U512

Overview

License: MIT

library U512

Low-level library that implements unsigned 512-bit arithmetic.

Statistic	Avg
add	269 gas
sub	278 gas
mul	353 gas
mod	682 gas
modinv	6083 gas
modadd	780 gas
redadd	590 gas
modmul	1176 gas
modsub	1017 gas
redsub	533 gas
modexp	5981 gas
modexpU256	692 gas
moddiv	7092 gas
and	251 gas
or	251 gas
xor	251 gas
not	216 gas
shl	272 gas
shr	272 gas

Imports:

First import the library and all the necessary types.

import {U512, uint512, call512} from "U512.sol";

Usage example:

using U512 for uint512;

uint512 a_ = U512.fromUint256(3);
uint512 b_ = U512.fromUint256(6);
uint512 m_ = U512.fromUint256(5);
uint512 r_ = a.modadd(b_, m_);
r_.eq(U512.fromUint256(4)); // true

Note that each mod call allocates extra memory for invoking the precompile. This is fine for lightweight functions. However, for heavy functions, consider allocating memory once and reusing it in subsequent calls. This approach can help reduce gas costs. Additionally, use assignment functions to avoid allocating memory for new local variables, instead assigning values to existing ones.

using U512 for uint512;

call512 call_ = U512.initCall();
uint512 a_ = U512.fromUint256(3);
uint512 b_ = U512.fromUint256(6);
uint512 m_ = U512.fromUint256(5);
uint512 r_ = a.modadd(call_, b_, m_); // 4
r_.modmulAssign(a_, m_); // 2
r_.eq(U512.fromUint256(2)); // true
r_.toBytes(); // "0x00..02"

Functions info

initCall

function initCall() internal pure returns (call512 call_)

Initializes a memory pointer for precompile call arguments.

Return values:

Name	Type	Description
call_	call512	A memory pointer for precompile operations.

fromUint256

function fromUint256(uint256 u256_) internal pure returns (uint512 u512_)

Converts a 256-bit unsigned integer to a 512-bit unsigned integer.

Parameters:

Name	Type	Description
u256_	uint256	The 256-bit unsigned integer to convert.

Return values:

Name	Type	Description
u512_	uint512	The 512-bit representation of the input.

fromBytes

function fromBytes(bytes memory bytes_) internal view returns (uint512 u512_)

Converts a byte array to a 512-bit unsigned integer.

The byte array must be less than 65 bytes.

Parameters:

Name	Type	Description
bytes_	bytes	The byte array to convert.

Return values:

Name	Type	Description
u512_	uint512	The 512-bit representation of the byte array.

copy

function copy(uint512 u512_) internal pure returns (uint512 u512Copy_)

Copies a 512-bit unsigned integer to a new memory location.

Parameters:

Name	Type	Description
u512_	uint512	The 512-bit unsigned integer to copy.

Return values:

Name	Type	Description
u512Copy_	uint512	A pointer to the new copy of the 512-bit unsigned integer.

assign

function assign(uint512 u512_, uint512 to_) internal pure

Assigns a 512-bit unsigned integer to another.

Parameters:

Name	Type	Description
u512_	uint512	The 512-bit unsigned integer to assign.
to_	uint512	The target 512-bit unsigned integer to store the result.

toBytes

function toBytes(uint512 u512_) internal pure returns (bytes memory bytes_)

Converts a 512-bit unsigned integer to a byte array.

Parameters:

Name	Type	Description
u512_	uint512	The 512-bit unsigned integer to convert.

Return values:

Name	Type	Description
bytes_	bytes	A byte array representation of the 512-bit unsigned integer.

isNull

function isNull(uint512 u512_) internal pure returns (bool isNull_)

Checks if a uint512 pointer is null.

Parameters:

Name	Type	Description
u512_	uint512	The uint512 pointer to check.

Return values:

Name	Type	Description
isNull_	bool	True if the pointer is null, false otherwise.

eq

function eq(uint512 a_, uint512 b_) internal pure returns (bool eq_)

Compares two 512-bit unsigned integers for equality.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

Return values:

Name	Type	Description
eq_	bool	True if the integers are equal, false otherwise.

eqU256

function eqU256(uint512 a_, uint256 u256_) internal pure returns (bool eq_)

Compares a 512-bit unsigned integer with a 256-bit unsigned integer for equality.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer.
u256_	uint256	The 256-bit unsigned integer.

Return values:

Name	Type	Description
eq_	bool	True if the integers are equal, false otherwise.

cmp

function cmp(uint512 a_, uint512 b_) internal pure returns (int256)

Compares two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

Return values:

Name	Type	Description
[0]	int256	1 if a_ > b_, -1 if a_ < b_, and 0 if they are equal.

mod

function mod(
    call512 call_,
    uint512 a_,
    uint512 m_
) internal view returns (uint512 r_)

Performs modular arithmetic on 512-bit integers.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular operation (a_ % m_).

mod

function mod(uint512 a_, uint512 m_) internal view returns (uint512 r_)

Performs modular arithmetic on 512-bit integers.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The dividend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular operation (a_ % m_).

modAssign

function modAssign(call512 call_, uint512 a_, uint512 m_) internal view

Performs modular assignment on a 512-bit unsigned integer.

Updates the value of a_ to (a_ % m_).

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
m_	uint512	The modulus.

modAssignTo

function modAssignTo(
    call512 call_,
    uint512 a_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular assignment and stores the result in a separate 512-bit unsigned integer.

Assigns the result (a_ % m_) to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modinv

function modinv(
    call512 call_,
    uint512 a_,
    uint512 m_
) internal view returns (uint512 r_)

Computes the modular inverse of a 512-bit unsigned integer.

IMPORTANT: The modulus m_ must be a prime number

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The 512-bit unsigned integer to invert.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The modular inverse result a_^(-1) % m_.

modinv

function modinv(uint512 a_, uint512 m_) internal view returns (uint512 r_)

Computes the modular inverse of a 512-bit unsigned integer.

IMPORTANT: The modulus m_ must be a prime number

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to invert.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The modular inverse result a_^(-1) % m_.

modinvAssign

function modinvAssign(call512 call_, uint512 a_, uint512 m_) internal view

Performs the modular inverse assignment on a 512-bit unsigned integer.

IMPORTANT: The modulus m_ must be a prime number

Updates the value of a_ to a_^(-1) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The 512-bit unsigned integer to invert.
m_	uint512	The modulus.

modinvAssignTo

function modinvAssignTo(
    call512 call_,
    uint512 a_,
    uint512 m_,
    uint512 to_
) internal view

Computes the modular inverse and stores it in a separate 512-bit unsigned integer.

IMPORTANT: The modulus m_ must be a prime number

Assigns the result of a_^(-1) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The 512-bit unsigned integer to invert.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modexp

function modexp(
    call512 call_,
    uint512 b_,
    uint512 e_,
    uint512 m_
) internal view returns (uint512 r_)

Performs modular exponentiation on 512-bit unsigned integers.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint512	The exponent.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of modular exponentiation (b_^e_) % m_.

modexp

function modexp(
    uint512 b_,
    uint512 e_,
    uint512 m_
) internal view returns (uint512 r_)

Performs modular exponentiation on 512-bit unsigned integers.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
b_	uint512	The base.
e_	uint512	The exponent.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of modular exponentiation (b_^e_) % m_.

modexpAssign

function modexpAssign(
    call512 call_,
    uint512 b_,
    uint512 e_,
    uint512 m_
) internal view

Performs modular exponentiation assignment on the base.

Updates the value of b_ to (b_^e_) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint512	The exponent.
m_	uint512	The modulus.

modexpAssignTo

function modexpAssignTo(
    call512 call_,
    uint512 b_,
    uint512 e_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular exponentiation and stores the result in a separate 512-bit unsigned integer.

Assigns the result of (b_^e_) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint512	The exponent.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modexpU256

function modexpU256(
    call512 call_,
    uint512 b_,
    uint256 e_,
    uint512 m_
) internal view returns (uint512 r_)

Performs modular exponentiation on 512-bit unsigned integers.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint256	The exponent.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of modular exponentiation (b_^e_) % m_.

modexpU256

function modexpU256(
    uint512 b_,
    uint256 e_,
    uint512 m_
) internal view returns (uint512 r_)

Performs modular exponentiation of a 512-bit unsigned integer base and a 256-bit unsigned integer exponent.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
b_	uint512	The base.
e_	uint256	The exponent.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of modular exponentiation (b_^e_) % m_.

modexpU256Assign

function modexpU256Assign(
    call512 call_,
    uint512 b_,
    uint256 e_,
    uint512 m_
) internal view

Performs modular exponentiation of a 512-bit unsigned integer base and a 256-bit unsigned integer exponent.

Updates the value of b_ to (b_^e_) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint256	The exponent.
m_	uint512	The modulus.

modexpU256AssignTo

function modexpU256AssignTo(
    call512 call_,
    uint512 b_,
    uint256 e_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular exponentiation of a 512-bit unsigned integer base and a 256-bit unsigned integer exponent.

Assigns the result of (b_^e_) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
b_	uint512	The base.
e_	uint256	The exponent.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modadd

function modadd(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Adds two 512-bit unsigned integers under a modulus.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend.
b_	uint512	The second addend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular addition (a_ + b_) % m_.

modadd

function modadd(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Adds two 512-bit unsigned integers under a modulus.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The first addend.
b_	uint512	The second addend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular addition (a_ + b_) % m_.

modaddAssign

function modaddAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view

Performs modular addition assignment on the first 512-bit unsigned integer addend.

Updates the value of a_ to (a_ + b_) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend.
b_	uint512	The second addend.
m_	uint512	The modulus.

modaddAssignTo

function modaddAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular addition and stores the result in a separate 512-bit unsigned integer.

Assigns the result of (a_ + b_) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend.
b_	uint512	The second addend.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

add

function add(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Adds two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first addend.
b_	uint512	The second addend.

Return values:

Name	Type	Description
r_	uint512	The result of the addition.

addAssign

function addAssign(uint512 a_, uint512 b_) internal pure

Performs addition assignment on the first 512-bit unsigned addend.

Updates the value of a_ to a_ + b_.

Parameters:

Name	Type	Description
a_	uint512	The first addend.
b_	uint512	The second addend.

addAssignTo

function addAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs addition and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ + b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The first addend.
b_	uint512	The second addend.
to_	uint512	The target 512-bit unsigned integer to store the result.

redadd

function redadd(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure returns (uint512 r_)

Adds two 512-bit unsigned integers under a modulus.

This is an optimized version of modadd where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend, reduced by m_.
b_	uint512	The second addend, reduced by m_.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular addition (a_ + b_) % m_.

redadd

function redadd(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure returns (uint512 r_)

Adds two 512-bit unsigned integers under a modulus.

This is an optimized version of modadd where the inputs must be pre-reduced by m_.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The first addend, reduced by m_.
b_	uint512	The second addend, reduced by m_.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular addition (a_ + b_) % m_.

redaddAssign

function redaddAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure

Performs modular addition assignment on the first 512-bit unsigned integer addend.

This is an optimized version of modaddAssign where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend, reduced by m_.
b_	uint512	The second addend, reduced by m_.
m_	uint512	The modulus.

redaddAssignTo

function redaddAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal pure

Performs modular addition and stores the result in a separate 512-bit unsigned integer.

This is an optimized version of modaddAssignTo where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first addend, reduced by m_.
b_	uint512	The second addend, reduced by m_.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modsub

function modsub(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Subtracts one 512-bit unsigned integer from another under a modulus.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend.
b_	uint512	The subtrahend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular subtraction (a_ - b_) % m_.

modsub

function modsub(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Subtracts one 512-bit unsigned integer from another under a modulus.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The minuend.
b_	uint512	The subtrahend.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular subtraction (a_ - b_) % m_.

modsubAssign

function modsubAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view

Performs modular subtraction assignment on the 512-bit unsigned integer minuend.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend.
b_	uint512	The subtrahend.
m_	uint512	The modulus.

modsubAssignTo

function modsubAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular subtraction and stores the result in a separate 512-bit unsigned integer.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend.
b_	uint512	The subtrahend.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

sub

function sub(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Subtracts one 512-bit unsigned integer from another.

Parameters:

Name	Type	Description
a_	uint512	The minuend.
b_	uint512	The subtrahend.

Return values:

Name	Type	Description
r_	uint512	The result of the subtraction.

subAssign

function subAssign(uint512 a_, uint512 b_) internal pure

Performs subtraction assignment on the 512-bit unsigned minuend.

Updates the value of a_ to a_ - b_.

Parameters:

Name	Type	Description
a_	uint512	The minuend.
b_	uint512	The subtrahend.

subAssignTo

function subAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs subtraction and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ - b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The minuend.
b_	uint512	The subtrahend.
to_	uint512	The target 512-bit unsigned integer to store the result.

redsub

function redsub(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure returns (uint512 r_)

Subtracts one 512-bit unsigned integer from another under a modulus.

This is an optimized version of modsub where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend, reduced by m_.
b_	uint512	The subtrahend, reduced by m_.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular subtraction (a_ - b_) % m_.

redsub

function redsub(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure returns (uint512 r_)

Subtracts one 512-bit unsigned integer from another under a modulus.

This is an optimized version of modsub where the inputs must be pre-reduced by m_.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The minuend, reduced by m_.
b_	uint512	The subtrahend, reduced by m_.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular subtraction (a_ - b_) % m_.

redsubAssign

function redsubAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal pure

Performs modular subtraction assignment on the 512-bit unsigned integer minuend.

This is an optimized version of modsubAssign where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend, reduced by m_.
b_	uint512	The subtrahend, reduced by m_.
m_	uint512	The modulus.

redsubAssignTo

function redsubAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal pure

Performs modular subtraction and stores the result in a separate 512-bit unsigned integer.

This is an optimized version of modsubAssignTo where the inputs must be pre-reduced by m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The minuend, reduced by m_.
b_	uint512	The subtrahend, reduced by m_.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

modmul

function modmul(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Multiplies two 512-bit unsigned integers under a modulus.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first factor.
b_	uint512	The second factor.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular multiplication (a_ * b_) % m_.

modmul

function modmul(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Multiplies two 512-bit unsigned integers under a modulus.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The first factor.
b_	uint512	The second factor.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular multiplication (a_ * b_) % m_.

modmulAssign

function modmulAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view

Performs modular multiplication assignment on the first 512-bit unsigned integer factor.

Updates the value of a_ to (a_ * b_) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first factor.
b_	uint512	The second factor.
m_	uint512	The modulus.

modmulAssignTo

function modmulAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal view

Performs modular multiplication and stores the result in a separate 512-bit unsigned integer.

Assigns the result of (a_ * b_) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The first factor.
b_	uint512	The second factor.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

mul

function mul(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Multiplies two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first factor.
b_	uint512	The second factor.

Return values:

Name	Type	Description
r_	uint512	The result of the multiplication.

mulAssign

function mulAssign(uint512 a_, uint512 b_) internal pure

Performs multiplication assignment on the first 512-bit unsigned factor.

Updates the value of a_ to a_ * b_.

Parameters:

Name	Type	Description
a_	uint512	The first factor.
b_	uint512	The second factor.

mulAssignTo

function mulAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs multiplication and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ * b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The first factor.
b_	uint512	The second factor.
to_	uint512	The target 512-bit unsigned integer to store the result.

moddiv

function moddiv(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Divides two 512-bit unsigned integers under a modulus.

IMPORTANT: The modulus m_ must be a prime number.

Returns the result of (a_ * b_^(-1)) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
b_	uint512	The divisor.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular division.

moddiv

function moddiv(
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view returns (uint512 r_)

Divides two 512-bit unsigned integers under a modulus.

IMPORTANT: The modulus m_ must be a prime number.

Returns the result of (a_ * b_^(-1)) % m_.

Allocates memory for call every time it's called.

Parameters:

Name	Type	Description
a_	uint512	The dividend.
b_	uint512	The divisor.
m_	uint512	The modulus.

Return values:

Name	Type	Description
r_	uint512	The result of the modular division.

moddivAssign

function moddivAssign(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_
) internal view

Performs the modular division assignment on a 512-bit unsigned dividend.

IMPORTANT: The modulus m_ must be a prime number.

Updates the value of a_ to (a_ * b_^(-1)) % m_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
b_	uint512	The divisor.
m_	uint512	The modulus.

moddivAssignTo

function moddivAssignTo(
    call512 call_,
    uint512 a_,
    uint512 b_,
    uint512 m_,
    uint512 to_
) internal view

Performs the modular division and stores the result in a separate 512-bit unsigned integer.

IMPORTANT: The modulus m_ must be a prime number.

Assigns the result of (a_ * b_^(-1)) % m_ to to_.

Parameters:

Name	Type	Description
call_	call512	A memory pointer for precompile call arguments.
a_	uint512	The dividend.
b_	uint512	The divisor.
m_	uint512	The modulus.
to_	uint512	The target 512-bit unsigned integer to store the result.

and

function and(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Performs bitwise AND of two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

Return values:

Name	Type	Description
r_	uint512	The result of the bitwise AND operation.

andAssign

function andAssign(uint512 a_, uint512 b_) internal pure

Performs bitwise AND assignment on the first 512-bit unsigned integer.

Updates the value of a_ to a_ & b_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

andAssignTo

function andAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs bitwise AND and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ & b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.
to_	uint512	The target 512-bit unsigned integer to store the result.

or

function or(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Performs bitwise OR of two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

Return values:

Name	Type	Description
r_	uint512	The result of the bitwise OR operation.

orAssign

function orAssign(uint512 a_, uint512 b_) internal pure

Performs bitwise OR assignment on the first 512-bit unsigned integer.

Updates the value of a_ to a_ | b_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

orAssignTo

function orAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs bitwise OR and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ | b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.
to_	uint512	The target 512-bit unsigned integer to store the result.

xor

function xor(uint512 a_, uint512 b_) internal pure returns (uint512 r_)

Performs bitwise XOR of two 512-bit unsigned integers.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

Return values:

Name	Type	Description
r_	uint512	The result of the bitwise XOR operation.

xorAssign

function xorAssign(uint512 a_, uint512 b_) internal pure

Performs bitwise XOR assignment on the first 512-bit unsigned integer.

Updates the value of a_ to a_ ^ b_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.

xorAssignTo

function xorAssignTo(uint512 a_, uint512 b_, uint512 to_) internal pure

Performs bitwise XOR and stores the result in a separate 512-bit unsigned integer.

Assigns the result of a_ ^ b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The first 512-bit unsigned integer.
b_	uint512	The second 512-bit unsigned integer.
to_	uint512	The target 512-bit unsigned integer to store the result.

not

function not(uint512 a_) internal pure returns (uint512 r_)

Performs bitwise NOT of a 512-bit unsigned integer.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer.

Return values:

Name	Type	Description
r_	uint512	The result of the bitwise NOT operation.

notAssign

function notAssign(uint512 a_) internal pure

Performs bitwise NOT assignment on a 512-bit unsigned integer.

Updates the value of a_ to ~a_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer.

notAssignTo

function notAssignTo(uint512 a_, uint512 to_) internal pure

Performs bitwise NOT and stores the result in a separate 512-bit unsigned integer.

Assigns the result of ~a_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer.
to_	uint512	The target 512-bit unsigned integer to store the result.

shl

function shl(uint512 a_, uint8 b_) internal pure returns (uint512 r_)

Shifts a 512-bit unsigned integer to the left by a specified number of bits.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.

Return values:

Name	Type	Description
r_	uint512	The result of the left shift operation.

shlAssign

function shlAssign(uint512 a_, uint8 b_) internal pure

Shifts a 512-bit unsigned integer to the left by a specified number of bits.

Updates the value of a_ to a_ << b_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.

shlAssignTo

function shlAssignTo(uint512 a_, uint8 b_, uint512 to_) internal pure

Shifts a 512-bit unsigned integer to the left by a specified number of bits.

Assigns the result of a_ << b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.
to_	uint512	The target 512-bit unsigned integer to store the result.

shr

function shr(uint512 a_, uint8 b_) internal pure returns (uint512 r_)

Shifts a 512-bit unsigned integer to the right by a specified number of bits.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.

Return values:

Name	Type	Description
r_	uint512	The result of the right shift operation.

shrAssign

function shrAssign(uint512 a_, uint8 b_) internal pure

Shifts a 512-bit unsigned integer to the right by a specified number of bits.

Updates the value of a_ to a_ >> b_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.

shrAssignTo

function shrAssignTo(uint512 a_, uint8 b_, uint512 to_) internal pure

Shifts a 512-bit unsigned integer to the right by a specified number of bits.

Assigns the result of a_ >> b_ to to_.

Parameters:

Name	Type	Description
a_	uint512	The 512-bit unsigned integer to shift.
b_	uint8	The number of bits to shift by.
to_	uint512	The target 512-bit unsigned integer to store the result.