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pow.go
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pow.go
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package types
import (
"fmt"
sdk "github.com/cosmos/cosmos-sdk/types"
)
// Don't EVER change after initializing
// TODO: Analyze choice here.
var powPrecision, _ = sdk.NewDecFromStr("0.00000001")
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
// nolint: unused
// eulersNumber = sdk.MustNewDecFromStr("2.718281828459045235360287471352662498")
)
// Pow computes base^(exp)
// However since the exponent is not an integer, we must do an approximation algorithm.
// TODO: In the future, lets add some optimized routines for common exponents, e.g. for common wIn / wOut ratios
// Many simple exponents like 2:1 pools.
func Pow(base sdk.Dec, exp sdk.Dec) sdk.Dec {
// Exponentiation of a negative base with an arbitrary real exponent is not closed within the reals.
// You can see this by recalling that `i = (-1)^(.5)`. We have to go to complex numbers to define this.
// (And would have to implement complex logarithms)
// We don't have a need for negative bases, so we don't include any such logic.
if !base.IsPositive() {
panic(fmt.Errorf("base must be greater than 0"))
}
// TODO: Remove this if we want to generalize the function,
// we can adjust the algorithm in this setting.
if base.GTE(two) {
panic(fmt.Errorf("base must be lesser than two"))
}
// We will use an approximation algorithm to compute the power.
// Since computing an integer power is easy, we split up the exponent into
// an integer component and a fractional component.
integer := exp.TruncateDec()
fractional := exp.Sub(integer)
integerPow := base.Power(uint64(integer.TruncateInt64()))
if fractional.IsZero() {
return integerPow
}
fractionalPow := PowApprox(base, fractional, powPrecision)
return integerPow.Mul(fractionalPow)
}