Exponential.md

layout	title
default	Exponential

Exponential.sol

View Source: contracts/Exponential.sol

↗ Extends: ErrorReporter, CarefulMath ↘ Derived Contracts: AlkemiEarnPublic, AlkemiEarnVerified, AlkemiRateModel, ExchangeRateModel, PriceOracle

{{ContractName}}

Structs

Exp

struct Exp {
 uint256 mantissa
}

ExpNegative

struct ExpNegative {
 int256 mantissa
}

Contract Members

Constants & Variables

uint256 internal constant expScale;
uint256 internal constant halfExpScale;
uint256 internal constant mantissaOne;
uint256 internal constant mantissaOneTenth;

Functions

• getExp(uint256 num, uint256 denom)
• addExp(struct Exponential.Exp a, struct Exponential.Exp b)
• addExpNegative(struct Exponential.Exp a, struct Exponential.ExpNegative b)
• subExp(struct Exponential.Exp a, struct Exponential.Exp b)
• subExpNegative(struct Exponential.Exp a, struct Exponential.Exp b)
• mulScalar(struct Exponential.Exp a, uint256 scalar)
• divScalar(struct Exponential.Exp a, uint256 scalar)
• divScalarByExp(uint256 scalar, struct Exponential.Exp divisor)
• mulExp(struct Exponential.Exp a, struct Exponential.Exp b)
• divExp(struct Exponential.Exp a, struct Exponential.Exp b)
• truncate(struct Exponential.Exp exp)
• lessThanExp(struct Exponential.Exp left, struct Exponential.Exp right)
• lessThanOrEqualExp(struct Exponential.Exp left, struct Exponential.Exp right)
• greaterThanExp(struct Exponential.Exp left, struct Exponential.Exp right)
• isZeroExp(struct Exponential.Exp value)

getExp

Creates an exponential from numerator and denominator values. Note: Returns an error if (num * 10e18) > MAX_INT, or if denom is zero.

function getExp(uint256 num, uint256 denom) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
num	uint256
denom	uint256

addExp

Adds two exponentials, returning a new exponential.

function addExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.Exp

addExpNegative

Adds two exponentials, returning a new exponential.

function addExpNegative(struct Exponential.Exp a, struct Exponential.ExpNegative b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.ExpNegative

subExp

Subtracts two exponentials, returning a new exponential.

function subExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.Exp

subExpNegative

Subtracts two exponentials, returning a new exponential.

function subExpNegative(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.ExpNegative)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.Exp

mulScalar

Multiply an Exp by a scalar, returning a new Exp.

function mulScalar(struct Exponential.Exp a, uint256 scalar) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
scalar	uint256

divScalar

Divide an Exp by a scalar, returning a new Exp.

function divScalar(struct Exponential.Exp a, uint256 scalar) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
scalar	uint256

divScalarByExp

Divide a scalar by an Exp, returning a new Exp.

function divScalarByExp(uint256 scalar, struct Exponential.Exp divisor) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
scalar	uint256
divisor	struct Exponential.Exp

mulExp

Multiplies two exponentials, returning a new exponential.

function mulExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.Exp

divExp

Divides two exponentials, returning a new exponential. (a/scale) / (b/scale) = (a/scale) * (scale/b) = a/b, which we can scale as an Exp by calling getExp(a.mantissa, b.mantissa)

function divExp(struct Exponential.Exp a, struct Exponential.Exp b) internal pure
returns(enum ErrorReporter.Error, struct Exponential.Exp)

Arguments

Name	Type	Description
a	struct Exponential.Exp
b	struct Exponential.Exp

truncate

Truncates the given exp to a whole number value. For example, truncate(Exp{mantissa: 15 * (10**18)}) = 15

function truncate(struct Exponential.Exp exp) internal pure
returns(uint256)

Arguments

Name	Type	Description
exp	struct Exponential.Exp

lessThanExp

Checks if first Exp is less than second Exp.

function lessThanExp(struct Exponential.Exp left, struct Exponential.Exp right) internal pure
returns(bool)

Arguments

Name	Type	Description
left	struct Exponential.Exp
right	struct Exponential.Exp

lessThanOrEqualExp

Checks if left Exp <= right Exp.

function lessThanOrEqualExp(struct Exponential.Exp left, struct Exponential.Exp right) internal pure
returns(bool)

Arguments

Name	Type	Description
left	struct Exponential.Exp
right	struct Exponential.Exp

greaterThanExp

Checks if first Exp is greater than second Exp.

function greaterThanExp(struct Exponential.Exp left, struct Exponential.Exp right) internal pure
returns(bool)

Arguments

Name	Type	Description
left	struct Exponential.Exp
right	struct Exponential.Exp

isZeroExp

returns true if Exp is exactly zero

function isZeroExp(struct Exponential.Exp value) internal pure
returns(bool)

Arguments

Name	Type	Description
value	struct Exponential.Exp