/*
* @(#)Math.java 1.57 06/10/10
*
* Copyright 1990-2008 Sun Microsystems, Inc. All Rights Reserved.
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER
*
* This program is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License version
* 2 only, as published by the Free Software Foundation.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License version 2 for more details (a copy is
* included at /legal/license.txt).
*
* You should have received a copy of the GNU General Public License
* version 2 along with this work; if not, write to the Free Software
* Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
* 02110-1301 USA
*
* Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa
* Clara, CA 95054 or visit www.sun.com if you need additional
* information or have any questions.
*
*/
package java.lang;
import java.util.Random;
/**
* The class <code>Math</code> contains methods for performing basic
* numeric operations such as the elementary exponential, logarithm,
* square root, and trigonometric functions.
* <p>
* Unlike some of the numeric methods of class
* <code>StrictMath</code>, all implementations of the equivalent
* functions of class <code>Math</code> are not defined to return the
* bit-for-bit same results. This relaxation permits
* better-performing implementations where strict reproducibility is
* not required.
* <p>
* By default many of the <code>Math</code> methods simply call
* the equivalent method in <code>StrictMath</code> for their
* implementation. Code generators are encouraged to use
* platform-specific native libraries or microprocessor instructions,
* where available, to provide higher-performance implementations of
* <code>Math</code> methods. Such higher-performance
* implementations still must conform to the specification for
* <code>Math</code>.
* <p>
* The quality of implementation specifications concern two
* properties, accuracy of the returned result and monotonicity of the
* method. Accuracy of the floating-point <code>Math</code> methods
* is measured in terms of <i>ulps</i>, units in the last place. For
* a given floating-point format, an ulp of a specific real number
* value is the difference between the two floating-point values
* closest to 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 <i>correctly rounded</i>. 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 <code>Math</code> 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; otherwise, either of
* the two floating-point numbers closest to the exact result may be
* returned. Besides accuracy at individual arguments, maintaining
* proper relations between the method at different arguments is also
* important. Therefore, methods with more than 0.5 ulp errors are
* required to be <i>semi-monotonic</i>: 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 unascribed
* @version 1.50, 02/02/00
* @since JDK1.0
*/
public final strictfp class Math {
/**
* Don't let anyone instantiate this class.
*/
private Math() {}
/**
* The <code>double</code> value that is closer than any other to
* <i>e</i>, the base of the natural logarithms.
*/
public static final double E = 2.7182818284590452354;
/**
* The <code>double</code> value that is closer than any other to
* <i>pi</i>, the ratio of the circumference of a circle to its
* diameter.
*/
public static final double PI = 3.14159265358979323846;
/**
* Returns the trigonometric sine of an angle. Special cases:
* <ul><li>If the argument is NaN or an infinity, then the
* result is NaN.
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the sine of the argument.
*/
public static double sin(double a) {
return StrictMath.sin(a); // default impl. delegates to StrictMath
}
/**
* Returns the trigonometric cosine of an angle. Special cases:
* <ul><li>If the argument is NaN or an infinity, then the
* result is NaN.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the cosine of the argument.
*/
public static double cos(double a) {
return StrictMath.cos(a); // default impl. delegates to StrictMath
}
/**
* Returns the trigonometric tangent of an angle. Special cases:
* <ul><li>If the argument is NaN or an infinity, then the result
* is NaN.
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a an angle, in radians.
* @return the tangent of the argument.
*/
public static double tan(double a) {
return StrictMath.tan(a); // default impl. delegates to StrictMath
}
/**
* Returns the arc sine of an angle, in the range of -<i>pi</i>/2 through
* <i>pi</i>/2. Special cases:
* <ul><li>If the argument is NaN or its absolute value is greater
* than 1, then the result is NaN.
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a the value whose arc sine is to be returned.
* @return the arc sine of the argument.
*/
public static double asin(double a) {
return StrictMath.asin(a); // default impl. delegates to StrictMath
}
/**
* Returns the arc cosine of an angle, in the range of 0.0 through
* <i>pi</i>. Special case:
* <ul><li>If the argument is NaN or its absolute value is greater
* than 1, then the result is NaN.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a the value whose arc cosine is to be returned.
* @return the arc cosine of the argument.
*/
public static double acos(double a) {
return StrictMath.acos(a); // default impl. delegates to StrictMath
}
/**
* Returns the arc tangent of an angle, in the range of -<i>pi</i>/2
* through <i>pi</i>/2. Special cases:
* <ul><li>If the argument is NaN, then the result is NaN.
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a the value whose arc tangent is to be returned.
* @return the arc tangent of the argument.
*/
public static double atan(double a) {
return StrictMath.atan(a); // default impl. delegates to StrictMath
}
/**
* Converts an angle measured in degrees to an approximately
* equivalent angle measured in radians. The conversion from
* degrees to radians is generally inexact.
*
* @param angdeg an angle, in degrees
* @return the measurement of the angle <code>angdeg</code>
* in radians.
* @since 1.2
*/
public static double toRadians(double angdeg) {
return angdeg / 180.0 * PI;
}
/**
* 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
* <i>not</i> expect <code>cos(toRadians(90.0))</code> to exactly
* equal <code>0.0</code>.
*
* @param angrad an angle, in radians
* @return the measurement of the angle <code>angrad</code>
* in degrees.
* @since 1.2
*/
public static double toDegrees(double angrad) {
return angrad * 180.0 / PI;
}
/**
* Returns Euler's number <i>e</i> raised to the power of a
* <code>double</code> value. Special cases:
* <ul><li>If the argument is NaN, the result is NaN.
* <li>If the argument is positive infinity, then the result is
* positive infinity.
* <li>If the argument is negative infinity, then the result is
* positive zero.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a the exponent to raise <i>e</i> to.
* @return the value <i>e</i><sup><code>a</code></sup>,
* where <i>e</i> is the base of the natural logarithms.
*/
public static double exp(double a) {
return StrictMath.exp(a); // default impl. delegates to StrictMath
}
/**
* Returns the natural logarithm (base <i>e</i>) of a <code>double</code>
* value. Special cases:
* <ul><li>If the argument is NaN or less than zero, then the result
* is NaN.
* <li>If the argument is positive infinity, then the result is
* positive infinity.
* <li>If the argument is positive zero or negative zero, then the
* result is negative infinity.</ul>
* <p>
* A result must be within 1 ulp of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param a a number greater than <code>0.0</code>.
* @return the value ln <code>a</code>, the natural logarithm of
* <code>a</code>.
*/
public static double log(double a) {
return StrictMath.log(a); // default impl. delegates to StrictMath
}
/**
* Returns the correctly rounded positive square root of a
* <code>double</code> value.
* Special cases:
* <ul><li>If the argument is NaN or less than zero, then the result
* is NaN.
* <li>If the argument is positive infinity, then the result is positive
* infinity.
* <li>If the argument is positive zero or negative zero, then the
* result is the same as the argument.</ul>
* Otherwise, the result is the <code>double</code> value closest to
* the true mathematical square root of the argument value.
*
* @param a a value.
* <!--@return the value of √ <code>a</code>.-->
* @return the positive square root of <code>a</code>.
* If the argument is NaN or less than zero, the result is NaN.
*/
public static double sqrt(double a) {
return StrictMath.sqrt(a); // default impl. delegates to StrictMath
// Note that hardware sqrt instructions
// frequently can be directly used by JITs
// and should be much faster than doing
// Math.sqrt in software.
}
/**
* Computes the remainder operation on two arguments as prescribed
* by the IEEE 754 standard.
* The remainder value is mathematically equal to
* <code>f1 - f2</code> × <i>n</i>,
* where <i>n</i> is the mathematical integer closest to the exact
* mathematical value of the quotient <code>f1/f2</code>, and if two
* mathematical integers are equally close to <code>f1/f2</code>,
* then <i>n</i> 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:
* <ul><li>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.
* <li>If the first argument is finite and the second argument is
* infinite, then the result is the same as the first argument.</ul>
*
* @param f1 the dividend.
* @param f2 the divisor.
* @return the remainder when <code>f1</code> is divided by
* <code>f2</code>.
*/
public static double IEEEremainder(double f1, double f2) {
return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
}
/**
* Returns the smallest (closest to negative infinity)
* <code>double</code> value that is not less than the argument and is
* equal to a mathematical integer. Special cases:
* <ul><li>If the argument value is already equal to a mathematical
* integer, then the result is the same as the argument.
* <li>If the argument is NaN or an infinity or positive zero or negative
* zero, then the result is the same as the argument.
* <li>If the argument value is less than zero but greater than -1.0,
* then the result is negative zero.</ul>
* Note that the value of <code>Math.ceil(x)</code> is exactly the
* value of <code>-Math.floor(-x)</code>.
*
* @param a a value.
* <!--@return the value ⌈ <code>a</code> ⌉.-->
* @return the smallest (closest to negative infinity)
* floating-point value that is not less than the argument
* and is equal to a mathematical integer.
*/
public static double ceil(double a) {
return StrictMath.ceil(a); // default impl. delegates to StrictMath
}
/**
* Returns the largest (closest to positive infinity)
* <code>double</code> value that is not greater than the argument and
* is equal to a mathematical integer. Special cases:
* <ul><li>If the argument value is already equal to a mathematical
* integer, then the result is the same as the argument.
* <li>If the argument is NaN or an infinity or positive zero or
* negative zero, then the result is the same as the argument.</ul>
*
* @param a a value.
* <!--@return the value ⌊ <code>a</code> ⌋.-->
* @return the largest (closest to positive infinity)
* floating-point value that is not greater than the argument
* and is equal to a mathematical integer.
*/
public static double floor(double a) {
return StrictMath.floor(a); // default impl. delegates to StrictMath
}
/**
* Returns the <code>double</code> value that is closest in value
* to the argument and is equal to a mathematical integer. If two
* <code>double</code> values that are mathematical integers are
* equally close, the result is the integer value that is
* even. Special cases:
* <ul><li>If the argument value is already equal to a mathematical
* integer, then the result is the same as the argument.
* <li>If the argument is NaN or an infinity or positive zero or negative
* zero, then the result is the same as the argument.</ul>
*
* @param a a <code>double</code> value.
* @return the closest floating-point value to <code>a</code> that is
* equal to a mathematical integer.
*/
public static double rint(double a) {
return StrictMath.rint(a); // default impl. delegates to StrictMath
}
/**
* Converts rectangular coordinates (<code>x</code>, <code>y</code>)
* to polar (r, <i>theta</i>).
* This method computes the phase <i>theta</i> by computing an arc tangent
* of <code>y/x</code> in the range of -<i>pi</i> to <i>pi</i>. Special
* cases:
* <ul><li>If either argument is NaN, then the result is NaN.
* <li>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.
* <li>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.
* <li>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
* <code>double</code> value closest to <i>pi</i>.
* <li>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
* <code>double</code> value closest to -<i>pi</i>.
* <li>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
* <code>double</code> value closest to <i>pi</i>/2.
* <li>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
* <code>double</code> value closest to -<i>pi</i>/2.
* <li>If both arguments are positive infinity, then the result is the
* <code>double</code> value closest to <i>pi</i>/4.
* <li>If the first argument is positive infinity and the second argument
* is negative infinity, then the result is the <code>double</code>
* value closest to 3*<i>pi</i>/4.
* <li>If the first argument is negative infinity and the second argument
* is positive infinity, then the result is the <code>double</code> value
* closest to -<i>pi</i>/4.
* <li>If both arguments are negative infinity, then the result is the
* <code>double</code> value closest to -3*<i>pi</i>/4.</ul>
* <p>
* A result must be within 2 ulps of the correctly rounded result. Results
* must be semi-monotonic.
*
* @param y the ordinate coordinate
* @param x the abscissa coordinate
* @return the <i>theta</i> component of the point
* (<i>r</i>, <i>theta</i>)
* in polar coordinates that corresponds to the point
* (<i>x</i>, <i>y</i>) in Cartesian coordinates.
*/
public static double atan2(double y, double x) {
return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
}
/**
* Returns the value of the first argument raised to the power of the
* second argument. Special cases:
*
* <ul><li>If the second argument is positive or negative zero, then the
* result is 1.0.
* <li>If the second argument is 1.0, then the result is the same as the
* first argument.
* <li>If the second argument is NaN, then the result is NaN.
* <li>If the first argument is NaN and the second argument is nonzero,
* then the result is NaN.
*
* <li>If
* <ul>
* <li>the absolute value of the first argument is greater than 1
* and the second argument is positive infinity, or
* <li>the absolute value of the first argument is less than 1 and
* the second argument is negative infinity,
* </ul>
* then the result is positive infinity.
*
* <li>If
* <ul>
* <li>the absolute value of the first argument is greater than 1 and
* the second argument is negative infinity, or
* <li>the absolute value of the
* first argument is less than 1 and the second argument is positive
* infinity,
* </ul>
* then the result is positive zero.
*
* <li>If the absolute value of the first argument equals 1 and the
* second argument is infinite, then the result is NaN.
*
* <li>If
* <ul>
* <li>the first argument is positive zero and the second argument
* is greater than zero, or
* <li>the first argument is positive infinity and the second
* argument is less than zero,
* </ul>
* then the result is positive zero.
*
* <li>If
* <ul>
* <li>the first argument is positive zero and the second argument
* is less than zero, or
* <li>the first argument is positive infinity and the second
* argument is greater than zero,
* </ul>
* then the result is positive infinity.
*
* <li>If
* <ul>
* <li>the first argument is negative zero and the second argument
* is greater than zero but not a finite odd integer, or
* <li>the first argument is negative infinity and the second
* argument is less than zero but not a finite odd integer,
* </ul>
* then the result is positive zero.
*
* <li>If
* <ul>
* <li>the first argument is negative zero and the second argument
* is a positive finite odd integer, or
* <li>the first argument is negative infinity and the second
* argument is a negative finite odd integer,
* </ul>
* then the result is negative zero.
*
* <li>If
* <ul>
* <li>the first argument is negative zero and the second argument
* is less than zero but not a finite odd integer, or
* <li>the first argument is negative infinity and the second
* argument is greater than zero but not a finite odd integer,
* </ul>
* then the result is positive infinity.
*
* <li>If
* <ul>
* <li>the first argument is negative zero and the second argument
* is a negative finite odd integer, or
* <li>the first argument is negative infinity and the second
* argument is a positive finite odd integer,
* </ul>
* then the result is negative infinity.
*
* <li>If the first argument is finite and less than zero
* <ul>
* <li> 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
*
* <li>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
*
* <li>if the second argument is finite and not an integer, then
* the result is NaN.
* </ul>
*
* <li>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 <code>double</code> value.</ul>
*
* <p>(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 {@link #ceil <tt>ceil</tt>} or,
* equivalently, a fixed point of the method {@link #floor
* <tt>floor</tt>}. 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.)
*
* <p>A result must be within 1 ulp of the correctly rounded
* result. Results must be semi-monotonic.
*
* @param a the base.
* @param b the exponent.
* @return the value <code>a<sup>b</sup></code>.
*/
public static double pow(double a, double b) {
return StrictMath.pow(a, b); // default impl. delegates to StrictMath
}
/**
* Returns the closest <code>int</code> 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 <code>int</code>.
* In other words, the result is equal to the value of the expression:
* <p><pre>(int)Math.floor(a + 0.5f)</pre>
* <p>
* Special cases:
* <ul><li>If the argument is NaN, the result is 0.
* <li>If the argument is negative infinity or any value less than or
* equal to the value of <code>Integer.MIN_VALUE</code>, the result is
* equal to the value of <code>Integer.MIN_VALUE</code>.
* <li>If the argument is positive infinity or any value greater than or
* equal to the value of <code>Integer.MAX_VALUE</code>, the result is
* equal to the value of <code>Integer.MAX_VALUE</code>.</ul>
*
* @param a a floating-point value to be rounded to an integer.
* @return the value of the argument rounded to the nearest
* <code>int</code> value.
* @see java.lang.Integer#MAX_VALUE
* @see java.lang.Integer#MIN_VALUE
*/
public static int round(float a) {
return (int)floor(a + 0.5f);
}
/**
* Returns the closest <code>long</code> 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 <code>long</code>. In other
* words, the result is equal to the value of the expression:
* <p><pre>(long)Math.floor(a + 0.5d)</pre>
* <p>
* Special cases:
* <ul><li>If the argument is NaN, the result is 0.
* <li>If the argument is negative infinity or any value less than or
* equal to the value of <code>Long.MIN_VALUE</code>, the result is
* equal to the value of <code>Long.MIN_VALUE</code>.
* <li>If the argument is positive infinity or any value greater than or
* equal to the value of <code>Long.MAX_VALUE</code>, the result is
* equal to the value of <code>Long.MAX_VALUE</code>.</ul>
*
* @param a a floating-point value to be rounded to a
* <code>long</code>.
* @return the value of the argument rounded to the nearest
* <code>long</code> value.
* @see java.lang.Long#MAX_VALUE
* @see java.lang.Long#MIN_VALUE
*/
public static long round(double a) {
return (long)floor(a + 0.5d);
}
private static Random randomNumberGenerator;
private static synchronized void initRNG() {
if (randomNumberGenerator == null)
randomNumberGenerator = new Random();
}
/**
* Returns a <code>double</code> value with a positive sign, greater
* than or equal to <code>0.0</code> and less than <code>1.0</code>.
* Returned values are chosen pseudorandomly with (approximately)
* uniform distribution from that range.
* <p>
* When this method is first called, it creates a single new
* pseudorandom-number generator, exactly as if by the expression
* <blockquote><pre>new java.util.Random</pre></blockquote>
* This new pseudorandom-number generator is used thereafter for all
* calls to this method and is used nowhere else.
* <p>
* 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.
*
* @return a pseudorandom <code>double</code> greater than or equal
* to <code>0.0</code> and less than <code>1.0</code>.
* @see java.util.Random#nextDouble()
*/
public static double random() {
if (randomNumberGenerator == null) initRNG();
return randomNumberGenerator.nextDouble();
}
/**
* Returns the absolute value of an <code>int</code> value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
* <p>
* Note that if the argument is equal to the value of
* <code>Integer.MIN_VALUE</code>, the most negative representable
* <code>int</code> value, the result is that same value, which is
* negative.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
* @see java.lang.Integer#MIN_VALUE
*/
public static int abs(int a) {
return (a < 0) ? -a : a;
}
/**
* Returns the absolute value of a <code>long</code> value.
* If the argument is not negative, the argument is returned.
* If the argument is negative, the negation of the argument is returned.
* <p>
* Note that if the argument is equal to the value of
* <code>Long.MIN_VALUE</code>, the most negative representable
* <code>long</code> value, the result is that same value, which is
* negative.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
* @see java.lang.Long#MIN_VALUE
*/
public static long abs(long a) {
return (a < 0) ? -a : a;
}
/**
* Returns the absolute value of a <code>float</code> 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:
* <ul><li>If the argument is positive zero or negative zero, the
* result is positive zero.
* <li>If the argument is infinite, the result is positive infinity.
* <li>If the argument is NaN, the result is NaN.</ul>
* In other words, the result is the same as the value of the expression:
* <p><pre>Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))</pre>
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static float abs(float a) {
return (a <= 0.0F) ? 0.0F - a : a;
}
/**
* Returns the absolute value of a <code>double</code> 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:
* <ul><li>If the argument is positive zero or negative zero, the result
* is positive zero.
* <li>If the argument is infinite, the result is positive infinity.
* <li>If the argument is NaN, the result is NaN.</ul>
* In other words, the result is the same as the value of the expression:
* <p><code>Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)</code>
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument.
*/
public static double abs(double a) {
return (a <= 0.0D) ? 0.0D - a : a;
}
/**
* Returns the greater of two <code>int</code> values. That is, the
* result is the argument closer to the value of
* <code>Integer.MAX_VALUE</code>. If the arguments have the same value,
* the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the larger of <code>a</code> and <code>b</code>.
* @see java.lang.Long#MAX_VALUE
*/
public static int max(int a, int b) {
return (a >= b) ? a : b;
}
/**
* Returns the greater of two <code>long</code> values. That is, the
* result is the argument closer to the value of
* <code>Long.MAX_VALUE</code>. If the arguments have the same value,
* the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the larger of <code>a</code> and <code>b</code>.
* @see java.lang.Long#MAX_VALUE
*/
public static long max(long a, long b) {
return (a >= b) ? a : b;
}
private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
/**
* Returns the greater of two <code>float</code> 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 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.
*
* @param a an argument.
* @param b another argument.
* @return the larger of <code>a</code> and <code>b</code>.
*/
public static float max(float a, float b) {
if (a != a) return a; // a is NaN
if ((a == 0.0f) && (b == 0.0f)
&& (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
return b;
}
return (a >= b) ? a : b;
}
/**
* Returns the greater of two <code>double</code> 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 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.
*
* @param a an argument.
* @param b another argument.
* @return the larger of <code>a</code> and <code>b</code>.
*/
public static double max(double a, double b) {
if (a != a) return a; // a is NaN
if ((a == 0.0d) && (b == 0.0d)
&& (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
return b;
}
return (a >= b) ? a : b;
}
/**
* Returns the smaller of two <code>int</code> values. That is,
* the result the argument closer to the value of
* <code>Integer.MIN_VALUE</code>. If the arguments have the same
* value, the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of <code>a</code> and <code>b</code>.
* @see java.lang.Long#MIN_VALUE
*/
public static int min(int a, int b) {
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two <code>long</code> values. That is,
* the result is the argument closer to the value of
* <code>Long.MIN_VALUE</code>. If the arguments have the same
* value, the result is that same value.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of <code>a</code> and <code>b</code>.
* @see java.lang.Long#MIN_VALUE
*/
public static long min(long a, long b) {
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two <code>float</code> 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 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.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of <code>a</code> and <code>b.</code>
*/
public static float min(float a, float b) {
if (a != a) return a; // a is NaN
if ((a == 0.0f) && (b == 0.0f)
&& (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
return b;
}
return (a <= b) ? a : b;
}
/**
* Returns the smaller of two <code>double</code> 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 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.
*
* @param a an argument.
* @param b another argument.
* @return the smaller of <code>a</code> and <code>b</code>.
*/
public static double min(double a, double b) {
if (a != a) return a; // a is NaN
if ((a == 0.0d) && (b == 0.0d)
&& (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
return b;
}
return (a <= b) ? a : b;
}
}