topic real rounding in Intel® Fortran Compiler

real rounding

jim_cox — Thu, 29 Mar 2012 01:38:48 GMT

We are finding some awkward rounding going on with real numbers

For example our program has

real beta
beta = 1.0

real betastep
betastep = 0.01

but when you examine with the debugger betastep = 9.9999998E-3, which is not quite the same

unfortuantely this showing up in our results - after a number of loops of

beta = beta - betastep

the beta counter drifts off

5.98004 instead of 5.98, 4.63001 instead of 4.63 etc

I've tried the /fp:strict and /fp:precise and /Qfp_port compiler switches, but they dont seem to change anything

Is there an easy fix?

Or is it just 'one-of-those' rounding things?

Thankx

Jim

real rounding

DavidWhite — Thu, 29 Mar 2012 02:51:47 GMT

Real numbers can rarely be expressed exactly in binary, so this problem is typical of working with reals.

Is your example typical of what you want to do - always an exact number of steps (in this case 100).

Suggest that you use an integer counter, and calculate
Beta = Betastart - (I-1)*Betastep

or something silimar.

Regards,

David

real rounding

Lars_Jakobsen — Thu, 29 Mar 2012 09:00:43 GMT

You could delay the drift (at lest I would think so) ifyou use double precission.

real(8) beta = 1.0d
real(8) betastep=0.01d

Regards

Lars

Real rounding

SergeyKostrov — Thu, 29 Mar 2012 13:01:35 GMT

You're dealing with limitations of IEEE 754 Standard. In case of a single-precision data type ( 24-bit precision) a rounding or inexact
issues start affecting a precision very quickly. The only solution is touse a double-precision data type ( 53-bit or 64-bitprecisions ) instead.

Best regards,
Sergey

real rounding

TimP — Thu, 29 Mar 2012 13:27:50 GMT

Depending on what you are looking for, the "easy fix" might resemble;

do i = 1,100
beta = (100 - i) / 100.
.....

Not only would this avoid drift, it is a classic vectorizability transformation.
I think David (in the earlier response) may have meant this.

real rounding

jimdempseyatthecove — Thu, 29 Mar 2012 16:03:25 GMT

real beta, betaBase
betaBase = 1.0

real betaStepMultiplier, betaStepInverse
betaStepMultiplier = 0.0
betaStepInverse = 100.0

do I=1,N
beta = betaBase - (betaStepMultiplier / betaStepInverse)
...
betaStepMultiplier = betaStepMultiplier + 1.0
end do

The above will provide better precision, and more importantly, will not accumulate roundoff errors.
Note, division is relatively fast on current processors.

Jim Dempsey