<linux@horizon.com> wrote:
This is an extremely well-known technique. You can see a similar version that
uses a multiply for the last few steps at
http://graphics.stanford.edu/~seander/bithacks.html#CountBitsSetParallel whch
refers to "Software Optimization Guide for AMD Athlon 64 and Opteron
Processors"
http://www.amd.com/us-en/assets/content_type/white_papers_and_tech_docs/25112.PDF
It's section 8.6, "Efficient Implementation of Population-Count Function in
32-bit Mode", pages 179-180.
It uses the name that I am more familiar with, "popcount" (population count),
although "Hamming weight" also makes sense.
Anyway, the proof of correctness proceeds as follows:
b = a - ((a >> 1) & 0x55555555);
c = (b & 0x33333333) + ((b >> 2) & 0x33333333);
d = (c + (c >> 4)) & 0x0f0f0f0f;
#if SLOW_MULTIPLY
e = d + (d >> 8)
f = e + (e >> 16);
return f & 63;
#else
/* Useful if multiply takes at most 4 cycles */
return (d * 0x01010101) >> 24;
#endif
The input value a can be thought of as 32 1-bit fields each holding their own
hamming weight. Now look at it as 16 2-bit fields. Each 2-bit field a1..a0
has the value 2*a1 + a0. This can be converted into the hamming weight of the
2-bit field a1+a0 by subtracting a1.
That's what the (a >> 1) & mask subtraction does. Since there can be no
borrows, you can just do it all at once.
Enumerating the 4 possible cases:
0b00 = 0 -> 0 - 0 = 0
0b01 = 1 -> 1 - 0 = 1
0b10 = 2 -> 2 - 1 = 1
0b11 = 3 -> 3 - 1 = 2
The next step consists of breaking up b (made of 16 2-bir fields) into
even and odd halves and adding them into 4-bit fields. Since the largest
possible sum is 2+2 = 4, which will not fit into a 4-bit field, the 2-bit
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
"which will not fit into a 2-bit field"
fields have to be masked before they are added.
After this point, the masking can be delayed. Each 4-bit field holds a
population count from 0..4, taking at most 3 bits. These numbers can be added
without overflowing a 4-bit field, so we can compute c + (c >> 4), and only
then mask off the unwanted bits.
This produces d, a number of 4 8-bit fields, each in the range 0..8. From
this point, we can shift and add d multiple times without overflowing an 8-bit
field, and only do a final mask at the end.
The number to mask with has to be at least 63 (so that 32 on't be truncated),
but can also be 128 or 255. The x86 has a special encoding for signed
immediate byte values -128..127, so the value of 255 is slower. On other
processors, a special "sign extend byte" instruction might be faster.
On a processor with fast integer multiplies (Athlon but not P4), you can
reduce the final few serially dependent instructions to a single integer
multiply. Consider d to be 3 8-bit values d3, d2, d1 and d0, each in the
range 0..8. The multiply forms the partial products:
d3 d2 d1 d0
d3 d2 d1 d0
d3 d2 d1 d0
+ d3 d2 d1 d0
----------------------
e3 e2 e1 e0
Where e3 = d3 + d2 + d1 + d0. e2, e1 and e0 obviously cannot generate
any carries.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
By defining generic hweight*() routines
- hweight64() will be defined on all architectures
- hweight_long() will use architecture optimized hweight32() or hweight64()
I found two possible cleanups by these reasons.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
generic_{ffs,fls,fls64,hweight{64,32,16,8}}() were moved into
include/asm-generic/bitops.h. So all architectures don't use them.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
Now the only user who are using generic_ffs() is ntfs filesystem. This patch
isolates generic_ffs() as ntfs_ffs() for ntfs.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Cc: Anton Altaparmakov <aia21@cantab.net>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
The find_*_bit() routines are defined to work on a pointer to unsigned long.
But partial_page.bitmap is unsigned int and it is passed to find_*_bit() in
arch/ia64/ia32/sys_ia32.c. So the compiler will print warnings.
This patch changes to unsigned long instead.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Cc: "Luck, Tony" <tony.luck@intel.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
The test_bit() routines are defined to work on a pointer to unsigned long.
But thread_info.flags is __u32 (unsigned int) on sh and it is passed to flag
set/clear/test wrappers in include/linux/thread_info.h. So the compiler will
print warnings.
This patch changes to unsigned long instead.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Cc: Paul Mundt <lethal@linux-sh.org>
Cc: Kazumoto Kojima <kkojima@rr.iij4u.or.jp>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
Currently include/asm-generic/bitops.h is not referenced from anywhere. But
it will be the benefit of those who are trying to port Linux to another
architecture.
So update it by same manner
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
int minix_test_and_set_bit(int nr, volatile unsigned long *addr);
int minix_set_bit(int nr, volatile unsigned long *addr);
int minix_test_and_clear_bit(int nr, volatile unsigned long *addr);
int minix_test_bit(int nr, const volatile unsigned long *addr);
unsigned long minix_find_first_zero_bit(const unsigned long *addr,
unsigned long size);
In include/asm-generic/bitops/minix.h
and include/asm-generic/bitops/minix-le.h
This code largely copied from: include/asm-sparc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
int ext2_set_bit_atomic(int nr, volatile unsigned long *addr);
int ext2_clear_bit_atomic(int nr, volatile unsigned long *addr);
In include/asm-generic/bitops/ext2-atomic.h
This code largely copied from: include/asm-sparc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
int ext2_set_bit(int nr, volatile unsigned long *addr);
int ext2_clear_bit(int nr, volatile unsigned long *addr);
int ext2_test_bit(int nr, const volatile unsigned long *addr);
unsigned long ext2_find_first_zero_bit(const unsigned long *addr,
unsigned long size);
unsinged long ext2_find_next_zero_bit(const unsigned long *addr,
unsigned long size);
In include/asm-generic/bitops/ext2-non-atomic.h
This code largely copied from:
include/asm-powerpc/bitops.h
include/asm-parisc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
Build fix for s390 declare __u32 and __u64.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
unsigned int hweight32(unsigned int w);
unsigned int hweight16(unsigned int w);
unsigned int hweight8(unsigned int w);
unsigned long hweight64(__u64 w);
In include/asm-generic/bitops/hweight.h
This code largely copied from: include/linux/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: int ffs(int
x);
In include/asm-generic/bitops/ffs.h
This code largely copied from: include/linux/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: int
sched_find_first_bit(const unsigned long *b);
In include/asm-generic/bitops/sched.h
This code largely copied from: include/asm-powerpc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
unsigned logn find_next_bit(const unsigned long *addr, unsigned long size,
unsigned long offset);
unsigned long find_next_zero_bit(const unsigned long *addr, unsigned long size,
unsigned long offset);
unsigned long find_first_zero_bit(const unsigned long *addr,
unsigned long size);
unsigned long find_first_bit(const unsigned long *addr, unsigned long size);
In include/asm-generic/bitops/find.h
This code largely copied from: arch/powerpc/lib/bitops.c
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: int
fls64(__u64 x);
In include/asm-generic/bitops/fls64.h
This code largely copied from: include/linux/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: int fls(int
x);
In include/asm-generic/bitops/fls.h
This code largely copied from: include/linux/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: unsigned long
ffz(unsigned long word);
In include/asm-generic/bitops/ffz.h
This code largely copied from: include/asm-parisc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalent of the function: unsigned long
__ffs(unsigned long word);
In include/asm-generic/bitops/__ffs.h
This code largely copied from: include/asm-sparc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
void __set_bit(int nr, volatile unsigned long *addr);
void __clear_bit(int nr, volatile unsigned long *addr);
void __change_bit(int nr, volatile unsigned long *addr);
int __test_and_set_bit(int nr, volatile unsigned long *addr);
int __test_and_clear_bit(int nr, volatile unsigned long *addr);
int __test_and_change_bit(int nr, volatile unsigned long *addr);
int test_bit(int nr, const volatile unsigned long *addr);
In include/asm-generic/bitops/non-atomic.h
This code largely copied from: asm-powerpc/bitops.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
This patch introduces the C-language equivalents of the functions below:
void set_bit(int nr, volatile unsigned long *addr);
void clear_bit(int nr, volatile unsigned long *addr);
void change_bit(int nr, volatile unsigned long *addr);
int test_and_set_bit(int nr, volatile unsigned long *addr);
int test_and_clear_bit(int nr, volatile unsigned long *addr);
int test_and_change_bit(int nr, volatile unsigned long *addr);
In include/asm-generic/bitops/atomic.h
This code largely copied from:
include/asm-powerpc/bitops.h
include/asm-parisc/bitops.h
include/asm-parisc/atomic.h
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
Bitmap functions for the minix filesystem and the ext2 filesystem except
ext2_set_bit_atomic() and ext2_clear_bit_atomic() do not require the atomic
guarantees.
But these are defined by using atomic bit operations on several architectures.
(cris, frv, h8300, ia64, m32r, m68k, m68knommu, mips, s390, sh, sh64, sparc,
sparc64, v850, and xtensa)
This patch switches to non atomic bit operation.
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
remove unnecessary local_irq_restore() after cris_atomic_restore() in
test_and_set_bit().
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Cc: Mikael Starvik <starvik@axis.com>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
Noticed by Michael Tokarev
add missing ()-pair in __ffz() macro for parisc
Signed-off-by: Akinobu Mita <mita@miraclelinux.com>
Cc: Kyle McMartin <kyle@mcmartin.ca>
Signed-off-by: Andrew Morton <akpm@osdl.org>
Signed-off-by: Linus Torvalds <torvalds@osdl.org>
