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path: root/ops.go
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package main

import (
	"container/list"
	"log"
)

var (
	alphabet  *list.List
	zero, one *list.Element
)

func init() {
	alphabet = list.New()
	for i := 0; i <= maxValue; i++ {
		alphabet.PushBack(i)
	}
	zero = alphabet.Front()
	one = zero.Next()
}

// next returns next char in alphabet
func next(n *list.Element) *list.Element {
	if nxt := n.Next(); nxt != nil {
		return nxt
	}
	log.Fatal("out of range", n.Value)
	return nil
}

// prev returns previous char in alphabet
func prev(n *list.Element) *list.Element {
	if prv := n.Prev(); prv != nil {
		return prv
	}
	return zero
}

// add defines addition
func add(m, n *list.Element) *list.Element {
	if m == zero {
		return n
	}
	return next(add(prev(m), n))
}

// times defines mutiplication
func times(m, n *list.Element) *list.Element {
	if m == zero {
		return zero
	}
	return add(times(prev(m), n), n)
}

// pot defines power function
func pot(m, n *list.Element) *list.Element {
	if n == zero {
		return one
	}
	return times(pot(m, prev(n)), m)
}

// sub defines substraction
func sub(m, n *list.Element) *list.Element {
	if n == zero {
		return m
	}
	return prev(sub(m, prev(n)))
}

// scan lookups element representation
func scan(n int) *list.Element {
	if n > alphabet.Len() {
		log.Fatal("out of range")
		return nil
	}
	e := alphabet.Front()
	for i := 0; i < n; i++ {
		e = e.Next()
	}
	return e
}