/*
* @(#)Math.java 1.72 05/11/17
*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* SUN PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
*/
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 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 <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 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 <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
* @author Joseph D. Darcy
* @version 1.72, 11/17/05
* @since JDK1.0
*/
public final 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>The computed result must be within 1 ulp of the exact 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>The computed result must be within 1 ulp of the exact 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>The computed result must be within 1 ulp of the exact 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 a value; the returned angle is in the
* range -<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>The computed result must be within 1 ulp of the exact 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 a value; the returned angle is in the
* range 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>The computed result must be within 1 ulp of the exact 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 a value; the returned angle is in the
* range -<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>The computed result must be within 1 ulp of the exact 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>The computed result must be within 1 ulp of the exact 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>The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a a value
* @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 base 10 logarithm 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.
* <li> If the argument is equal to 10<sup><i>n</i></sup> for
* integer <i>n</i>, then the result is <i>n</i>.
* </ul>
*
* <p>The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param a a value
* @return the base 10 logarithm of <code>a</code>.
* @since 1.5
*/
public static double log10(double a) {
return StrictMath.log10(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 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.
}
/**
* Returns the cube root of a <code>double</code> value. For
* positive finite <code>x</code>, <code>cbrt(-x) ==
* -cbrt(x)</code>; that is, the cube root of a negative value is
* the negative of the cube root of that value's magnitude.
*
* Special cases:
*
* <ul>
*
* <li>If the argument is NaN, then the result is NaN.
*
* <li>If the argument is infinite, then the result is an infinity
* with the same sign as the argument.
*
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* </ul>
*
* <p>The computed result must be within 1 ulp of the exact result.
*
* @param a a value.
* @return the cube root of <code>a</code>.
* @since 1.5
*/
public static double cbrt(double a) {
return StrictMath.cbrt(a);
}
/**
* 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 greater than or equal to 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 smallest (closest to negative infinity)
* floating-point value that is greater than or equal to
* 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 less than or equal to 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 largest (closest to positive infinity)
* floating-point value that less than or equal to 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
}
/**
* Returns the angle <i>theta</i> from the conversion of rectangular
* coordinates (<code>x</code>, <code>y</code>) to polar
* coordinates (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>The computed result must be within 2 ulps of the exact 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>The computed result must be within 1 ulp of the exact 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 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 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 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 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;
}
/**
* Returns the size of an ulp of the argument. An ulp of a
* <code>double</code> value is the positive distance between this
* floating-point value and the <code>double</code> value next
* larger in magnitude. Note that for non-NaN <i>x</i>,
* <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, then the result is NaN.
* <li> If the argument is positive or negative infinity, then the
* result is positive infinity.
* <li> If the argument is positive or negative zero, then the result is
* <code>Double.MIN_VALUE</code>.
* <li> If the argument is ±<code>Double.MAX_VALUE</code>, then
* the result is equal to 2<sup>971</sup>.
* </ul>
*
* @param d the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static double ulp(double d) {
return sun.misc.FpUtils.ulp(d);
}
/**
* Returns the size of an ulp of the argument. An ulp of a
* <code>float</code> value is the positive distance between this
* floating-point value and the <code>float</code> value next
* larger in magnitude. Note that for non-NaN <i>x</i>,
* <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, then the result is NaN.
* <li> If the argument is positive or negative infinity, then the
* result is positive infinity.
* <li> If the argument is positive or negative zero, then the result is
* <code>Float.MIN_VALUE</code>.
* <li> If the argument is ±<code>Float.MAX_VALUE</code>, then
* the result is equal to 2<sup>104</sup>.
* </ul>
*
* @param f the floating-point value whose ulp is to be returned
* @return the size of an ulp of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static float ulp(float f) {
return sun.misc.FpUtils.ulp(f);
}
/**
* 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.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, then the result is NaN.
* <li> If the argument is positive zero or negative zero, then the
* result is the same as the argument.
* </ul>
*
* @param d the floating-point value whose signum is to be returned
* @return the signum function of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static double signum(double d) {
return sun.misc.FpUtils.signum(d);
}
/**
* 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.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, then the result is NaN.
* <li> If the argument is positive zero or negative zero, then the
* result is the same as the argument.
* </ul>
*
* @param f the floating-point value whose signum is to be returned
* @return the signum function of the argument
* @author Joseph D. Darcy
* @since 1.5
*/
public static float signum(float f) {
return sun.misc.FpUtils.signum(f);
}
/**
* Returns the hyperbolic sine of a <code>double</code> value.
* The hyperbolic sine of <i>x</i> is defined to be
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
* where <i>e</i> is {@linkplain Math#E Euler's number}.
*
* <p>Special cases:
* <ul>
*
* <li>If the argument is NaN, then the result is NaN.
*
* <li>If the argument is infinite, then the result is an infinity
* with the same sign as the argument.
*
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* </ul>
*
* <p>The computed result must be within 2.5 ulps of the exact result.
*
* @param x The number whose hyperbolic sine is to be returned.
* @return The hyperbolic sine of <code>x</code>.
* @since 1.5
*/
public static double sinh(double x) {
return StrictMath.sinh(x);
}
/**
* Returns the hyperbolic cosine of a <code>double</code> value.
* The hyperbolic cosine of <i>x</i> is defined to be
* (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
* where <i>e</i> is {@linkplain Math#E Euler's number}.
*
* <p>Special cases:
* <ul>
*
* <li>If the argument is NaN, then the result is NaN.
*
* <li>If the argument is infinite, then the result is positive
* infinity.
*
* <li>If the argument is zero, then the result is <code>1.0</code>.
*
* </ul>
*
* <p>The computed result must be within 2.5 ulps of the exact result.
*
* @param x The number whose hyperbolic cosine is to be returned.
* @return The hyperbolic cosine of <code>x</code>.
* @since 1.5
*/
public static double cosh(double x) {
return StrictMath.cosh(x);
}
/**
* Returns the hyperbolic tangent of a <code>double</code> value.
* The hyperbolic tangent of <i>x</i> is defined to be
* (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
* in other words, {@linkplain Math#sinh
* sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
* that the absolute value of the exact tanh is always less than
* 1.
*
* <p>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.
*
* <li>If the argument is positive infinity, then the result is
* <code>+1.0</code>.
*
* <li>If the argument is negative infinity, then the result is
* <code>-1.0</code>.
*
* </ul>
*
* <p>The computed result must be within 2.5 ulps of the exact result.
* The result of <code>tanh</code> 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 ±<code>1.0</code> should
* be returned.
*
* @param x The number whose hyperbolic tangent is to be returned.
* @return The hyperbolic tangent of <code>x</code>.
* @since 1.5
*/
public static double tanh(double x) {
return StrictMath.tanh(x);
}
/**
* Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* without intermediate overflow or underflow.
*
* <p>Special cases:
* <ul>
*
* <li> If either argument is infinite, then the result
* is positive infinity.
*
* <li> If either argument is NaN and neither argument is infinite,
* then the result is NaN.
*
* </ul>
*
* <p>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.
*
* @param x a value
* @param y a value
* @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
* without intermediate overflow or underflow
* @since 1.5
*/
public static double hypot(double x, double y) {
return StrictMath.hypot(x, y);
}
/**
* Returns <i>e</i><sup>x</sup> -1. Note that for values of
* <i>x</i> near 0, the exact sum of
* <code>expm1(x)</code> + 1 is much closer to the true
* result of <i>e</i><sup>x</sup> than <code>exp(x)</code>.
*
* <p>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
* -1.0.
*
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* </ul>
*
* <p>The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic. The result of
* <code>expm1</code> for any finite input must be greater than or
* equal to <code>-1.0</code>. Note that once the exact result of
* <i>e</i><sup><code>x</code></sup> - 1 is within 1/2
* ulp of the limit value -1, <code>-1.0</code> should be
* returned.
*
* @param x the exponent to raise <i>e</i> to in the computation of
* <i>e</i><sup><code>x</code></sup> -1.
* @return the value <i>e</i><sup><code>x</code></sup> - 1.
* @since 1.5
*/
public static double expm1(double x) {
return StrictMath.expm1(x);
}
/**
* Returns the natural logarithm of the sum of the argument and 1.
* Note that for small values <code>x</code>, the result of
* <code>log1p(x)</code> is much closer to the true result of ln(1
* + <code>x</code>) than the floating-point evaluation of
* <code>log(1.0+x)</code>.
*
* <p>Special cases:
*
* <ul>
*
* <li>If the argument is NaN or less than -1, then the result is
* NaN.
*
* <li>If the argument is positive infinity, then the result is
* positive infinity.
*
* <li>If the argument is negative one, then the result is
* negative infinity.
*
* <li>If the argument is zero, then the result is a zero with the
* same sign as the argument.
*
* </ul>
*
* <p>The computed result must be within 1 ulp of the exact result.
* Results must be semi-monotonic.
*
* @param x a value
* @return the value ln(<code>x</code> + 1), the natural
* log of <code>x</code> + 1
* @since 1.5
*/
public static double log1p(double x) {
return StrictMath.log1p(x);
}
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. Note that unlike the {@link
* StrictMath#copySign(double, double) StrictMath.copySign}
* method, this method does not require NaN <code>sign</code>
* 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.
*
* @param magnitude the parameter providing the magnitude of the result
* @param sign the parameter providing the sign of the result
* @return a value with the magnitude of <code>magnitude</code>
* and the sign of <code>sign</code>.
* @since 1.6
*/
public static double copySign(double magnitude, double sign) {
return sun.misc.FpUtils.rawCopySign(magnitude, sign);
}
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. Note that unlike the {@link
* StrictMath#copySign(float, float) StrictMath.copySign}
* method, this method does not require NaN <code>sign</code>
* 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.
*
* @param magnitude the parameter providing the magnitude of the result
* @param sign the parameter providing the sign of the result
* @return a value with the magnitude of <code>magnitude</code>
* and the sign of <code>sign</code>.
* @since 1.6
*/
public static float copySign(float magnitude, float sign) {
return sun.misc.FpUtils.rawCopySign(magnitude, sign);
}
/**
* Returns the unbiased exponent used in the representation of a
* {@code float}. Special cases:
*
* <ul>
* <li>If the argument is NaN or infinite, then the result is
* {@link Float#MAX_EXPONENT} + 1.
* <li>If the argument is zero or subnormal, then the result is
* {@link Float#MIN_EXPONENT} -1.
* </ul>
* @param f a {@code float} value
* @return the unbiased exponent of the argument
* @since 1.6
*/
public static int getExponent(float f) {
return sun.misc.FpUtils.getExponent(f);
}
/**
* Returns the unbiased exponent used in the representation of a
* {@code double}. Special cases:
*
* <ul>
* <li>If the argument is NaN or infinite, then the result is
* {@link Double#MAX_EXPONENT} + 1.
* <li>If the argument is zero or subnormal, then the result is
* {@link Double#MIN_EXPONENT} -1.
* </ul>
* @param d a {@code double} value
* @return the unbiased exponent of the argument
* @since 1.6
*/
public static int getExponent(double d) {
return sun.misc.FpUtils.getExponent(d);
}
/**
* 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.
*
* <p>
* Special cases:
* <ul>
* <li> If either argument is a NaN, then NaN is returned.
*
* <li> If both arguments are signed zeros, {@code direction}
* is returned unchanged (as implied by the requirement of
* returning the second argument if the arguments compare as
* equal).
*
* <li> If {@code start} is
* ±{@link Double#MIN_VALUE} and {@code direction}
* has a value such that the result should have a smaller
* magnitude, then a zero with the same sign as {@code start}
* is returned.
*
* <li> If {@code start} is infinite and
* {@code direction} has a value such that the result should
* have a smaller magnitude, {@link Double#MAX_VALUE} with the
* same sign as {@code start} is returned.
*
* <li> If {@code start} is equal to ±
* {@link Double#MAX_VALUE} and {@code direction} has a
* value such that the result should have a larger magnitude, an
* infinity with same sign as {@code start} is returned.
* </ul>
*
* @param start starting floating-point value
* @param direction value indicating which of
* {@code start}'s neighbors or {@code start} should
* be returned
* @return The floating-point number adjacent to {@code start} in the
* direction of {@code direction}.
* @since 1.6
*/
public static double nextAfter(double start, double direction) {
return sun.misc.FpUtils.nextAfter(start, direction);
}
/**
* 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.
*
* <p>
* Special cases:
* <ul>
* <li> If either argument is a NaN, then NaN is returned.
*
* <li> If both arguments are signed zeros, a value equivalent
* to {@code direction} is returned.
*
* <li> If {@code start} is
* ±{@link Float#MIN_VALUE} and {@code direction}
* has a value such that the result should have a smaller
* magnitude, then a zero with the same sign as {@code start}
* is returned.
*
* <li> If {@code start} is infinite and
* {@code direction} has a value such that the result should
* have a smaller magnitude, {@link Float#MAX_VALUE} with the
* same sign as {@code start} is returned.
*
* <li> If {@code start} is equal to ±
* {@link Float#MAX_VALUE} and {@code direction} has a
* value such that the result should have a larger magnitude, an
* infinity with same sign as {@code start} is returned.
* </ul>
*
* @param start starting floating-point value
* @param direction value indicating which of
* {@code start}'s neighbors or {@code start} should
* be returned
* @return The floating-point number adjacent to {@code start} in the
* direction of {@code direction}.
* @since 1.6
*/
public static float nextAfter(float start, double direction) {
return sun.misc.FpUtils.nextAfter(start, direction);
}
/**
* Returns the floating-point value adjacent to {@code d} in
* the direction of positive infinity. This method is
* semantically equivalent to {@code nextAfter(d,
* Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
* implementation may run faster than its equivalent
* {@code nextAfter} call.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, the result is NaN.
*
* <li> If the argument is positive infinity, the result is
* positive infinity.
*
* <li> If the argument is zero, the result is
* {@link Double#MIN_VALUE}
*
* </ul>
*
* @param d starting floating-point value
* @return The adjacent floating-point value closer to positive
* infinity.
* @since 1.6
*/
public static double nextUp(double d) {
return sun.misc.FpUtils.nextUp(d);
}
/**
* Returns the floating-point value adjacent to {@code f} in
* the direction of positive infinity. This method is
* semantically equivalent to {@code nextAfter(f,
* Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
* implementation may run faster than its equivalent
* {@code nextAfter} call.
*
* <p>Special Cases:
* <ul>
* <li> If the argument is NaN, the result is NaN.
*
* <li> If the argument is positive infinity, the result is
* positive infinity.
*
* <li> If the argument is zero, the result is
* {@link Float#MIN_VALUE}
*
* </ul>
*
* @param f starting floating-point value
* @return The adjacent floating-point value closer to positive
* infinity.
* @since 1.6
*/
public static float nextUp(float f) {
return sun.misc.FpUtils.nextUp(f);
}
/**
* Return {@code d} ×
* 2<sup>{@code scaleFactor}</sup> 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 {@link
* Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
* answer is calculated exactly. If the exponent of the result
* would be larger than {@code Double.MAX_EXPONENT}, an
* infinity is returned. Note that if the result is subnormal,
* precision may be lost; that is, when {@code scalb(x, n)}
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
* <i>x</i>. When the result is non-NaN, the result has the same
* sign as {@code d}.
*
*<p>
* Special cases:
* <ul>
* <li> If the first argument is NaN, NaN is returned.
* <li> If the first argument is infinite, then an infinity of the
* same sign is returned.
* <li> If the first argument is zero, then a zero of the same
* sign is returned.
* </ul>
*
* @param d number to be scaled by a power of two.
* @param scaleFactor power of 2 used to scale {@code d}
* @return {@code d} × 2<sup>{@code scaleFactor}</sup>
* @since 1.6
*/
public static double scalb(double d, int scaleFactor) {
return sun.misc.FpUtils.scalb(d, scaleFactor);
}
/**
* Return {@code f} ×
* 2<sup>{@code scaleFactor}</sup> 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 {@link
* Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
* answer is calculated exactly. If the exponent of the result
* would be larger than {@code Float.MAX_EXPONENT}, an
* infinity is returned. Note that if the result is subnormal,
* precision may be lost; that is, when {@code scalb(x, n)}
* is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
* <i>x</i>. When the result is non-NaN, the result has the same
* sign as {@code f}.
*
*<p>
* Special cases:
* <ul>
* <li> If the first argument is NaN, NaN is returned.
* <li> If the first argument is infinite, then an infinity of the
* same sign is returned.
* <li> If the first argument is zero, then a zero of the same
* sign is returned.
* </ul>
*
* @param f number to be scaled by a power of two.
* @param scaleFactor power of 2 used to scale {@code f}
* @return {@code f} × 2<sup>{@code scaleFactor}</sup>
* @since 1.6
*/
public static float scalb(float f, int scaleFactor) {
return sun.misc.FpUtils.scalb(f, scaleFactor);
}
}
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