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