Safe Arithmetic
DS-Math provides arithmetic functions for the common numerical primitive typesi
of Solidity. You can safely add, subtract, multiply, and divide uint
numbers
without fear of integer overflow. You can also find the minimum and maximum of
two numbers.
Additionally, this package provides arithmetic functions for new two higher level numerical concepts called wad (18 decimals) and ray (27 decimals). These are used to represent fixed-point decimal numbers.
A wad is a decimal number with 18 digits of precision and a ray is a decimal
number with 27 digits of precision. These functions are necessary to account for
the difference between how integer arithmetic behaves normally, and how decimal
arithmetic should actually work. A brief example using wmul
, which returns the
product of a wad and another number:
1.1 * 2.2 == 2.24
//Regular integer arithmetic adds orders of magnitude:
110 * 220 == 24200
// Wad arithmetic does not add orders of magnitude:
wmul(1.1 ether, 2.2 ether) == 2.24 ether
The standard functions are the uint
set, so their function names are not
prefixed: add
, sub
, mul
, min
, and max
. There is no div
function, as
divide-by-zero checking is built into the Solidity compiler.
The int
functions have an i
prefix: imin
, and imax
.
Wad functions have a w
prefix: wmul
, wdiv
.
Ray functions have a r
prefix: rmul
, rdiv
, rpow
.
Return x + y
or an exception in case of uint
overflow.
Return x - y
or an exception in case of uint
overflow.
Return x * y
or an exception in case of uint
overflow.
Return the smaller number of x
and y
.
Return the larger number of x
and y
.
Return the smaller number of x
and y
.
Return the larger number of x
and y
.
Multiply two Wads and return a new Wad with the correct level of precision. A Wad is a decimal number with 18 digits of precision that is being represented as an integer.
Divide two Wads and return a new Wad with the correct level of precision. A Wad is a decimal number with 18 digits of precision that is being represented as an integer.
Multiply two Rays and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.
Divide two Rays and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.
Raise a Ray to the n^th power and return a new Ray with the correct level of precision. A Ray is a decimal number with 27 digits of precision that is being represented as an integer.