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| 1 // Copyright 2011 the V8 project authors. All rights reserved. | 1 // Copyright 2011 the V8 project authors. All rights reserved. |
| 2 // Redistribution and use in source and binary forms, with or without | 2 // Redistribution and use in source and binary forms, with or without |
| 3 // modification, are permitted provided that the following conditions are | 3 // modification, are permitted provided that the following conditions are |
| 4 // met: | 4 // met: |
| 5 // | 5 // |
| 6 // * Redistributions of source code must retain the above copyright | 6 // * Redistributions of source code must retain the above copyright |
| 7 // notice, this list of conditions and the following disclaimer. | 7 // notice, this list of conditions and the following disclaimer. |
| 8 // * Redistributions in binary form must reproduce the above | 8 // * Redistributions in binary form must reproduce the above |
| 9 // copyright notice, this list of conditions and the following | 9 // copyright notice, this list of conditions and the following |
| 10 // disclaimer in the documentation and/or other materials provided | 10 // disclaimer in the documentation and/or other materials provided |
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| 150 } | 150 } |
| 151 | 151 |
| 152 var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2); | 152 var err_rms = Math.sqrt(squares[0] / test_inputs.length / 2); |
| 153 assertEqualsDelta(0, err_rms, 1E-14); | 153 assertEqualsDelta(0, err_rms, 1E-14); |
| 154 | 154 |
| 155 assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } })); | 155 assertEquals(-1, Math.cos({ valueOf: function() { return Math.PI; } })); |
| 156 assertEquals(0, Math.sin("0x00000")); | 156 assertEquals(0, Math.sin("0x00000")); |
| 157 assertEquals(1, Math.cos("0x00000")); | 157 assertEquals(1, Math.cos("0x00000")); |
| 158 assertTrue(isNaN(Math.sin(Infinity))); | 158 assertTrue(isNaN(Math.sin(Infinity))); |
| 159 assertTrue(isNaN(Math.cos("-Infinity"))); | 159 assertTrue(isNaN(Math.cos("-Infinity"))); |
| 160 assertTrue(Math.tan(Math.PI/2) > 1e16); | 160 assertEquals("Infinity", String(Math.tan(Math.PI/2))); |
| 161 assertTrue(Math.tan(-Math.PI/2) < -1e16); | 161 assertEquals("-Infinity", String(Math.tan(-Math.PI/2))); |
| 162 assertEquals("-Infinity", String(1/Math.sin("-0"))); | 162 assertEquals("-Infinity", String(1/Math.sin("-0"))); |
| 163 | 163 |
| 164 // Assert that the remainder after division by pi is reasonably precise. | 164 // Assert that the remainder after division by pi is reasonably precise. |
| 165 function assertError(expected, x, epsilon) { | 165 function assertError(expected, x, epsilon) { |
| 166 assertTrue(Math.abs(x - expected) < epsilon); | 166 assertTrue(Math.abs(x - expected) < epsilon); |
| 167 } | 167 } |
| 168 | 168 |
| 169 assertEqualsDelta(0.9367521275331447, Math.cos(1e06), 1e-15); | 169 assertEqualsDelta(0.9367521275331447, Math.cos(1e06), 1e-15); |
| 170 assertEqualsDelta(0.8731196226768560, Math.cos(1e10), 1e-08); | 170 assertEqualsDelta(0.8731196226768560, Math.cos(1e10), 1e-08); |
| 171 assertEqualsDelta(0.9367521275331447, Math.cos(-1e06), 1e-15); | 171 assertEqualsDelta(0.9367521275331447, Math.cos(-1e06), 1e-15); |
| 172 assertEqualsDelta(0.8731196226768560, Math.cos(-1e10), 1e-08); | 172 assertEqualsDelta(0.8731196226768560, Math.cos(-1e10), 1e-08); |
| 173 assertEqualsDelta(-0.3499935021712929, Math.sin(1e06), 1e-15); | 173 assertEqualsDelta(-0.3499935021712929, Math.sin(1e06), 1e-15); |
| 174 assertEqualsDelta(-0.4875060250875106, Math.sin(1e10), 1e-08); | 174 assertEqualsDelta(-0.4875060250875106, Math.sin(1e10), 1e-08); |
| 175 assertEqualsDelta(0.3499935021712929, Math.sin(-1e06), 1e-15); | 175 assertEqualsDelta(0.3499935021712929, Math.sin(-1e06), 1e-15); |
| 176 assertEqualsDelta(0.4875060250875106, Math.sin(-1e10), 1e-08); | 176 assertEqualsDelta(0.4875060250875106, Math.sin(-1e10), 1e-08); |
| 177 assertEqualsDelta(0.7796880066069787, Math.sin(1e16), 1e-05); | 177 assertEqualsDelta(0.7796880066069787, Math.sin(1e16), 1e-05); |
| 178 assertEqualsDelta(-0.6261681981330861, Math.cos(1e16), 1e-05); | 178 assertEqualsDelta(-0.6261681981330861, Math.cos(1e16), 1e-05); |
| 179 | 179 |
| 180 // Assert that remainder calculation terminates. | 180 // Assert that remainder calculation terminates. |
| 181 for (var i = -1024; i < 1024; i++) { | 181 for (var i = -1024; i < 1024; i++) { |
| 182 assertFalse(isNaN(Math.sin(Math.pow(2, i)))); | 182 assertFalse(isNaN(Math.sin(Math.pow(2, i)))); |
| 183 } | 183 } |
| 184 | 184 |
| 185 assertFalse(isNaN(Math.cos(1.57079632679489700))); | 185 assertFalse(isNaN(Math.cos(1.57079632679489700))); |
| 186 assertFalse(isNaN(Math.cos(-1e-100))); | 186 assertFalse(isNaN(Math.cos(-1e-100))); |
| 187 assertFalse(isNaN(Math.cos(-1e-323))); | 187 assertFalse(isNaN(Math.cos(-1e-323))); |
| 188 | |
| 189 // Tests for specific values expected from the fdlibm implementation. | |
| 190 | |
| 191 var two_32 = Math.pow(2, -32); | |
| 192 var two_28 = Math.pow(2, -28); | |
| 193 | |
| 194 // Tests for Math.sin for |x| < pi/4 | |
| 195 assertEquals(Infinity, 1/Math.sin(+0.0)); | |
| 196 assertEquals(-Infinity, 1/Math.sin(-0.0)); | |
| 197 // sin(x) = x for x < 2^-27 | |
| 198 assertEquals(two_32, Math.sin(two_32)); | |
| 199 assertEquals(-two_32, Math.sin(-two_32)); | |
| 200 // sin(pi/8) = sqrt(sqrt(2)-1)/2^(3/4) | |
| 201 assertEquals(0.3826834323650898, Math.sin(Math.PI/8)); | |
| 202 assertEquals(-0.3826834323650898, -Math.sin(Math.PI/8)); | |
| 203 | |
| 204 // Tests for Math.cos for |x| < pi/4 | |
| 205 // cos(x) = 1 for |x| < 2^-27 | |
| 206 assertEquals(1, Math.cos(two_32)); | |
| 207 assertEquals(1, Math.cos(-two_32)); | |
| 208 // Test KERNELCOS for |x| < 0.3. | |
| 209 // cos(pi/20) = sqrt(sqrt(2)*sqrt(sqrt(5)+5)+4)/2^(3/2) | |
| 210 assertEquals(0.9876883405951378, Math.cos(Math.PI/20)); | |
| 211 // Test KERNELCOS for x ~= 0.78125 | |
| 212 assertEquals(0.7100335477927638, Math.cos(0.7812504768371582)); | |
| 213 assertEquals(0.7100338835660797, Math.cos(0.78125)); | |
| 214 // Test KERNELCOS for |x| > 0.3. | |
| 215 // cos(pi/8) = sqrt(sqrt(2)+1)/2^(3/4) | |
| 216 assertEquals(0.9238795325112867, Math.cos(Math.PI/8)); | |
| 217 // Test KERNELTAN for |x| < 0.67434. | |
| 218 assertEquals(0.9238795325112867, Math.cos(-Math.PI/8)); | |
| 219 | |
| 220 // Tests for Math.tan for |x| < pi/4 | |
| 221 assertEquals(Infinity, 1/Math.tan(0.0)); | |
| 222 assertEquals(-Infinity, 1/Math.tan(-0.0)); | |
| 223 // tan(x) = x for |x| < 2^-28 | |
| 224 assertEquals(two_32, Math.tan(two_32)); | |
| 225 assertEquals(-two_32, Math.tan(-two_32)); | |
| 226 // Test KERNELTAN for |x| > 0.67434. | |
| 227 assertEquals(0.8211418015898941, Math.tan(11/16)); | |
| 228 assertEquals(-0.8211418015898941, Math.tan(-11/16)); | |
| 229 assertEquals(0.41421356237309503, Math.tan(Math.PI / 8)); | |
| 230 | |
| 231 // Tests for Math.sin. | |
| 232 assertEquals(0.479425538604203, Math.sin(0.5)); | |
| 233 assertEquals(-0.479425538604203, Math.sin(-0.5)); | |
| 234 assertEquals(1, Math.sin(Math.PI/2)); | |
| 235 assertEquals(-1, Math.sin(-Math.PI/2)); | |
| 236 // Test that Math.sin(Math.PI) != 0 since Math.PI is not exact. | |
| 237 assertEquals(1.2246467991473532e-16, Math.sin(Math.PI)); | |
| 238 assertEquals(-7.047032979958965e-14, Math.sin(2200*Math.PI)); | |
| 239 // Test Math.sin for various phases. | |
| 240 assertEquals(-0.7071067811865477, Math.sin(7/4 * Math.PI)); | |
| 241 assertEquals(0.7071067811865474, Math.sin(9/4 * Math.PI)); | |
| 242 assertEquals(0.7071067811865483, Math.sin(11/4 * Math.PI)); | |
| 243 assertEquals(-0.7071067811865479, Math.sin(13/4 * Math.PI)); | |
| 244 assertEquals(-3.2103381051568376e-11, Math.sin(1048576/4 * Math.PI)); | |
| 245 | |
| 246 // Tests for Math.cos. | |
| 247 assertEquals(1, Math.cos(two_28)); | |
| 248 // Cover different code paths in KERNELCOS. | |
| 249 assertEquals(0.9689124217106447, Math.cos(0.25)); | |
| 250 assertEquals(0.8775825618903728, Math.cos(0.5)); | |
| 251 assertEquals(0.7073882691671998, Math.cos(0.785)); | |
| 252 // Test that Math.cos(Math.PI/2) != 0 since Math.PI is not exact. | |
| 253 assertEquals(6.123233995736766e-17, Math.cos(Math.PI/2)); | |
| 254 // Test Math.cos for various phases. | |
| 255 assertEquals(0.7071067811865474, Math.cos(7/4 * Math.PI)); | |
| 256 assertEquals(0.7071067811865477, Math.cos(9/4 * Math.PI)); | |
| 257 assertEquals(-0.7071067811865467, Math.cos(11/4 * Math.PI)); | |
| 258 assertEquals(-0.7071067811865471, Math.cos(13/4 * Math.PI)); | |
| 259 assertEquals(0.9367521275331447, Math.cos(1000000)); | |
| 260 assertEquals(-3.435757038074824e-12, Math.cos(1048575/2 * Math.PI)); | |
| 261 | |
| 262 // Tests for Math.tan. | |
| 263 assertEquals(two_28, Math.tan(two_28)); | |
| 264 // Test that Math.tan(Math.PI/2) != Infinity since Math.PI is not exact. | |
| 265 assertEquals(1.633123935319537e16, Math.tan(Math.PI/2)); | |
| 266 // Cover different code paths in KERNELTAN (tangent and cotangent) | |
| 267 assertEquals(0.5463024898437905, Math.tan(0.5)); | |
| 268 assertEquals(2.0000000000000027, Math.tan(1.107148717794091)); | |
| 269 assertEquals(-1.0000000000000004, Math.tan(7/4*Math.PI)); | |
| 270 assertEquals(0.9999999999999994, Math.tan(9/4*Math.PI)); | |
| 271 assertEquals(-6.420676210313675e-11, Math.tan(1048576/2*Math.PI)); | |
| 272 assertEquals(2.910566692924059e11, Math.tan(1048575/2*Math.PI)); | |
| 273 | |
| 274 // Test Hayne-Panek reduction. | |
| 275 assertEquals(0.377820109360752e0, Math.sin(Math.pow(2, 120))); | |
| 276 assertEquals(-0.9258790228548379e0, Math.cos(Math.pow(2, 120))); | |
| 277 assertEquals(-0.40806638884180424e0, Math.tan(Math.pow(2, 120))); | |
| 278 assertEquals(-0.377820109360752e0, Math.sin(-Math.pow(2, 120))); | |
| 279 assertEquals(-0.9258790228548379e0, Math.cos(-Math.pow(2, 120))); | |
| 280 assertEquals(0.40806638884180424e0, Math.tan(-Math.pow(2, 120))); | |
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