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class Math

Overview

Math is a library for mathematics. The same methods are bound to the special object of Integer and Double, so you don't have to use Math instead of those. For example, you can use;

var a = 2.pow(10);     // Math.pow(2, 10)   => 1024
var b = 2.0.pow(10);   // Math.pow(2.0, 10) => 1024
var c = (-10).abs();   // Math.abs(-10)     => 10

As an unary minus is lower priority than the function call, you need parentheses for -10 above. You can also use random() with the receiver of Integer or Double, but the receiver does not mean anything.

var a = 1000.random(); // 1000 is nothing to mean.
var b = 10.0.random(); // 10.0 is nothing to mean.
var c = Math.random(); // Normal.

Math Functions

Here are methods of Math. By the way, the first argument is x and the second argument is y below.

Method Meaning
Math.sin(dbl) $$\sin x$$
Math.cos(dbl) $$\cos x$$
Math.tan(dbl) $$\tan x$$
Math.asin(dbl) $$\theta$$ for $$\sin \theta=x$$
Math.acos(dbl) $$\theta$$ for $$\cos \theta=x$$
Math.atan(dbl) $$\theta$$ for $$\tan \theta=x$$
Math.atan2(dbl, dbl) the angle between the positive x axis and the ray to the point $$(x, y) \neq (0, 0)$$
Math.sinh(dbl) $$\sinh x$$
Math.cosh(dbl) $$\cosh x$$
Math.tanh(dbl) $$\tanh x$$
Math.exp(dbl) $$e^x$$
Math.ldexp(dbl, int) $$x \times 2^y$$
Math.log(dbl) $$\log_e x$$
Math.log10(dbl) $$\log_{10} x$$
Math.pow(dbl, dbl) $$x^y$$
Math.sqrt(dbl) $$\sqrt x$$
Math.ceil(dbl) Minimum value of integer over $$x$$ by Double
Math.floor(dbl) Maximum value of integer under $$x$$ by Double
Math.fmod(dbl, dbl) Floating point remainder for $$x \div y$$
Math.abs(dbl) Absolute value of $$x$$ by Double
Math.random() Random value between $$0 \leq r < 1$$

Look at above with LaTeX in your brain...

Examples

Example 1. acos

Code

function calc1(n) {
    return Math.acos(n);
}
function calc2(n) {
    return n.acos();
}
function calc3(n) {
    return Math.acos(n);
}
function calc4(n) {
    return n.acos();
}
var r1 = Math.acos(0.8);
var r2 = Math.acos(0);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(0) % r2);
System.println("%g, should be %g" % calc4(0) % r2);

Result

0.643501, should be 0.643501
0.643501, should be 0.643501
1.5708, should be 1.5708
1.5708, should be 1.5708

Example 2. asin

Code

function calc1(n) {
    return Math.asin(n);
}
function calc2(n) {
    return n.asin();
}
function calc3(n) {
    return Math.asin(n);
}
function calc4(n) {
    return n.asin();
}
var r1 = Math.asin(0.8);
var r2 = Math.asin(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.927295, should be 0.927295
0.927295, should be 0.927295
1.5708, should be 1.5708
1.5708, should be 1.5708

Example 3. atan

Code

function calc1(n) {
    return Math.atan(n);
}
function calc2(n) {
    return n.atan();
}
function calc3(n) {
    return Math.atan(n);
}
function calc4(n) {
    return n.atan();
}
var r1 = Math.atan(0.8);
var r2 = Math.atan(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.674741, should be 0.674741
0.674741, should be 0.674741
0.785398, should be 0.785398
0.785398, should be 0.785398

Example 4. atan2

Code

function calc1(n) {
    return Math.atan2(n, 0.9);
}
function calc2(n) {
    return n.atan2(0.9);
}
function calc3(n) {
    return Math.atan2(n, 1);
}
function calc4(n) {
    return n.atan2(1);
}
var r1 = Math.atan2(0.8, 0.9);
var r2 = Math.atan2(1, 1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.726642, should be 0.726642
0.726642, should be 0.726642
0.785398, should be 0.785398
0.785398, should be 0.785398

Example 5. cos

Code

function calc1(n) {
    return Math.cos(n);
}
function calc2(n) {
    return n.cos();
}
function calc3(n) {
    return Math.cos(n);
}
function calc4(n) {
    return n.cos();
}
var r1 = Math.cos(0.8);
var r2 = Math.cos(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.696707, should be 0.696707
0.696707, should be 0.696707
0.540302, should be 0.540302
0.540302, should be 0.540302

Example 6. sin

Code

function calc1(n) {
    return Math.sin(n);
}
function calc2(n) {
    return n.sin();
}
function calc3(n) {
    return Math.sin(n);
}
function calc4(n) {
    return n.sin();
}
var r1 = Math.sin(0.8);
var r2 = Math.sin(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.717356, should be 0.717356
0.717356, should be 0.717356
0.841471, should be 0.841471
0.841471, should be 0.841471

Example 7. tan

Code

function calc1(n) {
    return Math.tan(n);
}
function calc2(n) {
    return n.tan();
}
function calc3(n) {
    return Math.tan(n);
}
function calc4(n) {
    return n.tan();
}
var r1 = Math.tan(0.8);
var r2 = Math.tan(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

1.02964, should be 1.02964
1.02964, should be 1.02964
1.55741, should be 1.55741
1.55741, should be 1.55741

Example 8. cosh

Code

function calc1(n) {
    return Math.cosh(n);
}
function calc2(n) {
    return n.cosh();
}
function calc3(n) {
    return Math.cosh(n);
}
function calc4(n) {
    return n.cosh();
}
var r1 = Math.cosh(0.8);
var r2 = Math.cosh(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

1.33743, should be 1.33743
1.33743, should be 1.33743
1.54308, should be 1.54308
1.54308, should be 1.54308

Example 9. sinh

Code

function calc1(n) {
    return Math.sinh(n);
}
function calc2(n) {
    return n.sinh();
}
function calc3(n) {
    return Math.sinh(n);
}
function calc4(n) {
    return n.sinh();
}
var r1 = Math.sinh(0.8);
var r2 = Math.sinh(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.888106, should be 0.888106
0.888106, should be 0.888106
1.1752, should be 1.1752
1.1752, should be 1.1752

Example 10. tanh

Code

function calc1(n) {
    return Math.tanh(n);
}
function calc2(n) {
    return n.tanh();
}
function calc3(n) {
    return Math.tanh(n);
}
function calc4(n) {
    return n.tanh();
}
var r1 = Math.tanh(0.8);
var r2 = Math.tanh(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

0.664037, should be 0.664037
0.664037, should be 0.664037
0.761594, should be 0.761594
0.761594, should be 0.761594

Example 11. exp

Code

function calc1(n) {
    return Math.exp(n);
}
function calc2(n) {
    return n.exp();
}
function calc3(n) {
    return Math.exp(n);
}
function calc4(n) {
    return n.exp();
}
var r1 = Math.exp(0.8);
var r2 = Math.exp(1);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(1) % r2);
System.println("%g, should be %g" % calc4(1) % r2);

Result

2.22554, should be 2.22554
2.22554, should be 2.22554
2.71828, should be 2.71828
2.71828, should be 2.71828

Example 12. ldexp

Code

function calc1(n) {
    return Math.ldexp(n, 10.0);
}
function calc2(n) {
    return n.ldexp(10.0);
}
function calc3(n) {
    return Math.ldexp(n, 10);
}
function calc4(n) {
    return n.ldexp(10);
}
var r1 = Math.ldexp(2.1, 10.0);
var r2 = Math.ldexp(2, 10);
System.println("%g, should be %g" % calc1(2.1) % r1);
System.println("%g, should be %g" % calc2(2.1) % r1);
System.println("%g, should be %g" % calc3(2) % r2);
System.println("%g, should be %g" % calc4(2) % r2);

Result

2150.4, should be 2150.4
2150.4, should be 2150.4
2048, should be 2048
2048, should be 2048

Example 12. log

Code

function calc1(n) {
    return Math.log(n);
}
function calc2(n) {
    return n.log();
}
function calc3(n) {
    return Math.log(n);
}
function calc4(n) {
    return n.log();
}
var r1 = Math.log(0.8);
var r2 = Math.log(10);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(10) % r2);
System.println("%g, should be %g" % calc4(10) % r2);

Result

-0.223144, should be -0.223144
-0.223144, should be -0.223144
2.30259, should be 2.30259
2.30259, should be 2.30259

Example 13. log10

Code

function calc1(n) {
    return Math.log10(n);
}
function calc2(n) {
    return n.log10();
}
function calc3(n) {
    return Math.log10(n);
}
function calc4(n) {
    return n.log10();
}
var r1 = Math.log10(0.8);
var r2 = Math.log10(100);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(100) % r2);
System.println("%g, should be %g" % calc4(100) % r2);

Result

-0.09691, should be -0.09691
-0.09691, should be -0.09691
2, should be 2
2, should be 2

Example 14. pow

Code

function calc1(n) {
    return Math.pow(n, 10.0);
}
function calc2(n) {
    return n.pow(10.0);
}
function calc3(n) {
    return Math.pow(n, 10);
}
function calc4(n) {
    return n.pow(10);
}
var r1 = Math.pow(2.1, 10.0);
var r2 = Math.pow(2, 10);
System.println("%g, should be %g" % calc1(2.1) % r1);
System.println("%g, should be %g" % calc2(2.1) % r1);
System.println("%g, should be %g" % calc3(2) % r2);
System.println("%g, should be %g" % calc4(2) % r2);

Result

1667.99, should be 1667.99
1667.99, should be 1667.99
1024, should be 1024
1024, should be 1024

Example 15. sqrt

Code

function calc1(n) {
    return Math.sqrt(n);
}
function calc2(n) {
    return n.sqrt();
}
function calc3(n) {
    return Math.sqrt(n);
}
function calc4(n) {
    return n.sqrt();
}
var r1 = Math.sqrt(0.8);
var r2 = Math.sqrt(100);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(100) % r2);
System.println("%g, should be %g" % calc4(100) % r2);

Result

0.894427, should be 0.894427
0.894427, should be 0.894427
10, should be 10
10, should be 10

Example 16. abs

Code

function calc1(n) {
    return Math.abs(n);
}
function calc2(n) {
    return n.abs();
}
function calc3(n) {
    return Math.abs(n);
}
function calc4(n) {
    return n.abs();
}
var r1 = Math.abs(-0.8);
var r2 = Math.abs(100);
System.println("%g, should be %g" % calc1(-0.8) % r1);
System.println("%g, should be %g" % calc2(-0.8) % r1);
System.println("%g, should be %g" % calc3(100) % r2);
System.println("%g, should be %g" % calc4(100) % r2);

Result

0.8, should be 0.8
0.8, should be 0.8
100, should be 100
100, should be 100

Example 17. ceil

Code

function calc1(n) {
    return Math.ceil(n);
}
function calc2(n) {
    return n.ceil();
}
function calc3(n) {
    return Math.ceil(n);
}
function calc4(n) {
    return n.ceil();
}
var r1 = Math.ceil(0.8);
var r2 = Math.ceil(100);
System.println("%g, should be %g" % calc1(0.8) % r1);
System.println("%g, should be %g" % calc2(0.8) % r1);
System.println("%g, should be %g" % calc3(100) % r2);
System.println("%g, should be %g" % calc4(100) % r2);

Result

1, should be 1
1, should be 1
100, should be 100
100, should be 100

Example 18. floor

Code

function calc1(n) {
    return Math.floor(n);
}
function calc2(n) {
    return n.floor();
}
function calc3(n) {
    return Math.floor(n);
}
function calc4(n) {
    return n.floor();
}
var r1 = Math.floor(2.8);
var r2 = Math.floor(100);
System.println("%g, should be %g" % calc1(2.8) % r1);
System.println("%g, should be %g" % calc2(2.8) % r1);
System.println("%g, should be %g" % calc3(100) % r2);
System.println("%g, should be %g" % calc4(100) % r2);

Result

2, should be 2
2, should be 2
100, should be 100
100, should be 100

Example 19. fmod

Code

function calc1(n) {
    return Math.fmod(n, 10.0);
}
function calc2(n) {
    return n.fmod(10.0);
}
function calc3(n) {
    return Math.fmod(n, 10);
}
function calc4(n) {
    return n.fmod(10);
}
var r1 = Math.fmod(202.1, 10.0);
var r2 = Math.fmod(202, 10);
System.println("%g, should be %g" % calc1(202.1) % r1);
System.println("%g, should be %g" % calc2(202.1) % r1);
System.println("%g, should be %g" % calc3(202) % r2);
System.println("%g, should be %g" % calc4(202) % r2);

Result

2.1, should be 2.1
2.1, should be 2.1
2, should be 2
2, should be 2