[fpc-devel] SSE in FPC

[Alain Michaud]

Vinzent Höfler wrote:
> Alain Michaud wrote:
>> Hi,
>>
>>   Not exactly related to this thread, but worth mentioning:
>>
>>   Some time ago I was interested in (numerical) computing some Bessel 
>> function to the highest precision!
>>
>>     I looked at MMX, SSE, SSE2, SSE3, SSE4, FP87, 3D-something  
>> etc...   And all that jazz...
>>
>>    It turns out that only the "old" FP87 (FPU)  has the 80 bit 
>> (extended) floating format!  Anything else, and you are limited to the 
>> 64 bit (double) floating numbers.
>>
>>    I fell sorry to see that even 25 years after the original 8087, 
>> modern CPUs are not even capable to have the same precision!
> 
> If you need precision you have to do integer math anyway. Floating point 
> numbers are always crude approximations, no matter how many bits they 
> have. Considering that the numerical range of an 80-bit floating point 
> number is larger than the relation between the diameter of an atom and 
> the diameter of the known universe, this so-called "precision" is hardly 
> ever needed. Or to express this a bit (pun intended) differently: How 
> much of the universe do you expect to fit into 80 bits?
> 
> 
> Vinzent.
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I think that high precision numerical computing is very useful in many 
fields of science and technology:

The Rydberg constant is defined using 13 digits.

The second is measured using 15 digits

Some laser spectroscopist make measurements using 18 digits.

The Lamb shift in hydrogen has been measured using 13 digits. Right now 
this measurement is more accurate than the theoretical evaluation:

In order to evaluate this number (to 12 digits), the researchers had to 
         make a long calculation involving the sum of about 2000 
numerical integrals.

You are right, they have used symbolic computation. However, in order to 
make sure that the did not miss someting, they have also checked every 
integral by performing a numerical integration a test!

Therefore, I think that 64 bits is a limit !

Alain