feat(osmomath): Power with decimal exponent (#3731)

* feat(osmomath): exp2 function * export exp2 * changelog * refactor ErrTolerance to use Dec instead of Int for additive tolerance * Update osmomath/exp2.go * Update osmomath/exp2.go * Update osmomath/exp2.go * Update osmomath/exp2_test.go * Update osmomath/exp2_test.go * feat(osmomath): Power and PowerMut with decimal exponent * changelog * merge conflict * clean up * remove `PowerMut` * update spec about error bound * Update CHANGELOG.md * Update CHANGELOG.md Co-authored-by: Dev Ojha <[email protected]> Co-authored-by: Dev Ojha <[email protected]>
osmosis-labs · Dec 21, 2022 · c52d5b2 · c52d5b2
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diff --git a/CHANGELOG.md b/CHANGELOG.md
@@ -51,6 +51,7 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 * [#3678](https://github.com/osmosis-labs/osmosis/pull/3678) implement mutative `PowerIntegerMut` function on `osmomath.BigDec`.
 * [#3708](https://github.com/osmosis-labs/osmosis/pull/3708) `Exp2` function to compute 2^decimal.
 * [#3693](https://github.com/osmosis-labs/osmosis/pull/3693) Add `EstimateSwapExactAmountOut` query to stargate whitelist
+* [#3731](https://github.com/osmosis-labs/osmosis/pull/3731) BigDec Power functions with decimal exponent.
 
 ### API breaks
 

diff --git a/osmomath/decimal.go b/osmomath/decimal.go
@@ -997,3 +997,39 @@ func (d BigDec) PowerIntegerMut(power uint64) BigDec {
 
 	return d.MulMut(tmp)
 }
+
+// Power returns a result of raising the given big dec to
+// a positive decimal power. Panics if the power is negative.
+// Panics if the base is negative. Does not mutate the receiver.
+// The max supported exponent is defined by the global maxSupportedExponent.
+// If a greater exponent is given, the function panics.
+// The error is not bounded but expected to be around 10^-18, use with care.
+// See the underlying Exp2, LogBase2 and Mul for the details of their bounds.
+func (d BigDec) Power(power BigDec) BigDec {
+	if d.IsNegative() {
+		panic(fmt.Sprintf("negative base is not supported for Power(), base was (%s)", d))
+	}
+	if power.IsNegative() {
+		panic(fmt.Sprintf("negative power is not supported for Power(), power was (%s)", power))
+	}
+	if power.Abs().GT(maxSupportedExponent) {
+		panic(fmt.Sprintf("integer exponent %s is too large, max (%s)", power, maxSupportedExponent))
+	}
+	if power.IsInteger() {
+		return d.PowerInteger(power.TruncateInt().Uint64())
+	}
+	if power.IsZero() {
+		return OneDec()
+	}
+	if d.IsZero() {
+		return ZeroDec()
+	}
+	if d.Equal(twoBigDec) {
+		return Exp2(power)
+	}
+
+	// d^power = exp2(power * log_2{base})
+	result := Exp2(d.LogBase2().Mul(power))
+
+	return result
+}
diff --git a/osmomath/decimal_test.go b/osmomath/decimal_test.go
@@ -12,6 +12,7 @@ import (
 	"github.com/stretchr/testify/suite"
 	"gopkg.in/yaml.v2"
 
+	"github.com/osmosis-labs/osmosis/v13/app/apptesting/osmoassert"
 	"github.com/osmosis-labs/osmosis/v13/osmomath"
 	gammtypes "github.com/osmosis-labs/osmosis/v13/x/gamm/types"
 )
@@ -20,6 +21,12 @@ type decimalTestSuite struct {
 	suite.Suite
 }
 
+var (
+	zeroAdditiveErrTolerance = osmomath.ErrTolerance{
+		AdditiveTolerance: sdk.ZeroDec(),
+	}
+)
+
 func TestDecimalTestSuite(t *testing.T) {
 	suite.Run(t, new(decimalTestSuite))
 }
@@ -1144,9 +1151,18 @@ func (s *decimalTestSuite) TestPowerInteger() {
 				tolerance = tc.expectedToleranceOverwrite
 			}
 
+			// Main system under test
 			actualResult := tc.base.PowerInteger(tc.exponent)
 			require.True(osmomath.DecApproxEq(s.T(), tc.expectedResult, actualResult, tolerance))
 
+			// Secondary system under test.
+			// To reduce boilerplate from the same test cases when exponent is a
+			// positive integer, we also test Power().
+			// Negative exponent and base are not supported for Power()
+			if tc.exponent >= 0 && !tc.base.IsNegative() {
+				actualResult2 := tc.base.Power(osmomath.NewDecFromInt(osmomath.NewIntFromUint64(tc.exponent)))
+				require.True(osmomath.DecApproxEq(s.T(), tc.expectedResult, actualResult2, tolerance))
+			}
 		})
 	}
 }
@@ -1219,7 +1235,7 @@ func (s *decimalTestSuite) TestMul_Mutation() {
 	}
 }
 
-// TestMul_Mutation tests that PowerIntegerMut mutates the receiver
+// TestPowerInteger_Mutation tests that PowerIntegerMut mutates the receiver
 // while PowerInteger is not.
 func (s *decimalTestSuite) TestPowerInteger_Mutation() {
 
@@ -1260,3 +1276,114 @@ func (s *decimalTestSuite) TestPowerInteger_Mutation() {
 		})
 	}
 }
+
+func (s *decimalTestSuite) TestPower() {
+	tests := map[string]struct {
+		base           osmomath.BigDec
+		exponent       osmomath.BigDec
+		expectedResult osmomath.BigDec
+		expectPanic    bool
+		errTolerance   osmomath.ErrTolerance
+	}{
+		// N.B.: integer exponents are tested under TestPowerInteger.
+
+		"3 ^ 2 = 9 (integer base and integer exponent)": {
+			base:     osmomath.NewBigDec(3),
+			exponent: osmomath.NewBigDec(2),
+
+			expectedResult: osmomath.NewBigDec(9),
+
+			errTolerance: zeroAdditiveErrTolerance,
+		},
+		"2^0.5 (base of 2 and non-integer exponent)": {
+			base:     osmomath.MustNewDecFromStr("2"),
+			exponent: osmomath.MustNewDecFromStr("0.5"),
+
+			// https://www.wolframalpha.com/input?i=2%5E0.5+37+digits
+			expectedResult: osmomath.MustNewDecFromStr("1.414213562373095048801688724209698079"),
+
+			errTolerance: osmomath.ErrTolerance{
+				AdditiveTolerance: minDecTolerance,
+				RoundingDir:       osmomath.RoundDown,
+			},
+		},
+		"3^0.33 (integer base other than 2 and non-integer exponent)": {
+			base:     osmomath.MustNewDecFromStr("3"),
+			exponent: osmomath.MustNewDecFromStr("0.33"),
+
+			// https://www.wolframalpha.com/input?i=3%5E0.33+37+digits
+			expectedResult: osmomath.MustNewDecFromStr("1.436977652184851654252692986409357265"),
+
+			errTolerance: osmomath.ErrTolerance{
+				AdditiveTolerance: minDecTolerance,
+				RoundingDir:       osmomath.RoundDown,
+			},
+		},
+		"e^0.98999 (non-integer base and non-integer exponent)": {
+			base:     osmomath.EulersNumber,
+			exponent: osmomath.MustNewDecFromStr("0.9899"),
+
+			// https://www.wolframalpha.com/input?i=e%5E0.9899+37+digits
+			expectedResult: osmomath.MustNewDecFromStr("2.690965362357751196751808686902156603"),
+
+			errTolerance: osmomath.ErrTolerance{
+				AdditiveTolerance: minDecTolerance,
+				RoundingDir:       osmomath.RoundUnconstrained,
+			},
+		},
+		"10^0.001 (small non-integer exponent)": {
+			base:     osmomath.NewBigDec(10),
+			exponent: osmomath.MustNewDecFromStr("0.001"),
+
+			// https://www.wolframalpha.com/input?i=10%5E0.001+37+digits
+			expectedResult: osmomath.MustNewDecFromStr("1.002305238077899671915404889328110554"),
+
+			errTolerance: osmomath.ErrTolerance{
+				AdditiveTolerance: minDecTolerance,
+				RoundingDir:       osmomath.RoundUnconstrained,
+			},
+		},
+		"13^100.7777 (large non-integer exponent)": {
+			base:     osmomath.NewBigDec(13),
+			exponent: osmomath.MustNewDecFromStr("100.7777"),
+
+			// https://www.wolframalpha.com/input?i=13%5E100.7777+37+digits
+			expectedResult: osmomath.MustNewDecFromStr("1.822422110233759706998600329118969132").Mul(osmomath.NewBigDec(10).PowerInteger(112)),
+
+			errTolerance: osmomath.ErrTolerance{
+				MultiplicativeTolerance: minDecTolerance,
+				RoundingDir:             osmomath.RoundDown,
+			},
+		},
+		"large non-integer exponent with large non-integer base - panics": {
+			base:     osmomath.MustNewDecFromStr("169.137"),
+			exponent: osmomath.MustNewDecFromStr("100.7777"),
+
+			expectPanic: true,
+		},
+		"negative base - panic": {
+			base:     osmomath.NewBigDec(-3),
+			exponent: osmomath.MustNewDecFromStr("4"),
+
+			expectPanic: true,
+		},
+		"negative exponent - panic": {
+			base:     osmomath.NewBigDec(1),
+			exponent: osmomath.MustNewDecFromStr("-4"),
+
+			expectPanic: true,
+		},
+	}
+
+	for name, tc := range tests {
+		tc := tc
+		s.Run(name, func() {
+			osmoassert.ConditionalPanic(s.T(), tc.expectPanic, func() {
+
+				actualResult := tc.base.Power(tc.exponent)
+
+				s.Require().Equal(0, tc.errTolerance.CompareBigDec(tc.expectedResult, actualResult))
+			})
+		})
+	}
+}