One would suspect programming faults, such as uninitialized data or array bounds violations. Use of options such as /fp:source /Qimf-arch-consistency:true /arch:SSE3 would avoid differences among various CPU brands, once you have resolved such faults.

# Multiple machines, multiple outputs

>>...I'm having different results in floating point operations in my algorithms depending on the machine that is

>>being executed...

>>...

>>Is this normal?

Yes and it would be nice if you provide an example of your results.

>>...Is it possible to produce reproducible results?

Yes - If all software and hardware systems are the same.

No - If some software or some hardware systems are Not the same ( this is your case )

What are your relative and absolute errors?

>>...One would suspect programming faults, such as **uninitialized data** or **array bounds violations**...

The user doesn't have these cases ( from my point of view... ) because he gets some results. Anyway, let's see if he will provide some results for review.

PS: I really miss the **Preview Post** feature of the old ISN website...

Is the result of an iterative method that computes hundred of millions times some instructions. i.e.:

------

t=difx1[i]*d[i]*difx[i+m];

dd=(c[i+1]-d[i])/(t-c[i+1]);

d[i]=c[i+1]*dd;

c[i]=t*dd;

-------

All are double operations. On each iteration I compare the error with a thresold (order 10^-3= and I decide whether to continue or not. So it is not easy to show results (too many output data)

In that case, this could be just an inestable algorithm? How can I do it better? Using more precission?

>>...Using more precission?

Yes and a double-precision floating point data type ( **long double** / 80-bit precision ) needs to be used. Also, regarding applications of **long double** take a look at these threads:

Forum topic: **Mathimf and Windows**

Web-link: software.intel.com/en-us/forums/topic/357759

Forum topic: **Support of Extended or Quad IEEE FP formats**

Web-link: software.intel.com/en-us/forums/topic/358472

Forum topic: **Using 'long double' in Parallel Studio?**

Web-link: software.intel.com/en-us/forums/topic/266290

Forum topic: **Why function printf does not support long double?**

Web-link: software.intel.com/en-us/forums/topic/372720

Also, take a look at:

Forum topic: **Mixing of Floating-Point Types ( MFPT ) when performing calculations. Does it improve accuracy?**

Web-link: software.intel.com/en-us/forums/topic/361134

Results of a real test provided in the thread.

Computation using irrational numbers mostly produce irrational results. Double precision floating point uses 52 bits for mantissa with and implied 1 (53 bits of precision for fraction). Some fractional numbers cannot be exactly represented using a finite number of bits (some whole cannot either). A good example of this is the binary value of the decimal 0.1, this is 0.1100110011001100... This is an infinite repeating fraction. In DP FP this fraction will be left shifted by 1 bit and binary exponent diminished by 1 (to account for the shift). the 1. is removed as excepting for 0 and denormalized numbers, it will always be 1. this leave a binary fraction of:

1001100110011001100110011001100110011001100110011001100110011001100... (infinite irrational) 0000000001111111111222222222233333333334444444444555 (10's bit counter) 1234567890123456789012345678901234567890123456789012 (1's bit counter) 1001100110011001100110011001100110011001100110011010 (rounded to 52 bits) 00000000000000000000000000000000000000000000000000000110011001100... (+error)

Depending on how and how often you manipulate these numbers, the error grows. Using longer floating point formats postpone the error from creaping into the results beyond acceptible levels, but will not eliminate it from happening. Programmers can work around these errors if need be but in many cases the error is within an acceptible range and can be ignored.

Even before the days of binary computers, numerical computations had to take into consideration error in values. SIN, COS, LN tables were published to finite number of places.

Jim Dempsey

As Jim said usage of irrational numbers and also real numbers witch are not exactly representable by binary number encoding can lead tonaccumulation of the errors related to the accuracy of the final result.

>>... How can I do it better? Using more precission?

Aurora, please let me know if you need more practical help rather then theoretical.

Hi,

We are testing our algorithms with long double type data in terms of accuracy and times. A priori, we think the problem is solved. Would you say that operations with long double are much heavier in time?

I understand your explanations, but I still dont see why results changes depending on the machine. i.e. Intel Xeon and Core Duo with same binaries.

Thanks

>>...Would you say that operations with long double are much heavier in time?

Yes.

>>>but I still dont see why results changes depending on the machine. i.e. Intel Xeon and Core Duo with same binaries.>>>

Maybe this is due to various microcode and/or hardware implementation of the rounding algorithms.As Tim said there are also programming errors and there is also some possibility of the hardware errors which could manifest themselves as a loss of accurracy.

>>... I still dont see why results changes depending on the machine. i.e. Intel Xeon and Core Duo with same binaries...

Please try to look at CRT-libraries since older versions could be considered as "obsolete" ( it is applicable for any platform ). In practice, I never had identical results when the same test-case was compiled with, for example Visual C++ v6.0 and Visual Studio 2005, and then executed.

The article at http://software.intel.com/en-us/articles/consistency-of-floating-point-r... may provide some additional insights.

--mark

@mark-sabahi

It was a very interesting article.Thanks for link.

## Multiple machines, multiple outputs

Hi,

I'm having different results in floating point operations in my algorithms depending on the machine that is being executed. Same architecture (x64), same binaries, but not same processor. It also occurs with /debug:full, /Qfp-speculation:off, /fp:strict...

NOT using BLAS, LAPACK, any external library or random data. Only floating point instructions.

Is this normal? Is it possible to produce reproducible results?

Thanks in advance!

Intel C++ Compiler 12.1 update 258