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1. Can 0.99999999999 be rounded to 1.0 when multiplying?
When multiplying a floating number that is very close to 1 with an int > 0, can it ever be interpreted as 1. That is, if Math.random() returns its highest possible result (which is 1 step below 1.0), will (int)(Math.random() * 8) be 8 or 7? For a practical example, can this often-used (AFAIK) construct give an index out of bounds error: Object element = elementArray[(int)(Math.random() *...
2. In what areas of programming is a knowledge of mathematics helpful?
For example, math logic, graph theory. Everyone around tell me that math is necessary for programmer. I saw a lot of threads where people say that they used linear algebra and some other math, but no one described concrete cases when they used it. I know that there are similar threads, but I couldn't see any description of such a case.
3. Java: Static Class?
I have a class full of utility functions. Instantiating an instance of it makes no semantic sense, but I still want to call its methods. What is the best way to deal with this? Static class? Abstract?
4. Why does Math.floor return a double?
Official javadoc says that Math.floor returns a double that is "equal to a mathematical integer", but then why shouldn't it return an int?
5. What does the ^ operator do in Java?
What function does the "^" operator serve in Java? When I try this: int a = 5^n; ...it gives me: for n = 5, returns 0 for n = 4, returns 1 for n = 6, returns 3 ...so I guess it doesn't indicate exponentiation. But what is it then?
6. Is it bad form to have a a MiscUtilities class?
Our company keeps a MiscUtilities class that consists solely of public static methods that do often unrelated tasks like converting dates from String to Calendar and writing ArrayLists to files. We refer to it in other classes and find it pretty convenient. However, I've seen that sort of Utilities class derided on TheDailyWTF. I'm just wondering if there's any actual downside to this sort of c...
7. Why does Math.round return a long but Math.floor return a double?
Why the inconsistency?
8. Rounding negative numbers in Java
According to Wikipedia when rounding a negative number, you round the absolute number. So by that reasoning, -3.5 would be rounded to -4. But when I use java.lang.Math.round(-3.5) returns -3. Can someone please explain this?
9. IEEE-754 Double (64-bit floating point) vs. Long (64-bit Integer) Revisited
I'm revisiting a question (How to test if numeric conversion will change value?) that as far as I was concerned was fully solved. The problem was to detect when a particular numeric value would overflow JavaScript's IEEE-754 Number type. The previous question was using C# and the marked answer worked perfectly. Now I'm doing the exact same task but this time in Java and it doesn't work. AFAIK,...
10. Automatic parallelization
What is your opinion regarding a project that will try to take a code and split it to threads automatically(maybe compile time, probably in runtime). Take a look at the code below: for(int i=0;i<100;i++) sum1 += rand(100) for(int j=0;j<100;j++) sum2 += rand(100)/2 This kind of code can automatically get split to 2 different threads that run in parallel. Do you think it's even po...
11. Predicting the number of digits of a multiplication
I need to find the number of digits of very large multiplications (about 300 digits each). I was wondering if there is a trick to predict the number of digits that the product will be without actually performing the calculation.
12. How to round *down* integers in Java?
I'd like to round integers down to their nearest 1000 in Java. So for example: 13,623 rounds to 13,000 18,999 rounds to 18,000 etc
13. Basic question on Java's int
Why does the below code prints 2147483647, the actual value being 2147483648? i = (int)Math.pow(2,31) ; System.out.println(i); I understand that the max positive value that a int can hold is 2147483647. Then why does a code like this auto wraps to the negative side and prints -2147483648? i = (int)Math.pow(2,31) +1 ; System.out.println(i); i is of type Integer. If the second code...
14. What does it mean that Squeak runs "bit-identically" across platforms, in a way Java doesn't?
Alan Kay points out that "Unlike Java, [Squeak] runs bit-identical on every machine -- we invented this 20 years ago". The wikipedia page mentions this also: Squeak is available for many platforms, and programs produced on one platform run bit-identical on all other platforms. Since machines with different instruction sets obviously can't run bit-identical programs natively, what do...
15. Make a negative number positive in Java
I'm sure this is a very simple question! I have a Java method in which I'm summing a set of numbers. However, I want any negatives numbers to be treated as positives. So (1)+(2)+(1)+(-1) should equal 5. I'm sure there is very easy way of doing this - I just don't know how!! Any tips would be much appreciated.
16. Do you always use nouns for class names?
I was inspired to ask this here based on this blog post. Do you always try to use nouns for class names?
17. Java - Draw a ruler (line with tick marks at 90 degree angle)
I'm using Java AWT to draw lines on a panel (Line2D and Graphics2D.drawLine()) and I'm wondering how I can draw a line with tick marks, similar to: |----|----|----|----|----| I know the positions I'd like to draw the ticks at in advance. The lines could be in any position, so the ticks must be drawn at an angle releative to the line itself. My basic geometry & ability to apply it in Jav...
18. Random number generator that generates integers for Java
I want to generate some random integers in Java, but this according to some distribution laws. More specific: I want to generate some random integers for gaussian distribution. I found out only generators which return double results for the gaussian distribution. Why is that? I want to generate some random integers between some limits for exponential distribution? Here I also found out only a...
19. Can Java's random function be zero?
Just out of curiosity, can Math.random() ever be zero? For example, if I were to have: while (true){ if (Math.random() == 0) return 1; } Would I ever actually get a return of one? There's also rounding error to consider because Math.random() returns a double. I ask because my CS professor stated that random() goes from 0 to 1 inclusive, and I always thought it was exclusive.
20. How do I round up currency values in Java?
Okay, here's my problem. Basically I have this problem. I have a number like .53999999. How do I round it up to 54 without using any of the Math functions? I'm guessing I have to multiply by 100 to scale it, then divide? Something like that? Thanks guys! EDIT: more info The issue is with money. let's say I have $50.5399999 I know how to get the $50, but I don't have how to get the cents. I...
21. No ordinary "function" in java?
in php you can declare a function in a global scope with function. is this not possible in java? looks like every function is in a class as a method. so everything is OOP in java? no procedural code? 
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   /*
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    * Copyright 1994-2006 Sun Microsystems, Inc.  All Rights Reserved.
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    * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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    *
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    * This code is free software; you can redistribute it and/or modify it
6
    * under the terms of the GNU General Public License version 2 only, as
7
    * published by the Free Software Foundation.  Sun designates this
8
    * particular file as subject to the "Classpath" exception as provided
9
    * by Sun in the LICENSE file that accompanied this code.
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   *
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   * This code is distributed in the hope that it will be useful, but WITHOUT
12
   * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13
   * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
14
   * version 2 for more details (a copy is included in the LICENSE file that
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   * accompanied this code).
16
   *
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   * You should have received a copy of the GNU General Public License version
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   * 2 along with this work; if not, write to the Free Software Foundation,
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   * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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   *
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   * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
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   * CA 95054 USA or visit www.sun.com if you need additional information or
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   * have any questions.
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   */
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  package java.lang;
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  import java.util.Random;


The class Math contains methods for performing basic numeric operations such as the elementary exponential, logarithm, square root, and trigonometric functions.

Unlike some of the numeric methods of class StrictMath, all implementations of the equivalent functions of class Math are not defined to return the bit-for-bit same results. This relaxation permits better-performing implementations where strict reproducibility is not required.

By default many of the Math methods simply call the equivalent method in StrictMath for their implementation. Code generators are encouraged to use platform-specific native libraries or microprocessor instructions, where available, to provide higher-performance implementations of Math methods. Such higher-performance implementations still must conform to the specification for Math.

The quality of implementation specifications concern two properties, accuracy of the returned result and monotonicity of the method. Accuracy of the floating-point Math methods is measured in terms of ulps, units in the last place. For a given floating-point format, an ulp of a specific real number value is the distance between the two floating-point values bracketing that numerical value. When discussing the accuracy of a method as a whole rather than at a specific argument, the number of ulps cited is for the worst-case error at any argument. If a method always has an error less than 0.5 ulps, the method always returns the floating-point number nearest the exact result; such a method is correctly rounded. A correctly rounded method is generally the best a floating-point approximation can be; however, it is impractical for many floating-point methods to be correctly rounded. Instead, for the Math class, a larger error bound of 1 or 2 ulps is allowed for certain methods. Informally, with a 1 ulp error bound, when the exact result is a representable number, the exact result should be returned as the computed result; otherwise, either of the two floating-point values which bracket the exact result may be returned. For exact results large in magnitude, one of the endpoints of the bracket may be infinite. Besides accuracy at individual arguments, maintaining proper relations between the method at different arguments is also important. Therefore, most methods with more than 0.5 ulp errors are required to be semi-monotonic: whenever the mathematical function is non-decreasing, so is the floating-point approximation, likewise, whenever the mathematical function is non-increasing, so is the floating-point approximation. Not all approximations that have 1 ulp accuracy will automatically meet the monotonicity requirements.

Author(s):
unascribed
Joseph D. Darcy
Since:
JDK1.0
85
  
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  public final class Math {

    
Don't let anyone instantiate this class. 
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      private Math() {}

    
The double value that is closer than any other to e, the base of the natural logarithms. 
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      public static final double E = 2.7182818284590452354;

    
The double value that is closer than any other to pi, the ratio of the circumference of a circle to its diameter. 
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105
     public static final double PI = 3.14159265358979323846;

    
Returns the trigonometric sine of an angle. Special cases:
  • If the argument is NaN or an infinity, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a an angle, in radians.
Returns:
the sine of the argument.
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120
     public static double sin(double a) {
121
         return StrictMath.sin(a); // default impl. delegates to StrictMath
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     }

    
Returns the trigonometric cosine of an angle. Special cases:
  • If the argument is NaN or an infinity, then the result is NaN.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a an angle, in radians.
Returns:
the cosine of the argument.
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     public static double cos(double a) {
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         return StrictMath.cos(a); // default impl. delegates to StrictMath
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     }

    
Returns the trigonometric tangent of an angle. Special cases:
  • If the argument is NaN or an infinity, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a an angle, in radians.
Returns:
the tangent of the argument.
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     public static double tan(double a) {
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         return StrictMath.tan(a); // default impl. delegates to StrictMath
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     }

    
Returns the arc sine of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
  • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a the value whose arc sine is to be returned.
Returns:
the arc sine of the argument.
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     public static double asin(double a) {
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         return StrictMath.asin(a); // default impl. delegates to StrictMath
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     }

    
Returns the arc cosine of a value; the returned angle is in the range 0.0 through pi. Special case:
  • If the argument is NaN or its absolute value is greater than 1, then the result is NaN.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a the value whose arc cosine is to be returned.
Returns:
the arc cosine of the argument.
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     public static double acos(double a) {
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         return StrictMath.acos(a); // default impl. delegates to StrictMath
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     }

    
Returns the arc tangent of a value; the returned angle is in the range -pi/2 through pi/2. Special cases:
  • If the argument is NaN, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a the value whose arc tangent is to be returned.
Returns:
the arc tangent of the argument.
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     public static double atan(double a) {
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         return StrictMath.atan(a); // default impl. delegates to StrictMath
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     }

    
Converts an angle measured in degrees to an approximately equivalent angle measured in radians. The conversion from degrees to radians is generally inexact.

Parameters:
angdeg an angle, in degrees
Returns:
the measurement of the angle angdeg in radians.
Since:
1.2
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     public static double toRadians(double angdeg) {
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         return angdeg / 180.0 * ;
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     }

    
Converts an angle measured in radians to an approximately equivalent angle measured in degrees. The conversion from radians to degrees is generally inexact; users should not expect cos(toRadians(90.0)) to exactly equal 0.0.

Parameters:
angrad an angle, in radians
Returns:
the measurement of the angle angrad in degrees.
Since:
1.2
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     public static double toDegrees(double angrad) {
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         return angrad * 180.0 / ;
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     }

    
Returns Euler's number e raised to the power of a double value. Special cases:
  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative infinity, then the result is positive zero.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a the exponent to raise e to.
Returns:
the value ea, where e is the base of the natural logarithms.
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     public static double exp(double a) {
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         return StrictMath.exp(a); // default impl. delegates to StrictMath
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     }

    
Returns the natural logarithm (base e) of a double value. Special cases:
  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is negative infinity.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a a value
Returns:
the value ln a, the natural logarithm of a.
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     public static double log(double a) {
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         return StrictMath.log(a); // default impl. delegates to StrictMath
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     }

    
Returns the base 10 logarithm of a double value. Special cases:
  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is negative infinity.
  • If the argument is equal to 10n for integer n, then the result is n.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a a value
Returns:
the base 10 logarithm of a.
Since:
1.5
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     public static double log10(double a) {
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         return StrictMath.log10(a); // default impl. delegates to StrictMath
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     }

    
Returns the correctly rounded positive square root of a double value. Special cases:
  • If the argument is NaN or less than zero, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.
Otherwise, the result is the double value closest to the true mathematical square root of the argument value.

Parameters:
a a value.
Returns:
the positive square root of a. If the argument is NaN or less than zero, the result is NaN.
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     public static double sqrt(double a) {
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         return StrictMath.sqrt(a); // default impl. delegates to StrictMath
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                                    // Note that hardware sqrt instructions
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                                    // frequently can be directly used by JITs
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                                    // and should be much faster than doing
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                                    // Math.sqrt in software.
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     }


    
Returns the cube root of a double value. For positive finite x, cbrt(-x) == -cbrt(x); that is, the cube root of a negative value is the negative of the cube root of that value's magnitude. Special cases:
  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is an infinity with the same sign as the argument.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result.

Parameters:
a a value.
Returns:
the cube root of a.
Since:
1.5
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     public static double cbrt(double a) {
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         return StrictMath.cbrt(a);
357
     }

    
Computes the remainder operation on two arguments as prescribed by the IEEE 754 standard. The remainder value is mathematically equal to f1 - f2 × n, where n is the mathematical integer closest to the exact mathematical value of the quotient f1/f2, and if two mathematical integers are equally close to f1/f2, then n is the integer that is even. If the remainder is zero, its sign is the same as the sign of the first argument. Special cases:
  • If either argument is NaN, or the first argument is infinite, or the second argument is positive zero or negative zero, then the result is NaN.
  • If the first argument is finite and the second argument is infinite, then the result is the same as the first argument.

Parameters:
f1 the dividend.
f2 the divisor.
Returns:
the remainder when f1 is divided by f2.
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     public static double IEEEremainder(double f1, double f2) {
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         return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
383
     }

    
Returns the smallest (closest to negative infinity) double value that is greater than or equal to the argument and is equal to a mathematical integer. Special cases:
  • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
  • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.
  • If the argument value is less than zero but greater than -1.0, then the result is negative zero.
Note that the value of Math.ceil(x) is exactly the value of -Math.floor(-x).

Parameters:
a a value.
Returns:
the smallest (closest to negative infinity) floating-point value that is greater than or equal to the argument and is equal to a mathematical integer.
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404
     public static double ceil(double a) {
405
         return StrictMath.ceil(a); // default impl. delegates to StrictMath
406
     }

    
Returns the largest (closest to positive infinity) double value that is less than or equal to the argument and is equal to a mathematical integer. Special cases:
  • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
  • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

Parameters:
a a value.
Returns:
the largest (closest to positive infinity) floating-point value that less than or equal to the argument and is equal to a mathematical integer.
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423
     public static double floor(double a) {
424
         return StrictMath.floor(a); // default impl. delegates to StrictMath
425
     }

    
Returns the double value that is closest in value to the argument and is equal to a mathematical integer. If two double values that are mathematical integers are equally close, the result is the integer value that is even. Special cases:
  • If the argument value is already equal to a mathematical integer, then the result is the same as the argument.
  • If the argument is NaN or an infinity or positive zero or negative zero, then the result is the same as the argument.

Parameters:
a a double value.
Returns:
the closest floating-point value to a that is equal to a mathematical integer.
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442
     public static double rint(double a) {
443
         return StrictMath.rint(a); // default impl. delegates to StrictMath
444
     }

    
Returns the angle theta from the conversion of rectangular coordinates (x, y) to polar coordinates (r, theta). This method computes the phase theta by computing an arc tangent of y/x in the range of -pi to pi. Special cases:
  • If either argument is NaN, then the result is NaN.
  • If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero.
  • If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
  • If the first argument is positive zero and the second argument is negative, or the first argument is positive and finite and the second argument is negative infinity, then the result is the double value closest to pi.
  • If the first argument is negative zero and the second argument is negative, or the first argument is negative and finite and the second argument is negative infinity, then the result is the double value closest to -pi.
  • If the first argument is positive and the second argument is positive zero or negative zero, or the first argument is positive infinity and the second argument is finite, then the result is the double value closest to pi/2.
  • If the first argument is negative and the second argument is positive zero or negative zero, or the first argument is negative infinity and the second argument is finite, then the result is the double value closest to -pi/2.
  • If both arguments are positive infinity, then the result is the double value closest to pi/4.
  • If the first argument is positive infinity and the second argument is negative infinity, then the result is the double value closest to 3*pi/4.
  • If the first argument is negative infinity and the second argument is positive infinity, then the result is the double value closest to -pi/4.
  • If both arguments are negative infinity, then the result is the double value closest to -3*pi/4.

The computed result must be within 2 ulps of the exact result. Results must be semi-monotonic.

Parameters:
y the ordinate coordinate
x the abscissa coordinate
Returns:
the theta component of the point (r, theta) in polar coordinates that corresponds to the point (x, y) in Cartesian coordinates.
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498
     public static double atan2(double y, double x) {
499
         return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
500
     }

    
Returns the value of the first argument raised to the power of the second argument. Special cases:
  • If the second argument is positive or negative zero, then the result is 1.0.
  • If the second argument is 1.0, then the result is the same as the first argument.
  • If the second argument is NaN, then the result is NaN.
  • If the first argument is NaN and the second argument is nonzero, then the result is NaN.
  • If
    • the absolute value of the first argument is greater than 1 and the second argument is positive infinity, or
    • the absolute value of the first argument is less than 1 and the second argument is negative infinity,
    then the result is positive infinity.
  • If
    • the absolute value of the first argument is greater than 1 and the second argument is negative infinity, or
    • the absolute value of the first argument is less than 1 and the second argument is positive infinity,
    then the result is positive zero.
  • If the absolute value of the first argument equals 1 and the second argument is infinite, then the result is NaN.
  • If
    • the first argument is positive zero and the second argument is greater than zero, or
    • the first argument is positive infinity and the second argument is less than zero,
    then the result is positive zero.
  • If
    • the first argument is positive zero and the second argument is less than zero, or
    • the first argument is positive infinity and the second argument is greater than zero,
    then the result is positive infinity.
  • If
    • the first argument is negative zero and the second argument is greater than zero but not a finite odd integer, or
    • the first argument is negative infinity and the second argument is less than zero but not a finite odd integer,
    then the result is positive zero.
  • If
    • the first argument is negative zero and the second argument is a positive finite odd integer, or
    • the first argument is negative infinity and the second argument is a negative finite odd integer,
    then the result is negative zero.
  • If
    • the first argument is negative zero and the second argument is less than zero but not a finite odd integer, or
    • the first argument is negative infinity and the second argument is greater than zero but not a finite odd integer,
    then the result is positive infinity.
  • If
    • the first argument is negative zero and the second argument is a negative finite odd integer, or
    • the first argument is negative infinity and the second argument is a positive finite odd integer,
    then the result is negative infinity.
  • If the first argument is finite and less than zero
    • if the second argument is a finite even integer, the result is equal to the result of raising the absolute value of the first argument to the power of the second argument
    • if the second argument is a finite odd integer, the result is equal to the negative of the result of raising the absolute value of the first argument to the power of the second argument
    • if the second argument is finite and not an integer, then the result is NaN.
  • If both arguments are integers, then the result is exactly equal to the mathematical result of raising the first argument to the power of the second argument if that result can in fact be represented exactly as a double value.

(In the foregoing descriptions, a floating-point value is considered to be an integer if and only if it is finite and a fixed point of the method ceil or, equivalently, a fixed point of the method floor. A value is a fixed point of a one-argument method if and only if the result of applying the method to the value is equal to the value.)

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
a the base.
b the exponent.
Returns:
the value ab.
624
 
625
     public static double pow(double a, double b) {
626
         return StrictMath.pow(a, b); // default impl. delegates to StrictMath
627
     }

    
Returns the closest int to the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type int. In other words, the result is equal to the value of the expression:

(int)Math.floor(a + 0.5f)

Special cases:

  • If the argument is NaN, the result is 0.
  • If the argument is negative infinity or any value less than or equal to the value of Integer.MIN_VALUE, the result is equal to the value of Integer.MIN_VALUE.
  • If the argument is positive infinity or any value greater than or equal to the value of Integer.MAX_VALUE, the result is equal to the value of Integer.MAX_VALUE.

Parameters:
a a floating-point value to be rounded to an integer.
Returns:
the value of the argument rounded to the nearest int value.
See also:
Integer.MAX_VALUE
Integer.MIN_VALUE
650
 
651
     public static int round(float a) {
652
         return (int)floor(a + 0.5f);
653
     }

    
Returns the closest long to the argument. The result is rounded to an integer by adding 1/2, taking the floor of the result, and casting the result to type long. In other words, the result is equal to the value of the expression:

(long)Math.floor(a + 0.5d)

Special cases:

  • If the argument is NaN, the result is 0.
  • If the argument is negative infinity or any value less than or equal to the value of Long.MIN_VALUE, the result is equal to the value of Long.MIN_VALUE.
  • If the argument is positive infinity or any value greater than or equal to the value of Long.MAX_VALUE, the result is equal to the value of Long.MAX_VALUE.

Parameters:
a a floating-point value to be rounded to a long.
Returns:
the value of the argument rounded to the nearest long value.
See also:
Long.MAX_VALUE
Long.MIN_VALUE
677
 
678
     public static long round(double a) {
679
         return (long)floor(a + 0.5d);
680
     }
681
 
682
     private static Random randomNumberGenerator;
683
 
684
     private static synchronized void initRNG() {
685
         if ( == null)
686
              = new Random();
687
     }

    
Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.

When this method is first called, it creates a single new pseudorandom-number generator, exactly as if by the expression

new java.util.Random
This new pseudorandom-number generator is used thereafter for all calls to this method and is used nowhere else.

This method is properly synchronized to allow correct use by more than one thread. However, if many threads need to generate pseudorandom numbers at a great rate, it may reduce contention for each thread to have its own pseudorandom-number generator.

Returns:
a pseudorandom double greater than or equal to 0.0 and less than 1.0.
See also:
java.util.Random.nextDouble()
709
 
710
     public static double random() {
711
         if ( == null) initRNG();
712
         return .nextDouble();
713
     }

    
Returns the absolute value of an int value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

Note that if the argument is equal to the value of Integer.MIN_VALUE, the most negative representable int value, the result is that same value, which is negative.

Parameters:
a the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
727
 
728
     public static int abs(int a) {
729
         return (a < 0) ? -a : a;
730
     }

    
Returns the absolute value of a long value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned.

Note that if the argument is equal to the value of Long.MIN_VALUE, the most negative representable long value, the result is that same value, which is negative.

Parameters:
a the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
744
 
745
     public static long abs(long a) {
746
         return (a < 0) ? -a : a;
747
     }

    
Returns the absolute value of a float value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
  • If the argument is positive zero or negative zero, the result is positive zero.
  • If the argument is infinite, the result is positive infinity.
  • If the argument is NaN, the result is NaN.
In other words, the result is the same as the value of the expression:

Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))

Parameters:
a the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
763
 
764
     public static float abs(float a) {
765
         return (a <= 0.0F) ? 0.0F - a : a;
766
     }

    
Returns the absolute value of a double value. If the argument is not negative, the argument is returned. If the argument is negative, the negation of the argument is returned. Special cases:
  • If the argument is positive zero or negative zero, the result is positive zero.
  • If the argument is infinite, the result is positive infinity.
  • If the argument is NaN, the result is NaN.
In other words, the result is the same as the value of the expression:

Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)

Parameters:
a the argument whose absolute value is to be determined
Returns:
the absolute value of the argument.
782
 
783
     public static double abs(double a) {
784
         return (a <= 0.0D) ? 0.0D - a : a;
785
     }

    
Returns the greater of two int values. That is, the result is the argument closer to the value of Integer.MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters:
a an argument.
b another argument.
Returns:
the larger of a and b.
796
 
797
     public static int max(int a, int b) {
798
         return (a >= b) ? a : b;
799
     }

    
Returns the greater of two long values. That is, the result is the argument closer to the value of Long.MAX_VALUE. If the arguments have the same value, the result is that same value.

Parameters:
a an argument.
b another argument.
Returns:
the larger of a and b.
810
 
811
     public static long max(long a, long b) {
812
         return (a >= b) ? a : b;
813
     }
814
 
815
     private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
816
     private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);

    
Returns the greater of two float values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters:
a an argument.
b another argument.
Returns:
the larger of a and b.
831
 
832
     public static float max(float a, float b) {
833
         if (a != a) return a;   // a is NaN
834
         if ((a == 0.0f) && (b == 0.0f)
835
             && (Float.floatToIntBits(a) == )) {
836
             return b;
837
         }
838
         return (a >= b) ? a : b;
839
     }

    
Returns the greater of two double values. That is, the result is the argument closer to positive infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other negative zero, the result is positive zero.

Parameters:
a an argument.
b another argument.
Returns:
the larger of a and b.
854
 
855
     public static double max(double a, double b) {
856
         if (a != a) return a;   // a is NaN
857
         if ((a == 0.0d) && (b == 0.0d)
858
             && (Double.doubleToLongBits(a) == )) {
859
             return b;
860
         }
861
         return (a >= b) ? a : b;
862
     }

    
Returns the smaller of two int values. That is, the result the argument closer to the value of Integer.MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters:
a an argument.
b another argument.
Returns:
the smaller of a and b.
873
 
874
     public static int min(int a, int b) {
875
         return (a <= b) ? a : b;
876
     }

    
Returns the smaller of two long values. That is, the result is the argument closer to the value of Long.MIN_VALUE. If the arguments have the same value, the result is that same value.

Parameters:
a an argument.
b another argument.
Returns:
the smaller of a and b.
887
 
888
     public static long min(long a, long b) {
889
         return (a <= b) ? a : b;
890
     }

    
Returns the smaller of two float values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters:
a an argument.
b another argument.
Returns:
the smaller of a and b.
905
 
906
     public static float min(float a, float b) {
907
         if (a != a) return a;   // a is NaN
908
         if ((a == 0.0f) && (b == 0.0f)
909
             && (Float.floatToIntBits(b) == )) {
910
             return b;
911
         }
912
         return (a <= b) ? a : b;
913
     }

    
Returns the smaller of two double values. That is, the result is the value closer to negative infinity. If the arguments have the same value, the result is that same value. If either value is NaN, then the result is NaN. Unlike the numerical comparison operators, this method considers negative zero to be strictly smaller than positive zero. If one argument is positive zero and the other is negative zero, the result is negative zero.

Parameters:
a an argument.
b another argument.
Returns:
the smaller of a and b.
928
 
929
     public static double min(double a, double b) {
930
         if (a != a) return a;   // a is NaN
931
         if ((a == 0.0d) && (b == 0.0d)
932
             && (Double.doubleToLongBits(b) == )) {
933
             return b;
934
         }
935
         return (a <= b) ? a : b;
936
     }

    
Returns the size of an ulp of the argument. An ulp of a double value is the positive distance between this floating-point value and the double value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive or negative infinity, then the result is positive infinity.
  • If the argument is positive or negative zero, then the result is Double.MIN_VALUE.
  • If the argument is ±Double.MAX_VALUE, then the result is equal to 2971.

Parameters:
d the floating-point value whose ulp is to be returned
Returns:
the size of an ulp of the argument
Author(s):
Joseph D. Darcy
Since:
1.5
960
 
961
     public static double ulp(double d) {
962
         return sun.misc.FpUtils.ulp(d);
963
     }

    
Returns the size of an ulp of the argument. An ulp of a float value is the positive distance between this floating-point value and the float value next larger in magnitude. Note that for non-NaN x, ulp(-x) == ulp(x).

Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive or negative infinity, then the result is positive infinity.
  • If the argument is positive or negative zero, then the result is Float.MIN_VALUE.
  • If the argument is ±Float.MAX_VALUE, then the result is equal to 2104.

Parameters:
f the floating-point value whose ulp is to be returned
Returns:
the size of an ulp of the argument
Author(s):
Joseph D. Darcy
Since:
1.5
987
 
988
     public static float ulp(float f) {
989
         return sun.misc.FpUtils.ulp(f);
990
     }

    
Returns the signum function of the argument; zero if the argument is zero, 1.0 if the argument is greater than zero, -1.0 if the argument is less than zero.

Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.

Parameters:
d the floating-point value whose signum is to be returned
Returns:
the signum function of the argument
Author(s):
Joseph D. Darcy
Since:
1.5
1009
    public static double signum(double d) {
1010
        return sun.misc.FpUtils.signum(d);
1011
    }

    
Returns the signum function of the argument; zero if the argument is zero, 1.0f if the argument is greater than zero, -1.0f if the argument is less than zero.

Special Cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is positive zero or negative zero, then the result is the same as the argument.

Parameters:
f the floating-point value whose signum is to be returned
Returns:
the signum function of the argument
Author(s):
Joseph D. Darcy
Since:
1.5
1030
    public static float signum(float f) {
1031
        return sun.misc.FpUtils.signum(f);
1032
    }

    
Returns the hyperbolic sine of a double value. The hyperbolic sine of x is defined to be (ex - e-x)/2 where e is Euler's number.

Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is an infinity with the same sign as the argument.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 2.5 ulps of the exact result.

Parameters:
x The number whose hyperbolic sine is to be returned.
Returns:
The hyperbolic sine of x.
Since:
1.5
1059
    public static double sinh(double x) {
1060
        return StrictMath.sinh(x);
1061
    }

    
Returns the hyperbolic cosine of a double value. The hyperbolic cosine of x is defined to be (ex + e-x)/2 where e is Euler's number.

Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is infinite, then the result is positive infinity.
  • If the argument is zero, then the result is 1.0.

The computed result must be within 2.5 ulps of the exact result.

Parameters:
x The number whose hyperbolic cosine is to be returned.
Returns:
The hyperbolic cosine of x.
Since:
1.5
1087
    public static double cosh(double x) {
1088
        return StrictMath.cosh(x);
1089
    }

    
Returns the hyperbolic tangent of a double value. The hyperbolic tangent of x is defined to be (ex - e-x)/(ex + e-x), in other words, sinh(x)/cosh(x). Note that the absolute value of the exact tanh is always less than 1.

Special cases:

  • If the argument is NaN, then the result is NaN.
  • If the argument is zero, then the result is a zero with the same sign as the argument.
  • If the argument is positive infinity, then the result is +1.0.
  • If the argument is negative infinity, then the result is -1.0.

The computed result must be within 2.5 ulps of the exact result. The result of tanh for any finite input must have an absolute value less than or equal to 1. Note that once the exact result of tanh is within 1/2 of an ulp of the limit value of ±1, correctly signed ±1.0 should be returned.

Parameters:
x The number whose hyperbolic tangent is to be returned.
Returns:
The hyperbolic tangent of x.
Since:
1.5
1127
    public static double tanh(double x) {
1128
        return StrictMath.tanh(x);
1129
    }

    
Returns sqrt(x2 +y2) without intermediate overflow or underflow.

Special cases:

  • If either argument is infinite, then the result is positive infinity.
  • If either argument is NaN and neither argument is infinite, then the result is NaN.

The computed result must be within 1 ulp of the exact result. If one parameter is held constant, the results must be semi-monotonic in the other parameter.

Parameters:
x a value
y a value
Returns:
sqrt(x2 +y2) without intermediate overflow or underflow
Since:
1.5
1156
    public static double hypot(double x, double y) {
1157
        return StrictMath.hypot(x, y);
1158
    }

    
Returns ex -1. Note that for values of x near 0, the exact sum of expm1(x) + 1 is much closer to the true result of ex than exp(x).

Special cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative infinity, then the result is -1.0.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic. The result of expm1 for any finite input must be greater than or equal to -1.0. Note that once the exact result of ex - 1 is within 1/2 ulp of the limit value -1, -1.0 should be returned.

Parameters:
x the exponent to raise e to in the computation of ex -1.
Returns:
the value ex - 1.
Since:
1.5
1194
    public static double expm1(double x) {
1195
        return StrictMath.expm1(x);
1196
    }

    
Returns the natural logarithm of the sum of the argument and 1. Note that for small values x, the result of log1p(x) is much closer to the true result of ln(1 + x) than the floating-point evaluation of log(1.0+x).

Special cases:

  • If the argument is NaN or less than -1, then the result is NaN.
  • If the argument is positive infinity, then the result is positive infinity.
  • If the argument is negative one, then the result is negative infinity.
  • If the argument is zero, then the result is a zero with the same sign as the argument.

The computed result must be within 1 ulp of the exact result. Results must be semi-monotonic.

Parameters:
x a value
Returns:
the value ln(x + 1), the natural log of x + 1
Since:
1.5
1231
    public static double log1p(double x) {
1232
        return StrictMath.log1p(x);
1233
    }

    
Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign(double,double) method, this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.

Parameters:
magnitude the parameter providing the magnitude of the result
sign the parameter providing the sign of the result
Returns:
a value with the magnitude of magnitude and the sign of sign.
Since:
1.6
1250
    public static double copySign(double magnitude, double sign) {
1251
        return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1252
    }

    
Returns the first floating-point argument with the sign of the second floating-point argument. Note that unlike the StrictMath.copySign(float,float) method, this method does not require NaN sign arguments to be treated as positive values; implementations are permitted to treat some NaN arguments as positive and other NaN arguments as negative to allow greater performance.

Parameters:
magnitude the parameter providing the magnitude of the result
sign the parameter providing the sign of the result
Returns:
a value with the magnitude of magnitude and the sign of sign.
Since:
1.6
1269
    public static float copySign(float magnitude, float sign) {
1270
        return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1271
    }

    
Returns the unbiased exponent used in the representation of a float. Special cases:

Parameters:
f a float value
Returns:
the unbiased exponent of the argument
Since:
1.6
1287
    public static int getExponent(float f) {
1288
        return sun.misc.FpUtils.getExponent(f);
1289
    }

    
Returns the unbiased exponent used in the representation of a double. Special cases:

Parameters:
d a double value
Returns:
the unbiased exponent of the argument
Since:
1.6
1305
    public static int getExponent(double d) {
1306
        return sun.misc.FpUtils.getExponent(d);
1307
    }

    
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal the second argument is returned.

Special cases:

  • If either argument is a NaN, then NaN is returned.
  • If both arguments are signed zeros, direction is returned unchanged (as implied by the requirement of returning the second argument if the arguments compare as equal).
  • If start is ±Double.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.
  • If start is infinite and direction has a value such that the result should have a smaller magnitude, Double.MAX_VALUE with the same sign as start is returned.
  • If start is equal to ± Double.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.

Parameters:
start starting floating-point value
direction value indicating which of start's neighbors or start should be returned
Returns:
The floating-point number adjacent to start in the direction of direction.
Since:
1.6
1349
    public static double nextAfter(double start, double direction) {
1350
        return sun.misc.FpUtils.nextAfter(start, direction);
1351
    }

    
Returns the floating-point number adjacent to the first argument in the direction of the second argument. If both arguments compare as equal a value equivalent to the second argument is returned.

Special cases:

  • If either argument is a NaN, then NaN is returned.
  • If both arguments are signed zeros, a value equivalent to direction is returned.
  • If start is ±Float.MIN_VALUE and direction has a value such that the result should have a smaller magnitude, then a zero with the same sign as start is returned.
  • If start is infinite and direction has a value such that the result should have a smaller magnitude, Float.MAX_VALUE with the same sign as start is returned.
  • If start is equal to ± Float.MAX_VALUE and direction has a value such that the result should have a larger magnitude, an infinity with same sign as start is returned.

Parameters:
start starting floating-point value
direction value indicating which of start's neighbors or start should be returned
Returns:
The floating-point number adjacent to start in the direction of direction.
Since:
1.6
1392
    public static float nextAfter(float start, double direction) {
1393
        return sun.misc.FpUtils.nextAfter(start, direction);
1394
    }

    
Returns the floating-point value adjacent to d in the direction of positive infinity. This method is semantically equivalent to nextAfter(d, Double.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call.

Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, the result is positive infinity.
  • If the argument is zero, the result is Double.MIN_VALUE

Parameters:
d starting floating-point value
Returns:
The adjacent floating-point value closer to positive infinity.
Since:
1.6
1421
    public static double nextUp(double d) {
1422
        return sun.misc.FpUtils.nextUp(d);
1423
    }

    
Returns the floating-point value adjacent to f in the direction of positive infinity. This method is semantically equivalent to nextAfter(f, Float.POSITIVE_INFINITY); however, a nextUp implementation may run faster than its equivalent nextAfter call.

Special Cases:

  • If the argument is NaN, the result is NaN.
  • If the argument is positive infinity, the result is positive infinity.
  • If the argument is zero, the result is Float.MIN_VALUE

Parameters:
f starting floating-point value
Returns:
The adjacent floating-point value closer to positive infinity.
Since:
1.6
1450
    public static float nextUp(float f) {
1451
        return sun.misc.FpUtils.nextUp(f);
1452
    }


    
Return d × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the double value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Double.MIN_EXPONENT and Double.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Double.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as d.

Special cases:

  • If the first argument is NaN, NaN is returned.
  • If the first argument is infinite, then an infinity of the same sign is returned.
  • If the first argument is zero, then a zero of the same sign is returned.

Parameters:
d number to be scaled by a power of two.
scaleFactor power of 2 used to scale d
Returns:
d × 2scaleFactor
Since:
1.6
1485
    public static double scalb(double d, int scaleFactor) {
1486
        return sun.misc.FpUtils.scalb(d, scaleFactor);
1487
    }

    
Return f × 2scaleFactor rounded as if performed by a single correctly rounded floating-point multiply to a member of the float value set. See the Java Language Specification for a discussion of floating-point value sets. If the exponent of the result is between Float.MIN_EXPONENT and Float.MAX_EXPONENT, the answer is calculated exactly. If the exponent of the result would be larger than Float.MAX_EXPONENT, an infinity is returned. Note that if the result is subnormal, precision may be lost; that is, when scalb(x, n) is subnormal, scalb(scalb(x, n), -n) may not equal x. When the result is non-NaN, the result has the same sign as f.

Special cases:

  • If the first argument is NaN, NaN is returned.
  • If the first argument is infinite, then an infinity of the same sign is returned.
  • If the first argument is zero, then a zero of the same sign is returned.

Parameters:
f number to be scaled by a power of two.
scaleFactor power of 2 used to scale f
Returns:
f × 2scaleFactor
Since:
1.6
1519
    public static float scalb(float f, int scaleFactor) {
1520
        return sun.misc.FpUtils.scalb(f, scaleFactor);
1521
    }
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