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src/ntzreisers.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 5-27.
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 smallest constant was found that has the property that when it was used to divide the 33 arguments 0, 1, 2, ..., 2**31, the remainder is different for each argument. This constant is 37.
In the algorithm, the remainder is used as an index into a table of size 37, with 4 entries unused. The table's values were chosen so that they give the correct number of trailing zeros for the inputs.
This algorithm was proposed by John Reiser in the comp.arch.arithmetic newsgroup on December 11, 1998: https://groups.google.com/g/comp.arch.arithmetic/c/yBt-QHRVEGE/m/QcQ75P6tmJ4J