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cherry-pick #7140: Fix ApproxRoot Infinite Looping #7199

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Aug 31, 2020
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cherry-pick #7140: Fix ApproxRoot Infinite Looping #7199

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1 change: 1 addition & 0 deletions CHANGELOG.md
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Expand Up @@ -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]
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9 changes: 7 additions & 2 deletions types/decimal.go
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Expand Up @@ -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 (
Expand Down Expand Up @@ -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 {
Expand Down Expand Up @@ -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()
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21 changes: 14 additions & 7 deletions types/decimal_test.go
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Expand Up @@ -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)
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