Find integer log base 2 of a 32-bit IEEE float
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const float v; // find int(log2(v)), where v > 0.0 && finite(v) && isnormal(v)
int c; // 32-bit int c gets the result;
c = *(const int *) &v; // OR, for portability: memcpy(&c, &v, sizeof c);
c = (c >> 23) - 127;
The above is fast, but IEEE 754-compliant architectures utilize subnormal (also called denormal) floating point numbers. These have the exponent bits set to zero (signifying pow(2,-127)), and the mantissa is not normalized, so it contains leading zeros and thus the log2 must be computed from the mantissa. To accomodate for subnormal numbers, use the following:
const float v; // find int(log2(v)), where v > 0.0 && finite(v)
int c; // 32-bit int c gets the result;
int x = *(const int *) &v; // OR, for portability: memcpy(&x, &v, sizeof x);
c = x >> 23;
if (c)
{
c -= 127;
}
else
{ // subnormal, so recompute using mantissa: c = intlog2(x) - 149;
unsigned int t; // temporary
// Note that LogTable256 was defined earlier
if (t = x >> 16)
{
c = LogTable256[t] - 133;
}
else
{
c = (t = x >> 8) ? LogTable256[t] - 141 : LogTable256[x] - 149;
}
}