Question

I saw the function below that should return sign of double d. But I couldn’t understand how it works?

int sgn(double d){ 
    return d<-eps?-1:d>eps;
}

Answer 1

return d<-eps?-1:d>eps;

That means:

• If d is less than -eps, the result is “negative”
• If d is more than eps, the result is “positive” (d>eps returns 1)
• Otherwise we return 0 (meaning the number is “zero”)

eps would normally be a small number, so we consider numbers between, say -1e-5 and 1e-5 as “practically zero”. This approach is used to water down some deficiencies of the computer’s floating-point numbers, like that sin(pi)!=0. However, it comes at the cost of introducing an arbitrary number eps in the calculation, and losing the property that eg. if a and b are positive numbers, a*b is positive provided underflow doesn’t occur.