How many bits are '1' in a integer variable?

C

Cuthbert

Hi folks,

I am trying to find a more efficient way to count "How many bits are
'1' in a integer variable?".

I still have no idea to count the bits except using a loop and "if"
statements.
Could you know any other more efficient way?

Cuthbert

int main (void)
{
int var = 0xFF0F;
int i, count = 0;
int mask = 1;
for ( i = 0; i < sizeof(int)*8 ; i++ )
if ( mask<<i & var) count++ ;

printf("%d\n", count);

return 0;
}
 
T

T.M. Sommers

Cuthbert said:
Hi folks,

I am trying to find a more efficient way to count "How many bits are
'1' in a integer variable?".

I still have no idea to count the bits except using a loop and "if"
statements.
Could you know any other more efficient way?
Click to expand...

Break the int into bytes and use a lookup table.
 
F

Frederick Gotham

T.M. Sommers posted:
Break the int into bytes and use a lookup table.
Click to expand...


I'm sure there's a better way than that... perhaps even an expression
yielding a compile-time constant. Maybe something like:


#define UINT_BITS_SET(x)\
!!((x)&1U) + !!((x)&1U<<1) + !!((x)&1U<<2) + !!((x)&1U<<3)\
+ !!((x)&1U<<4) + !!((x)&1U<<5) + !!((x)&1U<<6) + !!((x)&1U<<7)\
+ !!((x)&1U<<8) + !!((x)&1U<<9) + !!((x)&1U<<10) + !!((x)&1U<<11)\
+ !!((x)&1U<<12) + !!((x)&1U<<13) + !!((x)&1U<<14) + !!((x)&1U<<15)\
+ !!((x)&1U<<16) + !!((x)&1U<<17) + !!((x)&1U<<18) + !!((x)&1U<<19)\
+ !!((x)&1U<<20)

I'm not sure if it's undefined behaviour to left shift an unsigned int by
more places than it has bits; if not, then you can simply go as high as you
want:

+ !!((x)&1U<<63548)

If it is however, then you could use the IMAX_BITS macro in conjunction
with the modulus and division operators to keep things safe.
 
A

Ancient_Hacker

Cuthbert said:
Hi folks,
Click to expand...
a bit simpler and therefore perhaps somewhat faster:

int main (void)
{
int var = 0xFF0F;
int i, count = 0;

for ( i = 0; i < sizeof(int)*8 ; i++ )
{ count += var & 1; var >>= 1; }

printf("%d\n", count);

return 0;
}

a byte lookup table might or might not be faster, depending on what
happens with the cache.
 
W

Walter Roberson

Please quote enough context so that people know what is being discussed.
In this case it is counting the number of 1 bits in an integer variable.
a bit simpler and therefore perhaps somewhat faster:
Click to expand...
int main (void)
{
int var = 0xFF0F;
int i, count = 0;
Click to expand...
for ( i = 0; i < sizeof(int)*8 ; i++ )
{ count += var & 1; var >>= 1; }
Click to expand...
printf("%d\n", count);

return 0;
}
Click to expand...

Why sizeof(int)*8 ?

It appears to me that you have assumed CHAR_BIT to be 8.
 
R

Richard Heathfield

Frederick Gotham said:
T.M. Sommers posted:



I'm sure there's a better way than that... perhaps even an expression
yielding a compile-time constant. Maybe something like:


#define UINT_BITS_SET(x)\
!!((x)&1U) + !!((x)&1U<<1) + !!((x)&1U<<2) + !!((x)&1U<<3)\
+ !!((x)&1U<<4) + !!((x)&1U<<5) + !!((x)&1U<<6) + !!((x)&1U<<7)\
+ !!((x)&1U<<8) + !!((x)&1U<<9) + !!((x)&1U<<10) + !!((x)&1U<<11)\
+ !!((x)&1U<<12) + !!((x)&1U<<13) + !!((x)&1U<<14) + !!((x)&1U<<15)\
+ !!((x)&1U<<16) + !!((x)&1U<<17) + !!((x)&1U<<18) + !!((x)&1U<<19)\
+ !!((x)&1U<<20)
Click to expand...

I'm not convinced that's a better way than:

unsigned int count_set_bits(unsigned long n)
{
unsigned int set_bits[] =
{
0, 1, 1, 2, 1, 2, 2, 3, 1, 2, 2, 3, 2, 3, 3, 4
};
unsigned int count = 0;
while(n > 0)
{
count += set_bits[n & 0xf];
n >>= 4;
}
return count;
}

Your solution doesn't appear to cope with integers wider than 21 bits, for a
start. Secondly, it doesn't cope with integers that are /fewer/ than 21
bits wide! Thirdly, it could conceivably be counting "padding bits", bits
that do not contribute to the value of the integer.
I'm not sure if it's undefined behaviour to left shift an unsigned int by
more places than it has bits; if not, then you can simply go as high as
you want:
Click to expand...

Quoth 3.3.7 of C90: "The integral promotions are performed on each of the
operands. The type of the result is that of the promoted left operand. If
the value of the right operand is negative or is greater than or equal to
the width in bits of the promoted left operand, the behavior is undefined."
 
P

pete

Cuthbert said:
Hi folks,

I am trying to find a more efficient way to count "How many bits are
'1' in a integer variable?".

I still have no idea to count the bits except using a loop and "if"
statements.
Could you know any other more efficient way?

Cuthbert

int main (void)
{
int var = 0xFF0F;
int i, count = 0;
int mask = 1;
for ( i = 0; i < sizeof(int)*8 ; i++ )
if ( mask<<i & var) count++ ;

printf("%d\n", count);

return 0;
}
Click to expand...

/* BEGIN new.c */

#include <stdio.h>

unsigned bit_count(unsigned n);

int main (void)
{
unsigned var = 0xFF0F;
unsigned count = bit_count(var);

printf("%u\n", count);
return 0;
}

unsigned bit_count(unsigned n)
{
unsigned count;

for (count = 0; n != 0; n &= n - 1) {
++count;
}
return count;
}

/* END new.c */
 
K

kondal

Cuthbert said:
Hi folks,

I am trying to find a more efficient way to count "How many bits are
'1' in a integer variable?".

I still have no idea to count the bits except using a loop and "if"
statements.
Could you know any other more efficient way?

Cuthbert

int main (void)
{
int var = 0xFF0F;
int i, count = 0;
int mask = 1;
for ( i = 0; i < sizeof(int)*8 ; i++ )
if ( mask<<i & var) count++ ;

printf("%d\n", count);

return 0;
}
Click to expand...

There is a faster program easy to remember and i.e x&=(x-1) and doesn't
require any storage requirements. Here is the program

int main(void)
{
x = 0xFF0F;
int n = 0;

while(x)
{
x &= (x-1)
n++;
}

printf("No of bits = %d\n", n);
}

The worst case for the loop would be when all the bits are set.
Actually for each iteration the statement x=x&(x-1) would remove one
bit. Just check it out manually.

There is even better and faster algorithm but difficult to remember.

#define MASK_01010101 (((unsigned int)(-1))/3)
#define MASK_00110011 (((unsigned int)(-1))/5)
#define MASK_00001111 (((unsigned int)(-1))/17)

int bitcount (unsigned int n)
{
n = (n & MASK_01010101) + ((n >> 1) & MASK_01010101) ;
n = (n & MASK_00110011) + ((n >> 2) & MASK_00110011) ;
n = (n & MASK_00001111) + ((n >> 4) & MASK_00001111) ;
return n % 255 ;
}

I got this algorithm from my old book, hard to remember (atleast for me)
 
J

jaysome

a bit simpler and therefore perhaps somewhat faster:

int main (void)
{
int var = 0xFF0F;
int i, count = 0;

for ( i = 0; i < sizeof(int)*8 ; i++ )
{ count += var & 1; var >>= 1; }

printf("%d\n", count);

return 0;
}

a byte lookup table might or might not be faster, depending on what
happens with the cache.
Click to expand...

On the TI 5501 DSP I'm currently working with, where sizeof(int) == 1
and CHAR_BIT == 16 (and the byte ordering is Big Endian, to boot), I'm
skeptical that this would work.

Use of a lookup table could easily result in exceeding the size of my
available EEPROM that stores my program memory (and that assumes that
you constructed the table with a priori knowledge that CHAR_BIT ==
16).

The least of my worries about this code may well be what happens with
the cache.

My PC-lint warnings make me even more twitchy about this code:

STD_FILE: std_5501.lnt
PC-lint for C/C++ (NT) Vers. 8.00u, Copyright Gimpel Software
1985-2006

--- Module: bits.c (C)
_
int var = 0xFF0F;
bits.c(3) : Warning 569: Loss of information (initialization) (16 bits
to 15 bits)
_
for ( i = 0; i < sizeof(int)*8 ; i++ )
bits.c(6) : Warning 574: Signed-unsigned mix with relational
_
{ count += var & 1; var >>= 1; }
bits.c(7) : Info 702: Shift right of signed quantity (int)
_
printf("%d\n", count);
bits.c(9) : Info 718: Symbol 'printf' undeclared, assumed to return
int
bits.c(9) : Info 746: call to function 'printf()' not made in the
presence of a prototype

/// Start of Pass 2 ///

--- Module: bits.c (C)

--- Global Wrap-up

Note 900: Successful completion, 5 messages produced
Tool returned code: 0

Regards
 
R

russell kym horsell

Cuthbert said:
Hi folks,
I am trying to find a more efficient way to count "How many bits are
'1' in a integer variable?".
I still have no idea to count the bits except using a loop and "if"
statements.
Could you know any other more efficient way?
Click to expand...

There are a couple.



E.g. when you take the 2's complement of a number, you do not complement
the lowest-order-bit. Using (-x)&x is therefore a way of "skiiping to
the next bit that's set" rather than having to go through bit positions
1 at a time -- 1/2 the time finding a 0.


Then there's the mysterious method that relies on carry in 2s complement
allowing you to "count" the 1's directly.
It's a recursive method (which you later can flatten out for particular
sizes of your compiuter's native word) based on the idea "how many bits
are set in a 2 bit quantity b1b2". To find out how many in this 2-bit
problem, you want to add b1 and b2. I.e. (x&1)+((x>>1)&1).


Now, what if we have (say) 4 bits b1b2b3b4? We can use
(x&5)+((x>>1)&5) to get [sum b1,b2][sum b3,b4] -- i.e. 2 x 2-bit quantities,
and then use
(x&3)+((x>>2)&3) to convert that to [sum b1,b2,b3,b4].


Just build up logically, as the old short story said. :)
 
R

Richard Heathfield

kondal said:

There is even better and faster algorithm but difficult to remember.

#define MASK_01010101 (((unsigned int)(-1))/3)
#define MASK_00110011 (((unsigned int)(-1))/5)
#define MASK_00001111 (((unsigned int)(-1))/17)

int bitcount (unsigned int n)
{
n = (n & MASK_01010101) + ((n >> 1) & MASK_01010101) ;
n = (n & MASK_00110011) + ((n >> 2) & MASK_00110011) ;
n = (n & MASK_00001111) + ((n >> 4) & MASK_00001111) ;
return n % 255 ;
}
Click to expand...

What makes you think this is faster? And what happens when the code is
ported to a platform with 64-bit unsigned ints?
 
K

kondal

Richard said:
kondal said:



What makes you think this is faster? And what happens when the code is
ported to a platform with 64-bit unsigned ints?

--
Richard Heathfield
"Usenet is a strange place" - dmr 29/7/1999
http://www.cpax.org.uk
email: rjh at above domain (but drop the www, obviously)
Click to expand...

There is no loop here to check and no of clock cycles to be executed
would be fas less than my previous algorithm.

Here is the program for 64 bits

#define MASK_01010101 (((unsigned int)(-1))/3)
#define MASK_00110011 (((unsigned int)(-1))/5)
#define MASK_00001111 (((unsigned int)(-1))/17)
#define MASK_00111100 (((unsigned int)(-1))/257)

int bitcount (unsigned int n)
{
n = (n & MASK_01010101) + ((n >> 1) & MASK_01010101) ;
n = (n & MASK_00110011) + ((n >> 2) & MASK_00110011) ;
n = (n & MASK_00001111) + ((n >> 4) & MASK_00001111) ;
n = (n & MASK_00111100) + ((n >> 8) & MASK_00111100) ;
return n % 255 ;
}

-kondal
 
K

kondal

kondal said:
#define MASK_01010101 (((unsigned int)(-1))/3)
#define MASK_00110011 (((unsigned int)(-1))/5)
#define MASK_00001111 (((unsigned int)(-1))/17)
#define MASK_00111100 (((unsigned int)(-1))/257)

int bitcount (unsigned int n)
{
n = (n & MASK_01010101) + ((n >> 1) & MASK_01010101) ;
n = (n & MASK_00110011) + ((n >> 2) & MASK_00110011) ;
n = (n & MASK_00001111) + ((n >> 4) & MASK_00001111) ;
n = (n & MASK_00111100) + ((n >> 8) & MASK_00111100) ;
return n % 255 ;
}
Click to expand...

Sorry I forgot, 'unsigned int' should be replaced by to 'unsigned long
long int'

-kondal
 
R

Richard Heathfield

kondal said:
Here is the program for 64 bits

#define MASK_01010101 (((unsigned int)(-1))/3)
#define MASK_00110011 (((unsigned int)(-1))/5)
#define MASK_00001111 (((unsigned int)(-1))/17)
#define MASK_00111100 (((unsigned int)(-1))/257)

int bitcount (unsigned int n)
{
n = (n & MASK_01010101) + ((n >> 1) & MASK_01010101) ;
n = (n & MASK_00110011) + ((n >> 2) & MASK_00110011) ;
n = (n & MASK_00001111) + ((n >> 4) & MASK_00001111) ;
n = (n & MASK_00111100) + ((n >> 8) & MASK_00111100) ;
return n % 255 ;
}
Click to expand...

What happens when the code is ported to a platform with 180-bit ints?
 
F

Frederick Gotham

Richard Heathfield posted:
Your solution doesn't appear to cope with integers wider than 21 bits,
for a start. Secondly, it doesn't cope with integers that are /fewer/
than 21 bits wide! Thirdly, it could conceivably be counting "padding
bits", bits that do not contribute to the value of the integer.
Click to expand...
"If the value of the right operand is negative or is greater
than or equal to the width in bits of the promoted left operand, the
behavior is undefined."
Click to expand...


I meant something more along the following lines. Do compilers nowadays
optimise away Bitwise-AND operations when one of the operands is known to
be 0 at compile-time?

/* Macro: QUANT_BITS_SET

This macro determines the quantity of bits which
are set in an integer expression whose signedness
is unsigned.

The typedef, "BitsSetType", specifies the unsigned
integer type which is to be used for processing.

Before processing takes place, the argument is
converted to BitsSetType.

This macro should work with unsigned integer types
as wide as 1024 bits.

NB: This macro evaluates its argument more than once.
*/

typedef unsigned BitsSetType;

#define IMAX_BITS(m) (\
(m) /((m)%0x3fffffffL+1) /0x3fffffffL \
%0x3fffffffL *30 \
+ (m)%0x3fffffffL /((m)%31+1)/31%31*5 \
+ 4 \
- 12 / ((m)%31+3) )

#define MASK_ZERO_IF_OVER(shift_left_by) (\
shift_left_by < IMAX_BITS((BitsSetType)-1) \
? (BitsSetType)1 << shift_left_by \
: (BitsSetType)0 )

#define QUANT_BITS_SET_RAW(x) (\
!!((x)&(BitsSetType)1) + !!((x)&(BitsSetType)1<<1) \
+!!((x)&(BitsSetType)1<<2) + !!((x)&(BitsSetType)1<<3) \
+!!((x)&(BitsSetType)1<<4) + !!((x)&(BitsSetType)1<<5) \
+!!((x)&(BitsSetType)1<<6) + !!((x)&(BitsSetType)1<<7) \
+!!((x)&(BitsSetType)1<<8) + !!((x)&(BitsSetType)1<<9) \
+!!((x)&(BitsSetType)1<<10) +!!((x)&(BitsSetType)1<<11) \
+!!((x)&(BitsSetType)1<<12) +!!((x)&(BitsSetType)1<<13) \
+!!((x)&(BitsSetType)1<<14) +!!((x)&(BitsSetType)1<<15) \
+!!((x)&MASK_ZERO_IF_OVER(16))+!!((x)&MASK_ZERO_IF_OVER(17))\
+!!((x)&MASK_ZERO_IF_OVER(18))+!!((x)&MASK_ZERO_IF_OVER(19))\
+!!((x)&MASK_ZERO_IF_OVER(20))+!!((x)&MASK_ZERO_IF_OVER(21))\
+!!((x)&MASK_ZERO_IF_OVER(22))+!!((x)&MASK_ZERO_IF_OVER(23))\
+!!((x)&MASK_ZERO_IF_OVER(24))+!!((x)&MASK_ZERO_IF_OVER(25))\
+!!((x)&MASK_ZERO_IF_OVER(26))+!!((x)&MASK_ZERO_IF_OVER(27))\
+!!((x)&MASK_ZERO_IF_OVER(28))+!!((x)&MASK_ZERO_IF_OVER(29))\
+!!((x)&MASK_ZERO_IF_OVER(30))+!!((x)&MASK_ZERO_IF_OVER(31))\
+!!((x)&MASK_ZERO_IF_OVER(32))+!!((x)&MASK_ZERO_IF_OVER(33))\
+!!((x)&MASK_ZERO_IF_OVER(34))+!!((x)&MASK_ZERO_IF_OVER(35))\
+!!((x)&MASK_ZERO_IF_OVER(36))+!!((x)&MASK_ZERO_IF_OVER(37))\
+!!((x)&MASK_ZERO_IF_OVER(38))+!!((x)&MASK_ZERO_IF_OVER(39))\
+!!((x)&MASK_ZERO_IF_OVER(40))+!!((x)&MASK_ZERO_IF_OVER(41))\
+!!((x)&MASK_ZERO_IF_OVER(42))+!!((x)&MASK_ZERO_IF_OVER(43))\
+!!((x)&MASK_ZERO_IF_OVER(44))+!!((x)&MASK_ZERO_IF_OVER(45))\
+!!((x)&MASK_ZERO_IF_OVER(46))+!!((x)&MASK_ZERO_IF_OVER(47))\
+!!((x)&MASK_ZERO_IF_OVER(48))+!!((x)&MASK_ZERO_IF_OVER(49))\
+!!((x)&MASK_ZERO_IF_OVER(50))+!!((x)&MASK_ZERO_IF_OVER(51))\
+!!((x)&MASK_ZERO_IF_OVER(52))+!!((x)&MASK_ZERO_IF_OVER(53))\
+!!((x)&MASK_ZERO_IF_OVER(54))+!!((x)&MASK_ZERO_IF_OVER(55))\
+!!((x)&MASK_ZERO_IF_OVER(56))+!!((x)&MASK_ZERO_IF_OVER(57))\
+!!((x)&MASK_ZERO_IF_OVER(58))+!!((x)&MASK_ZERO_IF_OVER(59))\
+!!((x)&MASK_ZERO_IF_OVER(60))+!!((x)&MASK_ZERO_IF_OVER(61))\
+!!((x)&MASK_ZERO_IF_OVER(62))+!!((x)&MASK_ZERO_IF_OVER(63))\
+!!((x)&MASK_ZERO_IF_OVER(64))+!!((x)&MASK_ZERO_IF_OVER(65))\
+!!((x)&MASK_ZERO_IF_OVER(66))+!!((x)&MASK_ZERO_IF_OVER(67))\
+!!((x)&MASK_ZERO_IF_OVER(68))+!!((x)&MASK_ZERO_IF_OVER(69))\
+!!((x)&MASK_ZERO_IF_OVER(70))+!!((x)&MASK_ZERO_IF_OVER(71))\
+!!((x)&MASK_ZERO_IF_OVER(72))+!!((x)&MASK_ZERO_IF_OVER(73))\
+!!((x)&MASK_ZERO_IF_OVER(74))+!!((x)&MASK_ZERO_IF_OVER(75))\
+!!((x)&MASK_ZERO_IF_OVER(76))+!!((x)&MASK_ZERO_IF_OVER(77))\
+!!((x)&MASK_ZERO_IF_OVER(78))+!!((x)&MASK_ZERO_IF_OVER(79))\
+!!((x)&MASK_ZERO_IF_OVER(80))+!!((x)&MASK_ZERO_IF_OVER(81))\
+!!((x)&MASK_ZERO_IF_OVER(82))+!!((x)&MASK_ZERO_IF_OVER(83))\
+!!((x)&MASK_ZERO_IF_OVER(84))+!!((x)&MASK_ZERO_IF_OVER(85))\
+!!((x)&MASK_ZERO_IF_OVER(86))+!!((x)&MASK_ZERO_IF_OVER(87))\
+!!((x)&MASK_ZERO_IF_OVER(88))+!!((x)&MASK_ZERO_IF_OVER(89))\
+!!((x)&MASK_ZERO_IF_OVER(90))+!!((x)&MASK_ZERO_IF_OVER(91))\
+!!((x)&MASK_ZERO_IF_OVER(92))+!!((x)&MASK_ZERO_IF_OVER(93))\
+!!((x)&MASK_ZERO_IF_OVER(94))+!!((x)&MASK_ZERO_IF_OVER(95))\
+!!((x)&MASK_ZERO_IF_OVER(96))+!!((x)&MASK_ZERO_IF_OVER(97))\
+!!((x)&MASK_ZERO_IF_OVER(98))+!!((x)&MASK_ZERO_IF_OVER(99))\
+!!((x)&MASK_ZERO_IF_OVER(100))+!!((x)&MASK_ZERO_IF_OVER(101))\
+!!((x)&MASK_ZERO_IF_OVER(102))+!!((x)&MASK_ZERO_IF_OVER(103))\
+!!((x)&MASK_ZERO_IF_OVER(104))+!!((x)&MASK_ZERO_IF_OVER(105))\
+!!((x)&MASK_ZERO_IF_OVER(106))+!!((x)&MASK_ZERO_IF_OVER(107))\
+!!((x)&MASK_ZERO_IF_OVER(108))+!!((x)&MASK_ZERO_IF_OVER(109))\
+!!((x)&MASK_ZERO_IF_OVER(110))+!!((x)&MASK_ZERO_IF_OVER(111))\
+!!((x)&MASK_ZERO_IF_OVER(112))+!!((x)&MASK_ZERO_IF_OVER(113))\
+!!((x)&MASK_ZERO_IF_OVER(114))+!!((x)&MASK_ZERO_IF_OVER(115))\
+!!((x)&MASK_ZERO_IF_OVER(116))+!!((x)&MASK_ZERO_IF_OVER(117))\
+!!((x)&MASK_ZERO_IF_OVER(118))+!!((x)&MASK_ZERO_IF_OVER(119))\
+!!((x)&MASK_ZERO_IF_OVER(120))+!!((x)&MASK_ZERO_IF_OVER(121))\
+!!((x)&MASK_ZERO_IF_OVER(122))+!!((x)&MASK_ZERO_IF_OVER(123))\
+!!((x)&MASK_ZERO_IF_OVER(124))+!!((x)&MASK_ZERO_IF_OVER(125))\
+!!((x)&MASK_ZERO_IF_OVER(126))+!!((x)&MASK_ZERO_IF_OVER(127))\
+!!((x)&MASK_ZERO_IF_OVER(128))+!!((x)&MASK_ZERO_IF_OVER(129))\
+!!((x)&MASK_ZERO_IF_OVER(130))+!!((x)&MASK_ZERO_IF_OVER(131))\
+!!((x)&MASK_ZERO_IF_OVER(132))+!!((x)&MASK_ZERO_IF_OVER(133))\
+!!((x)&MASK_ZERO_IF_OVER(134))+!!((x)&MASK_ZERO_IF_OVER(135))\
+!!((x)&MASK_ZERO_IF_OVER(136))+!!((x)&MASK_ZERO_IF_OVER(137))\
+!!((x)&MASK_ZERO_IF_OVER(138))+!!((x)&MASK_ZERO_IF_OVER(139))\
+!!((x)&MASK_ZERO_IF_OVER(140))+!!((x)&MASK_ZERO_IF_OVER(141))\
+!!((x)&MASK_ZERO_IF_OVER(142))+!!((x)&MASK_ZERO_IF_OVER(143))\
+!!((x)&MASK_ZERO_IF_OVER(144))+!!((x)&MASK_ZERO_IF_OVER(145))\
+!!((x)&MASK_ZERO_IF_OVER(146))+!!((x)&MASK_ZERO_IF_OVER(147))\
+!!((x)&MASK_ZERO_IF_OVER(148))+!!((x)&MASK_ZERO_IF_OVER(149))\
+!!((x)&MASK_ZERO_IF_OVER(150))+!!((x)&MASK_ZERO_IF_OVER(151))\
+!!((x)&MASK_ZERO_IF_OVER(152))+!!((x)&MASK_ZERO_IF_OVER(153))\
+!!((x)&MASK_ZERO_IF_OVER(154))+!!((x)&MASK_ZERO_IF_OVER(155))\
+!!((x)&MASK_ZERO_IF_OVER(156))+!!((x)&MASK_ZERO_IF_OVER(157))\
+!!((x)&MASK_ZERO_IF_OVER(158))+!!((x)&MASK_ZERO_IF_OVER(159))\
+!!((x)&MASK_ZERO_IF_OVER(160))+!!((x)&MASK_ZERO_IF_OVER(161))\
+!!((x)&MASK_ZERO_IF_OVER(162))+!!((x)&MASK_ZERO_IF_OVER(163))\
+!!((x)&MASK_ZERO_IF_OVER(164))+!!((x)&MASK_ZERO_IF_OVER(165))\
+!!((x)&MASK_ZERO_IF_OVER(166))+!!((x)&MASK_ZERO_IF_OVER(167))\
+!!((x)&MASK_ZERO_IF_OVER(168))+!!((x)&MASK_ZERO_IF_OVER(169))\
+!!((x)&MASK_ZERO_IF_OVER(170))+!!((x)&MASK_ZERO_IF_OVER(171))\
+!!((x)&MASK_ZERO_IF_OVER(172))+!!((x)&MASK_ZERO_IF_OVER(173))\
+!!((x)&MASK_ZERO_IF_OVER(174))+!!((x)&MASK_ZERO_IF_OVER(175))\
+!!((x)&MASK_ZERO_IF_OVER(176))+!!((x)&MASK_ZERO_IF_OVER(177))\
+!!((x)&MASK_ZERO_IF_OVER(178))+!!((x)&MASK_ZERO_IF_OVER(179))\
+!!((x)&MASK_ZERO_IF_OVER(180))+!!((x)&MASK_ZERO_IF_OVER(181))\
+!!((x)&MASK_ZERO_IF_OVER(182))+!!((x)&MASK_ZERO_IF_OVER(183))\
+!!((x)&MASK_ZERO_IF_OVER(184))+!!((x)&MASK_ZERO_IF_OVER(185))\
+!!((x)&MASK_ZERO_IF_OVER(186))+!!((x)&MASK_ZERO_IF_OVER(187))\
+!!((x)&MASK_ZERO_IF_OVER(188))+!!((x)&MASK_ZERO_IF_OVER(189))\
+!!((x)&MASK_ZERO_IF_OVER(190))+!!((x)&MASK_ZERO_IF_OVER(191))\
+!!((x)&MASK_ZERO_IF_OVER(192))+!!((x)&MASK_ZERO_IF_OVER(193))\
+!!((x)&MASK_ZERO_IF_OVER(194))+!!((x)&MASK_ZERO_IF_OVER(195))\
+!!((x)&MASK_ZERO_IF_OVER(196))+!!((x)&MASK_ZERO_IF_OVER(197))\
+!!((x)&MASK_ZERO_IF_OVER(198))+!!((x)&MASK_ZERO_IF_OVER(199))\
+!!((x)&MASK_ZERO_IF_OVER(200))+!!((x)&MASK_ZERO_IF_OVER(201))\
+!!((x)&MASK_ZERO_IF_OVER(202))+!!((x)&MASK_ZERO_IF_OVER(203))\
+!!((x)&MASK_ZERO_IF_OVER(204))+!!((x)&MASK_ZERO_IF_OVER(205))\
+!!((x)&MASK_ZERO_IF_OVER(206))+!!((x)&MASK_ZERO_IF_OVER(207))\
+!!((x)&MASK_ZERO_IF_OVER(208))+!!((x)&MASK_ZERO_IF_OVER(209))\
+!!((x)&MASK_ZERO_IF_OVER(210))+!!((x)&MASK_ZERO_IF_OVER(211))\
+!!((x)&MASK_ZERO_IF_OVER(212))+!!((x)&MASK_ZERO_IF_OVER(213))\
+!!((x)&MASK_ZERO_IF_OVER(214))+!!((x)&MASK_ZERO_IF_OVER(215))\
+!!((x)&MASK_ZERO_IF_OVER(216))+!!((x)&MASK_ZERO_IF_OVER(217))\
+!!((x)&MASK_ZERO_IF_OVER(218))+!!((x)&MASK_ZERO_IF_OVER(219))\
+!!((x)&MASK_ZERO_IF_OVER(220))+!!((x)&MASK_ZERO_IF_OVER(221))\
+!!((x)&MASK_ZERO_IF_OVER(222))+!!((x)&MASK_ZERO_IF_OVER(223))\
+!!((x)&MASK_ZERO_IF_OVER(224))+!!((x)&MASK_ZERO_IF_OVER(225))\
+!!((x)&MASK_ZERO_IF_OVER(226))+!!((x)&MASK_ZERO_IF_OVER(227))\
+!!((x)&MASK_ZERO_IF_OVER(228))+!!((x)&MASK_ZERO_IF_OVER(229))\
+!!((x)&MASK_ZERO_IF_OVER(230))+!!((x)&MASK_ZERO_IF_OVER(231))\
+!!((x)&MASK_ZERO_IF_OVER(232))+!!((x)&MASK_ZERO_IF_OVER(233))\
+!!((x)&MASK_ZERO_IF_OVER(234))+!!((x)&MASK_ZERO_IF_OVER(235))\
+!!((x)&MASK_ZERO_IF_OVER(236))+!!((x)&MASK_ZERO_IF_OVER(237))\
+!!((x)&MASK_ZERO_IF_OVER(238))+!!((x)&MASK_ZERO_IF_OVER(239))\
+!!((x)&MASK_ZERO_IF_OVER(240))+!!((x)&MASK_ZERO_IF_OVER(241))\
+!!((x)&MASK_ZERO_IF_OVER(242))+!!((x)&MASK_ZERO_IF_OVER(243))\
+!!((x)&MASK_ZERO_IF_OVER(244))+!!((x)&MASK_ZERO_IF_OVER(245))\
+!!((x)&MASK_ZERO_IF_OVER(246))+!!((x)&MASK_ZERO_IF_OVER(247))\
+!!((x)&MASK_ZERO_IF_OVER(248))+!!((x)&MASK_ZERO_IF_OVER(249))\
+!!((x)&MASK_ZERO_IF_OVER(250))+!!((x)&MASK_ZERO_IF_OVER(251))\
+!!((x)&MASK_ZERO_IF_OVER(252))+!!((x)&MASK_ZERO_IF_OVER(253))\
+!!((x)&MASK_ZERO_IF_OVER(254))+!!((x)&MASK_ZERO_IF_OVER(255))\
+!!((x)&MASK_ZERO_IF_OVER(256))+!!((x)&MASK_ZERO_IF_OVER(257))\
+!!((x)&MASK_ZERO_IF_OVER(258))+!!((x)&MASK_ZERO_IF_OVER(259))\
+!!((x)&MASK_ZERO_IF_OVER(260))+!!((x)&MASK_ZERO_IF_OVER(261))\
+!!((x)&MASK_ZERO_IF_OVER(262))+!!((x)&MASK_ZERO_IF_OVER(263))\
+!!((x)&MASK_ZERO_IF_OVER(264))+!!((x)&MASK_ZERO_IF_OVER(265))\
+!!((x)&MASK_ZERO_IF_OVER(266))+!!((x)&MASK_ZERO_IF_OVER(267))\
+!!((x)&MASK_ZERO_IF_OVER(268))+!!((x)&MASK_ZERO_IF_OVER(269))\
+!!((x)&MASK_ZERO_IF_OVER(270))+!!((x)&MASK_ZERO_IF_OVER(271))\
+!!((x)&MASK_ZERO_IF_OVER(272))+!!((x)&MASK_ZERO_IF_OVER(273))\
+!!((x)&MASK_ZERO_IF_OVER(274))+!!((x)&MASK_ZERO_IF_OVER(275))\
+!!((x)&MASK_ZERO_IF_OVER(276))+!!((x)&MASK_ZERO_IF_OVER(277))\
+!!((x)&MASK_ZERO_IF_OVER(278))+!!((x)&MASK_ZERO_IF_OVER(279))\
+!!((x)&MASK_ZERO_IF_OVER(280))+!!((x)&MASK_ZERO_IF_OVER(281))\
+!!((x)&MASK_ZERO_IF_OVER(282))+!!((x)&MASK_ZERO_IF_OVER(283))\
+!!((x)&MASK_ZERO_IF_OVER(284))+!!((x)&MASK_ZERO_IF_OVER(285))\
+!!((x)&MASK_ZERO_IF_OVER(286))+!!((x)&MASK_ZERO_IF_OVER(287))\
+!!((x)&MASK_ZERO_IF_OVER(288))+!!((x)&MASK_ZERO_IF_OVER(289))\
+!!((x)&MASK_ZERO_IF_OVER(290))+!!((x)&MASK_ZERO_IF_OVER(291))\
+!!((x)&MASK_ZERO_IF_OVER(292))+!!((x)&MASK_ZERO_IF_OVER(293))\
+!!((x)&MASK_ZERO_IF_OVER(294))+!!((x)&MASK_ZERO_IF_OVER(295))\
+!!((x)&MASK_ZERO_IF_OVER(296))+!!((x)&MASK_ZERO_IF_OVER(297))\
+!!((x)&MASK_ZERO_IF_OVER(298))+!!((x)&MASK_ZERO_IF_OVER(299))\
+!!((x)&MASK_ZERO_IF_OVER(300))+!!((x)&MASK_ZERO_IF_OVER(301))\
+!!((x)&MASK_ZERO_IF_OVER(302))+!!((x)&MASK_ZERO_IF_OVER(303))\
+!!((x)&MASK_ZERO_IF_OVER(304))+!!((x)&MASK_ZERO_IF_OVER(305))\
+!!((x)&MASK_ZERO_IF_OVER(306))+!!((x)&MASK_ZERO_IF_OVER(307))\
+!!((x)&MASK_ZERO_IF_OVER(308))+!!((x)&MASK_ZERO_IF_OVER(309))\
+!!((x)&MASK_ZERO_IF_OVER(310))+!!((x)&MASK_ZERO_IF_OVER(311))\
+!!((x)&MASK_ZERO_IF_OVER(312))+!!((x)&MASK_ZERO_IF_OVER(313))\
+!!((x)&MASK_ZERO_IF_OVER(314))+!!((x)&MASK_ZERO_IF_OVER(315))\
+!!((x)&MASK_ZERO_IF_OVER(316))+!!((x)&MASK_ZERO_IF_OVER(317))\
+!!((x)&MASK_ZERO_IF_OVER(318))+!!((x)&MASK_ZERO_IF_OVER(319))\
+!!((x)&MASK_ZERO_IF_OVER(320))+!!((x)&MASK_ZERO_IF_OVER(321))\
+!!((x)&MASK_ZERO_IF_OVER(322))+!!((x)&MASK_ZERO_IF_OVER(323))\
+!!((x)&MASK_ZERO_IF_OVER(324))+!!((x)&MASK_ZERO_IF_OVER(325))\
+!!((x)&MASK_ZERO_IF_OVER(326))+!!((x)&MASK_ZERO_IF_OVER(327))\
+!!((x)&MASK_ZERO_IF_OVER(328))+!!((x)&MASK_ZERO_IF_OVER(329))\
+!!((x)&MASK_ZERO_IF_OVER(330))+!!((x)&MASK_ZERO_IF_OVER(331))\
+!!((x)&MASK_ZERO_IF_OVER(332))+!!((x)&MASK_ZERO_IF_OVER(333))\
+!!((x)&MASK_ZERO_IF_OVER(334))+!!((x)&MASK_ZERO_IF_OVER(335))\
+!!((x)&MASK_ZERO_IF_OVER(336))+!!((x)&MASK_ZERO_IF_OVER(337))\
+!!((x)&MASK_ZERO_IF_OVER(338))+!!((x)&MASK_ZERO_IF_OVER(339))\
+!!((x)&MASK_ZERO_IF_OVER(340))+!!((x)&MASK_ZERO_IF_OVER(341))\
+!!((x)&MASK_ZERO_IF_OVER(342))+!!((x)&MASK_ZERO_IF_OVER(343))\
+!!((x)&MASK_ZERO_IF_OVER(344))+!!((x)&MASK_ZERO_IF_OVER(345))\
+!!((x)&MASK_ZERO_IF_OVER(346))+!!((x)&MASK_ZERO_IF_OVER(347))\
+!!((x)&MASK_ZERO_IF_OVER(348))+!!((x)&MASK_ZERO_IF_OVER(349))\
+!!((x)&MASK_ZERO_IF_OVER(350))+!!((x)&MASK_ZERO_IF_OVER(351))\
+!!((x)&MASK_ZERO_IF_OVER(352))+!!((x)&MASK_ZERO_IF_OVER(353))\
+!!((x)&MASK_ZERO_IF_OVER(354))+!!((x)&MASK_ZERO_IF_OVER(355))\
+!!((x)&MASK_ZERO_IF_OVER(356))+!!((x)&MASK_ZERO_IF_OVER(357))\
+!!((x)&MASK_ZERO_IF_OVER(358))+!!((x)&MASK_ZERO_IF_OVER(359))\
+!!((x)&MASK_ZERO_IF_OVER(360))+!!((x)&MASK_ZERO_IF_OVER(361))\
+!!((x)&MASK_ZERO_IF_OVER(362))+!!((x)&MASK_ZERO_IF_OVER(363))\
+!!((x)&MASK_ZERO_IF_OVER(364))+!!((x)&MASK_ZERO_IF_OVER(365))\
+!!((x)&MASK_ZERO_IF_OVER(366))+!!((x)&MASK_ZERO_IF_OVER(367))\
+!!((x)&MASK_ZERO_IF_OVER(368))+!!((x)&MASK_ZERO_IF_OVER(369))\
+!!((x)&MASK_ZERO_IF_OVER(370))+!!((x)&MASK_ZERO_IF_OVER(371))\
+!!((x)&MASK_ZERO_IF_OVER(372))+!!((x)&MASK_ZERO_IF_OVER(373))\
+!!((x)&MASK_ZERO_IF_OVER(374))+!!((x)&MASK_ZERO_IF_OVER(375))\
+!!((x)&MASK_ZERO_IF_OVER(376))+!!((x)&MASK_ZERO_IF_OVER(377))\
+!!((x)&MASK_ZERO_IF_OVER(378))+!!((x)&MASK_ZERO_IF_OVER(379))\
+!!((x)&MASK_ZERO_IF_OVER(380))+!!((x)&MASK_ZERO_IF_OVER(381))\
+!!((x)&MASK_ZERO_IF_OVER(382))+!!((x)&MASK_ZERO_IF_OVER(383))\
+!!((x)&MASK_ZERO_IF_OVER(384))+!!((x)&MASK_ZERO_IF_OVER(385))\
+!!((x)&MASK_ZERO_IF_OVER(386))+!!((x)&MASK_ZERO_IF_OVER(387))\
+!!((x)&MASK_ZERO_IF_OVER(388))+!!((x)&MASK_ZERO_IF_OVER(389))\
+!!((x)&MASK_ZERO_IF_OVER(390))+!!((x)&MASK_ZERO_IF_OVER(391))\
+!!((x)&MASK_ZERO_IF_OVER(392))+!!((x)&MASK_ZERO_IF_OVER(393))\
+!!((x)&MASK_ZERO_IF_OVER(394))+!!((x)&MASK_ZERO_IF_OVER(395))\
+!!((x)&MASK_ZERO_IF_OVER(396))+!!((x)&MASK_ZERO_IF_OVER(397))\
+!!((x)&MASK_ZERO_IF_OVER(398))+!!((x)&MASK_ZERO_IF_OVER(399))\
+!!((x)&MASK_ZERO_IF_OVER(400))+!!((x)&MASK_ZERO_IF_OVER(401))\
+!!((x)&MASK_ZERO_IF_OVER(402))+!!((x)&MASK_ZERO_IF_OVER(403))\
+!!((x)&MASK_ZERO_IF_OVER(404))+!!((x)&MASK_ZERO_IF_OVER(405))\
+!!((x)&MASK_ZERO_IF_OVER(406))+!!((x)&MASK_ZERO_IF_OVER(407))\
+!!((x)&MASK_ZERO_IF_OVER(408))+!!((x)&MASK_ZERO_IF_OVER(409))\
+!!((x)&MASK_ZERO_IF_OVER(410))+!!((x)&MASK_ZERO_IF_OVER(411))\
+!!((x)&MASK_ZERO_IF_OVER(412))+!!((x)&MASK_ZERO_IF_OVER(413))\
+!!((x)&MASK_ZERO_IF_OVER(414))+!!((x)&MASK_ZERO_IF_OVER(415))\
+!!((x)&MASK_ZERO_IF_OVER(416))+!!((x)&MASK_ZERO_IF_OVER(417))\
+!!((x)&MASK_ZERO_IF_OVER(418))+!!((x)&MASK_ZERO_IF_OVER(419))\
+!!((x)&MASK_ZERO_IF_OVER(420))+!!((x)&MASK_ZERO_IF_OVER(421))\
+!!((x)&MASK_ZERO_IF_OVER(422))+!!((x)&MASK_ZERO_IF_OVER(423))\
+!!((x)&MASK_ZERO_IF_OVER(424))+!!((x)&MASK_ZERO_IF_OVER(425))\
+!!((x)&MASK_ZERO_IF_OVER(426))+!!((x)&MASK_ZERO_IF_OVER(427))\
+!!((x)&MASK_ZERO_IF_OVER(428))+!!((x)&MASK_ZERO_IF_OVER(429))\
+!!((x)&MASK_ZERO_IF_OVER(430))+!!((x)&MASK_ZERO_IF_OVER(431))\
+!!((x)&MASK_ZERO_IF_OVER(432))+!!((x)&MASK_ZERO_IF_OVER(433))\
+!!((x)&MASK_ZERO_IF_OVER(434))+!!((x)&MASK_ZERO_IF_OVER(435))\
+!!((x)&MASK_ZERO_IF_OVER(436))+!!((x)&MASK_ZERO_IF_OVER(437))\
+!!((x)&MASK_ZERO_IF_OVER(438))+!!((x)&MASK_ZERO_IF_OVER(439))\
+!!((x)&MASK_ZERO_IF_OVER(440))+!!((x)&MASK_ZERO_IF_OVER(441))\
+!!((x)&MASK_ZERO_IF_OVER(442))+!!((x)&MASK_ZERO_IF_OVER(443))\
+!!((x)&MASK_ZERO_IF_OVER(444))+!!((x)&MASK_ZERO_IF_OVER(445))\
+!!((x)&MASK_ZERO_IF_OVER(446))+!!((x)&MASK_ZERO_IF_OVER(447))\
+!!((x)&MASK_ZERO_IF_OVER(448))+!!((x)&MASK_ZERO_IF_OVER(449))\
+!!((x)&MASK_ZERO_IF_OVER(450))+!!((x)&MASK_ZERO_IF_OVER(451))\
+!!((x)&MASK_ZERO_IF_OVER(452))+!!((x)&MASK_ZERO_IF_OVER(453))\
+!!((x)&MASK_ZERO_IF_OVER(454))+!!((x)&MASK_ZERO_IF_OVER(455))\
+!!((x)&MASK_ZERO_IF_OVER(456))+!!((x)&MASK_ZERO_IF_OVER(457))\
+!!((x)&MASK_ZERO_IF_OVER(458))+!!((x)&MASK_ZERO_IF_OVER(459))\
+!!((x)&MASK_ZERO_IF_OVER(460))+!!((x)&MASK_ZERO_IF_OVER(461))\
+!!((x)&MASK_ZERO_IF_OVER(462))+!!((x)&MASK_ZERO_IF_OVER(463))\
+!!((x)&MASK_ZERO_IF_OVER(464))+!!((x)&MASK_ZERO_IF_OVER(465))\
+!!((x)&MASK_ZERO_IF_OVER(466))+!!((x)&MASK_ZERO_IF_OVER(467))\
+!!((x)&MASK_ZERO_IF_OVER(468))+!!((x)&MASK_ZERO_IF_OVER(469))\
+!!((x)&MASK_ZERO_IF_OVER(470))+!!((x)&MASK_ZERO_IF_OVER(471))\
+!!((x)&MASK_ZERO_IF_OVER(472))+!!((x)&MASK_ZERO_IF_OVER(473))\
+!!((x)&MASK_ZERO_IF_OVER(474))+!!((x)&MASK_ZERO_IF_OVER(475))\
+!!((x)&MASK_ZERO_IF_OVER(476))+!!((x)&MASK_ZERO_IF_OVER(477))\
+!!((x)&MASK_ZERO_IF_OVER(478))+!!((x)&MASK_ZERO_IF_OVER(479))\
+!!((x)&MASK_ZERO_IF_OVER(480))+!!((x)&MASK_ZERO_IF_OVER(481))\
+!!((x)&MASK_ZERO_IF_OVER(482))+!!((x)&MASK_ZERO_IF_OVER(483))\
+!!((x)&MASK_ZERO_IF_OVER(484))+!!((x)&MASK_ZERO_IF_OVER(485))\
+!!((x)&MASK_ZERO_IF_OVER(486))+!!((x)&MASK_ZERO_IF_OVER(487))\
+!!((x)&MASK_ZERO_IF_OVER(488))+!!((x)&MASK_ZERO_IF_OVER(489))\
+!!((x)&MASK_ZERO_IF_OVER(490))+!!((x)&MASK_ZERO_IF_OVER(491))\
+!!((x)&MASK_ZERO_IF_OVER(492))+!!((x)&MASK_ZERO_IF_OVER(493))\
+!!((x)&MASK_ZERO_IF_OVER(494))+!!((x)&MASK_ZERO_IF_OVER(495))\
+!!((x)&MASK_ZERO_IF_OVER(496))+!!((x)&MASK_ZERO_IF_OVER(497))\
+!!((x)&MASK_ZERO_IF_OVER(498))+!!((x)&MASK_ZERO_IF_OVER(499))\
+!!((x)&MASK_ZERO_IF_OVER(500))+!!((x)&MASK_ZERO_IF_OVER(501))\
+!!((x)&MASK_ZERO_IF_OVER(502))+!!((x)&MASK_ZERO_IF_OVER(503))\
+!!((x)&MASK_ZERO_IF_OVER(504))+!!((x)&MASK_ZERO_IF_OVER(505))\
+!!((x)&MASK_ZERO_IF_OVER(506))+!!((x)&MASK_ZERO_IF_OVER(507))\
+!!((x)&MASK_ZERO_IF_OVER(508))+!!((x)&MASK_ZERO_IF_OVER(509))\
+!!((x)&MASK_ZERO_IF_OVER(510))+!!((x)&MASK_ZERO_IF_OVER(511))\
+!!((x)&MASK_ZERO_IF_OVER(512))+!!((x)&MASK_ZERO_IF_OVER(513))\
+!!((x)&MASK_ZERO_IF_OVER(514))+!!((x)&MASK_ZERO_IF_OVER(515))\
+!!((x)&MASK_ZERO_IF_OVER(516))+!!((x)&MASK_ZERO_IF_OVER(517))\
+!!((x)&MASK_ZERO_IF_OVER(518))+!!((x)&MASK_ZERO_IF_OVER(519))\
+!!((x)&MASK_ZERO_IF_OVER(520))+!!((x)&MASK_ZERO_IF_OVER(521))\
+!!((x)&MASK_ZERO_IF_OVER(522))+!!((x)&MASK_ZERO_IF_OVER(523))\
+!!((x)&MASK_ZERO_IF_OVER(524))+!!((x)&MASK_ZERO_IF_OVER(525))\
+!!((x)&MASK_ZERO_IF_OVER(526))+!!((x)&MASK_ZERO_IF_OVER(527))\
+!!((x)&MASK_ZERO_IF_OVER(528))+!!((x)&MASK_ZERO_IF_OVER(529))\
+!!((x)&MASK_ZERO_IF_OVER(530))+!!((x)&MASK_ZERO_IF_OVER(531))\
+!!((x)&MASK_ZERO_IF_OVER(532))+!!((x)&MASK_ZERO_IF_OVER(533))\
+!!((x)&MASK_ZERO_IF_OVER(534))+!!((x)&MASK_ZERO_IF_OVER(535))\
+!!((x)&MASK_ZERO_IF_OVER(536))+!!((x)&MASK_ZERO_IF_OVER(537))\
+!!((x)&MASK_ZERO_IF_OVER(538))+!!((x)&MASK_ZERO_IF_OVER(539))\
+!!((x)&MASK_ZERO_IF_OVER(540))+!!((x)&MASK_ZERO_IF_OVER(541))\
+!!((x)&MASK_ZERO_IF_OVER(542))+!!((x)&MASK_ZERO_IF_OVER(543))\
+!!((x)&MASK_ZERO_IF_OVER(544))+!!((x)&MASK_ZERO_IF_OVER(545))\
+!!((x)&MASK_ZERO_IF_OVER(546))+!!((x)&MASK_ZERO_IF_OVER(547))\
+!!((x)&MASK_ZERO_IF_OVER(548))+!!((x)&MASK_ZERO_IF_OVER(549))\
+!!((x)&MASK_ZERO_IF_OVER(550))+!!((x)&MASK_ZERO_IF_OVER(551))\
+!!((x)&MASK_ZERO_IF_OVER(552))+!!((x)&MASK_ZERO_IF_OVER(553))\
+!!((x)&MASK_ZERO_IF_OVER(554))+!!((x)&MASK_ZERO_IF_OVER(555))\
+!!((x)&MASK_ZERO_IF_OVER(556))+!!((x)&MASK_ZERO_IF_OVER(557))\
+!!((x)&MASK_ZERO_IF_OVER(558))+!!((x)&MASK_ZERO_IF_OVER(559))\
+!!((x)&MASK_ZERO_IF_OVER(560))+!!((x)&MASK_ZERO_IF_OVER(561))\
+!!((x)&MASK_ZERO_IF_OVER(562))+!!((x)&MASK_ZERO_IF_OVER(563))\
+!!((x)&MASK_ZERO_IF_OVER(564))+!!((x)&MASK_ZERO_IF_OVER(565))\
+!!((x)&MASK_ZERO_IF_OVER(566))+!!((x)&MASK_ZERO_IF_OVER(567))\
+!!((x)&MASK_ZERO_IF_OVER(568))+!!((x)&MASK_ZERO_IF_OVER(569))\
+!!((x)&MASK_ZERO_IF_OVER(570))+!!((x)&MASK_ZERO_IF_OVER(571))\
+!!((x)&MASK_ZERO_IF_OVER(572))+!!((x)&MASK_ZERO_IF_OVER(573))\
+!!((x)&MASK_ZERO_IF_OVER(574))+!!((x)&MASK_ZERO_IF_OVER(575))\
+!!((x)&MASK_ZERO_IF_OVER(576))+!!((x)&MASK_ZERO_IF_OVER(577))\
+!!((x)&MASK_ZERO_IF_OVER(578))+!!((x)&MASK_ZERO_IF_OVER(579))\
+!!((x)&MASK_ZERO_IF_OVER(580))+!!((x)&MASK_ZERO_IF_OVER(581))\
+!!((x)&MASK_ZERO_IF_OVER(582))+!!((x)&MASK_ZERO_IF_OVER(583))\
+!!((x)&MASK_ZERO_IF_OVER(584))+!!((x)&MASK_ZERO_IF_OVER(585))\
+!!((x)&MASK_ZERO_IF_OVER(586))+!!((x)&MASK_ZERO_IF_OVER(587))\
+!!((x)&MASK_ZERO_IF_OVER(588))+!!((x)&MASK_ZERO_IF_OVER(589))\
+!!((x)&MASK_ZERO_IF_OVER(590))+!!((x)&MASK_ZERO_IF_OVER(591))\
+!!((x)&MASK_ZERO_IF_OVER(592))+!!((x)&MASK_ZERO_IF_OVER(593))\
+!!((x)&MASK_ZERO_IF_OVER(594))+!!((x)&MASK_ZERO_IF_OVER(595))\
+!!((x)&MASK_ZERO_IF_OVER(596))+!!((x)&MASK_ZERO_IF_OVER(597))\
+!!((x)&MASK_ZERO_IF_OVER(598))+!!((x)&MASK_ZERO_IF_OVER(599))\
+!!((x)&MASK_ZERO_IF_OVER(600))+!!((x)&MASK_ZERO_IF_OVER(601))\
+!!((x)&MASK_ZERO_IF_OVER(602))+!!((x)&MASK_ZERO_IF_OVER(603))\
+!!((x)&MASK_ZERO_IF_OVER(604))+!!((x)&MASK_ZERO_IF_OVER(605))\
+!!((x)&MASK_ZERO_IF_OVER(606))+!!((x)&MASK_ZERO_IF_OVER(607))\
+!!((x)&MASK_ZERO_IF_OVER(608))+!!((x)&MASK_ZERO_IF_OVER(609))\
+!!((x)&MASK_ZERO_IF_OVER(610))+!!((x)&MASK_ZERO_IF_OVER(611))\
+!!((x)&MASK_ZERO_IF_OVER(612))+!!((x)&MASK_ZERO_IF_OVER(613))\
+!!((x)&MASK_ZERO_IF_OVER(614))+!!((x)&MASK_ZERO_IF_OVER(615))\
+!!((x)&MASK_ZERO_IF_OVER(616))+!!((x)&MASK_ZERO_IF_OVER(617))\
+!!((x)&MASK_ZERO_IF_OVER(618))+!!((x)&MASK_ZERO_IF_OVER(619))\
+!!((x)&MASK_ZERO_IF_OVER(620))+!!((x)&MASK_ZERO_IF_OVER(621))\
+!!((x)&MASK_ZERO_IF_OVER(622))+!!((x)&MASK_ZERO_IF_OVER(623))\
+!!((x)&MASK_ZERO_IF_OVER(624))+!!((x)&MASK_ZERO_IF_OVER(625))\
+!!((x)&MASK_ZERO_IF_OVER(626))+!!((x)&MASK_ZERO_IF_OVER(627))\
+!!((x)&MASK_ZERO_IF_OVER(628))+!!((x)&MASK_ZERO_IF_OVER(629))\
+!!((x)&MASK_ZERO_IF_OVER(630))+!!((x)&MASK_ZERO_IF_OVER(631))\
+!!((x)&MASK_ZERO_IF_OVER(632))+!!((x)&MASK_ZERO_IF_OVER(633))\
+!!((x)&MASK_ZERO_IF_OVER(634))+!!((x)&MASK_ZERO_IF_OVER(635))\
+!!((x)&MASK_ZERO_IF_OVER(636))+!!((x)&MASK_ZERO_IF_OVER(637))\
+!!((x)&MASK_ZERO_IF_OVER(638))+!!((x)&MASK_ZERO_IF_OVER(639))\
+!!((x)&MASK_ZERO_IF_OVER(640))+!!((x)&MASK_ZERO_IF_OVER(641))\
+!!((x)&MASK_ZERO_IF_OVER(642))+!!((x)&MASK_ZERO_IF_OVER(643))\
+!!((x)&MASK_ZERO_IF_OVER(644))+!!((x)&MASK_ZERO_IF_OVER(645))\
+!!((x)&MASK_ZERO_IF_OVER(646))+!!((x)&MASK_ZERO_IF_OVER(647))\
+!!((x)&MASK_ZERO_IF_OVER(648))+!!((x)&MASK_ZERO_IF_OVER(649))\
+!!((x)&MASK_ZERO_IF_OVER(650))+!!((x)&MASK_ZERO_IF_OVER(651))\
+!!((x)&MASK_ZERO_IF_OVER(652))+!!((x)&MASK_ZERO_IF_OVER(653))\
+!!((x)&MASK_ZERO_IF_OVER(654))+!!((x)&MASK_ZERO_IF_OVER(655))\
+!!((x)&MASK_ZERO_IF_OVER(656))+!!((x)&MASK_ZERO_IF_OVER(657))\
+!!((x)&MASK_ZERO_IF_OVER(658))+!!((x)&MASK_ZERO_IF_OVER(659))\
+!!((x)&MASK_ZERO_IF_OVER(660))+!!((x)&MASK_ZERO_IF_OVER(661))\
+!!((x)&MASK_ZERO_IF_OVER(662))+!!((x)&MASK_ZERO_IF_OVER(663))\
+!!((x)&MASK_ZERO_IF_OVER(664))+!!((x)&MASK_ZERO_IF_OVER(665))\
+!!((x)&MASK_ZERO_IF_OVER(666))+!!((x)&MASK_ZERO_IF_OVER(667))\
+!!((x)&MASK_ZERO_IF_OVER(668))+!!((x)&MASK_ZERO_IF_OVER(669))\
+!!((x)&MASK_ZERO_IF_OVER(670))+!!((x)&MASK_ZERO_IF_OVER(671))\
+!!((x)&MASK_ZERO_IF_OVER(672))+!!((x)&MASK_ZERO_IF_OVER(673))\
+!!((x)&MASK_ZERO_IF_OVER(674))+!!((x)&MASK_ZERO_IF_OVER(675))\
+!!((x)&MASK_ZERO_IF_OVER(676))+!!((x)&MASK_ZERO_IF_OVER(677))\
+!!((x)&MASK_ZERO_IF_OVER(678))+!!((x)&MASK_ZERO_IF_OVER(679))\
+!!((x)&MASK_ZERO_IF_OVER(680))+!!((x)&MASK_ZERO_IF_OVER(681))\
+!!((x)&MASK_ZERO_IF_OVER(682))+!!((x)&MASK_ZERO_IF_OVER(683))\
+!!((x)&MASK_ZERO_IF_OVER(684))+!!((x)&MASK_ZERO_IF_OVER(685))\
+!!((x)&MASK_ZERO_IF_OVER(686))+!!((x)&MASK_ZERO_IF_OVER(687))\
+!!((x)&MASK_ZERO_IF_OVER(688))+!!((x)&MASK_ZERO_IF_OVER(689))\
+!!((x)&MASK_ZERO_IF_OVER(690))+!!((x)&MASK_ZERO_IF_OVER(691))\
+!!((x)&MASK_ZERO_IF_OVER(692))+!!((x)&MASK_ZERO_IF_OVER(693))\
+!!((x)&MASK_ZERO_IF_OVER(694))+!!((x)&MASK_ZERO_IF_OVER(695))\
+!!((x)&MASK_ZERO_IF_OVER(696))+!!((x)&MASK_ZERO_IF_OVER(697))\
+!!((x)&MASK_ZERO_IF_OVER(698))+!!((x)&MASK_ZERO_IF_OVER(699))\
+!!((x)&MASK_ZERO_IF_OVER(700))+!!((x)&MASK_ZERO_IF_OVER(701))\
+!!((x)&MASK_ZERO_IF_OVER(702))+!!((x)&MASK_ZERO_IF_OVER(703))\
+!!((x)&MASK_ZERO_IF_OVER(704))+!!((x)&MASK_ZERO_IF_OVER(705))\
+!!((x)&MASK_ZERO_IF_OVER(706))+!!((x)&MASK_ZERO_IF_OVER(707))\
+!!((x)&MASK_ZERO_IF_OVER(708))+!!((x)&MASK_ZERO_IF_OVER(709))\
+!!((x)&MASK_ZERO_IF_OVER(710))+!!((x)&MASK_ZERO_IF_OVER(711))\
+!!((x)&MASK_ZERO_IF_OVER(712))+!!((x)&MASK_ZERO_IF_OVER(713))\
+!!((x)&MASK_ZERO_IF_OVER(714))+!!((x)&MASK_ZERO_IF_OVER(715))\
+!!((x)&MASK_ZERO_IF_OVER(716))+!!((x)&MASK_ZERO_IF_OVER(717))\
+!!((x)&MASK_ZERO_IF_OVER(718))+!!((x)&MASK_ZERO_IF_OVER(719))\
+!!((x)&MASK_ZERO_IF_OVER(720))+!!((x)&MASK_ZERO_IF_OVER(721))\
+!!((x)&MASK_ZERO_IF_OVER(722))+!!((x)&MASK_ZERO_IF_OVER(723))\
+!!((x)&MASK_ZERO_IF_OVER(724))+!!((x)&MASK_ZERO_IF_OVER(725))\
+!!((x)&MASK_ZERO_IF_OVER(726))+!!((x)&MASK_ZERO_IF_OVER(727))\
+!!((x)&MASK_ZERO_IF_OVER(728))+!!((x)&MASK_ZERO_IF_OVER(729))\
+!!((x)&MASK_ZERO_IF_OVER(730))+!!((x)&MASK_ZERO_IF_OVER(731))\
+!!((x)&MASK_ZERO_IF_OVER(732))+!!((x)&MASK_ZERO_IF_OVER(733))\
+!!((x)&MASK_ZERO_IF_OVER(734))+!!((x)&MASK_ZERO_IF_OVER(735))\
+!!((x)&MASK_ZERO_IF_OVER(736))+!!((x)&MASK_ZERO_IF_OVER(737))\
+!!((x)&MASK_ZERO_IF_OVER(738))+!!((x)&MASK_ZERO_IF_OVER(739))\
+!!((x)&MASK_ZERO_IF_OVER(740))+!!((x)&MASK_ZERO_IF_OVER(741))\
+!!((x)&MASK_ZERO_IF_OVER(742))+!!((x)&MASK_ZERO_IF_OVER(743))\
+!!((x)&MASK_ZERO_IF_OVER(744))+!!((x)&MASK_ZERO_IF_OVER(745))\
+!!((x)&MASK_ZERO_IF_OVER(746))+!!((x)&MASK_ZERO_IF_OVER(747))\
+!!((x)&MASK_ZERO_IF_OVER(748))+!!((x)&MASK_ZERO_IF_OVER(749))\
+!!((x)&MASK_ZERO_IF_OVER(750))+!!((x)&MASK_ZERO_IF_OVER(751))\
+!!((x)&MASK_ZERO_IF_OVER(752))+!!((x)&MASK_ZERO_IF_OVER(753))\
+!!((x)&MASK_ZERO_IF_OVER(754))+!!((x)&MASK_ZERO_IF_OVER(755))\
+!!((x)&MASK_ZERO_IF_OVER(756))+!!((x)&MASK_ZERO_IF_OVER(757))\
+!!((x)&MASK_ZERO_IF_OVER(758))+!!((x)&MASK_ZERO_IF_OVER(759))\
+!!((x)&MASK_ZERO_IF_OVER(760))+!!((x)&MASK_ZERO_IF_OVER(761))\
+!!((x)&MASK_ZERO_IF_OVER(762))+!!((x)&MASK_ZERO_IF_OVER(763))\
+!!((x)&MASK_ZERO_IF_OVER(764))+!!((x)&MASK_ZERO_IF_OVER(765))\
+!!((x)&MASK_ZERO_IF_OVER(766))+!!((x)&MASK_ZERO_IF_OVER(767))\
+!!((x)&MASK_ZERO_IF_OVER(768))+!!((x)&MASK_ZERO_IF_OVER(769))\
+!!((x)&MASK_ZERO_IF_OVER(770))+!!((x)&MASK_ZERO_IF_OVER(771))\
+!!((x)&MASK_ZERO_IF_OVER(772))+!!((x)&MASK_ZERO_IF_OVER(773))\
+!!((x)&MASK_ZERO_IF_OVER(774))+!!((x)&MASK_ZERO_IF_OVER(775))\
+!!((x)&MASK_ZERO_IF_OVER(776))+!!((x)&MASK_ZERO_IF_OVER(777))\
+!!((x)&MASK_ZERO_IF_OVER(778))+!!((x)&MASK_ZERO_IF_OVER(779))\
+!!((x)&MASK_ZERO_IF_OVER(780))+!!((x)&MASK_ZERO_IF_OVER(781))\
+!!((x)&MASK_ZERO_IF_OVER(782))+!!((x)&MASK_ZERO_IF_OVER(783))\
+!!((x)&MASK_ZERO_IF_OVER(784))+!!((x)&MASK_ZERO_IF_OVER(785))\
+!!((x)&MASK_ZERO_IF_OVER(786))+!!((x)&MASK_ZERO_IF_OVER(787))\
+!!((x)&MASK_ZERO_IF_OVER(788))+!!((x)&MASK_ZERO_IF_OVER(789))\
+!!((x)&MASK_ZERO_IF_OVER(790))+!!((x)&MASK_ZERO_IF_OVER(791))\
+!!((x)&MASK_ZERO_IF_OVER(792))+!!((x)&MASK_ZERO_IF_OVER(793))\
+!!((x)&MASK_ZERO_IF_OVER(794))+!!((x)&MASK_ZERO_IF_OVER(795))\
+!!((x)&MASK_ZERO_IF_OVER(796))+!!((x)&MASK_ZERO_IF_OVER(797))\
+!!((x)&MASK_ZERO_IF_OVER(798))+!!((x)&MASK_ZERO_IF_OVER(799))\
+!!((x)&MASK_ZERO_IF_OVER(800))+!!((x)&MASK_ZERO_IF_OVER(801))\
+!!((x)&MASK_ZERO_IF_OVER(802))+!!((x)&MASK_ZERO_IF_OVER(803))\
+!!((x)&MASK_ZERO_IF_OVER(804))+!!((x)&MASK_ZERO_IF_OVER(805))\
+!!((x)&MASK_ZERO_IF_OVER(806))+!!((x)&MASK_ZERO_IF_OVER(807))\
+!!((x)&MASK_ZERO_IF_OVER(808))+!!((x)&MASK_ZERO_IF_OVER(809))\
+!!((x)&MASK_ZERO_IF_OVER(810))+!!((x)&MASK_ZERO_IF_OVER(811))\
+!!((x)&MASK_ZERO_IF_OVER(812))+!!((x)&MASK_ZERO_IF_OVER(813))\
+!!((x)&MASK_ZERO_IF_OVER(814))+!!((x)&MASK_ZERO_IF_OVER(815))\
+!!((x)&MASK_ZERO_IF_OVER(816))+!!((x)&MASK_ZERO_IF_OVER(817))\
+!!((x)&MASK_ZERO_IF_OVER(818))+!!((x)&MASK_ZERO_IF_OVER(819))\
+!!((x)&MASK_ZERO_IF_OVER(820))+!!((x)&MASK_ZERO_IF_OVER(821))\
+!!((x)&MASK_ZERO_IF_OVER(822))+!!((x)&MASK_ZERO_IF_OVER(823))\
+!!((x)&MASK_ZERO_IF_OVER(824))+!!((x)&MASK_ZERO_IF_OVER(825))\
+!!((x)&MASK_ZERO_IF_OVER(826))+!!((x)&MASK_ZERO_IF_OVER(827))\
+!!((x)&MASK_ZERO_IF_OVER(828))+!!((x)&MASK_ZERO_IF_OVER(829))\
+!!((x)&MASK_ZERO_IF_OVER(830))+!!((x)&MASK_ZERO_IF_OVER(831))\
+!!((x)&MASK_ZERO_IF_OVER(832))+!!((x)&MASK_ZERO_IF_OVER(833))\
+!!((x)&MASK_ZERO_IF_OVER(834))+!!((x)&MASK_ZERO_IF_OVER(835))\
+!!((x)&MASK_ZERO_IF_OVER(836))+!!((x)&MASK_ZERO_IF_OVER(837))\
+!!((x)&MASK_ZERO_IF_OVER(838))+!!((x)&MASK_ZERO_IF_OVER(839))\
+!!((x)&MASK_ZERO_IF_OVER(840))+!!((x)&MASK_ZERO_IF_OVER(841))\
+!!((x)&MASK_ZERO_IF_OVER(842))+!!((x)&MASK_ZERO_IF_OVER(843))\
+!!((x)&MASK_ZERO_IF_OVER(844))+!!((x)&MASK_ZERO_IF_OVER(845))\
+!!((x)&MASK_ZERO_IF_OVER(846))+!!((x)&MASK_ZERO_IF_OVER(847))\
+!!((x)&MASK_ZERO_IF_OVER(848))+!!((x)&MASK_ZERO_IF_OVER(849))\
+!!((x)&MASK_ZERO_IF_OVER(850))+!!((x)&MASK_ZERO_IF_OVER(851))\
+!!((x)&MASK_ZERO_IF_OVER(852))+!!((x)&MASK_ZERO_IF_OVER(853))\
+!!((x)&MASK_ZERO_IF_OVER(854))+!!((x)&MASK_ZERO_IF_OVER(855))\
+!!((x)&MASK_ZERO_IF_OVER(856))+!!((x)&MASK_ZERO_IF_OVER(857))\
+!!((x)&MASK_ZERO_IF_OVER(858))+!!((x)&MASK_ZERO_IF_OVER(859))\
+!!((x)&MASK_ZERO_IF_OVER(860))+!!((x)&MASK_ZERO_IF_OVER(861))\
+!!((x)&MASK_ZERO_IF_OVER(862))+!!((x)&MASK_ZERO_IF_OVER(863))\
+!!((x)&MASK_ZERO_IF_OVER(864))+!!((x)&MASK_ZERO_IF_OVER(865))\
+!!((x)&MASK_ZERO_IF_OVER(866))+!!((x)&MASK_ZERO_IF_OVER(867))\
+!!((x)&MASK_ZERO_IF_OVER(868))+!!((x)&MASK_ZERO_IF_OVER(869))\
+!!((x)&MASK_ZERO_IF_OVER(870))+!!((x)&MASK_ZERO_IF_OVER(871))\
+!!((x)&MASK_ZERO_IF_OVER(872))+!!((x)&MASK_ZERO_IF_OVER(873))\
+!!((x)&MASK_ZERO_IF_OVER(874))+!!((x)&MASK_ZERO_IF_OVER(875))\
+!!((x)&MASK_ZERO_IF_OVER(876))+!!((x)&MASK_ZERO_IF_OVER(877))\
+!!((x)&MASK_ZERO_IF_OVER(878))+!!((x)&MASK_ZERO_IF_OVER(879))\
+!!((x)&MASK_ZERO_IF_OVER(880))+!!((x)&MASK_ZERO_IF_OVER(881))\
+!!((x)&MASK_ZERO_IF_OVER(882))+!!((x)&MASK_ZERO_IF_OVER(883))\
+!!((x)&MASK_ZERO_IF_OVER(884))+!!((x)&MASK_ZERO_IF_OVER(885))\
+!!((x)&MASK_ZERO_IF_OVER(886))+!!((x)&MASK_ZERO_IF_OVER(887))\
+!!((x)&MASK_ZERO_IF_OVER(888))+!!((x)&MASK_ZERO_IF_OVER(889))\
+!!((x)&MASK_ZERO_IF_OVER(890))+!!((x)&MASK_ZERO_IF_OVER(891))\
+!!((x)&MASK_ZERO_IF_OVER(892))+!!((x)&MASK_ZERO_IF_OVER(893))\
+!!((x)&MASK_ZERO_IF_OVER(894))+!!((x)&MASK_ZERO_IF_OVER(895))\
+!!((x)&MASK_ZERO_IF_OVER(896))+!!((x)&MASK_ZERO_IF_OVER(897))\
+!!((x)&MASK_ZERO_IF_OVER(898))+!!((x)&MASK_ZERO_IF_OVER(899))\
+!!((x)&MASK_ZERO_IF_OVER(900))+!!((x)&MASK_ZERO_IF_OVER(901))\
+!!((x)&MASK_ZERO_IF_OVER(902))+!!((x)&MASK_ZERO_IF_OVER(903))\
+!!((x)&MASK_ZERO_IF_OVER(904))+!!((x)&MASK_ZERO_IF_OVER(905))\
+!!((x)&MASK_ZERO_IF_OVER(906))+!!((x)&MASK_ZERO_IF_OVER(907))\
+!!((x)&MASK_ZERO_IF_OVER(908))+!!((x)&MASK_ZERO_IF_OVER(909))\
+!!((x)&MASK_ZERO_IF_OVER(910))+!!((x)&MASK_ZERO_IF_OVER(911))\
+!!((x)&MASK_ZERO_IF_OVER(912))+!!((x)&MASK_ZERO_IF_OVER(913))\
+!!((x)&MASK_ZERO_IF_OVER(914))+!!((x)&MASK_ZERO_IF_OVER(915))\
+!!((x)&MASK_ZERO_IF_OVER(916))+!!((x)&MASK_ZERO_IF_OVER(917))\
+!!((x)&MASK_ZERO_IF_OVER(918))+!!((x)&MASK_ZERO_IF_OVER(919))\
+!!((x)&MASK_ZERO_IF_OVER(920))+!!((x)&MASK_ZERO_IF_OVER(921))\
+!!((x)&MASK_ZERO_IF_OVER(922))+!!((x)&MASK_ZERO_IF_OVER(923))\
+!!((x)&MASK_ZERO_IF_OVER(924))+!!((x)&MASK_ZERO_IF_OVER(925))\
+!!((x)&MASK_ZERO_IF_OVER(926))+!!((x)&MASK_ZERO_IF_OVER(927))\
+!!((x)&MASK_ZERO_IF_OVER(928))+!!((x)&MASK_ZERO_IF_OVER(929))\
+!!((x)&MASK_ZERO_IF_OVER(930))+!!((x)&MASK_ZERO_IF_OVER(931))\
+!!((x)&MASK_ZERO_IF_OVER(932))+!!((x)&MASK_ZERO_IF_OVER(933))\
+!!((x)&MASK_ZERO_IF_OVER(934))+!!((x)&MASK_ZERO_IF_OVER(935))\
+!!((x)&MASK_ZERO_IF_OVER(936))+!!((x)&MASK_ZERO_IF_OVER(937))\
+!!((x)&MASK_ZERO_IF_OVER(938))+!!((x)&MASK_ZERO_IF_OVER(939))\
+!!((x)&MASK_ZERO_IF_OVER(940))+!!((x)&MASK_ZERO_IF_OVER(941))\
+!!((x)&MASK_ZERO_IF_OVER(942))+!!((x)&MASK_ZERO_IF_OVER(943))\
+!!((x)&MASK_ZERO_IF_OVER(944))+!!((x)&MASK_ZERO_IF_OVER(945))\
+!!((x)&MASK_ZERO_IF_OVER(946))+!!((x)&MASK_ZERO_IF_OVER(947))\
+!!((x)&MASK_ZERO_IF_OVER(948))+!!((x)&MASK_ZERO_IF_OVER(949))\
+!!((x)&MASK_ZERO_IF_OVER(950))+!!((x)&MASK_ZERO_IF_OVER(951))\
+!!((x)&MASK_ZERO_IF_OVER(952))+!!((x)&MASK_ZERO_IF_OVER(953))\
+!!((x)&MASK_ZERO_IF_OVER(954))+!!((x)&MASK_ZERO_IF_OVER(955))\
+!!((x)&MASK_ZERO_IF_OVER(956))+!!((x)&MASK_ZERO_IF_OVER(957))\
+!!((x)&MASK_ZERO_IF_OVER(958))+!!((x)&MASK_ZERO_IF_OVER(959))\
+!!((x)&MASK_ZERO_IF_OVER(960))+!!((x)&MASK_ZERO_IF_OVER(961))\
+!!((x)&MASK_ZERO_IF_OVER(962))+!!((x)&MASK_ZERO_IF_OVER(963))\
+!!((x)&MASK_ZERO_IF_OVER(964))+!!((x)&MASK_ZERO_IF_OVER(965))\
+!!((x)&MASK_ZERO_IF_OVER(966))+!!((x)&MASK_ZERO_IF_OVER(967))\
+!!((x)&MASK_ZERO_IF_OVER(968))+!!((x)&MASK_ZERO_IF_OVER(969))\
+!!((x)&MASK_ZERO_IF_OVER(970))+!!((x)&MASK_ZERO_IF_OVER(971))\
+!!((x)&MASK_ZERO_IF_OVER(972))+!!((x)&MASK_ZERO_IF_OVER(973))\
+!!((x)&MASK_ZERO_IF_OVER(974))+!!((x)&MASK_ZERO_IF_OVER(975))\
+!!((x)&MASK_ZERO_IF_OVER(976))+!!((x)&MASK_ZERO_IF_OVER(977))\
+!!((x)&MASK_ZERO_IF_OVER(978))+!!((x)&MASK_ZERO_IF_OVER(979))\
+!!((x)&MASK_ZERO_IF_OVER(980))+!!((x)&MASK_ZERO_IF_OVER(981))\
+!!((x)&MASK_ZERO_IF_OVER(982))+!!((x)&MASK_ZERO_IF_OVER(983))\
+!!((x)&MASK_ZERO_IF_OVER(984))+!!((x)&MASK_ZERO_IF_OVER(985))\
+!!((x)&MASK_ZERO_IF_OVER(986))+!!((x)&MASK_ZERO_IF_OVER(987))\
+!!((x)&MASK_ZERO_IF_OVER(988))+!!((x)&MASK_ZERO_IF_OVER(989))\
+!!((x)&MASK_ZERO_IF_OVER(990))+!!((x)&MASK_ZERO_IF_OVER(991))\
+!!((x)&MASK_ZERO_IF_OVER(992))+!!((x)&MASK_ZERO_IF_OVER(993))\
+!!((x)&MASK_ZERO_IF_OVER(994))+!!((x)&MASK_ZERO_IF_OVER(995))\
+!!((x)&MASK_ZERO_IF_OVER(996))+!!((x)&MASK_ZERO_IF_OVER(997))\
+!!((x)&MASK_ZERO_IF_OVER(998))+!!((x)&MASK_ZERO_IF_OVER(999))\
+!!((x)&MASK_ZERO_IF_OVER(1000))+!!((x)&MASK_ZERO_IF_OVER(1001))\
+!!((x)&MASK_ZERO_IF_OVER(1002))+!!((x)&MASK_ZERO_IF_OVER(1003))\
+!!((x)&MASK_ZERO_IF_OVER(1004))+!!((x)&MASK_ZERO_IF_OVER(1005))\
+!!((x)&MASK_ZERO_IF_OVER(1006))+!!((x)&MASK_ZERO_IF_OVER(1007))\
+!!((x)&MASK_ZERO_IF_OVER(1008))+!!((x)&MASK_ZERO_IF_OVER(1009))\
+!!((x)&MASK_ZERO_IF_OVER(1010))+!!((x)&MASK_ZERO_IF_OVER(1011))\
+!!((x)&MASK_ZERO_IF_OVER(1012))+!!((x)&MASK_ZERO_IF_OVER(1013))\
+!!((x)&MASK_ZERO_IF_OVER(1014))+!!((x)&MASK_ZERO_IF_OVER(1015))\
+!!((x)&MASK_ZERO_IF_OVER(1016))+!!((x)&MASK_ZERO_IF_OVER(1017))\
+!!((x)&MASK_ZERO_IF_OVER(1018))+!!((x)&MASK_ZERO_IF_OVER(1019))\
+!!((x)&MASK_ZERO_IF_OVER(1020))+!!((x)&MASK_ZERO_IF_OVER(1021))\
+!!((x)&MASK_ZERO_IF_OVER(1022))+!!((x)&MASK_ZERO_IF_OVER(1023)))

#define QUANT_BITS_SET(x) QUANT_BITS_SET_RAW( ((BitsSetType)(x)) )

#include <stdio.h>

int main(void)
{
/* Let's make an array of length 4 */

int arr[QUANT_BITS_SET(17)];

printf("%u",(unsigned)(sizeof arr/sizeof*arr));
}

The codes prints 2 on my system, but you get the idea...
 
S

Skarmander

Frederick said:
Richard Heathfield posted:




I meant something more along the following lines. Do compilers nowadays
optimise away Bitwise-AND operations when one of the operands is known to
be 0 at compile-time?
Click to expand...
Yes. Constant folding is somethings almost all compilers handle well. (Those
that don't are usually too hopeless to consider for optmizing purposes.)
Take care that the compiler still has to parse the entire expression; some
low-end systems may barf on such enormous constructs.
/* Macro: QUANT_BITS_SET

This macro determines the quantity of bits which
are set in an integer expression whose signedness
is unsigned.
Click to expand...
I prefer my desktop calculator, but YMMV.

/* Let's make an array of length 4 */
Click to expand...
A misleading comment if ever I saw one.
int arr[QUANT_BITS_SET(17)];
Click to expand...
Hmm, I'd write that

#define BITS_SET_IN_THE_BINARY_REPRESENTATION_OF_17 2
[...]
int arr[BITS_SET_IN_THE_BINARY_REPRESENTATION_OF_17]

Still uses a rather unwieldy macro, but it's a tad shorter nonetheless.
printf("%u",(unsigned)(sizeof arr/sizeof*arr));
}

The codes prints 2 on my system, but you get the idea...
Click to expand...
Yes, the preprocessor is neat.

S.
 
F

Frederick Gotham

Skarmander posted:
Constant folding is somethings almost all compilers handle well. (Those
that don't are usually too hopeless to consider for optmizing
purposes.)
Click to expand...


We could always write more macros which use the ternary operator to get rid
of redundant Bitwise-AND operations. Something like:

#define BitwiseAND(x,mask) (\
(mask) \
? x & (mask) \
: 0 )

And we could even go further to strip out the additions:

#define Add(a,b) (\
(b) \
? (a) + (b) \
: (a) )

A misleading comment if ever I saw one.
Click to expand...


Don't ask me how, but I somehow calculated that 17 had four bits set.
 

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