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+# bit32.countlz/countrz
+
+## Summary
+
+Add bit32.countlz (count left zeroes) and bit32.countrz (count right zeroes) to accelerate bit scanning
+
+## Motivation
+
+All CPUs have instructions to determine the position of first/last set bit in an integer. These instructions have a variety of uses, the popular ones being:
+
+- Fast implementation of integer logarithm (essentially allowing to compute `floor(log2(value))` quickly)
+- Scanning set bits in an integer, which allows efficient traversal of compact representation of bitmaps
+- Allocating bits out of a bitmap quickly
+
+Today it's possible to approximate `countlz` using `floor` and `log` but this approximation is relatively slow; approximating `countrz` is difficult without iterating through each bit.
+
+## Design
+
+`bit32` library will gain two new functions, `countlz` and `countrz`:
+
+```
+function bit32.countlz(n: number): number
+function bit32.countrz(n: number): number
+```
+
+`countlz` takes an integer number (converting the input number to a 32-bit unsigned integer as all other `bit32` functions do), and returns the number of consecutive left-most zero bits - that is, the number of most significant zero bits in a 32-bit number until the first 1. The result is in `[0, 32]` range.
+
+For example, when the input number is `0`, it's `32`. When the input number is `2^k`, the result is `31-k`.
+
+`countrz` takes an integer number (converting the input number to a 32-bit unsigned integer as all other `bit32` functions do), and returns the number of consecutive right-most zero bits - that is,
+the number of least significant zero bits in a 32-bit number until the first 1. The result is in `[0, 32]` range.
+
+For example, when the input number is `0`, it's `32`. When the input number is `2^k`, the result is `k`.
+
+> Non-normative: a proof of concept implementation shows that a polyfill for `countlz` takes ~34 ns per loop iteration when computing `countlz` for an increasing number sequence, whereas
+> a builtin implementation takes ~4 ns.
+
+## Drawbacks
+
+None known.
+
+## Alternatives
+
+These functions can be alternatively specified as "find the position of the most/least significant bit set" (e.g. "ffs"/"fls" for "find first set"/"find last set"). This formulation
+can be more immediately useful since the bit position is usually more important than the number of bits. However, the bit position is undefined when the input number is zero,
+returning a sentinel such as -1 seems non-idiomatic, and returning `nil` seems awkward for calling code. Counting functions don't have this problem.
+
+An early version of this proposal suggested `clz`/`ctz` (leading/trailing) as names; however, using a full verb is more consistent with other operations like shift/rotate, and left/right may be easier to understand intuitively compared to leading/trailing. left/right are used by C++20.
+
+Of the two functions, `countlz` is vastly more useful than `countrz`; we could implement just `countlz`, but having both is nice for symmetry.