Errors in handling real numbers ?

*To*: mathgroup at smc.vnet.net*Subject*: [mg8660] Errors in handling real numbers ?*From*: "Piotr G. Kin" <Piotr.Kin at per.clw.csiro.au>*Date*: Mon, 15 Sep 1997 02:48:49 -0400*Organization*: CSIRO*Sender*: owner-wri-mathgroup at wolfram.com

I was trying to develop a function that would return number of digits after the decimal point in a real number. The function would work as follows: In[]:= a = 1. 5.1234; b = 1. 0.00123; c = 1. 0.5; digitsafterdot[{a,b,c}] Out[]= {4,5,1} ( The results would differ from those obtained through application of RealDigits[] i.e., In[]:= Apply[Length[#1] - #2 &, RealDigits[{a,b,c}], {1}] Out[]= {15,18,16} ) I was REALLY surprised to discover that there is a serious error in handling real numbers. Consider the expressions: In[]:= x = 0.11; NestList[FractionalPart[10#] &, x, 5] NestList[(10. # - IntegerPart[10. #]) &, x, 5] Out[]= -16 -15 -14 -13 {0.11, 0.1, 8.88178 10 , 8.88178 10 ,8.88178 10 , 8.88178 10 } -16 -15 -14 -13 {0.11, 0.1, 8.88178 10 , 8.88178 10 ,8.88178 10 , 8.88178 10 } The results are as expected and are identical for both expressions. Remarkably, when value of x changes to (say) 0.12 the following happens: In[]:= x = 0.12; NestList[FractionalPart[10#] &, x, 5] NestList[(10. # - IntegerPart[10. #]) &, x, 5] Out[]= {0.12, 0.2, 1., 1., 1., 1.} {0.12, 0.2, 1., 1., 1., 1.} The results are identical again but hardly expected. For visual demonstration run the expression: In[]:= Plot[Function[x, Chop[Nest[FractionalPart[10 #] &, x ,2]]][y],{y, 0.00, 0.10}, PlotPoints -> 100] It gets even funnier with numbers with precision higher than $MachinePrecision: In[]:= x = 0.20000000000000000; NestList[FractionalPart[10#] &, x, 5] NestList[(10. # - IntegerPart[10. #]) &, x, 5] Out[]= 17 {0.2000000000000000,1.000000000000000,1.00000000000000,1.0000000000000,1.000000000000,1.00000000000} {0.2000000000000000,0.,0.,0.,0.,0.} The results of two mathematically equivalent expression are significantly different. Am I to sensitive or is this a serious problem? Peter. P.S. All the above results were obtained on INTEL Pentium 166 PC. ___________PLEASE NOTE NEW TEL, FAX NUMBERS AND E-MAIL ADDRESS_____________ Piotr G. Kin CSIRO Land & Water e-mail: Piotr.Kin at per.clw.csiro.au Private Bag WWW: www.dwr.csiro.au PO Wembley WA 6014 Phone +61 8 9333 6205 Australia Fax +61 8 9387 8211 ___________________________________________________________________________ This is NOT an official form of communication, it is however. It does NOT commit me to anything or any place or even CSIRO. All views stated here are wholly or partially my own or conveniently borrowed or vaguely remembered. ___________________________________________________________________________ ... And now for something completely different ... The information in this message is IN-CONFIDENCE and is intended for CSIRO personnel only. Distribution of this information to non-CSIRO personnel must be authorised in accordance with CSIRO Code of Conduct (Policy 94/18) ___________________________________________________________________________