Dice graph

main.go

package main

import (
	"flag"
	"fmt"
	"math/big"
	"strconv"

	"github.com/ALTree/bigfloat"
)

type set struct {
	n, k, s int64
}

func main() {
	flag.Parse()
	length := flag.NArg()
	if length < 1 {
		fmt.Println("missing number of dices")
		return
	}
	n, err := strconv.Atoi(flag.Arg(0))
	if err != nil {
		fmt.Println("argument is not a number")
		return
	}
	omega := bigfloat.Pow(big.NewFloat(6), big.NewFloat(float64(n)))
	plotValues(n, 6*n, func(s int64) float64 {
		r := würfelSummenSatz(s, int64(n))
		f := new(big.Float).SetInt(r)
		v, _ := f.Quo(f, omega).Float64()
		return v
	}, "plot-"+strconv.Itoa(n)+".png")
}

func würfelSummenSatz(s, n int64) *big.Int {
	return sum(0, n, func(k int64) *big.Int {
		return partialSum(s, n, k)
	})
}

func partialSum(s, n, k int64) *big.Int {
	nk := big.NewInt(0).Binomial(n, k)
	skn := big.NewInt(0).Binomial(s-6*k-1, s-6*k-n)
	result := nk.Mul(nk, skn)
	if k%2 == 1 {
		result.Neg(result)
	}
	return result
}

func sum(start, end int64, f func(int64) *big.Int) *big.Int {
	sum := big.NewInt(0)
	for i := start; i <= end; i++ {
		sum.Add(sum, f(i))
	}
	return sum
}

plot.go

package main

import (
	"bytes"
	"fmt"
	"io/ioutil"
	"strconv"

	"github.com/wcharczuk/go-chart"
)

func plotValues(start, end int, f func(int64) float64, fileName string) {

	values := make([]chart.Value, end-start+2)
	for i := start; i <= end; i++ {
		values[i-start] = chart.Value{
			Value: f(int64(i)),
			Label: strconv.Itoa(i),
		}
	}

	graph := chart.BarChart{
		Title:      "",
		TitleStyle: chart.StyleShow(),
		Background: chart.Style{
			Padding: chart.Box{
				Top: 40,
			},
		},
		Height:   512,
		BarWidth: 60,
		XAxis: chart.Style{
			Show: true,
		},
		YAxis: chart.YAxis{
			Style: chart.Style{
				Show: true,
			},
		},
		Bars: values,
	}

	buffer := bytes.NewBuffer([]byte{})
	err := graph.Render(chart.PNG, buffer)
	if err != nil {
		fmt.Println(err)
	}
	ioutil.WriteFile(fileName, buffer.Bytes(), 0644)
}