[fpc-devel] Rounding inconsistent (critical)

[Graeme Geldenhuys]

On 02/10/06, Vincent Snijders <vsnijders at quicknet.nl> wrote:
>
> But 0.125 and 0.375 are representable ACCURATELY on a computer, aren't they?
>
> Vincent

Yes they can, so FPC still has a bug in Banker's Rounding.

What is really interresting is that I never really thought about
irrational number and how they are represented in computers.  From
that article in MSDN, here is a few basic calulations that don't work
on computers.  Multiply is the only test that worked!  All other tests
didn't. :-)

var
  sumE: extended;
  sumD: double;
  sumS: single;
  i: integer;
  t1, t2, t3: single;
begin
  write('multiply: ');
  writeln(0.0001 * 10000);
  writeln('=========');

  // should be 1.0 in theory
  sumE := 0;
  for I := 1 to 10000 do
    sumE := sumE + 0.0001;
  write('sum E: ');
  writeln(sumE);
  writeln('=========');

  // should be 1.0 in theory
  sumD := 0;
  for I := 1 to 10000 do
    sumD := sumD + 0.0001;
  write('sum D: ');
  writeln(sumD);
  writeln('=========');

  // should be 1.0 in theory
  sumS := 0;
  for I := 1 to 10000 do
    sumS := sumS + 0.0001;
  write('sum S: ');
  writeln(sumS);
  writeln('=========');


  writeln(' ');
  writeln('testing the follow:  69.82 = 69.20 + 0.62 ');
  t1 := 69.82;
  t2 := 69.20;
  t3 := 0.62;
  writeln(t1);
  writeln(t2);
  writeln(t3);

  if t1 = (t2 + t3) then
    writeln('equality')
  else
    writeln('non equals');   <=== prints this!!!
  writeln('=========');


Regards,
  - Graeme -