aindiana@osiris.cso.uiuc.edu (Daiv Stoner) (08/15/90)
A little technical question for all you net wizards.
The following piece of code written and compiled in Turbo Pascal
5.5 on an IBM Model 50 gives strange results.
Here's the code:
program a;
var
rate,reg:real;
x,value:real;
begin
rate:=2.01;
reg:=12.5;
value:=rate*reg*100+0.5;
x := int(value)/100;
writeln('rate=',rate:8:4,' reg=',reg:8:4,' total=',rate*reg:8:4,' x=',x:8:4);
end.
I get this output:
rate= 2.0100 reg= 12.5000 total= 25.1250 x= 25.1200
Borland Tech. Support says "round-off" error. I say it's a bug.
Any ideas?
--
Daiv Stoner +===============================================+
aindiana@osiris.cso.uiuc.edu | I work for the Gov't. If I want your opinion |
oinxds@ria-emh1.army.mil | I'll ask you to fill out the necessary forms. |
Disclaimer: The Dept. of +===============================================+
Defense doesn't even know what it's doing, let alone what I'm doing.rowley@cs.umn.edu (Henry A. Rowley) (08/16/90)
In article <1990Aug15.160719.12762@ux1.cso.uiuc.edu> aindiana@osiris.cso.uiuc.edu (Daiv Stoner) writes: > rate:=2.01; > reg:=12.5; > value:=rate*reg*100+0.5; > x := int(value)/100; >writeln('rate=',rate:8:4,' reg=',reg:8:4,' total=',rate*reg:8:4,' x=',x:8:4); >I get this output: > >rate= 2.0100 reg= 12.5000 total= 25.1250 x= 25.1200 It is probably a round off error. You could verify the following statements by printing the entire number, not a rounded version of it: ie writeln(rate), not writeln(rate:8:4). Anyway, here is where the round off is occurring: Lets say the actual value of rate is 25.124999999999999. Then, if you multiply by 100, you get 2512.49999999999. Adding 0.5 gives 2512.999999999. Then, truncate to the integer part of the number, and you get 2512. Dividing by one hundred gives you the final answer 25.12. As you can see, this is due to rounding errors, not a bug. Henry A. Rowley Internet: rowley@cs.umn.edu -or- rowley@ux.acs.umn.edu THE CONTENT OF THE PROPOSITIONS - _The Shockwave Rider_ by John Brunner-------- #1: That this is a rich planet. Therefore poverty and hunger are unworthy of it, and since we can abolish them, we must. #2: That we are a civilized species. Therefore none shall henceforth gain illict advantage by reason of the fact that we together know more that one of us can know.
winfave@dutrun.UUCP (Alexander Verbraeck) (08/16/90)
In article <1990Aug15.160719.12762@ux1.cso.uiuc.edu> aindiana@osiris.cso.uiuc.edu (Daiv Stoner) writes: > > >A little technical question for all you net wizards. >The following piece of code written and compiled in Turbo Pascal >5.5 on an IBM Model 50 gives strange results. > >Here's the code: > >program a; >var > rate,reg:real; > x,value:real; >begin > rate:=2.01; > reg:=12.5; > value:=rate*reg*100+0.5; > x := int(value)/100; > >writeln('rate=',rate:8:4,' reg=',reg:8:4,' total=',rate*reg:8:4,' x=',x:8:4); >end. > >I get this output: > >rate= 2.0100 reg= 12.5000 total= 25.1250 x= 25.1200 > >Borland Tech. Support says "round-off" error. I say it's a bug. >Any ideas? > I think Borland Tech Support is right: it's a "roud off" error. The Int() function "Returns the integer part of the argument" according to page 321 of my TP 5.5 manual. As real values are not stored in decimal form, but in binary form, it might be that 2.01*12.5*100+0.5 will be stored as the equivalent of 2512.99999999. The value of Int(2512.99999999) is, however sadly in this case, 2512 instead of 2513, the value you would expect. A possible solution: use Int(value+epsilon) instead of Int(value), with epsilon a value that is very small, for instance covering only one or two of the least significant bits. This is especially important in financial programs, as I once found out the hard way. You'll be loosing cents in no time, when you store financial values as reals, and then perform arithmetic on them. Solution: either use (long)ints, or apply the epsilon-trick. I used a function "CleanMoney" for that, that looked something like this: function CleanMoney(m:real):real; begin CleanMoney:=Int(100.0*m+epsilon)/100.0; end; ---------------------------------------------------------------------- Alexander Verbraeck e-mail: winfave@dutrun.tudelft.nl Delft University of Technology winfave@hdetud1.bitnet Department of Information Systems winfave@dutrun.uucp PO Box 356, 2600 AJ The Netherlands dutrun!winfave@hp4nl.uucp ----------------------------------------------------------------------