linux/lib/int_sqrt.c

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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
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
/*
* Copyright (C) 2013 Davidlohr Bueso <davidlohr.bueso@hp.com>
*
* Based on the shift-and-subtract algorithm for computing integer
* square root from Guy L. Steele.
*/
#include <linux/kernel.h>
#include <linux/export.h>
lib/int_sqrt: optimize initial value compute The initial value (@m) compute is: m = 1UL << (BITS_PER_LONG - 2); while (m > x) m >>= 2; Which is a linear search for the highest even bit smaller or equal to @x We can implement this using a binary search using __fls() (or better when its hardware implemented). m = 1UL << (__fls(x) & ~1UL); Especially for small values of @x; which are the more common arguments when doing a CDF on idle times; the linear search is near to worst case, while the binary search of __fls() is a constant 6 (or 5 on 32bit) branches. cycles: branches: branch-misses: PRE: hot: 43.633557 +- 0.034373 45.333132 +- 0.002277 0.023529 +- 0.000681 cold: 207.438411 +- 0.125840 45.333132 +- 0.002277 6.976486 +- 0.004219 SOFTWARE FLS: hot: 29.576176 +- 0.028850 26.666730 +- 0.004511 0.019463 +- 0.000663 cold: 165.947136 +- 0.188406 26.666746 +- 0.004511 6.133897 +- 0.004386 HARDWARE FLS: hot: 24.720922 +- 0.025161 20.666784 +- 0.004509 0.020836 +- 0.000677 cold: 132.777197 +- 0.127471 20.666776 +- 0.004509 5.080285 +- 0.003874 Averages computed over all values <128k using a LFSR to generate order. Cold numbers have a LFSR based branch trace buffer 'confuser' ran between each int_sqrt() invocation. Link: http://lkml.kernel.org/r/20171020164644.936577234@infradead.org Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org> Suggested-by: Joe Perches <joe@perches.com> Acked-by: Will Deacon <will.deacon@arm.com> Acked-by: Linus Torvalds <torvalds@linux-foundation.org> Cc: Anshul Garg <aksgarg1989@gmail.com> Cc: Davidlohr Bueso <dave@stgolabs.net> Cc: David Miller <davem@davemloft.net> Cc: Ingo Molnar <mingo@kernel.org> Cc: Kees Cook <keescook@chromium.org> Cc: Matthew Wilcox <mawilcox@microsoft.com> Cc: Michael Davidson <md@google.com> Cc: Thomas Gleixner <tglx@linutronix.de> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2017-11-17 23:28:08 +00:00
#include <linux/bitops.h>
/**
* int_sqrt - computes the integer square root
* @x: integer of which to calculate the sqrt
*
* Computes: floor(sqrt(x))
*/
unsigned long int_sqrt(unsigned long x)
{
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
unsigned long b, m, y = 0;
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
if (x <= 1)
return x;
lib/int_sqrt: optimize initial value compute The initial value (@m) compute is: m = 1UL << (BITS_PER_LONG - 2); while (m > x) m >>= 2; Which is a linear search for the highest even bit smaller or equal to @x We can implement this using a binary search using __fls() (or better when its hardware implemented). m = 1UL << (__fls(x) & ~1UL); Especially for small values of @x; which are the more common arguments when doing a CDF on idle times; the linear search is near to worst case, while the binary search of __fls() is a constant 6 (or 5 on 32bit) branches. cycles: branches: branch-misses: PRE: hot: 43.633557 +- 0.034373 45.333132 +- 0.002277 0.023529 +- 0.000681 cold: 207.438411 +- 0.125840 45.333132 +- 0.002277 6.976486 +- 0.004219 SOFTWARE FLS: hot: 29.576176 +- 0.028850 26.666730 +- 0.004511 0.019463 +- 0.000663 cold: 165.947136 +- 0.188406 26.666746 +- 0.004511 6.133897 +- 0.004386 HARDWARE FLS: hot: 24.720922 +- 0.025161 20.666784 +- 0.004509 0.020836 +- 0.000677 cold: 132.777197 +- 0.127471 20.666776 +- 0.004509 5.080285 +- 0.003874 Averages computed over all values <128k using a LFSR to generate order. Cold numbers have a LFSR based branch trace buffer 'confuser' ran between each int_sqrt() invocation. Link: http://lkml.kernel.org/r/20171020164644.936577234@infradead.org Signed-off-by: Peter Zijlstra (Intel) <peterz@infradead.org> Suggested-by: Joe Perches <joe@perches.com> Acked-by: Will Deacon <will.deacon@arm.com> Acked-by: Linus Torvalds <torvalds@linux-foundation.org> Cc: Anshul Garg <aksgarg1989@gmail.com> Cc: Davidlohr Bueso <dave@stgolabs.net> Cc: David Miller <davem@davemloft.net> Cc: Ingo Molnar <mingo@kernel.org> Cc: Kees Cook <keescook@chromium.org> Cc: Matthew Wilcox <mawilcox@microsoft.com> Cc: Michael Davidson <md@google.com> Cc: Thomas Gleixner <tglx@linutronix.de> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2017-11-17 23:28:08 +00:00
m = 1UL << (__fls(x) & ~1UL);
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
while (m != 0) {
b = y + m;
y >>= 1;
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
if (x >= b) {
x -= b;
y += m;
}
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
m >>= 2;
}
lib/int_sqrt.c: optimize square root algorithm Optimize the current version of the shift-and-subtract (hardware) algorithm, described by John von Newmann[1] and Guy L Steele. Iterating 1,000,000 times, perf shows for the current version: Performance counter stats for './sqrt-curr' (10 runs): 27.170996 task-clock # 0.979 CPUs utilized ( +- 3.19% ) 3 context-switches # 0.103 K/sec ( +- 4.76% ) 0 cpu-migrations # 0.004 K/sec ( +-100.00% ) 104 page-faults # 0.004 M/sec ( +- 0.16% ) 64,921,199 cycles # 2.389 GHz ( +- 0.03% ) 28,967,789 stalled-cycles-frontend # 44.62% frontend cycles idle ( +- 0.18% ) <not supported> stalled-cycles-backend 104,502,623 instructions # 1.61 insns per cycle # 0.28 stalled cycles per insn ( +- 0.00% ) 34,088,368 branches # 1254.587 M/sec ( +- 0.00% ) 4,901 branch-misses # 0.01% of all branches ( +- 1.32% ) 0.027763015 seconds time elapsed ( +- 3.22% ) And for the new version: Performance counter stats for './sqrt-new' (10 runs): 0.496869 task-clock # 0.519 CPUs utilized ( +- 2.38% ) 0 context-switches # 0.000 K/sec 0 cpu-migrations # 0.403 K/sec ( +-100.00% ) 104 page-faults # 0.209 M/sec ( +- 0.15% ) 590,760 cycles # 1.189 GHz ( +- 2.35% ) 395,053 stalled-cycles-frontend # 66.87% frontend cycles idle ( +- 3.67% ) <not supported> stalled-cycles-backend 398,963 instructions # 0.68 insns per cycle # 0.99 stalled cycles per insn ( +- 0.39% ) 70,228 branches # 141.341 M/sec ( +- 0.36% ) 3,364 branch-misses # 4.79% of all branches ( +- 5.45% ) 0.000957440 seconds time elapsed ( +- 2.42% ) Furthermore, this saves space in instruction text: text data bss dec hex filename 111 0 0 111 6f lib/int_sqrt-baseline.o 89 0 0 89 59 lib/int_sqrt.o [1] http://en.wikipedia.org/wiki/First_Draft_of_a_Report_on_the_EDVAC Signed-off-by: Davidlohr Bueso <davidlohr.bueso@hp.com> Reviewed-by: Jonathan Gonzalez <jgonzlez@linets.cl> Tested-by: Jonathan Gonzalez <jgonzlez@linets.cl> Signed-off-by: Andrew Morton <akpm@linux-foundation.org> Signed-off-by: Linus Torvalds <torvalds@linux-foundation.org>
2013-04-29 23:18:09 +00:00
return y;
}
EXPORT_SYMBOL(int_sqrt);
#if BITS_PER_LONG < 64
/**
* int_sqrt64 - strongly typed int_sqrt function when minimum 64 bit input
* is expected.
* @x: 64bit integer of which to calculate the sqrt
*/
u32 int_sqrt64(u64 x)
{
u64 b, m, y = 0;
if (x <= ULONG_MAX)
return int_sqrt((unsigned long) x);
m = 1ULL << (fls64(x) & ~1ULL);
while (m != 0) {
b = y + m;
y >>= 1;
if (x >= b) {
x -= b;
y += m;
}
m >>= 2;
}
return y;
}
EXPORT_SYMBOL(int_sqrt64);
#endif