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src/ntzdebruijn.leo
Build Guide
To compile and run this Leo program, run:
leo run
The Algorithm
This algorithm is detailed in "Hacker's Delight, 2nd edition" by Henry S. Warren, section 5-4, figure 5-26. Here is a summary.
After handling the all-zeros case,
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).
A constant was discovered with the property that when it was multiplied
by 1, 2, 4, ... 2**31, the 32 values all had different high 5-bit patterns.
This constant is 0x04D7651F.
In the algorithm, the 5 high bits are used as an index into the table
{0, 1, 2, 24, 3, 19, ...}. The table's values were chosen so that
they gave the correct number of trailing zeros for the inputs.
For example, if the isolated bit has 4 trailing zeros, the number is 2**4.
The high 5 bits of 2**4 * 0x04D7651F are 01001 which is 9. The table
value at index 9 is therefore 4.
This algorithm was proposed by Danny Dubé in the comp.compression.research newsgroup: https://groups.google.com/g/comp.compression.research/c/x0NaZ3CJ6O4/m/PfGuchA7o60J
A description of de Bruijn cycles and their use for bit indexing can be seen here: http://supertech.csail.mit.edu/papers/debruijn.pdf