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Jiong Wang 06ae48269d 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>
2018-07-07 01:45:31 +02:00
arch net: Add a new socket option for a future transmit time. 2018-07-04 22:30:27 +09:00
block for-linus-20180629 2018-06-30 10:47:46 -07:00
certs certs/blacklist: fix const confusion 2018-06-26 09:43:03 -07:00
crypto Revert changes to convert to ->poll_mask() and aio IOCB_CMD_POLL 2018-06-28 10:40:47 -07:00
Documentation net: dsa: Add DT bindings for Vitesse VSC73xx switches 2018-07-04 11:30:01 +09:00
drivers cxgb4: Fix the condition to check if the card is T5 2018-07-05 20:14:29 +09:00
firmware kbuild: remove all dummy assignments to obj- 2017-11-18 11:46:06 +09:00
fs for-4.18-rc2-tag 2018-07-01 12:38:16 -07:00
include lib: reciprocal_div: implement the improved algorithm on the paper mentioned 2018-07-07 01:45:31 +02:00
init Kbuild fixes for v4.18 2018-06-30 13:05:30 -07:00
ipc rhashtable: split rhashtable.h 2018-06-22 13:43:27 +09:00
kernel Merge git://git.kernel.org/pub/scm/linux/kernel/git/davem/net 2018-07-02 11:18:28 -07:00
lib lib: reciprocal_div: implement the improved algorithm on the paper mentioned 2018-07-07 01:45:31 +02:00
LICENSES LICENSES: Add Linux-OpenIB license text 2018-04-27 16:41:53 -06:00
mm slub: fix failure when we delete and create a slab cache 2018-06-28 11:16:44 -07:00
net net: ipv6: listify ipv6_rcv() and ip6_rcv_finish() 2018-07-06 11:19:07 +09:00
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security selinux/stable-4.18 PR 20180629 2018-06-30 11:15:12 -07:00
sound ALSA: seq: Fix UBSAN warning at SNDRV_SEQ_IOCTL_QUERY_NEXT_CLIENT ioctl 2018-06-25 11:18:04 +02:00
tools bpftool: add bash completion for cgroup tree command 2018-07-07 01:38:38 +02:00
usr kbuild: rename built-in.o to built-in.a 2018-03-26 02:01:19 +09:00
virt KVM: arm64: Prevent KVM_COMPAT from being selected 2018-06-21 17:17:50 +01:00
.clang-format clang-format: add configuration file 2018-04-11 10:28:35 -07:00
.cocciconfig scripts: add Linux .cocciconfig for coccinelle 2016-07-22 12:13:39 +02:00
.get_maintainer.ignore Add hch to .get_maintainer.ignore 2015-08-21 14:30:10 -07:00
.gitattributes .gitattributes: set git diff driver for C source code files 2016-10-07 18:46:30 -07:00
.gitignore Kbuild updates for v4.17 (2nd) 2018-04-15 17:21:30 -07:00
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COPYING COPYING: use the new text with points to the license files 2018-03-23 12:41:45 -06:00
CREDITS MAINTAINERS/CREDITS: Drop METAG ARCHITECTURE 2018-03-05 16:34:24 +00:00
Kbuild Kbuild updates for v4.15 2017-11-17 17:45:29 -08:00
Kconfig kconfig: add basic helper macros to scripts/Kconfig.include 2018-05-29 03:31:19 +09:00
MAINTAINERS Merge ra.kernel.org:/pub/scm/linux/kernel/git/davem/net 2018-07-03 10:29:26 +09:00
Makefile Merge git://git.kernel.org/pub/scm/linux/kernel/git/davem/net 2018-07-02 11:18:28 -07:00
README Docs: Added a pointer to the formatted docs to README 2018-03-21 09:02:53 -06:00

Linux kernel
============

There are several guides for kernel developers and users. These guides can
be rendered in a number of formats, like HTML and PDF. Please read
Documentation/admin-guide/README.rst first.

In order to build the documentation, use ``make htmldocs`` or
``make pdfdocs``.  The formatted documentation can also be read online at:

    https://www.kernel.org/doc/html/latest/

There are various text files in the Documentation/ subdirectory,
several of them using the Restructured Text markup notation.
See Documentation/00-INDEX for a list of what is contained in each file.

Please read the Documentation/process/changes.rst file, as it contains the
requirements for building and running the kernel, and information about
the problems which may result by upgrading your kernel.