Find First Set - Applications

Applications

The count leading zeros (clz) operation can be used to efficiently implement normalization, which encodes an integer as m × 2e, where m has its most significant bit in a known position (such as the highest position). This can in turn be used to implement Newton-Raphson division, perform integer to floating point conversion in software, and other applications.

Count leading zeros (clz) can be used to compute the 32-bit predicate "x=y" (zero if true, one if false) via the identity clz(x-y) >> 5, where ">>" is unsigned right shift. It can be used to perform more sophisticated bit operations like finding the first string of n 1 bits. The expression 16 − clz(x − 1)/2 is an effective initial guess for computing the square root of a 32-bit integer using Newton's method. CLZ can efficiently implement null suppression, a fast data compression technique that encodes an integer as the number of leading zero bytes together with the nonzero bytes. It can also efficiently generate exponentially distributed integers by taking the clz of uniformly random integers.

The log base 2 can be used to anticipate whether a multiplication will overflow, since .

Count leading zeros and count trailing zeros can be used together to implement Gosper's loop-detection algorithm, which can find the period of a function of finite range using limited resources.

A bottleneck in the binary GCD algorithm is a loop removing trailing zeros, which can be replaced by a count trailing zeros (ctz) followed by a shift. A similar loop appears in computations of the hailstone sequence.

A bit array can be used to implement a priority queue. In this context, find first set (ffs) is useful in implementing the "pop" or "pull highest priority element" operation efficiently. The Linux kernel real-time scheduler internally uses sched_find_first_bit for this purpose.

The count trailing zeros operation gives a simple optimal solution to the Tower of Hanoi problem: the disks are numbered from zero, and at move k, disk number ctz(k) is moved the minimum possible distance to the right (circling back around to the left as needed). It can also generate a Gray code by taking an arbitrary word and flipping bit ctz(k) at step k.