fix(math): revert to correct version of ApproxRoot from a former state breaking change (#17725)

math/CHANGELOG.md

@@ -34,6 +34,12 @@ Ref: https://github.com/commitizen/conventional-commit-types/blob/v3.0.0/index.j
 
 # Changelog
 
+## [Unreleased]
+
+### Bug Fixes
+
+* [#17725](https://github.com/cosmos/cosmos-sdk/pull/17725) Fix state break in ApproxRoot. This has been present since math/v1.0.1. It changed the rounding behavior at precision end in an intermediary division from banker's to truncation. The truncation occurs from binary right shift in the case of square roots. The change is now reverted back to banker's rounding universally for any root.
+
 ## [math/v1.1.2](https://github.com/cosmos/cosmos-sdk/releases/tag/math/v1.1.2) - 2023-08-21
 
 ### Bug Fixes

math/dec.go

@@ -42,6 +42,7 @@ var (
 	zeroInt              = big.NewInt(0)
 	oneInt               = big.NewInt(1)
 	tenInt               = big.NewInt(10)
+	smallestDec          = LegacySmallestDec()
 )
 
 // Decimal errors
@@ -470,27 +471,15 @@ func (d LegacyDec) ApproxRoot(root uint64) (guess LegacyDec, err error) {
 	}
 
 	guess, delta := scratchOneDec, LegacyOneDec()
-	smallestDec := LegacySmallestDec()
 
-	for iter := 0; delta.AbsMut().GT(smallestDec) && iter < maxApproxRootIterations; iter++ {
-		// Set prev = guess^{root - 1}, with an optimization for sqrt
-		// where root=2 => prev = guess. (And thus no extra heap allocations)
-		prev := guess
-		if root != 2 {
-			prev = guess.Power(root - 1)
-		}
+	for iter := 0; iter < maxApproxRootIterations && delta.Abs().GT(smallestDec); iter++ {
+		prev := guess.Power(root - 1)
 		if prev.IsZero() {
 			prev = smallestDec
 		}
 		delta.Set(d).QuoMut(prev)
 		delta.SubMut(guess)
-		// delta = delta / root.
-		// We optimize for sqrt, where root=2 => delta = delta >> 1
-		if root == 2 {
-			delta.i.Rsh(delta.i, 1)
-		} else {
-			delta.QuoInt64Mut(int64(root))
-		}
+		delta.QuoInt64Mut(int64(root))
 
 		guess.AddMut(delta)
 	}

math/dec_test.go

@@ -480,6 +480,7 @@ func (s *decimalTestSuite) TestApproxSqrt() {
 			math.LegacyNewDec(2).Power(127).Sub(math.LegacyOneDec()),
 			math.LegacyMustNewDecFromStr("13043817825332782212.349571806252508369"),
 		},
+		{math.LegacyMustNewDecFromStr("1.000000011823380862"), math.LegacyMustNewDecFromStr("1.000000005911690414")},
 	}
 
 	for i, tc := range testCases {