Merge a3267013b7 into 0e69d5cd53

* Adjust Pow implementation
* Add PowWithPrecision method
* Add PowInt32 method
* Add PowBigInt method

.github/workflows/ci.yml

@@ -1,5 +1,9 @@
 name: ci
-on: [push]
+on:
+  push:
+    branches:
+      - master
+  pull_request:
 jobs:
   ci-job:
     runs-on: ubuntu-latest

decimal.go

@@ -43,6 +43,20 @@ import (
 //	d4.String() // output: "0.667"
 var DivisionPrecision = 16
 
+// PowPrecisionNegativeExponent specifies the maximum precision of the result (digits after decimal point)
+// when calculating decimal power. Only used for cases where the exponent is a negative number.
+// This constant applies to Pow, PowInt32 and PowBigInt methods, PowWithPrecision method is not constrained by it.
+//
+// Example:
+//
+//	d1, err := decimal.NewFromFloat(15.2).PowInt32(-2)
+//	d1.String() // output: "0.0043282548476454"
+//
+//	decimal.PowPrecisionNegativeExponent = 24
+//	d2, err := decimal.NewFromFloat(15.2).PowInt32(-2)
+//	d2.String() // output: "0.004328254847645429362881"
+var PowPrecisionNegativeExponent = 16
+
 // MarshalJSONWithoutQuotes should be set to true if you want the decimal to
 // be JSON marshaled as a number, instead of as a string.
 // WARNING: this is dangerous for decimals with many digits, since many JSON
@@ -129,11 +143,10 @@ func NewFromBigInt(value *big.Int, exp int32) Decimal {
 //
 // Example:
 //
-//     d1 := NewFromBigRat(big.NewRat(0, 1), 0)    // output: "0"
-//     d2 := NewFromBigRat(big.NewRat(4, 5), 1)    // output: "0.8"
-//     d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333"
-//     d4 := NewFromBigRat(big.NewRat(2, 7), 4)    // output: "0.2857"
-//
+//	d1 := NewFromBigRat(big.NewRat(0, 1), 0)    // output: "0"
+//	d2 := NewFromBigRat(big.NewRat(4, 5), 1)    // output: "0.8"
+//	d3 := NewFromBigRat(big.NewRat(1000, 3), 3) // output: "333.333"
+//	d4 := NewFromBigRat(big.NewRat(2, 7), 4)    // output: "0.2857"
 func NewFromBigRat(value *big.Rat, precision int32) Decimal {
 	return Decimal{
 		value: new(big.Int).Set(value.Num()),
@@ -650,20 +663,274 @@ func (d Decimal) Mod(d2 Decimal) Decimal {
 	return r
 }
 
-// Pow returns d to the power d2
+// Pow returns d to the power of d2.
+// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
+//
+// Pow returns 0 (zero-value of Decimal) instead of error for power operation edge cases, to handle those edge cases use PowWithPrecision
+// Edge cases not handled by Pow:
+//   - 0 ** 0 => undefined value
+//   - 0 ** y, where y < 0 => infinity
+//   - x ** y, where x < 0 and y is non-integer decimal => imaginary value
+//
+// Example:
+//
+//	d1 := decimal.NewFromFloat(4.0)
+//	d2 := decimal.NewFromFloat(4.0)
+//	res1 := d1.Pow(d2)
+//	res1.String() // output: "256"
+//
+//	d3 := decimal.NewFromFloat(5.0)
+//	d4 := decimal.NewFromFloat(5.73)
+//	res2 := d3.Pow(d4)
+//	res2.String() // output: "10118.08037125"
 func (d Decimal) Pow(d2 Decimal) Decimal {
-	var temp Decimal
-	if d2.IntPart() == 0 {
-		return NewFromFloat(1)
+	baseSign := d.Sign()
+	expSign := d2.Sign()
+
+	if baseSign == 0 {
+		if expSign == 0 {
+			return Decimal{}
+		}
+		if expSign == 1 {
+			return Decimal{zeroInt, 0}
+		}
+		if expSign == -1 {
+			return Decimal{}
+		}
 	}
-	temp = d.Pow(d2.Div(NewFromFloat(2)))
-	if d2.IntPart()%2 == 0 {
-		return temp.Mul(temp)
+
+	if expSign == 0 {
+		return Decimal{oneInt, 0}
 	}
-	if d2.IntPart() > 0 {
-		return temp.Mul(temp).Mul(d)
+
+	// TODO: optimize extraction of fractional part
+	one := Decimal{oneInt, 0}
+	expIntPart, expFracPart := d2.QuoRem(one, 0)
+
+	if baseSign == -1 && !expFracPart.IsZero() {
+		return Decimal{}
 	}
-	return temp.Mul(temp).Div(d)
+
+	intPartPow, _ := d.PowBigInt(expIntPart.value)
+
+	// if exponent is an integer we don't need to calculate d1**frac(d2)
+	if expFracPart.value.Sign() == 0 {
+		return intPartPow
+	}
+
+	// TODO: optimize NumDigits for more performant precision adjustment
+	digitsBase := d.NumDigits()
+	digitsExponent := d2.NumDigits()
+
+	precision := digitsBase
+
+	if digitsExponent > precision {
+		precision += digitsExponent
+	}
+
+	precision += 6
+
+	// Calculate x ** frac(y), where
+	// x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y))
+	fracPartPow, err := d.Abs().Ln(-d.exp + int32(precision))
+	if err != nil {
+		return Decimal{}
+	}
+
+	fracPartPow = fracPartPow.Mul(expFracPart)
+
+	fracPartPow, err = fracPartPow.ExpTaylor(-d.exp + int32(precision))
+	if err != nil {
+		return Decimal{}
+	}
+
+	// Join integer and fractional part,
+	// base ** (expBase + expFrac) = base ** expBase * base ** expFrac
+	res := intPartPow.Mul(fracPartPow)
+
+	return res
+}
+
+// PowWithPrecision returns d to the power of d2.
+// Precision parameter specifies minimum precision of the result (digits after decimal point).
+// Returned decimal is not rounded to 'precision' places after decimal point.
+//
+// PowWithPrecision returns error when:
+//   - 0 ** 0 => undefined value
+//   - 0 ** y, where y < 0 => infinity
+//   - x ** y, where x < 0 and y is non-integer decimal => imaginary value
+//
+// Example:
+//
+//	d1 := decimal.NewFromFloat(4.0)
+//	d2 := decimal.NewFromFloat(4.0)
+//	res1, err := d1.PowWithPrecision(d2, 2)
+//	res1.String() // output: "256"
+//
+//	d3 := decimal.NewFromFloat(5.0)
+//	d4 := decimal.NewFromFloat(5.73)
+//	res2, err := d3.PowWithPrecision(d4, 5)
+//	res2.String() // output: "10118.080371595015625"
+//
+//	d5 := decimal.NewFromFloat(-3.0)
+//	d6 := decimal.NewFromFloat(-6.0)
+//	res3, err := d5.PowWithPrecision(d6, 10)
+//	res3.String() // output: "0.0013717421"
+func (d Decimal) PowWithPrecision(d2 Decimal, precision int32) (Decimal, error) {
+	baseSign := d.Sign()
+	expSign := d2.Sign()
+
+	if baseSign == 0 {
+		if expSign == 0 {
+			return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
+		}
+		if expSign == 1 {
+			return Decimal{zeroInt, 0}, nil
+		}
+		if expSign == -1 {
+			return Decimal{}, fmt.Errorf("cannot represent infinity value of 0 ** y, where y < 0")
+		}
+	}
+
+	if expSign == 0 {
+		return Decimal{oneInt, 0}, nil
+	}
+
+	// TODO: optimize extraction of fractional part
+	one := Decimal{oneInt, 0}
+	expIntPart, expFracPart := d2.QuoRem(one, 0)
+
+	if baseSign == -1 && !expFracPart.IsZero() {
+		return Decimal{}, fmt.Errorf("cannot represent imaginary value of x ** y, where x < 0 and y is non-integer decimal")
+	}
+
+	intPartPow, _ := d.powBigIntWithPrecision(expIntPart.value, precision)
+
+	// if exponent is an integer we don't need to calculate d1**frac(d2)
+	if expFracPart.value.Sign() == 0 {
+		return intPartPow, nil
+	}
+
+	// TODO: optimize NumDigits for more performant precision adjustment
+	digitsBase := d.NumDigits()
+	digitsExponent := d2.NumDigits()
+
+	if int32(digitsBase) > precision {
+		precision = int32(digitsBase)
+	}
+	if int32(digitsExponent) > precision {
+		precision += int32(digitsExponent)
+	}
+	// increase precision by 10 to compensate for errors in further calculations
+	precision += 10
+
+	// Calculate x ** frac(y), where
+	// x ** frac(y) = exp(ln(x ** frac(y)) = exp(ln(x) * frac(y))
+	fracPartPow, err := d.Abs().Ln(precision)
+	if err != nil {
+		return Decimal{}, err
+	}
+
+	fracPartPow = fracPartPow.Mul(expFracPart)
+
+	fracPartPow, err = fracPartPow.ExpTaylor(precision)
+	if err != nil {
+		return Decimal{}, err
+	}
+
+	// Join integer and fractional part,
+	// base ** (expBase + expFrac) = base ** expBase * base ** expFrac
+	res := intPartPow.Mul(fracPartPow)
+
+	return res, nil
+}
+
+// PowInt32 returns d to the power of exp, where exp is int32.
+// Only returns error when d and exp is 0, thus result is undefined.
+//
+// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
+//
+// Example:
+//
+//	d1, err := decimal.NewFromFloat(4.0).PowInt32(4)
+//	d1.String() // output: "256"
+//
+//	d2, err := decimal.NewFromFloat(3.13).PowInt32(5)
+//	d2.String() // output: "300.4150512793"
+func (d Decimal) PowInt32(exp int32) (Decimal, error) {
+	if d.IsZero() && exp == 0 {
+		return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
+	}
+
+	isExpNeg := exp < 0
+	exp = abs(exp)
+
+	n, result := d, New(1, 0)
+
+	for exp > 0 {
+		if exp%2 == 1 {
+			result = result.Mul(n)
+		}
+		exp /= 2
+
+		if exp > 0 {
+			n = n.Mul(n)
+		}
+	}
+
+	if isExpNeg {
+		return New(1, 0).DivRound(result, int32(PowPrecisionNegativeExponent)), nil
+	}
+
+	return result, nil
+}
+
+// PowBigInt returns d to the power of exp, where exp is big.Int.
+// Only returns error when d and exp is 0, thus result is undefined.
+//
+// When exponent is negative the returned decimal will have maximum precision of PowPrecisionNegativeExponent places after decimal point.
+//
+// Example:
+//
+//	d1, err := decimal.NewFromFloat(3.0).PowBigInt(big.NewInt(3))
+//	d1.String() // output: "27"
+//
+//	d2, err := decimal.NewFromFloat(629.25).PowBigInt(big.NewInt(5))
+//	d2.String() // output: "98654323103449.5673828125"
+func (d Decimal) PowBigInt(exp *big.Int) (Decimal, error) {
+	return d.powBigIntWithPrecision(exp, int32(PowPrecisionNegativeExponent))
+}
+
+func (d Decimal) powBigIntWithPrecision(exp *big.Int, precision int32) (Decimal, error) {
+	if d.IsZero() && exp.Sign() == 0 {
+		return Decimal{}, fmt.Errorf("cannot represent undefined value of 0**0")
+	}
+
+	tmpExp := new(big.Int).Set(exp)
+	isExpNeg := exp.Sign() < 0
+
+	if isExpNeg {
+		tmpExp.Abs(tmpExp)
+	}
+
+	n, result := d, New(1, 0)
+
+	for tmpExp.Sign() > 0 {
+		if tmpExp.Bit(0) == 1 {
+			result = result.Mul(n)
+		}
+		tmpExp.Rsh(tmpExp, 1)
+
+		if tmpExp.Sign() > 0 {
+			n = n.Mul(n)
+		}
+	}
+
+	if isExpNeg {
+		return New(1, 0).DivRound(result, precision), nil
+	}
+
+	return result, nil
 }
 
 // ExpHullAbrham calculates the natural exponent of decimal (e to the power of d) using Hull-Abraham algorithm.
@@ -920,7 +1187,10 @@ func (d Decimal) Ln(precision int32) (Decimal, error) {
 		// Halley's Iteration.
 		// Calculating n-th term of formula: a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z),
 		// until the difference between current and next term is smaller than epsilon
-		for {
+		var prevStep Decimal
+		maxIters := calcPrecision*2 + 10
+
+		for i := int32(0); i < maxIters; i++ {
 			// exp(a_n)
 			comp3, _ = comp1.ExpTaylor(calcPrecision)
 			// exp(a_n) - z
@@ -934,9 +1204,17 @@ func (d Decimal) Ln(precision int32) (Decimal, error) {
 			// comp1 = a_(n+1) = a_n - 2 * (exp(a_n) - z) / (exp(a_n) + z)
 			comp1 = comp1.Sub(comp3)
 
+			if prevStep.Add(comp3).IsZero() {
+				// If iteration steps oscillate we should return early and prevent an infinity loop
+				// NOTE(mwoss): This should be quite a rare case, returning error is not necessary
+				break
+			}
+
 			if comp3.Abs().Cmp(epsilon) <= 0 {
 				break
 			}
+
+			prevStep = comp3
 		}
 	}
 
@@ -946,14 +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
 	}
-	return len(d.value.String())
+
+	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 estimatedNumDigits
 }
 
 // IsInteger returns true when decimal can be represented as an integer value, otherwise, it returns false.
@@ -1506,19 +1803,18 @@ func (d *Decimal) UnmarshalBinary(data []byte) error {
 
 // MarshalBinary implements the encoding.BinaryMarshaler interface.
 func (d Decimal) MarshalBinary() (data []byte, err error) {
-	// Write the exponent first since it's a fixed size
-	v1 := make([]byte, 4)
-	binary.BigEndian.PutUint32(v1, uint32(d.exp))
-
-	// Add the value
-	var v2 []byte
-	if v2, err = d.value.GobEncode(); err != nil {
-		return
+	// exp is written first, but encode value first to know output size
+	var valueData []byte
+	if valueData, err = d.value.GobEncode(); err != nil {
+		return nil, err
 	}
 
+	// Write the exponent in front, since it's a fixed size
+	expData := make([]byte, 4, len(valueData)+4)
+	binary.BigEndian.PutUint32(expData, uint32(d.exp))
+
 	// Return the byte array
-	data = append(v1, v2...)
-	return
+	return append(expData, valueData...), nil
 }
 
 // Scan implements the sql.Scanner interface for database deserialization.

decimal_bench_test.go

@@ -3,6 +3,7 @@ package decimal
 import (
 	"fmt"
 	"math"
+	"math/big"
 	"math/rand"
 	"sort"
 	"strconv"
@@ -120,6 +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++ {
@@ -131,7 +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))
 
@@ -142,7 +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))
 
@@ -153,7 +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)
 
@@ -164,7 +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)
 
@@ -185,6 +214,41 @@ func BenchmarkDecimal_IsInteger(b *testing.B) {
 	}
 }
 
+func BenchmarkDecimal_Pow(b *testing.B) {
+	d1 := RequireFromString("5.2")
+	d2 := RequireFromString("6.3")
+
+	for i := 0; i < b.N; i++ {
+		d1.Pow(d2)
+	}
+}
+
+func BenchmarkDecimal_PowWithPrecision(b *testing.B) {
+	d1 := RequireFromString("5.2")
+	d2 := RequireFromString("6.3")
+
+	for i := 0; i < b.N; i++ {
+		_, _ = d1.PowWithPrecision(d2, 8)
+	}
+}
+func BenchmarkDecimal_PowInt32(b *testing.B) {
+	d1 := RequireFromString("5.2")
+	d2 := int32(10)
+
+	for i := 0; i < b.N; i++ {
+		_, _ = d1.PowInt32(d2)
+	}
+}
+
+func BenchmarkDecimal_PowBigInt(b *testing.B) {
+	d1 := RequireFromString("5.2")
+	d2 := big.NewInt(10)
+
+	for i := 0; i < b.N; i++ {
+		_, _ = d1.PowBigInt(d2)
+	}
+}
+
 func BenchmarkDecimal_NewFromString(b *testing.B) {
 	count := 72
 	prices := make([]string, 0, count)

decimal_test.go

@@ -2621,21 +2621,241 @@ func TestDecimal_Cmp2(t *testing.T) {
 	}
 }
 
-func TestPow(t *testing.T) {
-	a := New(4, 0)
-	b := New(2, 0)
-	x := a.Pow(b)
-	if x.String() != "16" {
-		t.Errorf("Error, saw %s", x.String())
+func TestDecimal_Pow(t *testing.T) {
+	for _, testCase := range []struct {
+		Base     string
+		Exponent string
+		Expected string
+	}{
+		{"0.0", "1.0", "0.0"},
+		{"0.0", "5.7", "0.0"},
+		{"0.0", "-3.2", "0.0"},
+		{"3.13", "0.0", "1.0"},
+		{"-591.5", "0.0", "1.0"},
+		{"3.0", "3.0", "27.0"},
+		{"3.0", "10.0", "59049.0"},
+		{"3.13", "5.0", "300.4150512793"},
+		{"4.0", "2.0", "16.0"},
+		{"4.0", "-2.0", "0.0625"},
+		{"629.25", "5.0", "98654323103449.5673828125"},
+		{"5.0", "5.73", "10118.08037159375"},
+		{"962.0", "3.2791", "6055212360.0000044205714144"},
+		{"5.69169126", "5.18515912", "8242.26344757948412597909547972726268869189399260047793106028930864"},
+		{"13.1337", "3.5196719618391835", "8636.856220644773844815693636723928750940666269885"},
+		{"67762386.283696923", "4.85917691669163916681738", "112761146905370140621385730157437443321.91755738117317148674362233906499698561022574811238435007575701773212242750262081945556470501"},
+		{"-3.0", "6.0", "729"},
+		{"-13.757", "5.0", "-492740.983929899460557"},
+		{"3.0", "-6.0", "0.0013717421124829"},
+		{"13.757", "-5.0", "0.000002029463821"},
+		{"66.12", "-7.61313", "0.000000000000013854086588876805036"},
+		{"6696871.12", "-2.61313", "0.000000000000000001455988684546983"},
+		{"-3.0", "-6.0", "0.0013717421124829"},
+		{"-13.757", "-5.0", "-0.000002029463821"},
+	} {
+		base, _ := NewFromString(testCase.Base)
+		exp, _ := NewFromString(testCase.Exponent)
+		expected, _ := NewFromString(testCase.Expected)
+
+		result := base.Pow(exp)
+
+		if result.Cmp(expected) != 0 {
+			t.Errorf("expected %s, got %s, for %s^%s", testCase.Expected, result.String(), testCase.Base, testCase.Exponent)
+		}
 	}
 }
 
-func TestNegativePow(t *testing.T) {
-	a := New(4, 0)
-	b := New(-2, 0)
-	x := a.Pow(b)
-	if x.String() != "0.0625" {
-		t.Errorf("Error, saw %s", x.String())
+func TestDecimal_PowWithPrecision(t *testing.T) {
+	for _, testCase := range []struct {
+		Base      string
+		Exponent  string
+		Precision int32
+		Expected  string
+	}{
+		{"0.0", "1.0", 2, "0.0"},
+		{"0.0", "5.7", 2, "0.0"},
+		{"0.0", "-3.2", 2, "0.0"},
+		{"3.13", "0.0", 2, "1.0"},
+		{"-591.5", "0.0", 2, "1.0"},
+		{"3.0", "3.0", 2, "27.0"},
+		{"3.0", "10.0", 2, "59049.0"},
+		{"3.13", "5.0", 5, "300.4150512793"},
+		{"4.0", "2.0", 2, "16.0"},
+		{"4.0", "-2.0", 2, "0.06"},
+		{"4.0", "-2.0", 4, "0.0625"},
+		{"629.25", "5.0", 6, "98654323103449.5673828125"},
+		{"5.0", "5.73", 20, "10118.080371595019317118681359884375"},
+		{"962.0", "3.2791", 15, "6055212360.000004406551603058195732"},
+		{"5.69169126", "5.18515912", 4, "8242.26344757948412587366859330429895955552280978668983459852256"},
+		{"13.1337", "3.5196719618391835", 8, "8636.85622064477384481569363672392591908386390769375"},
+		{"67762386.283696923", "4.85917691669163916681738", 10, "112761146905370140621385730157437443321.917557381173174638304347353880676293576708009282115993465286373470882947470198597518762"},
+		{"-3.0", "6.0", 2, "729"},
+		{"-13.757", "5.0", 4, "-492740.983929899460557"},
+		{"3.0", "-6.0", 10, "0.0013717421"},
+		{"13.757", "-5.0", 20, "0.00000202946382098037"},
+		{"66.12", "-7.61313", 20, "0.00000000000001385381563049821591633907104023700216"},
+		{"6696871.12", "-2.61313", 24, "0.0000000000000000014558252733872790626400278983397459207418"},
+		{"-3.0", "-6.0", 8, "0.00137174"},
+		{"-13.757", "-5.0", 16, "-0.000002029463821"},
+	} {
+		base, _ := NewFromString(testCase.Base)
+		exp, _ := NewFromString(testCase.Exponent)
+		expected, _ := NewFromString(testCase.Expected)
+
+		result, _ := base.PowWithPrecision(exp, testCase.Precision)
+
+		if result.Cmp(expected) != 0 {
+			t.Errorf("expected %s, got %s, for %s^%s", testCase.Expected, result.String(), testCase.Base, testCase.Exponent)
+		}
+	}
+}
+
+func TestDecimal_PowWithPrecision_Infinity(t *testing.T) {
+	for _, testCase := range []struct {
+		Base     string
+		Exponent string
+	}{
+		{"0.0", "0.0"},
+		{"0.0", "-2.0"},
+		{"0.0", "-4.6"},
+		{"-66.12", "7.61313"},      // Imaginary value
+		{"-5696871.12", "5.61313"}, // Imaginary value
+	} {
+		base, _ := NewFromString(testCase.Base)
+		exp, _ := NewFromString(testCase.Exponent)
+
+		_, err := base.PowWithPrecision(exp, 5)
+
+		if err == nil {
+			t.Errorf("lool it should be error")
+		}
+	}
+}
+
+func TestDecimal_PowWithPrecision_UndefinedResult(t *testing.T) {
+	base := RequireFromString("0")
+	exponent := RequireFromString("0")
+
+	_, err := base.PowWithPrecision(exponent, 4)
+
+	if err == nil {
+		t.Errorf("expected error, cannot be represent undefined value of 0**0")
+	}
+}
+
+func TestDecimal_PowWithPrecision_InfinityResult(t *testing.T) {
+	for _, testCase := range []struct {
+		Base     string
+		Exponent string
+	}{
+		{"0.0", "-2.0"},
+		{"0.0", "-4.6"},
+		{"0.0", "-9239.671333"},
+	} {
+		base, _ := NewFromString(testCase.Base)
+		exp, _ := NewFromString(testCase.Exponent)
+
+		_, err := base.PowWithPrecision(exp, 4)
+
+		if err == nil {
+			t.Errorf("expected error, cannot represent infinity value of 0 ** y, where y < 0")
+		}
+	}
+}
+
+func TestDecimal_PowWithPrecision_ImaginaryResult(t *testing.T) {
+	for _, testCase := range []struct {
+		Base     string
+		Exponent string
+	}{
+		{"-0.2261", "106.12"},
+		{"-66.12", "7.61313"},
+		{"-5696871.12", "5.61313"},
+	} {
+		base, _ := NewFromString(testCase.Base)
+		exp, _ := NewFromString(testCase.Exponent)
+
+		_, err := base.PowWithPrecision(exp, 4)
+
+		if err == nil {
+			t.Errorf("expected error, cannot represent imaginary value of x ** y, where x < 0 and y is non-integer decimal")
+		}
+	}
+}
+
+func TestDecimal_PowInt32(t *testing.T) {
+	for _, testCase := range []struct {
+		Decimal  string
+		Exponent int32
+		Expected string
+	}{
+		{"0.0", 1, "0.0"},
+		{"3.13", 0, "1.0"},
+		{"-591.5", 0, "1.0"},
+		{"3.0", 3, "27.0"},
+		{"3.0", 10, "59049.0"},
+		{"3.13", 5, "300.4150512793"},
+		{"629.25", 5, "98654323103449.5673828125"},
+		{"-3.0", 6, "729"},
+		{"-13.757", 5, "-492740.983929899460557"},
+		{"3.0", -6, "0.0013717421124829"},
+		{"-13.757", -5, "-0.000002029463821"},
+	} {
+		base, _ := NewFromString(testCase.Decimal)
+		expected, _ := NewFromString(testCase.Expected)
+
+		result, _ := base.PowInt32(testCase.Exponent)
+
+		if result.Cmp(expected) != 0 {
+			t.Errorf("expected %s, got %s, for %s**%d", testCase.Expected, result.String(), testCase.Decimal, testCase.Exponent)
+		}
+	}
+}
+
+func TestDecimal_PowInt32_UndefinedResult(t *testing.T) {
+	base := RequireFromString("0")
+
+	_, err := base.PowInt32(0)
+
+	if err == nil {
+		t.Errorf("expected error, cannot be represent undefined value of 0**0")
+	}
+}
+
+func TestDecimal_PowBigInt(t *testing.T) {
+	for _, testCase := range []struct {
+		Decimal  string
+		Exponent *big.Int
+		Expected string
+	}{
+		{"3.13", big.NewInt(0), "1.0"},
+		{"-591.5", big.NewInt(0), "1.0"},
+		{"3.0", big.NewInt(3), "27.0"},
+		{"3.0", big.NewInt(10), "59049.0"},
+		{"3.13", big.NewInt(5), "300.4150512793"},
+		{"629.25", big.NewInt(5), "98654323103449.5673828125"},
+		{"-3.0", big.NewInt(6), "729"},
+		{"-13.757", big.NewInt(5), "-492740.983929899460557"},
+		{"3.0", big.NewInt(-6), "0.0013717421124829"},
+		{"-13.757", big.NewInt(-5), "-0.000002029463821"},
+	} {
+		base, _ := NewFromString(testCase.Decimal)
+		expected, _ := NewFromString(testCase.Expected)
+
+		result, _ := base.PowBigInt(testCase.Exponent)
+
+		if result.Cmp(expected) != 0 {
+			t.Errorf("expected %s, got %s, for %s**%d", testCase.Expected, result.String(), testCase.Decimal, testCase.Exponent)
+		}
+	}
+}
+
+func TestDecimal_PowBigInt_UndefinedResult(t *testing.T) {
+	base := RequireFromString("0")
+
+	_, err := base.PowBigInt(big.NewInt(0))
+
+	if err == nil {
+		t.Errorf("expected error, undefined value of 0**0 cannot be represented")
 	}
 }
 
@@ -2822,6 +3042,7 @@ func TestDecimal_Ln(t *testing.T) {
 		{"839101.0351094726488848490572028502", 50, "13.64008640145229044389152437468283605382056561604272"},
 		{"5023583755703750094849.03519358513093500275017501750602739169823", 25, "49.9684305274348922267409953"},
 		{"5023583755703750094849.03519358513093500275017501750602739169823", -1, "50.0"},
+		{"66.12", 18, "4.191471272952823429"},
 	} {
 		d, _ := NewFromString(testCase.Dec)
 		expected, _ := NewFromString(testCase.Expected)