Rational approximations

[CBFalconer]

Here is an amusing toy, which may be of especial interest to the
Forthians who use rational fractions to represent real numbers.
The handling of criterion may also be interesting to some.

/* Find best rational approximation to a double */
/* by C.B. Falconer, 2006-09-07. Released to public domain */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <float.h>
#include <limits.h>
#include <errno.h>

int main(int argc, char **argv)
{
int num, approx, bestnum, bestdenom;
int lastnum = 500;
double error, leasterr, value, criterion, tmp;
char *eptr;

value = 4 * atan(1.0);
if (argc 2) lastnum = strtol(argv[2], NULL, 10);
if (lastnum <= 0) lastnum = 500;
if (argc 1) {
tmp = strtod(argv[1], &eptr);
if ((0.0 >= tmp) || (tmp INT_MAX) || (ERANGE == errno)) {
puts("Invalid number, using PI");
}
else value = tmp;
}
criterion = 2 * value * DBL_EPSILON;
puts("Usage: ratvalue [number [maxnumerator]]\n"
"number defaults to PI, maxnumerator to 500");
printf("Rationa l approximation to %.*f\n", DBL_DIG, value);
for (leasterr = value, num = 1; num < lastnum; num++) {
approx = (int)(num / value + 0.5);
error = fabs((double)nu m / approx - value);
if (error < leasterr) {
bestnum = num;
bestdenom = approx;
leasterr = error;
printf("%8d / %-8d = %.*f with error %.*f\n",
bestnum, bestdenom,
DBL_DIG, (double)bestnum / bestdenom,
DBL_DIG, leasterr);
if (leasterr <= criterion) break;
}
}
return 0;
} /* main */

--
Chuck F (cbfalconer at maineline dot net)
Available for consulting/temporary embedded and systems.
<http://cbfalconer.home .att.net>

[CBFalconer]

dc*****@connx.c om wrote:

Keith Thompson wrote:

>dc*****@connx.c om writes:

>>Reminiscien t of:
http://www.acm.org/pubs/tog/Graphics...sv/ch1-4/rat.h
http://www.acm.org/pubs/tog/Graphics...sv/ch1-4/rat.c

What is?

C. B. Falconer's algorithm is like the graphics gems algorithm
(continued fraction to find best numerator/denomiator to fit a float).
The gem is somewhat more generalized. CB's algorithm is more compact.

Whew. I'll say it is (more compact). Gem?

--
"I was born lazy. I am no lazier now than I was forty years
ago, but that is because I reached the limit forty years ago.
You can't go beyond possibility." -- Mark Twain
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