1 // Copyright 2016 the V8 project authors. All rights reserved.
2 // Use of this source code is governed by a BSD-style license that can be
3 // found in the LICENSE file.
4
5 #include <limits>
6
7 #include "src/base/ieee754.h"
8 #include "src/base/macros.h"
9 #include "testing/gmock-support.h"
10 #include "testing/gtest-support.h"
11
12 using testing::BitEq;
13 using testing::IsNaN;
14
15 namespace v8 {
16 namespace base {
17 namespace ieee754 {
18
19 namespace {
20
21 double const kE = 2.718281828459045;
22 double const kPI = 3.141592653589793;
23 double const kTwo120 = 1.329227995784916e+36;
24
25 } // namespace
26
TEST(Ieee754,Atan)27 TEST(Ieee754, Atan) {
28 EXPECT_THAT(atan(std::numeric_limits<double>::quiet_NaN()), IsNaN());
29 EXPECT_THAT(atan(std::numeric_limits<double>::signaling_NaN()), IsNaN());
30 EXPECT_THAT(atan(-0.0), BitEq(-0.0));
31 EXPECT_THAT(atan(0.0), BitEq(0.0));
32 EXPECT_DOUBLE_EQ(1.5707963267948966,
33 atan(std::numeric_limits<double>::infinity()));
34 EXPECT_DOUBLE_EQ(-1.5707963267948966,
35 atan(-std::numeric_limits<double>::infinity()));
36 }
37
TEST(Ieee754,Atan2)38 TEST(Ieee754, Atan2) {
39 EXPECT_THAT(atan2(std::numeric_limits<double>::quiet_NaN(),
40 std::numeric_limits<double>::quiet_NaN()),
41 IsNaN());
42 EXPECT_THAT(atan2(std::numeric_limits<double>::quiet_NaN(),
43 std::numeric_limits<double>::signaling_NaN()),
44 IsNaN());
45 EXPECT_THAT(atan2(std::numeric_limits<double>::signaling_NaN(),
46 std::numeric_limits<double>::quiet_NaN()),
47 IsNaN());
48 EXPECT_THAT(atan2(std::numeric_limits<double>::signaling_NaN(),
49 std::numeric_limits<double>::signaling_NaN()),
50 IsNaN());
51 EXPECT_DOUBLE_EQ(0.7853981633974483,
52 atan2(std::numeric_limits<double>::infinity(),
53 std::numeric_limits<double>::infinity()));
54 EXPECT_DOUBLE_EQ(2.356194490192345,
55 atan2(std::numeric_limits<double>::infinity(),
56 -std::numeric_limits<double>::infinity()));
57 EXPECT_DOUBLE_EQ(-0.7853981633974483,
58 atan2(-std::numeric_limits<double>::infinity(),
59 std::numeric_limits<double>::infinity()));
60 EXPECT_DOUBLE_EQ(-2.356194490192345,
61 atan2(-std::numeric_limits<double>::infinity(),
62 -std::numeric_limits<double>::infinity()));
63 }
64
TEST(Ieee754,Atanh)65 TEST(Ieee754, Atanh) {
66 EXPECT_THAT(atanh(std::numeric_limits<double>::quiet_NaN()), IsNaN());
67 EXPECT_THAT(atanh(std::numeric_limits<double>::signaling_NaN()), IsNaN());
68 EXPECT_THAT(atanh(std::numeric_limits<double>::infinity()), IsNaN());
69 EXPECT_EQ(std::numeric_limits<double>::infinity(), atanh(1));
70 EXPECT_EQ(-std::numeric_limits<double>::infinity(), atanh(-1));
71 EXPECT_DOUBLE_EQ(0.54930614433405478, atanh(0.5));
72 }
73
TEST(Ieee754,Cos)74 TEST(Ieee754, Cos) {
75 // Test values mentioned in the EcmaScript spec.
76 EXPECT_THAT(cos(std::numeric_limits<double>::quiet_NaN()), IsNaN());
77 EXPECT_THAT(cos(std::numeric_limits<double>::signaling_NaN()), IsNaN());
78 EXPECT_THAT(cos(std::numeric_limits<double>::infinity()), IsNaN());
79 EXPECT_THAT(cos(-std::numeric_limits<double>::infinity()), IsNaN());
80
81 // Tests for cos for |x| < pi/4
82 EXPECT_EQ(1.0, 1 / cos(-0.0));
83 EXPECT_EQ(1.0, 1 / cos(0.0));
84 // cos(x) = 1 for |x| < 2^-27
85 EXPECT_EQ(1, cos(2.3283064365386963e-10));
86 EXPECT_EQ(1, cos(-2.3283064365386963e-10));
87 // Test KERNELCOS for |x| < 0.3.
88 // cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2)
89 EXPECT_EQ(0.9876883405951378, cos(0.15707963267948966));
90 // Test KERNELCOS for x ~= 0.78125
91 EXPECT_EQ(0.7100335477927638, cos(0.7812504768371582));
92 EXPECT_EQ(0.7100338835660797, cos(0.78125));
93 // Test KERNELCOS for |x| > 0.3.
94 // cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4)
95 EXPECT_EQ(0.9238795325112867, cos(0.39269908169872414));
96 // Test KERNELTAN for |x| < 0.67434.
97 EXPECT_EQ(0.9238795325112867, cos(-0.39269908169872414));
98
99 // Tests for cos.
100 EXPECT_EQ(1, cos(3.725290298461914e-9));
101 // Cover different code paths in KERNELCOS.
102 EXPECT_EQ(0.9689124217106447, cos(0.25));
103 EXPECT_EQ(0.8775825618903728, cos(0.5));
104 EXPECT_EQ(0.7073882691671998, cos(0.785));
105 // Test that cos(Math.PI/2) != 0 since Math.PI is not exact.
106 EXPECT_EQ(6.123233995736766e-17, cos(1.5707963267948966));
107 // Test cos for various phases.
108 EXPECT_EQ(0.7071067811865474, cos(7.0 / 4 * kPI));
109 EXPECT_EQ(0.7071067811865477, cos(9.0 / 4 * kPI));
110 EXPECT_EQ(-0.7071067811865467, cos(11.0 / 4 * kPI));
111 EXPECT_EQ(-0.7071067811865471, cos(13.0 / 4 * kPI));
112 EXPECT_EQ(0.9367521275331447, cos(1000000.0));
113 EXPECT_EQ(-3.435757038074824e-12, cos(1048575.0 / 2 * kPI));
114
115 // Test Hayne-Panek reduction.
116 EXPECT_EQ(-0.9258790228548379e0, cos(kTwo120));
117 EXPECT_EQ(-0.9258790228548379e0, cos(-kTwo120));
118 }
119
TEST(Ieee754,Exp)120 TEST(Ieee754, Exp) {
121 EXPECT_THAT(exp(std::numeric_limits<double>::quiet_NaN()), IsNaN());
122 EXPECT_THAT(exp(std::numeric_limits<double>::signaling_NaN()), IsNaN());
123 EXPECT_EQ(0.0, exp(-std::numeric_limits<double>::infinity()));
124 EXPECT_EQ(0.0, exp(-1000));
125 EXPECT_EQ(0.0, exp(-745.1332191019412));
126 EXPECT_EQ(2.2250738585072626e-308, exp(-708.39641853226408));
127 EXPECT_EQ(3.307553003638408e-308, exp(-708.0));
128 EXPECT_EQ(4.9406564584124654e-324, exp(-7.45133219101941108420e+02));
129 EXPECT_EQ(0.36787944117144233, exp(-1.0));
130 EXPECT_EQ(1.0, exp(-0.0));
131 EXPECT_EQ(1.0, exp(0.0));
132 EXPECT_EQ(1.0, exp(2.2250738585072014e-308));
133
134 // Test that exp(x) is monotonic near 1.
135 EXPECT_GE(exp(1.0), exp(0.9999999999999999));
136 EXPECT_LE(exp(1.0), exp(1.0000000000000002));
137
138 // Test that we produce the correctly rounded result for 1.
139 EXPECT_EQ(kE, exp(1.0));
140
141 EXPECT_EQ(7.38905609893065e0, exp(2.0));
142 EXPECT_EQ(1.7976931348622732e308, exp(7.09782712893383973096e+02));
143 EXPECT_EQ(2.6881171418161356e+43, exp(100.0));
144 EXPECT_EQ(8.218407461554972e+307, exp(709.0));
145 EXPECT_EQ(1.7968190737295725e308, exp(709.7822265625e0));
146 EXPECT_EQ(std::numeric_limits<double>::infinity(), exp(709.7827128933841e0));
147 EXPECT_EQ(std::numeric_limits<double>::infinity(), exp(710.0));
148 EXPECT_EQ(std::numeric_limits<double>::infinity(), exp(1000.0));
149 EXPECT_EQ(std::numeric_limits<double>::infinity(),
150 exp(std::numeric_limits<double>::infinity()));
151 }
152
TEST(Ieee754,Expm1)153 TEST(Ieee754, Expm1) {
154 EXPECT_THAT(expm1(std::numeric_limits<double>::quiet_NaN()), IsNaN());
155 EXPECT_THAT(expm1(std::numeric_limits<double>::signaling_NaN()), IsNaN());
156 EXPECT_EQ(-1.0, expm1(-std::numeric_limits<double>::infinity()));
157 EXPECT_EQ(std::numeric_limits<double>::infinity(),
158 expm1(std::numeric_limits<double>::infinity()));
159 EXPECT_EQ(0.0, expm1(-0.0));
160 EXPECT_EQ(0.0, expm1(0.0));
161 EXPECT_EQ(1.718281828459045, expm1(1.0));
162 EXPECT_EQ(2.6881171418161356e+43, expm1(100.0));
163 EXPECT_EQ(8.218407461554972e+307, expm1(709.0));
164 EXPECT_EQ(std::numeric_limits<double>::infinity(), expm1(710.0));
165 }
166
TEST(Ieee754,Log)167 TEST(Ieee754, Log) {
168 EXPECT_THAT(log(std::numeric_limits<double>::quiet_NaN()), IsNaN());
169 EXPECT_THAT(log(std::numeric_limits<double>::signaling_NaN()), IsNaN());
170 EXPECT_THAT(log(-std::numeric_limits<double>::infinity()), IsNaN());
171 EXPECT_THAT(log(-1.0), IsNaN());
172 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log(-0.0));
173 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log(0.0));
174 EXPECT_EQ(0.0, log(1.0));
175 EXPECT_EQ(std::numeric_limits<double>::infinity(),
176 log(std::numeric_limits<double>::infinity()));
177
178 // Test that log(E) produces the correctly rounded result.
179 EXPECT_EQ(1.0, log(kE));
180 }
181
TEST(Ieee754,Log1p)182 TEST(Ieee754, Log1p) {
183 EXPECT_THAT(log1p(std::numeric_limits<double>::quiet_NaN()), IsNaN());
184 EXPECT_THAT(log1p(std::numeric_limits<double>::signaling_NaN()), IsNaN());
185 EXPECT_THAT(log1p(-std::numeric_limits<double>::infinity()), IsNaN());
186 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log1p(-1.0));
187 EXPECT_EQ(0.0, log1p(0.0));
188 EXPECT_EQ(-0.0, log1p(-0.0));
189 EXPECT_EQ(std::numeric_limits<double>::infinity(),
190 log1p(std::numeric_limits<double>::infinity()));
191 EXPECT_EQ(6.9756137364252422e-03, log1p(0.007));
192 EXPECT_EQ(709.782712893384, log1p(1.7976931348623157e308));
193 EXPECT_EQ(2.7755575615628914e-17, log1p(2.7755575615628914e-17));
194 EXPECT_EQ(9.313225741817976e-10, log1p(9.313225746154785e-10));
195 EXPECT_EQ(-0.2876820724517809, log1p(-0.25));
196 EXPECT_EQ(0.22314355131420976, log1p(0.25));
197 EXPECT_EQ(2.3978952727983707, log1p(10));
198 EXPECT_EQ(36.841361487904734, log1p(10e15));
199 EXPECT_EQ(37.08337388996168, log1p(12738099905822720));
200 EXPECT_EQ(37.08336444902049, log1p(12737979646738432));
201 EXPECT_EQ(1.3862943611198906, log1p(3));
202 EXPECT_EQ(1.3862945995384413, log1p(3 + 9.5367431640625e-7));
203 EXPECT_EQ(0.5596157879354227, log1p(0.75));
204 EXPECT_EQ(0.8109302162163288, log1p(1.25));
205 }
206
TEST(Ieee754,Log2)207 TEST(Ieee754, Log2) {
208 EXPECT_THAT(log2(std::numeric_limits<double>::quiet_NaN()), IsNaN());
209 EXPECT_THAT(log2(std::numeric_limits<double>::signaling_NaN()), IsNaN());
210 EXPECT_THAT(log2(-std::numeric_limits<double>::infinity()), IsNaN());
211 EXPECT_THAT(log2(-1.0), IsNaN());
212 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log2(0.0));
213 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log2(-0.0));
214 EXPECT_EQ(std::numeric_limits<double>::infinity(),
215 log2(std::numeric_limits<double>::infinity()));
216 }
217
TEST(Ieee754,Log10)218 TEST(Ieee754, Log10) {
219 EXPECT_THAT(log10(std::numeric_limits<double>::quiet_NaN()), IsNaN());
220 EXPECT_THAT(log10(std::numeric_limits<double>::signaling_NaN()), IsNaN());
221 EXPECT_THAT(log10(-std::numeric_limits<double>::infinity()), IsNaN());
222 EXPECT_THAT(log10(-1.0), IsNaN());
223 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log10(0.0));
224 EXPECT_EQ(-std::numeric_limits<double>::infinity(), log10(-0.0));
225 EXPECT_EQ(std::numeric_limits<double>::infinity(),
226 log10(std::numeric_limits<double>::infinity()));
227 EXPECT_EQ(3.0, log10(1000.0));
228 EXPECT_EQ(14.0, log10(100000000000000)); // log10(10 ^ 14)
229 EXPECT_EQ(3.7389561269540406, log10(5482.2158));
230 EXPECT_EQ(14.661551142893833, log10(458723662312872.125782332587));
231 EXPECT_EQ(-0.9083828622192334, log10(0.12348583358871));
232 EXPECT_EQ(5.0, log10(100000.0));
233 }
234
TEST(Ieee754,Cbrt)235 TEST(Ieee754, Cbrt) {
236 EXPECT_THAT(cbrt(std::numeric_limits<double>::quiet_NaN()), IsNaN());
237 EXPECT_THAT(cbrt(std::numeric_limits<double>::signaling_NaN()), IsNaN());
238 EXPECT_EQ(std::numeric_limits<double>::infinity(),
239 cbrt(std::numeric_limits<double>::infinity()));
240 EXPECT_EQ(-std::numeric_limits<double>::infinity(),
241 cbrt(-std::numeric_limits<double>::infinity()));
242 EXPECT_EQ(1.4422495703074083, cbrt(3));
243 EXPECT_EQ(100, cbrt(100 * 100 * 100));
244 EXPECT_EQ(46.415888336127786, cbrt(100000));
245 }
246
TEST(Ieee754,Sin)247 TEST(Ieee754, Sin) {
248 // Test values mentioned in the EcmaScript spec.
249 EXPECT_THAT(sin(std::numeric_limits<double>::quiet_NaN()), IsNaN());
250 EXPECT_THAT(sin(std::numeric_limits<double>::signaling_NaN()), IsNaN());
251 EXPECT_THAT(sin(std::numeric_limits<double>::infinity()), IsNaN());
252 EXPECT_THAT(sin(-std::numeric_limits<double>::infinity()), IsNaN());
253
254 // Tests for sin for |x| < pi/4
255 EXPECT_EQ(-std::numeric_limits<double>::infinity(), 1 / sin(-0.0));
256 EXPECT_EQ(std::numeric_limits<double>::infinity(), 1 / sin(0.0));
257 // sin(x) = x for x < 2^-27
258 EXPECT_EQ(2.3283064365386963e-10, sin(2.3283064365386963e-10));
259 EXPECT_EQ(-2.3283064365386963e-10, sin(-2.3283064365386963e-10));
260 // sin(pi/8) = sqrt(sqrt(2)-1)/2^(3/4)
261 EXPECT_EQ(0.3826834323650898, sin(0.39269908169872414));
262 EXPECT_EQ(-0.3826834323650898, sin(-0.39269908169872414));
263
264 // Tests for sin.
265 EXPECT_EQ(0.479425538604203, sin(0.5));
266 EXPECT_EQ(-0.479425538604203, sin(-0.5));
267 EXPECT_EQ(1, sin(kPI / 2.0));
268 EXPECT_EQ(-1, sin(-kPI / 2.0));
269 // Test that sin(Math.PI) != 0 since Math.PI is not exact.
270 EXPECT_EQ(1.2246467991473532e-16, sin(kPI));
271 EXPECT_EQ(-7.047032979958965e-14, sin(2200.0 * kPI));
272 // Test sin for various phases.
273 EXPECT_EQ(-0.7071067811865477, sin(7.0 / 4.0 * kPI));
274 EXPECT_EQ(0.7071067811865474, sin(9.0 / 4.0 * kPI));
275 EXPECT_EQ(0.7071067811865483, sin(11.0 / 4.0 * kPI));
276 EXPECT_EQ(-0.7071067811865479, sin(13.0 / 4.0 * kPI));
277 EXPECT_EQ(-3.2103381051568376e-11, sin(1048576.0 / 4 * kPI));
278
279 // Test Hayne-Panek reduction.
280 EXPECT_EQ(0.377820109360752e0, sin(kTwo120));
281 EXPECT_EQ(-0.377820109360752e0, sin(-kTwo120));
282 }
283
TEST(Ieee754,Tan)284 TEST(Ieee754, Tan) {
285 // Test values mentioned in the EcmaScript spec.
286 EXPECT_THAT(tan(std::numeric_limits<double>::quiet_NaN()), IsNaN());
287 EXPECT_THAT(tan(std::numeric_limits<double>::signaling_NaN()), IsNaN());
288 EXPECT_THAT(tan(std::numeric_limits<double>::infinity()), IsNaN());
289 EXPECT_THAT(tan(-std::numeric_limits<double>::infinity()), IsNaN());
290
291 // Tests for tan for |x| < pi/4
292 EXPECT_EQ(std::numeric_limits<double>::infinity(), 1 / tan(0.0));
293 EXPECT_EQ(-std::numeric_limits<double>::infinity(), 1 / tan(-0.0));
294 // tan(x) = x for |x| < 2^-28
295 EXPECT_EQ(2.3283064365386963e-10, tan(2.3283064365386963e-10));
296 EXPECT_EQ(-2.3283064365386963e-10, tan(-2.3283064365386963e-10));
297 // Test KERNELTAN for |x| > 0.67434.
298 EXPECT_EQ(0.8211418015898941, tan(11.0 / 16.0));
299 EXPECT_EQ(-0.8211418015898941, tan(-11.0 / 16.0));
300 EXPECT_EQ(0.41421356237309503, tan(0.39269908169872414));
301 // crbug/427468
302 EXPECT_EQ(0.7993357819992383, tan(0.6743358));
303
304 // Tests for tan.
305 EXPECT_EQ(3.725290298461914e-9, tan(3.725290298461914e-9));
306 // Test that tan(PI/2) != Infinity since PI is not exact.
307 EXPECT_EQ(1.633123935319537e16, tan(kPI / 2));
308 // Cover different code paths in KERNELTAN (tangent and cotangent)
309 EXPECT_EQ(0.5463024898437905, tan(0.5));
310 EXPECT_EQ(2.0000000000000027, tan(1.107148717794091));
311 EXPECT_EQ(-1.0000000000000004, tan(7.0 / 4.0 * kPI));
312 EXPECT_EQ(0.9999999999999994, tan(9.0 / 4.0 * kPI));
313 EXPECT_EQ(-6.420676210313675e-11, tan(1048576.0 / 2.0 * kPI));
314 EXPECT_EQ(2.910566692924059e11, tan(1048575.0 / 2.0 * kPI));
315
316 // Test Hayne-Panek reduction.
317 EXPECT_EQ(-0.40806638884180424e0, tan(kTwo120));
318 EXPECT_EQ(0.40806638884180424e0, tan(-kTwo120));
319 }
320
321 } // namespace ieee754
322 } // namespace base
323 } // namespace v8
324