How to compute the integer absolute value

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How to compute the integer absolute value without using if condition. I guess we need to use some bitwise operation. Can anybody help?

1) Set the mask as right shift of integer by 31 (assuming integers are stored as two's-complement 32-bit values and that the right-shift operator does sign extension).

 mask = n>>31 

2) XOR the mask with number

mask ^ n 

3) Subtract mask from result of step 2 and return the result.

(mask^n) - mask 

How to compute the integer absolute value, is the numerical value without regard to whether the sign is negative or positive. On a number line it is the distance between the number and zero. 10 Answers 10. 1) Set the mask as right shift of integer by 31 (assuming integers are stored as two's-complement 32-bit values and that the right-shift operator does sign extension). 3) Subtract mask from result of step 2 and return the result. Keep in mind that not all languages intepret integer the same way.

Same as existing answers, but with more explanations:

Let's assume a twos-complement number (as it's the usual case and you don't say otherwise) and let's assume 32-bit:

First, we perform an arithmetic right-shift by 31 bits. This shifts in all 1s for a negative number or all 0s for a positive one (but note that the actual >>-operator's behaviour in C or C++ is implementation defined for negative numbers, but will usually also perform an arithmetic shift, but let's just assume pseudocode or actual hardware instructions, since it sounds like homework anyway):

mask = x >> 31;

So what we get is 111...111 (-1) for negative numbers and 000...000 (0) for positives

Now we XOR this with x, getting the behaviour of a NOT for mask=111...111 (negative) and a no-op for mask=000...000 (positive):

x = x XOR mask;

And finally subtract our mask, which means +1 for negatives and +0/no-op for positives:

x = x - mask;

So for positives we perform an XOR with 0 and a subtraction of 0 and thus get the same number. And for negatives, we got (NOT x) + 1, which is exactly -x when using twos-complement representation.

Absolute Value of Integers, of a number x takes x and makes it positive. Finding the absolute value of a number is one of the most important nonbinary operations. Binary operations require two numbers and involve the kind of math you’re used to doing: addition, subtraction, multiplication, and division. But nonbinary operations in algebra use only one number,

Assume int is of 32-bit.

int my_abs(int x)
{
    int y = (x >> 31);
    return (x ^ y) - y;
}

What is the absolute value of 10?, Given an integer, compute its absolute value (abs) without branching We can use the expression ((n + mask) ^ mask) where mask is (n >> 31) (assuming 32 bit​  // Abs returns the absolute value of x. func Abs(x int64) int64 { if x < 0 { return -x } return x } Warning: The smallest value of a signed integer doesn’t have a matching positive value. math.MinInt64 is -9223372036854775808, but; math.MaxInt64 is 9223372036854775807. Unfortunately, our Abs function returns a negative value in this case.

One can also perform the above operation as:

return n*(((n>0)<<1)-1);

where n is the number whose absolute need to be calculated.

Bit Hacks, Compute the integer absolute value without branching - Bit Algorithm - We need not do anything if a no is positive. We want to change only  Conveniently, Python has bottled up the concept of absolute value for use in the standard library. In fact, there’s no need to import any modules. The following function works right out of the box: x = -5 x = abs(x) In other words, if you need to compute an absolute value directly—for instance, as a part of an expression—this is the way to go.

I wrote my own, before discovering this question.

My answer is probably slower, but still valid:

int abs_of_x = ((x*(x >> 31)) | ((~x + 1) * ((~x + 1) >> 31)));

Compute the integer absolute value (abs) without branching, Learn how to find the absolute value of 5, -10, and 12. Apart from zero, yes always positive Duration: 2:22 Posted: Aug 27, 2011 If v is positive, the expression (v>0) is true and will have the value 1 while (v<0) is false (with a value 0 for false). Hence, when v is positive ((v>0) - (v<0)) = (1-0) = 1. And the whole expression is: v * (1) == v. If v is negative, the expression (v>0) is false and will have the value 0 while (v<0) is true (value 1).

Absolute value examples (video), This video lecture is produced by S. Saurabh. He is B.Tech from IIT and MS from USA. Compute Duration: 7:31 Posted: Sep 10, 2012 The absolute value (or modulus) of a real number is the corresponding nonnegative value that disregards the sign. For a real value, a, the absolute value is: a, if a is greater than or equal to zero. -a, if a is less than zero.

Programming Interview: Absolute Value of Integer without Branching , The absolute value of an integer is the numerical value without regard to whether the sign is negative or positive. On a number line it is the distance between the  What is the ABSOLUTE Function in Excel (ABS)? The ABSOLUTE function in Excel returns the absolute value of a number. The function converts negative numbers to positive numbers while positive numbers remain unaffected. Formula. ABSOLUTE Value = ABS(number) Where number is the numeric value for which we need to calculate the Absolute value.

Absolute value (Pre-Algebra, Explore and understand integers , In this section you'll learn how to the find the absolute value of integers. 4 - 0 = 4 4 - 1 = 3 4 - 2 = 2 4 - 3 = 1 4 - 4 = 0 4 - 5 = -1. In this pattern you can see that 4  In C, abs is only declared in <stdlib.h> (and operates on int values). Since C++11, additional overloads are provided in this header for the integral types: These overloads effectively cast x to a double before calculations (defined for T being any integral type). Parameters x Value whose absolute value is returned. Return Value The absolute

Comments
  • Is the ternary operator allowed ?
  • No, I guess you cannot use that too.
  • graphics.stanford.edu/~seander/bithacks.html#IntegerAbs
  • What's the motivation? Performance? Are you trying to solve a branch-predication failure by eliminating the branch? Intellectual curiosity? Homework? Something else?
  • What is the proper answer for ABS(INT_MIN)? (use 8-bits for simplicity): ABS(-128) ideally should be 128. But the maximum signed 8-bit int is only 127!
  • Keep in mind that not all languages intepret integer the same way. There are some that support positive and negative zero where abs(~int)-abs(int) results in 0 while your solution requires: abs(abs(~int)-abs(int)) beeing 1.
  • Upvote for the clear explanation, much better than the accepted answer!
  • In C or C++, can't this result in undefined behavior? If x is INT_MIN, then the XOR operation will make x == INT_MAX, and adding 1 to INT_MAX is an overflow error (aka undefined behavior for signed integers)
  • @JoshuaWise Well, I didn't assume a specific programming language, though. In that case, the signed right-shift would already be implementation-defined behaviour.
  • Where should I start if I came here searching for ways to refine a solution I wrote on Hacker Rank and have literally no clue what any of the stuff in this answer means? For context: in my HR solution I implemented absolute value of i by checking if the value is less than 0 and, if so, doing i = i + (i * -2).
  • If you don't what any of the stuff in this answer means, I'm afraid you might have to look somewhere else. Your solution for the absolute value might work, too. It's not what was asked about, though. In general, for more information on how bitwise operations work, a general learning resource on those might work better than trying to crawl through SO answers.
  • Well, I'm pretty sure that's also outruled by the question. Of course using a prebuilt functions is always easiest ;)
  • I can see that now. Worth trying to help though. Good thing he got his answer.