How to manipulate and represent binary numbers in C++ - c++

I'm currently trying to build a lookup table for a huffman tree using a pretty simple preorder traversal algorithm, but I'm getting stuck carrying out very basic bit wise operations. The psuedo code follows:
void preOrder(huffNode *node, int bit) //not sure how to represent bit
{
if (node == NULL)
return;
(1) bit = bit + 0; //I basically want to add a 0 onto this number (01 would go to 010)
preOrder(node->getLeft(), bit);
(2) bit = bit - 0 + 1; //This should subtract the last 0 and add a 1 (010 would go to 011)
preOrder(node->getRight());
}
I'm getting quite confused about how to carry out the operations defined on lines (1) and (2)
What data type type does one use to represent and print binary numbers? In the above example I have the number represented as an int, but i'm pretty sure that that is incorrect. Also how do you add or subtract values? I understand how & and | types logic works, but I'm getting confused as to how one carries out these sorts of operations in code.
Could anyone post some very simple examples?

Here's some basic examples of binary operations. I've used mostly in-place operations here.
int bit = 0x02; // 0010
bit |= 1; // OR 0001 -> 0011
bit ^= 1; // XOR 0001 -> 0010
bit ^= 7; // XOR 0111 -> 0101
bit &= 14; // AND 1110 -> 0100
bit <<= 1; // LSHIFT 1 -> 1000
bit >>= 2; // RSHIFT 2 -> 0010
bit = ~bit; // COMPLEMENT -> 1101
If you want to print a binary number you need to do it yourself... Here's one slightly inefficient, but moderately readable, way to do it:
char bitstr[33] = {0};
for( int b = 0; b < 32; b++ ) {
if( bit & (1 << (31-b)) )
bitstr[b] = '1';
else
bitstr[b] = '0';
}
printf( "%s\n", bitstr );
[edit] If I wanted faster code, I might pre-generate (or hardcode) a lookup table with the 8-bit sequences for all numbers from 0-255.
// This turns a 32-bit integer into a binary string.
char lookup[256][9] = {
"00000000",
"00000001",
"00000010",
"00000011",
// ... etc (you don't want to do this by hand)
"11111111"
};
char * lolo = lookup[val & 0xff];
char * lohi = lookup[(val>>8) & 0xff];
char * hilo = lookup[(val>>16) & 0xff];
char * hihi = lookup[(val>>24) & 0xff];
// This part is maybe a bit lazy =)
char bitstr[33];
sprintf( "%s%s%s%s", hihi, hilo, lohi, lolo );
Instead, you could do this:
char *bits = bitstr;
while( *hihi ) *bits++ = *hihi++;
while( *hilo ) *bits++ = *hilo++;
while( *lohi ) *bits++ = *lohi++;
while( *lolo ) *bits++ = *lolo++;
*bits = 0;
Or just unroll the whole thing. ;-)
char bitstr[33] = {
hihi[0], hihi[1], hihi[2], hihi[3], hihi[4], hihi[5], hihi[6], hihi[7],
hilo[0], hilo[1], hilo[2], hilo[3], hilo[4], hilo[5], hilo[6], hilo[7],
lohi[0], lohi[1], lohi[2], lohi[3], lohi[4], lohi[5], lohi[6], lohi[7],
lolo[0], lolo[1], lolo[2], lolo[3], lolo[4], lolo[5], lolo[6], lolo[7],
0 };
Of course, those 8 bytes in the lookup are the same length as a 64-bit integer... So what about this? Much faster than all that pointless meandering through character arrays.
char bitstr[33];
__int64 * intbits = (__int64*)bitstr;
intbits[0] = *(__int64*)lookup[(val >> 24) & 0xff];
intbits[1] = *(__int64*)lookup[(val >> 16) & 0xff];
intbits[2] = *(__int64*)lookup[(val >> 8) & 0xff];
intbits[3] = *(__int64*)lookup[val & 0xff];
bitstr[32] = 0;
Naturally, in the above code you would represent your lookup values as int64 instead of strings.
Anyway, just pointing out that you can write it however is appropriate for your purposes. If you need to optimize, things get fun, but for most practical applications such optimizations are negligible or pointless.

Unless your binary sequences will get longer than the number of bits in an int, you can just use an int.
To add a 0 to the end of the current representation of a, you can use
a << 1
To replace a 0 at the end of the current representation of a with a 1, you can use
a ^= 1
Note that to use an int in this way, you will also need to keep track of where in the int your bits start, so that if you have e.g., the value 0x0, you can know which of 0, 00, 000, ... it is.

Operations in your code:
(1) bit = bit << 1;
(2) bit = bit|1;
However, you must also keep the length of the sequence.
If length of an int is good enough for you, there's no reason not to use it. However, in huffman algorithm it would really depend on the data. C++ programmers should use boost::dynamic_bitset for bit sequences of an arbitrary length. It also supports the bit operations above. http://www.boost.org/doc/libs/1_42_0/libs/dynamic_bitset/dynamic_bitset.html

Related

How to shift left one specific bit?

I want to shift left only one bit in a specific place leaving its position 0, so I do not want to shift the whole variable with << operator, here is an example: say the variable has the value 1100 1010 and I want to shift the fourth bit then the result should be 1101 0010.
Steps to get there.
Pull out bit value from the original number.
Left shift the bit value by one.
Merge the bit-shifted value back to the original number.
// Assuming C++14 or later to be able to use the binary literal integers
int a = 0b11001010;
int t = a & 0b00001000; // Pull out the 4-th bit.
t <<= 1; // Left shift the 4-th bit.
a = a & 0b11100111; // Clear the 4-th and the 5-th bit
a |= t; // Merge the left-shifted 4-th bit.
For C++, I'd just use a std::bitset. Since you set the bit of pos + 1 to the value of the bit at pos, and then set the bit at pos to 0 this translate into bitset code that is quite easy to read. That would give you a function like
unsigned char shift_bit_bitset(unsigned char val, unsigned pos)
{
std::bitset<8> new_val(val);
new_val[pos + 1] = new_val[pos];
new_val[pos] = 0;
return new_val.to_ulong();
}
Maybe not the shortest/cleanest way, but this'll do it:
unsigned shift_bit = 4;
unsigned char val = 0xCA; // 1100 1010
unsigned char bit_val = val & (1 << shift_bit - 1); // Get current bit value
val = val & ~(1 << shift_bit - 1); // Clear initial bit location
val = bit_val ? // Update next bit to 0 or 1
val | (1 << shift_bit) :
val & ~(1 << shift_bit);
See it work with the test cases specified in your question and comments here: ideone
A simpler way is
(x & 0b11101111) + (x & 0b00001000)
that is, clear the bit that will be shifted into and add the bit to be shifted, which will overflow to the left if it is 1.

how to optimize C++/C code for a large number of integers

I have written the below mentioned code. The code checks the first bit of every byte. If the first bit of every byte of is equal to 0, then it concatenates this value with the previous byte and stores it in a different variable var1. Here pos points to bytes of an integer. An integer in my implementation is uint64_t and can occupy upto 8 bytes.
uint64_t func(char* data)
{
uint64_t var1 = 0; int i=0;
while ((data[i] >> 7) == 0)
{
variable = (variable << 7) | (data[i]);
i++;
}
return variable;
}
Since I am repeatedly calling func() a trillion times for trillions of integers. Therefore it runs slow, is there a way by which I may optimize this code?
EDIT: Thanks to Joe Z..its indeed a form of uleb128 unpacking.
I have only tested this minimally; I am happy to fix glitches with it. With modern processors, you want to bias your code heavily toward easily predicted branches. And, if you can safely read the next 10 bytes of input, there's nothing to be saved by guarding their reads by conditional branches. That leads me to the following code:
// fast uleb128 decode
// assumes you can read all 10 bytes at *data safely.
// assumes standard uleb128 format, with LSB first, and
// ... bit 7 indicating "more data in next byte"
uint64_t unpack( const uint8_t *const data )
{
uint64_t value = ((data[0] & 0x7F ) << 0)
| ((data[1] & 0x7F ) << 7)
| ((data[2] & 0x7F ) << 14)
| ((data[3] & 0x7F ) << 21)
| ((data[4] & 0x7Full) << 28)
| ((data[5] & 0x7Full) << 35)
| ((data[6] & 0x7Full) << 42)
| ((data[7] & 0x7Full) << 49)
| ((data[8] & 0x7Full) << 56)
| ((data[9] & 0x7Full) << 63);
if ((data[0] & 0x80) == 0) value &= 0x000000000000007Full; else
if ((data[1] & 0x80) == 0) value &= 0x0000000000003FFFull; else
if ((data[2] & 0x80) == 0) value &= 0x00000000001FFFFFull; else
if ((data[3] & 0x80) == 0) value &= 0x000000000FFFFFFFull; else
if ((data[4] & 0x80) == 0) value &= 0x00000007FFFFFFFFull; else
if ((data[5] & 0x80) == 0) value &= 0x000003FFFFFFFFFFull; else
if ((data[6] & 0x80) == 0) value &= 0x0001FFFFFFFFFFFFull; else
if ((data[7] & 0x80) == 0) value &= 0x00FFFFFFFFFFFFFFull; else
if ((data[8] & 0x80) == 0) value &= 0x7FFFFFFFFFFFFFFFull;
return value;
}
The basic idea is that small values are common (and so most of the if-statements won't be reached), but assembling the 64-bit value that needs to be masked is something that can be efficiently pipelined. With a good branch predictor, I think the above code should work pretty well. You might also try removing the else keywords (without changing anything else) to see if that makes a difference. Branch predictors are subtle beasts, and the exact character of your data also matters. If nothing else, you should be able to see that the else keywords are optional from a logic standpoint, and are there only to guide the compiler's code generation and provide an avenue for optimizing the hardware's branch predictor behavior.
Ultimately, whether or not this approach is effective depends on the distribution of your dataset. If you try out this function, I would be interested to know how it turns out. This particular function focuses on standard uleb128, where the value gets sent LSB first, and bit 7 == 1 means that the data continues.
There are SIMD approaches, but none of them lend themselves readily to 7-bit data.
Also, if you can mark this inline in a header, then that may also help. It all depends on how many places this gets called from, and whether those places are in a different source file. In general, though, inlining when possible is highly recommended.
Your code is problematic
uint64_t func(const unsigned char* pos)
{
uint64_t var1 = 0; int i=0;
while ((pos[i] >> 7) == 0)
{
var1 = (var1 << 7) | (pos[i]);
i++;
}
return var1;
}
First a minor thing: i should be unsigned.
Second: You don't assert that you don't read beyond the boundary of pos. E.g. if all values of your pos array are 0, then you will reach pos[size] where size is the size of the array, hence you invoke undefined behaviour. You should pass the size of your array to the function and check that i is smaller than this size.
Third: If pos[i] has most significant bit equal to zero for i=0,..,k with k>10, then previous work get's discarded (as you push the old value out of var1).
The third point actually helps us:
uint64_t func(const unsigned char* pos, size_t size)
{
size_t i(0);
while ( i < size && (pos[i] >> 7) == 0 )
{
++i;
}
// At this point, i is either equal to size or
// i is the index of the first pos value you don't want to use.
// Therefore we want to use the values
// pos[i-10], pos[i-9], ..., pos[i-1]
// if i is less than 10, we obviously need to ignore some of the values
const size_t start = (i >= 10) ? (i - 10) : 0;
uint64_t var1 = 0;
for ( size_t j(start); j < i; ++j )
{
var1 <<= 7;
var1 += pos[j];
}
return var1;
}
In conclusion: We separated logic and got rid of all discarded entries. The speed-up depends on the actual data you have. If lot's of entries are discarded then you save a lot of writes to var1 with this approach.
Another thing: Mostly, if one function is called massively, the best optimization you can do is call it less. Perhaps you can have come up with an additional condition that makes the call of this function useless.
Keep in mind that if you actually use 10 values, the first value ends up the be truncated.
64bit means that there are 9 values with their full 7 bits of information are represented, leaving exactly one bit left foe the tenth. You might want to switch to uint128_t.
A small optimization would be:
while ((pos[i] & 0x80) == 0)
Bitwise and is generally faster than a shift. This of course depends on the platform, and it's also possible that the compiler will do this optimization itself.
Can you change the encoding?
Google came across the same problem, and Jeff Dean describes a really cool solution on slide 55 of his presentation:
http://research.google.com/people/jeff/WSDM09-keynote.pdf‎
http://videolectures.net/wsdm09_dean_cblirs/
The basic idea is that reading the first bit of several bytes is poorly supported on modern architectures. Instead, let's take 8 of these bits, and pack them as a single byte preceding the data. We then use the prefix byte to index into a 256-item lookup table, which holds masks describing how to extract numbers from the rest of the data.
I believe it's how protocol buffers are currently encoded.
Can you change your encoding? As you've discovered, using a bit on each byte to indicate if there's another byte following really sucks for processing efficiency.
A better way to do it is to model UTF-8, which encodes the length of the full int into the first byte:
0xxxxxxx // one byte with 7 bits of data
10xxxxxx 10xxxxxx // two bytes with 12 bits of data
110xxxxx 10xxxxxx 10xxxxxx // three bytes with 16 bits of data
1110xxxx 10xxxxxx 10xxxxxx 10xxxxxx // four bytes with 22 bits of data
// etc.
But UTF-8 has special properties to make it easier to distinguish from ASCII. This bloats the data and you don't care about ASCII, so you'd modify it to look like this:
0xxxxxxx // one byte with 7 bits of data
10xxxxxx xxxxxxxx // two bytes with 14 bits of data.
110xxxxx xxxxxxxx xxxxxxxx // three bytes with 21 bits of data
1110xxxx xxxxxxxx xxxxxxxx xxxxxxxx // four bytes with 28 bits of data
// etc.
This has the same compression level as your method (up to 64 bits = 9 bytes), but is significantly easier for a CPU to process.
From this you can build a lookup table for the first byte which gives you a mask and length:
// byte_counts[255] contains the number of additional
// bytes if the first byte has a value of 255.
uint8_t const byte_counts[256]; // a global constant.
// byte_masks[255] contains a mask for the useful bits in
// the first byte, if the first byte has a value of 255.
uint8_t const byte_masks[256]; // a global constant.
And then to decode:
// the resulting value.
uint64_t v = 0;
// mask off the data bits in the first byte.
v = *data & byte_masks[*data];
// read in the rest.
switch(byte_counts[*data])
{
case 3: v = v << 8 | *++data;
case 2: v = v << 8 | *++data;
case 1: v = v << 8 | *++data;
case 0: return v;
default:
// If you're on VC++, this'll make it take one less branch.
// Better make sure you've got all the valid inputs covered, though!
__assume(0);
}
No matter the size of the integer, this hits only one branch point: the switch, which will likely be put into a jump table. You can potentially optimize it even further for ILP by not letting each case fall through.
First, rather than shifting, you can do a bitwise test on the
relevant bit. Second, you can use a pointer, rather than
indexing (but the compiler should do this optimization itself.
Thus:
uint64_t
readUnsignedVarLength( unsigned char const* pos )
{
uint64_t results = 0;
while ( (*pos & 0x80) == 0 ) {
results = (results << 7) | *pos;
++ pos;
}
return results;
}
At least, this corresponds to what your code does. For variable
length encoding of unsigned integers, it is incorrect, since
1) variable length encodings are little endian, and your code is
big endian, and 2) your code doesn't or in the high order byte.
Finally, the Wiki page suggests that you've got the test
inversed. (I know this format mainly from BER encoding and
Google protocol buffers, both of which set bit 7 to indicate
that another byte will follow.
The routine I use is:
uint64_t
readUnsignedVarLen( unsigned char const* source )
{
int shift = 0;
uint64_t results = 0;
uint8_t tmp = *source ++;
while ( ( tmp & 0x80 ) != 0 ) {
*value |= ( tmp & 0x7F ) << shift;
shift += 7;
tmp = *source ++;
}
return results | (tmp << shift);
}
For the rest, this wasn't written with performance in mind, but
I doubt that you could do significantly better. An alternative
solution would be to pick up all of the bytes first, then
process them in reverse order:
uint64_t
readUnsignedVarLen( unsigned char const* source )
{
unsigned char buffer[10];
unsigned char* p = std::begin( buffer );
while ( p != std::end( buffer ) && (*source & 0x80) != 0 ) {
*p = *source & 0x7F;
++ p;
}
assert( p != std::end( buffer ) );
*p = *source;
++ p;
uint64_t results = 0;
while ( p != std::begin( buffer ) ) {
-- p;
results = (results << 7) + *p;
}
return results;
}
The necessity of checking for buffer overrun will likely make
this slightly slower, but on some architectures, shifting by
a constant is significantly faster than shifting by a variable,
so this could be faster on them.
Globally, however, don't expect miracles. The motivation for
using variable length integers is to reduce data size, at
a cost in runtime for decoding and encoding.

How to set specific bits?

Let's say I've got a uint16_t variable where I must set specific bits.
Example:
uint16_t field = 0;
That would mean the bits are all zero: 0000 0000 0000 0000
Now I get some values that I need to set at specific positions.
val1=1; val2=2, val3=0, val4=4, val5=0;
The structure how to set the bits is the following
0|000| 0000| 0000 000|0
val1 should be set at the first bit on the left. so its only one or zero.
val2 should be set at the next three bits. val3 on the next four bits. val4 on the next seven bits and val5 one the last bit.
The result would be this:
1010 0000 0000 1000
I only found out how to the one specific bit but not 'groups'. (shift or bitset)
Does anyone have an idea how to solve this issue?
There are (at least) two basic approaches. One would be to create a struct with some bitfields:
struct bits {
unsigned a : 1;
unsigned b : 7;
unsigned c : 4;
unsigned d : 3;
unsigned e : 1;
};
bits b;
b.a = val1;
b.b = val2;
b.c = val3;
b.d = val4;
b.e = val5;
To get the 16-bit value, you could (for one example) create a union of that struct with a uint16_t. Just one minor problem: the standard doesn't guarantee what order the bit fields will end up in when you look at the 16-bit value. Just for example, you might need to reverse the order I've given above to get the order from most to least significant bits that you really want (but changing compilers might muck things up again).
The other obvious possibility would be to use shifting and masking to put the pieces together into a number:
int16_t result = val1 | (val2 << 1) | (val3 << 8) | (val4 << 12) | (val5 << 15);
For the moment, I've assumed each of the inputs starts out in the correct range (i.e., has a value that can be represented in the chosen number of bits). If there's a possibility that could be wrong, you'd want to mask it to the correct number of bits first. The usual way to do that is something like:
uint16_t result = input & ((1 << num_bits) - 1);
In case you're curious about the math there, it works like this. Lets's assume we want to ensure an input fits in 4 bits. Shifting 1 left 4 bits produces 00010000 (in binary). Subtracting one from that then clears the one bit that's set, and sets all the less significant bits than that, giving 00001111 for our example. That gives us the first least significant bits set. When we do a bit-wise AND between that and the input, any higher bits that were set in the input are cleared in the result.
One of the solutions would be to set a K-bit value starting at the N-th bit of field as:
uint16_t value_mask = ((1<<K)-1) << N; // for K=4 and N=3 will be 00..01111000
field = field & ~value_mask; // zeroing according bits inside the field
field = field | ((value << N) & value_mask); // AND with value_mask is for extra safety
Or, if you can use struct instead of uint16_t, you can use Bit fields and let the compiler to perform all these actions for you.
finalvle = 0;
finalvle = (val1&0x01)<<15;
finalvle += (val2&0x07)<<12;
finalvle += (val3&0x0f)<<8
finalvle += (val4&0xfe)<<1;
finalvle += (val5&0x01);
You can use the bitwise or and shift operators to achieve this.
Use shift << to 'move bytes to the left':
int i = 1; // ...0001
int j = i << 3 // ...1000
You can then use bitwise or | to put it at the right place, (assuming you have all zeros at the bits you are trying to overwrite).
int k = 0; // ...0000
k |= i // ...0001
k |= j // ...1001
Edit: Note that #Inspired's answer also explains with zeroing out a certain area of bits. It overall explains how you would go about implementing it properly.
try this code:
uint16_t shift(uint16_t num, int shift)
{
return num | (int)pow (2, shift);
}
where shift is position of bit that you wanna set

How to convert 8 17-bit integers into 17 8-bit integers efficiently

Okay, I have the following problem: I have a set of 8 (unsigned) numbers that are all 17bit (a.k.a. none of them are any bigger than 131071). Since 17bit numbers are annoying work work with (keeping them in a 32-bit int is a waste of space), I would like to turn these into 17 8-bit numbers, like so:
If I have these 8 17-bit integers:
[25409, 23885, 24721, 23159, 25409, 23885, 24721, 23159]
I would turn them into a base 2 representationL
["00110001101000001", "00101110101001101", "00110000010010001", "00101101001110111", "00110001101000001", "00101110101001101", "00110000010010001", "00101101001110111"]
Then join that into one big string:
"0011000110100000100101110101001101001100000100100010010110100111011100110001101000001001011101010011010011000001001000100101101001110111"
Then split that into 17 strings, each with 8 chars:
["00110001", "10100000", "10010111", "01010011", "01001100", "00010010", "00100101", "10100111", "01110011", "00011010", "00001001", "01110101", "00110100", "11000001", "00100010", "01011010", "01110111"]
And, finally, convert the binary representations back into integers
[49, 160, 151, 83, 76, 18, 37, 167, 115, 26, 9, 117, 52, 193, 34, 90, 119]
This method works, but it's not very efficient, I am looking for something more efficient than this, preferrably coded in C++, since that's the language I am working with. I just can't think of any way to do this more efficient, and 17-bit numbers aren't exactly easy to work with (16-bit numbers would be much nicer to work with).
Thanks in advance, xfbs
Store the lowest 16 bits of each number as-is (i.e. in two bytes). This leaves the most significant bit of each number. Since there are eight such numbers, simply combine the eight bits into one extra byte.
This will require exactly the same amount of memory as your method, but will involve a lot less bit twiddling.
P.S. Regardless of the storage method, you should be using bit-manipulation operators (<<, >>, &, | and so on) to do the job; there should not be any intermediate string-based representations involved.
Have a look at std::bitset<N>. May be you can stuff them into that?
Efficiently? Then don't use string conversions, bitfields, etc. Manage to do shifts yourself to achieve that. (Note that the arrays must be unsigned so that we don't encounter problems when shifting).
uint32 A[8]; //Your input, unsigned int
ubyte B[17]; //Output, unsigned byte
B[0] = (ubyte)A[0];
B[1] = (ubyte)(A[0] >> 8);
B[2] = (ubyte)A[1];
B[3] = (ubyte)(A[1] >> 8);
.
:
And for the last one, we do what ajx said. We take the most significant digit of each number (shifting them 16 bits to the right leaves the 17th digit) and fill the bits of our output by shifting each of the most significant digits from 0 to 7 to the left:
B[16] = (A[0] >> 16) | ((A[1] >> 16) << 1) | ((A[2] >> 16) << 2) | ((A[3] >> 16) << 3) | ... | ((A[7] >> 16) << 7);
Well, "efficient" was this. Other easier methods exist, too.
Though you say they are 17-bit numbers, they must be stored into an array of 32bit integers, where only the less significant 17 bits are used. You can extract from the first directly two bytes (dst[0] = src[0] >> 9 is the first, dst[1] = (src[0] >> 1) & 0xff the second); then you "push" the first bit as the 18th bit of the second, so that
dst[2] = (src[0] & 1) << 7 | src[1] >> 10;
dst[3] = (src[1] >> 2) & 0xff;
if you generalize it, you will see that this "formula" may be applied
dst[2*i] = src[i] >> (9+i) | (src[i-1] & BITS(i)) << (8-i);
dst[2*i + 1] = (src[i] >> (i+1)) & 0xff;
and for the last one: dst[16] = src[7] & 0xff;.
The whole code could look like
dst[0] = src[0] >> 9;
dst[1] = (src[0] >> 1) & 0xff;
for(i = 1; i < 8; i++)
{
dst[2*i] = src[i] >> (9+i) | (src[i-1] & BITS(i)) << (8-i);
dst[2*i + 1] = (src[i] >> (i+1)) & 0xff;
}
dst[16] = src[7] & 0xff;
Likely analysing better the loops, optimizations can be done so that we don't need to treat in a special manner the cases on the boundaries. The BITS macro create a mask of N bits set to 1 (least significant bits). Something like (to be checked for a better way, if any)
#define BITS(I) (~((~0)<<(I)))
ADD
Here I supposed src is e.g. int32_t and dst int8_t or alike.
This is in C, so you can use vector instead.
#define srcLength 8
#define destLength 17
int src[srcLength] = { 25409, 23885, 24721, 23159, 25409, 23885, 24721, 23159 };
unsigned char dest[destLength] = { 0 };
int srcElement = 0;
int bits = 0;
int i = 0;
int j = 0;
do {
while( bits >= srcLength ) {
dest[i++] = srcElement >> (bits - srcLength);
srcElement = srcElement & ((1 << bits) - 1);
bits -= srcLength;
}
if( j < srcLength ) {
srcElement <<= destLength;
bits += destLength;
srcElement |= src[j++];
}
} while (bits > 0);
Disclaimer: if you literally have seventeen integers (and not 100000 groups by 17), you should forget these optimizations as long as your program doesn't run veeery slowly.
I'd probably go about it this way. I don't want to deal with weird types when I'm doing my processing. Maybe I need to store them in some funky formatting due to legacy problems though. The values that are hard-coded should probably be based off of the 17 value, just didn't bother.
struct int_block {
static const uint32 w = 17;
static const uint32 m = 131071;
int_block() : data(151, 0) {} // w * 8 + (sizeof(uint32) - w)
uint32 get(size_t i) const {
uint32 retval = *reinterpret_cast<const uint32 *>( &data[i*w] );
retval &= m;
return retval;
}
void set(size_t i, uint32 val) {
uint32 prev = *reinterpret_cast<const uint32 *>( &data[i*w] );
prev &= ~m;
val |= prev;
*reinterpret_cast<uint32 *>( &data[i*w] ) = val;
}
std::vector<char> data;
};
TEST(int_block_test) {
int_block ib;
for (uint32 i = 0; i < 8; i++)
ib.set(i, i+25);
for (uint32 i = 0; i < 8; i++)
CHECK_EQUAL(i+25, ib.get(i));
}
You'd be able to break this by giving it bad values, but I'll leave that as an exercise for the reader. :))
Quite honestly, I think you'd be happier off representing them as 32-bit integers and just writing conversion functions. But I suspect you don't have control over that.

Create a file that uses 4-bit encoding to represent integers 0 -9

How can I create a file that uses 4-bit encoding to represent integers 0-9 separated by a comma ('1111')? for example:
2,34,99 = 0010 1111 0011 0100 1111 1001 1001 => actually becomes without spaces
0010111100110100111110011001 = binary.txt
Therefore 0010111100110100111110011001 is what I see when I view the file ('binary.txt')in WINHEX in binary view but I would see 2,34,99 when view the file (binary.txt) in Notepad.
If not Notepad, is there another decoder that will do '4-bit encoding' or do I have a write a 'decoder program' to view the integers?
How can I do this in C++?
The basic idea of your format (4 bits per decimal digit) is well known and called BCD (Binary Coded Decimal). But I doubt the use of 0xF as an encoding for a coma is something well established and even more supported by notepad.
Writing a program in C++ to do the encoding and decoding would be quite easy. The only difficulty would be that the standard IO use byte as the more basic unit, not bit, so you'd have to group yourself the bits into a byte.
You can decode the files using od -tx1 if you have that (digits will show up as digits, commas will show up as f). You can also use xxd to go both directions; it comes with Vim. Use xxd -r -p to copy hex characters from stdin to a binary file on stdout, and xxd -p to go the other way. You can use sed or tr to change f back and forth to ,.
This is the simplest C++ 4-bit (BCD) encoding algorithm I could come up with - wouldn't call it exactly easy, but no rocket science either. Extracts one digit at a time by dividing and then adds them to the string:
#include <iostream>
int main() {
const unsigned int ints = 3;
unsigned int a[ints] = {2,34,99}; // these are the original ints
unsigned int bytes_per_int = 6;
char * result = new char[bytes_per_int * ints + 1];
// enough space for 11 digits per int plus comma, 8-bit chars
for (int j=0; j < bytes_per_int * ints; ++j)
{
result[j] = 0xFF; // fill with FF
}
result[bytes_per_int*ints] = 0; // null terminated string
unsigned int rpos = bytes_per_int * ints * 2; // result position, start from the end of result
int i = ints; // start from the end of the array too.
while (i != 0) {
--i;
unsigned int b = a[i];
while (b != 0) {
--rpos;
unsigned int digit = b % 10; // take the lowest decimal digit of b
if (rpos & 1) {
// odd rpos means we set the lowest bits of a char
result[(rpos >> 1)] = digit;
}
else {
// even rpos means we set the highest bits of a char
result[(rpos >> 1)] |= (digit << 4);
}
b /= 10; // make the next digit the new lowest digit
}
if (i != 0 || (rpos & 1))
{
// add the comma
--rpos;
if (rpos & 1) {
result[(rpos >> 1)] = 0x0F;
}
else {
result[(rpos >> 1)] |= 0xF0;
}
}
}
std::cout << result;
}
Trimming the bogus data left at the start portion of the result according to rpos will be left as an exercise for the reader.
The subproblem of BCD conversion has also been discussed before: Unsigned Integer to BCD conversion?
If you want a more efficient algorithm, here's a bunch of lecture slides with conversion from 8-bit ints to BCD: http://edda.csie.dyu.edu.tw/course/fpga/Binary2BCD.pdf