The choice of this "epsilon" is not a trivial task. Like (int)(Math.log(x)/Math.log(2)+1e-10) should never fail. The usual trick here is using "epsilon" when rounding. I didn't find a value for x where (int)(Math.log(x)/Math.log(2)) fails (just because there are only 32 "dangerous" values), but it does not mean that it will work the same way on any PC.
#Log calculator base 2 Pc#
For example, Math.ceil(Math.log(1<<29) / Math.log(2)) is 30 on my PC where mathematically it should be exactly 29. You can never know for sure what will (int)(Math.log(65536)/Math.log(2)) evaluate to. I usually try to avoid FP calculations whenever possible.įloating-point operations are not exact. If you are thinking about using floating-point to help with integer arithmetics, you have to be careful. This is the test code: int sum = 0, x = 0 ĭo sum += log2nlz( x ) while( ++x != 0 ) What are the 3 types of logarithms The three types of logarithms are common logarithms (base 10), natural logarithms (base e), and logarithms with an arbitrary base. In the same way, since 102 equals 100, 2 equals log10 100.
For example, 23 8, therefore 3 is the base 2 logarithm of 8, or 3 log2 8. If bx n, then x is the logarithm of n to the base b, which is written as x logb n in mathematics. Here are the actual runtimes on my PC (Sandy Bridge i7): What is logarithm equation A logarithmic equation is an equation that involves the logarithm of an expression containing a varaible. The exponent or power to which a base must be increased to generate a particular number is called a logarithm. This implementation also returns the same results for all 2^32 possible input values as the the other two implementations I posted above. Return 31 - Integer.numberOfLeadingZeros( bits ) Unfortunatly the client JIT doesn't seem to have this optimization. So with a 1.7 or newer server VM, a implementation like the one in the question is actually slightly faster than the binlog above. One of those functions is Integer.numberOfLeadingZeros(). The Java 1.7 server JIT is able to replace a few static math functions with alternative implementations based on CPU intrinsics. Return (int) ( Math.log( bits & 0xffffffffL ) * log2div ) īoth functions return the same results for all possible input values. It is slightly faster than Integer.numberOfLeadingZeros() (20-30%) and almost 10 times faster (jdk 1.6 圆4) than a Math.log() based implementation like this one: private static final double log2div = 1.000000000001 / Math.log( 2 ) This is the function that I use for this calculation: public static int binlog( int bits ) // returns 0 for bits=0
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