I have a method that receives 3 parameters: int x, int n, and int m. It returns an int with the nth and mth bytes of x swapped
x is just a normal integer, set to any value. n and m are integers between 0 and 3.
For example, let the hex representation of x be 0x12345678, n is 0, and m is 2.
The last and 3rd to last byte are supposed to be switched (n = 78, m = 34).
I have figured out how extract the nth and mth byte from x, but I can't figure out how to recombine all 4 bytes into the integer that the method is supposed to return.
Here is my current code:
`
int byteSwap(int x, int n, int m)
{
// Initialize variables which will hold nth and mth byte
int xn = x;
int xm = x;
// If n is in bytes, n << 3 will be the number of bits in that byte
// For example, if n is 2 (as in 2 bytes), n << 3 will be 16 (as in 16 bits)
xn = x >> (n << 3);
// Mask off everything except the part we want
xn = xn & 0xFF;
// Do the same for m
xm = x >> (m << 3);
xm = xm & 0xFF;
}
`
There are some additional constraints - only the following are allowed:
~ & ^ | ! + << >>
(That means no - * /, loops, ifs, etc. However, additional variables can be initialized and adding is still OK.)
My code can get the nth and mth byte extracted, but I don't get how to recombine everything without using ifs.
Couple of things
You can recombine by masking x with a value that is all FF except for bytes m and n
You can compute the mask by left shifting 0xFF m times and n times and combining the result and then XOR it with 0xFFFFFFFF
int mask = 0;
int mask_m = 0xFF << (m << 3);
int mask_n = 0xFF << (n << 3);
mask = (mask_m | mask_n) ^ 0xFFFFFFFF;
int x_swapped = (x & mask) | (xm << (n <<3)) | (xn << (m <<3));
return x_swapped;
FYI when you right shift a signed value, it may or may not propagates 1s instead of 0 into the high order bit and is implementation defined. Either way 0xFF will protect against that.
Related
I'm working on exercise 2-8 in K&R which asks us to write function rightrot(int x, int n) such that all bits of x are shifted n times to the right with the bits that fall off the right-end reappearing on the left-end.
Here is my attempted solution in which I shift each bit one-by-one:
int rightrot(int x, int n)
{
int i, rmb;
for(i = 0; i < n; ++i)
{
// get right-most bit
rmb = x & 1;
// shift 1 to right
x = x >> 1;
// if right-most bit is set, set left-most bit
if (rmb == 1)
x = x | (~0 ^ (~0 >> 1) );
}
return x;
}
When I execute rightrot(122, 2), I expect to get 94 since 122 is 1111010 and 94 is 1011110. Instead, I get 30 which happens to be 0011110. Clearly, my method for setting the left-most bit is not working as I expect it to. Does anyone spot an obvious error? I'm just learning about capturing bits and the like.
NOTE: I got the technique for setting the left-most bit from this post.
Let's analyse (~0 ^ (~0 >> 1) ):
~0 is -1
~0 >> 1 is again -1, if the sign bit is 1 rightshift will fill the new bits with 1s.
-1 ^ -1 is 0.
x = x | 0 is x.
The solution is that you should use unsigned datatypes if you want to do bitoperations.
So you should use the line x = x | (~0u ^ (~0u >> 1) );
To avoid other problems the parameter x should also be unsigned int.
https://ideone.com/7zPTQk
I've been working on this puzzle for awhile. I'm trying to figure out how to rotate 4 bits in a number (x) around to the left (with wrapping) by n where 0 <= n <= 31.. The code will look like:
moveNib(int x, int n){
//... some code here
}
The trick is that I can only use these operators:
~ & ^ | + << >>
and of them only a combination of 25. I also can not use If statements, loops, function calls. And I may only use type int.
An example would be moveNib(0x87654321,1) = 0x76543218.
My attempt: I have figured out how to use a mask to store the the bits and all but I can't figure out how to move by an arbitrary number. Any help would be appreciated thank you!
How about:
uint32_t moveNib(uint32_t x, int n) { return x<<(n<<2) | x>>((8-n)<<2); }
It uses <<2 to convert from nibbles to bits, and then shifts the bits by that much. To handle wraparound, we OR by a copy of the number which has been shifted by the opposite amount in the opposite direciton. For example, with x=0x87654321 and n=1, the left part is shifted 4 bits to the left and becomes 0x76543210, and the right part is shifted 28 bits to the right and becomes 0x00000008, and when ORed together, the result is 0x76543218, as requested.
Edit: If - really isn't allowed, then this will get the same result (assuming an architecture with two's complement integers) without using it:
uint32_t moveNib(uint32_t x, int n) { return x<<(n<<2) | x>>((9+~n)<<2); }
Edit2: OK. Since you aren't allowed to use anything but int, how about this, then?
int moveNib(int x, int n) { return (x&0xffffffff)<<(n<<2) | (x&0xffffffff)>>((9+~n)<<2); }
The logic is the same as before, but we force the calculation to use unsigned integers by ANDing with 0xffffffff. All this assumes 32 bit integers, though. Is there anything else I have missed now?
Edit3: Here's one more version, which should be a bit more portable:
int moveNib(int x, int n) { return ((x|0u)<<((n&7)<<2) | (x|0u)>>((9+~(n&7))<<2))&0xffffffff; }
It caps n as suggested by chux, and uses |0u to convert to unsigned in order to avoid the sign bit duplication you get with signed integers. This works because (from the standard):
Otherwise, if the operand that has unsigned integer type has rank greater or equal to the rank of the type of the other operand, then the operand with signed integer type is converted to the type of the operand with unsigned integer type.
Since int and 0u have the same rank, but 0u is unsigned, then the result is unsigned, even though ORing with 0 otherwise would be a null operation.
It then truncates the result to the range of a 32-bit int so that the function will still work if ints have more bits than this (though the rotation will still be performed on the lowest 32 bits in that case. A 64-bit version would replace 7 by 15, 9 by 17 and truncate using 0xffffffffffffffff).
This solution uses 12 operators (11 if you skip the truncation, 10 if you store n&7 in a variable).
To see what happens in detail here, let's go through it for the example you gave: x=0x87654321, n=1. x|0u results in a the unsigned number 0x87654321u. (n&7)<<2=4, so we will shift 4 bits to the left, while ((9+~(n&7))<<2=28, so we will shift 28 bits to the right. So putting this together, we will compute 0x87654321u<<4 | 0x87654321u >> 28. For 32-bit integers, this is 0x76543210|0x8=0x76543218. But for 64-bit integers it is 0x876543210|0x8=0x876543218, so in that case we need to truncate to 32 bits, which is what the final &0xffffffff does. If the integers are shorter than 32 bits, then this won't work, but your example in the question had 32 bits, so I assume the integer types are at least that long.
As a small side-note: If you allow one operator which is not on the list, the sizeof operator, then we can make a version that works with all the bits of a longer int automatically. Inspired by Aki, we get (using 16 operators (remember, sizeof is an operator in C)):
int moveNib(int x, int n) {
int nbit = (n&((sizeof(int)<<1)+~0u))<<2;
return (x|0u)<<nbit | (x|0u)>>((sizeof(int)<<3)+1u+~nbit);
}
Without the additional restrictions, the typical rotate_left operation (by 0 < n < 32) is trivial.
uint32_t X = (x << 4*n) | (x >> 4*(8-n));
Since we are talking about rotations, n < 0 is not a problem. Rotation right by 1 is the same as rotation left by 7 units. Ie. nn=n & 7; and we are through.
int nn = (n & 7) << 2; // Remove the multiplication
uint32_t X = (x << nn) | (x >> (32-nn));
When nn == 0, x would be shifted by 32, which is undefined. This can be replaced simply with x >> 0, i.e. no rotation at all. (x << 0) | (x >> 0) == x.
Replacing the subtraction with addition: a - b = a + (~b+1) and simplifying:
int nn = (n & 7) << 2;
int mm = (33 + ~nn) & 31;
uint32_t X = (x << nn) | (x >> mm); // when nn=0, also mm=0
Now the only problem is in shifting a signed int x right, which would duplicate the sign bit. That should be cured by a mask: (x << nn) - 1
int nn = (n & 7) << 2;
int mm = (33 + ~nn) & 31;
int result = (x << nn) | ((x >> mm) & ((1 << nn) + ~0));
At this point we have used just 12 of the allowed operations -- next we can start to dig into the problem of sizeof(int)...
int nn = (n & (sizeof(int)-1)) << 2; // etc.
A value has even parity if it has an even number of '1' bits. A value has an odd parity if it has an odd number of '1' bits. For example, 0110 has even parity, and 1110 has odd parity.
I have to return 1 if x has even parity.
int has_even_parity(unsigned int x) {
return
}
x ^= x >> 16;
x ^= x >> 8;
x ^= x >> 4;
x ^= x >> 2;
x ^= x >> 1;
return (~x) & 1;
Assuming you know ints are 32 bits.
Let's see how this works. To keep it simple, let's use an 8 bit integer, for which we can skip the first two shift/XORs. Let's label the bits a through h. If we look at our number we see:
( a b c d e f g h )
The first operation is x ^= x >> 4 (remember we're skipping the first two operations since we're only dealing with an 8-bit integer in this example). Let's write the new values of each bit by combining the letters that are XOR'd together (for example, ab means the bit has the value a xor b).
( a b c d e f g h )
xor
( 0 0 0 0 a b c d )
The result is the following bits:
( a b c d ae bf cg dh )
The next operation is x ^= x >> 2:
( a b c d ae bf cg dh )
xor
( 0 0 a b c d ae bf )
The result is the following bits:
( a b ac bd ace bdf aceg bdfh )
Notice how we are beginning to accumulate all the bits on the right-hand side.
The next operation is x ^= x >> 1:
( a b ac bd ace bdf aceg bdfh )
xor
( 0 a b ac bd ace bdf aceg )
The result is the following bits:
( a ab abc abcd abcde abcdef abcdefg abcdefgh )
We have accumulated all the bits in the original word, XOR'd together, in the least-significant bit. So this bit is now zero if and only if there were an even number of 1 bits in the input word (even parity). The same process works on 32-bit integers (but requires those two additional shifts that we skipped in this demonstration).
The final line of code simply strips off all but the least-significant bit (& 1) and then flips it (~x). The result, then, is 1 if the parity of the input word was even, or zero otherwise.
GCC has built-in functions for this:
Built-in Function: int __builtin_parity (unsigned int x)
Returns the parity of x, i.e. the number of 1-bits in x modulo 2.
and similar functions for unsigned long and unsigned long long.
I.e. this function behaves like has_odd_parity. Invert the value for has_even_parity.
These should be the fastest alternative on GCC. Of course its use is not portable as such, but you can use it in your implementation, guarded by a macro for example.
The following answer was unashamedly lifted directly from Bit Twiddling Hacks By Sean Eron Anderson, seander#cs.stanford.edu
Compute parity of word with a multiply
The following method computes the parity of the 32-bit value in only 8 operations >using a multiply.
unsigned int v; // 32-bit word
v ^= v >> 1;
v ^= v >> 2;
v = (v & 0x11111111U) * 0x11111111U;
return (v >> 28) & 1;
Also for 64-bits, 8 operations are still enough.
unsigned long long v; // 64-bit word
v ^= v >> 1;
v ^= v >> 2;
v = (v & 0x1111111111111111UL) * 0x1111111111111111UL;
return (v >> 60) & 1;
Andrew Shapira came up with this and sent it to me on Sept. 2, 2007.
Try:
int has_even_parity(unsigned int x){
unsigned int count = 0, i, b = 1;
for(i = 0; i < 32; i++){
if( x & (b << i) ){count++;}
}
if( (count % 2) ){return 0;}
return 1;
}
To generalise TypeIA's answer for any architecture:
int has_even_parity(unsigned int x)
{
unsigned char shift = 1;
while (shift < (sizeof(x)*8))
{
x ^= (x >> shift);
shift <<= 1;
}
return !(x & 0x1);
}
The main idea is this. Unset the rightmost '1' bit by using x & ( x - 1 ). Let’s say x = 13(1101) and the operation of x & ( x - 1 ) is 1101 & 1100 which is 1100, notice that the rightmost set bit is converted to 0.
Now x is 1100. The operation of x & ( x - 1 ), i.e., 1100 & 1011 is 1000. Notice that the original x is 1101 and after two operations of x & (x - 1) the x is 1000, i.e., two set bits are removed after two operations. If after an odd number of operations, the x becomes zero, then it's an odd parity, else it's an even parity.
Here's a one line #define that does the trick for a char:
#define PARITY(x) ((~(x ^= (x ^= (x ^= x >> 4) >> 2) >> 1)) & 1) /* even parity */
int main()
{
char x=3;
printf("parity = %d\n", PARITY(x));
}
It's portable as heck and easily modified to work with bigger words (16, 32 bit). It's important to note also, using a #define speeds the code up, each function call requires time to push the stack and allocate memory. Code size doesn't suffer, especially if it's implemented only a few times in your code - the function call might take up as much object code as the XORs.
Admittedly, the same efficiencies may be obtained by using the inline function version of this, inline char parity(char x) {return PARITY(x);} (GCC) or __inline char parity(char x) {return PARITY(x);} (MSVC). Presuming you keep the one line define.
int parity_check(unsigned x) {
int parity = 0;
while(x != 0) {
parity ^= x;
x >>= 1;
}
return (parity & 0x1);
}
In case the end result is supposed to be a piece of code that can work (be compiled) with a C program then I suggest the following:
.code
; bool CheckParity(size_t Result)
CheckParity PROC
mov rax, 0
add rcx, 0
jnp jmp_over
mov rax, 1
jmp_over:
ret
CheckParity ENDP
END
This is a piece of code I'm using to check the parity of calculated results in a 64-bit C program compiled using MSVC. You can obviously port it to 32 bit or other compilers.
This has the advantage of being much faster than using C and it also leverages the CPU's functionality.
What this example does is take as input a parameter (passed in RCX - __fastcall calling convention). It increments it by 0 thus setting the CPU's parity flag and then setting a variable (RAX) to 0 or 1 if the parity flag is on or not.
my solution
get the rightmost n bits of y
a = ~(~0 << n) & y
clean the n bits of x beginning from p
c = ( ~0 << p | ~(~0 << (p-n+1))) & x
set the cleaned n bits to the n rightmost bits of y
c | (a << (p-n+1))
it is rather long statements. do we have a better one?
i.e
x = 0 1 1 1 0 1 1 0 1 1 1 0
p = 4
y = 0 1 0 1 1 0 1 0 1 0
n = 3
the 3 rightmost bits of y is 0 1 0
it will replace x from bits 4 to bits 2 which is 1 1 1
I wrote similar one:
unsigned setbits (unsigned x, int p, int n, unsigned y)
{
return (x & ~(~(~0<<n)<<(p+1-n)))|((y & ~(~0<<n))<<(p+1-n));
}
There are two reasonable approaches.
One is yours: Grab the low n bits of y, nuke the middle n bits of x, and "or" them into place.
The other is to build the answer from three parts: Low bits "or" middle bits "or" high bits.
I think I actually like your version better, because I bet n and p are more likely to be compile-time constants than x and y. So your answer becomes two masking operations with constants and one "or"; I doubt you will do better.
I might modify it slightly to make it easier to read:
mask = (~0 << p | ~(~0 << (p-n+1)))
result = (mask & a) | (~mask & (y << (p-n+1)))
...but this is the same speed (indeed, code) as yours when mask is a constant, and quite possibly slower when mask is a variable.
Finally, make sure you have a good reason to worry about this in the first place. Clean code is good, but for something this short, put it in a well-documented function and it does not matter that much. Fast code is good, but do not attempt to micro-optimize something like this until your profiler tells you do. (Modern CPUs do this stuff very fast; it is unlikely your application's performance is bounded by this sort of function. At the very least it is "innocent until proven guilty".)
Have a look at the following descriptive code:
int setbitsKR(int x, int p, int n, int y){
int shiftingDistance = p - n + 1,
bitmask = (1 << n) - 1, // example, 11
digitsOfY = (y & bitmask) << shiftingDistance, // whatever
bitmaskShiftedToLeft = bitmask << shiftingDistance, // 001100
invertedBitmaskShiftedToLeft = ~bitmaskShiftedToLeft; // 110011
// erase those middle bits of x
x &= invertedBitmaskShiftedToLeft;
// add those bits from y into x
x |= digitsOfY;
return x;
}
In short, it creates a bitmask (string of 1s), shifts them to get to that middle position of x, nukes those bits of x by &ing with a string of 0s (inverted bitmask), and finally |s that position with the right digits of y.
Let's say I have a byte with six unknown values:
???1?0??
and I want to swap bits 2 and 4 (without changing any of the ? values):
???0?1??
But how would I do this in one operation in C?
I'm performing this operation thousands of times per second on a microcontroller so performance is the top priority.
It would be fine to "toggle" these bits. Even though this is not the same as swapping the bits, toggling would work fine for my purposes.
Try:
x ^= 0x14;
That toggles both bits. It's a little bit unclear in question as you first mention swap and then give a toggle example. Anyway, to swap the bits:
x = precomputed_lookup [x];
where precomputed_lookup is a 256 byte array, could be the fastest way, it depends on the memory speed relative to the processor speed. Otherwise, it's:
x = (x & ~0x14) | ((x & 0x10) >> 2) | ((x & 0x04) << 2);
EDIT: Some more information about toggling bits.
When you xor (^) two integer values together, the xor is performed at the bit level, like this:
for each (bit in value 1 and value 2)
result bit = value 1 bit xor value 2 bit
so that bit 0 of the first value is xor'ed with bit 0 of the second value, bit 1 with bit 1 and so on. The xor operation doesn't affect the other bits in the value. In effect, it's a parallel bit xor on many bits.
Looking at the truth table for xor, you will see that xor'ing a bit with the value '1' effectively toggles the bit.
a b a^b
0 0 0
0 1 1
1 0 1
1 1 0
So, to toggle bits 1 and 3, write a binary number with a one where you want the bit to toggle and a zero where you want to leave the value unchanged:
00001010
convert to hex: 0x0a. You can toggle as many bits as you want:
0x39 = 00111001
will toggle bits 0, 3, 4 and 5
You cannot "swap" two bits (i.e. the bits change places, not value) in a single instruction using bit-fiddling.
The optimum approach if you want to really swap them is probably a lookup table. This holds true for many 'awkward' transformations.
BYTE lookup[256] = {/* left this to your imagination */};
for (/*all my data values */)
newValue = lookup[oldValue];
The following method is NOT a single C instruction, it's just another bit fiddling method. The method was simplified from Swapping individual bits with XOR.
As stated in Roddy's answer, a lookup table would be best. I only suggest this in case you didn't want to use one. This will indeed swap bits also, not just toggle (that is, whatever is in bit 2 will be in 4 and vice versa).
b: your original value - ???1?0?? for instance
x: just a temp
r: the result
x = ((b >> 2) ^ (b >> 4)) & 0x01
r = b ^ ((x << 2) | (x << 4))
Quick explanation: get the two bits you want to look at and XOR them, store the value to x. By shifting this value back to bits 2 and 4 (and OR'ing together) you get a mask that when XORed back with b will swap your two original bits. The table below shows all possible cases.
bit2: 0 1 0 1
bit4: 0 0 1 1
x : 0 1 1 0 <-- Low bit of x only in this case
r2 : 0 0 1 1
r4 : 0 1 0 1
I did not fully test this, but for the few cases I tried quickly it seemed to work.
This might not be optimized, but it should work:
unsigned char bit_swap(unsigned char n, unsigned char pos1, unsigned char pos2)
{
unsigned char mask1 = 0x01 << pos1;
unsigned char mask2 = 0x01 << pos2;
if ( !((n & mask1) != (n & mask2)) )
n ^= (mask1 | mask2);
return n;
}
The function below will swap bits 2 and 4. You can use this to precompute a lookup table, if necessary (so that swapping becomes a single operation):
unsigned char swap24(unsigned char bytein) {
unsigned char mask2 = ( bytein & 0x04 ) << 2;
unsigned char mask4 = ( bytein & 0x10 ) >> 2;
unsigned char mask = mask2 | mask4 ;
return ( bytein & 0xeb ) | mask;
}
I wrote each operation on a separate line to make it clearer.
void swap_bits(uint32_t& n, int a, int b) {
bool r = (n & (1 << a)) != 0;
bool s = (n & (1 << b)) != 0;
if(r != s) {
if(r) {
n |= (1 << b);
n &= ~(1 << a);
}
else {
n &= ~(1 << b);
n |= (1 << a);
}
}
}
n is the integer you want to be swapped in, a and b are the positions (indexes) of the bits you want to be swapped, counting from the less significant bit and starting from zero.
Using your example (n = ???1?0??), you'd call the function as follows:
swap_bits(n, 2, 4);
Rationale: you only need to swap the bits if they are different (that's why r != s). In this case, one of them is 1 and the other is 0. After that, just notice you want to do exactly one bit set operation and one bit clear operation.
Say your value is x i.e, x=???1?0??
The two bits can be toggled by this operation:
x = x ^ ((1<<2) | (1<<4));
#include<stdio.h>
void printb(char x) {
int i;
for(i =7;i>=0;i--)
printf("%d",(1 & (x >> i)));
printf("\n");
}
int swapb(char c, int p, int q) {
if( !((c & (1 << p)) >> p) ^ ((c & (1 << q)) >> q) )
printf("bits are not same will not be swaped\n");
else {
c = c ^ (1 << p);
c = c ^ (1 << q);
}
return c;
}
int main()
{
char c = 10;
printb(c);
c = swapb(c, 3, 1);
printb(c);
return 0;
}