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> 10 3223
CBFalconer wrote:
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 */
Actually, doubles are already rational numbers. The denominator
is always power of 2.
Now the numbers they approximate, that's a different story...
- Logan
CBFalconer a écrit :
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 */
Excuse me Chuck but I think you invoke UB in the first iteration
when we have:
num = 1
value = PI
we have then:
1/PI = 0.31830 ....
(int) 0.31830 == ZERO
Then you do
num/approx and you have a division by zero...
jacob
CBFalconer wrote:
/* Find best rational approximation to a double */
One could try to argue they solve a slightly different problem,
but continued fractions provide optimal approximations, are
easy to code, and yield fascinating results, eg.
e = 2.71828... is {2;1,2,1,1,4,1, 1,6,1,1,8,1,1,1 0,...] in
continued fraction form, and
the Golden Ratio is [1;1,1,1,1,1,1,1 ,...].
(This c.f. form of Golden Ratio means it is the real number
hardest to approximate by a rational! The Golden Ratio
bus scheduling algorithm depends on that property IIRC,
though most comp-sci algorithms called "Golden Ratio
algorithm" don't.)
As is so often the case these days, Wikipedia seems to
offer a good discussion: http://en.wikipedia.org/wiki/Continued_fraction
value = 4 * atan(1.0);
Can't remember how to spell M_PI, eh? Neither can I, though
I usually just spell it prosaically: 3.141592635897
James Dow Allen
"James Dow Allen" <jd*********@ya hoo.comwrote:
CBFalconer wrote:
value = 4 * atan(1.0);
Can't remember how to spell M_PI, eh?
No, he can remember that M_PI is not in ISO C.
Richard
jacob navia wrote:
CBFalconer a écrit :
>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 */
Excuse me Chuck but I think you invoke UB in the first iteration
when we have:
num = 1
value = PI
we have then:
1/PI = 0.31830 ....
(int) 0.31830 == ZERO
Then you do
num/approx and you have a division by zero...
You are right. Sloppy of me. I added the line:
if (0 == (int)approx) continue;
after the "apprex = ..." line.
--
"If you want to post a followup via groups.google.c om, don't use
the broken "Reply" link at the bottom of the article. Click on
"show options" at the top of the article, then click on the
"Reply" at the bottom of the article headers." - Keith Thompson
More details at: <http://cfaj.freeshell. org/google/>
Also see <http://www.safalra.com/special/googlegroupsrep ly/>
["Followup-To:" header set to comp.programmin g.]
On 2006-09-08 07:43, James Dow Allen <jd*********@ya hoo.comwrote:
CBFalconer wrote:
> value = 4 * atan(1.0);
Can't remember how to spell M_PI, eh? Neither can I, though
I usually just spell it prosaically: 3.141592635897
I just found a spare "5". Would you like to buy it?
hp
--
_ | Peter J. Holzer | Wieso sollte man etwas erfinden was nicht
|_|_) | Sysadmin WSR | ist?
| | | hj*@hjp.at | Was sonst wäre der Sinn des Erfindens?
__/ | http://www.hjp.at/ | -- P. Einstein u. V. Gringmuth in desd This thread has been closed and replies have been disabled. Please start a new discussion. Similar topics |
by: Mike Meyer |
last post by:
PEP: XXX
Title: A rational number module for Python
Version: $Revision: 1.4 $
Last-Modified: $Date: 2003/09/22 04:51:50 $
Author: Mike Meyer <mwm@mired.org>
Status: Draft
Type: Staqndards
Content-Type: text/x-rst
Created: 16-Dec-2004
Python-Version: 2.5
|
by: Mike Meyer |
last post by:
This version includes the input from various and sundry people. Thanks
to everyone who contributed.
<mike
PEP: XXX
Title: A rational number module for Python
Version: $Revision: 1.4 $
Last-Modified: $Date: 2003/09/22 04:51:50 $
Author: Mike Meyer <mwm@mired.org>
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