🚀 go-pugleaf

In article: <zaccone@rigel.bucknell.edu's message of 23 May 89
01:19:53 GMT> Rick Zaccone writes:
>The following program produces incorrect results in LSP 2.01:
>
>program test (input, output);
>var
>        a, out: real;
>begin
>        a := 16807.0;
>        out := a * a;
>        writeln(out : 10 : 0);
>end.
>
>The program prints 282475264 instead of the correct 282475249.  If I
>type "a*a" in the observe window, I can see that a*a is being computed
>correctly.  The error occurs when the assignment is made to out.  Can
>anyone else reproduce this?  Am I missing something obvious?

Your missing something obvious.  If you look at Apple's numerics
manual (SANE manual) you'll find that real numbers have an definite
accuracy of only _6_ digits.  Anything else you see is affected by
remaining bit patterns in the real number that may or may not be
accurate.  When a*a is used in the observe window, LSP converts the
reals to extended format (as it does in the program as well) and then
prints out the answer using the _extended_ result.  The difference
lies in assigning the answer to 'out'.  The result has to be converted
back into single precision and stored in 'out' (loosing several digits
of accuracy as it's converted).  If you had done something like this:

...
    a := 16807.0
    writeln(a*a:10:0);
...

you'd get the correct answer.  If you need that precision inside a
variable then just change your variable declaration to:

var
  a : real;
  out : extended;

and everything should work fine and dandy.  Remember, floating point
numbers by the virtue of being represented by a finite number of bits
can _never_ represent the entirety (?sp?) of all real numbers.

Enjoy the limited world of computer programming...

					-Kelesi
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