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printf (awk,perl,shell) float rounding issue

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# 8  
Old 10-14-2012
Quote:
Originally Posted by Don Cragun
There are some statistics books that recommend rounding even values down (4.5 -> 4) and odd values up (5.5 -> 6) assuming that doing so will produce sums of rounded numbers closer to the value of the sums of the unrounded values. But I doubt that ksh is trying to provide that capability. I would guess that this could easily be caused by some programs using float, others using double, and still others using long double and having the process of converting 4.5 to the closest value in those formats sitting on opposite sides of the not quite exact value 4.5 representable in the various formats.
If it were something that is a random consquence of some conversion, then I think the rounding would not be as consistent as it is in those shells other than ksh... The rounding of half-integers are a special case and a choice needs to be made...

Apparently "round half to even" is the default and/or recommended way according to IEE754
Last edited by Scrutinizer; 10-14-2012 at 04:11 PM..
# 9  
Old 10-14-2012
Quote:
Originally Posted by Corona688
They must have taken effort to make it do so. I don't know why they bothered, since it's not a feature really needed, undesirable in most cases, and easy to do yourself if you really want it.

Floating point numbers are represented internally as an exponent, like 1.5*10^3 or so forth.
On the machines most of us work on, floating point numbers are represented as x*2^y or x*16^y rather than x*10^y, but .5 is exactly representable in any of them. On the other hand 0.1 is not exactly representable on any system that uses an exponent of 2 or 16.

As pointed out by Scrutinizer, the real answer lies in the rounding mode being used by whatever function is converting the internal floating point value to a printable decimal representation of that value.
# 10  
Old 10-14-2012
Quote:
Originally Posted by Don Cragun
On the machines most of us work on, floating point numbers are represented as x*2^y or x*16^y rather than x*10^y
I know how it works. It wasn't too relevant to the example. The point is it uses an exponent, it's not stored literally.
Quote:
but .5 is exactly representable in any of them.
0.5 is. Anything else .5 depends.
Quote:
As pointed out by Scrutinizer, the real answer lies in the rounding mode being used by whatever function is converting the internal floating point value to a printable decimal representation of that value.
Yes, which I pointed out most generally don't. ksh93 would be an exception.
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