Money exchange solver in Go

package main

import (
    "fmt"
    "math/big"
)

var big_zero = big.NewInt(0)
var big_one = big.NewInt(1)

func count_exchanges(sum int, coins []int) *big.Int {
    cache := make([]*big.Int, (sum + 1) * (len(coins) + 1))

    var internal_count func (sum int, coin_index int) *big.Int

    internal_count = func (sum int, coin_index int) *big.Int {
        switch {
            case sum < 0: return big_zero
            case sum == 0: return big_one
            case coin_index < 0 || coin_index >= len(coins): return big_zero
        }

        cached_index := sum + (sum + 1) * coin_index
        cached_value := cache[cached_index]

        if cached_value != nil {
            return cached_value
        }

        for coin_index < len(coins) && sum < coins[coin_index] {
            coin_index++
        }

        result := big.NewInt(0).Add(
            internal_count(sum - coins[coin_index], coin_index),
            internal_count(sum, coin_index + 1))

        cache[cached_index] = result
        return result
    }

    return internal_count(sum, 0)
}

func main() {
    fmt.Printf("%d\n", count_exchanges(1000000, []int { 50, 25, 10, 5, 1 }))
}