🚀 go-pugleaf

In article <4dbos6$o7q@umbc9.umbc.edu>,
Jonas J. Schlein <schlein@umbc.edu> wrote:
>Jeff Tomich <jtomich@IntNet.net> wrote:
>|> Having a hard time to figure out a function on how to compare doubles. 
>|> Any ideas?
>
>I'd go along with what the c.l.c. FAQ has to say about this one:
>
>14.5:	What's a good way to check for "close enough" floating-point
>	equality?
>
>A:	Since the absolute accuracy of floating point values varies, by
>	definition, with their magnitude, the best way of comparing two
>	floating point values is to use an accuracy threshold which is
>	relative to the magnitude of the numbers being compared.  Rather
>	than
>
>		double a, b;
>		...
>		if(a == b)	/* WRONG */
>
>	use something like
>
>		#include <math.h>
>
>		if(fabs(a - b) <= epsilon * a)
>
>	for some suitably-chosen epsilon.
>
>	References: Knuth Sec. 4.2.2 pp. 217-8.

As stated, this is dangerous.  Perhaps the FAQ needs revision.

Knuth is careful to put absolute value signs on both sides.
For once, he is not careful to consider the case that a is
zero.  A safer test is of the form

    | a - b | / sqrt( a^2 + b^2 + delta ) < epsilon

or (equvalently, but in decently-efficient C):

    ( t = a - b )*t < esquared * ( a*a + b*b  + delta )

The choice of esquared == delta == 1e-20  gives this a
colloquial English meaning of 

    "a and b agree to about 10 significant digits"

which is a reasonable version of "are approximately equal"
for doubles.


Carlie J. Coats, Jr.              coats@ncsc.org    *or*    xcc@hpcc.epa.gov
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