Add Zeckendorf in m4 (#5345)

Author: rzuckerm

archive/m/m4/zeckendorf.m4

@@ -0,0 +1,88 @@
+divert(-1)
+define(`show_usage',
+`Usage: please input a non-negative integer
+m4exit(`1')')
+
+dnl is_valid(n)
+define(`is_valid', `eval(regexp(`$1', `^\s*-?[0-9]+\s*$') >= 0)')
+
+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 show_int_list(varname):
+dnl   for i = 0 to varname["length"] - 1:
+dnl      if i > 0:
+dnl        Output ", "
+dnl      Output varname[i]
+define(`show_int_list', `_show_int_list(`$1', 0)')
+define(`_show_int_list',
+`ifelse(eval(`$2' < array_get(`$1', `length')), 1,
+`ifelse(eval(`$2' > 0), 1, `, ')dnl
+array_get(`$1', `$2')`'dnl
+_show_int_list(`$1', incr($2))'`'dnl
+)'dnl
+)
+
+dnl fibonacci(value, result_varname):
+dnl   a = 1
+dnl   b = 2
+dnl   result_varname["length"] = 0
+dnl   while a <= value:
+dnl     result_varname[result_varname["length"]] = a
+dnl     result_varname["length"] = result_varname["length"] + 1
+dnl     a, b = b, a + b
+define(`fibonacci',
+`array_set(`$2', `length', 0)dnl
+_fibonacci(`$1', `$2', 1, 2)'dnl
+)
+
+dnl value=$1, result_varname=$2, a=$3, b=$4
+define(`_fibonacci',
+`ifelse(eval(`$3' <= `$1'), 1,
+`array_set(`$2', array_get(`$2', `length'), `$3')dnl
+array_set(`$2', `length', eval(incr(array_get(`$2', `length'))))dnl
+_fibonacci(`$1', `$2', `$4', eval(`$3 + $4'))'dnl
+)'dnl
+)
+
+dnl zeckendorf(value, fibs_varname, zecks_varname)
+dnl   fibonacci(value, fibs_varname)
+dnl   zecks_varname["length"] = 0
+dnl   n = fibs_varname["length"] - 1
+dnl   while n >= 0 and value > 0:
+dnl     if fibs_varname[n] >= value:
+dnl       zecks_varname[zecks_varname["length"]] = fibs_varname[n]
+dnl       zecks_varname["length"] = zecks_varname["length"] + 1
+dnl       value = value - fibs_varname[n]
+dnl       n = n - 2
+dnl     else:
+dnl       n = n - 1
+define(`zeckendorf',
+`fibonacci(`$1', `$2')dnl
+array_set(`$3', `length', 0)dnl
+_zeckendorf(`$1', `$2', `$3', decr(array_get(`$2', `length')))dnl
+'dnl
+)
+
+dnl value=$1, fibs_varname=$2, zecks_varname=$3, n=$4
+define(`_zeckendorf',
+`ifelse(eval(`$4' >= 0 && `$1' > 0), 1,
+`ifelse(eval(array_get(`$2', `$4') <= `$1'), 1,
+`array_set(`$3', array_get(`$3', `length'), array_get(`$2', `$4'))dnl
+array_set(`$3', `length', incr(array_get(`$3', `length')))dnl
+_zeckendorf(eval(`$1' - array_get(`$2', `$4')), `$2', `$3', eval(`$4' - 2))dnl
+',dnl
+`_zeckendorf(`$1', `$2', `$3', decr(`$4'))'dnl
+)'dnl
+)'dnl
+)
+
+divert(0)dnl
+ifelse(eval(ARGC < 1 || len(ARGV1) < 1 || !is_valid(ARGV1)), 1, `show_usage()')dnl
+ifelse(eval(ARGV1 < 0), 1, `show_usage()')dnl
+zeckendorf(ARGV1, `fibs', `zecks')dnl
+show_int_list(`zecks')