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"bugs" in Mathematica?
*To*: mathgroup at yoda.physics.unc.edu
*Subject*: "bugs" in Mathematica?
*From*: J.Wilson at cc.uq.oz.au
*Date*: Tue, 1 Jun 1993 08:23:53 +1000
I am using Mathematica for Windows 2.2 Student Edition, and I have
encountered what might be considered "bugs":
In[1]:=
2^32
Out[1]=
4294991158 <-- 2^32 is in fact 4294967296!!
In[2]:=
1048576 4096 <-- 2^20 2^12
Out[2]=
4294967296 <-- This is the correct answer for 2^32
In[3]:=
65536 65536 <-- 2^16 2^16
Out[3]=
4295003988 <-- Huh?
In[4]:=
N[2^32, 10]
Out[4]=
9
4.295003988 10 <-- Not equal to 2^32!!
In[5]:=
Precision[ % ]
Out[5]=
10 <-- More like 3!
I suspect that this problem may be caused by insufficient memory
(I am running on a 386SX-20 with 4M of RAM and 8M swap disk), however
I wrote a short program to calculate pi using 20,000 digit numbers and
I know at least the first 10,000 are correct! Surely accurate integer
operations are trivial compared to 20,000-digit floating point!
Speaking of pi, I was somewhat surprised to see that, according to
Mathematica:
In[6]:=
pi = N[Pi, 100]
Out[6]=
3.14159265358979323847726475672949236948651245467951244082474929\
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
57180162869915824851952128135649755605
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This number only has 20 correct digits of pi in it! (incorrect digits
labelled with ^). The actual figures (you can check this in
countless places) are:
3.1415926535897932384626433832795028841971693993751058209749445923\
07816406286208998628034825342117067982148 etc.
This in itself is not particularly important (who would use 100-digit
values of pi in a computation?) but I'm surprised that Mathematica
gives an inaccurate value for this and for the 2^32 calculations above!
Further evidence:
In[7]:=
3^100 <-- The Mathematica book, p. 2
Out[7]=
515375413085732364763604855061513610239342074529
The Mathematica Book itself gives the answer as:
515377520732011331036461129765621272702107522001
It is interesting to note that N[EulerGamma, 40] agrees 100% with
the Mathematica book example, p.566.
Am I doing something wrong? Is something wrong with my hardware
setup (386SX-20, 4M RAM, 8M swap disk, Win 3.1, 500MB hard disk,
running Stacker 2.01, DOS 6)? Is Mathematica 2.2 Student Ed. to
blame? I think Mathematica is a great program, especially with
functions and graphics etc. (the symbolic stuff is elegant and
reminds me of C++...)
Please help!
________________________________________
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