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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
..
842 License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
fonts License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
lz4 lib/lz4: make arrays static const, reduces object code size 2017-10-03 17:54:25 -07:00
lzo License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
mpi treewide: kzalloc() -> kcalloc() 2018-06-12 16:19:22 -07:00
raid6 powerpc updates for 4.17 2018-04-07 12:08:19 -07:00
reed_solomon treewide: kmalloc() -> kmalloc_array() 2018-06-12 16:19:22 -07:00
xz lib/xz: Add fall-through comments to a switch statement 2017-10-12 15:10:12 +02:00
zlib_deflate
zlib_inflate lib/zlib_inflate/inftrees.c: fix potential buffer overflow 2017-05-08 17:15:12 -07:00
zstd lib: zstd: clean up Makefile for simpler composite object handling 2018-03-26 02:01:27 +09:00
.gitignore
argv_split.c treewide: kmalloc() -> kmalloc_array() 2018-06-12 16:19:22 -07:00
ashldi3.c move libgcc.h to include/linux 2017-12-01 13:09:40 -08:00
ashrdi3.c move libgcc.h to include/linux 2017-12-01 13:09:40 -08:00
asn1_decoder.c ASN.1: check for error from ASN1_OP_END__ACT actions 2017-12-08 15:13:27 +00:00
assoc_array.c lib/assoc_array: Remove smp_read_barrier_depends() 2017-12-04 10:52:56 -08:00
atomic64_test.c lib/atomic64_test.c: add a test that atomic64_inc_not_zero() returns an int 2017-07-14 15:05:13 -07:00
atomic64.c
audit.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
bcd.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
bch.c
bitmap.c lib/bitmap.c: micro-optimization for __bitmap_complement() 2018-06-07 17:34:39 -07:00
bitrev.c
bsearch.c lib/bsearch.c: micro-optimize pivot position calculation 2017-07-10 16:32:35 -07:00
btree.c btree: avoid variable-length allocations 2018-03-14 16:55:29 -07:00
bucket_locks.c mm: kvmalloc does not fallback to vmalloc for incompatible gfp flags 2018-06-07 17:34:38 -07:00
bug.c lib/bug.c: exclude non-BUG/WARN exceptions from report_bug() 2018-03-09 16:40:01 -08:00
build_OID_registry
bust_spinlocks.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
chacha20.c crypto: chacha20 - use rol32() macro from bitops.h 2018-01-12 23:03:01 +11:00
check_signature.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
checksum.c
clz_ctz.c
clz_tab.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
cmdline.c lib/cmdline.c: remove meaningless comment 2017-09-08 18:26:49 -07:00
cmpdi2.c move libgcc.h to include/linux 2017-12-01 13:09:40 -08:00
compat_audit.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
cordic.c
cpu_rmap.c
cpumask.c lib: optimize cpumask_next_and() 2018-02-06 18:32:44 -08:00
crc4.c docs: clean up and add rest of CRC functions to kernel-api.rst 2017-09-26 15:01:20 -06:00
crc7.c
crc8.c docs: clean up and add rest of CRC functions to kernel-api.rst 2017-09-26 15:01:20 -06:00
crc16.c
crc32.c docs: clean up and add rest of CRC functions to kernel-api.rst 2017-09-26 15:01:20 -06:00
crc32defs.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
crc32test.c lib: add module support to crc32 tests 2017-02-24 17:46:57 -08:00
crc-ccitt.c lib/crc-ccitt: Add CCITT-FALSE CRC16 variant 2018-01-08 10:08:33 +00:00
crc-itu-t.c
crc-t10dif.c
ctype.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
debug_info.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
debug_locks.c
debugobjects.c debugobjects: Avoid another unused variable warning 2018-03-14 20:20:01 +01:00
dec_and_lock.c atomic: Add irqsave variant of atomic_dec_and_lock() 2018-06-12 23:33:24 +02:00
decompress_bunzip2.c
decompress_inflate.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
decompress_unlz4.c lib/decompress_unlz4: change module to work with new LZ4 module version 2017-02-24 17:46:57 -08:00
decompress_unlzma.c
decompress_unlzo.c
decompress_unxz.c
decompress.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
devres.c devres: combine function devm_ioremap* 2018-03-15 18:08:55 +01:00
digsig.c lib/digsig: fix dereference of NULL user_key_payload 2017-10-12 17:16:40 +01:00
div64.c A relatively calm cycle for the docs tree again. 2017-11-13 08:25:06 -08:00
dump_stack.c printk: move dump stack related code to lib/dump_stack.c 2018-03-15 13:25:36 +01:00
dynamic_debug.c dynamic-debug-howto: fix optional/omitted ending line number to be LARGE instead of 0 2017-11-17 16:10:01 -08:00
dynamic_queue_limits.c Merge git://git.kernel.org/pub/scm/linux/kernel/git/davem/net-next 2017-11-15 11:56:19 -08:00
earlycpio.c
error-inject.c error-injection: Add injectable error types 2018-01-12 17:33:38 -08:00
errseq.c errseq: Always report a writeback error once 2018-04-27 08:51:26 -04:00
extable.c lib/extable.c: use bsearch() library function in search_extable() 2017-07-10 16:32:35 -07:00
fault-inject.c fault-inject: fix wrong should_fail() decision in task context 2017-08-10 15:54:06 -07:00
fdt_empty_tree.c
fdt_ro.c
fdt_rw.c
fdt_strerror.c
fdt_sw.c
fdt_wip.c
fdt.c
find_bit_benchmark.c lib/find_bit_benchmark.c: avoid soft lockup in test_find_first_bit() 2018-05-11 17:28:45 -07:00
find_bit.c lib: optimize cpumask_next_and() 2018-02-06 18:32:44 -08:00
flex_array.c
flex_proportions.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
gcd.c lib/gcd: add kernel-doc notation 2017-10-07 10:45:14 -06:00
gen_crc32table.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
genalloc.c lib/genalloc.c: make the avail variable an atomic_long_t 2017-11-17 16:10:02 -08:00
glob.c lib: add module support to glob tests 2017-02-24 17:46:57 -08:00
globtest.c lib: add module support to glob tests 2017-02-24 17:46:57 -08:00
hexdump.c lib/hexdump.c: return -EINVAL in case of error in hex2bin() 2017-09-08 18:26:49 -07:00
hweight.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
idr.c lib/idr.c: remove simple_ida_lock 2018-06-07 17:34:39 -07:00
inflate.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
int_sqrt.c lib: Add strongly typed 64bit int_sqrt 2018-02-04 10:17:21 +00:00
interval_tree_test.c treewide: kmalloc() -> kmalloc_array() 2018-06-12 16:19:22 -07:00
interval_tree.c
iomap_copy.c
iomap.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
iommu-helper.c iommu-helper: mark iommu_is_span_boundary as inline 2018-05-09 06:55:44 +02:00
ioremap.c mm/vmalloc: add interfaces to free unmapped page table 2018-03-22 17:07:01 -07:00
iov_iter.c Merge branch 'for-4.18/mcsafe' into libnvdimm-for-next 2018-06-08 15:16:44 -07:00
irq_poll.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
irq_regs.c
is_single_threaded.c sched/headers: Prepare to move 'init_task' and 'init_thread_union' from <linux/sched.h> to <linux/sched/task.h> 2017-03-02 08:42:38 +01:00
jedec_ddr_data.c
kasprintf.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
Kconfig Move all the dma-mapping code to kernel/dma 2018-06-20 16:30:01 +09:00
Kconfig.debug fault-injection: reorder config entries 2018-06-15 07:55:24 +09:00
Kconfig.kasan kasan: depend on CONFIG_SLUB_DEBUG 2018-06-28 11:16:44 -07:00
Kconfig.kgdb lib: update location of kgdb documentation 2017-05-16 08:44:22 -03:00
Kconfig.ubsan lib: add testing module for UBSAN 2018-04-11 10:28:35 -07:00
kfifo.c treewide: kmalloc() -> kmalloc_array() 2018-06-12 16:19:22 -07:00
klist.c
kobject_uevent.c netns: restrict uevents 2018-05-01 10:22:41 -04:00
kobject.c kobject: don't use WARN for registration failures 2018-04-23 13:14:55 +02:00
kstrtox.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
kstrtox.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
lcm.c
libcrc32c.c libcrc32c: Add crc32c_impl function 2018-03-26 15:09:38 +02:00
list_debug.c lib/list_debug.c: print unmangled addresses 2018-04-11 10:28:35 -07:00
list_sort.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
llist.c locking/atomics: COCCINELLE/treewide: Convert trivial ACCESS_ONCE() patterns to READ_ONCE()/WRITE_ONCE() 2017-10-25 11:01:08 +02:00
locking-selftest-hardirq.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-mutex.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-rlock-hardirq.h
locking-selftest-rlock-softirq.h
locking-selftest-rlock.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-rsem.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-rtmutex.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-softirq.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-spin-hardirq.h
locking-selftest-spin-softirq.h
locking-selftest-spin.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-wlock-hardirq.h
locking-selftest-wlock-softirq.h
locking-selftest-wlock.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest-wsem.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
locking-selftest.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
lockref.c lockref: Add lockref_put_not_zero 2018-04-12 09:41:19 -07:00
logic_pio.c lib: Add generic PIO mapping method 2018-03-21 17:18:34 -05:00
lru_cache.c treewide: kzalloc() -> kcalloc() 2018-06-12 16:19:22 -07:00
lshrdi3.c move libgcc.h to include/linux 2017-12-01 13:09:40 -08:00
Makefile Merge branch 'locking-urgent-for-linus' of git://git.kernel.org/pub/scm/linux/kernel/git/tip/tip 2018-06-24 19:36:16 +08:00
memory-notifier-error-inject.c
memweight.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
muldi3.c move libgcc.h to include/linux 2017-12-01 13:09:40 -08:00
net_utils.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
netdev-notifier-error-inject.c
nlattr.c netlink: Return extack message if attribute validation fails 2018-06-28 16:18:04 +09:00
nmi_backtrace.c lib/nmi_backtrace.c: fix kernel text address leak 2017-11-17 16:10:02 -08:00
nodemask.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
notifier-error-inject.c
notifier-error-inject.h License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
of-reconfig-notifier-error-inject.c
oid_registry.c 509: fix printing uninitialized stack memory when OID is empty 2017-12-08 15:13:28 +00:00
once.c Merge git://git.kernel.org/pub/scm/linux/kernel/git/davem/net 2017-11-04 09:26:51 +09:00
parman.c lib: Introduce priority array area manager 2017-02-03 16:35:42 -05:00
parser.c
pci_iomap.c PCI: Add SPDX GPL-2.0 when no license was specified 2018-01-26 11:45:16 -06:00
percpu_counter.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
percpu_ida.c lib/percpu_ida.c: don't do alloc from per-CPU list if there is none 2018-06-28 11:16:44 -07:00
percpu_test.c
percpu-refcount.c percpu_ref: Update doc to dissuade users from depending on internal RCU grace periods 2018-03-19 10:09:44 -07:00
plist.c sched/headers: Prepare for new header dependencies before moving code to <linux/sched/clock.h> 2017-03-02 08:42:27 +01:00
pm-notifier-error-inject.c
prime_numbers.c lib/prime_numbers: Suppress warn on kmalloc failure 2017-01-23 09:17:12 +01:00
radix-tree.c idr: fix invalid ptr dereference on item delete 2018-05-25 18:12:10 -07:00
random32.c treewide: Switch DEFINE_TIMER callbacks to struct timer_list * 2017-11-21 15:57:05 -08:00
ratelimit.c lib/ratelimit.c: use deferred printk() version 2017-10-03 17:54:26 -07:00
rational.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
rbtree_test.c treewide: kmalloc() -> kmalloc_array() 2018-06-12 16:19:22 -07:00
rbtree.c lib/rbtree,drm/mm: add rbtree_replace_node_cached() 2017-12-14 16:00:48 -08:00
reciprocal_div.c lib: reciprocal_div: implement the improved algorithm on the paper mentioned 2018-07-07 01:45:31 +02:00
refcount.c locking/refcounts: Implement refcount_dec_and_lock_irqsave() 2018-06-12 23:33:25 +02:00
rhashtable.c rhashtable: clean up dereference of ->future_tbl. 2018-06-22 13:43:28 +09:00
sbitmap.c treewide: kzalloc_node() -> kcalloc_node() 2018-06-12 16:19:22 -07:00
scatterlist.c for-linus-20180629 2018-06-30 10:47:46 -07:00
seq_buf.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
sg_pool.c
sg_split.c
sha1.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
sha256.c kernel/kexec_file.c: move purgatories sha256 to common code 2018-04-13 17:10:28 -07:00
show_mem.c lib/show_mem.c: teach show_mem to work with the given nodemask 2017-02-22 16:41:30 -08:00
siphash.c siphash: implement HalfSipHash1-3 for hash tables 2017-01-09 13:58:57 -05:00
smp_processor_id.c lib: do not use print_symbol() 2018-01-05 15:24:00 +01:00
sort.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
stackdepot.c lib/stackdepot.c: use a non-instrumented version of memcmp() 2018-02-06 18:32:44 -08:00
stmp_device.c
string_helpers.c mm: treewide: remove GFP_TEMPORARY allocation flag 2017-09-13 18:53:16 -07:00
string.c lib/strscpy: Shut up KASAN false-positives in strscpy() 2018-02-01 12:20:21 -08:00
strncpy_from_user.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
strnlen_user.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
syscall.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
test_bitmap.c lib/test_bitmap.c: fix bitmap optimisation tests to report errors correctly 2018-05-18 17:17:12 -07:00
test_bpf.c test_bpf: flag tests that cannot be jited on s390 2018-06-28 23:58:39 +02:00
test_debug_virtual.c lib: add test module for CONFIG_DEBUG_VIRTUAL 2017-09-08 18:26:49 -07:00
test_firmware.c treewide: Use array_size() in vzalloc() 2018-06-12 16:19:22 -07:00
test_hash.c
test_hexdump.c
test_kasan.c kasan: fix invalid-free test crashing the kernel 2018-04-11 10:28:32 -07:00
test_kmod.c treewide: Use array_size() in vzalloc() 2018-06-12 16:19:22 -07:00
test_list_sort.c lib/test: delete five error messages for failed memory allocations 2017-11-17 16:10:01 -08:00
test_module.c
test_overflow.c test_overflow: fix an IS_ERR() vs NULL bug 2018-06-12 16:19:22 -07:00
test_parman.c lib: fix spelling mistake: "actualy" -> "actually" 2017-02-26 11:03:38 -05:00
test_printf.c Revert "lib/test_printf.c: call wait_for_random_bytes() before plain %p tests" 2018-06-25 13:44:20 +02:00
test_rhashtable.c rhashtable: remove nulls_base and related code. 2018-06-22 13:43:27 +09:00
test_siphash.c siphash: implement HalfSipHash1-3 for hash tables 2017-01-09 13:58:57 -05:00
test_sort.c lib/test_sort.c: add module unload support 2018-02-06 18:32:45 -08:00
test_static_key_base.c
test_static_keys.c
test_string.c lib: add module support to string tests 2017-11-17 16:10:01 -08:00
test_sysctl.c test_sysctl: test against int proc_dointvec() array support 2017-07-12 16:26:00 -07:00
test_ubsan.c lib/test_ubsan.c: make test_ubsan_misaligned_access() static 2018-04-11 10:28:35 -07:00
test_user_copy.c treewide: simplify Kconfig dependencies for removed archs 2018-03-26 15:55:57 +02:00
test_uuid.c uuid: fix incorrect uuid_equal conversion in test_uuid_test 2017-07-21 09:38:30 +02:00
test-kstrtox.c
test-string_helpers.c
textsearch.c textsearch: fix kernel-doc warnings and add kernel-api section 2018-04-16 18:53:13 -04:00
timerqueue.c timerqueue: Document return values of timerqueue_add/del() 2017-12-29 23:13:10 +01:00
ts_bm.c
ts_fsm.c textsearch: fix typos in library helpers 2017-10-22 03:14:07 +01:00
ts_kmp.c textsearch: fix typos in library helpers 2017-10-22 03:14:07 +01:00
ubsan.c lib/ubsan: remove returns-nonnull-attribute checks 2018-02-06 18:32:46 -08:00
ubsan.h lib/ubsan: remove returns-nonnull-attribute checks 2018-02-06 18:32:46 -08:00
ucmpdi2.c Add notrace to lib/ucmpdi2.c 2018-04-23 16:39:35 +01:00
ucs2_string.c lib/ucs2_string.c: add MODULE_LICENSE() 2018-06-07 17:34:39 -07:00
usercopy.c Fix misannotated out-of-line _copy_to_user() 2017-12-11 09:35:11 -05:00
uuid.c Documentation: add UUID/GUID to kernel-api 2017-12-11 15:03:08 -07:00
vsprintf.c Printk changes for 4.18 2018-06-06 16:04:55 -07:00
win_minmax.c License cleanup: add SPDX GPL-2.0 license identifier to files with no license 2017-11-02 11:10:55 +01:00
xxhash.c lib: Add xxhash module 2017-08-15 09:02:07 -07:00