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ABDK Math 64.64

Library of mathematical functions operating with signed 64.64-bit fixed point numbers.

Copyright (c) 2019, ABDK Consulting

All rights reserved.

Signed 64.64 Fixed Point Numbers

Signed 64.64-bit fixed point number is basically a simple fraction whose numerator is a signed 128-bit integer and denominator is 2^64. As long as denominator is always the same, there is no need to store it, thus in Solidity signed 64.64-bit fixed point numbers are represented by int128 type holding only the numerator.

Signed 64.64-bit fixed point numbers combine wide range and decent precision with good performance, and should be a good fit for most applications that need to deal with real numbers.

Simple Arithmetic

Here is the list of simple arithmetic functions provided by the library.

function add (int128 x, int128 y) internal pure returns (int128)

Add one signed 64.64 fixed point number to another and return the result as a signed 64.64 fixed point number.

function sub (int128 x, int128 y) internal pure returns (int128)

Subtract one signed 64.64 fixed point number from another and return the result as a signed 64.64 fixed point number.

function mul (int128 x, int128 y) internal pure returns (int128)

Multiply one signed 64.64 fixed point number by another and return the result as a signed 64.64 fixed point number.

function muli (int128 x, int256 y) internal pure returns (int256)

Multiply a signed 64.64 fixed point number by a signed 256-bit integer number and return the result as a signed 256-bit integer number.

function mulu (int128 x, uint256 y) internal pure returns (uint256)

Multiply a signed 64.64 fixed point number by an unsigned 256-bit integer number and return the result as an unsigned 256-bit integer number.

function div (int128 x, int128 y) internal pure returns (int128)

Divide one signed 64.64 fixed point number by another and return the result as a signed 64.64 fixed point number.

function divi (int256 x, int256 y) internal pure returns (int128)

Divide one signed 256-bit integer number by another and return the result as a signed 64.64 fixed point number.

function divu (uint256 x, uint256 y) internal pure returns (int128)

Divide one unsigned 256-bit integer number by another and return the result as a signed 64.64 fixed point number.

function neg (int128 x) internal pure returns (int128)

Calculate the opposite for a signed 64.64 fixed point number, i.e. -x, and return the result as a signed 64.64 fixed point number.

function abs (int128 x) internal pure returns (int128)

Calculate absolute value of a signed 64.64 fixed point number and return the result as a signed 64.64 fixed point number.

function inv (int128 x) internal pure returns (int128)

Calculate the reciprocal for a signed 64.64 fixed point number, i.e. 1/x, and return the result as a signed 64.64 fixed point number.

Average Values

Here are average value functions.

function avg (int128 x, int128 y) internal pure returns (int128)

Calculate the arithmetic average of two signed 64.64 fixed point numbers and return the result as a signed 64.64 fixed point number.

function gavg (int128 x, int128 y) internal pure returns (int128)

Calculate the geometric average of two signed 64.64 fixed point numbers and return the result as a signed 64.64 fixed point number.

Power and Root

Here are power and root functions.

function pow (int128 x, uint256 y) internal pure returns (int128)

Raise a signed 64.64 fixed point number to a non-negative integer power and return the result as a signed 64.64 fixed point number.

function sqrt (int128 x) internal pure returns (int128)

Calculate the square root of a signed 64.64 fixed point number and return the result as a signed 64.64 fixed point number.

Exponentiation and Logarithm

Here are exponential and logarithm functions.

function log_2 (int128 x) internal pure returns (int128)

Calculate the binary logarithm of a signed 64.64 fixed point number and return the result as a signed 64.64 fixed point number.

function ln (int128 x) internal pure returns (int128)

Calculate the natural logarithm of a signed 64.64 fixed point number and return the result as a signed 64.64 fixed point number.

function exp_2 (int128 x) internal pure returns (int128)

Raise 2 to the power of a signed 64.64 fixed point number, i.e. calculate 2^x, and return the result as a signed 64.64 fixed point number.

function exp (int128 x) internal pure returns (int128)

Exponentiate a signed 64.64 fixed point number, i.e. calculate e^x, and return the result as a signed 64.64 fixed point number.

Conversions

Here are conversion functions.

function fromInt (int256 x) internal pure returns (int128)

Convert a signed 256 bit integer number into a signed 64.64 bit fixed point number.

function toInt (int128 x) internal pure returns (int64)

Convert a signed 64.64 bit fixed point number into a signed 64 bit integer number.

function fromUInt (uint256 x) internal pure returns (int128)

Convert an unsigned 256 bit integer number into a signed 64.64 bit fixed point number.

function toUInt (int128 x) internal pure returns (uint64)

Convert a signed 64.64 bit fixed point number into a unsigned 64 bit integer number.

function from128x128 (int256 x) internal pure returns (int128)

Convert a signed 128.128 bit fixed point number into a signed 64.64 bit fixed point number.

function to128x128 (int128 x) internal pure returns (int256)

Convert a signed 64.64 bit fixed point number into a signed 128.128 bit fixed point number.