update dart:math

test/codegen/lib/math/math_test.dart

+// Copyright (c) 2011, 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.
+
+library math_test;
+import "package:expect/expect.dart";
+import 'dart:math';
+
+class MathTest {
+  static void testConstants() {
+    // Source for mathematical constants is Wolfram Alpha.
+    Expect.equals(2.7182818284590452353602874713526624977572470936999595749669,
+                  E);
+    Expect.equals(2.3025850929940456840179914546843642076011014886287729760333,
+                  LN10);
+    Expect.equals(0.6931471805599453094172321214581765680755001343602552541206,
+                  LN2);
+    Expect.equals(1.4426950408889634073599246810018921374266459541529859341354,
+                  LOG2E);
+    Expect.equals(0.4342944819032518276511289189166050822943970058036665661144,
+                  LOG10E);
+    Expect.equals(3.1415926535897932384626433832795028841971693993751058209749,
+                  PI);
+    Expect.equals(0.7071067811865475244008443621048490392848359376884740365883,
+                  SQRT1_2);
+    Expect.equals(1.4142135623730950488016887242096980785696718753769480731766,
+                  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, sin(0.0), EPSILON);
+    checkClose(0.0, sin(PI), EPSILON);
+    checkClose(0.0, sin(2.0 * PI), EPSILON);
+    checkClose(1.0, sin(PI / 2.0), EPSILON);
+    checkClose(-1.0, sin(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, cos(0.0), EPSILON);
+    checkClose(-1.0, cos(PI), EPSILON);
+    checkClose(1.0, cos(2.0 * PI), EPSILON);
+    checkClose(0.0, cos(PI / 2.0), EPSILON);
+    checkClose(0.0, cos(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, tan(0.0), EPSILON);
+    checkClose(0.0, tan(PI), EPSILON);
+    checkClose(0.0, tan(2.0 * PI), EPSILON);
+    checkClose(1.0, tan(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, asin(0.0), EPSILON);
+    checkClose(PI / 2.0, asin(1.0), EPSILON);
+    checkClose(-PI / 2.0, 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, acos(1.0), EPSILON);
+    checkClose(PI, acos(-1.0), EPSILON);
+    checkClose(PI / 2.0, 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, atan(0.0), EPSILON);
+    checkClose(PI / 4.0, atan(1.0), EPSILON);
+    checkClose(-PI / 4.0, 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, atan2(0.0, 5.0), EPSILON);
+    checkClose(PI / 4.0, atan2(2.0, 2.0), EPSILON);
+    checkClose(3 * PI / 4.0, atan2(0.5, -0.5), EPSILON);
+    checkClose(-3 * PI / 4.0, 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, sqrt(4.0));
+    checkVeryClose(SQRT2, sqrt(2.0));
+    checkVeryClose(SQRT1_2, sqrt(0.5));
+    checkVeryClose(1e50, sqrt(1e100));
+    checkVeryClose(1.1111111061110855443054405046358901279277111935183977e56,
+                   sqrt(12345678901234e99));
+  }
+
+  static void testExp() {
+    checkVeryClose(E, exp(1.0));
+    final EPSILON = 1e-15;
+    checkClose(10.0, exp(LN10), EPSILON);
+    checkClose(2.0, exp(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, log(E), 1e-16);
+    checkVeryClose(LN10, log(10.0));
+    checkVeryClose(LN2, log(2.0));
+  }
+
+  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();
+    testParseInt();
+  }
+}
+
+main() {
+  MathTest.testMain();
+}