1// Licensed to the .NET Foundation under one or more agreements.
2// The .NET Foundation licenses this file to you under the MIT license.
3// See the LICENSE file in the project root for more information.
4
5/*=====================================================================
6**
7** Source: test1.c
8**
9** Purpose: Tests that atan2 returns correct values for a subset of values.
10** Tests with positive and negative values of x and y to ensure
11** atan2 is returning results from the correct quadrant.
12**
13**===================================================================*/
14
15#include <palsuite.h>
16
17// binary64 (double) has a machine epsilon of 2^-52 (approx. 2.22e-16). However, this
18// is slightly too accurate when writing tests meant to run against libm implementations
19// for various platforms. 2^-50 (approx. 8.88e-16) seems to be as accurate as we can get.
20//
21// The tests themselves will take PAL_EPSILON and adjust it according to the expected result
22// so that the delta used for comparison will compare the most significant digits and ignore
23// any digits that are outside the double precision range (15-17 digits).
24
25// For example, a test with an expect result in the format of 0.xxxxxxxxxxxxxxxxx will use
26// PAL_EPSILON for the variance, while an expected result in the format of 0.0xxxxxxxxxxxxxxxxx
27// will use PAL_EPSILON / 10 and and expected result in the format of x.xxxxxxxxxxxxxxxx will
28// use PAL_EPSILON * 10.
29#define PAL_EPSILON 8.8817841970012523e-16
30
31#define PAL_NAN sqrt(-1.0)
32#define PAL_POSINF -log(0.0)
33#define PAL_NEGINF log(0.0)
34
35/**
36 * Helper test structure
37 */
38struct test
39{
40 double x; /* first component of the value to test the function with */
41 double y; /* second component of the value to test the function with */
42 double expected; /* expected result */
43 double variance; /* maximum delta between the expected and actual result */
44};
45
46/**
47 * validate
48 *
49 * test validation function
50 */
51void __cdecl validate(double x, double y, double expected, double variance)
52{
53 double result = pow(x, y);
54
55 /*
56 * The test is valid when the difference between result
57 * and expected is less than or equal to variance
58 */
59 double delta = fabs(result - expected);
60
61 if (delta > variance)
62 {
63 Fail("pow(%g, %g) returned %20.17g when it should have returned %20.17g",
64 x, y, result, expected);
65 }
66}
67
68/**
69 * validate
70 *
71 * test validation function for values returning NaN
72 */
73void __cdecl validate_isnan(double x, double y)
74{
75 double result = pow(x, y);
76
77 if (!_isnan(result))
78 {
79 Fail("pow(%g, %g) returned %20.17g when it should have returned %20.17g",
80 x, y, result, PAL_NAN);
81 }
82}
83
84/**
85 * main
86 *
87 * executable entry point
88 */
89int __cdecl main(int argc, char **argv)
90{
91 struct test tests[] =
92 {
93 /* x y expected variance */
94 { PAL_NEGINF, PAL_NEGINF, 0, PAL_EPSILON },
95 { PAL_NEGINF, PAL_POSINF, PAL_POSINF, 0 },
96
97 { -10, PAL_NEGINF, 0, PAL_EPSILON },
98 { -10, -1, -0.1, PAL_EPSILON },
99 { -10, 0, 1, PAL_EPSILON * 10 },
100 { -10, 1, -10, PAL_EPSILON * 100 },
101 { -10, PAL_POSINF, PAL_POSINF, 0 },
102
103 { -2.7182818284590452, PAL_NEGINF, 0, PAL_EPSILON }, // x: -(e)
104 { -2.7182818284590452, -1, -0.36787944117144232, PAL_EPSILON }, // x: -(e)
105 { -2.7182818284590452, 0, 1, PAL_EPSILON * 10 }, // x: -(e)
106 { -2.7182818284590452, 1, -2.7182818284590452, PAL_EPSILON * 10 }, // x: -(e) expected: e
107 { -2.7182818284590452, PAL_POSINF, PAL_POSINF, 0 }, // x: -(e)
108
109 { -1.0, PAL_NEGINF, 1.0, PAL_EPSILON * 10 },
110 { -1.0, PAL_POSINF, 1.0, PAL_EPSILON * 10 },
111
112 { -0.0, PAL_NEGINF, PAL_POSINF, 0 },
113 { -0.0, -1, PAL_NEGINF, 0 },
114 { -0.0, -0.0, 1, PAL_EPSILON * 10 },
115 { -0.0, 0, 1, PAL_EPSILON * 10 },
116 { -0.0, 1, -0.0, PAL_EPSILON },
117 { -0.0, PAL_POSINF, 0, PAL_EPSILON },
118
119 { PAL_NAN, -0.0, 1.0, PAL_EPSILON * 10 },
120 { PAL_NAN, 0, 1.0, PAL_EPSILON * 10 },
121
122 { 0.0, PAL_NEGINF, PAL_POSINF, 0 },
123 { 0.0, -1, PAL_POSINF, 0 },
124 { 0, -0.0, 1, PAL_EPSILON * 10 },
125 { 0, 0, 1, PAL_EPSILON * 10 },
126 { 0.0, 1, 0, PAL_EPSILON },
127 { 0.0, PAL_POSINF, 0, PAL_EPSILON },
128
129 { 1, PAL_NEGINF, 1, PAL_EPSILON * 10 },
130 { 1, PAL_POSINF, 1, PAL_EPSILON * 10 },
131
132 { 2.7182818284590452, PAL_NEGINF, 0, PAL_EPSILON },
133 { 2.7182818284590452, -3.1415926535897932, 0.043213918263772250, PAL_EPSILON / 10 }, // x: e y: -(pi)
134 { 2.7182818284590452, -2.7182818284590452, 0.065988035845312537, PAL_EPSILON / 10 }, // x: e y: -(e)
135 { 2.7182818284590452, -2.3025850929940457, 0.1, PAL_EPSILON }, // x: e y: -(ln(10))
136 { 2.7182818284590452, -1.5707963267948966, 0.20787957635076191, PAL_EPSILON }, // x: e y: -(pi / 2)
137 { 2.7182818284590452, -1.4426950408889634, 0.23629008834452270, PAL_EPSILON }, // x: e y: -(log2(e))
138 { 2.7182818284590452, -1.4142135623730950, 0.24311673443421421, PAL_EPSILON }, // x: e y: -(sqrt(2))
139 { 2.7182818284590452, -1.1283791670955126, 0.32355726390307110, PAL_EPSILON }, // x: e y: -(2 / sqrt(pi))
140 { 2.7182818284590452, -1, 0.36787944117144232, PAL_EPSILON }, // x: e y: -(1)
141 { 2.7182818284590452, -0.78539816339744831, 0.45593812776599624, PAL_EPSILON }, // x: e y: -(pi / 4)
142 { 2.7182818284590452, -0.70710678118654752, 0.49306869139523979, PAL_EPSILON }, // x: e y: -(1 / sqrt(2))
143 { 2.7182818284590452, -0.69314718055994531, 0.5, PAL_EPSILON }, // x: e y: -(ln(2))
144 { 2.7182818284590452, -0.63661977236758134, 0.52907780826773535, PAL_EPSILON }, // x: e y: -(2 / pi)
145 { 2.7182818284590452, -0.43429448190325183, 0.64772148514180065, PAL_EPSILON }, // x: e y: -(log10(e))
146 { 2.7182818284590452, -0.31830988618379067, 0.72737734929521647, PAL_EPSILON }, // x: e y: -(1 / pi)
147 { 2.7182818284590452, 0, 1, PAL_EPSILON * 10 }, // x: e
148 { 2.7182818284590452, 0.31830988618379067, 1.3748022274393586, PAL_EPSILON * 10 }, // x: e y: 1 / pi
149 { 2.7182818284590452, 0.43429448190325183, 1.5438734439711811, PAL_EPSILON * 10 }, // x: e y: log10(e)
150 { 2.7182818284590452, 0.63661977236758134, 1.8900811645722220, PAL_EPSILON * 10 }, // x: e y: 2 / pi
151 { 2.7182818284590452, 0.69314718055994531, 2, PAL_EPSILON * 10 }, // x: e y: ln(2)
152 { 2.7182818284590452, 0.70710678118654752, 2.0281149816474725, PAL_EPSILON * 10 }, // x: e y: 1 / sqrt(2)
153 { 2.7182818284590452, 0.78539816339744831, 2.1932800507380155, PAL_EPSILON * 10 }, // x: e y: pi / 4
154 { 2.7182818284590452, 1, 2.7182818284590452, PAL_EPSILON * 10 }, // x: e expected: e
155 { 2.7182818284590452, 1.1283791670955126, 3.0906430223107976, PAL_EPSILON * 10 }, // x: e y: 2 / sqrt(pi)
156 { 2.7182818284590452, 1.4142135623730950, 4.1132503787829275, PAL_EPSILON * 10 }, // x: e y: sqrt(2)
157 { 2.7182818284590452, 1.4426950408889634, 4.2320861065570819, PAL_EPSILON * 10 }, // x: e y: log2(e)
158 { 2.7182818284590452, 1.5707963267948966, 4.8104773809653517, PAL_EPSILON * 10 }, // x: e y: pi / 2
159 { 2.7182818284590452, 2.3025850929940457, 10, PAL_EPSILON * 100 }, // x: e y: ln(10)
160 { 2.7182818284590452, 2.7182818284590452, 15.154262241479264, PAL_EPSILON * 100 }, // x: e y: e
161 { 2.7182818284590452, 3.1415926535897932, 23.140692632779269, PAL_EPSILON * 100 }, // x: e y: pi
162 { 2.7182818284590452, PAL_POSINF, PAL_POSINF, 0 }, // x: e
163
164 { 10, PAL_NEGINF, 0, 0 },
165 { 10, -3.1415926535897932, 0.00072178415907472774, PAL_EPSILON / 1000 }, // y: -(pi)
166 { 10, -2.7182818284590452, 0.0019130141022243176, PAL_EPSILON / 100 }, // y: -(e)
167 { 10, -2.3025850929940457, 0.0049821282964407206, PAL_EPSILON / 100 }, // y: -(ln(10))
168 { 10, -1.5707963267948966, 0.026866041001136132, PAL_EPSILON / 10 }, // y: -(pi / 2)
169 { 10, -1.4426950408889634, 0.036083192820787210, PAL_EPSILON / 10 }, // y: -(log2(e))
170 { 10, -1.4142135623730950, 0.038528884700322026, PAL_EPSILON / 10 }, // y: -(sqrt(2))
171 { 10, -1.1283791670955126, 0.074408205860642723, PAL_EPSILON / 10 }, // y: -(2 / sqrt(pi))
172 { 10, -1, 0.1, PAL_EPSILON }, // y: -(1)
173 { 10, -0.78539816339744831, 0.16390863613957665, PAL_EPSILON }, // y: -(pi / 4)
174 { 10, -0.70710678118654752, 0.19628775993505562, PAL_EPSILON }, // y: -(1 / sqrt(2))
175 { 10, -0.69314718055994531, 0.20269956628651730, PAL_EPSILON }, // y: -(ln(2))
176 { 10, -0.63661977236758134, 0.23087676451600055, PAL_EPSILON }, // y: -(2 / pi)
177 { 10, -0.43429448190325183, 0.36787944117144232, PAL_EPSILON }, // y: -(log10(e))
178 { 10, -0.31830988618379067, 0.48049637305186868, PAL_EPSILON }, // y: -(1 / pi)
179 { 10, 0, 1, PAL_EPSILON * 10 },
180 { 10, 0.31830988618379067, 2.0811811619898573, PAL_EPSILON * 10 }, // y: 1 / pi
181 { 10, 0.43429448190325183, 2.7182818284590452, PAL_EPSILON * 10 }, // y: log10(e) expected: e
182 { 10, 0.63661977236758134, 4.3313150290214525, PAL_EPSILON * 10 }, // y: 2 / pi
183 { 10, 0.69314718055994531, 4.9334096679145963, PAL_EPSILON * 10 }, // y: ln(2)
184 { 10, 0.70710678118654752, 5.0945611704512962, PAL_EPSILON * 10 }, // y: 1 / sqrt(2)
185 { 10, 0.78539816339744831, 6.1009598002416937, PAL_EPSILON * 10 }, // y: pi / 4
186 { 10, 1, 10, PAL_EPSILON * 100 },
187 { 10, 1.1283791670955126, 13.439377934644400, PAL_EPSILON * 100 }, // y: 2 / sqrt(pi)
188 { 10, 1.4142135623730950, 25.954553519470081, PAL_EPSILON * 100 }, // y: sqrt(2)
189 { 10, 1.4426950408889634, 27.713733786437790, PAL_EPSILON * 100 }, // y: log2(e)
190 { 10, 1.5707963267948966, 37.221710484165167, PAL_EPSILON * 100 }, // y: pi / 2
191 { 10, 2.3025850929940457, 200.71743249053009, PAL_EPSILON * 1000 }, // y: ln(10)
192 { 10, 2.7182818284590452, 522.73529967043665, PAL_EPSILON * 1000 }, // y: e
193 { 10, 3.1415926535897932, 1385.4557313670111, PAL_EPSILON * 10000 }, // y: pi
194 { 10, PAL_POSINF, PAL_POSINF, 0 },
195
196 { PAL_POSINF, PAL_NEGINF, 0, PAL_EPSILON },
197 { PAL_POSINF, PAL_POSINF, PAL_POSINF, 0 },
198 };
199
200 if (PAL_Initialize(argc, argv) != 0)
201 {
202 return FAIL;
203 }
204
205 for (int i = 0; i < (sizeof(tests) / sizeof(struct test)); i++)
206 {
207 validate(tests[i].x, tests[i].y, tests[i].expected, tests[i].variance);
208 }
209
210 validate_isnan(-10, -1.5707963267948966); // y: -(pi / 2)
211 validate_isnan(-10, -0.78539816339744828); // y: -(pi / 4)
212 validate_isnan(-10, 0.78539816339744828); // y: pi / 4
213 validate_isnan(-10, 1.5707963267948966); // y: pi / 2
214
215 validate_isnan(-2.7182818284590452, -1.5707963267948966); // x: -(e) y: -(pi / 2)
216 validate_isnan(-2.7182818284590452, -0.78539816339744828); // x: -(e) y: -(pi / 4)
217 validate_isnan(-2.7182818284590452, 0.78539816339744828); // x: -(e) y: pi / 4
218 validate_isnan(-2.7182818284590452, 1.5707963267948966); // x: -(e) y: pi / 2
219
220 validate_isnan(PAL_NEGINF, PAL_NAN);
221 validate_isnan(PAL_NAN, PAL_NEGINF);
222
223 validate_isnan(PAL_POSINF, PAL_NAN);
224 validate_isnan(PAL_NAN, PAL_POSINF);
225
226 validate_isnan(PAL_NAN, PAL_NAN);
227
228 PAL_Terminate();
229 return PASS;
230}
231