One of the ways to implement the required function would be to add a check on the situation where x == y. You could also remove the else which is redundant and just return bit = 0 if your function reaches the end of execution. You would get something like this:

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == y) {
        return(bit=1);
    }
    if (x == -y) {
        return (bit=1);
    }
    return(bit=0);
}

You need a forest...

...of IFs. Yes Cairo doesn't support logic operators. (like ||)

So you need to add:

if (x == y) {
    return (bit=1);
}

Unfortunately seems like Cairo doesn't support logical operators (|| , &&, !) so something like this is not possible:

if (x == -y || x == y) {
    return (bit=1);
}

So the solution is to use multiple if-s (or one if and use abs_value as other users pointed out)

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == -y) {
        return (bit=1);
    }
    if (x == y) {
        return (bit=1);
    } else { // else can be omitted, but if it's not, it must be in the same line as {
        return (bit=0); 
    }
}

I wondered that such a basic function as abs should exist on cairo. Therefore, I went through the cairo-lang repository and found the function I wanted.

However, I had a problem with the implementation of the abs function. But thanks to the help from the cairo community I was able to solve it. Here is the error

My answer for the day 3

%builtins range_check

from starkware.cairo.common.math import abs_value

func abs_eq{range_check_ptr}(x: felt, y: felt) -> (bit: felt) {
    if (abs_value(x) == abs_value(y)) {
        return (bit=1);
    } else {
        return (bit=0);
    }
}

func main{range_check_ptr}() {
    let (bit) = abs_eq(2, -2);
    assert bit = 1;

    let (bit) = abs_eq(2, 3);
    assert bit = 0;

    let (bit) = abs_eq(2, 2);
    assert bit = 1;

    return ();
}

Repository challenge

Problem

// The function `abs_eq` should return 1 if its inputs
// are equal or differ only in sign and 0 otherwise.
// Its current implementation is incorrect.
// Returns 1 if |x| = |y| (that is, x = y or x = -y),
// 0 otherwise.
func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == -y) { 
        return (bit=1);
    } else {
        return (bit=0);
    }
}

func main() {
    let (bit) = abs_eq(2, -2);
    assert bit = 1;

    let (bit) = abs_eq(2, 3);
    assert bit = 0;

    let (bit) = abs_eq(2, 2);
    assert bit = 1;

    return ();
}

Solution

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == y) { //2===2 or -2 ==. -2 
        return (bit=1);
    }
    if (x == -y) { // 2 == -(-2) or -2 == -2 
        return (bit=1);
    } 
return (bit=0);
}
func main() {
    let (bit) = abs_eq(2, -2);
    assert bit = 1;

     let (bit) = abs_eq(2, 2);
    assert bit = 1;
    
     let (bit) = abs_eq(-2, 2);
    assert bit = 1;
    
     let (bit) = abs_eq(-2, -2);
    assert bit = 1;

    let (bit) = abs_eq(2, 3);
    assert bit = 0;
    
    return ();
}

Explanation

abs_eq function accepts two arguments x and y, if x and y equal in magnitude or differ only in sign it will return 1 otherwise 0.

First if statement checks the both magnitude and signs should be equal to return true that is (2,2), (-2,-2)

Second if statement checks the both magnitude should be same but return true only if signs are different that is (-2,2) , (2,-2)

main function uses assert to verifies the computation of all the test cases possible for the conditions.

// The function abs_eq should return 1 if its inputs // are equal or differ only in sign and 0 otherwise. // Its current implementation is incorrect. // // 1. Click on "Run" to see the where it fails. // 2. Fix the body of abs_eq, so that the // program terminates successfully.

// Returns 1 if |x| = |y| (that is, x = y or x = -y), // 0 otherwise. func abs_eq(x: felt, y: felt) -> (bit: felt) { if( x == y){ return (bit=1); } if (x == -y) { return (bit=1); } else { return (bit=0); } }

func main() { let (bit) = abs_eq(2, -2); assert bit = 1;

let (bit) = abs_eq(2, 3);
assert bit = 0;

let (bit) = abs_eq(2, 2);
assert bit = 1;

return ();

}

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == -y) {
        return (bit=1);
    } 
    
    if (x == y) {
        return (bit=1);
    }
    
    return (bit=0);
}

func main() {
    let (bit) = abs_eq(2, -2);
    assert bit = 1;

    let (bit) = abs_eq(2, 3);
    assert bit = 0;

    let (bit) = abs_eq(2, 2);
    assert bit = 1;

    return ();
}

func abs_eq(x: felt, y: felt) -> (bit: felt) { if (x == y) { return(bit = 1); } if (x == -y) { return(bit = 1);
} return (bit = 0); }

func main() { let (bit) = abs_eq(2, -2); assert bit = 1;

let (bit) = abs_eq(2, 3);
assert bit = 0;

let (bit) = abs_eq(2, 2);
assert bit = 1;

return ();

}

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    //return 1 if x = -y
    if (x == -y) {
        return (bit=1); 
    }

    //return 1 if x = y
    if (x == y) {
        return (bit=1);
    }  

    //otherwise  
    return (bit=0);
}

func abs_eq(x: felt, y: felt) -> (bit: felt) {
    if (x == y) {
        return (bit=1);
    }
    if (x == -y) {
        return (bit=1);
    } 
    return (bit=0);
}