DP recurrence for popcount that avoids host bitwise operations:
result[i] = result[i / 2] + (i mod 2)
Drops the low bit (i / 2 stands in for i lsr 1) and adds it back
if it was 1 (i mod 2 stands in for i land 1).
sum over 0..100 of popcount(i) = 319
Tests pure-arithmetic popcount, accumulating ref + DP array,
classic look-back to half-index pattern.
197 baseline programs total.
