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
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
|
/*
Copyright 2018 ZeroEx Intl.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
pragma solidity 0.4.24;
import "../../../utils/SafeMath/SafeMath.sol";
contract LibMath is
SafeMath
{
/// @dev Calculates partial value given a numerator and denominator.
/// @param numerator Numerator.
/// @param denominator Denominator.
/// @param target Value to calculate partial of.
/// @return Partial value of target rounded down.
function getPartialAmount(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (uint256 partialAmount)
{
require(denominator > 0, "DIVISION_BY_ZERO");
partialAmount = safeDiv(
safeMul(numerator, target),
denominator
);
return partialAmount;
}
/// @dev Calculates partial value given a numerator and denominator.
/// @param numerator Numerator.
/// @param denominator Denominator.
/// @param target Value to calculate partial of.
/// @return Partial value of target rounded up.
function getPartialAmountCeil(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (uint256 partialAmount)
{
require(denominator > 0, "DIVISION_BY_ZERO");
// safeDiv computes `floor(a / b)`. We use the identity (a, b integer):
// ceil(a / b) = floor((a + b - 1) / b)
// To implement `ceil(a / b)` using safeDiv.
partialAmount = safeDiv(
safeAdd(safeMul(numerator, target), safeSub(denominator, 1)),
denominator
);
return partialAmount;
}
/// @dev Checks if rounding error > 0.1%.
/// @param numerator Numerator.
/// @param denominator Denominator.
/// @param target Value to multiply with numerator/denominator.
/// @return Rounding error is present.
function isRoundingError(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (bool isError)
{
require(denominator > 0, "DIVISION_BY_ZERO");
// The absolute rounding error is the difference between the rounded
// value and the ideal value. The relative rounding error is the
// absolute rounding error divided by the absolute value of the
// ideal value. This is undefined when the ideal value is zero.
//
// The ideal value is `numerator * target / denominator`.
// Let's call `numerator * target % denominator` the remainder.
// The absolute error is `remainder / denominator`.
//
// When the ideal value is zero, we require the absolute error to
// be zero. Fortunately, this is always the case. The ideal value is
// zero iff `numerator == 0` and/or `target == 0`. In this case the
// remainder and absolute error are also zero.
if (target == 0 || numerator == 0) {
return false;
}
// Otherwise, we want the relative rounding error to be strictly
// less than 0.1%.
// The relative error is `remainder / numerator * target`.
// We want the relative error less than 1 / 1000:
// remainder / numerator * denominator < 1 / 1000
// or equivalently:
// 1000 * remainder < numerator * target
// so we have a rounding error iff:
// 1000 * remainder >= numerator * target
uint256 remainder = mulmod(target, numerator, denominator);
isError = safeMul(1000, remainder) >= safeMul(numerator, target);
return isError;
}
/// @dev Checks if rounding error > 0.1%.
/// @param numerator Numerator.
/// @param denominator Denominator.
/// @param target Value to multiply with numerator/denominator.
/// @return Rounding error is present.
function isRoundingErrorCeil(
uint256 numerator,
uint256 denominator,
uint256 target
)
internal
pure
returns (bool isError)
{
require(denominator > 0, "DIVISION_BY_ZERO");
if (target == 0 || numerator == 0) {
return false;
}
uint256 remainder = mulmod(target, numerator, denominator);
if (remainder == 0) {
return false;
}
remainder = safeSub(denominator, remainder);
isError = safeMul(1000, remainder) >= safeMul(numerator, target);
return isError;
}
}
|
