Optimize NumDigits

Dividing BitLen by math.Log2(10) is what math/big does underneath

Not including the Int64/Uint64 check makes this slightly slower than old method

Included 2 benchmarks, for 10 digit numbers & 100 digit numbers:

-- before
> go test -bench=NumDigit -run=NumDigit
goos: linux
goarch: amd64
pkg: github.com/shopspring/decimal
cpu: AMD Ryzen 7 7840U w/ Radeon  780M Graphics
BenchmarkDecimal_NumDigits10-16     	18317293	        63.87 ns/op
BenchmarkDecimal_NumDigits100-16    	 3645015	       329.6 ns/op

-- after
...
BenchmarkDecimal_NumDigits10-16     	143781325	         8.488 ns/op
BenchmarkDecimal_NumDigits100-16    	 5931247	       207.4 ns/op

decimal.go

@@ -946,14 +946,35 @@ func (d Decimal) Ln(precision int32) (Decimal, error) {
 }
 
 // NumDigits returns the number of digits of the decimal coefficient (d.Value)
-// Note: Current implementation is extremely slow for large decimals and/or decimals with large fractional part
 func (d Decimal) NumDigits() int {
-	d.ensureInitialized()
-	// Note(mwoss): It can be optimized, unnecessary cast of big.Int to string
-	if d.IsNegative() {
-		return len(d.value.String()) - 1
+	if d.value == nil {
+		return 1
+	}
+
+	if d.value.IsUint64() {
+		u64 := d.value.Uint64()
+		if u64 < (1 << 53) {
+			if u64 == 0 {
+				return 1
+			}
+			return int(math.Log10(float64(u64))) + 1
+		}
+	} else if d.value.IsInt64() {
+		i64 := d.value.Int64()
+		if i64 > -(1 << 53) {
+			return int(math.Log10(float64(-i64))) + 1
+		}
 	}
-	return len(d.value.String())
+
+	abs := new(big.Int).Abs(d.value)
+	// lg10 may be off by 1, need to verify
+	lg10 := int(float64(abs.BitLen())/math.Log2(10)) + 1
+	check := big.NewInt(int64(lg10))
+	check.Exp(tenInt, check, nil)
+	if abs.Mul(abs, tenInt).Cmp(check) == -1 {
+		return lg10 - 1
+	}
+	return lg10
 }
 
 // IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false.

decimal_bench_test.go

@@ -120,6 +120,34 @@ func BenchmarkDecimal_RoundCash_Five(b *testing.B) {
 	}
 }
 
+func numDigits(b *testing.B, want int, val Decimal) {
+	b.Helper()
+	for i := 0; i < b.N; i++ {
+		if have := val.NumDigits(); have != want {
+			b.Fatalf("\nHave: %q\nWant: %q", have, want)
+		}
+	}
+}
+
+func BenchmarkDecimal_NumDigits10(b *testing.B) {
+	numDigits(b, 10, New(3478512345, -3))
+}
+
+func BenchmarkDecimal_NumDigits100(b *testing.B) {
+	s := make([]byte, 102)
+	for i := range s {
+		s[i] = byte('0' + i%10)
+	}
+	s[0] = '-'
+	s[100] = '.'
+	d, err := NewFromString(string(s))
+	if err != nil {
+		b.Log(d)
+		b.Error(err)
+	}
+	numDigits(b, 100, d)
+}
+
 func Benchmark_Cmp(b *testing.B) {
 	decimals := DecimalSlice([]Decimal{})
 	for i := 0; i < 1000000; i++ {
@@ -131,7 +159,7 @@ func Benchmark_Cmp(b *testing.B) {
 	}
 }
 
-func Benchmark_decimal_Decimal_Add_different_precision(b *testing.B) {
+func BenchmarkDecimal_Add_different_precision(b *testing.B) {
 	d1 := NewFromFloat(1000.123)
 	d2 := NewFromFloat(500).Mul(NewFromFloat(0.12))
 
@@ -142,7 +170,7 @@ func Benchmark_decimal_Decimal_Add_different_precision(b *testing.B) {
 	}
 }
 
-func Benchmark_decimal_Decimal_Sub_different_precision(b *testing.B) {
+func BenchmarkDecimal_Sub_different_precision(b *testing.B) {
 	d1 := NewFromFloat(1000.123)
 	d2 := NewFromFloat(500).Mul(NewFromFloat(0.12))
 
@@ -153,7 +181,7 @@ func Benchmark_decimal_Decimal_Sub_different_precision(b *testing.B) {
 	}
 }
 
-func Benchmark_decimal_Decimal_Add_same_precision(b *testing.B) {
+func BenchmarkDecimal_Add_same_precision(b *testing.B) {
 	d1 := NewFromFloat(1000.123)
 	d2 := NewFromFloat(500.123)
 
@@ -164,7 +192,7 @@ func Benchmark_decimal_Decimal_Add_same_precision(b *testing.B) {
 	}
 }
 
-func Benchmark_decimal_Decimal_Sub_same_precision(b *testing.B) {
+func BenchmarkDecimal_Sub_same_precision(b *testing.B) {
 	d1 := NewFromFloat(1000.123)
 	d2 := NewFromFloat(500.123)