Re: erroneous result when adding reals

*To*: mathgroup at smc.vnet.net*Subject*: [mg100907] Re: [mg100853] erroneous result when adding reals*From*: Sseziwa Mukasa <mukasa at jeol.com>*Date*: Thu, 18 Jun 2009 04:51:06 -0400 (EDT)*References*: <200906170151.VAA25825@smc.vnet.net>

On Jun 16, 2009, at 9:51 PM, 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 result of mixing machine precision values with infinite precision values is a machine precision value, adding 0. to an infinite precision value effectively means converting that value to a machine precision value, which is what you observe. > 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. tcur + h requires converting h to machine precision and doing the sum at that precision the append then stores the machine precision result in ts, for some values of x/100 there is no exact machine precision representation and whenever you are near such a value your calculation will deviate from the exact precision calculation from that point on. > Do any of you know why this happens and how I could avoid it, other > than working with *only* rational numbers? Thank you! What are you interested in? Doing the calculation at machine precision or doing it exactly? Regards, Ssezi

**References**:**erroneous result when adding reals***From:*Vlad Seghete <vlad.seghete@gmail.com>