QUOTE (uart @ Mar 10 2009, 13:04)

QUOTE
Other mathematical "deviations" known are anything/10, some floating point decimals... e.g 5.76 becomes 5.7600000034 on a P4... And compatibles...
Yes I understand that the different architectures and optimized execution units (3dnow, SSE1, SSE2 etc) give numerical calculations of differing precision and that in any case floating point computations give results that are only accurate to a certain number of significant digits. But look at the example above, 5.7600000034 to 5.76 is only in error by about 6E-8% (6 times 10^(-8) percent). This is an error level corresponding to about 2E-5 (0.00005) part of one least significant bit in a wav file. Even the accumulation of many thousands of such rounding errors would be lucky to make even a one LSB error in the wav file!
Like I said I wouldn't have been the least bit surprised if the two decoded wav files differed by one or two LSB's, however I'm am really surprised that they differed by several hundred LSB's in some places.
I haven't seen the sources, but since they're dealing with lossy sound compression, probably they are using trigonometrical functions at some point... combine trigonometrical math+the floating point errors due the optimizations done by the processor+optimizatios done by the compiller and you **will** have errors of some orders of magnitude (through in the sound context, it can be just discarded... IMHO). Scientific software and software that uses precision critical math operations uses software algorithms based on "safe" math functions found in the processors. (think CAD, for example). But, as they deal with complex calculations in software, they are slower.
Personally i don't care much about it in case of lossy codecs, since they throw out data anyway... But where we CAN get some worries is when some uses a overoptimized lossless codecs... I haven't seen any case... but one never knows...
About the errors... try to divide 9/10 under the actual processors... the results can be interesting...
Decimal -> binary
0.9 -> 0.9
And again:
0.09 -> 0.089999996
Of course is just a two level division... The errors are all acummulative... even if you round this, the error will accumulate (rounding the second result using hardware will result in 0.8... glorious eh??) in case of complex operations (e.g. sin(x) or cos(x) ) things can get really screwed.
My last example:
#include <stdio.h>
int main(int argc, char *argv[]) {
double x = 0.49999999999999994;
int i = (int)(x+0.5);
printf("%0.17f %d\n", x, i);
return 0;
}
This is used to convert a floating-point number to an integer. Unfortunately in this particular case the value of x is rounded up during the addition, so it ends up with the value 1 instead of the expected 0. And we're dealing with just additions here...
What's the point??... well.. depending of what compiller you use and what kind of optimizations and what processor are you working on, you might get pretty diferent results... specially in the binary floating point area... where results may vary...
Regards.
J.