Bits of integer

[mfleming]

(12-14-2022 02:35 PM)Albert Chan Wrote:  Thanks for APL code. I tried this in https://tryapl.org/. (my first APL session!)

It does not work if number more than 53 bits (I think numbers is binary64)
First example, 2^54-1 just round back to 2^54 (half-way to even).

I couldn't find specifics about integer representation in the language reference manual so I suppose it's platform-dependent. What's interesting is that the function is perfectly happy with floating point numbers.

Dyalog Ltd maintains the tryapl web site in addition to https://aplcart.info/ (look up problems, find APL solutions) and https://aplwiki.com/wiki/Main_Page (all about APL). Here's another version of numbits that shows tail recursion of dfns

Code:


numbits←{⍺←1 ⋄ ⍵≤1:⍺ ⋄ (⍺+1)∇⌊⍵÷2}

The ≤ comparison is there to catch zero or negative values. Computation may be a little cheaper by replacing division with multiplication by 0.5.

Code:


numbits←{⍺←1 ⋄ ⍵≤1:⍺ ⋄ (⍺+1)∇⌊0.5×⍵}

Sadly, decades of procedural programming has left me barely able to grasp APL, but I keep trying (Engineer, not Mathematician)