PRBMath__MulDivFixedPointOverflow
error PRBMath__MulDivFixedPointOverflow(uint256 prod1)
Emitted when the result overflows uint256.
PRBMath__MulDivOverflow
error PRBMath__MulDivOverflow(uint256 prod1, uint256 denominator)
Emitted when the result overflows uint256.
PRBMath__MulDivSignedInputTooSmall
error PRBMath__MulDivSignedInputTooSmall()
Emitted when one of the inputs is type(int256).min.
PRBMath__MulDivSignedOverflow
error PRBMath__MulDivSignedOverflow(uint256 rAbs)
Emitted when the intermediary absolute result overflows int256.
PRBMathSD59x18__AbsInputTooSmall
error PRBMathSD59x18__AbsInputTooSmall()
Emitted when the input is MIN_SD59x18.
PRBMathSD59x18__CeilOverflow
error PRBMathSD59x18__CeilOverflow(int256 x)
Emitted when ceiling a number overflows SD59x18.
PRBMathSD59x18__DivInputTooSmall
error PRBMathSD59x18__DivInputTooSmall()
Emitted when one of the inputs is MIN_SD59x18.
PRBMathSD59x18__DivOverflow
error PRBMathSD59x18__DivOverflow(uint256 rAbs)
Emitted when one of the intermediary unsigned results overflows SD59x18.
PRBMathSD59x18__ExpInputTooBig
error PRBMathSD59x18__ExpInputTooBig(int256 x)
Emitted when the input is greater than 133.084258667509499441.
PRBMathSD59x18__Exp2InputTooBig
error PRBMathSD59x18__Exp2InputTooBig(int256 x)
Emitted when the input is greater than 192.
PRBMathSD59x18__FloorUnderflow
error PRBMathSD59x18__FloorUnderflow(int256 x)
Emitted when flooring a number underflows SD59x18.
PRBMathSD59x18__FromIntOverflow
error PRBMathSD59x18__FromIntOverflow(int256 x)
Emitted when converting a basic integer to the fixed-point format overflows SD59x18.
PRBMathSD59x18__FromIntUnderflow
error PRBMathSD59x18__FromIntUnderflow(int256 x)
Emitted when converting a basic integer to the fixed-point format underflows SD59x18.
PRBMathSD59x18__GmNegativeProduct
error PRBMathSD59x18__GmNegativeProduct(int256 x, int256 y)
Emitted when the product of the inputs is negative.
PRBMathSD59x18__GmOverflow
error PRBMathSD59x18__GmOverflow(int256 x, int256 y)
Emitted when multiplying the inputs overflows SD59x18.
PRBMathSD59x18__LogInputTooSmall
error PRBMathSD59x18__LogInputTooSmall(int256 x)
Emitted when the input is less than or equal to zero.
PRBMathSD59x18__MulInputTooSmall
error PRBMathSD59x18__MulInputTooSmall()
Emitted when one of the inputs is MIN_SD59x18.
PRBMathSD59x18__MulOverflow
error PRBMathSD59x18__MulOverflow(uint256 rAbs)
Emitted when the intermediary absolute result overflows SD59x18.
PRBMathSD59x18__PowuOverflow
error PRBMathSD59x18__PowuOverflow(uint256 rAbs)
Emitted when the intermediary absolute result overflows SD59x18.
PRBMathSD59x18__SqrtNegativeInput
error PRBMathSD59x18__SqrtNegativeInput(int256 x)
Emitted when the input is negative.
PRBMathSD59x18__SqrtOverflow
error PRBMathSD59x18__SqrtOverflow(int256 x)
Emitted when the calculating the square root overflows SD59x18.
PRBMathUD60x18__AddOverflow
error PRBMathUD60x18__AddOverflow(uint256 x, uint256 y)
Emitted when addition overflows UD60x18.
PRBMathUD60x18__CeilOverflow
error PRBMathUD60x18__CeilOverflow(uint256 x)
Emitted when ceiling a number overflows UD60x18.
PRBMathUD60x18__ExpInputTooBig
error PRBMathUD60x18__ExpInputTooBig(uint256 x)
Emitted when the input is greater than 133.084258667509499441.
PRBMathUD60x18__Exp2InputTooBig
error PRBMathUD60x18__Exp2InputTooBig(uint256 x)
Emitted when the input is greater than 192.
PRBMathUD60x18__FromUintOverflow
error PRBMathUD60x18__FromUintOverflow(uint256 x)
Emitted when converting a basic integer to the fixed-point format format overflows UD60x18.
PRBMathUD60x18__GmOverflow
error PRBMathUD60x18__GmOverflow(uint256 x, uint256 y)
Emitted when multiplying the inputs overflows UD60x18.
PRBMathUD60x18__LogInputTooSmall
error PRBMathUD60x18__LogInputTooSmall(uint256 x)
Emitted when the input is less than 1.
PRBMathUD60x18__SqrtOverflow
error PRBMathUD60x18__SqrtOverflow(uint256 x)
Emitted when the calculating the square root overflows UD60x18.
PRBMathUD60x18__SubUnderflow
error PRBMathUD60x18__SubUnderflow(uint256 x, uint256 y)
Emitted when subtraction underflows UD60x18.
PRBMath
Common mathematical functions used in both PRBMathSD59x18 and PRBMathUD60x18. Note that this shared library does not always assume the signed 59.18-decimal fixed-point or the unsigned 60.18-decimal fixed-point representation. When it does not, it is explicitly mentioned in the NatSpec documentation.
SD59x18
struct SD59x18 {
int256 value;
}
UD60x18
struct UD60x18 {
uint256 value;
}
SCALE
uint256 SCALE
How many trailing decimals can be represented.
SCALE_LPOTD
uint256 SCALE_LPOTD
Largest power of two divisor of SCALE.
SCALE_INVERSE
uint256 SCALE_INVERSE
SCALE inverted mod 2^256.
exp2
function exp2(uint256 x) internal pure returns (uint256 result)
Calculates the binary exponent of x using the binary fraction method.
Has to use 192.64-bit fixed-point numbers. See https://ethereum.stackexchange.com/a/96594/24693.
| Name | Type | Description |
|---|---|---|
| x | uint256 | The exponent as an unsigned 192.64-bit fixed-point number. |
| Name | Type | Description |
|---|---|---|
| result | uint256 | The result as an unsigned 60.18-decimal fixed-point number. |
mostSignificantBit
function mostSignificantBit(uint256 x) internal pure returns (uint256 msb)
Finds the zero-based index of the first one in the binary representation of x.
See the note on msb in the "Find First Set" Wikipedia article https://en.wikipedia.org/wiki/Find_first_set
| Name | Type | Description |
|---|---|---|
| x | uint256 | The uint256 number for which to find the index of the most significant bit. |
| Name | Type | Description |
|---|---|---|
| msb | uint256 | The index of the most significant bit as an uint256. |
mulDiv
function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result)
Calculates floor(x*y÷denominator) with full precision.
_Credit to Remco Bloemen under MIT license https://xn--2-umb.com/21/muldiv.
Requirements: - The denominator cannot be zero. - The result must fit within uint256.
Caveats: - This function does not work with fixed-point numbers._
| Name | Type | Description |
|---|---|---|
| x | uint256 | The multiplicand as an uint256. |
| y | uint256 | The multiplier as an uint256. |
| denominator | uint256 | The divisor as an uint256. |
| Name | Type | Description |
|---|---|---|
| result | uint256 | The result as an uint256. |
mulDivFixedPoint
function mulDivFixedPoint(uint256 x, uint256 y) internal pure returns (uint256 result)
Calculates floor(x*y÷1e18) with full precision.
_Variant of "mulDiv" with constant folding, i.e. in which the denominator is always 1e18. Before returning the final result, we add 1 if (x * y) % SCALE >= HALF_SCALE. Without this, 6.6e-19 would be truncated to 0 instead of being rounded to 1e-18. See "Listing 6" and text above it at https://accu.org/index.php/journals/1717.
Requirements: - The result must fit within uint256.
Caveats: - The body is purposely left uncommented; see the NatSpec comments in "PRBMath.mulDiv" to understand how this works. - It is assumed that the result can never be type(uint256).max when x and y solve the following two equations: 1. x * y = type(uint256).max * SCALE 2. (x * y) % SCALE >= SCALE / 2_
| Name | Type | Description |
|---|---|---|
| x | uint256 | The multiplicand as an unsigned 60.18-decimal fixed-point number. |
| y | uint256 | The multiplier as an unsigned 60.18-decimal fixed-point number. |
| Name | Type | Description |
|---|---|---|
| result | uint256 | The result as an unsigned 60.18-decimal fixed-point number. |
mulDivSigned
function mulDivSigned(int256 x, int256 y, int256 denominator) internal pure returns (int256 result)
Calculates floor(x*y÷denominator) with full precision.
_An extension of "mulDiv" for signed numbers. Works by computing the signs and the absolute values separately.
Requirements: - None of the inputs can be type(int256).min. - The result must fit within int256._
| Name | Type | Description |
|---|---|---|
| x | int256 | The multiplicand as an int256. |
| y | int256 | The multiplier as an int256. |
| denominator | int256 | The divisor as an int256. |
| Name | Type | Description |
|---|---|---|
| result | int256 | The result as an int256. |
sqrt
function sqrt(uint256 x) internal pure returns (uint256 result)
Calculates the square root of x, rounding down.
_Uses the Babylonian method https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method.
Caveats: - This function does not work with fixed-point numbers._
| Name | Type | Description |
|---|---|---|
| x | uint256 | The uint256 number for which to calculate the square root. |
| Name | Type | Description |
|---|---|---|
| result | uint256 | The result as an uint256. |