C++: how can I test if a number is power of ten?

Question

I want to test if a number double x is an integer power of 10. I could perhaps use cmath\'s log10 and then test if x == (int) x?

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Answer 1

A variant of this one:

double log10_value= log10(value);
double integer_value;
double fractional_value= modf(log10_value, &integer_value);

return fractional_value==0.0;

Note that the comparison to 0.0 is exact rather than within a particular epsilon since you want to ensure that log10_value is an integer.

EDIT: Since this sparked a bit of controversy due to log10 possibly being imprecise and the generic understanding that you shouldn't compare doubles without an epsilon, here's a more precise way of determining if a double is a power of 10 using only properties of powers of 10 and IEEE 754 doubles.

First, a clarification: a double can represent up to 1E22, as 1e22 has only 52 significant bits. Luckily, 5^22 also only has 52 significant bits, so we can determine if a double is (2*5)^n for n= [0, 22]:

bool is_pow10(double value)
{
    int exponent;
    double mantissa= frexp(value, &exponent);

    int exponent_adjustment= exponent/10;

    int possible_10_exponent= (exponent - exponent_adjustment)/3;

    if (possible_10_exponent>=0 && 
        possible_10_exponent<=22)
    {
        mantissa*= pow(2.0, exponent - possible_10_exponent);

        return mantissa==pow(5.0, possible_10_exponent);
    }
    else
    {
        return false;
    }
}

Since 2^10==1024, that adds an extra bit of significance that we have to remove from the possible power of 5.