| // Copyright (c) 2012, the Dart project authors. Please see the AUTHORS file |
| // for details. All rights reserved. Use of this source code is governed by a |
| // BSD-style license that can be found in the LICENSE file. |
| |
| // We temporarily test both the new math library and the old Math |
| // class. This can easily be simplified once we get rid of the Math |
| // class entirely. |
| library math_test; |
| |
| import "package:expect/expect.dart"; |
| import 'dart:math' as math; |
| |
| class MathLibraryTest { |
| static void testConstants() { |
| // Source for mathematical constants is Wolfram Alpha. |
| Expect.equals( |
| 2.7182818284590452353602874713526624977572470936999595749669, math.e); |
| Expect.equals(2.3025850929940456840179914546843642076011014886287729760333, |
| math.ln10); |
| Expect.equals( |
| 0.6931471805599453094172321214581765680755001343602552541206, math.ln2); |
| Expect.equals(1.4426950408889634073599246810018921374266459541529859341354, |
| math.log2e); |
| Expect.equals(0.4342944819032518276511289189166050822943970058036665661144, |
| math.log10e); |
| Expect.equals( |
| 3.1415926535897932384626433832795028841971693993751058209749, math.pi); |
| Expect.equals(0.7071067811865475244008443621048490392848359376884740365883, |
| math.sqrt1_2); |
| Expect.equals(1.4142135623730950488016887242096980785696718753769480731766, |
| math.sqrt2); |
| } |
| |
| static checkClose(double a, double b, EPSILON) { |
| Expect.equals(true, a - EPSILON <= b); |
| Expect.equals(true, b <= a + EPSILON); |
| } |
| |
| static void testSin() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.sin(0.0), EPSILON); |
| checkClose(0.0, math.sin(math.pi), EPSILON); |
| checkClose(0.0, math.sin(2.0 * math.pi), EPSILON); |
| checkClose(1.0, math.sin(math.pi / 2.0), EPSILON); |
| checkClose(-1.0, math.sin(math.pi * (3.0 / 2.0)), EPSILON); |
| } |
| |
| static void testCos() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(1.0, math.cos(0.0), EPSILON); |
| checkClose(-1.0, math.cos(math.pi), EPSILON); |
| checkClose(1.0, math.cos(2.0 * math.pi), EPSILON); |
| checkClose(0.0, math.cos(math.pi / 2.0), EPSILON); |
| checkClose(0.0, math.cos(math.pi * (3.0 / 2.0)), EPSILON); |
| } |
| |
| static void testTan() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.tan(0.0), EPSILON); |
| checkClose(0.0, math.tan(math.pi), EPSILON); |
| checkClose(0.0, math.tan(2.0 * math.pi), EPSILON); |
| checkClose(1.0, math.tan(math.pi / 4.0), EPSILON); |
| } |
| |
| static void testAsin() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.asin(0.0), EPSILON); |
| checkClose(math.pi / 2.0, math.asin(1.0), EPSILON); |
| checkClose(-math.pi / 2.0, math.asin(-1.0), EPSILON); |
| } |
| |
| static void testAcos() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.acos(1.0), EPSILON); |
| checkClose(math.pi, math.acos(-1.0), EPSILON); |
| checkClose(math.pi / 2.0, math.acos(0.0), EPSILON); |
| } |
| |
| static void testAtan() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.atan(0.0), EPSILON); |
| checkClose(math.pi / 4.0, math.atan(1.0), EPSILON); |
| checkClose(-math.pi / 4.0, math.atan(-1.0), EPSILON); |
| } |
| |
| static void testAtan2() { |
| // Given the imprecision of pi we can't expect better results than this. |
| final double EPSILON = 1e-15; |
| checkClose(0.0, math.atan2(0.0, 5.0), EPSILON); |
| checkClose(math.pi / 4.0, math.atan2(2.0, 2.0), EPSILON); |
| checkClose(3 * math.pi / 4.0, math.atan2(0.5, -0.5), EPSILON); |
| checkClose(-3 * math.pi / 4.0, math.atan2(-2.5, -2.5), EPSILON); |
| } |
| |
| static checkVeryClose(double a, double b) { |
| // We find a ulp (unit in the last place) by shifting the original number |
| // to the right. This only works if we are not too close to infinity or if |
| // we work with denormals. |
| // We special case or 0.0, but not for infinity. |
| if (a == 0.0) { |
| final minimalDouble = 4.9406564584124654e-324; |
| Expect.equals(true, b.abs() <= minimalDouble); |
| return; |
| } |
| if (b == 0.0) { |
| // No need to look if they are close. Otherwise the check for 'a' above |
| // whould have triggered. |
| Expect.equals(a, b); |
| } |
| final double shiftRightBy52 = 2.220446049250313080847263336181640625e-16; |
| final double shiftedA = (a * shiftRightBy52).abs(); |
| // Compared to 'a', 'shiftedA' is now ~1-2 ulp. |
| |
| final double limitLow = a - shiftedA; |
| final double limitHigh = a + shiftedA; |
| Expect.equals(false, a == limitLow); |
| Expect.equals(false, a == limitHigh); |
| Expect.equals(true, limitLow <= b); |
| Expect.equals(true, b <= limitHigh); |
| } |
| |
| static void testSqrt() { |
| checkVeryClose(2.0, math.sqrt(4.0)); |
| checkVeryClose(math.sqrt2, math.sqrt(2.0)); |
| checkVeryClose(math.sqrt1_2, math.sqrt(0.5)); |
| checkVeryClose(1e50, math.sqrt(1e100)); |
| checkVeryClose(1.1111111061110855443054405046358901279277111935183977e56, |
| math.sqrt(12345678901234e99)); |
| } |
| |
| static void testExp() { |
| checkVeryClose(math.e, math.exp(1.0)); |
| final EPSILON = 1e-15; |
| checkClose(10.0, math.exp(math.ln10), EPSILON); |
| checkClose(2.0, math.exp(math.ln2), EPSILON); |
| } |
| |
| static void testLog() { |
| // Even though E is imprecise, it is good enough to get really close to 1. |
| // We still provide an epsilon. |
| checkClose(1.0, math.log(math.e), 1e-16); |
| checkVeryClose(math.ln10, math.log(10.0)); |
| checkVeryClose(math.ln2, math.log(2.0)); |
| } |
| |
| static void testPow() { |
| checkVeryClose(16.0, math.pow(4.0, 2.0)); |
| checkVeryClose(math.sqrt2, math.pow(2.0, 0.5)); |
| checkVeryClose(math.sqrt1_2, math.pow(0.5, 0.5)); |
| } |
| |
| static bool parseIntThrowsFormatException(str) { |
| try { |
| int.parse(str); |
| return false; |
| } on FormatException catch (e) { |
| return true; |
| } |
| } |
| |
| static void testParseInt() { |
| Expect.equals(499, int.parse("499")); |
| Expect.equals(499, int.parse("+499")); |
| Expect.equals(-499, int.parse("-499")); |
| Expect.equals(499, int.parse(" 499 ")); |
| Expect.equals(499, int.parse(" +499 ")); |
| Expect.equals(-499, int.parse(" -499 ")); |
| Expect.equals(0, int.parse("0")); |
| Expect.equals(0, int.parse("+0")); |
| Expect.equals(0, int.parse("-0")); |
| Expect.equals(0, int.parse(" 0 ")); |
| Expect.equals(0, int.parse(" +0 ")); |
| Expect.equals(0, int.parse(" -0 ")); |
| Expect.equals(0x1234567890, int.parse("0x1234567890")); |
| Expect.equals(-0x1234567890, int.parse("-0x1234567890")); |
| Expect.equals(0x1234567890, int.parse(" 0x1234567890 ")); |
| Expect.equals(-0x1234567890, int.parse(" -0x1234567890 ")); |
| Expect.equals(256, int.parse("0x100")); |
| Expect.equals(-256, int.parse("-0x100")); |
| Expect.equals(256, int.parse(" 0x100 ")); |
| Expect.equals(-256, int.parse(" -0x100 ")); |
| Expect.equals(0xabcdef, int.parse("0xabcdef")); |
| Expect.equals(0xABCDEF, int.parse("0xABCDEF")); |
| Expect.equals(0xabcdef, int.parse("0xabCDEf")); |
| Expect.equals(-0xabcdef, int.parse("-0xabcdef")); |
| Expect.equals(-0xABCDEF, int.parse("-0xABCDEF")); |
| Expect.equals(0xabcdef, int.parse(" 0xabcdef ")); |
| Expect.equals(0xABCDEF, int.parse(" 0xABCDEF ")); |
| Expect.equals(-0xabcdef, int.parse(" -0xabcdef ")); |
| Expect.equals(-0xABCDEF, int.parse(" -0xABCDEF ")); |
| Expect.equals(0xabcdef, int.parse("0x00000abcdef")); |
| Expect.equals(0xABCDEF, int.parse("0x00000ABCDEF")); |
| Expect.equals(-0xabcdef, int.parse("-0x00000abcdef")); |
| Expect.equals(-0xABCDEF, int.parse("-0x00000ABCDEF")); |
| Expect.equals(0xabcdef, int.parse(" 0x00000abcdef ")); |
| Expect.equals(0xABCDEF, int.parse(" 0x00000ABCDEF ")); |
| Expect.equals(-0xabcdef, int.parse(" -0x00000abcdef ")); |
| Expect.equals(-0xABCDEF, int.parse(" -0x00000ABCDEF ")); |
| Expect.equals(10, int.parse("010")); |
| Expect.equals(-10, int.parse("-010")); |
| Expect.equals(10, int.parse(" 010 ")); |
| Expect.equals(-10, int.parse(" -010 ")); |
| Expect.equals(9, int.parse("09")); |
| Expect.equals(9, int.parse(" 09 ")); |
| Expect.equals(-9, int.parse("-09")); |
| Expect.equals(0x1234567890, int.parse("+0x1234567890")); |
| Expect.equals(0x1234567890, int.parse(" +0x1234567890 ")); |
| Expect.equals(0x100, int.parse("+0x100")); |
| Expect.equals(0x100, int.parse(" +0x100 ")); |
| |
| Expect.equals(true, parseIntThrowsFormatException("1b")); |
| Expect.equals(true, parseIntThrowsFormatException(" 1b ")); |
| Expect.equals(true, parseIntThrowsFormatException(" 1 b ")); |
| Expect.equals(true, parseIntThrowsFormatException("1e2")); |
| Expect.equals(true, parseIntThrowsFormatException(" 1e2 ")); |
| Expect.equals(true, parseIntThrowsFormatException("00x12")); |
| Expect.equals(true, parseIntThrowsFormatException(" 00x12 ")); |
| Expect.equals(true, parseIntThrowsFormatException("-1b")); |
| Expect.equals(true, parseIntThrowsFormatException(" -1b ")); |
| Expect.equals(true, parseIntThrowsFormatException(" -1 b ")); |
| Expect.equals(true, parseIntThrowsFormatException("-1e2")); |
| Expect.equals(true, parseIntThrowsFormatException(" -1e2 ")); |
| Expect.equals(true, parseIntThrowsFormatException("-00x12")); |
| Expect.equals(true, parseIntThrowsFormatException(" -00x12 ")); |
| Expect.equals(true, parseIntThrowsFormatException(" -00x12 ")); |
| Expect.equals(true, parseIntThrowsFormatException("0x0x12")); |
| Expect.equals(true, parseIntThrowsFormatException("0.1")); |
| Expect.equals(true, parseIntThrowsFormatException("0x3.1")); |
| Expect.equals(true, parseIntThrowsFormatException("5.")); |
| Expect.equals(true, parseIntThrowsFormatException("+-5")); |
| Expect.equals(true, parseIntThrowsFormatException("-+5")); |
| Expect.equals(true, parseIntThrowsFormatException("--5")); |
| Expect.equals(true, parseIntThrowsFormatException("++5")); |
| Expect.equals(true, parseIntThrowsFormatException("+ 5")); |
| Expect.equals(true, parseIntThrowsFormatException("- 5")); |
| Expect.equals(true, parseIntThrowsFormatException("")); |
| Expect.equals(true, parseIntThrowsFormatException(" ")); |
| } |
| |
| static testMain() { |
| testConstants(); |
| testSin(); |
| testCos(); |
| testTan(); |
| testAsin(); |
| testAcos(); |
| testAtan(); |
| testAtan2(); |
| testSqrt(); |
| testLog(); |
| testExp(); |
| testPow(); |
| testParseInt(); |
| } |
| } |
| |
| main() { |
| MathLibraryTest.testMain(); |
| } |