DSMath
Safe Arithmetic
DS-Math provides arithmetic functions for the common numerical primitive types
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 == 2.42
//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) == 2.42 etherNaming Convention
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.
API Reference
add
Return x + y or an exception in case of uint overflow.
sub
Return x - y or an exception in case of uint overflow.
mul
Return x * y or an exception in case of uint overflow.
min
Return the smaller number of x and y.
max
Return the larger number of x and y.
imin
Return the smaller number of x and y.
imax
Return the larger number of x and y.
wmul
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.
wdiv
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.
rmul
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.
rdiv
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.
rpow
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.