add convolve command

cmd/common.go

@@ -0,0 +1,32 @@
+/*
+Copyright © 2026 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package cmd
+
+import (
+	"bufio"
+	"os"
+)
+
+func splitLines(file *os.File) []string {
+	slice := make([]string, 0)
+	scanner := bufio.NewScanner(file)
+	for scanner.Scan() {
+		slice = append(slice, scanner.Text())
+	}
+
+	return slice
+}

cmd/convolve.go

@@ -0,0 +1,110 @@
+/*
+Copyright © 2026 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package cmd
+
+import (
+	"bufio"
+	"fmt"
+	"os"
+	"strconv"
+
+	"github.com/spf13/cobra"
+	"scm.dairydemon.net/filifa/mathtools/internal/lib"
+)
+
+var convolveA string
+var convolveB string
+
+func readSequenceFromFile(filepath string) ([]complex128, error) {
+	// initial length 1 so index math works
+	seq := make([]complex128, 1)
+	file, err := os.Open(filepath)
+	if err != nil {
+		return seq, err
+	}
+	defer file.Close()
+
+	lines := splitLines(file)
+	for _, line := range lines {
+		x, err := strconv.ParseComplex(line, 128)
+		if err != nil {
+			return seq, err
+		}
+
+		seq = append(seq, x)
+	}
+
+	return seq, nil
+}
+
+func convolve(cmd *cobra.Command, args []string) {
+	a, err := readSequenceFromFile(convolveA)
+	if err != nil {
+		cobra.CheckErr(err)
+	}
+
+	b, err := readSequenceFromFile(convolveB)
+	if err != nil {
+		cobra.CheckErr(err)
+	}
+
+	bufStdout := bufio.NewWriter(os.Stdout)
+	defer bufStdout.Flush()
+
+	for i, n := range lib.DirichletConvolve(a, b) {
+		if i == 0 {
+			continue
+		}
+
+		if imag(n) == 0 {
+			fmt.Fprintln(bufStdout, real(n))
+		} else {
+			fmt.Fprintln(bufStdout, n)
+		}
+	}
+}
+
+// convolveCmd represents the convolve command
+var convolveCmd = &cobra.Command{
+	Use:   "convolve",
+	Short: "Compute the Dirichlet convolution of two sequences",
+	Long: `Compute the Dirichlet convolution of two sequences.
+
+Each sequence is provided as a file, where line k of the file gives the kth term of the sequence.
+`,
+	Run: convolve,
+}
+
+func init() {
+	rootCmd.AddCommand(convolveCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// convolveCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// convolveCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	convolveCmd.Flags().StringVarP(&convolveA, "first", "a", "", "first sequence")
+	convolveCmd.MarkFlagRequired("first")
+
+	convolveCmd.Flags().StringVarP(&convolveB, "second", "b", "", "second sequence")
+	convolveCmd.MarkFlagRequired("second")
+}

cmd/quadraticResidues.go

@@ -0,0 +1,75 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package cmd
+
+import (
+	"bufio"
+	"fmt"
+	"os"
+
+	"github.com/spf13/cobra"
+	"scm.dairydemon.net/filifa/mathtools/internal/lib/sieve"
+)
+
+var quadraticResiduesN uint
+var quadraticResiduesCoprime bool
+
+func quadraticResidues(cmd *cobra.Command, args []string) {
+	bufStdout := bufio.NewWriter(os.Stdout)
+	defer bufStdout.Flush()
+
+	ch := sieve.QuadraticResidues(quadraticResiduesN, quadraticResiduesCoprime, 1000)
+	for i := 0; ; i++ {
+		v, ok := <-ch
+		if !ok {
+			break
+		}
+
+		if i == 0 {
+			continue
+		}
+
+		fmt.Fprintln(bufStdout, v)
+	}
+}
+
+// quadraticResiduesCmd represents the quadraticResidues command
+var quadraticResiduesCmd = &cobra.Command{
+	Use:   "quadratic-residues",
+	Short: "Compute the number of quadratic residues for all moduli less than n",
+	Long:  `Compute the number of quadratic residues for all moduli less than n.`,
+	Run:   quadraticResidues,
+}
+
+func init() {
+	sieveCmd.AddCommand(quadraticResiduesCmd)
+
+	// Here you will define your flags and configuration settings.
+
+	// Cobra supports Persistent Flags which will work for this command
+	// and all subcommands, e.g.:
+	// quadraticResiduesCmd.PersistentFlags().String("foo", "", "A help for foo")
+
+	// Cobra supports local flags which will only run when this command
+	// is called directly, e.g.:
+	// quadraticResiduesCmd.Flags().BoolP("toggle", "t", false, "Help message for toggle")
+
+	quadraticResiduesCmd.Flags().UintVarP(&quadraticResiduesN, "limit", "n", 0, "upper limit")
+	quadraticResiduesCmd.MarkFlagRequired("limit")
+
+	quadraticResiduesCmd.Flags().BoolVarP(&quadraticResiduesCoprime, "coprime-only", "c", false, "only count residues coprime to the modulus")
+}

cmd/shoelace.go

@@ -17,7 +17,6 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 package cmd
 
 import (
-	"bufio"
 	"fmt"
 	"os"
 	"strconv"
@@ -29,16 +28,6 @@ import (
 
 var shoelaceFile string
 
-func splitLines(file *os.File) []string {
-	slice := make([]string, 0)
-	scanner := bufio.NewScanner(file)
-	for scanner.Scan() {
-		slice = append(slice, scanner.Text())
-	}
-
-	return slice
-}
-
 func readFromFile(filepath string) ([]lib.Point, error) {
 	points := make([]lib.Point, 0)
 	file, err := os.Open(filepath)

internal/lib/convolve.go

@@ -0,0 +1,32 @@
+/*
+Copyright © 2026 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package lib
+
+func DirichletConvolve(a, b []complex128) []complex128 {
+	c := make([]complex128, min(len(a), len(b)))
+	for i, x := range a {
+		for j, y := range b {
+			if i*j >= len(c) {
+				break
+			}
+
+			c[i*j] += x * y
+		}
+	}
+
+	return c
+}

internal/lib/sieve/qresidue.go

@@ -0,0 +1,131 @@
+/*
+Copyright © 2025 filifa
+
+This program is free software: you can redistribute it and/or modify
+it under the terms of the GNU General Public License as published by
+the Free Software Foundation, either version 3 of the License, or
+(at your option) any later version.
+
+This program is distributed in the hope that it will be useful,
+but WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+GNU General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program. If not, see <http://www.gnu.org/licenses/>.
+*/
+package sieve
+
+// NOTE: these formulas come from https://web.archive.org/web/20151224013638/http://www.maa.org/sites/default/files/Walter_D22068._Stangl.pdf
+
+func qrPowersOfTwoCoprime(sieve []uint, n uint) {
+	for q := uint(8); 2*q < n; q *= 2 {
+		// q(2^n) = 2^(n-3) for n >= 3
+		sieve[2*q] = 2 * sieve[q]
+	}
+}
+
+func qrPowersOfOddPrimesCoprime(sieve []uint, p uint, n uint) {
+	for q := p; p*q < n; q *= p {
+		// q(p^n) = (p^n - p^(n-1)) / 2
+		sieve[p*q] = (p*q - q) / 2
+	}
+}
+
+func qrPowersOfTwo(sieve []uint, n uint) {
+	k := 1
+	for q := uint(1); 2*q < n; q *= 2 {
+		if k%2 == 0 {
+			// s(2^n) = (2^(n-1) + 4) / 3 for even n
+			sieve[2*q] = (q + 4) / 3
+		} else {
+			// s(2^n) = (2^(n-1) + 5) / 3 for odd n
+			sieve[2*q] = (q + 5) / 3
+		}
+
+		k += 1
+	}
+}
+
+func qrPowersOfOddPrimes(sieve []uint, p uint, n uint) {
+	k := 3
+	for q := p * p; p*q < n; q *= p {
+		if k%2 == 0 {
+			// s(p^n) = (p^(n+1) + p + 2) / (2*(p+1)) for even n
+			sieve[p*q] = (p*p*q + p + 2) / (2 * (p + 1))
+		} else {
+			// s(p^n) = (p^(n+1) + 2*p + 1) / (2*(p+1)) for odd n
+			sieve[p*q] = (p*p*q + 2*p + 1) / (2 * (p + 1))
+		}
+
+		k += 1
+	}
+}
+
+/*
+QuadraticResidues computes the number of quadratic residues modulo k for k=1 to n.
+
+see https://oeis.org/A000224 and https://oeis.org/A046073
+*/
+func QuadraticResidues(n uint, coprime bool, buflen uint) chan uint {
+	sieve := make([]uint, n)
+	for i := uint(0); i < n; i++ {
+		sieve[i] = 1
+	}
+
+	ch := make(chan uint, buflen)
+	go func() {
+		defer close(ch)
+		if coprime {
+			sieveQRCoprime(sieve, n, ch)
+		} else {
+			sieveQR(sieve, n, ch)
+		}
+	}()
+
+	return ch
+}
+
+func sieveQRCoprime(sieve []uint, n uint, ch chan uint) {
+	for i := uint(0); i < n; i++ {
+		if i == 0 || i == 1 || i == 4 || i == 6 || i == 8 || i == 12 || i == 24 || sieve[i] != 1 {
+			ch <- sieve[i]
+			continue
+		}
+
+		if i == 2 {
+			qrPowersOfTwoCoprime(sieve, n)
+		} else {
+			// q(p) = (p - 1) / 2
+			sieve[i] = (i - 1) / 2
+			qrPowersOfOddPrimesCoprime(sieve, i, n)
+		}
+
+		updateMultiples(sieve, i, n, false)
+		ch <- sieve[i]
+	}
+}
+
+func sieveQR(sieve []uint, n uint, ch chan uint) {
+	for i := uint(0); i < n; i++ {
+		if i == 0 || i == 1 || sieve[i] != 1 {
+			ch <- sieve[i]
+			continue
+		}
+
+		if i == 2 {
+			qrPowersOfTwo(sieve, n)
+		} else {
+			// s(p) = (p + 1) / 2
+			sieve[i] = (i + 1) / 2
+			if i*i < n {
+				// s(p^2) = (p^2 - p + 2) / 2
+				sieve[i*i] = (i*i - i + 2) / 2
+			}
+			qrPowersOfOddPrimes(sieve, i, n)
+		}
+
+		updateMultiples(sieve, i, n, false)
+		ch <- sieve[i]
+	}
+}

internal/lib/sieve/radical.go

@@ -16,24 +16,6 @@ along with this program. If not, see <http://www.gnu.org/licenses/>.
 */
 package sieve
 
-func radicalUpdateMultiples(sieve []uint, p uint, n uint) {
-	for q := p; ; q *= p {
-		// rad(a*b) = rad(a) * rad(b) if gcd(a,b) = 1
-		for i := 2 * q; i < n; i += q {
-			if i%(p*q) != 0 {
-				sieve[i] *= sieve[q]
-			}
-		}
-
-		if p*q >= n {
-			break
-		}
-
-		// rad(p^k) = rad(p)
-		sieve[p*q] = sieve[q]
-	}
-}
-
 /*
 Radical computes rad(k) for k=1 to n, where rad(n) is the radical of n.
 */