Fix ApproxRoot Infinite Looping (#7140)

Added a maximum number of iterations (100) to ApproxRoot
(and ApproxSqrt) to serve as a hard limit on the number of
iterations that the algorithm performs. If the answer converges
before the maximum iterations, it returns immediately. Otherwise,
if the answer never converges enough to satisfy the primary loop
condition, the looping stops after a hundred iterations.

Closes: #7038

CHANGELOG.md

@@ -39,6 +39,7 @@ Ref: https://keepachangelog.com/en/1.0.0/
 
 ### Bug Fixes
 
+* (types) [\#7038](https://github.com/cosmos/cosmos-sdk/issues/7038) Fix infinite looping of `ApproxRoot` by including a hard-coded maximum iterations limit of 100.
 * (types) [\#7084](https://github.com/cosmos/cosmos-sdk/pull/7084) Fix panic when calling `BigInt()` on an uninitialized `Int`.
 
 ## [v0.39.1]

types/decimal.go

@@ -16,13 +16,16 @@ type Dec struct {
 	*big.Int `json:"int"`
 }
 
-// number of decimal places
 const (
+	// number of decimal places
 	Precision = 18
 
 	// bytes required to represent the above precision
 	// Ceiling[Log2[999 999 999 999 999 999]]
 	DecimalPrecisionBits = 60
+
+	// max number of iterations in ApproxRoot function
+	maxApproxRootIterations = 100
 )
 
 var (
@@ -339,6 +342,8 @@ func (d Dec) QuoInt64(i int64) Dec {
 // 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 `|d|.ApproxRoot() * -1` if input is negative.
+// A maximum number of 100 iterations is used a backup boundary condition for
+// cases where the answer never converges enough to satisfy the main condition.
 func (d Dec) ApproxRoot(root uint64) (guess Dec, err error) {
 	defer func() {
 		if r := recover(); r != nil {
@@ -366,7 +371,7 @@ func (d Dec) ApproxRoot(root uint64) (guess Dec, err error) {
 	rootInt := NewIntFromUint64(root)
 	guess, delta := OneDec(), OneDec()
 
-	for delta.Abs().GT(SmallestDec()) {
+	for iter := 0; delta.Abs().GT(SmallestDec()) && iter < maxApproxRootIterations; iter++ {
 		prev := guess.Power(root - 1)
 		if prev.IsZero() {
 			prev = SmallestDec()

types/decimal_test.go

@@ -451,15 +451,22 @@ func TestApproxRoot(t *testing.T) {
 		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")},
+		{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 ^ (0.5) => 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")}, // 1.005 ^ (1/31536000) ≈ 1.00000000016
+		{SmallestDec(), 2, NewDecWithPrec(1, 9)},                                       // 1e-18 ^ (0.5) => 1e-9
+		{SmallestDec(), 3, MustNewDecFromStr("0.000000999999999997")},                  // 1e-18 ^ (1/3) => 1e-6
+		{NewDecWithPrec(1, 8), 3, MustNewDecFromStr("0.002154434690031900")},           // 1e-8 ^ (1/3) ≈ 0.00215443469
 	}
 
+	// In the case of 1e-8 ^ (1/3), the result repeats every 5 iterations starting from iteration 24
+	// (i.e. 24, 29, 34, ... give the same result) and never converges enough. The maximum number of
+	// iterations (100) causes the result at iteration 100 to be returned, regardless of convergence.
+
 	for i, tc := range testCases {
 		res, err := tc.input.ApproxRoot(tc.root)
 		require.NoError(t, err)