logN

The logarithm function performs a mathematical operation that is opposite of an exponential function (raising a base constant to a power). The logarithm of a number x in base base is any number n such that x = baseⁿ. This function takes and returns fixed-point numbers.

This was adapted from the Python code on Literate Programs.

#define MATH_E 178145
function int logN (int x, int base)
{
    if (!base) base = MATH_E;
    int integer = 0;

    if (x < 1.0 && base < 1.0) return 0;
      
    while (x < 1)
    {
        integer -= 1;
        x = FixedMul (x, base);
    }
    while (x >= base)
    {
        integer += 1;
        x = FixedDiv (x, base);
    }
    int partial = 0.5;
    x = FixedMul (x, x);
    int decimal = 0;
    while (partial > 1) // Actually 0.0000152587890625
    {
        if (x >= base)
        {
            decimal += partial;
            x = FixedDiv (x, base);
        }
        partial = FixedMul (partial, 0.5);
        x = FixedMul (x, x);
    }
    return ((integer << 16) + decimal);
}