linux/lib/reciprocal_div.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: reciprocal_div: implement the improved algorithm on the paper mentioned The new added "reciprocal_value_adv" implements the advanced version of the algorithm described in Figure 4.2 of the paper except when "divisor > (1U << 31)" whose ceil(log2(d)) result will be 32 which then requires u128 divide on host. The exception case could be easily handled before calling "reciprocal_value_adv". The advanced version requires more complex calculation to get the reciprocal multiplier and other control variables, but then could reduce the required emulation operations. It makes no sense to use this advanced version for host divide emulation, those extra complexities for calculating multiplier etc could completely waive our saving on emulation operations. However, it makes sense to use it for JIT divide code generation (for example eBPF JIT backends) for which we are willing to trade performance of JITed code with that of host. As shown by the following pseudo code, the required emulation operations could go down from 6 (the basic version) to 3 or 4. To use the result of "reciprocal_value_adv", suppose we want to calculate n/d, the C-style pseudo code will be the following, it could be easily changed to real code generation for other JIT targets. struct reciprocal_value_adv rvalue; u8 pre_shift, exp; // handle exception case. if (d >= (1U << 31)) { result = n >= d; return; } rvalue = reciprocal_value_adv(d, 32) exp = rvalue.exp; if (rvalue.is_wide_m && !(d & 1)) { // floor(log2(d & (2^32 -d))) pre_shift = fls(d & -d) - 1; rvalue = reciprocal_value_adv(d >> pre_shift, 32 - pre_shift); } else { pre_shift = 0; } // code generation starts. if (imm == 1U << exp) { result = n >> exp; } else if (rvalue.is_wide_m) { // pre_shift must be zero when reached here. t = (n * rvalue.m) >> 32; result = n - t; result >>= 1; result += t; result >>= rvalue.sh - 1; } else { if (pre_shift) result = n >> pre_shift; result = ((u64)result * rvalue.m) >> 32; result >>= rvalue.sh; } Signed-off-by: Jiong Wang <jiong.wang@netronome.com> Reviewed-by: Jakub Kicinski <jakub.kicinski@netronome.com> Signed-off-by: Daniel Borkmann <daniel@iogearbox.net>
2018-07-06 22:13:18 +00:00
#include <linux/bug.h>
reciprocal_divide: update/correction of the algorithm Jakub Zawadzki noticed that some divisions by reciprocal_divide() were not correct [1][2], which he could also show with BPF code after divisions are transformed into reciprocal_value() for runtime invariance which can be passed to reciprocal_divide() later on; reverse in BPF dump ended up with a different, off-by-one K in some situations. This has been fixed by Eric Dumazet in commit aee636c4809fa5 ("bpf: do not use reciprocal divide"). This follow-up patch improves reciprocal_value() and reciprocal_divide() to work in all cases by using Granlund and Montgomery method, so that also future use is safe and without any non-obvious side-effects. Known problems with the old implementation were that division by 1 always returned 0 and some off-by-ones when the dividend and divisor where very large. This seemed to not be problematic with its current users, as far as we can tell. Eric Dumazet checked for the slab usage, we cannot surely say so in the case of flex_array. Still, in order to fix that, we propose an extension from the original implementation from commit 6a2d7a955d8d resp. [3][4], by using the algorithm proposed in "Division by Invariant Integers Using Multiplication" [5], Torbjörn Granlund and Peter L. Montgomery, that is, pseudocode for q = n/d where q, n, d is in u32 universe: 1) Initialization: int l = ceil(log_2 d) uword m' = floor((1<<32)*((1<<l)-d)/d)+1 int sh_1 = min(l,1) int sh_2 = max(l-1,0) 2) For q = n/d, all uword: uword t = (n*m')>>32 q = (t+((n-t)>>sh_1))>>sh_2 The assembler implementation from Agner Fog [6] also helped a lot while implementing. We have tested the implementation on x86_64, ppc64, i686, s390x; on x86_64/haswell we're still half the latency compared to normal divide. Joint work with Daniel Borkmann. [1] http://www.wireshark.org/~darkjames/reciprocal-buggy.c [2] http://www.wireshark.org/~darkjames/set-and-dump-filter-k-bug.c [3] https://gmplib.org/~tege/division-paper.pdf [4] http://homepage.cs.uiowa.edu/~jones/bcd/divide.html [5] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2556 [6] http://www.agner.org/optimize/asmlib.zip Reported-by: Jakub Zawadzki <darkjames-ws@darkjames.pl> Cc: Eric Dumazet <eric.dumazet@gmail.com> Cc: Austin S Hemmelgarn <ahferroin7@gmail.com> Cc: linux-kernel@vger.kernel.org Cc: Jesse Gross <jesse@nicira.com> Cc: Jamal Hadi Salim <jhs@mojatatu.com> Cc: Stephen Hemminger <stephen@networkplumber.org> Cc: Matt Mackall <mpm@selenic.com> Cc: Pekka Enberg <penberg@kernel.org> Cc: Christoph Lameter <cl@linux-foundation.org> Cc: Andy Gospodarek <andy@greyhouse.net> Cc: Veaceslav Falico <vfalico@redhat.com> Cc: Jay Vosburgh <fubar@us.ibm.com> Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl> Signed-off-by: Daniel Borkmann <dborkman@redhat.com> Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org> Signed-off-by: David S. Miller <davem@davemloft.net>
2014-01-22 01:29:41 +00:00
#include <linux/kernel.h>
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#include <asm/div64.h>
#include <linux/reciprocal_div.h>
sch_red: Adaptative RED AQM Adaptative RED AQM for linux, based on paper from Sally FLoyd, Ramakrishna Gummadi, and Scott Shenker, August 2001 : http://icir.org/floyd/papers/adaptiveRed.pdf Goal of Adaptative RED is to make max_p a dynamic value between 1% and 50% to reach the target average queue : (max_th - min_th) / 2 Every 500 ms: if (avg > target and max_p <= 0.5) increase max_p : max_p += alpha; else if (avg < target and max_p >= 0.01) decrease max_p : max_p *= beta; target :[min_th + 0.4*(min_th - max_th), min_th + 0.6*(min_th - max_th)]. alpha : min(0.01, max_p / 4) beta : 0.9 max_P is a Q0.32 fixed point number (unsigned, with 32 bits mantissa) Changes against our RED implementation are : max_p is no longer a negative power of two (1/(2^Plog)), but a Q0.32 fixed point number, to allow full range described in Adatative paper. To deliver a random number, we now use a reciprocal divide (thats really a multiply), but this operation is done once per marked/droped packet when in RED_BETWEEN_TRESH window, so added cost (compared to previous AND operation) is near zero. dump operation gives current max_p value in a new TCA_RED_MAX_P attribute. Example on a 10Mbit link : tc qdisc add dev $DEV parent 1:1 handle 10: est 1sec 8sec red \ limit 400000 min 30000 max 90000 avpkt 1000 \ burst 55 ecn adaptative bandwidth 10Mbit # tc -s -d qdisc show dev eth3 ... qdisc red 10: parent 1:1 limit 400000b min 30000b max 90000b ecn adaptative ewma 5 max_p=0.113335 Scell_log 15 Sent 50414282 bytes 34504 pkt (dropped 35, overlimits 1392 requeues 0) rate 9749Kbit 831pps backlog 72056b 16p requeues 0 marked 1357 early 35 pdrop 0 other 0 Signed-off-by: Eric Dumazet <eric.dumazet@gmail.com> Signed-off-by: David S. Miller <davem@davemloft.net>
2011-12-08 06:06:03 +00:00
#include <linux/export.h>
2006-12-13 08:34:27 +00:00
reciprocal_divide: update/correction of the algorithm Jakub Zawadzki noticed that some divisions by reciprocal_divide() were not correct [1][2], which he could also show with BPF code after divisions are transformed into reciprocal_value() for runtime invariance which can be passed to reciprocal_divide() later on; reverse in BPF dump ended up with a different, off-by-one K in some situations. This has been fixed by Eric Dumazet in commit aee636c4809fa5 ("bpf: do not use reciprocal divide"). This follow-up patch improves reciprocal_value() and reciprocal_divide() to work in all cases by using Granlund and Montgomery method, so that also future use is safe and without any non-obvious side-effects. Known problems with the old implementation were that division by 1 always returned 0 and some off-by-ones when the dividend and divisor where very large. This seemed to not be problematic with its current users, as far as we can tell. Eric Dumazet checked for the slab usage, we cannot surely say so in the case of flex_array. Still, in order to fix that, we propose an extension from the original implementation from commit 6a2d7a955d8d resp. [3][4], by using the algorithm proposed in "Division by Invariant Integers Using Multiplication" [5], Torbjörn Granlund and Peter L. Montgomery, that is, pseudocode for q = n/d where q, n, d is in u32 universe: 1) Initialization: int l = ceil(log_2 d) uword m' = floor((1<<32)*((1<<l)-d)/d)+1 int sh_1 = min(l,1) int sh_2 = max(l-1,0) 2) For q = n/d, all uword: uword t = (n*m')>>32 q = (t+((n-t)>>sh_1))>>sh_2 The assembler implementation from Agner Fog [6] also helped a lot while implementing. We have tested the implementation on x86_64, ppc64, i686, s390x; on x86_64/haswell we're still half the latency compared to normal divide. Joint work with Daniel Borkmann. [1] http://www.wireshark.org/~darkjames/reciprocal-buggy.c [2] http://www.wireshark.org/~darkjames/set-and-dump-filter-k-bug.c [3] https://gmplib.org/~tege/division-paper.pdf [4] http://homepage.cs.uiowa.edu/~jones/bcd/divide.html [5] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2556 [6] http://www.agner.org/optimize/asmlib.zip Reported-by: Jakub Zawadzki <darkjames-ws@darkjames.pl> Cc: Eric Dumazet <eric.dumazet@gmail.com> Cc: Austin S Hemmelgarn <ahferroin7@gmail.com> Cc: linux-kernel@vger.kernel.org Cc: Jesse Gross <jesse@nicira.com> Cc: Jamal Hadi Salim <jhs@mojatatu.com> Cc: Stephen Hemminger <stephen@networkplumber.org> Cc: Matt Mackall <mpm@selenic.com> Cc: Pekka Enberg <penberg@kernel.org> Cc: Christoph Lameter <cl@linux-foundation.org> Cc: Andy Gospodarek <andy@greyhouse.net> Cc: Veaceslav Falico <vfalico@redhat.com> Cc: Jay Vosburgh <fubar@us.ibm.com> Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl> Signed-off-by: Daniel Borkmann <dborkman@redhat.com> Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org> Signed-off-by: David S. Miller <davem@davemloft.net>
2014-01-22 01:29:41 +00:00
/*
* For a description of the algorithm please have a look at
* include/linux/reciprocal_div.h
*/
struct reciprocal_value reciprocal_value(u32 d)
2006-12-13 08:34:27 +00:00
{
reciprocal_divide: update/correction of the algorithm Jakub Zawadzki noticed that some divisions by reciprocal_divide() were not correct [1][2], which he could also show with BPF code after divisions are transformed into reciprocal_value() for runtime invariance which can be passed to reciprocal_divide() later on; reverse in BPF dump ended up with a different, off-by-one K in some situations. This has been fixed by Eric Dumazet in commit aee636c4809fa5 ("bpf: do not use reciprocal divide"). This follow-up patch improves reciprocal_value() and reciprocal_divide() to work in all cases by using Granlund and Montgomery method, so that also future use is safe and without any non-obvious side-effects. Known problems with the old implementation were that division by 1 always returned 0 and some off-by-ones when the dividend and divisor where very large. This seemed to not be problematic with its current users, as far as we can tell. Eric Dumazet checked for the slab usage, we cannot surely say so in the case of flex_array. Still, in order to fix that, we propose an extension from the original implementation from commit 6a2d7a955d8d resp. [3][4], by using the algorithm proposed in "Division by Invariant Integers Using Multiplication" [5], Torbjörn Granlund and Peter L. Montgomery, that is, pseudocode for q = n/d where q, n, d is in u32 universe: 1) Initialization: int l = ceil(log_2 d) uword m' = floor((1<<32)*((1<<l)-d)/d)+1 int sh_1 = min(l,1) int sh_2 = max(l-1,0) 2) For q = n/d, all uword: uword t = (n*m')>>32 q = (t+((n-t)>>sh_1))>>sh_2 The assembler implementation from Agner Fog [6] also helped a lot while implementing. We have tested the implementation on x86_64, ppc64, i686, s390x; on x86_64/haswell we're still half the latency compared to normal divide. Joint work with Daniel Borkmann. [1] http://www.wireshark.org/~darkjames/reciprocal-buggy.c [2] http://www.wireshark.org/~darkjames/set-and-dump-filter-k-bug.c [3] https://gmplib.org/~tege/division-paper.pdf [4] http://homepage.cs.uiowa.edu/~jones/bcd/divide.html [5] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1.2556 [6] http://www.agner.org/optimize/asmlib.zip Reported-by: Jakub Zawadzki <darkjames-ws@darkjames.pl> Cc: Eric Dumazet <eric.dumazet@gmail.com> Cc: Austin S Hemmelgarn <ahferroin7@gmail.com> Cc: linux-kernel@vger.kernel.org Cc: Jesse Gross <jesse@nicira.com> Cc: Jamal Hadi Salim <jhs@mojatatu.com> Cc: Stephen Hemminger <stephen@networkplumber.org> Cc: Matt Mackall <mpm@selenic.com> Cc: Pekka Enberg <penberg@kernel.org> Cc: Christoph Lameter <cl@linux-foundation.org> Cc: Andy Gospodarek <andy@greyhouse.net> Cc: Veaceslav Falico <vfalico@redhat.com> Cc: Jay Vosburgh <fubar@us.ibm.com> Cc: Jakub Zawadzki <darkjames-ws@darkjames.pl> Signed-off-by: Daniel Borkmann <dborkman@redhat.com> Signed-off-by: Hannes Frederic Sowa <hannes@stressinduktion.org> Signed-off-by: David S. Miller <davem@davemloft.net>
2014-01-22 01:29:41 +00:00
struct reciprocal_value R;
u64 m;
int l;
l = fls(d - 1);
m = ((1ULL << 32) * ((1ULL << l) - d));
do_div(m, d);
++m;
R.m = (u32)m;
R.sh1 = min(l, 1);
R.sh2 = max(l - 1, 0);
return R;
2006-12-13 08:34:27 +00:00
}
sch_red: Adaptative RED AQM Adaptative RED AQM for linux, based on paper from Sally FLoyd, Ramakrishna Gummadi, and Scott Shenker, August 2001 : http://icir.org/floyd/papers/adaptiveRed.pdf Goal of Adaptative RED is to make max_p a dynamic value between 1% and 50% to reach the target average queue : (max_th - min_th) / 2 Every 500 ms: if (avg > target and max_p <= 0.5) increase max_p : max_p += alpha; else if (avg < target and max_p >= 0.01) decrease max_p : max_p *= beta; target :[min_th + 0.4*(min_th - max_th), min_th + 0.6*(min_th - max_th)]. alpha : min(0.01, max_p / 4) beta : 0.9 max_P is a Q0.32 fixed point number (unsigned, with 32 bits mantissa) Changes against our RED implementation are : max_p is no longer a negative power of two (1/(2^Plog)), but a Q0.32 fixed point number, to allow full range described in Adatative paper. To deliver a random number, we now use a reciprocal divide (thats really a multiply), but this operation is done once per marked/droped packet when in RED_BETWEEN_TRESH window, so added cost (compared to previous AND operation) is near zero. dump operation gives current max_p value in a new TCA_RED_MAX_P attribute. Example on a 10Mbit link : tc qdisc add dev $DEV parent 1:1 handle 10: est 1sec 8sec red \ limit 400000 min 30000 max 90000 avpkt 1000 \ burst 55 ecn adaptative bandwidth 10Mbit # tc -s -d qdisc show dev eth3 ... qdisc red 10: parent 1:1 limit 400000b min 30000b max 90000b ecn adaptative ewma 5 max_p=0.113335 Scell_log 15 Sent 50414282 bytes 34504 pkt (dropped 35, overlimits 1392 requeues 0) rate 9749Kbit 831pps backlog 72056b 16p requeues 0 marked 1357 early 35 pdrop 0 other 0 Signed-off-by: Eric Dumazet <eric.dumazet@gmail.com> Signed-off-by: David S. Miller <davem@davemloft.net>
2011-12-08 06:06:03 +00:00
EXPORT_SYMBOL(reciprocal_value);
lib: reciprocal_div: implement the improved algorithm on the paper mentioned The new added "reciprocal_value_adv" implements the advanced version of the algorithm described in Figure 4.2 of the paper except when "divisor > (1U << 31)" whose ceil(log2(d)) result will be 32 which then requires u128 divide on host. The exception case could be easily handled before calling "reciprocal_value_adv". The advanced version requires more complex calculation to get the reciprocal multiplier and other control variables, but then could reduce the required emulation operations. It makes no sense to use this advanced version for host divide emulation, those extra complexities for calculating multiplier etc could completely waive our saving on emulation operations. However, it makes sense to use it for JIT divide code generation (for example eBPF JIT backends) for which we are willing to trade performance of JITed code with that of host. As shown by the following pseudo code, the required emulation operations could go down from 6 (the basic version) to 3 or 4. To use the result of "reciprocal_value_adv", suppose we want to calculate n/d, the C-style pseudo code will be the following, it could be easily changed to real code generation for other JIT targets. struct reciprocal_value_adv rvalue; u8 pre_shift, exp; // handle exception case. if (d >= (1U << 31)) { result = n >= d; return; } rvalue = reciprocal_value_adv(d, 32) exp = rvalue.exp; if (rvalue.is_wide_m && !(d & 1)) { // floor(log2(d & (2^32 -d))) pre_shift = fls(d & -d) - 1; rvalue = reciprocal_value_adv(d >> pre_shift, 32 - pre_shift); } else { pre_shift = 0; } // code generation starts. if (imm == 1U << exp) { result = n >> exp; } else if (rvalue.is_wide_m) { // pre_shift must be zero when reached here. t = (n * rvalue.m) >> 32; result = n - t; result >>= 1; result += t; result >>= rvalue.sh - 1; } else { if (pre_shift) result = n >> pre_shift; result = ((u64)result * rvalue.m) >> 32; result >>= rvalue.sh; } Signed-off-by: Jiong Wang <jiong.wang@netronome.com> Reviewed-by: Jakub Kicinski <jakub.kicinski@netronome.com> Signed-off-by: Daniel Borkmann <daniel@iogearbox.net>
2018-07-06 22:13:18 +00:00
struct reciprocal_value_adv reciprocal_value_adv(u32 d, u8 prec)
{
struct reciprocal_value_adv R;
u32 l, post_shift;
u64 mhigh, mlow;
/* ceil(log2(d)) */
l = fls(d - 1);
/* NOTE: mlow/mhigh could overflow u64 when l == 32. This case needs to
* be handled before calling "reciprocal_value_adv", please see the
* comment at include/linux/reciprocal_div.h.
*/
WARN(l == 32,
"ceil(log2(0x%08x)) == 32, %s doesn't support such divisor",
d, __func__);
post_shift = l;
mlow = 1ULL << (32 + l);
do_div(mlow, d);
mhigh = (1ULL << (32 + l)) + (1ULL << (32 + l - prec));
do_div(mhigh, d);
for (; post_shift > 0; post_shift--) {
u64 lo = mlow >> 1, hi = mhigh >> 1;
if (lo >= hi)
break;
mlow = lo;
mhigh = hi;
}
R.m = (u32)mhigh;
R.sh = post_shift;
R.exp = l;
R.is_wide_m = mhigh > U32_MAX;
return R;
}
EXPORT_SYMBOL(reciprocal_value_adv);