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/* This script is part of radix_info.
Copyright (C) 2023 Adrien Hopkins
This program is free software: you can redistribute it and/or modify
it under the terms of version 3 of the GNU General Public License
as published by the Free Software Foundation.
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 <https://www.gnu.org/licenses/>.
*/
package factors
import (
"fmt"
"math/rand"
"testing"
)
// TestFactorsDivisible ensures that every number returned by
// Factors is actually a factor of the argument.
func TestFactorsDivisible(t *testing.T) {
for r := uint(1); r < (1 << 16); r++ {
t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
testFactorsDivisibleOnce(t, r)
})
}
}
// One execution of TestFactorsDivisible
func testFactorsDivisibleOnce(t *testing.T, r uint) {
t.Parallel()
factors := Factors(r)
for _, factor := range factors {
if r%factor != 0 {
t.Errorf("%d reported as factor of %d, but not divisible", factor, r)
}
}
}
// TestTotatives ensures that every number returned by
// TotativeDigits is actually a totative of the argument.
// It also tests that len(TotativeDigits(r)) = Totient(r).
func TestTotatives(t *testing.T) {
for r := uint32(0); r < (1 << 12); r++ {
t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
testTotativesOnce(t, r)
})
}
}
// TestTotativesRandom is like TestTotatives,
// except it randomly chooses radices.
func TestTotativesRandom(t *testing.T) {
for testRun := 0; testRun < 144; testRun++ {
r := uint32(rand.Int31n(1 << 16))
t.Run(fmt.Sprintf("%d", r), func(t *testing.T) {
testTotativesOnce(t, r)
})
}
}
// One execution of TestTotatives
func testTotativesOnce(t *testing.T, r uint32) {
t.Parallel()
totatives := TotativeDigits(r)
for _, totative := range totatives {
if gcd(totative, r) != 1 {
t.Errorf("%d reported as totative of %d, but gcd(%d, %d) = %d",
totative, r, totative, r, gcd(totative, r))
}
}
totient := Totient(uint(r))
if uint(len(totatives)) != totient {
t.Errorf(
"len(TotativeDigits(%d)) = %d, Totient(%d) = %d, should be equal",
r, len(totatives), r, totient)
}
}
// TestSplitProperties tests Split(digit, radix) to ensure
// totative is a totative and regular * totative = digit.
func TestSplitProperties(t *testing.T) {
for radix := uint(1); radix < 1<<7; radix++ {
for digit := uint(1); digit < 1<<8; digit++ {
t.Run(fmt.Sprintf("radix=%d,digit=%d", radix, digit),
func(t *testing.T) { testSplitOnce(t, digit, radix) })
}
}
}
// TestSplitRandom is like TestSplitProperties,
// but with randomly chosen values.
func TestSplitRandom(t *testing.T) {
for i := 0; i < 1728; i++ {
radix := uint(rand.Int31n((1<<15)-1)) + 1
digit := uint(rand.Int31n((1<<16)-1)) + 1
t.Run(fmt.Sprintf("radix=%d,digit=%d", radix, digit),
func(t *testing.T) { testSplitOnce(t, digit, radix) })
}
}
// One execution of TestSplitProperties
func testSplitOnce(t *testing.T, digit, radix uint) {
t.Parallel()
regular, totative := Split(digit, radix)
if gcd(uint32(totative), uint32(radix)) != 1 {
t.Errorf("Split(%d, %d) = %d, %d; %d not coprime to %d.",
digit, radix, regular, totative, totative, radix)
}
if regular*totative != digit {
t.Errorf("Split(%d, %d) = %d, %d; %d * %d ≠ %d.",
digit, radix, regular, totative, regular, totative, digit)
}
}
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