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// 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();
}