// SPDX-License-Identifier: GPL-2.0
  /*
   * rational fractions
   *
   * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
   *
   * helper functions when coping with rational numbers
   */
  
  #include <linux/rational.h>
  #include <linux/compiler.h>
  #include <linux/export.h>
  
  /*
   * calculate best rational approximation for a given fraction
   * taking into account restricted register size, e.g. to find
   * appropriate values for a pll with 5 bit denominator and
   * 8 bit numerator register fields, trying to set up with a
   * frequency ratio of 3.1415, one would say:
   *
   * rational_best_approximation(31415, 10000,
   *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
   *
   * you may look at given_numerator as a fixed point number,
   * with the fractional part size described in given_denominator.
   *
   * for theoretical background, see:
   * http://en.wikipedia.org/wiki/Continued_fraction
   */
  
  void rational_best_approximation(
  	unsigned long given_numerator, unsigned long given_denominator,
  	unsigned long max_numerator, unsigned long max_denominator,
  	unsigned long *best_numerator, unsigned long *best_denominator)
  {
  	unsigned long n, d, n0, d0, n1, d1;
  	n = given_numerator;
  	d = given_denominator;
  	n0 = d1 = 0;
  	n1 = d0 = 1;
  	for (;;) {
  		unsigned long t, a;
  		if ((n1 > max_numerator) || (d1 > max_denominator)) {
  			n1 = n0;
  			d1 = d0;
  			break;
  		}
  		if (d == 0)
  			break;
  		t = d;
  		a = n / d;
  		d = n % d;
  		n = t;
  		t = n0 + a * n1;
  		n0 = n1;
  		n1 = t;
  		t = d0 + a * d1;
  		d0 = d1;
  		d1 = t;
  	}
  	*best_numerator = n1;
  	*best_denominator = d1;
  }
  
  EXPORT_SYMBOL(rational_best_approximation);