[PATCH 08/14] Add rational_best_approximation()

[Ahmad Fatoum]

On 18.05.21 13:49, Sascha Hauer wrote:
> Import rational_best_approximation() from Linux. This is used by an
> upcoming update of the clk_fractional_divider code.
> 
> Signed-off-by: Sascha Hauer <s.hauer at pengutronix.de>

Reviewed-by: Ahmad Fatoum <a.fatoum at pengutronix.de>

> ---
>  include/linux/rational.h |  20 ++++++++
>  lib/math/Makefile        |   1 +
>  lib/math/rational.c      | 100 +++++++++++++++++++++++++++++++++++++++
>  3 files changed, 121 insertions(+)
>  create mode 100644 include/linux/rational.h
>  create mode 100644 lib/math/rational.c
> 
> diff --git a/include/linux/rational.h b/include/linux/rational.h
> new file mode 100644
> index 0000000000..33f5f5fc3e
> --- /dev/null
> +++ b/include/linux/rational.h
> @@ -0,0 +1,20 @@
> +/* SPDX-License-Identifier: GPL-2.0 */
> +/*
> + * rational fractions
> + *
> + * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar at scara.com>
> + *
> + * helper functions when coping with rational numbers,
> + * e.g. when calculating optimum numerator/denominator pairs for
> + * pll configuration taking into account restricted register size
> + */
> +
> +#ifndef _LINUX_RATIONAL_H
> +#define _LINUX_RATIONAL_H
> +
> +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);
> +
> +#endif /* _LINUX_RATIONAL_H */
> diff --git a/lib/math/Makefile b/lib/math/Makefile
> index c2c892dd55..756d7dd90d 100644
> --- a/lib/math/Makefile
> +++ b/lib/math/Makefile
> @@ -1,2 +1,3 @@
>  obj-y += div64.o
>  pbl-y += div64.o
> +obj-y += rational.o
> diff --git a/lib/math/rational.c b/lib/math/rational.c
> new file mode 100644
> index 0000000000..e5367e6a8a
> --- /dev/null
> +++ b/lib/math/rational.c
> @@ -0,0 +1,100 @@
> +// SPDX-License-Identifier: GPL-2.0
> +/*
> + * rational fractions
> + *
> + * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar at scara.com>
> + * Copyright (C) 2019 Trent Piepho <tpiepho at gmail.com>
> + *
> + * helper functions when coping with rational numbers
> + */
> +
> +#include <linux/rational.h>
> +#include <linux/compiler.h>
> +#include <linux/export.h>
> +#include <linux/kernel.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:
> + * https://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)
> +{
> +	/* n/d is the starting rational, which is continually
> +	 * decreased 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 = given_numerator;
> +	d = given_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 maxes, 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 = min((max_numerator - n0) / n1,
> +					      (max_denominator - d0) / d1);
> +
> +			/* This tests if the semi-convergent is closer
> +			 * than the previous convergent.
> +			 */
> +			if (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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