Add Maximum Array Rotation in M4 (#4948)

Author: rzuckerm

archive/m/m4/maximum-array-rotation.m4

@@ -0,0 +1,72 @@
+divert(-1)
+define(`show_usage',
+`Usage: please provide a list of integers (e.g. "8, 3, 1, 2")
+m4exit(`1')')
+
+dnl Reference: https://www.gnu.org/software/m4/manual/m4.html#index-array
+dnl array_get(var_name, idx)
+define(`array_get', `defn(format(``%s[%s]'', `$1', `$2'))')
+
+dnl array_set(var_name, idx, value)
+define(`array_set', `define(format(``%s[%s]'', `$1', `$2'), `$3')')
+
+dnl is_valid(n)
+define(`is_valid', `eval(regexp(`$1', `^\s*-?[0-9]+\s*$') >= 0)')
+
+dnl parse_int_list(varname, args):
+dnl   varname[length] = 0
+dnl   foreach arg in args:
+dnl     if not is_valid(arg):
+dnl       Return 0
+dnl     varname[varname[length]] = arg
+dnl     varname[length] = varname[length] + 1
+dnl   Return 1
+define(`parse_int_list',
+`array_set(`$1', `length', 0)dnl
+_parse_int_list(`$1', $2)'dnl
+)
+define(`_parse_int_list',
+`ifelse(is_valid(`$2'), 0, `0',
+`array_set(`$1', array_get(`$1', `length'), `$2')dnl
+array_set(`$1', `length', incr(array_get(`$1', `length')))dnl
+ifelse(eval($# > 2), 1, `_parse_int_list(`$1', shift(shift($@)))', `1')'dnl
+)'dnl
+)
+
+dnl M4 does not have infinity so choose smallest integer value as minus infinity
+define(`MINUS_INF', -2147483648)
+
+dnl max(a, b)
+define(`max', `ifelse(eval($1 > $2), 1, `$1', `$2')')
+
+dnl maximum_array_rotation(varname):
+dnl   wmax = -infinity
+dnl   for n = 0 to varname[length] - 1:
+dnl     w = array_rotation_sum(varname, n, varname[length])
+dnl     wmax = max(wmax, w)
+dnl   return wmax
+define(`maximum_array_rotation', `_maxmimum_array_rotation(`$1', 0, MINUS_INF)')
+define(`_maxmimum_array_rotation',
+`ifelse(
+eval($2 >= array_get(`$1', `length')), 1, `$3',
+`_maxmimum_array_rotation(`$1', incr($2),
+    max($3, array_rotation_sum(`$1', $2, array_get(`$1', `length'))))'`'dnl
+)'dnl
+)
+
+dnl array_rotation_sum(varname, offset, mod):
+dnl   w = 0
+dnl   for n = 0 to mod - 1:
+dnl     w = w + n * varname[(n + offset) % mod]
+dnl   return w
+define(`array_rotation_sum', `_array_rotation_sum(`$1', $2, $3, 0, 0)')
+define(`_array_rotation_sum',
+`ifelse(
+eval($4 >= $3), 1, `$5',
+`_array_rotation_sum(`$1', $2, $3, incr($4),
+    eval($5 + $4 * array_get(`$1', eval(($4 + $2) % $3))))'`'dnl
+)'dnl
+)
+divert(0)dnl
+ifelse(eval(ARGC < 1 || len(ARGV1) < 1 || !parse_int_list(`arr', ARGV1)), 1, `show_usage()')dnl
+maximum_array_rotation(`arr')