2010/12/26 Andreas Raab andreas.raab@gmx.de:
On 12/26/2010 10:24 PM, Igor Stasenko wrote:
btw, how old that fdlibm portions there? maybe updating it will be a simple solution to that issue?
I've never found any newer release than here:
Oh, and please, can you shed some light on the history, why for floating-point math in Squeak, VM using non-standard math lib, which comes with any C compiler, but instead, a portions of separate 3rd party library?
You would be surprised to find out just how much the results of the C compiler libraries differ when it comes to edge cases. I've run the experiment in the past:
Using Python 2.4:
import math math.cos(1.0e32)
WinXP: -0.39929634612021897 LinuxX86: -0.49093671143542561
Yes, I like this one.
Considering that 1.0e32 is exactly 100000000000000005366162204393472, my own approximation would be: (1.0e32 asArbitraryPrecisionFloatNumBits: 53) cos asFloat storeString -> '0.8108648261576407'
which is in agreement with fdlibm because enough decimals of pi are considered for computing the modulo 1.0e32 cos storeString -> '0.8108648261576407'
But considering that 1.0e32 ulp -> 1.8014398509482e16, the least rounding error leads to an uncertainty interval [-1,1] on this result. So this kind of computation has no meaning at all, bit identical or not, and should better be forbidden. The IEEE 754 conceivers could as well have stated that the right answer was NaN (meaning undefined here).
Nicolas
In short, the results *dramatically* vary depending on processor family, processor version, C compiler libraries, and so on. None of the libraries produce cross-platform bit-identical results. fdlibm does.
Cheers, - Andreas