lib: rational: copy the rational fraction lib routines from Linux

Copy the best rational approximation calculation routines from Linux.
Typical usecase for these routines is to calculate the M/N divider
values for PLLs to reach a specific clock rate.

This is based on linux kernel commit:
"lib/math/rational.c: fix possible incorrect result from rational
fractions helper"
(sha1: 323dd2c3ed0641f49e89b4e420f9eef5d3d5a881)

Signed-off-by: Tero Kristo <[email protected]>
Reviewed-by: Tom Rini <[email protected]>
Signed-off-by: Tero Kristo <[email protected]>

include/linux/rational.h

@@ -0,0 +1,20 @@
+/* SPDX-License-Identifier: GPL-2.0 */
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[email protected]>
+ *
+ * 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 */

lib/Kconfig

@@ -674,6 +674,13 @@ config GENERATE_SMBIOS_TABLE
 	  See also SMBIOS_SYSINFO which allows SMBIOS values to be provided in
 	  the devicetree.
 
+config LIB_RATIONAL
+	bool "enable continued fraction calculation routines"
+
+config SPL_LIB_RATIONAL
+	bool "enable continued fraction calculation routines for SPL"
+	depends on SPL
+
 endmenu
 
 config ASN1_COMPILER

lib/Makefile

@@ -73,6 +73,8 @@ obj-$(CONFIG_$(SPL_)LZO) += lzo/
 obj-$(CONFIG_$(SPL_)LZMA) += lzma/
 obj-$(CONFIG_$(SPL_)LZ4) += lz4_wrapper.o
 
+obj-$(CONFIG_$(SPL_)LIB_RATIONAL) += rational.o
+
 obj-$(CONFIG_LIBAVB) += libavb/
 
 obj-$(CONFIG_$(SPL_TPL_)OF_LIBFDT) += libfdt/

lib/rational.c

@@ -0,0 +1,99 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <[email protected]>
+ * Copyright (C) 2019 Trent Piepho <[email protected]>
+ *
+ * helper functions when coping with rational numbers
+ */
+
+#include <linux/rational.h>
+#include <linux/compiler.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:
+ * 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)
+{
+	/* 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;
+}