From: Tero Kristo t-kristo@ti.com
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; +}