Editing Binary logarithm (section)

===Integer rounding===
The binary logarithm can be made into a function from integers and to integers by [[rounding]] it up or down.  These two forms of integer binary logarithm are related by this formula:

:<math> \lfloor \log_2(n) \rfloor = \lceil \log_2(n + 1) \rceil - 1, \text{ if }n \ge 1.</math><ref name="Warren_2002">{{citation |title=Hacker's Delight |title-link=Hacker's Delight |first=Henry S. |last=Warren Jr. |date=2002 |edition=1st |publisher=[[Addison Wesley]] |isbn=978-0-201-91465-8 |page=215}}</ref>
The definition can be extended by defining <math> \lfloor \log_2(0) \rfloor = -1</math>. Extended in this way, this function is related to the [[number of leading zeros]] of the 32-bit unsigned binary representation of {{mvar|x}}, {{math|nlz(''x'')}}.
:<math>\lfloor \log_2(n) \rfloor = 31 - \operatorname{nlz}(n).</math><ref name="Warren_2002" />

The integer binary logarithm can be interpreted as the zero-based index of the most significant {{math|1}} bit in the input. In this sense it is the complement of the [[find first set]] operation, which finds the index of the least significant {{math|1}} bit. Many hardware platforms include support for finding the number of leading zeros, or equivalent operations, which can be used to quickly find the binary logarithm. The <code>fls</code> and <code>flsl</code> functions in the [[Linux kernel]]<ref>[https://www.kernel.org/doc/htmldocs/kernel-api/API-fls.html fls], Linux kernel API, [[kernel.org]], retrieved 2010-10-17.</ref> and in some versions of the [[libc]] software library also compute the binary logarithm (rounded up to an integer, plus one).