What does "Error" mean in the output of CUDALucas?

ICWiener · 2018-06-16, 15:56

CUDALucas shows a lot of information at each step of its calculations. I don't understand one of these fields, the "Error" field. It fluctuates somewhere between 0.25 and 0.28.

The CUDALucas README does not document this unfortunately.

To my knowledge, the Lucas-Lehmer test is deterministic, therefore I am confused about what this "Error" field means.

paulunderwood · 2018-06-16, 16:01

I guess it mean the ROE (round off error) of the FFT (fast Fourier Transform) used. It should not go over 0.4 or 0.5 (??) as it would give a dubious result. Anything below this is safe.

ICWiener · 2018-06-16, 16:11

Quote:

Originally Posted by paulunderwood

I guess it mean the ROE (round off error) of the FFT (fast Fourier Transform) used. It should not go over 0.4 or 0.5 (??) as it would give a dubious result. Anything below this is safe.

Thank you!

kriesel · 2018-06-16, 17:21

From the readme:

Code:

Error check interval
If set to n, will check the roundoff error once every n iterations.  Slowest, 
but most accurate is with ErrorIterations=1. With any larger  value, the 
reported roundoff error is most likely smaller than the largest  roundoff 
error. Error thresholds are accordingly reduced for such values.  For 
example, if the error threshold is set to 45 and ErrorIterations is 1,  then 
any roundoff error  .45  triggers the error handling routines. But for 
ErrorIterations set to 100,  any roundoff errors > .35 will trigger the error 
handling routines.

This could be clarified in a future version of the readme to refer to the fft method of computing multiprecision integer results using floating point in the gpu for speed, which introduces small levels of imprecision. The results must be rounded back to integers. Round-off error above a certain threshold less than one half must be guarded for, since rounding from a value with an error of more than one half will give a different value than the correct one. Very small values of round-off error are associated with too-large fft lengths (which take longer for the same computation).

2018-06-16, 15:56	#1
ICWiener Jun 2018 17 Posts	What does "Error" mean in the output of CUDALucas? CUDALucas shows a lot of information at each step of its calculations. I don't understand one of these fields, the "Error" field. It fluctuates somewhere between 0.25 and 0.28. The CUDALucas README does not document this unfortunately. To my knowledge, the Lucas-Lehmer test is deterministic, therefore I am confused about what this "Error" field means.

2018-06-16, 17:21	#4
kriesel "TF79LL86GIMPS96gpu17" Mar 2017 US midwest 2⁴·3·163 Posts	From the readme: Code: Error check interval If set to n, will check the roundoff error once every n iterations. Slowest, but most accurate is with ErrorIterations=1. With any larger value, the reported roundoff error is most likely smaller than the largest roundoff error. Error thresholds are accordingly reduced for such values. For example, if the error threshold is set to 45 and ErrorIterations is 1, then any roundoff error .45 triggers the error handling routines. But for ErrorIterations set to 100, any roundoff errors > .35 will trigger the error handling routines. This could be clarified in a future version of the readme to refer to the fft method of computing multiprecision integer results using floating point in the gpu for speed, which introduces small levels of imprecision. The results must be rounded back to integers. Round-off error above a certain threshold less than one half must be guarded for, since rounding from a value with an error of more than one half will give a different value than the correct one. Very small values of round-off error are associated with too-large fft lengths (which take longer for the same computation).

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2018-06-16, 16:01	#2
paulunderwood Sep 2002 Database er0rr 4685₁₀ Posts	I guess it mean the ROE (round off error) of the FFT (fast Fourier Transform) used. It should not go over 0.4 or 0.5 (??) as it would give a dubious result. Anything below this is safe.