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
|
//===- MatrixTest.cpp - Tests for QuasiPolynomial -------------------------===//
//
// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
// See https://llvm.org/LICENSE.txt for license information.
// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
//
//===----------------------------------------------------------------------===//
#include "mlir/Analysis/Presburger/QuasiPolynomial.h"
#include "./Utils.h"
#include "mlir/Analysis/Presburger/Fraction.h"
#include <gmock/gmock.h>
#include <gtest/gtest.h>
using namespace mlir;
using namespace presburger;
// Test the arithmetic operations on QuasiPolynomials;
// addition, subtraction, multiplication, and division
// by a constant.
// Two QPs of 3 parameters each were generated randomly
// and their sum, difference, and product computed by hand.
TEST(QuasiPolynomialTest, arithmetic) {
QuasiPolynomial qp1(
3, {Fraction(1, 3), Fraction(1, 1), Fraction(1, 2)},
{{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4), Fraction(0, 1)}}});
QuasiPolynomial qp2(
3, {Fraction(1, 1), Fraction(2, 1)},
{{{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1), Fraction(0, 1)}}});
QuasiPolynomial sum = qp1 + qp2;
EXPECT_EQ_REPR_QUASIPOLYNOMIAL(
sum,
QuasiPolynomial(
3,
{Fraction(1, 3), Fraction(1, 1), Fraction(1, 2), Fraction(1, 1),
Fraction(2, 1)},
{{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4), Fraction(0, 1)}},
{{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1),
Fraction(0, 1)}}}));
QuasiPolynomial diff = qp1 - qp2;
EXPECT_EQ_REPR_QUASIPOLYNOMIAL(
diff,
QuasiPolynomial(
3,
{Fraction(1, 3), Fraction(1, 1), Fraction(1, 2), Fraction(-1, 1),
Fraction(-2, 1)},
{{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4), Fraction(0, 1)}},
{{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1),
Fraction(0, 1)}}}));
QuasiPolynomial prod = qp1 * qp2;
EXPECT_EQ_REPR_QUASIPOLYNOMIAL(
prod,
QuasiPolynomial(
3,
{Fraction(1, 3), Fraction(2, 3), Fraction(1, 1), Fraction(2, 1),
Fraction(1, 2), Fraction(1, 1)},
{{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)},
{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)},
{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1), Fraction(0, 1)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)},
{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)},
{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1), Fraction(0, 1)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4), Fraction(0, 1)},
{Fraction(1, 2), Fraction(0, 1), Fraction(-1, 3), Fraction(5, 3)},
{Fraction(2, 1), Fraction(5, 4), Fraction(9, 7), Fraction(-1, 5)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4), Fraction(0, 1)},
{Fraction(1, 3), Fraction(-2, 3), Fraction(1, 1),
Fraction(0, 1)}}}));
QuasiPolynomial quot = qp1 / 2;
EXPECT_EQ_REPR_QUASIPOLYNOMIAL(
quot,
QuasiPolynomial(
3, {Fraction(1, 6), Fraction(1, 2), Fraction(1, 4)},
{{{Fraction(1, 1), Fraction(-1, 2), Fraction(4, 5), Fraction(0, 1)},
{Fraction(2, 3), Fraction(3, 4), Fraction(-1, 1), Fraction(5, 7)}},
{{Fraction(1, 2), Fraction(1, 1), Fraction(4, 5), Fraction(1, 1)}},
{{Fraction(-3, 2), Fraction(1, 1), Fraction(5, 6), Fraction(7, 5)},
{Fraction(1, 4), Fraction(2, 1), Fraction(6, 5), Fraction(-9, 8)},
{Fraction(3, 2), Fraction(2, 5), Fraction(-7, 4),
Fraction(0, 1)}}}));
}
// Test the simplify() operation on QPs, which removes terms that
// are identically zero. A random QP was generated and terms were
// changed to account for each condition in simplify() –
// the term coefficient being zero, or all the coefficients in some
// affine term in the product being zero.
TEST(QuasiPolynomialTest, simplify) {
QuasiPolynomial qp(2,
{Fraction(2, 3), Fraction(0, 1), Fraction(1, 1),
Fraction(1, 2), Fraction(0, 1)},
{{{Fraction(1, 1), Fraction(3, 4), Fraction(5, 3)},
{Fraction(2, 1), Fraction(0, 1), Fraction(0, 1)}},
{{Fraction(1, 3), Fraction(8, 5), Fraction(2, 5)}},
{{Fraction(2, 7), Fraction(9, 5), Fraction(0, 1)},
{Fraction(0, 1), Fraction(0, 1), Fraction(0, 1)}},
{{Fraction(1, 1), Fraction(4, 5), Fraction(6, 5)}},
{{Fraction(1, 3), Fraction(4, 3), Fraction(7, 8)}}});
EXPECT_EQ_REPR_QUASIPOLYNOMIAL(
qp.simplify(),
QuasiPolynomial(2, {Fraction(2, 3), Fraction(1, 2)},
{{{Fraction(1, 1), Fraction(3, 4), Fraction(5, 3)},
{Fraction(2, 1), Fraction(0, 1), Fraction(0, 1)}},
{{Fraction(1, 1), Fraction(4, 5), Fraction(6, 5)}}}));
}
|
