jcs.org
Serenity Operating System
1/*
2 * Copyright (c) 2018-2021, Andreas Kling <kling@serenityos.org>
3 *
4 * SPDX-License-Identifier: BSD-2-Clause
5 */
6
7#include <AK/Platform.h>
8
9#if defined(AK_COMPILER_CLANG)
10# pragma clang optimize off
11#else
12# pragma GCC optimize("O0")
13#endif
14
15#include <LibTest/TestCase.h>
16
17#include <float.h>
18#include <math.h>
19
20TEST_CASE(atan2)
21{
22 EXPECT_APPROXIMATE(atan2(-1, -0.0e0), -M_PI_2);
23 EXPECT_APPROXIMATE(atan2(-0.0e0, -1), -M_PI);
24 EXPECT_APPROXIMATE(atan2(0.0e0, -1), M_PI);
25 EXPECT_APPROXIMATE(atan2(-0.0e0, 1), -0.0e0);
26 EXPECT_APPROXIMATE(atan2(0.0e0, 1), 0.0e0);
27}
28
29TEST_CASE(trig)
30{
31 EXPECT_APPROXIMATE(sin(1234), 0.601928);
32 EXPECT_APPROXIMATE(cos(1234), -0.798551);
33 EXPECT_APPROXIMATE(tan(1234), -0.753775);
34 EXPECT_APPROXIMATE(sqrt(1234), 35.128336);
35 EXPECT_APPROXIMATE(sin(-1), -0.8414709848078965);
36 EXPECT_APPROXIMATE(cos(-1), 0.5403023058681398);
37 EXPECT_APPROXIMATE(tan(-1), -1.5574077246549023);
38 EXPECT(isnan(sqrt(-1)));
39 EXPECT(isnan(asin(1.1)));
40 EXPECT(isnan(asin(-1.1)));
41 EXPECT_APPROXIMATE(asin(0), 0.0);
42 EXPECT_APPROXIMATE(asin(0.01), 0.01);
43 EXPECT_APPROXIMATE(asin(0.1), 0.100167);
44 EXPECT_APPROXIMATE(asin(0.3), 0.304693);
45 EXPECT_APPROXIMATE(asin(0.499), 0.522444);
46 EXPECT_APPROXIMATE(asin(0.5), 0.523599);
47 EXPECT_APPROXIMATE(asin(0.501), 0.524754);
48 EXPECT_APPROXIMATE(asin(0.9), 1.119770);
49 EXPECT_APPROXIMATE(asin(0.99), 1.429257);
50 EXPECT_APPROXIMATE(asin(1.0), 1.570796);
51 EXPECT_APPROXIMATE(atan(0), 0.0);
52 EXPECT_APPROXIMATE(atan(0.5), 0.463648);
53 EXPECT_APPROXIMATE(atan(-0.5), -0.463648);
54 EXPECT_APPROXIMATE(atan(5.5), 1.390943);
55 EXPECT_APPROXIMATE(atan(-5.5), -1.390943);
56 EXPECT_APPROXIMATE(atan(555.5), 1.568996);
57}
58
59TEST_CASE(other)
60{
61 EXPECT_EQ(trunc(9999999999999.5), 9999999999999.0);
62 EXPECT_EQ(trunc(-9999999999999.5), -9999999999999.0);
63}
64
65TEST_CASE(exponents)
66{
67 struct values {
68 double x;
69 double exp;
70 double sinh;
71 double cosh;
72 double tanh;
73 };
74
75 values values[8] {
76 { 1.500000, 4.481689, 2.129279, 2.352410, 0.905148 },
77 { 20.990000, 1305693298.670892, 652846649.335446, 652846649.335446, 1.000000 },
78 { 20.010000, 490041186.687082, 245020593.343541, 245020593.343541, 1.000000 },
79 { 0.000000, 1.000000, 0.000000, 1.000000, 0.000000 },
80 { 0.010000, 1.010050, 0.010000, 1.000050, 0.010000 },
81 { -0.010000, 0.990050, -0.010000, 1.000050, -0.010000 },
82 { -1.000000, 0.367879, -1.175201, 1.543081, -0.761594 },
83 { -17.000000, 0.000000, -12077476.376788, 12077476.376788, -1.000000 },
84 };
85 for (auto& v : values) {
86 EXPECT_APPROXIMATE(exp(v.x), v.exp);
87 EXPECT_APPROXIMATE(sinh(v.x), v.sinh);
88 EXPECT_APPROXIMATE(cosh(v.x), v.cosh);
89 EXPECT_APPROXIMATE(tanh(v.x), v.tanh);
90 }
91 EXPECT_EQ(exp(1000), __builtin_huge_val());
92}
93
94TEST_CASE(logarithms)
95{
96 EXPECT(isnan(log(-1)));
97 EXPECT(log(0) < -1000000);
98 EXPECT_APPROXIMATE(log(0.5), -0.693147);
99 EXPECT_APPROXIMATE(log(1.1), 0.095310);
100 EXPECT_APPROXIMATE(log(5), 1.609438);
101 EXPECT_APPROXIMATE(log(5.5), 1.704748);
102 EXPECT_APPROXIMATE(log(500), 6.214608);
103 EXPECT_APPROXIMATE(log2(5), 2.321928);
104 EXPECT_APPROXIMATE(log10(5), 0.698970);
105}
106
107union Extractor {
108 explicit Extractor(double d)
109 : d(d)
110 {
111 }
112 Extractor(unsigned sign, unsigned exponent, unsigned long long mantissa)
113 : mantissa(mantissa)
114 , exponent(exponent)
115 , sign(sign)
116 {
117 }
118 struct {
119 unsigned long long mantissa : 52;
120 unsigned exponent : 11;
121 unsigned sign : 1;
122 };
123 double d;
124
125 bool operator==(Extractor const& other) const
126 {
127 return other.sign == sign && other.exponent == exponent && other.mantissa == mantissa;
128 }
129};
130namespace AK {
131template<>
132struct Formatter<Extractor> : StandardFormatter {
133 ErrorOr<void> format(FormatBuilder& builder, Extractor const& value)
134 {
135 TRY(builder.put_literal("{"sv));
136 TRY(builder.put_u64(value.sign));
137 TRY(builder.put_literal(", "sv));
138 TRY(builder.put_u64(value.exponent, 16, true));
139 TRY(builder.put_literal(", "sv));
140 TRY(builder.put_u64(value.mantissa, 16, true));
141 TRY(builder.put_literal("}"sv));
142 return {};
143 }
144};
145}
146
147static Extractor nextafter_translator(Extractor x, Extractor target)
148{
149 return Extractor(nextafter(x.d, target.d));
150}
151
152TEST_CASE(nextafter)
153{
154 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
155 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x1, 0x1));
156 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe848200000000)), Extractor(0x0, 0x3ff, 0x1));
157 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
158 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x1));
159 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x412, 0xe847e00000000)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
160 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x412, 0xe848000000000)), Extractor(0x0, 0x0, 0x2));
161 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
162 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
163 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848200000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe8481ffffffff));
164 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
165 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x412, 0xe847fffffffff));
166 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe847e00000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x412, 0xe847dffffffff));
167 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x412, 0xe848000000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x412, 0xe847fffffffff));
168 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
169 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x0, 0x1, 0x0));
170 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x0, 0x3ff, 0x0));
171 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
172 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
173 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x3ff, 0x0));
174 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x0, 0x0, 0x1));
175 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x1, 0x7fe, 0xffffffffffffe));
176 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x1, 0x0), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x0, 0xfffffffffffff));
177 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
178 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
179 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
180 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
181 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x1), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x0, 0x0));
182 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x1, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xffffffffffffe));
183 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x1, 0x0)), Extractor(0x0, 0x0, 0xfffffffffffff));
184 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
185 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x0, 0x0, 0x0)), Extractor(0x0, 0x0, 0x0));
186 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x0, 0x0));
187 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x3fe, 0xfffffffffffff));
188 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x0, 0x1)), Extractor(0x0, 0x0, 0x0));
189 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
190 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x1, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0xfffffffffffff));
191 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d783fc000000)), Extractor(0x0, 0x3fe, 0xfffffffffffff));
192 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
193 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x0), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x1, 0x0, 0x1));
194 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x3ff, 0x0), Extractor(0x1, 0x419, 0x7d78404000000)), Extractor(0x1, 0x3ff, 0x1));
195 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x0, 0x1), Extractor(0x1, 0x419, 0x7d78400000000)), Extractor(0x0, 0x0, 0x0));
196 EXPECT_EQ(nextafter_translator(Extractor(0x0, 0x7fe, 0xfffffffffffff), Extractor(0x0, 0x7fe, 0xfffffffffffff)), Extractor(0x0, 0x7fe, 0xfffffffffffff));
197 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x1, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
198 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d783fc000000), Extractor(0x0, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d783fbffffff));
199 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x1, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
200 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x0)), Extractor(0x1, 0x419, 0x7d783ffffffff));
201 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78404000000), Extractor(0x1, 0x3ff, 0x0)), Extractor(0x1, 0x419, 0x7d78403ffffff));
202 EXPECT_EQ(nextafter_translator(Extractor(0x1, 0x419, 0x7d78400000000), Extractor(0x0, 0x0, 0x1)), Extractor(0x1, 0x419, 0x7d783ffffffff));
203}
204
205TEST_CASE(scalbn)
206{
207 EXPECT(isnan(scalbn(NAN, 3)));
208 EXPECT(!isfinite(scalbn(INFINITY, 5)));
209 EXPECT_EQ(scalbn(0, 3), 0);
210 EXPECT_EQ(scalbn(15.3, 0), 15.3);
211
212 // TODO: implement denormal handling in fallback scalbn
213 // EXPECT_EQ(scalbn(0x0.0000000000008p-1022, 16), 0x0.0000000000008p-1006);
214 static constexpr auto biggest_subnormal = DBL_MIN - DBL_TRUE_MIN;
215 auto smallest_normal = scalbn(biggest_subnormal, 1);
216 Extractor ex(smallest_normal);
217 EXPECT(ex.exponent != 0);
218
219 EXPECT_EQ(scalbn(2.0, 4), 32.0);
220}
221
222TEST_CASE(gamma)
223{
224 EXPECT(isinf(tgamma(+0.0)) && !signbit(tgamma(+0.0)));
225 EXPECT(isinf(tgamma(-0.0)) && signbit(tgamma(-0.0)));
226 EXPECT(isinf(tgamma(INFINITY)) && !signbit(tgamma(INFINITY)));
227 EXPECT(isnan(tgamma(NAN)));
228 EXPECT(isnan(tgamma(-INFINITY)));
229 EXPECT(isnan(tgamma(-5)));
230
231 // TODO: investigate Stirling approximation implementation of gamma function
232 // EXPECT_APPROXIMATE(tgamma(0.5), sqrt(M_PI));
233 EXPECT_EQ(tgammal(21.0l), 2'432'902'008'176'640'000.0l);
234 EXPECT_EQ(tgamma(19.0), 6'402'373'705'728'000.0);
235 EXPECT_EQ(tgammaf(11.0f), 3628800.0f);
236 EXPECT_EQ(tgamma(4.0), 6);
237
238 EXPECT_EQ(lgamma(1.0), 0.0);
239 EXPECT_EQ(lgamma(2.0), 0.0);
240 EXPECT(isinf(lgamma(0.0)));
241 EXPECT(!signbit(lgamma(-0.0)));
242 EXPECT(isnan(lgamma(NAN)));
243 EXPECT(isinf(lgamma(INFINITY)));
244 EXPECT(isinf(lgamma(-INFINITY)));
245 EXPECT_EQ(signgam, 1);
246 lgamma(-2.5);
247 EXPECT_EQ(signgam, -1);
248}
249
250TEST_CASE(fmax_and_fmin)
251{
252 EXPECT(fmax(-INFINITY, 0) == 0);
253 EXPECT(fmax(NAN, 12) == 12);
254 EXPECT(fmax(5, NAN) == 5);
255 EXPECT(isnan(fmax(NAN, NAN)));
256 EXPECT(isinf(fmax(1'000'000, INFINITY)));
257
258 EXPECT(isinf(fmin(-INFINITY, 0)));
259 EXPECT(fmin(0, INFINITY) == 0);
260 EXPECT(fmin(NAN, 5) == 5);
261 EXPECT(fmin(0, NAN) == 0);
262 EXPECT(isnan(fmin(NAN, NAN)));
263}
264
265TEST_CASE(acos)
266{
267 EXPECT_APPROXIMATE(acos(-1), M_PI);
268 EXPECT_APPROXIMATE(acos(0), 0.5 * M_PI);
269 EXPECT_APPROXIMATE(acos(1), 0);
270 EXPECT(isnan(acos(1.1)));
271}
272
273TEST_CASE(floor)
274{
275 EXPECT_EQ(floor(0.125), 0);
276 EXPECT_EQ(floor(-0.125), -1.0);
277 EXPECT_EQ(floor(0.5), 0);
278 EXPECT_EQ(floor(-0.5), -1.0);
279 EXPECT_EQ(floor(0.25), 0);
280 EXPECT_EQ(floor(-0.25), -1.0);
281 EXPECT_EQ(floor(-3.0 / 2.0), -2.0);
282}
283
284TEST_CASE(ceil)
285{
286 EXPECT_EQ(ceil(0.125), 1.0);
287 EXPECT_EQ(ceil(-0.125), 0);
288 EXPECT_EQ(ceil(0.5), 1.0);
289 EXPECT_EQ(ceil(-0.5), 0);
290 EXPECT_EQ(ceil(0.25), 1.0);
291 EXPECT_EQ(ceil(-0.25), 0);
292 EXPECT_EQ(ceil(-3.0 / 2.0), -1.0);
293}