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.
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