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@xxxxxxxxxxxxxx> Reviewed-by: Ahmad Fatoum <a.fatoum@xxxxxxxxxxxxxx> > --- > 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@xxxxxxxxx> > + * > + * 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@xxxxxxxxx> > + * Copyright (C) 2019 Trent Piepho <tpiepho@xxxxxxxxx> > + * > + * 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; > +} > -- Pengutronix e.K. | | Steuerwalder Str. 21 | http://www.pengutronix.de/ | 31137 Hildesheim, Germany | Phone: +49-5121-206917-0 | Amtsgericht Hildesheim, HRA 2686 | Fax: +49-5121-206917-5555 | _______________________________________________ barebox mailing list barebox@xxxxxxxxxxxxxxxxxxx http://lists.infradead.org/mailman/listinfo/barebox
