Added nth root function to sdk.Decimal type

CHANGELOG.md

@@ -174,6 +174,8 @@ that allows for arbitrary vesting periods.
     * Introduces cli commands and rest routes to query historical information at a given height
 * (modules) [\#5249](https://github.com/cosmos/cosmos-sdk/pull/5249) Funds are now allowed to be directly sent to the community pool (via the distribution module account).
 * (keys) [\#4941](https://github.com/cosmos/cosmos-sdk/issues/4941) Introduce keybase option to allow overriding the default private key implementation of a key generated through the `keys add` cli command.
+* (types) [\#5447](https://github.com/cosmos/cosmos-sdk/pull/5447) Added `ApproxRoot` function to sdk.Decimal type in order to get the nth root for a decimal number, where n is a positive integer.
+  * An `ApproxSqrt` function was also added for convenience around the common case of n=2.
 
 ### Improvements
 

types/decimal.go

@@ -269,7 +269,6 @@ func (d Dec) MulInt64(i int64) Dec {
 
 // quotient
 func (d Dec) Quo(d2 Dec) Dec {
-
 	// multiply precision twice
 	mul := new(big.Int).Mul(d.Int, precisionReuse)
 	mul.Mul(mul, precisionReuse)
@@ -326,30 +325,74 @@ func (d Dec) QuoInt64(i int64) Dec {
 	return Dec{mul}
 }
 
-// ApproxSqrt returns an approximate sqrt estimation using Newton's method to
-// compute square roots x=√d for d > 0. The algorithm starts with some guess and
+// ApproxRoot returns an approximate estimation of a Dec's positive real nth root
+// using Newton's method (where n is positive). The algorithm starts with some guess and
 // computes the sequence of improved guesses until an answer converges to an
-// approximate answer. It returns -(sqrt(abs(d)) if input is negative.
-func (d Dec) ApproxSqrt() Dec {
+// approximate answer.  It returns `|d|.ApproxRoot() * -1` if input is negative.
+func (d Dec) ApproxRoot(root uint64) (guess Dec, err error) {
+	defer func() {
+		if r := recover(); r != nil {
+			var ok bool
+			err, ok = r.(error)
+			if !ok {
+				err = errors.New("out of bounds")
+			}
+		}
+	}()
+
 	if d.IsNegative() {
-		return d.MulInt64(-1).ApproxSqrt().MulInt64(-1)
+		absRoot, err := d.MulInt64(-1).ApproxRoot(root)
+		return absRoot.MulInt64(-1), err
+	}
+
+	if root == 1 || d.IsZero() || d.Equal(OneDec()) {
+		return d, nil
+	}
+
+	if root == 0 {
+		return OneDec(), nil
 	}
 
-	if d.IsZero() {
-		return ZeroDec()
+	rootInt := NewIntFromUint64(root)
+	guess, delta := OneDec(), OneDec()
+
+	for delta.Abs().GT(SmallestDec()) {
+		prev := guess.Power(root - 1)
+		if prev.IsZero() {
+			prev = SmallestDec()
+		}
+		delta = d.Quo(prev)
+		delta = delta.Sub(guess)
+		delta = delta.QuoInt(rootInt)
+
+		guess = guess.Add(delta)
 	}
 
-	z := OneDec()
-	// first guess
-	z = z.Sub((z.Mul(z).Sub(d)).Quo(z.MulInt64(2)))
+	return guess, nil
+}
 
-	// iterate until change is very small
-	for zNew, delta := z, z; delta.GT(SmallestDec()); z = zNew {
-		zNew = zNew.Sub((zNew.Mul(zNew).Sub(d)).Quo(zNew.MulInt64(2)))
-		delta = z.Sub(zNew)
+// Power returns a the result of raising to a positive integer power
+func (d Dec) Power(power uint64) Dec {
+	if power == 0 {
+		return OneDec()
 	}
+	tmp := OneDec()
+	for i := power; i > 1; {
+		if i%2 == 0 {
+			i /= 2
+		} else {
+			tmp = tmp.Mul(d)
+			i = (i - 1) / 2
+		}
+		d = d.Mul(d)
+	}
+	return d.Mul(tmp)
+}
 
-	return z
+// ApproxSqrt is a wrapper around ApproxRoot for the common special case
+// of finding the square root of a number. It returns -(sqrt(abs(d)) if input is negative.
+func (d Dec) ApproxSqrt() (Dec, error) {
+	return d.ApproxRoot(2)
 }
 
 // is integer, e.g. decimals are zero

types/decimal_test.go

@@ -425,6 +425,48 @@ func TestDecCeil(t *testing.T) {
 	}
 }
 
+func TestPower(t *testing.T) {
+	testCases := []struct {
+		input    Dec
+		power    uint64
+		expected Dec
+	}{
+		{OneDec(), 10, OneDec()},                                               // 1.0 ^ (10) => 1.0
+		{NewDecWithPrec(5, 1), 2, NewDecWithPrec(25, 2)},                       // 0.5 ^ 2 => 0.25
+		{NewDecWithPrec(2, 1), 2, NewDecWithPrec(4, 2)},                        // 0.2 ^ 2 => 0.04
+		{NewDecFromInt(NewInt(3)), 3, NewDecFromInt(NewInt(27))},               // 3 ^ 3 => 27
+		{NewDecFromInt(NewInt(-3)), 4, NewDecFromInt(NewInt(81))},              // -3 ^ 4 = 81
+		{NewDecWithPrec(1414213562373095049, 18), 2, NewDecFromInt(NewInt(2))}, // 1.414213562373095049 ^ 2 = 2
+	}
+
+	for i, tc := range testCases {
+		res := tc.input.Power(tc.power)
+		require.True(t, tc.expected.Sub(res).Abs().LTE(SmallestDec()), "unexpected result for test case %d, input: %v", i, tc.input)
+	}
+}
+
+func TestApproxRoot(t *testing.T) {
+	testCases := []struct {
+		input    Dec
+		root     uint64
+		expected Dec
+	}{
+		{OneDec(), 10, OneDec()},                                               // 1.0 ^ (0.1) => 1.0
+		{NewDecWithPrec(25, 2), 2, NewDecWithPrec(5, 1)},                       // 0.25 ^ (0.5) => 0.5
+		{NewDecWithPrec(4, 2), 2, NewDecWithPrec(2, 1)},                        // 0.04 => 0.2
+		{NewDecFromInt(NewInt(27)), 3, NewDecFromInt(NewInt(3))},               // 27 ^ (1/3) => 3
+		{NewDecFromInt(NewInt(-81)), 4, NewDecFromInt(NewInt(-3))},             // -81 ^ (0.25) => -3
+		{NewDecFromInt(NewInt(2)), 2, NewDecWithPrec(1414213562373095049, 18)}, // 2 ^ (0.5) => 1.414213562373095049
+		{NewDecWithPrec(1005, 3), 31536000, MustNewDecFromStr("1.000000000158153904")},
+	}
+
+	for i, tc := range testCases {
+		res, err := tc.input.ApproxRoot(tc.root)
+		require.NoError(t, err)
+		require.True(t, tc.expected.Sub(res).Abs().LTE(SmallestDec()), "unexpected result for test case %d, input: %v", i, tc.input)
+	}
+}
+
 func TestApproxSqrt(t *testing.T) {
 	testCases := []struct {
 		input    Dec
@@ -439,7 +481,8 @@ func TestApproxSqrt(t *testing.T) {
 	}
 
 	for i, tc := range testCases {
-		res := tc.input.ApproxSqrt()
+		res, err := tc.input.ApproxSqrt()
+		require.NoError(t, err)
 		require.Equal(t, tc.expected, res, "unexpected result for test case %d, input: %v", i, tc.input)
 	}
 }

types/int.go

@@ -114,6 +114,13 @@ func NewInt(n int64) Int {
 	return Int{big.NewInt(n)}
 }
 
+// NewIntFromUint64 constructs an Int from a uint64.
+func NewIntFromUint64(n uint64) Int {
+	b := big.NewInt(0)
+	b.SetUint64(n)
+	return Int{b}
+}
+
 // NewIntFromBigInt constructs Int from big.Int
 func NewIntFromBigInt(i *big.Int) Int {
 	if i.BitLen() > maxBitLen {
@@ -178,6 +185,20 @@ func (i Int) IsInt64() bool {
 	return i.i.IsInt64()
 }
 
+// Uint64 converts Int to uint64
+// Panics if the value is out of range
+func (i Int) Uint64() uint64 {
+	if !i.i.IsUint64() {
+		panic("Uint64() out of bounds")
+	}
+	return i.i.Uint64()
+}
+
+// IsUint64 returns true if Uint64() not panics
+func (i Int) IsUint64() bool {
+	return i.i.IsUint64()
+}
+
 // IsZero returns true if Int is zero
 func (i Int) IsZero() bool {
 	return i.i.Sign() == 0

types/int_test.go

@@ -16,6 +16,14 @@ func TestFromInt64(t *testing.T) {
 	}
 }
 
+func TestFromUint64(t *testing.T) {
+	for n := 0; n < 20; n++ {
+		r := rand.Uint64()
+		require.True(t, NewIntFromUint64(r).IsUint64())
+		require.Equal(t, r, NewIntFromUint64(r).Uint64())
+	}
+}
+
 func TestIntPanic(t *testing.T) {
 	// Max Int = 2^255-1 = 5.789e+76
 	// Min Int = -(2^255-1) = -5.789e+76