Re: erroneous result when adding reals

*To*: mathgroup at smc.vnet.net*Subject*: [mg100877] Re: erroneous result when adding reals*From*: dh <dh at metrohm.com>*Date*: Wed, 17 Jun 2009 04:36:15 -0400 (EDT)*References*: <h19i46$p29$1@smc.vnet.net>

Hi Vlad, this is a very common question. Read about computer representation of real numbers. You will see that machine binary real numbers cover only a (unevenly spaced )grid in the domain of real numbers. Your problem is that 1/100 can not be exactly represented as a machine binary real number. Try e.g.: FromDigits@RealDigits[1/100, 2] Further, the sum can also not exact. Therefore, the error you get by subsequent summation depends on h and the current sum. Daniel Vlad Seghete wrote: > Hi all, > > I'm fairly new to Mathematica and today I ran into an issue that > confuses me endlessly. It has to do with simple addition of real > numbers. It seems like adding x (anything) to 0. (the real) produces a > result different from x, within something close to machine precision. > The problem becomes more serious when I do the addition in a Do loop, > like below: > > Module[{tnew, tcur = 0., h = 1/100}, > Clear[ts]; ts = {tcur}; (* ts is a list *) > Do[tcur = ts[[-1]]; > tnew = tcur + h; (* add h to the last element of the list > *) > AppendTo[ts, tnew], (* and then push it at the end of the list *) > {step, 1, 300} (* repead 300 times *) > ] > ]; > ListLinePlot[Table[h, {h, 0, 3, 1/100}] - ts, InterpolationOrder -> > 0] > > The plot I get is NOT constant, and the error introduced through the > "real addition" done in the Do loop is systematic and adds up to > something relatively large. Notice that if I substitute 0. (the real) > with 0 (the integer or rational), then the result is exactly like > expected. > > Do any of you know why this happens and how I could avoid it, other > than working with *only* rational numbers? Thank you! >