Example: Log2 of Floating-Point is the Exponent

Example: Log2 of Floating-Point is the Exponent

The log2 function for float types is a non-linear function that is quite expensive to compute. We already computed log2 of an integer with low-level bit fiddling methods based on a count-leading-zeros algorithm in the previous chapter. There's also a different bitwise trick for log2 of floating-point numbers. This method computes the truncated integer version of the log2 algorithm (e.g. for use in logarithmic power-of-two quantization). There's a very easy way:

    The base-2 logarithm is the exponent!

It's sitting right there, already calculated, hidden in plain sight amongst the 32 bits of your friendly float variables. Here's some C++ code to extract it:

    int ilog2_exponent(float f)  // Log2 for 32-bit float
    {
        unsigned int u = *(unsigned int*)&f;
        int iexp = ((u >> 23) & 255);  // 8-bit exponent
        iexp -= 127;  // Remove the "offset"
        return iexp;
    }

Alternatively, for greater portability and probably extra speed, too, there are some standardized builtin C++ functions available across various platforms (including Linux and Microsoft) that can extract the exponent: frexp, ldexp, ilogb, and scalbn, are some that come to mind.

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