96 lines
2.3 KiB
C
96 lines
2.3 KiB
C
/* SPDX-License-Identifier: GPL-2.0-only */
|
|
/*
|
|
* Helper functions for rational numbers.
|
|
*
|
|
* Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
|
|
* Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
|
|
*/
|
|
|
|
#include <commonlib/helpers.h>
|
|
#include <commonlib/rational.h>
|
|
#include <limits.h>
|
|
|
|
/*
|
|
* For theoretical background, see:
|
|
* https://en.wikipedia.org/wiki/Continued_fraction
|
|
*/
|
|
void rational_best_approximation(
|
|
unsigned long numerator, unsigned long denominator,
|
|
unsigned long max_numerator, unsigned long max_denominator,
|
|
unsigned long *best_numerator, unsigned long *best_denominator)
|
|
{
|
|
/*
|
|
* n/d is the starting rational, where both n and d will
|
|
* decrease in each iteration using the Euclidean algorithm.
|
|
*
|
|
* dp is the value of d from the prior iteration.
|
|
*
|
|
* n2/d2, n1/d1, and n0/d0 are our successively more accurate
|
|
* approximations of the rational. They are, respectively,
|
|
* the current, previous, and two prior iterations of it.
|
|
*
|
|
* a is current term of the continued fraction.
|
|
*/
|
|
unsigned long n, d, n0, d0, n1, d1, n2, d2;
|
|
n = numerator;
|
|
d = denominator;
|
|
n0 = d1 = 0;
|
|
n1 = d0 = 1;
|
|
|
|
for (;;) {
|
|
unsigned long dp, a;
|
|
|
|
if (d == 0)
|
|
break;
|
|
/*
|
|
* Find next term in continued fraction, 'a', via
|
|
* Euclidean algorithm.
|
|
*/
|
|
dp = d;
|
|
a = n / d;
|
|
d = n % d;
|
|
n = dp;
|
|
|
|
/*
|
|
* Calculate the current rational approximation (aka
|
|
* convergent), n2/d2, using the term just found and
|
|
* the two prior approximations.
|
|
*/
|
|
n2 = n0 + a * n1;
|
|
d2 = d0 + a * d1;
|
|
|
|
/*
|
|
* If the current convergent exceeds the maximum, then
|
|
* return either the previous convergent or the
|
|
* largest semi-convergent, the final term of which is
|
|
* found below as 't'.
|
|
*/
|
|
if ((n2 > max_numerator) || (d2 > max_denominator)) {
|
|
unsigned long t = ULONG_MAX;
|
|
|
|
if (d1)
|
|
t = (max_denominator - d0) / d1;
|
|
if (n1)
|
|
t = MIN(t, (max_numerator - n0) / n1);
|
|
|
|
/*
|
|
* This tests if the semi-convergent is closer than the previous
|
|
* convergent. If d1 is zero there is no previous convergent as
|
|
* this is the 1st iteration, so always choose the semi-convergent.
|
|
*/
|
|
if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
|
|
n1 = n0 + t * n1;
|
|
d1 = d0 + t * d1;
|
|
}
|
|
break;
|
|
}
|
|
n0 = n1;
|
|
n1 = n2;
|
|
d0 = d1;
|
|
d1 = d2;
|
|
}
|
|
|
|
*best_numerator = n1;
|
|
*best_denominator = d1;
|
|
}
|