osmomath things

osmomath/decimal.go

@@ -972,3 +972,22 @@ func (x BigDec) CustomBaseLog(base BigDec) BigDec {
 
 	return y
 }
+
+// TODO: spec and tests - taken from sdk.
+func (d BigDec) PowerMut(power uint64) BigDec {
+	// TODO: use mutable functions here
+	if power == 0 {
+		return OneDec()
+	}
+	tmp := OneDec()
+
+	for i := power; i > 1; {
+		if i%2 != 0 {
+			tmp = tmp.Mul(d)
+		}
+		i /= 2
+		d = d.Mul(d)
+	}
+
+	return d.Mul(tmp)
+}

osmomath/math.go

@@ -18,6 +18,9 @@ var (
 	one_half sdk.Dec = sdk.MustNewDecFromStr("0.5")
 	one      sdk.Dec = sdk.OneDec()
 	two      sdk.Dec = sdk.MustNewDecFromStr("2")
+
+	// https://www.wolframalpha.com/input?i=2.718281828459045235360287471352662498&assumption=%22ClashPrefs%22+-%3E+%7B%22Math%22%7D
+	eulersNumber = MustNewDecFromStr("2.718281828459045235360287471352662498")
 )
 
 // Returns the internal "power precision".
@@ -171,3 +174,31 @@ func PowApprox(base sdk.Dec, exp sdk.Dec, precision sdk.Dec) sdk.Dec {
 	}
 	return sum
 }
+
+// TODO: spec
+func Exp(exponent BigDec) BigDec {
+
+	// let exponent = i + f where i is the integer part and f is the fractional part.
+	// then e^exponent = e^i * e^f
+
+	integer := exponent.TruncateDec()
+	fractional := exponent.Sub(integer)
+
+	integerExp := eulersNumber.Power(uint64(integer.TruncateInt64()))
+
+	fractionalExp := expApprox(eulersNumber, fractional)
+
+	return integerExp.Add(fractionalExp)
+}
+
+// expApprox computes the exponential of a base.
+// 0 < exponent < 1
+// exp(0) = 1
+// exp(1) = e
+// Find Chebyshev nodes using Remez algorithm:
+// https://github.com/samhocevar/lolremez/wiki/Tutorial-1-of-5%3A-exp%28x%29-the-quick-way
+func expApprox(base BigDec, exponent BigDec) BigDec {
+	return ZeroDec()
+}
+
+// Step 1: find Chebushev

osmomath/math_test.go

@@ -5,10 +5,9 @@ import (
 	"testing"
 
 	sdk "github.com/cosmos/cosmos-sdk/types"
+	"github.com/stretchr/testify/require"
 
 	"github.com/osmosis-labs/osmosis/v13/app/apptesting/osmoassert"
-
-	"github.com/stretchr/testify/require"
 )
 
 func TestAbsDifferenceWithSign(t *testing.T) {
@@ -166,3 +165,28 @@ func TestPow(t *testing.T) {
 		})
 	}
 }
+
+func TestExp(t *testing.T) {
+
+	tests := map[string]struct {
+		exponent       BigDec
+		expectedResult BigDec
+		expectError    bool
+	}{
+		// The value below is log base 2 of Max Spot Price (2^128 - 1)
+		"exp(32) = 78962960182680.695160978022635108224219956195115352": {
+			exponent: NewBigDec(32),
+			// https://www.wolframalpha.com/input?i=exp%2832%29+50+sig+figs
+			expectedResult: MustNewDecFromStr("78962960182680.695160978022635108224219956195115352"),
+		},
+	}
+
+	for name, tc := range tests {
+		t.Run(name, func(t *testing.T) {
+
+			result := Exp(tc.exponent)
+
+			require.Equal(t, tc.expectedResult, result)
+		})
+	}
+}