82 lines
2.2 KiB
Go
82 lines
2.2 KiB
Go
/*
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Copyright © 2025 filifa
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This program is free software: you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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This program is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with this program. If not, see <http://www.gnu.org/licenses/>.
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*/
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package cmd
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import (
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"fmt"
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"math/big"
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"github.com/spf13/cobra"
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)
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// TODO: expand to work for different sigmas
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func divisorSummatory(n *big.Int) *big.Int {
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// employing Dirichlet's hyperbola method
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sqrt := new(big.Int).Sqrt(n)
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total := big.NewInt(0)
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for x := big.NewInt(1); x.Cmp(sqrt) <= 0; x.Add(x, big.NewInt(1)) {
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z := new(big.Int).Div(n, x)
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total.Add(total, z)
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}
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total.Mul(total, big.NewInt(2))
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sqrt.Exp(sqrt, big.NewInt(2), nil)
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total.Sub(total, sqrt)
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return total
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}
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func divisorSum(cmd *cobra.Command, args []string) {
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for _, arg := range args {
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n, ok := new(big.Int).SetString(arg, 10)
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if !ok {
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cmd.PrintErrln("invalid input " + arg)
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continue
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}
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d := divisorSummatory(n)
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fmt.Println(d)
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}
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}
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// divisorCmd represents the divisor command
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var divisorCmd = &cobra.Command{
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Use: "divisor N [N ...]",
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Short: "Compute the divisor summatory function",
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Long: `Compute the divisor summatory function.
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For each argument n, compute D(n) = d(1) + d(2) + d(3) + ... + d(n), where d(n) is the number of divisors of n.`,
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Args: cobra.MinimumNArgs(1),
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Run: divisorSum,
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}
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func init() {
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sumCmd.AddCommand(divisorCmd)
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// Here you will define your flags and configuration settings.
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// Cobra supports Persistent Flags which will work for this command
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// and all subcommands, e.g.:
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// divisorCmd.PersistentFlags().String("foo", "", "A help for foo")
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// Cobra supports local flags which will only run when this command
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// is called directly, e.g.:
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// divisorCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
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}
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