A BQN function performing associative reductions on paths of an array

associative_reduction.bqn

# s0‿o1 𝔽_associativeReduce 𝕩: 𝔽´¨ on paths in 𝕩 of s steps with stride (=𝕩)↑o1
#  
#  example: 
#      m    ≡   4‿(¯1‿1) +_associativeReduce     x
#  +-------+                                 +-------------+
#  | . . . |                                 | . . . . . . |
#  | y . . |                                 | . . . d . . |
#  +-------+                                 | . . c . . . |
#                                            | . b . . . . |
#   y ≡ +´a‿b‿c‿d                            | a . . . . . |
#                                            +-------------+
# 
# shortened forms:
# s0‿o0 𝔽_associativeReduce 𝕩    ←→     s0‿(⥊o0) 𝔽_associativeReduce 𝕩
# s0    𝔽_associativeReduce 𝕩    ←→     s0‿1     𝔽_associativeReduce 𝕩

_associativeReduce {
	s‿o←2↑𝕨∾1
	o<↩
	i←2⋆↕1+⌊2⋆⁼s # powers of 2: step sizes
	m←2|⌊s÷i     # base 2 representation of s
	l←»+`m/i
	# <combine>  <--trim to fit-->   <select>  <--length-i windows-->
	  𝔽´        (-o×s-l+m/i)↓¨(o×l)↓¨  m/      (-⊸↓𝔽↓)˜`(<𝕩)∾oׯ1↓i
}