License cleanup: add SPDX GPL-2.0 license identifier to files with no license
Many source files in the tree are missing licensing information, which
makes it harder for compliance tools to determine the correct license.
By default all files without license information are under the default
license of the kernel, which is GPL version 2.
Update the files which contain no license information with the 'GPL-2.0'
SPDX license identifier. The SPDX identifier is a legally binding
shorthand, which can be used instead of the full boiler plate text.
This patch is based on work done by Thomas Gleixner and Kate Stewart and
Philippe Ombredanne.
How this work was done:
Patches were generated and checked against linux-4.14-rc6 for a subset of
the use cases:
- file had no licensing information it it.
- file was a */uapi/* one with no licensing information in it,
- file was a */uapi/* one with existing licensing information,
Further patches will be generated in subsequent months to fix up cases
where non-standard license headers were used, and references to license
had to be inferred by heuristics based on keywords.
The analysis to determine which SPDX License Identifier to be applied to
a file was done in a spreadsheet of side by side results from of the
output of two independent scanners (ScanCode & Windriver) producing SPDX
tag:value files created by Philippe Ombredanne. Philippe prepared the
base worksheet, and did an initial spot review of a few 1000 files.
The 4.13 kernel was the starting point of the analysis with 60,537 files
assessed. Kate Stewart did a file by file comparison of the scanner
results in the spreadsheet to determine which SPDX license identifier(s)
to be applied to the file. She confirmed any determination that was not
immediately clear with lawyers working with the Linux Foundation.
Criteria used to select files for SPDX license identifier tagging was:
- Files considered eligible had to be source code files.
- Make and config files were included as candidates if they contained >5
lines of source
- File already had some variant of a license header in it (even if <5
lines).
All documentation files were explicitly excluded.
The following heuristics were used to determine which SPDX license
identifiers to apply.
- when both scanners couldn't find any license traces, file was
considered to have no license information in it, and the top level
COPYING file license applied.
For non */uapi/* files that summary was:
SPDX license identifier # files
---------------------------------------------------|-------
GPL-2.0 11139
and resulted in the first patch in this series.
If that file was a */uapi/* path one, it was "GPL-2.0 WITH
Linux-syscall-note" otherwise it was "GPL-2.0". Results of that was:
SPDX license identifier # files
---------------------------------------------------|-------
GPL-2.0 WITH Linux-syscall-note 930
and resulted in the second patch in this series.
- if a file had some form of licensing information in it, and was one
of the */uapi/* ones, it was denoted with the Linux-syscall-note if
any GPL family license was found in the file or had no licensing in
it (per prior point). Results summary:
SPDX license identifier # files
---------------------------------------------------|------
GPL-2.0 WITH Linux-syscall-note 270
GPL-2.0+ WITH Linux-syscall-note 169
((GPL-2.0 WITH Linux-syscall-note) OR BSD-2-Clause) 21
((GPL-2.0 WITH Linux-syscall-note) OR BSD-3-Clause) 17
LGPL-2.1+ WITH Linux-syscall-note 15
GPL-1.0+ WITH Linux-syscall-note 14
((GPL-2.0+ WITH Linux-syscall-note) OR BSD-3-Clause) 5
LGPL-2.0+ WITH Linux-syscall-note 4
LGPL-2.1 WITH Linux-syscall-note 3
((GPL-2.0 WITH Linux-syscall-note) OR MIT) 3
((GPL-2.0 WITH Linux-syscall-note) AND MIT) 1
and that resulted in the third patch in this series.
- when the two scanners agreed on the detected license(s), that became
the concluded license(s).
- when there was disagreement between the two scanners (one detected a
license but the other didn't, or they both detected different
licenses) a manual inspection of the file occurred.
- In most cases a manual inspection of the information in the file
resulted in a clear resolution of the license that should apply (and
which scanner probably needed to revisit its heuristics).
- When it was not immediately clear, the license identifier was
confirmed with lawyers working with the Linux Foundation.
- If there was any question as to the appropriate license identifier,
the file was flagged for further research and to be revisited later
in time.
In total, over 70 hours of logged manual review was done on the
spreadsheet to determine the SPDX license identifiers to apply to the
source files by Kate, Philippe, Thomas and, in some cases, confirmation
by lawyers working with the Linux Foundation.
Kate also obtained a third independent scan of the 4.13 code base from
FOSSology, and compared selected files where the other two scanners
disagreed against that SPDX file, to see if there was new insights. The
Windriver scanner is based on an older version of FOSSology in part, so
they are related.
Thomas did random spot checks in about 500 files from the spreadsheets
for the uapi headers and agreed with SPDX license identifier in the
files he inspected. For the non-uapi files Thomas did random spot checks
in about 15000 files.
In initial set of patches against 4.14-rc6, 3 files were found to have
copy/paste license identifier errors, and have been fixed to reflect the
correct identifier.
Additionally Philippe spent 10 hours this week doing a detailed manual
inspection and review of the 12,461 patched files from the initial patch
version early this week with:
- a full scancode scan run, collecting the matched texts, detected
license ids and scores
- reviewing anything where there was a license detected (about 500+
files) to ensure that the applied SPDX license was correct
- reviewing anything where there was no detection but the patch license
was not GPL-2.0 WITH Linux-syscall-note to ensure that the applied
SPDX license was correct
This produced a worksheet with 20 files needing minor correction. This
worksheet was then exported into 3 different .csv files for the
different types of files to be modified.
These .csv files were then reviewed by Greg. Thomas wrote a script to
parse the csv files and add the proper SPDX tag to the file, in the
format that the file expected. This script was further refined by Greg
based on the output to detect more types of files automatically and to
distinguish between header and source .c files (which need different
comment types.) Finally Greg ran the script using the .csv files to
generate the patches.
Reviewed-by: Kate Stewart <kstewart@linuxfoundation.org>
Reviewed-by: Philippe Ombredanne <pombredanne@nexb.com>
Reviewed-by: Thomas Gleixner <tglx@linutronix.de>
Signed-off-by: Greg Kroah-Hartman <gregkh@linuxfoundation.org>
2017-11-01 14:07:57 +00:00
|
|
|
// SPDX-License-Identifier: GPL-2.0
|
2009-06-11 13:51:15 +00:00
|
|
|
/*
|
|
|
|
|
* rational fractions
|
|
|
|
|
*
|
2012-05-16 09:41:19 +00:00
|
|
|
* Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
|
lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
|
|
|
* Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
|
2009-06-11 13:51:15 +00:00
|
|
|
*
|
|
|
|
|
* helper functions when coping with rational numbers
|
|
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
#include <linux/rational.h>
|
2011-11-17 02:29:17 +00:00
|
|
|
#include <linux/compiler.h>
|
|
|
|
|
#include <linux/export.h>
|
lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
|
|
|
#include <linux/kernel.h>
|
2009-06-11 13:51:15 +00:00
|
|
|
|
|
|
|
|
/*
|
|
|
|
|
* 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:
|
2020-08-12 01:34:50 +00:00
|
|
|
* https://en.wikipedia.org/wiki/Continued_fraction
|
2009-06-11 13:51:15 +00:00
|
|
|
*/
|
|
|
|
|
|
|
|
|
|
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)
|
|
|
|
|
{
|
lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
|
|
|
/* 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;
|
2009-06-11 13:51:15 +00:00
|
|
|
n = given_numerator;
|
|
|
|
|
d = given_denominator;
|
|
|
|
|
n0 = d1 = 0;
|
|
|
|
|
n1 = d0 = 1;
|
lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
|
|
|
|
2009-06-11 13:51:15 +00:00
|
|
|
for (;;) {
|
lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
|
|
|
unsigned long dp, a;
|
|
|
|
|
|
2009-06-11 13:51:15 +00:00
|
|
|
if (d == 0)
|
|
|
|
|
break;
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lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
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/* Find next term in continued fraction, 'a', via
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* Euclidean algorithm.
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*/
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dp = d;
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2009-06-11 13:51:15 +00:00
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a = n / d;
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d = n % d;
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lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
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n = dp;
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/* Calculate the current rational approximation (aka
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* convergent), n2/d2, using the term just found and
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* the two prior approximations.
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*/
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n2 = n0 + a * n1;
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d2 = d0 + a * d1;
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/* If the current convergent exceeds the maxes, then
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* return either the previous convergent or the
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* largest semi-convergent, the final term of which is
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* found below as 't'.
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*/
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if ((n2 > max_numerator) || (d2 > max_denominator)) {
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unsigned long t = min((max_numerator - n0) / n1,
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(max_denominator - d0) / d1);
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/* This tests if the semi-convergent is closer
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* than the previous convergent.
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*/
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if (2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
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n1 = n0 + t * n1;
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d1 = d0 + t * d1;
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}
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break;
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}
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2009-06-11 13:51:15 +00:00
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n0 = n1;
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lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
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n1 = n2;
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2009-06-11 13:51:15 +00:00
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d0 = d1;
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lib/math/rational.c: fix possible incorrect result from rational fractions helper
In some cases the previous algorithm would not return the closest
approximation. This would happen when a semi-convergent was the
closest, as the previous algorithm would only consider convergents.
As an example, consider an initial value of 5/4, and trying to find the
closest approximation with a maximum of 4 for numerator and denominator.
The previous algorithm would return 1/1 as the closest approximation,
while this version will return the correct answer of 4/3.
To do this, the main loop performs effectively the same operations as it
did before. It must now keep track of the last three approximations,
n2/d2 .. n0/d0, while before it only needed the last two.
If an exact answer is not found, the algorithm will now calculate the
best semi-convergent term, t, which is a single expression with two
divisions:
min((max_numerator - n0) / n1, (max_denominator - d0) / d1)
This will be used if it is better than previous convergent. The test
for this is generally a simple comparison, 2*t > a. But in an edge
case, where the convergent's final term is even and the best allowable
semi-convergent has a final term of exactly half the convergent's final
term, the more complex comparison (d0*dp > d1*d) is used.
I also wrote some comments explaining the code. While one still needs
to look up the math elsewhere, they should help a lot to follow how the
code relates to that math.
This routine is used in two places in the video4linux code, but in those
cases it is only used to reduce a fraction to lowest terms, which the
existing code will do correctly. This could be done more efficiently
with a different library routine but it would still be the Euclidean
alogrithm at its heart. So no change.
The remain users are places where a fractional PLL divider is
programmed. What would happen is something asked for a clock of X MHz
but instead gets Y MHz, where Y is close to X but not exactly due to the
hardware limitations. After this change they might, in some cases, get
Y' MHz, where Y' is a little closer to X then Y was.
Users like this are: Three UARTs, in 8250_mid, 8250_lpss, and imx. One
GPU in vp4_hdmi. And three clock drivers, clk-cdce706, clk-si5351, and
clk-fractional-divider. The last is a generic clock driver and so would
have more users referenced via device tree entries.
I think there's a bug in that one, it's limiting an N bit field that is
offset-by-1 to the range 0 .. (1<<N)-2, when it should be (1<<N)-1 as
the upper limit.
I have an IMX system, one of the UARTs using this, so I can provide a
real example. If I request a custom baud rate of 1499978, the driver
will program the PLL to produce a baud rate of 1500000. After this
change, the fractional divider in the UART is programmed to a ratio of
65535/65536, which produces a baud rate of 1499977.0625. Closer to the
requested value.
Link: http://lkml.kernel.org/r/20190330205855.19396-1-tpiepho@gmail.com
Signed-off-by: Trent Piepho <tpiepho@gmail.com>
Cc: Oskar Schirmer <oskar@scara.com>
Signed-off-by: Andrew Morton <akpm@linux-foundation.org>
Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2019-12-05 00:51:57 +00:00
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d1 = d2;
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2009-06-11 13:51:15 +00:00
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}
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*best_numerator = n1;
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*best_denominator = d1;
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}
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EXPORT_SYMBOL(rational_best_approximation);
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