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Efficiently shift an integer to the left and wrap around [duplicate]

I'm trying to implement a function that performs a circular rotation of a byte to the left and to the right.
I wrote the same code for both operations. For example, if you are rotating left 1010 becomes 0101. Is this right?
unsigned char rotl(unsigned char c) {
int w;
unsigned char s = c;
for (w = 7; w >= 0; w--) {
int b = (int)getBit(c, w);//
if (b == 0) {
s = clearBit(s, 7 - w);
} else if (b == 1) {
s = setBit(s, 7 - w);
}
}
return s;
}
unsigned char getBit(unsigned char c, int n) {
return c = (c & (1 << n)) >> n;
}
unsigned char setBit(unsigned char c, int n) {
return c = c | (1 << n);
}
unsigned char clearBit(unsigned char c, int n) {
return c = c &(~(1 << n));
}

There is no rotation operator in C, but if you write:
unsigned char rotl(unsigned char c)
{
return (c << 1) | (c >> 7);
}
then, according to this: http://www.linux-kongress.org/2009/slides/compiler_survey_felix_von_leitner.pdf (page 56), compilers will figure out what you want to do and perform the rotation it in only one (very fast) instruction.

Reading the answers and comments so far, there seems to be some confusion about what you are trying to accomplish - this may be because of the words you use. In bit manipulation, there are several "standard" things you can do. I will summarize some of these to help clarify different concepts. In all that follows, I will use abcdefgh to denote 8 bits (could be ones or zeros) - and as they move around, the same letter will refer to the same bit (maybe in a different position); if a bit becomes "definitely 0 or 1, I will denote it as such).
1) Bit shifting: This is essentially a "fast multiply or divide by a power of 2". The symbol used is << for "left shift" (multiply) or >> for right shift (divide). Thus
abcdefgh >> 2 = 00abcdef
(equivalent to "divide by four") and
abcdefgh << 3 = abcdefgh000
(equivalent to "multiply by eight" - and assuming there was "space" to shift the abc into; otherwise this might result in an overflow)
2) Bit masking: sometimes you want to set certain bits to zero. You do this by doing an AND operation with a number that has ones where you want to preserve a bit, and zeros where you want to clear a bit.
abcdefgh & 01011010 = 0b0de0g0
Or if you want to make sure certain bits are one, you use the OR operation:
abcdefgh | 01011010 = a1c11f1h
3) Circular shift: this is a bit trickier - there are instances where you want to "move bits around", with the ones that "fall off at one end" re-appearing at the other end. There is no symbol for this in C, and no "quick instruction" (although most processors have a built-in instruction which assembler code can take advantage of for FFT calculations and such). If you want to do a "left circular shift" by three positions:
circshift(abcdefgh, 3) = defghabc
(note: there is no circshift function in the standard C libraries, although it exists in other languages - e.g. Matlab). By the same token a "right shift" would be
circshift(abcdefgh, -2) = ghabcdef
4) Bit reversal: Sometimes you need to reverse the bits in a number. When reversing the bits, there is no "left" or "right" - reversed is reversed:
reverse(abcdefgh) = hgfedcba
Again, there isn't actually a "reverse" function in standard C libraries.
Now, let's take a look at some tricks for implementing these last two functions (circshift and reverse) in C. There are entire websites devoted to "clever ways to manipulate bits" - see for example this excellent one. for a wonderful collection of "bit hacks", although some of these may be a little advanced...
unsigned char circshift(unsigned char x, int n) {
return (x << n) | (x >> (8 - n));
}
This uses two tricks from the above: shifting bits, and using the OR operation to set bits to specific values. Let's look at how it works, for n = 3 (note - I am ignoring bits above the 8th bit since the return type of the function is unsigned char):
(abcdefgh << 3) = defgh000
(abcdefgh >> (8 - 3)) = 00000abc
Taking the bitwise OR of these two gives
defgh000 | 00000abc = defghabc
Which is exactly the result we wanted. Note also that a << n is the same as a >> (-n); in other words, right shifting by a negative number is the same as left shifting by a positive number, and vice versa.
Now let's look at the reverse function. There are "fast ways" and "slow ways" to do this. Your code above gave a "very slow" way - let me show you a "very fast" way, assuming that your compiler allows the use of 64 bit (long long) integers.
unsigned char reverse(unsigned char b) {
return (b * 0x0202020202ULL & 0x010884422010ULL) % 1023;
}
You may ask yourself "what just happened"??? Let me show you:
b = abcdefgh
* 0x0000000202020202 = 00000000 00000000 0000000a bcdefgha bcdefgha bcdefgha bcdefgha bcdefgh0
& 0x0000010884422010 = 00000000 00000000 00000001 00001000 10000100 01000010 00100000 00010000
= 00000000 00000000 0000000a 0000f000 b0000g00 0c0000h0 00d00000 000e0000
Note that we now have all the bits exactly once - they are just in a rather strange pattern. The modulo 1023 division "collapses" the bits of interest on top of each other - it's like magic, and I can't explain it. The result is indeed
hgfedcba
A slightly less obscure way to achieve the same thing (less efficient, but works for larger numbers quite efficiently) recognizes that if you swap adjacent bits , then adjacent bit pairs, then adjacent nibbles (4 bit groups), etc - you end up with a complete bit reversal. In that case, a byte reversal becomes
unsigned char bytereverse(unsigned char b) {
b = (b & 0x55) << 1 | (b & 0xAA) >> 1; // swap adjacent bits
b = (b & 0x33) << 2 | (b & 0xCC) >> 2; // swap adjacent pairs
b = (b & 0x0F) << 4 | (b & 0xF0) >> 4; // swap nibbles
return b;
}
In this case the following happens to byte b = abcdefgh:
b & 0x55 = abcdefgh & 01010101 = 0b0d0f0h << 1 = b0d0f0h0
b & 0xAA = abcdefgh & 10101010 = a0c0e0g0 >> 1 = 0a0c0e0g
OR these two to get badcfehg
Next line:
b & 0x33 = badcfehg & 00110011 = 00dc00hg << 2 = dc00hg00
b & 0xCC = badcfehg & 11001100 = ba00fe00 >> 2 = 00ba00fe
OR these to get dcbahgfe
last line:
b & 0x0F = dcbahgfe & 00001111 = 0000hgfe << 4 = hgfe0000
b & 0xF0 = dcbahgfe & 11110000 = dcba0000 >> 4 = 0000dcba
OR these to get hgfedcba
Which is the reversed byte you were after. It should be easy to see how just a couple more lines (similar to the above) get you to a reversed integer (32 bits). As the size of the number increases, this trick becomes more and more efficient, comparatively.
I trust that the answer you were looking for is "somewhere" in the above. If nothing else I hope you have a clearer understanding of the possibilities of bit manipulation in C.

If, as according to your comments, you want to shift one bit exactly, then one easy way to accomplish that would be this:
unsigned char rotl(unsigned char c)
{
return((c << 1) | (c >> 7));
}
What your code does is reversing the bits; not rotating them. For instance, it would make 10111001 into 10011101, not 01110011.

Operators and Expressions Problem that I can not solve in C#

We are given the number n, the value v (v = 0 or 1) and the position p. write a sequence of operations that changes the value of n, so the bit on the position p has the value of v. Example: n=35, p=5, v=0 -> n=3. Another example: n=35, p=2, v=1 -> n=39.
I am unable to find a way to only use that bit on the position p.
If i do n >> p with a number such as 35 in bits I will have
100011 >> 5 = 00001
I don't know how to get the value of v here.
Mathematically even if I think about it above the value of n becomes 1 not 3 after this operation. I am totally confused as I can not explain the problem to myself.
Console.Write("Enter n: ");
int n = Convert.ToInt32(Console.ReadLine());
Console.Write("Enter p: ");
int p = Convert.ToInt32(Console.ReadLine());
Console.Write("Enter v: ");
int v = Convert.ToInt32(Console.ReadLine());
int mask = n >> 5;
Console.WriteLine(mask);

I would take this approach:
Work out the shifted value of the bit using the << operator
If v is 1, set the bit using |
Otherwise, clear it using & (and ~ for bitwise negation to create a mask)
So something like:
int shifted = 1 << p;
if (v == 1)
{
n |= shifted; // Set the bit
}
else
{
// Clear the bit, by masking with the bitwise inverse of the shifted value
n &= ~shifted;
}

Any fast way to check if two doubles has the same sign?

Any fast way to check if two doubles have the same sign? Assume the two doubles cannot be 0.

Potential solutions:
a*b > 0: One floating-point multiply and one comparison.
(a>0) == (b>0): Three comparisons.
Math.Sign(a) == Math.Sign(b): Two function calls and one comparison.
Speed comparison:
It's about what you'd expect (see experimental setup at the bottom):
a*b > 0: 0.42 ± 0.02s
(a>0) == (b>0): 0.49 ± 0.01s
Math.Sign(a) == Math.Sign(b): 1.11 ± 0.9s
Important notes:
As noted by greybeard in the comments, method 1 is susceptible to problems if the values multiply to something smaller than Double.Epsilon. Unless you can guarantee that the multiple is always larger than this, you should probably go with method 2.
Experimental setup:
The following code was run 16 times on http://rextester.com/.
public static void Main(string[] args)
{
double a = 1e-273;
double b = a;
bool equiv = false;
for(int i=0; i<100000000; ++i) {
equiv = THE_COMPARISON;
b += a;
}
//Your code goes here
Console.WriteLine(equiv);
}

The simplest and fastest way for IEEE 754 I know of is just using XOR on the MSB bits of both numbers. Here is a small C# example (note the inlining to avoid the function overhead):
[MethodImpl(MethodImplOptions.AggressiveInlining)]
private unsafe static bool fpu_cmpsign(double a, double b)
{
byte* aa;
byte* bb;
aa = (byte*)(&a); // points to the a as 8bit integral type
bb = (byte*)(&b); // points to the b as 8bit integral type
return ((aa[7] ^ bb[7]) & 128) != 128;
}
Here result of +/- numbers combinations:
a b result
- - 1
- + 0
+ - 0
+ + 1
The idea is simple. The sign is stored in the highest bit (MSB) and XOR returns 1 for non equal bits so XOR the MSB of booth numbers together and negate the output. the [7] is just accessing highest BYTE of the double as 8 bit integral type so I can use CPU ALU instead FPU. If your platform has reversed order of BYTES then use [0] instead (MSByte first vs. LSByte first).
So what you need is just 3x 8 bit XORs for comparison and negation and 1x 8bit AND for extracting sign bit result only.
You can use unions instead of pointers and also use native bit-width for your platform to get best performance.

You could use:
if (copysign(x, y) == x)

Bits needed to change one number to another

Say I have two positive numbers a and b. How many bits must be inverted in order to convert a into b ?
I just want the count and not the exact position of the differing bits.
Lets assume a = 10 ( 1010 ) and b = 8 ( 1000 ). In this case the number of bits that should be inverted equals 1.
Any generalised algorithm?

The solution is simple
Step 1 ) Compute a XOR b
Step 2 ) Count the number of set bits in the result
Done!

int a = 10;
int b = 8;
int c = a ^ b; //xor
int count = 0;
while (c != 0)
{
if ((c & 1) != 0)
count++;
c = c >> 1;
}
return count;

changeMask = a XOR b
bitsToChange = 0
while changeMask>0
bitsToChange = bitsToChange + (changeMask AND 1)
changeMask = changeMask >> 1
loop
return bitsToChange

Good old-fashioned bit operations!
size_t countbits( unsigned int n )
{
size_t bits = 0;
while( n )
{
bits += n&1;
n >>= 1;
}
return bits;
}
countbits( a ^ b );
This could would work in C as well as C++. You could (in C++ only) make the countbits function a template.

Actually,humbly building on previous answer - this might work better for converting a to b:
the only difference with previous answer is that the bits already set in b dont need to be set again - so dont count them.
calculate (a XOR b) AND ~b
count the set bits
post corrected as per comment. Thanks!

abs(popcount(a) - popcount(b)) where popcount counts bits set in number (a lot of different variants exists)

how to loop through the digits of a binary number?

I have a binary number 1011011, how can I loop through all these binary digits one after the other ?
I know how to do this for decimal integers by using modulo and division.

int n = 0x5b; // 1011011
Really you should just do this, hexadecimal in general is much better representation:
printf("%x", n); // this prints "5b"
To get it in binary, (with emphasis on easy understanding) try something like this:
printf("%s", "0b"); // common prefix to denote that binary follows
bool leading = true; // we're processing leading zeroes
// starting with the most significant bit to the least
for (int i = sizeof(n) * CHAR_BIT - 1; i >= 0; --i) {
int bit = (n >> i) & 1;
leading |= bit; // if the bit is 1, we are no longer reading leading zeroes
if (!leading)
printf("%d", bit);
}
if (leading) // all zero, so just print 0
printf("0");
// at this point, for n = 0x5b, we'll have printed 0b1011011

You can use modulo and division by 2 exactly like you would in base 10. You can also use binary operators, but if you already know how to do that in base 10, it would be easier if you just used division and modulo

Expanding on Frédéric and Gabi's answers, all you need to do is realise that the rules in base 2 are no different to in base 10 - you just need to do your division and modulus with a divisor 2 instead of 10.
The next step is simply to use number >> 1 instead of number / 2 and number & 0x1 instead of number % 2 to improve performance. Mind you, with modern optimising compilers there's probably no difference...

Use an AND with increasing powers of two...

In C, at least, you can do something like:
while (val != 0)
{
printf("%d", val&0x1);
val = val>>1;
}

To expand on #Marco's answer with an example:
uint value = 0x82fa9281;
for (int i = 0; i < 32; i++)
{
bool set = (value & 0x1) != 0;
value >>= 1;
Console.WriteLine("Bit set: {0}", set);
}
What this does is test the last bit, and then shift everything one bit.

If you're already starting with a string, you could just iterate through each of the characters in the string:
var values = "1011011".Reverse().ToCharArray();
for(var index = 0; index < values.Length; index++) {
var isSet = (Boolean)Int32.Parse(values[index]); // Boolean.Parse only works on "true"/"false", not 0/1
// do whatever
}

byte input = Convert.ToByte("1011011", 2);
BitArray arr = new BitArray(new[] { input });
foreach (bool value in arr)
{
// ...
}

You can simply loop through every bit. The following C like pseudocode allows you to set the bit number you want to check. (You might also want to google endianness)
for()
{
bitnumber = <your bit>
printf("%d",(val & 1<<bitnumber)?1:0);
}
The code basically writes 1 if the bit it set or 0 if not. We shift the value 1 (which in binary is 1 ;) ) the number of bits set in bitnumber and then we AND it with the value in val to see if it matches up. Simple as that!
So if bitnumber is 3 we simply do this
00000100 ( The value 1 is shifted 3 left for example)
AND
10110110 (We check it with whatever you're value is)
=
00000100 = True! - Both values have bit 3 set!