Re: Numeric problem in BlackBox 1.4

From: [at]} <robert.d.campbell{>
Date: Wed, 19 Feb 2003 09:52:18 +0000 (GMT)

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This discussion of floating point comparison
is rather relevant.

Yesterday I posted the 'algorithm'

IF (a + b) = b THEN ...

which correctly tests that 'b is negligibly small compared to a'.

I also criticised the unconditional use of

IF ABS (a - b) < eps THEN ...

on the grounds that you do not always know a suitable value for eps.

A few weeks ago I published the Control CtlsRealField (on Helmut's page)
which uses the algorithm

IF a = b THEN ...

to correctly test that 'b hasn't changed since a copy of it was last stored in
a'.

A few days ago I published the Control CtlsUnitField which used the
algorithm

IF a = b THEN ...

to INCORRECTLY test that 'b hasn't changed since a copy of it was
last stored in a other than by being scaled up and down by the same
floating point number'.

I subsequently published a 'correction' which uses the algorithm

IF IsRelEq (a, b, 1.E-15) THEN ...

where the code for IsRelEq should be

PROCEDURE IsRelEq (x, y, relErr : REAL) : BOOLEAN;
  BEGIN
    ASSERT (relErr >= 0., 20);
    IF x = y THEN RETURN TRUE END;
    RETURN (ABS (x - y) / MAX (ABS (x), ABS (y))) <= relErr
  END IsRelEq;

(In fact the currently published version of IsRelEq contains another error;
I shall correct it shortly. And even this code is probably wrong if x = INF
& y = -INF)


>> I am very cautious with *any* expectations regarding floating point
>> expressions.

Unexpected behaviour, such as PROCEDURES returning 80-bit precision
on the stack, can be controlled by setting the floating point unit
flags explicitly. If anyone needs to do this I can give examples
on how to do this in BlackBox (on Pentiums & Athlons).


The bottom line? - numerical analysis is not always totally trivial.
And as for the start of this thread; I can't think of anything
more reasonable than rounding a symbolic constant (such as
1.000000000000000001) to the nearest representable 64-bit IEEE
REAL (eg 1.0 ).


Regards

Robert


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Received on Wed Feb 19 2003 - 10:52:18 UTC