/*
 * 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);
m'>log</a><a href='/cgit.cgi/linux/net-next.git/tree/sound/arm'>tree</a><a class='active' href='/cgit.cgi/linux/net-next.git/commit/sound/arm'>commit</a><a href='/cgit.cgi/linux/net-next.git/diff/sound/arm'>diff</a></td><td class='form'><form class='right' method='get' action='/cgit.cgi/linux/net-next.git/log/sound/arm'>
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<tr><th>author</th><td>Linus Torvalds &lt;torvalds@linux-foundation.org&gt;</td><td class='right'>2016-12-12 21:58:13 -0800</td></tr>
<tr><th>committer</th><td>Linus Torvalds &lt;torvalds@linux-foundation.org&gt;</td><td class='right'>2016-12-12 21:58:13 -0800</td></tr>
<tr><th>commit</th><td colspan='2' class='oid'><a href='/cgit.cgi/linux/net-next.git/commit/sound/arm?id=e7aa8c2eb11ba69b1b69099c3c7bd6be3087b0ba'>e7aa8c2eb11ba69b1b69099c3c7bd6be3087b0ba</a> (<a href='/cgit.cgi/linux/net-next.git/patch/sound/arm?id=e7aa8c2eb11ba69b1b69099c3c7bd6be3087b0ba'>patch</a>)</td></tr>
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<tr><th>parent</th><td colspan='2' class='oid'><a href='/cgit.cgi/linux/net-next.git/commit/sound/arm?id=e34bac726d27056081d0250c0e173e4b155aa340'>e34bac726d27056081d0250c0e173e4b155aa340</a> (<a href='/cgit.cgi/linux/net-next.git/diff/sound/arm?id2=e34bac726d27056081d0250c0e173e4b155aa340'>diff</a>)</td></tr><tr><th>parent</th><td colspan='2' class='oid'><a href='/cgit.cgi/linux/net-next.git/commit/sound/arm?id=868c97a846a73e937d835b09b8c885a69df50ec8'>868c97a846a73e937d835b09b8c885a69df50ec8</a> (<a href='/cgit.cgi/linux/net-next.git/diff/sound/arm?id2=868c97a846a73e937d835b09b8c885a69df50ec8'>diff</a>)</td></tr></table>
<div class='commit-subject'>Merge tag 'docs-4.10' of git://git.lwn.net/linux<span class='decoration'><a class='deco' href='/cgit.cgi/linux/net-next.git/commit/sound/arm?id=e7aa8c2eb11ba69b1b69099c3c7bd6be3087b0ba'>HEAD</a><a class='branch-deco' href='/cgit.cgi/linux/net-next.git/log/sound/arm'>master</a></span></div><div class='commit-msg'>Pull documentation update from Jonathan Corbet:
 "These are the documentation changes for 4.10.

  It's another busy cycle for the docs tree, as the sphinx conversion
  continues. Highlights include:

   - Further work on PDF output, which remains a bit of a pain but
     should be more solid now.

   - Five more DocBook template files converted to Sphinx. Only 27 to
     go... Lots of plain-text files have also been converted and
     integrated.

   - Images in binary formats have been replaced with more
     source-friendly versions.

   - Various bits of organizational work, including the renaming of
     various files discussed at the kernel summit.

   - New documentation for the device_link mechanism.

  ... and, of course, lots of typo fixes and small updates"

* tag 'docs-4.10' of git://git.lwn.net/linux: (193 commits)
  dma-buf: Extract dma-buf.rst
  Update Documentation/00-INDEX
  docs: 00-INDEX: document directories/files with no docs
  docs: 00-INDEX: remove non-existing entries
  docs: 00-INDEX: add missing entries for documentation files/dirs
  docs: 00-INDEX: consolidate process/ and admin-guide/ description
  scripts: add a script to check if Documentation/00-INDEX is sane
  Docs: change sh -&gt; awk in REPORTING-BUGS
  Documentation/core-api/device_link: Add initial documentation
  core-api: remove an unexpected unident
  ppc/idle: Add documentation for powersave=off
  Doc: Correct typo, "Introdution" =&gt; "Introduction"
  Documentation/atomic_ops.txt: convert to ReST markup
  Documentation/local_ops.txt: convert to ReST markup
  Documentation/assoc_array.txt: convert to ReST markup
  docs-rst: parse-headers.pl: cleanup the documentation
  docs-rst: fix media cleandocs target
  docs-rst: media/Makefile: reorganize the rules
  docs-rst: media: build SVG from graphviz files
  docs-rst: replace bayer.png by a SVG image
  ...
</div><div class='diffstat-header'><a href='/cgit.cgi/linux/net-next.git/diff/'>Diffstat</a> (limited to 'sound/arm')</div><table summary='diffstat' class='diffstat'>