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/* 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;
}
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