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| 1 // Copyright (c) 2011, the Dart project authors. Please see the AUTHORS file | 1 // Copyright (c) 2012, the Dart project authors. Please see the AUTHORS file |
| 2 // for details. All rights reserved. Use of this source code is governed by a | 2 // for details. All rights reserved. Use of this source code is governed by a |
| 3 // BSD-style license that can be found in the LICENSE file. | 3 // BSD-style license that can be found in the LICENSE file. |
| 4 | 4 |
| 5 // We temporarily test both the new math library and the old Math | 5 // We temporarily test both the new math library and the old Math |
| 6 // class. This can easily be simplified once we get rid of the Math | 6 // class. This can easily be simplified once we get rid of the Math |
| 7 // class entirely. | 7 // class entirely. |
| 8 #library('math_test'); | 8 #library('math_test'); |
| 9 #import('dart:math', prefix: 'math'); | 9 #import('dart:math', prefix: 'math'); |
| 10 | 10 |
| 11 class MathTest { | |
| 12 static void testConstants() { | |
| 13 // Source for mathematical constants is Wolfram Alpha. | |
| 14 Expect.equals(2.7182818284590452353602874713526624977572470936999595749669, | |
| 15 Math.E); | |
| 16 Expect.equals(2.3025850929940456840179914546843642076011014886287729760333, | |
| 17 Math.LN10); | |
| 18 Expect.equals(0.6931471805599453094172321214581765680755001343602552541206, | |
| 19 Math.LN2); | |
| 20 Expect.equals(1.4426950408889634073599246810018921374266459541529859341354, | |
| 21 Math.LOG2E); | |
| 22 Expect.equals(0.4342944819032518276511289189166050822943970058036665661144, | |
| 23 Math.LOG10E); | |
| 24 Expect.equals(3.1415926535897932384626433832795028841971693993751058209749, | |
| 25 Math.PI); | |
| 26 Expect.equals(0.7071067811865475244008443621048490392848359376884740365883, | |
| 27 Math.SQRT1_2); | |
| 28 Expect.equals(1.4142135623730950488016887242096980785696718753769480731766, | |
| 29 Math.SQRT2); | |
| 30 } | |
| 31 | |
| 32 static checkClose(double a, double b, EPSILON) { | |
| 33 Expect.equals(true, a - EPSILON <= b); | |
| 34 Expect.equals(true, b <= a + EPSILON); | |
| 35 } | |
| 36 | |
| 37 static void testSin() { | |
| 38 // Given the imprecision of PI we can't expect better results than this. | |
| 39 final double EPSILON = 1e-15; | |
| 40 checkClose(0.0, Math.sin(0.0), EPSILON); | |
| 41 checkClose(0.0, Math.sin(Math.PI), EPSILON); | |
| 42 checkClose(0.0, Math.sin(2.0 * Math.PI), EPSILON); | |
| 43 checkClose(1.0, Math.sin(Math.PI / 2.0), EPSILON); | |
| 44 checkClose(-1.0, Math.sin(Math.PI * (3.0 / 2.0)), EPSILON); | |
| 45 } | |
| 46 | |
| 47 static void testCos() { | |
| 48 // Given the imprecision of PI we can't expect better results than this. | |
| 49 final double EPSILON = 1e-15; | |
| 50 checkClose(1.0, Math.cos(0.0), EPSILON); | |
| 51 checkClose(-1.0, Math.cos(Math.PI), EPSILON); | |
| 52 checkClose(1.0, Math.cos(2.0 * Math.PI), EPSILON); | |
| 53 checkClose(0.0, Math.cos(Math.PI / 2.0), EPSILON); | |
| 54 checkClose(0.0, Math.cos(Math.PI * (3.0 / 2.0)), EPSILON); | |
| 55 } | |
| 56 | |
| 57 static void testTan() { | |
| 58 // Given the imprecision of PI we can't expect better results than this. | |
| 59 final double EPSILON = 1e-15; | |
| 60 checkClose(0.0, Math.tan(0.0), EPSILON); | |
| 61 checkClose(0.0, Math.tan(Math.PI), EPSILON); | |
| 62 checkClose(0.0, Math.tan(2.0 * Math.PI), EPSILON); | |
| 63 checkClose(1.0, Math.tan(Math.PI / 4.0), EPSILON); | |
| 64 } | |
| 65 | |
| 66 static void testAsin() { | |
| 67 // Given the imprecision of PI we can't expect better results than this. | |
| 68 final double EPSILON = 1e-15; | |
| 69 checkClose(0.0, Math.asin(0.0), EPSILON); | |
| 70 checkClose(Math.PI / 2.0, Math.asin(1.0), EPSILON); | |
| 71 checkClose(-Math.PI / 2.0, Math.asin(-1.0), EPSILON); | |
| 72 } | |
| 73 | |
| 74 | |
| 75 static void testAcos() { | |
| 76 // Given the imprecision of PI we can't expect better results than this. | |
| 77 final double EPSILON = 1e-15; | |
| 78 checkClose(0.0, Math.acos(1.0), EPSILON); | |
| 79 checkClose(Math.PI, Math.acos(-1.0), EPSILON); | |
| 80 checkClose(Math.PI / 2.0, Math.acos(0.0), EPSILON); | |
| 81 } | |
| 82 | |
| 83 static void testAtan() { | |
| 84 // Given the imprecision of PI we can't expect better results than this. | |
| 85 final double EPSILON = 1e-15; | |
| 86 checkClose(0.0, Math.atan(0.0), EPSILON); | |
| 87 checkClose(Math.PI / 4.0, Math.atan(1.0), EPSILON); | |
| 88 checkClose(-Math.PI / 4.0, Math.atan(-1.0), EPSILON); | |
| 89 } | |
| 90 | |
| 91 static void testAtan2() { | |
| 92 // Given the imprecision of PI we can't expect better results than this. | |
| 93 final double EPSILON = 1e-15; | |
| 94 checkClose(0.0, Math.atan2(0.0, 5.0), EPSILON); | |
| 95 checkClose(Math.PI / 4.0, Math.atan2(2.0, 2.0), EPSILON); | |
| 96 checkClose(3 * Math.PI / 4.0, Math.atan2(0.5, -0.5), EPSILON); | |
| 97 checkClose(-3 * Math.PI / 4.0, Math.atan2(-2.5, -2.5), EPSILON); | |
| 98 } | |
| 99 | |
| 100 static checkVeryClose(double a, double b) { | |
| 101 // We find a ulp (unit in the last place) by shifting the original number | |
| 102 // to the right. This only works if we are not too close to infinity or if | |
| 103 // we work with denormals. | |
| 104 // We special case or 0.0, but not for infinity. | |
| 105 if (a == 0.0) { | |
| 106 final minimalDouble = 4.9406564584124654e-324; | |
| 107 Expect.equals(true, b.abs() <= minimalDouble); | |
| 108 return; | |
| 109 } | |
| 110 if (b == 0.0) { | |
| 111 // No need to look if they are close. Otherwise the check for 'a' above | |
| 112 // whould have triggered. | |
| 113 Expect.equals(a, b); | |
| 114 } | |
| 115 final double shiftRightBy52 = 2.220446049250313080847263336181640625e-16; | |
| 116 final double shiftedA = (a * shiftRightBy52).abs(); | |
| 117 // Compared to 'a', 'shiftedA' is now ~1-2 ulp. | |
| 118 | |
| 119 final double limitLow = a - shiftedA; | |
| 120 final double limitHigh = a + shiftedA; | |
| 121 Expect.equals(false, a == limitLow); | |
| 122 Expect.equals(false, a == limitHigh); | |
| 123 Expect.equals(true, limitLow <= b); | |
| 124 Expect.equals(true, b <= limitHigh); | |
| 125 } | |
| 126 | |
| 127 static void testSqrt() { | |
| 128 checkVeryClose(2.0, Math.sqrt(4.0)); | |
| 129 checkVeryClose(Math.SQRT2, Math.sqrt(2.0)); | |
| 130 checkVeryClose(Math.SQRT1_2, Math.sqrt(0.5)); | |
| 131 checkVeryClose(1e50, Math.sqrt(1e100)); | |
| 132 checkVeryClose(1.1111111061110855443054405046358901279277111935183977e56, | |
| 133 Math.sqrt(12345678901234e99)); | |
| 134 } | |
| 135 | |
| 136 static void testExp() { | |
| 137 checkVeryClose(Math.E, Math.exp(1.0)); | |
| 138 final EPSILON = 1e-15; | |
| 139 checkClose(10.0, Math.exp(Math.LN10), EPSILON); | |
| 140 checkClose(2.0, Math.exp(Math.LN2), EPSILON); | |
| 141 } | |
| 142 | |
| 143 static void testLog() { | |
| 144 // Even though E is imprecise, it is good enough to get really close to 1. | |
| 145 // We still provide an epsilon. | |
| 146 checkClose(1.0, Math.log(Math.E), 1e-16); | |
| 147 checkVeryClose(Math.LN10, Math.log(10.0)); | |
| 148 checkVeryClose(Math.LN2, Math.log(2.0)); | |
| 149 } | |
| 150 | |
| 151 static void testPow() { | |
| 152 checkVeryClose(16.0, Math.pow(4.0, 2.0)); | |
| 153 checkVeryClose(Math.SQRT2, Math.pow(2.0, 0.5)); | |
| 154 checkVeryClose(Math.SQRT1_2, Math.pow(0.5, 0.5)); | |
| 155 } | |
| 156 | |
| 157 static bool parseIntThrowsFormatException(str) { | |
| 158 try { | |
| 159 Math.parseInt(str); | |
| 160 return false; | |
| 161 } catch (FormatException e) { | |
| 162 return true; | |
| 163 } | |
| 164 } | |
| 165 | |
| 166 static void testParseInt() { | |
| 167 Expect.equals(499, Math.parseInt("499")); | |
| 168 Expect.equals(499, Math.parseInt("+499")); | |
| 169 Expect.equals(-499, Math.parseInt("-499")); | |
| 170 Expect.equals(499, Math.parseInt(" 499 ")); | |
| 171 Expect.equals(499, Math.parseInt(" +499 ")); | |
| 172 Expect.equals(-499, Math.parseInt(" -499 ")); | |
| 173 Expect.equals(0, Math.parseInt("0")); | |
| 174 Expect.equals(0, Math.parseInt("+0")); | |
| 175 Expect.equals(0, Math.parseInt("-0")); | |
| 176 Expect.equals(0, Math.parseInt(" 0 ")); | |
| 177 Expect.equals(0, Math.parseInt(" +0 ")); | |
| 178 Expect.equals(0, Math.parseInt(" -0 ")); | |
| 179 Expect.equals(0x1234567890, Math.parseInt("0x1234567890")); | |
| 180 Expect.equals(-0x1234567890, Math.parseInt("-0x1234567890")); | |
| 181 Expect.equals(0x1234567890, Math.parseInt(" 0x1234567890 ")); | |
| 182 Expect.equals(-0x1234567890, Math.parseInt(" -0x1234567890 ")); | |
| 183 Expect.equals(256, Math.parseInt("0x100")); | |
| 184 Expect.equals(-256, Math.parseInt("-0x100")); | |
| 185 Expect.equals(256, Math.parseInt(" 0x100 ")); | |
| 186 Expect.equals(-256, Math.parseInt(" -0x100 ")); | |
| 187 Expect.equals(0xabcdef, Math.parseInt("0xabcdef")); | |
| 188 Expect.equals(0xABCDEF, Math.parseInt("0xABCDEF")); | |
| 189 Expect.equals(0xabcdef, Math.parseInt("0xabCDEf")); | |
| 190 Expect.equals(-0xabcdef, Math.parseInt("-0xabcdef")); | |
| 191 Expect.equals(-0xABCDEF, Math.parseInt("-0xABCDEF")); | |
| 192 Expect.equals(0xabcdef, Math.parseInt(" 0xabcdef ")); | |
| 193 Expect.equals(0xABCDEF, Math.parseInt(" 0xABCDEF ")); | |
| 194 Expect.equals(-0xabcdef, Math.parseInt(" -0xabcdef ")); | |
| 195 Expect.equals(-0xABCDEF, Math.parseInt(" -0xABCDEF ")); | |
| 196 Expect.equals(0xabcdef, Math.parseInt("0x00000abcdef")); | |
| 197 Expect.equals(0xABCDEF, Math.parseInt("0x00000ABCDEF")); | |
| 198 Expect.equals(-0xabcdef, Math.parseInt("-0x00000abcdef")); | |
| 199 Expect.equals(-0xABCDEF, Math.parseInt("-0x00000ABCDEF")); | |
| 200 Expect.equals(0xabcdef, Math.parseInt(" 0x00000abcdef ")); | |
| 201 Expect.equals(0xABCDEF, Math.parseInt(" 0x00000ABCDEF ")); | |
| 202 Expect.equals(-0xabcdef, Math.parseInt(" -0x00000abcdef ")); | |
| 203 Expect.equals(-0xABCDEF, Math.parseInt(" -0x00000ABCDEF ")); | |
| 204 Expect.equals(10, Math.parseInt("010")); | |
| 205 Expect.equals(-10, Math.parseInt("-010")); | |
| 206 Expect.equals(10, Math.parseInt(" 010 ")); | |
| 207 Expect.equals(-10, Math.parseInt(" -010 ")); | |
| 208 Expect.equals(9, Math.parseInt("09")); | |
| 209 Expect.equals(9, Math.parseInt(" 09 ")); | |
| 210 Expect.equals(-9, Math.parseInt("-09")); | |
| 211 Expect.equals(true, parseIntThrowsFormatException("1b")); | |
| 212 Expect.equals(true, parseIntThrowsFormatException(" 1b ")); | |
| 213 Expect.equals(true, parseIntThrowsFormatException(" 1 b ")); | |
| 214 Expect.equals(true, parseIntThrowsFormatException("1e2")); | |
| 215 Expect.equals(true, parseIntThrowsFormatException(" 1e2 ")); | |
| 216 Expect.equals(true, parseIntThrowsFormatException("00x12")); | |
| 217 Expect.equals(true, parseIntThrowsFormatException(" 00x12 ")); | |
| 218 Expect.equals(true, parseIntThrowsFormatException("-1b")); | |
| 219 Expect.equals(true, parseIntThrowsFormatException(" -1b ")); | |
| 220 Expect.equals(true, parseIntThrowsFormatException(" -1 b ")); | |
| 221 Expect.equals(true, parseIntThrowsFormatException("-1e2")); | |
| 222 Expect.equals(true, parseIntThrowsFormatException(" -1e2 ")); | |
| 223 Expect.equals(true, parseIntThrowsFormatException("-00x12")); | |
| 224 Expect.equals(true, parseIntThrowsFormatException(" -00x12 ")); | |
| 225 Expect.equals(true, parseIntThrowsFormatException(" -00x12 ")); | |
| 226 Expect.equals(true, parseIntThrowsFormatException("0x0x12")); | |
| 227 Expect.equals(true, parseIntThrowsFormatException("0.1")); | |
| 228 Expect.equals(true, parseIntThrowsFormatException("0x3.1")); | |
| 229 Expect.equals(true, parseIntThrowsFormatException("5.")); | |
| 230 Expect.equals(true, parseIntThrowsFormatException("+-5")); | |
| 231 Expect.equals(true, parseIntThrowsFormatException("-+5")); | |
| 232 Expect.equals(true, parseIntThrowsFormatException("--5")); | |
| 233 Expect.equals(true, parseIntThrowsFormatException("++5")); | |
| 234 Expect.equals(true, parseIntThrowsFormatException("+ 5")); | |
| 235 Expect.equals(true, parseIntThrowsFormatException("- 5")); | |
| 236 Expect.equals(true, parseIntThrowsFormatException("")); | |
| 237 Expect.equals(true, parseIntThrowsFormatException(" ")); | |
| 238 Expect.equals(true, parseIntThrowsFormatException("+0x1234567890")); | |
| 239 Expect.equals(true, parseIntThrowsFormatException(" +0x1234567890 ")); | |
| 240 Expect.equals(true, parseIntThrowsFormatException("+0x100")); | |
| 241 Expect.equals(true, parseIntThrowsFormatException(" +0x100 ")); | |
| 242 } | |
| 243 | |
| 244 static testMain() { | |
| 245 testConstants(); | |
| 246 testSin(); | |
| 247 testCos(); | |
| 248 testTan(); | |
| 249 testAsin(); | |
| 250 testAcos(); | |
| 251 testAtan(); | |
| 252 testAtan2(); | |
| 253 testSqrt(); | |
| 254 testLog(); | |
| 255 testExp(); | |
| 256 testPow(); | |
| 257 testParseInt(); | |
| 258 } | |
| 259 } | |
| 260 | |
| 261 class MathLibraryTest { | 11 class MathLibraryTest { |
| 262 static void testConstants() { | 12 static void testConstants() { |
| 263 // Source for mathematical constants is Wolfram Alpha. | 13 // Source for mathematical constants is Wolfram Alpha. |
| 264 Expect.equals(2.7182818284590452353602874713526624977572470936999595749669, | 14 Expect.equals(2.7182818284590452353602874713526624977572470936999595749669, |
| 265 math.E); | 15 math.E); |
| 266 Expect.equals(2.3025850929940456840179914546843642076011014886287729760333, | 16 Expect.equals(2.3025850929940456840179914546843642076011014886287729760333, |
| 267 math.LN10); | 17 math.LN10); |
| 268 Expect.equals(0.6931471805599453094172321214581765680755001343602552541206, | 18 Expect.equals(0.6931471805599453094172321214581765680755001343602552541206, |
| 269 math.LN2); | 19 math.LN2); |
| 270 Expect.equals(1.4426950408889634073599246810018921374266459541529859341354, | 20 Expect.equals(1.4426950408889634073599246810018921374266459541529859341354, |
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| 502 testAtan2(); | 252 testAtan2(); |
| 503 testSqrt(); | 253 testSqrt(); |
| 504 testLog(); | 254 testLog(); |
| 505 testExp(); | 255 testExp(); |
| 506 testPow(); | 256 testPow(); |
| 507 testParseInt(); | 257 testParseInt(); |
| 508 } | 258 } |
| 509 } | 259 } |
| 510 | 260 |
| 511 main() { | 261 main() { |
| 512 MathTest.testMain(); | |
| 513 MathLibraryTest.testMain(); | 262 MathLibraryTest.testMain(); |
| 514 } | 263 } |
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