It's possible to use a lookup table (sort of) in a register. With x86-64-v2 and later, the code is larger, but potentially faster due to the shorter dependency chain:

int div7 (int x) { return 9 - __builtin_popcountll (0x4081020408102040ULL >> x); }

https://godbolt.org/z/Wj6P6jYGM

I think any monotonic function on 0 .. 63 can be written this way, so should be possible to fold in the outer 63 - nlz expression, too.

I don't use lookup tables that much when optimizing these days, because most math instructions cost far fewer cycles than a cache miss. And even if your lookup table is in L3, it still costs ~40 cycles to retrieve each line.

Maybe easier, if limited to the specific case of an input in the range [0..63] and a divisor of 7, but not necessarily faster. Keep in mind the latency of a memory read is typically around 4 cycles, and at least some architectures have a tighter limit on the number of concurrent memory transactions than the number of concurrent integer math instructions, and keep in mind the article is generalizing beyond the initial problem involving the numbers 63 and 7- if you have more than a couple different divisors, and if you want to allow the input to go as large as possible, then a lookup table quickly becomes wasteful and impractical.

The divisor is from 0 to 63. The dividend is a variable bit length integer, i.e. a bigint.