Optimize NumDigits method (#356)

Author: serprex

decimal.go

@@ -1224,14 +1224,33 @@ 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.IsInt64() {
+		i64 := d.value.Int64()
+		// restrict fast path to integers with exact conversion to float64
+		if i64 <= (1<<53) && i64 >= -(1<<53) {
+			if i64 == 0 {
+				return 1
+			}
+			return int(math.Log10(math.Abs(float64(i64)))) + 1
+		}
+	}
+
+	estimatedNumDigits := int(float64(d.value.BitLen()) / math.Log2(10))
+
+	// estimatedNumDigits (lg10) may be off by 1, need to verify
+	digitsBigInt := big.NewInt(int64(estimatedNumDigits))
+	errorCorrectionUnit := digitsBigInt.Exp(tenInt, digitsBigInt, nil)
+
+	if d.value.CmpAbs(errorCorrectionUnit) >= 0 {
+		return estimatedNumDigits + 1
 	}
-	return len(d.value.String())
+
+	return estimatedNumDigits
 }
 
 // IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false.

decimal_bench_test.go

@@ -121,6 +121,34 @@ 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: %d\nWant: %d", 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++ {
@@ -132,7 +160,7 @@ 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))
 
@@ -143,7 +171,7 @@ 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))
 
@@ -154,7 +182,7 @@ 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)
 
@@ -165,7 +193,7 @@ 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)