An overflow-protected fixed-point arithmetic library for Solidity.
FixidityLib provide fixed point arithmetic for Solidity. This is achieved by using int256 as the type throughout the library and designating a number of digits in each int256 for holding the fractional part. This is equivalent to displacing the comma in a non-integer number a fixed number of positions to the left. All the arithmetic operations that have been implemented maintain constant the number of digits to the left of the comma that are represented.
The main arithmetic operations currently supported are addition, subtraction, multiplication, division and logarithms. In a near future exponentials and square roots might be supported.
In addition to fixed point arithmetic operations, FixidityLib is fully protected against overflow. Any operation that causes an overflow to happen will revert.
A number of constants have been provided that identify the safe limits for operation. When fixed-point arithmetic operations are done with values between zero and a limit there will be no overflows and therefore the functions will never revert. It would be then useful in some cases to use those limits to reject user inputs with an informative message when those inputs might cause erratic behaviour. With careful consideration it is possible to perform operations with values that are beyond the limits, but doing so must only be done with appropriate knowledge of range of each operator.
FixidityLib currently assumes 24 digits as the desired size for the decimal part. To change this to a different value the constants need to be adjusted. The formulas used to calculate the constants have been provided to facilitate this. All other functions will work as long as the constants are consistent.
An extensive collection of tests was created to prove the robustness of FixidityLib, and they should be run whenever a change in the digits is done.
Currently FixidityLib doesn't use its own type, so it is up to the user to remember whether a given int256 is a FixidityLib fixed point number or not, and to take care to use the toFixed() and toUint() functions accordingly to create fixed point numbers and convert them back to integers.