Add more tests & fix found bugs

- TotativeDigits was defined incorrectly, previously counted totatives
  from 0 to r-1, now counts digits from 1 to r.  This ensures that
  len(TotativeDigits(r)) = Totient(r).

1 files changed, 5 insertions, 5 deletions

diff --git a/factors/totative.go b/factors/totative.go
index abbbe89..d1947b6 100644
--- a/factors/totative.go
+++ b/factors/totative.go
@@ -1,7 +1,7 @@
 package factors
 
-// Totient calculates the number of numbers less than n that
-// are totatives of n (share no factors with n)
+// Totient calculates the number of numbers between 1 and n inclusive
+// that are totatives of n (share no factors with n)
 func Totient(n uint) uint {
 	if n == 0 {
 		return 0
@@ -18,12 +18,12 @@ func Totient(n uint) uint {
 	return num * (n / denom)
 }
 
-// TotativeDigits returns a slice containing every number less than r
-// that is a totative of r (shares no factors with r).
+// TotativeDigits returns a slice containing every number between 1 and r
+// inclusive that is a totative of r (shares no factors with r).
 func TotativeDigits(r uint32) []uint32 {
 	digits := make([]uint32, Totient(uint(r)))
 	totativesFound := 0
-	for d := uint32(0); d < r; d++ {
+	for d := uint32(1); d <= r; d++ {
 		if gcd(d, r) == 1 {
 			digits[totativesFound] = d
 			totativesFound++