| Re: Strange problem [message #28138 is a reply to message #2626] |
Sun, 25 November 2001 19:55   |
Bhautik Joshi
Messages: 21
Registered: November 2001
|
Junior Member |
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> type: for i=0., 0.8., 0.1 do print,i
> That's bad isn't it?
OK lets drag this out a little further :)
Lets translate this into a WHILE loop and try it again, using INTS.
MOO>i=0
MOO>while i le 8 do begin print, i & i=i+1
0
1
2
3
4
5
6
7
8
Now again, using FLOAT:
MOO>i=0.0
MOO>while i le 0.8 do begin print, i & i=i+0.1
0.00000
0.100000
0.200000
0.300000
0.400000
0.500000
0.600000
0.700000
What's going on? Shouldn't it count up to 0.8?
MOO>print, i-0.8
5.96046e-08
Basically what has happened is that when 0.1 gets added to 0.7, the
result is > 0.8, so the loop gets terminated early!
This is because what you see in the screen is rounded to a couple of
decimal places; where it says 0.7 it should really be something like
0.7000000001. As the addition occurs, accuracy is lost.
To demonstrate, try this routine:
pro foo, l
loopvar=FLOAT(0.0)
lim=FLOAT(l)
inc=FLOAT(0.1)
i=FIX(0)
while (loopvar le l) do begin
actvar=FLOAT(i)*inc
print, 'loopvar: ',loopvar,' actvar: ',actvar,'
diff:',(loopvar-actvar)
loopvar=loopvar+inc
i=i+1
end
end
So, trying it out:
MOO>foo, 0.8
loopvar: 0.00000 actvar: 0.00000 diff: 0.00000
loopvar: 0.100000 actvar: 0.100000 diff: 0.00000
loopvar: 0.200000 actvar: 0.200000 diff: 0.00000
loopvar: 0.300000 actvar: 0.300000 diff: 0.00000
loopvar: 0.400000 actvar: 0.400000 diff: 0.00000
loopvar: 0.500000 actvar: 0.500000 diff: 0.00000
loopvar: 0.600000 actvar: 0.600000 diff: 0.00000
loopvar: 0.700000 actvar: 0.700000 diff: 5.96046e-08
So whats printed on the screen is 0.700000, but the actual number is
0.70000006 (roughly - remember that on a computer, only exact multiples
or um.. whats the word - numbers that have been divided exactly by - 2
can be exactly represented. ie. ..2.0,1.0,0.5,0.25.. are prescise;
however, ..2.1,1.1,0.51,0.251.. have a degree of inaccuracy).
The exact same thing occurs when you write the same thing in C, so its
not just something limited to IDL.
The morals of this story:
* don't let your loop variable=data variable
* floats have only 7 digits of prescision (on most platforms); where you
are trying to be exact (and loop variables have to be exact) either use
a DOUBLE (which has 15 digits of prescision on most systems) or use an
INT to count the number of times the loop goes around
* The 29,249th digit of pi is a seven.
Cheers,
Bhautik
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