diff options
| -rw-r--r-- | factor_info.go | 12 | ||||
| -rw-r--r-- | factors/factors_test.go | 9 | ||||
| -rw-r--r-- | factors/totative.go | 15 |
3 files changed, 30 insertions, 6 deletions
diff --git a/factor_info.go b/factor_info.go index ce014ed..93cb9d2 100644 --- a/factor_info.go +++ b/factor_info.go @@ -20,6 +20,9 @@ type FactorInfo struct { Factors []uint // An estimate of the utility of the radix's factors. Score float64 + // The number of digits that are totatives (numbers that share no + // factors with the radix - they are the worst kind of digits) + TotativeCount uint // The fraction of digits that are totatives (numbers that share no // factors with the radix - they are the worst kind of digits) TotativeRatio float64 @@ -70,15 +73,16 @@ func GetFactorInfo(radix uint) *FactorInfo { } return &FactorInfo{radix, factors.PrimeFactorize(radix), - r_factors, factors.Score(radix), factors.TotativeRatio(radix), - factors.BasicRank(radix), r_type_ptr, mtc_ptr, - math.Log(float64(radix)), digitMap} + r_factors, factors.Score(radix), factors.TotativeCount(radix), + factors.TotativeRatio(radix), factors.BasicRank(radix), + r_type_ptr, mtc_ptr, math.Log(float64(radix)), digitMap} } func (fi *FactorInfo) WriteTo(w io.Writer) { fmt.Fprintln(w, fi.Radix, "=", fi.PrimeFactorization) fmt.Fprintf(w, "Factors: %v (Score: %.4f)\n", fi.Factors, fi.Score) - fmt.Fprintf(w, "Totative Ratio: %.3f%%\n", fi.TotativeRatio * 100.0) + fmt.Fprintf(w, "Totative Digit Count: %d (%.3f%%)\n", + fi.TotativeCount, fi.TotativeRatio * 100.0) fmt.Fprintln(w, "2345 Rank:", fi.BasicRank) if fi.Type != nil { writeTypeMessage(w, *fi.Type) diff --git a/factors/factors_test.go b/factors/factors_test.go index 8373ede..6b56e25 100644 --- a/factors/factors_test.go +++ b/factors/factors_test.go @@ -71,6 +71,15 @@ func TestTotativeRatio(t *testing.T) { tableTest(t, TotativeRatio, totativeRatioCases, stdEquals, "TotativeRatio") } +var totativeCountCases = map[uint]uint{ + 1: 1, 2: 1, 3: 2, 4: 2, 6: 2, 7: 6, 8: 4, 12: 4, + 14: 6, 15: 8, 30: 8, 60: 16, 120: 32, +} + +func TestTotativeCount(t *testing.T) { + tableTest(t, TotativeCount, totativeCountCases, stdEquals, "TotativeCount") +} + var factorScoreCases = map[uint]float64{ 1: 1.0, 2: 1.5, diff --git a/factors/totative.go b/factors/totative.go index 3a1f635..7a4bebe 100644 --- a/factors/totative.go +++ b/factors/totative.go @@ -1,12 +1,22 @@ package factors -// TotativeRatio calculates the fraction of numbers less than n that +// TotativeRatio calculates the fraction of numbers that // are totatives of n (share no factors with n) func TotativeRatio(n uint) float64 { if n == 0 { panic("0 has no totative ratio!") } + return float64(TotativeCount(n)) / float64(n) +} + +// TotativeCount calculates the number of numbers less than n that +// are totatives of n (share no factors with n) +func TotativeCount(n uint) uint { + if n == 0 { + return 0 + } + primeFactorization := PrimeFactorize(n) num, denom := uint(1), uint(1) @@ -14,5 +24,6 @@ func TotativeRatio(n uint) float64 { num *= p - 1 denom *= p } - return float64(num) / float64(denom) + + return num * (n / denom) } |