-
Notifications
You must be signed in to change notification settings - Fork 1
/
DSMath.sol
74 lines (67 loc) · 2.34 KB
/
DSMath.sol
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
// SPDX-License-Identifier: GPL-3.0
pragma solidity >0.4.13;
contract DSMath {
function add(uint x, uint y) internal pure returns (uint z) {
require((z = x + y) >= x, "ds-math-add-overflow");
}
function sub(uint x, uint y) internal pure returns (uint z) {
require((z = x - y) <= x, "ds-math-sub-underflow");
}
function mul(uint x, uint y) internal pure returns (uint z) {
require(y == 0 || (z = x * y) / y == x, "ds-math-mul-overflow");
}
function min(uint x, uint y) internal pure returns (uint z) {
return x <= y ? x : y;
}
function max(uint x, uint y) internal pure returns (uint z) {
return x >= y ? x : y;
}
function imin(int x, int y) internal pure returns (int z) {
return x <= y ? x : y;
}
function imax(int x, int y) internal pure returns (int z) {
return x >= y ? x : y;
}
uint constant WAD = 10 ** 18;
uint constant RAY = 10 ** 27;
//rounds to zero if x*y < WAD / 2
function wmul(uint x, uint y) internal pure returns (uint z) {
z = add(mul(x, y), WAD / 2) / WAD;
}
//rounds to zero if x*y < WAD / 2
function rmul(uint x, uint y) internal pure returns (uint z) {
z = add(mul(x, y), RAY / 2) / RAY;
}
//rounds to zero if x*y < WAD / 2
function wdiv(uint x, uint y) internal pure returns (uint z) {
z = add(mul(x, WAD), y / 2) / y;
}
//rounds to zero if x*y < RAY / 2
function rdiv(uint x, uint y) internal pure returns (uint z) {
z = add(mul(x, RAY), y / 2) / y;
}
// This famous algorithm is called "exponentiation by squaring"
// and calculates x^n with x as fixed-point and n as regular unsigned.
//
// It's O(log n), instead of O(n) for naive repeated multiplication.
//
// These facts are why it works:
//
// If n is even, then x^n = (x^2)^(n/2).
// If n is odd, then x^n = x * x^(n-1),
// and applying the equation for even x gives
// x^n = x * (x^2)^((n-1) / 2).
//
// Also, EVM division is flooring and
// floor[(n-1) / 2] = floor[n / 2].
//
function rpow(uint x, uint n) internal pure returns (uint z) {
z = n % 2 != 0 ? x : RAY;
for (n /= 2; n != 0; n /= 2) {
x = rmul(x, x);
if (n % 2 != 0) {
z = rmul(z, x);
}
}
}
}