HyperLogLog unique viewers.

The Week 8 capstone counts unique viewers per title, per day, and then per month. An exact set of viewer ids per title per day is gigabytes, and you can't add daily uniques: a viewer who watched on 5 days would count 5 times. The capstone's rollup stores a viewers_hll sketch instead, "mergeable across days" (Day 5, section 2.2: approximate algorithms).

HyperLogLog (Flajolet et al., 2007) keeps m = 2^p small registers:

1. Hash the item to 64 bits (hash64 is given).
2. The first p bits pick a register: idx = h >> (64 - p).
3. In the remaining 64 - p bits w, find the position of the leftmost 1-bit, counting from 1: rho = (64 - p) - w.bit_length() + 1. (If w is 0, rho = 64 - p + 1.)
4. The register keeps the largest rho it has seen.

A run of r leading zeros happens about once in 2^r distinct items, so the registers estimate the count:

E = alpha(m) * m * m / sum(2 ** -reg for reg in registers)
if E <= 2.5 * m and some registers are 0:      # small counts: linear counting is better
    E = m * ln(m / zero_registers)

alpha(m) is given. With p = 12 (4,096 registers, a few KB) the standard error is about 1.04 / sqrt(m) = 1.6%.

Implement HyperLogLog(p):

Rules the tests check:

• Adding the same item again changes nothing.
• A merged sketch is identical to one sketch fed both streams: that's what makes it safe to store per day and merge per month.
• Results are deterministic: hash64 is a fixed hash, not Python's per-process hash().

In JavaScript and TypeScript, hash64(item) returns the same 64-bit value as a BigInt (h >> 52n, h & mask), and the given bitLength(n) stands in for Python's int.bit_length(). registers is an array of numbers, count() uses Math.round, and every ValueError above is a RangeError.