[PATCHv6 01/26] lib: rational: copy the rational fraction lib routines from Linux

Tero Kristo
2021-06-11T08:46:01Z

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 <t-kristo@ti.com>
Reviewed-by: Tom Rini <trini@konsulko.com>
Signed-off-by: Tero Kristo <kristo@kernel.org>
---
include/linux/rational.h | 20 ++++++++
lib/Kconfig | 7 +++
lib/Makefile | 2 +
lib/rational.c | 99 ++++++++++++++++++++++++++++++++++++++++
4 files changed, 128 insertions(+)
create mode 100644 include/linux/rational.h
create mode 100644 lib/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@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/Kconfig b/lib/Kconfig
index 15019d2c65..ad0cd52edd 100644
--- a/lib/Kconfig
+++ b/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
diff --git a/lib/Makefile b/lib/Makefile
index b4795a62a0..881034f4ae 100644
--- a/lib/Makefile
+++ b/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/
diff --git a/lib/rational.c b/lib/rational.c
new file mode 100644
index 0000000000..316db3b590
--- /dev/null
+++ b/lib/rational.c
@@ -0,0 +1,99 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
+ * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
+ *
+ * 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;
+}
--
2.17.1