IEEE-754.
Dave
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