I am analysing an Internet guide, where I fond code like that. Can somebody explain me the usage of ~ and & operators?
Thanks in advance
uint8_t tx_fifo_put(tx_dataType data)
{
/*Check if FIFO is full*/
if((tx_put_itr - tx_get_itr) & ~(TXFIFOSIZE-1))
{
/*FIFO full - return TXFAIL*/
return (TXFAIL);
}
/*Put data into fifo*/
TX_FIFO[tx_put_itr & (TXFIFOSIZE - 1)] = data;
/*Incerment itr*/
tx_put_itr++;
return(TXSUCCESS);
}
What the code does, is an obfuscated way to replace a more human readable code.
As a commenter wrote before me, the TX_FIFO[tx_put_itr & (TXFIFOSIZE - 1)] = data; loops the output. Also as it was mentioned in comments, the code is meant to have size being power of two.
I do not know why it is done so, for me TX_FIFO[tx_put_itr % TXFIFOSIZE] = data does the same, but more readable. Also, a person expects predicate checks to be before data access. At least it is my nature.
The (w - r) &~ size part is a way to check for (1)w < r and, (2) as an edge case, w being equal to FIFOSIZE and r being zero. Semantically it should have meant, that "if the write pointer points to boundary, and read pointer points to start of a buffer, we suggest that, for our data structure, next write could be an overflow."
Let us see some code, numbers and their binary representation.
let s = 8 - 1, in binary is 00000111 and negated is 11111000.
let w = 0, let r = 1.
now in binary w = 00000000, r = 00000001.
w - r = 11111111, logical and that with ~(8 - 1) and get some value, other then zero.
Continuing the logic for the w < r case, we get that any negative integer will produce some bits in the above. So this definitely gives true for the OP if code.
Now the w = r case can not commit bits to the boolean test.
And last case,
let s = 8,
let w = 8
let r = 0
w - r = 00001000
~(8 - 1) = 11111000
(w - r) &~ 7 = 00001000
All other cases where w > r give zero.
Update
To my great grief, the #UkropUkraine had deleted all comments and his answer. There were some discussion there about the fact, that one can use (w - r) >= mask in place of (w - r) & mask.
Here I present a code, and an explanation that it is not an optimization, or just syntax, or whatever came to mind to the person who wrote the OP code. It is intended code. And it fails to do its purpose: to run as a FIFO or circular queue, or whatever that part of code was meant to do.
First, take an example of usage. The part where Ukrop user had difficulties. The w pointer can be less than r pointer. And the result of w - r will be negative.
The common usage is to add a byte to the buffer and wrap write pointer as soon as it reaches the end. Imagine situation where w pointer already wrapped.
#include <stdio.h>
int main()
{
unsigned char w = 0, r = 1;
int r;
r = (a - b) & 0xffffffff;
printf("%d\n", r);
return 0;
}
-1
I do not know what is a common boolean result type with micro controllers. For a common x86 C machine, it is int. So I expect the if((w - r) &~ size) to be converted to an int. And the result is negative. You can not just write the above with >=, '>', or == as it was stated by the comments and the other answer here.
More than that, the code fails its semantics. It is meant to be a FIFO, or something, I do not know. But in the above situation, the read pointer still has some sensible data to read. And it can be done, because the write pointer, even if it is wrapped, does not overwrite the read portion of a buffer, yet. But the code returns BUFFULL.
I thought about read/write being different directions, but it does not change anything. The code OP gave, fails to do what one would expect.
Maybe I do miss some insight here, as Ukrop user, and OP, point me to the fact that they know code semantics. The OP just did not get a ~ and & usage. Well, this is an answer, the ~& is used to test for a negative value and for the edge cases.
The two operators:
& is a bitwise and operator
~ is a bitwise complement operator
Now for the posted code it's important to notice that TXFIFOSIZE must have a value which is a power of 2, i.e. values like 2, 4, 8, 16, 32, ...
When that is true, the code:
TX_FIFO[tx_put_itr & (TXFIFOSIZE - 1)] = data;
is equivalent to:
TX_FIFO[tx_put_itr % TXFIFOSIZE] = data;
Notice that tx_put_itr is being incremented in such a way that it will take value higher than TXFIFOSIZE. So in order to get a valid array index the code must find the remainder of tx_put_itr with respect to TXFIFOSIZE.
So how does work? Why are the above lines equivalent?
Let's take a value as example.
Assume TXFIFOSIZE is 8 (2 to the power of 3)
So TXFIFOSIZE-1 is 7
7 is bitwise 00....00111
And when you do:
SOME_NUMBER & 00....00111
You keep the 3 least significant bits of SOME_NUMBER
And that is exactly the remainder of when diving by 8
So let's look at
if((tx_put_itr - tx_get_itr) & ~(TXFIFOSIZE-1))
It is equivalent to
if((tx_put_itr - tx_get_itr) >= TXFIFOSIZE)
So it checks for "FIFO full"
Again using an example it works like this:
Assume TXFIFOSIZE is 8 (2 to the power of 3)
So TXFIFOSIZE-1 is 7
7 is bitwise 00....00111
~7 is bitwise 11....11000
And when you do:
SOME_NUMBER & 11....11000
You clear the 3 least significant bits of SOME_NUMBER and keep the rest unchanged
So if the result is non-zero it means that the difference between
tx_put_itr and tx_get_itr is 8 (or more).
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Can anyone tell me how does this code work?
int Calc(int *arr, int m)
int result;
for (result &= 0; m; (arr[--m] & (0x1 << 0x1F)) ? result += arr[m]: Void());
return result;
I can't understand for loop:/
Where did you find this code so I can hunt that person down and beat him with a copy of Schildt?
It's no surprise you don't understand the loop; it wasn't written to be understandable. The only place this kind of code is acceptable is the IOCCC, except it's not obfuscated enough for that competition.
Taking each bit in turn:
result &= 0;
is a really funky way of initializing result to 0; it's shorthand for result = result & 0, which performs a bitwise-AND of result against 0 (giving 0) and assigns the result back to result. It's also unsafe, since an uninitialized object may contain a trap representation. That should have been written as simply result = 0.
m;
just checks the current value of m; the loop will run until it is 0. The loop basically starts at the last element and works its way down to the first.
(arr[--m] & (0x1 << 0x1F)) ? result += arr[m]: Void()
Ugh. So, the first thing it does is take the value of the array at index m-1 and does a bitwise and against 0x1 << 0x1F (1 shifted left 31 postitions, or essentially 0x80000000); if the result of this operation is non-zero, then we add the value of that array element to result, otherwise we execute some incredibly inappropriately named function that hopefully returns a 01. Given that we're dealing with signed integers, and that on most platforms an int is 32 bits wide, this code is obviously adding up negative values in result.
A slightly saner way of writing that would be
result = 0;
while ( m ) // or m != 0, or m > 0, whatever you prefer
{
if ( arr[--m] < 0 )
result += arr[m];
}
1. The conditional operator ?: isn't meant to be used as a control structure like this. The syntax is expr1 ? expr2 : expr3. First, expr1 is evaluated and all side effects applied; if it results in a non-zero value, then the result of the expression is expr2; otherwise, the result is expr3.
Part 1
Firstrly result &= 0 is used for setting 0 to result variable using bitwise AND operation. Bitwise with 0 will ever return 0.
You can write it simply this way: result = 0
The better (much optimal) way of doing this is: result ^= result. (Bitwise XOR)
Part 2
This loop will iterate while m is greater (or less) than 0. Because m expression will return true if m != 0.
Much secure way of doing it is m > 0.
Also you can use this expression, which is not making programm much optimal, but it will be cleaner to another programmer to understand your code: !!m (casting m variable to bool), which is equal to m != 0;
Part 3
In this part ternary operator (logical_expression ? expression_1 : expression_2) is used.
If logical_expression is true, then expression_1 will be executed, expression_2 will be executed otherwise.
So in your code, if this expression (arr[--m] & (0x1 << 0x1F)) returns true then we add arr[m] to result variable. And do nothing in another case.
Also m variable is decremented in ternary logical expression (arr[--m]).
Assume Z is an unsigned integer. Using ~, <<, >>, &, | , +, and - provide statements which return the desired result.
I am allowed to introduce new binary values if needed.
I have these problems:
1.Extract the 5th bit from the left Z.
For this I was thinking about doing something like
x x x x x x x x
& 0 0 0 0 1 0 0 0
___________________
0 0 0 0 1 0 0 0
Does this make sense for extracting the fifth bit? I am not totally sure how I would make this work by using just Z when I do not know its values. (I am relatively new to all of this). Would this type of idea work though?
2.Return the number of 1 bits in Z
Here I kind of have no idea how to work this out. What I really need to know is how to work on just Z with the operators, but I m not sure exactly how to.
Like I said I am new to this, so any help is appreciated.
Problem 1
You’re right on the money. I’d do an & and a >> so that you get either a nice 0 or 1.
result = (z & 0x08) >> 3;
However, this may not be strictly necessary. For example, if you’re trying to check whether the bit is set as part of an if conditional, you can exploit C’s definition of anything nonzero as true.
if (z & 0x08)
do_stuff();
Problem 2
There are a whole variety of ways to do this. According to that page, the following methodology dates from 1960, though it wasn’t published in C until 1988.
for (result = 0; z; result++)
z &= z - 1;
Exactly why this works might not be obvious at first, but if you work through a few examples, you’ll quickly see why it does.
It’s worth noting that this operation – determining the number of 1 bits in a number – is sufficiently important to have a name (population count or Hamming weight) and, on recent Intel and AMD processors, a dedicated instruction. If you’re using GCC, you can use the __builtin_popcount intrinsic.
Problem 1 looks right, except you should finish it by shifting the result right by 4 to get that bit after the mask.
To implement the mask, you need to know what integer is represented by a single 5th bit. That number is incidentally 2^5 = 32. So you can just AND z with 32 and shift it right by 4.
Problem 2:
int answer = 0;
while (z != 0){ //stop when there are no more 1 bits in z
//the following masks the lowest bit in z and adds it into answer
//if z ends with a 0, nothing is added, otherwise 1 is added
answer += (z & 1);
//this shifts z right by 1 to get the next higher bit
z >>= 1;
}
return answer;
To find out the value of the fifth bit, you don't care about the bottom bits so you can get rid of them:
unsigned int answer = z >> 4;
The fifth bit becomes the bottom bit, so you can strip it off with a bitwise-AND:
answer = answer & 1;
To find the number of 1-bits in a number you can apply stakSmashr's solution. You could optimise this further if you know you need to count the number of bits in a lot of integers - precompute the number of bits in every possible 8-bit number and store it in a table. There will only be 256 entries in the table so it won't use much memory. Then, you can loop over your data one byte at a time and find the answer from the table. This lookup will be quicker than looping again over each bit.
A buddy of mine had these puzzles and this is one that is eluding me. Here is the problem, you are given a number and you want to return that number times 3 and divided by 16 rounding towards 0. Should be easy. The catch? You can only use the ! ~ & ^ | + << >> operators and of them only a combination of 12.
int mult(int x){
//some code here...
return y;
}
My attempt at it has been:
int hold = x + x + x;
int hold1 = 8;
hold1 = hold1 & hold;
hold1 = hold1 >> 3;
hold = hold >> 4;
hold = hold + hold1;
return hold;
But that doesn't seem to be working. I think I have a problem of losing bits but I can't seem to come up with a way of saving them. Another perspective would be nice. Just to add, you also can only use variables of type int and no loops, if statements or function calls may be used.
Right now I have the number 0xfffffff. It is supposed to return 0x2ffffff but it is returning 0x3000000.
For this question you need to worry about the lost bits before your division (obviously).
Essentially, if it is negative then you want to add 15 after you multiply by 3. A simple if statement (using your operators) should suffice.
I am not going to give you the code but a step by step would look like,
x = x*3
get the sign and store it in variable foo.
have another variable hold x + 15;
Set up an if statement so that if x is negative it uses that added 15 and if not then it uses the regular number (times 3 which we did above).
Then divide by 16 which you already showed you know how to do. Good luck!
This seems to work (as long as no overflow occurs):
((num<<2)+~num+1)>>4
Try this JavaScript code, run in console:
for (var num = -128; num <= 128; ++num) {
var a = Math.floor(num * 3 / 16);
var b = ((num<<2)+~num+1)>>4;
console.log(
"Input:", num,
"Regular math:", a,
"Bit math:", b,
"Equal: ", a===b
);
}
The Maths
When you divide a positive integer n by 16, you get a positive integer quotient k and a remainder c < 16:
(n/16) = k + (c/16).
(Or simply apply the Euclidan algorithm.) The question asks for multiplication by 3/16, so multiply by 3
(n/16) * 3 = 3k + (c/16) * 3.
The number k is an integer, so the part 3k is still a whole number. However, int arithmetic rounds down, so the second term may lose precision if you divide first, And since c < 16, you can safely multiply first without overflowing (assuming sizeof(int) >= 7). So the algorithm design can be
(3n/16) = 3k + (3c/16).
The design
The integer k is simply n/16 rounded down towards 0. So k can be found by applying a single AND operation. Two further operations will give 3k. Operation count: 3.
The remainder c can also be found using an AND operation (with the missing bits). Multiplication by 3 uses two more operations. And shifts finishes the division. Operation count: 4.
Add them together gives you the final answer.
Total operation count: 8.
Negatives
The above algorithm uses shift operations. It may not work well on negatives. However, assuming two's complement, the sign of n is stored in a sign bit. It can be removed beforing applying the algorithm and reapplied on the answer.
To find and store the sign of n, a single AND is sufficient.
To remove this sign, OR can be used.
Apply the above algorithm.
To restore the sign bit, Use a final OR operation on the algorithm output with the stored sign bit.
This brings the final operation count up to 11.
what you can do is first divide by 4 then add 3 times then again devide by 4.
3*x/16=(x/4+x/4+x/4)/4
with this logic the program can be
main()
{
int x=0xefffffff;
int y;
printf("%x",x);
y=x&(0x80000000);
y=y>>31;
x=(y&(~x+1))+(~y&(x));
x=x>>2;
x=x&(0x3fffffff);
x=x+x+x;
x=x>>2;
x=x&(0x3fffffff);
x=(y&(~x+1))+(~y&(x));
printf("\n%x %d",x,x);
}
AND with 0x3fffffff to make msb's zero. it'l even convert numbers to positive.
This uses 2's complement of negative numbers. with direct methods to divide there will be loss of bit accuracy for negative numbers. so use this work arround of converting -ve to +ve number then perform division operations.
Note that the C99 standard states in section section 6.5.7 that right shifts of signed negative integer invokes implementation-defined behavior. Under the provisions that int is comprised of 32 bits and that right shifting of signed integers maps to an arithmetic shift instruction, the following code works for all int inputs. A fully portable solution that also fulfills the requirements set out in the question may be possible, but I cannot think of one right now.
My basic idea is to split the number into high and low bits to prevent intermediate overflow. The high bits are divided by 16 first (this is an exact operation), then multiplied by three. The low bits are first multiplied by three, then divided by 16. Since arithmetic right shift rounds towards negative infinity instead of towards zero like integer division, a correction needs to be applied to the right shift for negative numbers. For a right shift by N, one needs to add 2N-1 prior to the shift if the number to be shifted is negative.
#include <stdio.h>
#include <stdlib.h>
int ref (int a)
{
long long int t = ((long long int)a * 3) / 16;
return (int)t;
}
int main (void)
{
int a, t, r, c, res;
a = 0;
do {
t = a >> 4; /* high order bits */
r = a & 0xf; /* low order bits */
c = (a >> 31) & 15; /* shift correction. Portable alternative: (a < 0) ? 15 : 0 */
res = t + t + t + ((r + r + r + c) >> 4);
if (res != ref(a)) {
printf ("!!!! error a=%08x res=%08x ref=%08x\n", a, res, ref(a));
return EXIT_FAILURE;
}
a++;
} while (a);
return EXIT_SUCCESS;
}
I am using ROBOTC to program my robot, and I was using some code built by someone else. In a function, I see the line:
int leftDir = (left>0)*2-1;
leftDir is initialized to an integer, so what does the > do? I am under the impression that is is a binary shift, but I'm not sure. Can someone explain this?
Thanks.
The > is the greater than operator. In C result of comparison is either 1 for true or 0 for false. In other words the code above is logically equivalent to (but more compact):
int leftDir;
if (left > 0) {
leftDir = 1;
} else {
leftDir = -1;
}
The previous answer is correct, but i believe he intended it as a bit shifting operator. This would make sense because he went on to multiply the value by a number, implying that he isn't treating it as a boolean. He was incorrect, though, about the roobtc bit shifting notation. If you want to bit shift a number in robotc, use the following syntax:
int foo = 0b00001111 >> 2; //bit shifts the bianary number 00001111 over by two bits, so foo will be set to the result 00000011
In the book I am reading to learn C "The C programming language" in chapter 2.
The book is explaining Bitwise operations and it has a function that shows how many bits are in an integer.
The following is the function...
int Bitcount(unsigned x){
int b;
for(b = 0; x != 0; x >>=1){
if(x & 01){
b++
}
}
return b;
}
Then an exercise is given to us stating exactly this.
"In a two's complement number system, x &= (x-1) deletes the rightmost 1-bit in x;
Explain why. Use this observation to write a faster version of Bitcount".
The problem is I really cannot understand how "x &= (x-1)" would work? can someone explain this to me? or send me to a resource that could better help me understand?
I have been trying to figure this out but I really can't.
Thank you for any help that you may give.
also if there is anything wrong with my question this is my first post so please help me make my questions better.
X and X-1 cannot both have their rightmost bit set to 1, because in the binary system numbers ending in 0 and 1 alternate - so X & (X-1) is guaranteed to be a number whose rightmost bit set to 0 as AND only evaluates to true if both terms are true. Maybe the confusion stems from what Andrew W said, here a bitwise AND is used (which ANDs each bit individually)?
EDIT: now, as Inspired points out, this is only part of the answer as the original problem specifies that the rightmost 1-bit will get reset. As Andrew W already answered the correct version in detail, I'm not going to repeat his explanation here but I refer to his answer.
It is equivalent to x = x & (x-1) Here, the & is a bitwise and, not a logical and.
So here's what happens:
1) The expression on the right will be evaluated first, and that value will be stored in x.
2) Suppose x = 01001011 in binary (this isn't the case, since more than 8 bits will be used to represent x, but pretend it is for this example). Then x-1 = 01001010.
3) compute the bitwise and:
01001011 &
01001010 =
01001010
which deleted the rightmost one bit.
now suppose number didn't end with a 1 bit:
Say: x = 01001100, the (x-1) = 01001011
compute the bitwise and:
01001100 &
01001011 =
01001000
again removing the rightmost 1.
Good book by the way. I hope you enjoy it!
Let's take a closer look at the rightmost 1 bit in x: suppose x = AAAAAA10000..0, where AAAAAA are arbitrary bits. Then x-1 = AAAAAA01111..1. Bitwise AND of these two expressions gives AAAAAA00000..0. This is how it resets the rightmost non-zero bit.
The problem is I really cannot understand how "x &= (x-1)" would work?
Binary number is positional the same way as decimal number. When we increase the number we carry a bit to the left, when we decrease we borrow from the left the same way we do with decimals. So in case x-01 we borrow the first 1-bit from the right while others being set to 1-bit:
10101000
- 00000001
--------
10100111
which is inversion of those bits till the first 1-bit. And as stated before by others ~y & y = 0 that is why this method can be used to count 1-bits as proposed by the book to make the method faster comparing to bits shifting.