# bit manipulation question

Discussion in 'C Programming' started by Elijah Bailey, Dec 3, 2003.

1. ### Elijah BaileyGuest

I have a long x;
I want to write a function

long f(long x, int k)

such that it extracts every k-th bit of x, concatenates
them and returns it. Anyone can help me in writing this
function?

examples
x = 10101010 k = 1 f(x) = 10101010
x = 10101010 k = 2 f(x) = 1111
x = 10101010 k = 3 f(x) = 010
x = 10101010 k = 4 f(x) = 11

Any bit gurus here who can help me?

Thanks,
--Elijah

Elijah Bailey, Dec 3, 2003

2. ### Ben PfaffGuest

(Elijah Bailey) writes:

> I want to write a function
>
> long f(long x, int k)
>
> such that it extracts every k-th bit of x, concatenates
> them and returns it. Anyone can help me in writing this
> function?
>
> examples
> x = 10101010 k = 1 f(x) = 10101010
> x = 10101010 k = 2 f(x) = 1111
> x = 10101010 k = 3 f(x) = 010
> x = 10101010 k = 4 f(x) = 11

I don't understand your k = 3 example. Shouldn't f(x) = 101 for
consistency with the others?

/* I think this'll do the trick, but I haven't tested it or even
compiled it. In fact, I haven't even tried it out on paper,
so you'd better think it through carefully before assuming
anything. */
unsigned long f(unsigned long x, int k)
{
unsigned long out = 0; /* Output so far. */
unsigned long left = -1; /* Mask of bits left to extract from x. */
unsigned long msb = ~(left << 1 >> 1); /* Top bit in a unsigned long. */

do {
/* Extract MSB of x into LSB of out. */
out <<= 1;
if (x & msb)
out |= 1;

x <<= k;
left <<= k;
} while (left != 0);

return out;
}
--
int main(void){char p[]="ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz.\
\n",*q="kl BIcNBFr.NKEzjwCIxNJC";int i=sizeof p/2;char *strchr();int putchar(\
);while(*q){i+=strchr(p,*q++)-p;if(i>=(int)sizeof p)i-=sizeof p-1;putchar(p\
);}return 0;}

Ben Pfaff, Dec 3, 2003

3. ### CapstarGuest

Elijah Bailey wrote:
> I have a long x;
> I want to write a function
>
> long f(long x, int k)
>
> such that it extracts every k-th bit of x, concatenates
> them and returns it. Anyone can help me in writing this
> function?
>
> examples
> x = 10101010 k = 1 f(x) = 10101010
> x = 10101010 k = 2 f(x) = 1111
> x = 10101010 k = 3 f(x) = 010
> x = 10101010 k = 4 f(x) = 11
>
> Any bit gurus here who can help me?
>
> Thanks,
> --Elijah

Although this seems to me like a homework asignment, I couldn't resist
to try something.
I wouldn't try calling it as you do in your example, because I don't
think any C compiler would compile it.

This code is untested and does not take care any special cases. There is
at least on obvious one, but you can take care of that yourself.

long f(long x, int k)
{
long temp = 0;
long i, j;

for(i = 0, j = 0; i < sizeof(x) * 8; i += k, ++j)
temp |= (x & (1 << i)) >> (i - j);

return temp;
}

Mark

Capstar, Dec 3, 2003
4. ### CapstarGuest

Capstar wrote:
> Elijah Bailey wrote:
>
>> I have a long x;
>> I want to write a function
>> long f(long x, int k)
>>
>> such that it extracts every k-th bit of x, concatenates
>> them and returns it. Anyone can help me in writing this
>> function?
>> examples
>> x = 10101010 k = 1 f(x) = 10101010
>> x = 10101010 k = 2 f(x) = 1111
>> x = 10101010 k = 3 f(x) = 010 x = 10101010 k = 4 f(x) = 11
>>
>> Any bit gurus here who can help me?
>>
>> Thanks,
>> --Elijah

>
>
> Although this seems to me like a homework asignment, I couldn't resist
> to try something.
> I wouldn't try calling it as you do in your example, because I don't
> think any C compiler would compile it.
>
> This code is untested and does not take care any special cases. There is
> at least on obvious one, but you can take care of that yourself.
>
> long f(long x, int k)
> {
> long temp = 0;
> long i, j;
>
> for(i = 0, j = 0; i < sizeof(x) * 8; i += k, ++j)
> temp |= (x & (1 << i)) >> (i - j);
>
> return temp;
> }
>
> Mark
>

mistake. In my previous post you always start at bit 0. But when you say
take every k-th bit, you obviously want to start at bit k - 1.

I also tested it so I'll post my complete test program:
#include <stdio.h>
#include <string.h>
#include <stdlib.h>

char *bitprint(long x, unsigned long max)
{
unsigned long i, j;
static char bitstring[sizeof(x) * 8 + 1];

if(max > sizeof(x) * 8) max = sizeof(x) * 8;

for(i = max - 1, j = 0; j < max; --i, ++j)
{
if(x & (1 << i)) bitstring[j] = '1';
else bitstring[j] = '0';
}
bitstring[max] = '\0';

return bitstring;
}

long f(long x, int k)
{
long temp = 0;
unsigned long i, j;

for(i = k - 1, j = 0; i < sizeof(x) * 8; i += k, ++j)
temp |= (x & (1 << i)) >> (i - j);

return temp;
}

int main(void)
{
long x = 0xaa; /*10101010*/
int k;
char *xstring;

xstring = strdup(bitprint(x, 8));

for(k = 1; k <= 4; ++k)
printf("x = %s\tk = %d\t f(x, k) = %s\n", xstring, k, bitprint(f(x,
k), 8));

free(xstring);

return 0;
}

Mark

PS. Isn't strdup in the standard? If I compile this with gcc -W -Wall
-ansi -pedantic I get: warning: implicit declaration of function `strdup'.

Capstar, Dec 3, 2003
5. ### nrkGuest

<snip>

>
> PS. Isn't strdup in the standard? If I compile this with gcc -W -Wall
> -ansi -pedantic I get: warning: implicit declaration of function `strdup'.

No, strdup is *not* part of the standard.

<OT>
According to my manpage, conforms to SYS V R3 and BSD 4.3
</OT>

-nrk.

nrk, Dec 3, 2003
6. ### Mark GordonGuest

On Wed, 03 Dec 2003 10:10:04 +0100
Capstar <> wrote:

> Capstar wrote:
> > Elijah Bailey wrote:
> >
> >> I have a long x;
> >> I want to write a function
> >> long f(long x, int k)
> >>
> >> such that it extracts every k-th bit of x, concatenates
> >> them and returns it. Anyone can help me in writing this
> >> function?
> >> examples
> >> x = 10101010 k = 1 f(x) = 10101010
> >> x = 10101010 k = 2 f(x) = 1111
> >> x = 10101010 k = 3 f(x) = 010 x = 10101010 k = 4 f(x) = 11
> >>
> >> Any bit gurus here who can help me?
> >>
> >> Thanks,
> >> --Elijah

> >
> >
> > Although this seems to me like a homework asignment, I couldn't
> > resist to try something.
> > I wouldn't try calling it as you do in your example, because I don't
> > think any C compiler would compile it.
> >
> > This code is untested and does not take care any special cases.
> > There is at least on obvious one, but you can take care of that
> > yourself.
> >
> > long f(long x, int k)
> > {
> > long temp = 0;
> > long i, j;
> >
> > for(i = 0, j = 0; i < sizeof(x) * 8; i += k, ++j)

Tut, tut. Assuming CHAR_BIT==8

> > temp |= (x & (1 << i)) >> (i - j);
> >
> > return temp;
> > }
> >
> > Mark
> >

>
> mistake. In my previous post you always start at bit 0. But when you
> say take every k-th bit, you obviously want to start at bit k - 1.
>
> I also tested it so I'll post my complete test program:
> #include <stdio.h>
> #include <string.h>
> #include <stdlib.h>
>
> char *bitprint(long x, unsigned long max)

I would prefer to have the function take a parameter to the buffer
to be used rather than returning a pointer to a static buffer.

> {
> unsigned long i, j;
> static char bitstring[sizeof(x) * 8 + 1];

Tut, tut. Still assuming CHAR_BIT==8 throughout this new version.

> if(max > sizeof(x) * 8) max = sizeof(x) * 8;
>
> for(i = max - 1, j = 0; j < max; --i, ++j)
> {
> if(x & (1 << i)) bitstring[j] = '1';
> else bitstring[j] = '0';
> }
> bitstring[max] = '\0';
>
> return bitstring;
> }
>
> long f(long x, int k)
> {
> long temp = 0;
> unsigned long i, j;
>
> for(i = k - 1, j = 0; i < sizeof(x) * 8; i += k, ++j)
> temp |= (x & (1 << i)) >> (i - j);
>
> return temp;
> }
>
> int main(void)
> {
> long x = 0xaa; /*10101010*/
> int k;
> char *xstring;
>
> xstring = strdup(bitprint(x, 8));
>
> for(k = 1; k <= 4; ++k)
> printf("x = %s\tk = %d\t f(x, k) = %s\n", xstring, k,
> bitprint(f(x,
> k), 8));
>
> free(xstring);
>
> return 0;
> }
>
> Mark
>
> PS. Isn't strdup in the standard? If I compile this with gcc -W -Wall
> -ansi -pedantic I get: warning: implicit declaration of function
> `strdup'.

No, it's not part of the standard and so when you use -ansi -pedantic it
is not defined by string.h
--
Mark Gordon
Paid to be a Geek & a Senior Software Developer
Although my email address says spamtrap, it is real and I read it.

Mark Gordon, Dec 3, 2003
7. ### GrumbleGuest

Ben Pfaff wrote:
> Elijah Bailey writes:
>
>>I want to write a function
>>
>>long f(long x, int k)
>>
>>such that it extracts every k-th bit of x, concatenates
>>them and returns it. Anyone can help me in writing this
>>function?
>>
>>examples
>> x = 10101010 k = 1 f(x) = 10101010
>> x = 10101010 k = 2 f(x) = 1111
>> x = 10101010 k = 3 f(x) = 010
>> x = 10101010 k = 4 f(x) = 11

>
>
> I don't understand your k = 3 example. Shouldn't f(x) = 101 for
> consistency with the others?

Let x_i denote the i_th bit in x counting from right to left.

In particular, x_0 denotes the right-most bit in x.

Then f(x)_i = x_{k-1+i*k}

k=1 => f(x)_i = x_i
k=2 => f(x)_i = x_{2*i+1}
k=3 => f(x)_i = x_{3*i+2}

Thus, from right to left, x_2 | x_5 | x_8

Grumble, Dec 3, 2003
8. ### nrkGuest

Elijah Bailey wrote:

> I have a long x;
> I want to write a function
>
> long f(long x, int k)
>
> such that it extracts every k-th bit of x, concatenates
> them and returns it. Anyone can help me in writing this
> function?
>
> examples
> x = 10101010 k = 1 f(x) = 10101010
> x = 10101010 k = 2 f(x) = 1111
> x = 10101010 k = 3 f(x) = 010
> x = 10101010 k = 4 f(x) = 11
>
> Any bit gurus here who can help me?
>
> Thanks,
> --Elijah

Probably a bit of beating around the bush going on in the code below, but
hey, you can verify your function as well

-nrk.

#include <stdio.h>
#include <limits.h>
#include <string.h>

unsigned long bitextract(unsigned long input, int k) {
unsigned long ret = 0;
size_t i;
int j;

if ( k <= 1 ) return input;

for ( i = 0, j = 0; i < sizeof input * CHAR_BIT; i += k, ++j ) {
input >>= (k-1);
ret |= (input & 1) << j;
input >>= 1;
}

return ret;
}

char *printBinary(char *buf, unsigned long num) {
static char *hex2bin[] =
{
"0000", "0001", "0010", "0011",
"0100", "0101", "0110", "0111",
"1000", "1001", "1010", "1011",
"1100", "1101", "1110", "1111"
};

size_t i;

for ( i = 4; i <= (sizeof num * CHAR_BIT); i += 4 ) {
int shift = (sizeof num * CHAR_BIT) - i;
memcpy(buf, hex2bin[((num & (0xFUL << shift)) >> shift)], 4);
buf += 4;
}
*buf = 0;

return buf - (i - 4);
}

int verifyResult(int input, int k, int result) {
char input_str[sizeof input * CHAR_BIT + 1];
char result_str[sizeof input * CHAR_BIT + 1];
char extract_str[sizeof input * CHAR_BIT + 1];
int i, j;

printBinary(input_str, input);
printBinary(result_str, result);

for ( i = sizeof input_str - 1 - k, j = sizeof extract_str - 2;
i >= 0;
i -= k, --j )
{
extract_str[j] = input_str;
}

while ( j >= 0 ) extract_str[j--] = '0';

extract_str[sizeof extract_str - 1] = 0;

return strcmp(result_str, extract_str);
}

int main(void) {
unsigned long input = 0x12345678UL;
unsigned long result;
size_t i;

for ( i = 1; i <= sizeof input * CHAR_BIT; ++i ) {
result = bitextract(input, i);
if ( verifyResult(input, i, result) ) {
printf("Failed for bit %d\n", i);
break;
}
}

if ( i >= sizeof input * CHAR_BIT )
printf("Success!\n");

return 0;
}

nrk, Dec 3, 2003
9. ### CapstarGuest

Mark Gordon wrote:
> On Wed, 03 Dec 2003 10:10:04 +0100
> Capstar <> wrote:
>
>
>>Capstar wrote:
>>
>>>Elijah Bailey wrote:
>>>
>>>
>>>>I have a long x;
>>>>I want to write a function
>>>>long f(long x, int k)
>>>>
>>>>such that it extracts every k-th bit of x, concatenates
>>>>them and returns it. Anyone can help me in writing this
>>>>function?
>>>>examples
>>>> x = 10101010 k = 1 f(x) = 10101010
>>>> x = 10101010 k = 2 f(x) = 1111
>>>> x = 10101010 k = 3 f(x) = 010 x = 10101010 k = 4 f(x) = 11
>>>>
>>>>Any bit gurus here who can help me?
>>>>
>>>>Thanks,
>>>>--Elijah
>>>
>>>
>>>Although this seems to me like a homework asignment, I couldn't
>>>resist to try something.
>>>I wouldn't try calling it as you do in your example, because I don't
>>>think any C compiler would compile it.
>>>
>>>This code is untested and does not take care any special cases.
>>>There is at least on obvious one, but you can take care of that
>>>yourself.
>>>
>>>long f(long x, int k)
>>>{
>>> long temp = 0;
>>> long i, j;
>>>
>>> for(i = 0, j = 0; i < sizeof(x) * 8; i += k, ++j)

>
>
> Tut, tut. Assuming CHAR_BIT==8

I am not a c.l.c. guru and so I'm not an allmighty know it all. And I
thought sizeof returned in 8-bit bytes. I'll keep CHAR_BIT in mind next
time.

>
>
>>> temp |= (x & (1 << i)) >> (i - j);
>>>
>>> return temp;
>>>}
>>>
>>>Mark
>>>

>>
>>mistake. In my previous post you always start at bit 0. But when you
>>say take every k-th bit, you obviously want to start at bit k - 1.
>>
>>I also tested it so I'll post my complete test program:
>>#include <stdio.h>
>>#include <string.h>
>>#include <stdlib.h>
>>
>>char *bitprint(long x, unsigned long max)

>
>
> I would prefer to have the function take a parameter to the buffer
> to be used rather than returning a pointer to a static buffer.

I don't realy care wat you want. I just needed a function, which would
return a character array so I could display the value of f(x,k) to
verify the results easily.

>
>
>>{
>> unsigned long i, j;
>> static char bitstring[sizeof(x) * 8 + 1];

>
>
> Tut, tut. Still assuming CHAR_BIT==8 throughout this new version.

I didn't became an allmighty know it all c.l.c. guru in those 32
minutes, So I still thought sizeof returned in 8-bit bytes.

>
>
>> if(max > sizeof(x) * 8) max = sizeof(x) * 8;
>>
>> for(i = max - 1, j = 0; j < max; --i, ++j)
>> {
>> if(x & (1 << i)) bitstring[j] = '1';
>> else bitstring[j] = '0';
>> }
>> bitstring[max] = '\0';
>>
>> return bitstring;
>>}
>>
>>long f(long x, int k)
>>{
>> long temp = 0;
>> unsigned long i, j;
>>
>> for(i = k - 1, j = 0; i < sizeof(x) * 8; i += k, ++j)
>> temp |= (x & (1 << i)) >> (i - j);
>>
>> return temp;
>>}
>>
>>int main(void)
>>{
>> long x = 0xaa; /*10101010*/
>> int k;
>> char *xstring;
>>
>> xstring = strdup(bitprint(x, 8));
>>
>> for(k = 1; k <= 4; ++k)
>> printf("x = %s\tk = %d\t f(x, k) = %s\n", xstring, k,
>> bitprint(f(x,
>>k), 8));
>>
>> free(xstring);
>>
>> return 0;
>>}
>>
>>Mark
>>
>>PS. Isn't strdup in the standard? If I compile this with gcc -W -Wall
>>-ansi -pedantic I get: warning: implicit declaration of function
>>`strdup'.

>
>
> No, it's not part of the standard and so when you use -ansi -pedantic it
> is not defined by string.h

OK, thanks.

Capstar, Dec 3, 2003
10. ### Mark GordonGuest

On Wed, 03 Dec 2003 17:24:09 +0100
Capstar <> wrote:

> Mark Gordon wrote:

<snip>

> > Tut, tut. Assuming CHAR_BIT==8

>
> I am not a c.l.c. guru and so I'm not an allmighty know it all.

Nor am I. Perhaps I should not have said "Tut, tut" since it was not my
intent to cause offence.

> And I
> thought sizeof returned in 8-bit bytes. I'll keep CHAR_BIT in mind
> next time.

Well, I've been caught out a few times here. One of the good things
(and I do deliberately include myself) make.

<snip>

> > I would prefer to have the function take a parameter to the buffer
> > to be used rather than returning a pointer to a static buffer.

>
> I don't realy care wat you want. I just needed a function, which would
> return a character array so I could display the value of f(x,k) to
> verify the results easily.

It was merely intended as a helpful stylistic comment, not an
instruction.

<snip>

> > No, it's not part of the standard and so when you use -ansi
> > -pedantic it is not defined by string.h

>
> OK, thanks.

You're welcome.
--
Mark Gordon
Paid to be a Geek & a Senior Software Developer
Although my email address says spamtrap, it is real and I read it.

Mark Gordon, Dec 3, 2003
11. ### Michael Andrew FylesGuest

In article <bqkjp8\$8mr\$>, Grumble wrote:
>Ben Pfaff wrote:
>> Elijah Bailey writes:
>>
>>>I want to write a function
>>>
>>>long f(long x, int k)
>>>
>>>such that it extracts every k-th bit of x, concatenates
>>>them and returns it. Anyone can help me in writing this
>>>function?
>>>
>>>examples
>>> x = 10101010 k = 1 f(x) = 10101010
>>> x = 10101010 k = 2 f(x) = 1111
>>> x = 10101010 k = 3 f(x) = 010
>>> x = 10101010 k = 4 f(x) = 11

>>
>>
>> I don't understand your k = 3 example. Shouldn't f(x) = 101 for
>> consistency with the others?

>
>Let x_i denote the i_th bit in x counting from right to left.
>
>In particular, x_0 denotes the right-most bit in x.
>
>Then f(x)_i = x_{k-1+i*k}
>
>k=1 => f(x)_i = x_i
>k=2 => f(x)_i = x_{2*i+1}
>k=3 => f(x)_i = x_{3*i+2}
>
>Thus, from right to left, x_2 | x_5 | x_8

Unless I've misunderstood, if x_0 is the
right-most bit in x, that would make x_8 one to
the left of the left-most bit in x. For the
example given, this doesn't exist.

--
Michael

Michael Andrew Fyles, Dec 4, 2003
12. ### CapstarGuest

Mark Gordon wrote:
> On Wed, 03 Dec 2003 17:24:09 +0100
> Capstar <> wrote:
>
>
>>Mark Gordon wrote:

>
>
> <snip>
>
>>>Tut, tut. Assuming CHAR_BIT==8

>>
>>I am not a c.l.c. guru and so I'm not an allmighty know it all.

>
>
> Nor am I. Perhaps I should not have said "Tut, tut" since it was not my
> intent to cause offence.
>

OK, well then no offence taken. It was indeed the "Tut, tut" that pissed
me off. I normally don't mind any comment on my code, I even welcome it.

<snip>
>
>>>I would prefer to have the function take a parameter to the buffer
>>>to be used rather than returning a pointer to a static buffer.

>>
>>I don't realy care wat you want. I just needed a function, which would
>>return a character array so I could display the value of f(x,k) to
>>verify the results easily.

>
>
> It was merely intended as a helpful stylistic comment, not an
> instruction.
>

I know. Sorry, I normally wouldn't react like that. (Was still pissed).
than once in a printf statement for instance. That's why I did:

xstring = strdup(bitprint(x, 8));

Mark.

Capstar, Dec 4, 2003
13. ### Paul HsiehGuest

says...
> I have a long x;
> I want to write a function
>
> long f(long x, int k)
>
> such that it extracts every k-th bit of x, concatenates
> them and returns it. Anyone can help me in writing this
> function?
>
> examples
> x = 10101010 k = 1 f(x) = 10101010
> x = 10101010 k = 2 f(x) = 1111
> x = 10101010 k = 3 f(x) = 010
> x = 10101010 k = 4 f(x) = 11
>
> Any bit gurus here who can help me?

Its not portable, but I'm sure you can adapt it to your platform of choice:

long f(long x, int k) {
switch (k) {
case 1: return x;
case 2: x &= 0xAAAAAAAA;
x = (x | (x >> 1)) & 0x66666666;
x = (x | (x >> 2)) & 0x1E1E1E1E;
x = (x | (x >> 4)) & 0x01FE01FE;
x = (x | (x >> 8)) & 0x0001FFFE;
return x >> 1;
case 3: x &= 0x24924924;
x = (x | (x >> 2)) & 0x0C30C30C;
x = (x | (x >> 4)) & 0x0C03C03C;
x = (x | (x >> 8)) & 0x0C0003FC;
x = (x | (x >> 16)) & 0x00000FFC;
return x >> 2;
case 4: x &= 0x88888888;
x = (x | (x >> 3)) & 0x18181818;
x = (x | (x >> 6)) & 0x00780078;
x = (x | (x >> 12)) & 0x000007F8;
return x >> 3;
case 5: x &= 0x21084210;
x = (x | (x >> 4)) & 0x0300C030;
x = (x | (x >> 8)) & 0x030000F0;
x = (x | (x >> 16)) & 0x000003F0;
return x >> 4;
case 6: x &= 0x20820820;
x = (x | (x >> 5)) & 0x20060060;
x = (x | (x >> 10)) & 0x200001E0;
x = (x | (x >> 20)) & 0x000003E0;
return x >> 5;
case 7: x &= 0x08102040;
x = (x | (x >> 6)) & 0x003000C0;
x = (x | (x >> 12)) & 0x000003C0;
return x >> 6;
case 8: x &= 0x80808080;
x = (x | (x >> 7)) & 0x01800180;
x = (x | (x >> 14)) & 0x00000780;
return x >> 7;
case 9: x &= 0x04020100;
x = (x | (x >> 8)) & 0x04000300;
x = (x | (x >> 16)) & 0x00000700;
return x >> 8;
case 10: x &= 0x20080200;
x = (x | (x >> 9)) & 0x20000600;
x = (x | (x >> 18)) & 0x00000E00;
return x >> 9;
case 11: x &= 0x00200400;
x = (x | (x >> 10)) & 0x00000C00;
return x >> 10;
case 12: x &= 0x00800800;
x = (x | (x >> 11)) & 0x00001800;
return x >> 11;
case 13: x &= 0x02001000;
x = (x | (x >> 12)) & 0x00003000;
return x >> 12;
case 14: x &= 0x08002000;
x = (x | (x >> 13)) & 0x00006000;
return x >> 13;
case 15: x &= 0x20004000;
x = (x | (x >> 14)) & 0x0000C000;
return x >> 14;
case 16: x &= 0x80008000;
x = (x | (x >> 15)) & 0x00018000;
return x >> 15;
case 17: case 18: case 19: case 20: case 21:
case 22: case 23: case 24: case 25: case 26:
case 27: case 28: case 29: case 30: case 31:
case 32: return (x >> (k-1)) & 1;
default: break;
}
return 0;
}

--
Paul Hsieh
http://www.pobox.com/~qed/
http://bstring.sf.net/

Paul Hsieh, Dec 5, 2003
14. ### GrumbleGuest

Michael Andrew Fyles wrote:
> In article <bqkjp8\$8mr\$>, Grumble wrote:
>
>>Ben Pfaff wrote:
>>
>>>Elijah Bailey writes:
>>>
>>>
>>>>I want to write a function
>>>>
>>>>long f(long x, int k)
>>>>
>>>>such that it extracts every k-th bit of x, concatenates
>>>>them and returns it. Anyone can help me in writing this
>>>>function?
>>>>
>>>>examples
>>>>x = 10101010 k = 1 f(x) = 10101010
>>>>x = 10101010 k = 2 f(x) = 1111
>>>>x = 10101010 k = 3 f(x) = 010
>>>>x = 10101010 k = 4 f(x) = 11
>>>
>>>
>>>I don't understand your k = 3 example. Shouldn't f(x) = 101 for
>>>consistency with the others?

>>
>>Let x_i denote the i_th bit in x counting from right to left.
>>
>>In particular, x_0 denotes the right-most bit in x.
>>
>>Then f(x)_i = x_{k-1+i*k}
>>
>>k=1 => f(x)_i = x_i
>>k=2 => f(x)_i = x_{2*i+1}
>>k=3 => f(x)_i = x_{3*i+2}
>>
>>Thus, from right to left, x_2 | x_5 | x_8

>
>
> Unless I've misunderstood, if x_0 is the
> right-most bit in x, that would make x_8 one to
> the left of the left-most bit in x. For the
> example given, this doesn't exist.

You are correct.

Grumble, Dec 5, 2003