Add digit map calculation

This is not in the output yet, but it will be soon - printing it is
another task since I want colours in my output.

6 files changed, 248 insertions, 18 deletions

diff --git a/factors/digit_map.go b/factors/digit_map.go
new file mode 100644
index 0000000..e78cce0
--- /dev/null
+++ b/factors/digit_map.go
@@ -0,0 +1,140 @@
+package factors
+
+import "fmt"
+
+type DigitType struct {
+	regularity   uint8
+	totativeType TotativeType
+}
+
+type TotativeType uint8
+
+const (
+	// This number does not have any totative factors
+	Regular TotativeType = iota
+	// This number's totative part is divisible by (r^2 - 1)
+	// - this makes it easier to work with
+	Neighbour
+	// This number's totative part is not divisible by (r^2 - 1)
+	// - it will not be nice to work with
+	Opaque
+	// This number is zero, and doesn't have a true totative type.
+	Zero
+)
+
+// Zero and one will always have these types.
+var (
+	zeroType = DigitType{regularity: 0, totativeType: Zero}
+	oneType  = DigitType{regularity: 0, totativeType: Regular}
+)
+
+// Above this number, regularity indices will be shown as '+'
+// instead of the number; this is to keep the code 2 characters long
+const maxDisplayRegularity = 7
+
+// The regularity index of a number in a radix, the smallest power of the
+// radix that is divisible by the number's regular part.
+func (dt DigitType) Regularity() uint8 { return dt.regularity }
+
+// The type of a number's totative part in a radix
+func (dt DigitType) TotativeType() TotativeType { return dt.totativeType }
+
+// String returns a string representation of the digit type
+// as a two-character code - the first representing regularity,
+// the second totative type
+func (dt DigitType) String() string {
+	var rString string
+	if dt.regularity > maxDisplayRegularity {
+		rString = "+"
+	} else {
+		rString = fmt.Sprint(dt.regularity)
+	}
+
+	var tString string
+	switch dt.totativeType {
+	case Zero:
+		tString = "0"
+	case Regular:
+		tString = "R"
+	case Neighbour:
+		tString = "N"
+	case Opaque:
+		tString = "P"
+	}
+
+	return rString + tString
+}
+
+// Splits a digit in a radix into its regular and totative parts
+func splitPF(digit, radix PrimeFactorization) (regular, totative uint) {
+	regular, totative = 1, 1
+	for p, e := range digit.exponents {
+		if radix.exponents[p] != 0 {
+			regular *= uintpow(p, e)
+		} else {
+			totative *= uintpow(p, e)
+		}
+	}
+	return regular, totative
+}
+
+// Splits a digit in a radix into its regular and totative parts
+func Split(digit, radix uint) (regular, totative uint) {
+	return splitPF(PrimeFactorize(digit), PrimeFactorize(radix))
+}
+
+// Calculates the regularity index of a number's regular part
+func calcRegularity(regular, radix uint) uint8 {
+	regularity, radixPower := uint8(0), uint(1)
+	for radixPower%regular != 0 {
+		regularity++
+		radixPower *= radix
+	}
+	return regularity
+}
+
+// Calculates the totative type of a number's totative part
+func calcTotativeType(totative, radix uint) TotativeType {
+	switch true {
+	case totative == 0:
+		return Zero
+	case totative == 1:
+		return Regular
+	case (radix*radix-1)%totative == 0:
+		return Neighbour
+	default:
+		return Opaque
+	}
+}
+
+// Gets the regularity and totative type of one digit in a radix
+func GetDigitType(digit, radix uint) DigitType {
+	if radix < 2 {
+		panic("Radices cannot be less than 2!")
+	}
+	radixPF := PrimeFactorize(radix)
+	digitPF := PrimeFactorize(digit)
+	regular, totative := splitPF(digitPF, radixPF)
+	regularity := calcRegularity(regular, radix)
+	totativeType := calcTotativeType(totative, radix)
+	return DigitType{regularity, totativeType}
+}
+
+// Gets the regularity and totative type of each digit in a radix
+func DigitMap(radix uint) []DigitType {
+	if radix < 2 {
+		panic("Radices cannot be less than 2!")
+	}
+	radixPF := PrimeFactorize(radix)
+	types := make([]DigitType, radix, radix)
+	types[0] = zeroType
+	types[1] = oneType
+	for d := uint(2); d < radix; d++ {
+		digitPF := PrimeFactorize(d)
+		regular, totative := splitPF(digitPF, radixPF)
+		regularity := calcRegularity(regular, radix)
+		totativeType := calcTotativeType(totative, radix)
+		types[d] = DigitType{regularity, totativeType}
+	}
+	return types
+}
diff --git a/factors/factorize.go b/factors/factorize.go
index 2f7368a..8e82b16 100644
--- a/factors/factorize.go
+++ b/factors/factorize.go
@@ -11,14 +11,14 @@ func Factors(n uint) []uint {
 
 	factors := []uint{1}
 	for p, e := range primeFactorization.exponents {
-		next_factors := make([]uint, 0, len(factors) * int(e))
+		next_factors := make([]uint, 0, len(factors)*int(e))
 		for _, factor := range factors {
 			for i := uint(0); i <= e; i++ {
 				multiplier := uint(1)
 				for j := uint(0); j < i; j++ {
 					multiplier *= p
 				}
-				next_factors = append(next_factors, factor * multiplier)
+				next_factors = append(next_factors, factor*multiplier)
 			}
 		}
 		factors = next_factors
diff --git a/factors/factors_test.go b/factors/factors_test.go
index b7f48b9..8373ede 100644
--- a/factors/factors_test.go
+++ b/factors/factors_test.go
@@ -3,6 +3,7 @@ package factors
 import (
 	"fmt"
 	"maps"
+	"slices"
 	"testing"
 )
 
@@ -19,6 +20,8 @@ func tableTest[IN comparable, OUT any](t *testing.T, toTest func(IN) OUT,
 	}
 }
 
+type uintPair struct{ a, b uint }
+
 var primeFactorCases = map[uint]PrimeFactorization{
 	0:     PrimeFactorization{map[uint]uint{0: 1}},
 	1:     PrimeFactorization{map[uint]uint{}},
@@ -58,8 +61,8 @@ func TestFactors(t *testing.T) {
 }
 
 var totativeRatioCases = map[uint]float64{
-	1:  1.0, 2:  0.5, 3:  2.0 / 3.0, 4:  0.5,
-	6:  1.0 / 3.0, 7:  6.0 / 7.0, 8:  0.5,
+	1: 1.0, 2: 0.5, 3: 2.0 / 3.0, 4: 0.5,
+	6: 1.0 / 3.0, 7: 6.0 / 7.0, 8: 0.5,
 	12: 1.0 / 3.0, 14: 3.0 / 7.0, 15: 8.0 / 15.0,
 	30: 4.0 / 15.0, 60: 4.0 / 15.0, 120: 4.0 / 15.0,
 }
@@ -163,7 +166,7 @@ func TestPractical(t *testing.T) {
 	tableTest(t, practical, practicalCases, stdEquals, "practical")
 }
 
-var typeCases = map[uint32]NumberType {
+var typeCases = map[uint32]NumberType{
 	2: ColossallyAbundant, 3: NotPractical, 4: Superabundant,
 	6: ColossallyAbundant, 8: OrderedExponent, 10: NotPractical,
 	12: ColossallyAbundant, 18: Practical, 20: Practical, 24: Superabundant,
@@ -178,6 +181,92 @@ func TestType(t *testing.T) {
 	tableTest(t, Type, typeCases, stdEquals, "Type")
 }
 
+// ====== DIGIT MAP TESTS ======
+var (
+	zt = zeroType                // 00 - zero
+	ot = oneType                 // 0R - one
+	ft = DigitType{1, Regular}   // 1R - factors
+	rt = DigitType{2, Regular}   // 2R - regulars (index 2)
+	nt = DigitType{0, Neighbour} // 0N - neighbours
+	pt = DigitType{0, Opaque}    // 0P - opaque totatives
+)
+var digitMapCases = map[uint][]DigitType{
+	2: []DigitType{zt, ot},
+	3: []DigitType{zt, ot, nt},
+	4: []DigitType{zt, ot, ft, nt},
+	5: []DigitType{zt, ot, nt, nt, nt},
+	6: []DigitType{zt, ot, ft, ft, rt, nt},
+	8: []DigitType{zt, ot, ft, nt, ft, pt, DigitType{1, Neighbour}, nt},
+	10: []DigitType{zt, ot, ft, nt, rt, ft, DigitType{1, Neighbour}, pt,
+		DigitType{3, Regular}, nt},
+	12: []DigitType{zt, ot, ft, ft, ft, pt, ft, pt, rt, rt,
+		DigitType{1, Opaque}, nt},
+	16: []DigitType{zt, ot, ft, nt, ft, nt, DigitType{1, Neighbour}, pt,
+		ft, pt, DigitType{1, Neighbour}, pt, DigitType{1, Neighbour},
+		pt, DigitType{1, Opaque}, nt},
+}
+
+func TestDigitMap(t *testing.T) {
+	tableTest(t, DigitMap, digitMapCases, slices.Equal, "DigitMap")
+}
+
+// ensures GetDigitType(d, r) == DigitMap(r)[d];
+// does not ensure it has the correct value (that's TestDigitMap's job)
+func TestGetDigitType(t *testing.T) {
+	for radix := range digitMapCases {
+		digitMap := DigitMap(radix)
+		for digit := range digitMap {
+			actual := GetDigitType(uint(digit), radix)
+			if actual != digitMap[digit] {
+				t.Logf("GetDigitType(%d, %d) = %d", digit, radix, actual)
+				t.Errorf("GetDigitType(%d, %d) != DigitMap(%d)[%d]",
+					digit, radix, radix, digit)
+			}
+		}
+	}
+}
+
+var splitCases = map[uintPair]uintPair{
+	// digit, radix, regular part, totative part
+	uintPair{0, 0}:    uintPair{0, 1},
+	uintPair{0, 2}:    uintPair{1, 0},
+	uintPair{0, 12}:   uintPair{1, 0},
+	uintPair{1, 0}:    uintPair{1, 1},
+	uintPair{20, 0}:   uintPair{1, 20},
+	uintPair{360, 0}:  uintPair{1, 360},
+	uintPair{1, 2}:    uintPair{1, 1},
+	uintPair{1, 3}:    uintPair{1, 1},
+	uintPair{1, 7}:    uintPair{1, 1},
+	uintPair{1, 12}:   uintPair{1, 1},
+	uintPair{1, 39}:   uintPair{1, 1},
+	uintPair{1, 2948}: uintPair{1, 1},
+	uintPair{5, 6}:    uintPair{1, 5},
+	uintPair{10, 6}:   uintPair{2, 5},
+	uintPair{12, 6}:   uintPair{12, 1},
+	uintPair{15, 6}:   uintPair{3, 5},
+	uintPair{35, 6}:   uintPair{1, 35},
+	uintPair{56, 6}:   uintPair{8, 7},
+	uintPair{5, 12}:   uintPair{1, 5},
+	uintPair{10, 12}:  uintPair{2, 5},
+	uintPair{12, 12}:  uintPair{12, 1},
+	uintPair{15, 12}:  uintPair{3, 5},
+	uintPair{35, 12}:  uintPair{1, 35},
+	uintPair{56, 12}:  uintPair{8, 7},
+	uintPair{12, 7}:   uintPair{1, 12},
+	uintPair{56, 7}:   uintPair{7, 8},
+	uintPair{70, 10}:  uintPair{10, 7},
+}
+
+// testing version of Split
+func splitTest(a uintPair) uintPair {
+	regular, totative := Split(a.a, a.b)
+	return uintPair{regular, totative}
+}
+
+func TestSplit(t *testing.T) {
+	tableTest(t, splitTest, splitCases, stdEquals, "Split")
+}
+
 // to be used as the equal paramater for tableTest
 func stdEquals[T comparable](a, b T) bool { return a == b }
 
diff --git a/factors/mtc.go b/factors/mtc.go
index 522a35c..655124c 100644
--- a/factors/mtc.go
+++ b/factors/mtc.go
@@ -5,7 +5,7 @@ package factors
 // multiplication table.
 func MTC(n uint64) uint64 {
 	mtc := uint64(0)
-	for i := uint64(2); i <= n - 2; i++ {
+	for i := uint64(2); i <= n-2; i++ {
 		mtc += n / gcd(i, n)
 	}
 	return mtc
@@ -13,7 +13,7 @@ func MTC(n uint64) uint64 {
 
 func gcd(a, b uint64) uint64 {
 	for b > 0 {
-		a, b = b, a % b
+		a, b = b, a%b
 	}
 	return a
 }
diff --git a/factors/type.go b/factors/type.go
index e587ebb..39aab9b 100644
--- a/factors/type.go
+++ b/factors/type.go
@@ -52,7 +52,7 @@ func Type(n uint32) NumberType {
 func isSAN(n uint32) bool {
 	if n <= 2 {
 		return true
-	} else if n % 4 != 0 && n % 6 != 0 {
+	} else if n%4 != 0 && n%6 != 0 {
 		return false
 	}
 
@@ -77,7 +77,7 @@ func isSAN(n uint32) bool {
 func exponentsOrdered(n uint32) bool {
 	if n <= 2 {
 		return true
-	} else if n % 4 != 0 && n % 6 != 0 {
+	} else if n%4 != 0 && n%6 != 0 {
 		return false
 	}
 
@@ -102,7 +102,7 @@ func exponentsOrdered(n uint32) bool {
 func practical(n uint32) bool {
 	if n <= 2 {
 		return true
-	} else if n % 4 != 0 && n % 6 != 0 {
+	} else if n%4 != 0 && n%6 != 0 {
 		return false
 	}
 
@@ -126,11 +126,3 @@ func practical(n uint32) bool {
 
 	return true
 }
-
-func uintpow(a, b uint) uint {
-	result := uint(1)
-	for i := uint(0); i < b; i++ {
-		result *= a
-	}
-	return result
-}
diff --git a/factors/uintpow.go b/factors/uintpow.go
new file mode 100644
index 0000000..85db67f
--- /dev/null
+++ b/factors/uintpow.go
@@ -0,0 +1,9 @@
+package factors
+
+func uintpow(a, b uint) uint {
+	result := uint(1)
+	for i := uint(0); i < b; i++ {
+		result *= a
+	}
+	return result
+}