PackedUint128Math

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This library contains functions to encode and decode two uint128 into a single bytes32 and interact with the encoded bytes32.

State Variables

OFFSET

uint256 private constant OFFSET = 128;

MASK_128

uint256 private constant MASK_128 = 0xffffffffffffffffffffffffffffffff;

MASK_128_PLUS_ONE

uint256 private constant MASK_128_PLUS_ONE = MASK_128 + 1;

Functions

encode

Encodes two uint128 into a single bytes32

function encode(uint128 x1, uint128 x2) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x1	uint128	The first uint128
x2	uint128	The second uint128

Returns

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: x1 [128 - 256[: x2

encodeFirst

Encodes a uint128 into a single bytes32 as the first uint128

function encodeFirst(uint128 x1) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x1	uint128	The uint128

Returns

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: x1 [128 - 256[: empty

encodeSecond

Encodes a uint128 into a single bytes32 as the second uint128

function encodeSecond(uint128 x2) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x2	uint128	The uint128

Returns

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: empty [128 - 256[: x2

encode

Encodes a uint128 into a single bytes32 as the first or second uint128

function encode(uint128 x, bool first) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x	uint128	The uint128
first	bool	Whether to encode as the first or second uint128

Returns

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: if first: [0 - 128[: x [128 - 256[: empty else: [0 - 128[: empty [128 - 256[: x

decode

Decodes a bytes32 into two uint128

function decode(bytes32 z) internal pure returns (uint128 x1, uint128 x2);

Parameters

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: x1 [128 - 256[: x2

Returns

Name	Type	Description
x1	uint128	The first uint128
x2	uint128	The second uint128

decodeX

Decodes a bytes32 into a uint128 as the first uint128

function decodeX(bytes32 z) internal pure returns (uint128 x);

Parameters

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: x [128 - 256[: any

Returns

Name	Type	Description
x	uint128	The first uint128

decodeY

Decodes a bytes32 into a uint128 as the second uint128

function decodeY(bytes32 z) internal pure returns (uint128 y);

Parameters

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: [0 - 128[: any [128 - 256[: y

Returns

Name	Type	Description
y	uint128	The second uint128

decode

Decodes a bytes32 into a uint128 as the first or second uint128

function decode(bytes32 z, bool first) internal pure returns (uint128 x);

Parameters

Name	Type	Description
z	bytes32	The encoded bytes32 as follows: if first: [0 - 128[: x1 [128 - 256[: empty else: [0 - 128[: empty [128 - 256[: x2
first	bool	Whether to decode as the first or second uint128

Returns

Name	Type	Description
x	uint128	The decoded uint128

add

Adds two encoded bytes32, reverting on overflow on any of the uint128

function add(bytes32 x, bytes32 y) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x	bytes32	The first bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y	bytes32	The second bytes32 encoded as follows: [0 - 128[: y1 [128 - 256[: y2

Returns

Name	Type	Description
z	bytes32	The sum of x and y encoded as follows: [0 - 128[: x1 + y1 [128 - 256[: x2 + y2

add

Adds an encoded bytes32 and two uint128, reverting on overflow on any of the uint128

function add(bytes32 x, uint128 y1, uint128 y2) internal pure returns (bytes32);

Parameters

Name	Type	Description
x	bytes32	The bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y1	uint128	The first uint128
y2	uint128	The second uint128

Returns

Name	Type	Description
<none>	bytes32	z The sum of x and y encoded as follows: [0 - 128[: x1 + y1 [128 - 256[: x2 + y2

sub

Subtracts two encoded bytes32, reverting on underflow on any of the uint128

function sub(bytes32 x, bytes32 y) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x	bytes32	The first bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y	bytes32	The second bytes32 encoded as follows: [0 - 128[: y1 [128 - 256[: y2

Returns

Name	Type	Description
z	bytes32	The difference of x and y encoded as follows: [0 - 128[: x1 - y1 [128 - 256[: x2 - y2

sub

Subtracts an encoded bytes32 and two uint128, reverting on underflow on any of the uint128

function sub(bytes32 x, uint128 y1, uint128 y2) internal pure returns (bytes32);

Parameters

Name	Type	Description
x	bytes32	The bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y1	uint128	The first uint128
y2	uint128	The second uint128

Returns

Name	Type	Description
<none>	bytes32	z The difference of x and y encoded as follows: [0 - 128[: x1 - y1 [128 - 256[: x2 - y2

lt

Returns whether any of the uint128 of x is strictly greater than the corresponding uint128 of y

function lt(bytes32 x, bytes32 y) internal pure returns (bool);

Parameters

Name	Type	Description
x	bytes32	The first bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y	bytes32	The second bytes32 encoded as follows: [0 - 128[: y1 [128 - 256[: y2

Returns

Name	Type	Description
<none>	bool	x1 < y1

gt

Returns whether any of the uint128 of x is strictly greater than the corresponding uint128 of y

function gt(bytes32 x, bytes32 y) internal pure returns (bool);

Parameters

Name	Type	Description
x	bytes32	The first bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
y	bytes32	The second bytes32 encoded as follows: [0 - 128[: y1 [128 - 256[: y2

Returns

Name	Type	Description
<none>	bool	x1 < y1

scalarMulDivBasisPointRoundDown

Multiplies an encoded bytes32 by a uint128 then divides the result by 10_000, rounding down The result can't overflow as the multiplier needs to be smaller or equal to 10_000

function scalarMulDivBasisPointRoundDown(bytes32 x, uint128 multiplier) internal pure returns (bytes32 z);

Parameters

Name	Type	Description
x	bytes32	The bytes32 encoded as follows: [0 - 128[: x1 [128 - 256[: x2
multiplier	uint128	The uint128 to multiply by (must be smaller or equal to 10_000)

Returns

Name	Type	Description
z	bytes32	The product of x and multiplier encoded as follows: [0 - 128[: floor((x1 * multiplier) / 10_000) [128 - 256[: floor((x2 * multiplier) / 10_000)

Errors

PackedUint128Math__AddOverflow

error PackedUint128Math__AddOverflow();

PackedUint128Math__SubUnderflow

error PackedUint128Math__SubUnderflow();

PackedUint128Math__MultiplierTooLarge

error PackedUint128Math__MultiplierTooLarge();