# bit

## A peculiar way to get the biggest (max/maximum) value between two variables using bitwise operations3

Recently, we wanted to make a test and see how we could find the maximum value between two variables using bitwise operations.

We ended up with the following peculiar way to get the biggest value between two variables using bitwise operations

```
r = a ^ ((a ^ b) & -(a < b));

```

The above formula has two modes:

1. When `a < b`
2. When `a >= b`

### When `a < b` then the formula will change as follows:

```
r = a ^ ((a ^ b) & 0xFFFFFFFF);

```

As we all (should) know, when one of the operators on a bitwise `AND` operation is composed only from `1`s, then the result is whatever value the other operator was holding.
So, the formula then simplifies as follows:

```
r = a ^ (a ^ b);

```

which is equal to

```
r = b;

```

because we when we apply twice the same value using `XOR` on another value, we revert back to the original value (so the second `^a` nullifies the first `^a`)

### When `a >= b` then the formula will change as follows:

```
r = a ^ ((a ^ b) & 0x00000000);

```

When one of the operators on a bitwise `AND` operation is composed only from `0`s, then the result is always `0` no matter what value the other operator was holding.
So, the formula then simplifies as follows:

```
r = a ^ (0x00000000);

```

which is equal to

```
r = a;

```

because when one of the operators in a `XOR` operation is only composed from `0`s then the result will be the value of the other operator, no matter what it was.

### Full example

Below you will find a full example that compares the execution speed of the two methods by executing each several thousands of time on the same random data.

```
#include <stdio.h>
#include <time.h>
#include <stdlib.h>

int main() {
{
const clock_t start = clock();

srand(10);
unsigned long int i;
unsigned int max = 0;
for (i = 0; i < 1000000000; i++) {
const int a = rand();
max = max < a ? a : max;
}
const clock_t end = clock();
const float seconds = (float) (end - start) / CLOCKS_PER_SEC;
printf("Seconds elapsed %f\tIf statement. Overall max value = %u\n", seconds, max);
}

{
const clock_t start = clock();

srand(10);
unsigned long int i;
unsigned int max = 0;
for (i = 0; i < 1000000000; i++) {
const int a = rand();
max = a ^ ((a ^ max) & -(a < max));
}
const clock_t end = clock();
const float seconds = (float) (end - start) / CLOCKS_PER_SEC;
printf("Seconds elapsed %f\tBitwise operation. Overall max value = %u\n", seconds, max);
}
return 0;
}

```

### Results

Our results show that using the traditional if statement with assignment is faster than using our formula as expected.
Which makes sense as there is an if statement in the formula as well and then additional operations to get the result, instead of just the assignment.

```Seconds elapsed 5.770000 If statement. Overall max value = 2147483647
Seconds elapsed 6.180000 Bitwise operation. Overall max value = 2147483647```

10 times bigger input

```Seconds elapsed 57.450001 If statement. Overall max value = 2147483647
Seconds elapsed 63.869999 Bitwise operation. Overall max value = 2147483647```

## C: Split a buffer to a list of segments of a specific size in bits

The following code will split a buffer in `C` to a list of segments.
The size of the segments does not have to be a multiple of a byte.
User defines the size of the segments in `bits` when calling `node_t *segment(const unsigned char buffer[], const unsigned int buffer_bytes_size, const unsigned int segment_bit_size, const unsigned int first_segment_bit_size);`.

Each segment is an instance of `element_t` structure as follows:

```struct element_t {
unsigned char *segment;
unsigned int unused_bits;
unsigned int size;
};
```

Variable `unused_bits` defines the bits in the last byte that should not be used in future operations.

Following is the code that performs the segmentation:

```#include "segmentation.h"

#include <math.h>
#include <limits.h>
#include <malloc.h>
#include <string.h>

//This method will create a string made of 0s and 1s representing the bits in an object.
//It will skip printing the last n bits as per the input
char *create_bit_representation_string(const void *object, const unsigned int size,
const unsigned int skip_last_bits)
{
unsigned int i = 0;
const unsigned char *byte;
unsigned int temp_size = size;
const double mask_filter = pow(2, skip_last_bits);
const unsigned int skip_last_bytes = skip_last_bits / CHAR_BIT;
char *result = malloc(sizeof(char) * size * CHAR_BIT - skip_last_bits + 1);

for (byte = object; temp_size--; ++byte)
{
{
//We do not want to print the last n bits of the last byte as they should always be 0
if ((temp_size < skip_last_bytes) || (temp_size == 0 && mask < mask_filter))
{
break;
}
result[i++] = (char) (mask & *byte ? '1' : '0');
}
}

result[i] = '\0';
return result;
}

//Creating a mask where the first n bits are 1s and the rest are 0s to zero the unused bits of the segment
unsigned char create_left_mask(const unsigned int bits)
{

unsigned int i;
for (i = 0; i < bits; i++)
{
left_mask |= (1 << (CHAR_BIT - 1 - i));
}
}

//This function will shift to the left a char array for up to 7 bits.
//It will update the object and return the number of bits shifted
unsigned int
shift_left_char_array_n_bits(void *object, const unsigned int size, const unsigned int bits)
{
if (bits == 0)
{
return 0;
}

if (bits < 1 || bits > CHAR_BIT - 1)
{
fprintf(stderr, "%s: Bad value %u for 'bits', it should be [1,7]"
"\n\tIgnoring operation\n", __FUNCTION__, bits);
return 0;
}

//Creating a mask where the first n bits are 1s and the rest are 0s.

unsigned char *byte;
unsigned int temp_size = size;
//We use temp_size as a counter (until it reaches 0) and we move the byte pointer at each loop
for (byte = object; temp_size--; ++byte)
{
unsigned char carry = 0;
if (temp_size)
{
//We get the bits we want to carry using the mask
//Then shift them to the right, as this is where they will be in the new byte.
carry >>= (CHAR_BIT - bits);
}
//Shifting the new byte to make space for the carry
*byte <<= bits;
//Applying carry
*byte |= carry;
}
return bits;
}

const unsigned int calculate_unused_bits(const unsigned int segment_bit_size)
{
return (CHAR_BIT - (segment_bit_size % CHAR_BIT)) % CHAR_BIT;
}

element_t *create_element(const unsigned char buffer[], const unsigned int byte_size,
const unsigned int unused_bits, const unsigned int bytes_skipped,
{
element_t *element = (element_t *) malloc(sizeof(element_t));
element->segment = malloc(byte_size);
element->size = byte_size;
element->unused_bits = unused_bits;
memcpy(element->segment, &(buffer[bytes_skipped]), byte_size);
//Zeroing the unused bits at the end of the segment
return element;
}

//This method will split a buffer to segments of specific size in bits and it will return them as a list
//(each element contains the segment data, its size in bytes and the number of bits that are not used from the last byte)
//If the input buffer is less than the segment size, it will return one segment with all the data.
//The user can set the bit size of the first segment to be different than the rest using first_segment_bit_size > 0
node_t *segment(const unsigned char buffer[], const unsigned int buffer_bytes_size,
const unsigned int segment_bit_size, const unsigned int first_segment_bit_size)
{
if (buffer_bytes_size == 0)
{
fprintf(stderr, "%s: Bad value %u for 'buffer_bytes_size', it should be greater than 0"
"\n\tIgnoring operation\n", __FUNCTION__, buffer_bytes_size);
return NULL;
}
if (segment_bit_size == 0)
{
fprintf(stderr, "%s: Bad value %u for 'segment_bit_size', it should be greater than 0"
"\n\tIgnoring operation\n", __FUNCTION__, segment_bit_size);
return NULL;
}

const double char_bit = CHAR_BIT;
const unsigned int first_segment_byte_size = (unsigned int) ceil(
first_segment_bit_size / char_bit);
if (first_segment_byte_size > buffer_bytes_size)
{
append(&head, create_element(buffer, buffer_bytes_size, 0, 0, UCHAR_MAX));
}

unsigned char *temp_buffer = malloc(buffer_bytes_size);
memcpy(temp_buffer, buffer, buffer_bytes_size);

unsigned int bits_shifted = 0;
unsigned int bytes_skipped = 0;

if (first_segment_bit_size > 0)
{
const unsigned int first_segment_unused_bits = calculate_unused_bits(
first_segment_bit_size);
const unsigned int first_segment_byte_size_without_incomplete_byte =
first_segment_bit_size / CHAR_BIT;

const unsigned int first_segment_bits = CHAR_BIT - first_segment_unused_bits;

bytes_skipped += first_segment_byte_size_without_incomplete_byte;

if (bytes_skipped == buffer_bytes_size)
{
free(temp_buffer);
}
if (first_segment_bits > 0 && first_segment_bits < CHAR_BIT)
{
bits_shifted += shift_left_char_array_n_bits(&(temp_buffer[bytes_skipped]),
buffer_bytes_size - bytes_skipped -
(bits_shifted / CHAR_BIT),
first_segment_bits);
}
}

const unsigned int segment_byte_size = (unsigned int) ceil(segment_bit_size / char_bit);
const unsigned int buffer_bits_size =
(buffer_bytes_size - bytes_skipped) * CHAR_BIT - bits_shifted;
const unsigned int segments_count = buffer_bits_size / segment_bit_size;

if (segments_count == 0)
{
append(&head, create_element(temp_buffer, buffer_bytes_size - bytes_skipped, bits_shifted, bytes_skipped, UCHAR_MAX));
free(temp_buffer);
}

//Creating a mask where first n bits are 1s and the rest are 0s to zero the unused bits of the segment
const unsigned int segment_unused_bits = calculate_unused_bits(segment_bit_size);
const unsigned int last_segment_bits = CHAR_BIT - segment_unused_bits;
const unsigned int segment_byte_size_without_incomplete_byte = segment_bit_size / CHAR_BIT;
const unsigned int extra_bits = buffer_bits_size % segment_bit_size;

unsigned int i;
for (i = 0; i < segments_count; i++)
{
create_element(temp_buffer, segment_byte_size, segment_unused_bits, bytes_skipped,
bytes_skipped += segment_byte_size_without_incomplete_byte;

if ((segments_count > 1 || extra_bits > 0) &&
(last_segment_bits > 0 && last_segment_bits < CHAR_BIT))
{
bits_shifted += shift_left_char_array_n_bits(&(temp_buffer[bytes_skipped]),
buffer_bytes_size - bytes_skipped -
(bits_shifted / CHAR_BIT),
last_segment_bits);
}
}

if (extra_bits)
{
const unsigned int last_segment_bytes_size =
buffer_bytes_size - bytes_skipped - (bits_shifted / CHAR_BIT);
const unsigned int unused_bytes_for_last_segment =
segment_byte_size - last_segment_bytes_size;
const unsigned int last_segment_unused_bits =
segment_bit_size - (buffer_bits_size % segment_bit_size) + segment_unused_bits -
(unused_bytes_for_last_segment * CHAR_BIT);
last_segment_unused_bits, bytes_skipped, UCHAR_MAX));
}

free(temp_buffer);
}
```

Sample code that uses the function:

```#include <stdio.h>
#include <malloc.h>
#include <string.h>
#include <limits.h>
#include <stdlib.h>
#include <time.h>

#include "libs/segmentation/segmentation.h"

// This application will create a char array of size BUFFER_BYTE_SIZE that contains random values
// and later it will split it in segments of size SEGMENT_BIT_SIZE.
// The first segment will be of size FIRST_SEGMENT_BIT_SIZE.

#define BUFFER_BYTE_SIZE 420
#define SEGMENT_BIT_SIZE 222
#define FIRST_SEGMENT_BIT_SIZE 11
#define POSSIBLE_VALUES 256

int main()
{
srand(time(NULL));
const unsigned int buffer_byte_size = BUFFER_BYTE_SIZE;
fprintf(stdout, "Buffer Size: %uB\n", buffer_byte_size);
const unsigned int segment_bit_size = SEGMENT_BIT_SIZE;
fprintf(stdout, "Segment Size: %ub\n", segment_bit_size);
const unsigned int first_segment_bit_size = FIRST_SEGMENT_BIT_SIZE;
fprintf(stdout, "First Segment Size: %ub\n", first_segment_bit_size);
unsigned char buffer[buffer_byte_size];
unsigned int i;
for (i = 0; i < buffer_byte_size; i++)
{
buffer[i] = (unsigned char) (rand() % POSSIBLE_VALUES);
}
char *buffer_bits = create_bit_representation_string(buffer, buffer_byte_size, 0);
const size_t buffer_length = strlen(buffer_bits);
fprintf(stdout, "\tBuffer: '%s'\n", buffer_bits);
node_t *head = segment(buffer, buffer_byte_size, segment_bit_size, first_segment_bit_size);

unsigned int bytes_skipped = 0;
unsigned int segment_count = 0;
unsigned int total_segment_bit_size = 0;
while (element != NULL)
{

char *segment_bits = create_bit_representation_string(element->segment,
element->size,
element->unused_bits);
const size_t segment_length = strlen(segment_bits);
fprintf(stdout,
"\t\tSegment %04u: Size in bytes %02u - Unused bits %04u - '%.*s'\n",
++segment_count,
element->size, element->unused_bits,
element->size * CHAR_BIT - element->unused_bits, segment_bits);
if (segment_length == 0)
{
fprintf(stderr,
"Data validation failed."
"\n\tBuffer size in bytes %d"
"\n\tSegment size in bits %d"
"\n\tFirst Segment size in bits %d"
"\n\tFound empty segment\n",
buffer_byte_size, segment_bit_size, first_segment_bit_size);
free(segment_bits);
free(element->segment);
free(element);
free(buffer_bits);
return EXIT_FAILURE;
}
for (i = 0; i < segment_length && bytes_skipped + i < buffer_length; i++)
{
if (segment_bits[i] != buffer_bits[bytes_skipped + i])
{
fprintf(stderr,
"Data validation failed."
"\n\tBuffer size in bytes %d"
"\n\tSegment size in bits %d"
"\n\tFirst Segment size in bits %d"
"\n\tPosition %u of the buffer"
"\n\tPosition %u of the segment\n",
buffer_byte_size, segment_bit_size, first_segment_bit_size, bytes_skipped + i, i);
free(segment_bits);
free(element->segment);
free(element);
free(buffer_bits);
return EXIT_FAILURE;
}
}
free(segment_bits);
bytes_skipped += segment_length;

const unsigned int current_segment_bit_size = ((element->size - 1) * CHAR_BIT) + CHAR_BIT - element->unused_bits;
if (segment_length != current_segment_bit_size)
{
fprintf(stderr,
"Data validation failed."
"\n\tBuffer size in bytes %d"
"\n\tSegment size in bits %d"
"\n\tFirst Segment size in bits %d"
"\n\tCurrent Segment bit size (%u) not equal to its string representation (%lu)\n",
buffer_byte_size, segment_bit_size, first_segment_bit_size, current_segment_bit_size, segment_length);
free(segment_bits);
free(element->segment);
free(element);
free(buffer_bits);
return EXIT_FAILURE;
}
total_segment_bit_size += current_segment_bit_size;

free(element->segment);
free(element);
}

free(buffer_bits);

if (buffer_length != total_segment_bit_size) {
fprintf(stderr,
"Data validation failed."
"\n\tBuffer size in bytes %d"
"\n\tSegment size in bits %d"
"\n\tFirst Segment size in bits %d"
"\n\tTotal Segment bit size (%u) not equal to full string representation (%lu)\n",
buffer_byte_size, segment_bit_size, first_segment_bit_size, total_segment_bit_size, buffer_length);
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
```