| .. | ||
| build | ||
| inputs | ||
| src | ||
| .env | ||
| .gitignore | ||
| leo.lock | ||
| program.json | ||
| README.md | ||
src/ntzgaudet.leo
Build Guide
To compile and run this Leo program, run:
leo run <function-name> <inputs>
The Algorithm
This algorithm is described in "Hacker's Delight, 2nd edition" by Henry S. Warren, section 5-4, section 5-24, as interesting due to being branch-free, not using table lookups, and having parallelism. It is attributed to Dean Gaudet in private communication to Henry S. Warren.
First we isolate the rightmost 1 bit in the 32-bit input by
using the C idiom x & (-x). In Leo, the -x is
written as 0u32.sub_wrapped(x). The result is stored in y.
Then we compute six intermediate variables that count different numbers
of trailing zeros. The first variable, bz, just counts 1 if y is completely zero.
To get the other five variables, we do binary search in parallel, using 5 masks,
each looking at a different symmetric pattern of 16 bits. For example, b4 counts 16 if
the low 16 bits are zero and counts zero otherwise. Then b3 uses a mask y & 0x00FF00FF to count eight 0-bits if the result is zero and zero 0-bits
otherwise. The masks for b2, b1, and b0 can count four, two, and
one 0-bits similarly.
The variables bz, b4, .., b0 are all independent, and their values are added up
for the result.