`/*`

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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.

*

* This code 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.

Oracle designates this

* particular file as subject to the "Classpath" exception as provided

* by Oracle in the LICENSE file that accompanied this code.

*

* This code 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

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* 2 along with this work; if not, write to the Free Software Foundation,

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package java.lang;

import java.util.Random;

import sun.misc.FloatConsts;

import sun.misc.DoubleConsts;

/**

* The class {@code Math} 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}, all implementations of the equivalent

* functions of class {@code Math} 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} methods simply call

* the equivalent method in {@code 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

* {@code Math} methods.

Such higher-performance

* implementations still must conform to the specification for

* {@code Math}.

*

* <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} methods is

* measured in terms of <i>ulps</i>, units in the last place.

For a

* given floating-point format, an {@linkplain #ulp(double) 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} 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.

*

* <p>

* The platform uses signed two's complement integer arithmetic with

* int and long primitive types.

The developer should choose

* the primitive type to ensure that arithmetic operations consistently

* produce correct results, which in some cases means the operations

* will not overflow the range of values of the computation.

* The best practice is to choose the primitive type and algorithm to avoid

* overflow. In cases where the size is {@code int} or {@code long} and

* overflow errors need to be detected, the methods {@code addExact},

* {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}

* throw an {@code ArithmeticException} when the results overflow.

* For other arithmetic operations such as divide, absolute value,

* increment, decrement, and negation overflow occurs only with

* a specific minimum or maximum value and should be checked against

* the minimum or maximum as appropriate.

*

* @author

unascribed

* @author

Joseph D. Darcy

* @since

JDK1.0

*/

public final class Math {

/**

* Don't let anyone instantiate this class.

*/

private Math() {}

/**

* The {@code double} 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} 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

aan 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

aan 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

aan 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

athe 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

athe 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

athe 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

angdegan angle, in degrees

* @return

the measurement of the angle {@code angdeg}

*

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))} to exactly

* equal {@code 0.0}.

*

* @param

angradan angle, in radians

* @return

the measurement of the angle {@code angrad}

*

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} 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

athe exponent to raise <i>e</i> to.

* @return

the value <i>e</i><sup>{@code a}</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}

* 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

aa value

* @return

the value ln {@code a}, the natural logarithm of

*

{@code a}.

*/

public static double log(double a) {

return StrictMath.log(a); // default impl. delegates to StrictMath

}

/**

* Returns the base 10 logarithm of a {@code double} 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

aa value

* @return

the base 10 logarithm of{@code a}.

* @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} 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} value closest to

* the true mathematical square root of the argument value.

*

* @param

aa value.

* @return

the positive square root of {@code a}.

*

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} value.

For

* positive finite {@code x}, {@code 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:

*

* <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

aa value.

* @return

the cube root of {@code a}.

* @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}, and if two

* mathematical integers are equally close to {@code f1/f2},

* 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

f1the dividend.

* @param

f2the divisor.

* @return

the remainder when {@code f1} is divided by

*

{@code f2}.

*/

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} 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)} is exactly the

* value of {@code -Math.floor(-x)}.

*

*

* @param

aa 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} 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

aa 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} value that is closest in value

* to the argument and is equal to a mathematical integer. If two

* {@code double} 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

aa {@code double} value.

* @return

the closest floating-point value to {@code a} 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 y}) to polar

* coordinates (r, <i>theta</i>).

* This method computes the phase <i>theta</i> by computing an arc tangent

* of {@code y/x} 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} 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} 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} 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} value closest to -<i>pi</i>/2.

* <li>If both arguments are positive infinity, then the result is the

* {@code double} 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}

* 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} value

* closest to -<i>pi</i>/4.

* <li>If both arguments are negative infinity, then the result is the

* {@code double} 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

ythe ordinate coordinate

* @param

xthe 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} 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 ceil} or,

* equivalently, a fixed point of the method {@link #floor

* 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.)

*

* <p>The computed result must be within 1 ulp of the exact result.

* Results must be semi-monotonic.

*

* @param

athe base.

* @param

bthe exponent.

* @return

the value {@code a}<sup>{@code b}</sup>.

*/

public static double pow(double a, double b) {

return StrictMath.pow(a, b); // default impl. delegates to StrictMath

}

/**

* Returns the closest {@code int} to the argument, with ties

* rounding to positive infinity.

*

* <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}, the result is

* equal to the value of {@code Integer.MIN_VALUE}.

* <li>If the argument is positive infinity or any value greater than or

* equal to the value of {@code Integer.MAX_VALUE}, the result is

* equal to the value of {@code Integer.MAX_VALUE}.</ul>

*

* @param

aa floating-point value to be rounded to an integer.

* @return

the value of the argument rounded to the nearest

*

{@code int} value.

* @seejava.lang.Integer#MAX_VALUE

* @seejava.lang.Integer#MIN_VALUE

*/

public static int round(float a) {

int intBits = Float.floatToRawIntBits(a);

int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)

>> (FloatConsts.SIGNIFICAND_WIDTH - 1);

int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2

+ FloatConsts.EXP_BIAS) - biasedExp;

if ((shift & -32) == 0) { // shift >= 0 && shift < 32

// a is a finite number such that pow(2,-32) <= ulp(a) < 1

int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)

| (FloatConsts.SIGNIF_BIT_MASK + 1));

if (intBits < 0) {

r = -r;

}

// In the comments below each Java expression evaluates to the value

// the corresponding mathematical expression:

// (r) evaluates to a / ulp(a)

// (r >> shift) evaluates to floor(a * 2)

// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)

// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)

return ((r >> shift) + 1) >> 1;

} else {

// a is either

// - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2

// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer

// - an infinity or NaN

return (int) a;

}

}

/**

* Returns the closest {@code long} to the argument, with ties

* rounding to positive infinity.

*

* <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}, the result is

* equal to the value of {@code Long.MIN_VALUE}.

* <li>If the argument is positive infinity or any value greater than or

* equal to the value of {@code Long.MAX_VALUE}, the result is

* equal to the value of {@code Long.MAX_VALUE}.</ul>

*

* @param

aa floating-point value to be rounded to a

*

{@code long}.

* @return

the value of the argument rounded to the nearest

*

{@code long} value.

* @seejava.lang.Long#MAX_VALUE

* @seejava.lang.Long#MIN_VALUE

*/

public static long round(double a) {

long longBits = Double.doubleToRawLongBits(a);

long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)

>> (DoubleConsts.SIGNIFICAND_WIDTH - 1);

long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2

+ DoubleConsts.EXP_BIAS) - biasedExp;

if ((shift & -64) == 0) { // shift >= 0 && shift < 64

// a is a finite number such that pow(2,-64) <= ulp(a) < 1

long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)

| (DoubleConsts.SIGNIF_BIT_MASK + 1));

if (longBits < 0) {

r = -r;

}

// In the comments below each Java expression evaluates to the value

// the corresponding mathematical expression:

// (r) evaluates to a / ulp(a)

// (r >> shift) evaluates to floor(a * 2)

// ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)

// (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)

return ((r >> shift) + 1) >> 1;

} else {

// a is either

// - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2

// - a finite number with ulp(a) >= 1 and hence a is a mathematical integer

// - an infinity or NaN

return (long) a;

}

}

private static final class RandomNumberGeneratorHolder {

static final Random randomNumberGenerator = new Random();

}

/**

* Returns a {@code double} value with a positive sign, greater

* than or equal to {@code 0.0} and less than {@code 1.0}.

* 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>{@code new java.util.Random()}</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} greater than or equal

* to {@code 0.0} and less than {@code 1.0}.

* @see Random#nextDouble()

*/

public static double random() {

return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();

}

/**

* Returns the sum of its arguments,

* throwing an exception if the result overflows an {@code int}.

*

* @param x the first value

* @param y the second value

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int addExact(int x, int y) {

int r = x + y;

// HD 2-12 Overflow iff both arguments have the opposite sign of the result

if (((x ^ r) & (y ^ r)) < 0) {

throw new ArithmeticException("integer overflow");

}

return r;

}

/**

* Returns the sum of its arguments,

* throwing an exception if the result overflows a {@code long}.

*

* @param x the first value

* @param y the second value

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long addExact(long x, long y) {

long r = x + y;

// HD 2-12 Overflow iff both arguments have the opposite sign of the result

if (((x ^ r) & (y ^ r)) < 0) {

throw new ArithmeticException("long overflow");

}

return r;

}

/**

* Returns the difference of the arguments,

* throwing an exception if the result overflows an {@code int}.

*

* @param x the first value

* @param y the second value to subtract from the first

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int subtractExact(int x, int y) {

int r = x - y;

// HD 2-12 Overflow iff the arguments have different signs and

// the sign of the result is different than the sign of x

if (((x ^ y) & (x ^ r)) < 0) {

throw new ArithmeticException("integer overflow");

}

return r;

}

/**

* Returns the difference of the arguments,

* throwing an exception if the result overflows a {@code long}.

*

* @param x the first value

* @param y the second value to subtract from the first

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long subtractExact(long x, long y) {

long r = x - y;

// HD 2-12 Overflow iff the arguments have different signs and

// the sign of the result is different than the sign of x

if (((x ^ y) & (x ^ r)) < 0) {

throw new ArithmeticException("long overflow");

}

return r;

}

/**

* Returns the product of the arguments,

* throwing an exception if the result overflows an {@code int}.

*

* @param x the first value

* @param y the second value

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int multiplyExact(int x, int y) {

long r = (long)x * (long)y;

if ((int)r != r) {

throw new ArithmeticException("integer overflow");

}

return (int)r;

}

/**

* Returns the product of the arguments,

* throwing an exception if the result overflows a {@code long}.

*

* @param x the first value

* @param y the second value

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long multiplyExact(long x, long y) {

long r = x * y;

long ax = Math.abs(x);

long ay = Math.abs(y);

if (((ax | ay) >>> 31 != 0)) {

// Some bits greater than 2^31 that might cause overflow

// Check the result using the divide operator

// and check for the special case of Long.MIN_VALUE * -1

if (((y != 0) && (r / y != x)) ||

(x == Long.MIN_VALUE && y == -1)) {

throw new ArithmeticException("long overflow");

}

}

return r;

}

/**

* Returns the argument incremented by one, throwing an exception if the

* result overflows an {@code int}.

*

* @param a the value to increment

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int incrementExact(int a) {

if (a == Integer.MAX_VALUE) {

throw new ArithmeticException("integer overflow");

}

return a + 1;

}

/**

* Returns the argument incremented by one, throwing an exception if the

* result overflows a {@code long}.

*

* @param a the value to increment

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long incrementExact(long a) {

if (a == Long.MAX_VALUE) {

throw new ArithmeticException("long overflow");

}

return a + 1L;

}

/**

* Returns the argument decremented by one, throwing an exception if the

* result overflows an {@code int}.

*

* @param a the value to decrement

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int decrementExact(int a) {

if (a == Integer.MIN_VALUE) {

throw new ArithmeticException("integer overflow");

}

return a - 1;

}

/**

* Returns the argument decremented by one, throwing an exception if the

* result overflows a {@code long}.

*

* @param a the value to decrement

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long decrementExact(long a) {

if (a == Long.MIN_VALUE) {

throw new ArithmeticException("long overflow");

}

return a - 1L;

}

/**

* Returns the negation of the argument, throwing an exception if the

* result overflows an {@code int}.

*

* @param a the value to negate

* @return the result

* @throws ArithmeticException if the result overflows an int

* @since 1.8

*/

public static int negateExact(int a) {

if (a == Integer.MIN_VALUE) {

throw new ArithmeticException("integer overflow");

}

return -a;

}

/**

* Returns the negation of the argument, throwing an exception if the

* result overflows a {@code long}.

*

* @param a the value to negate

* @return the result

* @throws ArithmeticException if the result overflows a long

* @since 1.8

*/

public static long negateExact(long a) {

if (a == Long.MIN_VALUE) {

throw new ArithmeticException("long overflow");

}

return -a;

}

/**

* Returns the value of the {@code long} argument;

* throwing an exception if the value overflows an {@code int}.

*

* @param value the long value

* @return the argument as an int

* @throws ArithmeticException if the {@code argument} overflows an int

* @since 1.8

*/

public static int toIntExact(long value) {

if ((int)value != value) {

throw new ArithmeticException("integer overflow");

}

return (int)value;

}

/**

* Returns the largest (closest to positive infinity)

* {@code int} value that is less than or equal to the algebraic quotient.

* There is one special case, if the dividend is the

* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},

* then integer overflow occurs and

* the result is equal to the {@code Integer.MIN_VALUE}.

* <p>

* Normal integer division operates under the round to zero rounding mode

* (truncation).

This operation instead acts under the round toward

* negative infinity (floor) rounding mode.

* The floor rounding mode gives different results than truncation

* when the exact result is negative.

* <ul>

*

<li>If the signs of the arguments are the same, the results of

*

{@code floorDiv} and the {@code /} operator are the same.

<br>

*

For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>

*

<li>If the signs of the arguments are different,

the quotient is negative and

*

{@code floorDiv} returns the integer less than or equal to the quotient

*

and the {@code /} operator returns the integer closest to zero.<br>

*

For example, {@code floorDiv(-4, 3) == -2},

*

whereas {@code (-4 / 3) == -1}.

*

</li>

* </ul>

* <p>

*

* @param x the dividend

* @param y the divisor

* @return the largest (closest to positive infinity)

* {@code int} value that is less than or equal to the algebraic quotient.

* @throws ArithmeticException if the divisor {@code y} is zero

* @see #floorMod(int, int)

* @see #floor(double)

* @since 1.8

*/

public static int floorDiv(int x, int y) {

int r = x / y;

// if the signs are different and modulo not zero, round down

if ((x ^ y) < 0 && (r * y != x)) {

r--;

}

return r;

}

/**

* Returns the largest (closest to positive infinity)

* {@code long} value that is less than or equal to the algebraic quotient.

* There is one special case, if the dividend is the

* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},

* then integer overflow occurs and

* the result is equal to the {@code Long.MIN_VALUE}.

* <p>

* Normal integer division operates under the round to zero rounding mode

* (truncation).

This operation instead acts under the round toward

* negative infinity (floor) rounding mode.

* The floor rounding mode gives different results than truncation

* when the exact result is negative.

* <p>

* For examples, see {@link #floorDiv(int, int)}.

*

* @param x the dividend

* @param y the divisor

* @return the largest (closest to positive infinity)

* {@code long} value that is less than or equal to the algebraic quotient.

* @throws ArithmeticException if the divisor {@code y} is zero

* @see #floorMod(long, long)

* @see #floor(double)

* @since 1.8

*/

public static long floorDiv(long x, long y) {

long r = x / y;

// if the signs are different and modulo not zero, round down

if ((x ^ y) < 0 && (r * y != x)) {

r--;

}

return r;

}

/**

* Returns the floor modulus of the {@code int} arguments.

* <p>

* The floor modulus is {@code x - (floorDiv(x, y) * y)},

* has the same sign as the divisor {@code y}, and

* is in the range of {@code -abs(y) < r < +abs(y)}.

*

* <p>

* The relationship between {@code floorDiv} and {@code floorMod} is such that:

* <ul>

*

<li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}

* </ul>

* <p>

* The difference in values between {@code floorMod} and

* the {@code %} operator is due to the difference between

* {@code floorDiv} that returns the integer less than or equal to the quotient

* and the {@code /} operator that returns the integer closest to zero.

* <p>

* Examples:

* <ul>

*

<li>If the signs of the arguments are the same, the results

*

of {@code floorMod} and the {@code %} operator are the same.

<br>

*

<ul>

*

<li>{@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}</li>

*

</ul>

*

<li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br>

*

<ul>

*

<li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1} </li>

*

<li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1} </li>

*

<li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 } </li>

*

</ul>

*

</li>

* </ul>

* <p>

* If the signs of arguments are unknown and a positive modulus

* is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.

*

* @param x the dividend

* @param y the divisor

* @return the floor modulus {@code x - (floorDiv(x, y) * y)}

* @throws ArithmeticException if the divisor {@code y} is zero

* @see #floorDiv(int, int)

* @since 1.8

*/

public static int floorMod(int x, int y) {

int r = x - floorDiv(x, y) * y;

return r;

}

/**

* Returns the floor modulus of the {@code long} arguments.

* <p>

* The floor modulus is {@code x - (floorDiv(x, y) * y)},

* has the same sign as the divisor {@code y}, and

* is in the range of {@code -abs(y) < r < +abs(y)}.

*

* <p>

* The relationship between {@code floorDiv} and {@code floorMod} is such that:

* <ul>

*

<li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}

* </ul>

* <p>

* For examples, see {@link #floorMod(int, int)}.

*

* @param x the dividend

* @param y the divisor

* @return the floor modulus {@code x - (floorDiv(x, y) * y)}

* @throws ArithmeticException if the divisor {@code y} is zero

* @see #floorDiv(long, long)

* @since 1.8

*/

public static long floorMod(long x, long y) {

return x - floorDiv(x, y) * y;

}

/**

* Returns the absolute value of an {@code int} 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

* {@link Integer#MIN_VALUE}, the most negative representable

* {@code int} value, the result is that same value, which is

* negative.

*

* @param

athe argument whose absolute value is to be determined

* @return

the absolute value of the argument.

*/

public static int abs(int a) {

return (a < 0) ? -a : a;

}

/**

* Returns the absolute value of a {@code long} 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

* {@link Long#MIN_VALUE}, the most negative representable

* {@code long} value, the result is that same value, which

* is negative.

*

* @param

athe argument whose absolute value is to be determined

* @return

the absolute value of the argument.

*/

public static long abs(long a) {

return (a < 0) ? -a : a;

}

/**

* Returns the absolute value of a {@code 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:

* <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 Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}

*

* @param

athe 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} 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)}

*

* @param

athe 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} values. That is, the

* result is the argument closer to the value of

* {@link Integer#MAX_VALUE}. If the arguments have the same value,

* the result is that same value.

*

* @param

aan argument.

* @param

banother argument.

* @return

the larger of {@code a} and {@code b}.

*/

public static int max(int a, int b) {

return (a >= b) ? a : b;

}

/**

* Returns the greater of two {@code long} values. That is, the

* result is the argument closer to the value of

* {@link Long#MAX_VALUE}. If the arguments have the same value,

* the result is that same value.

*

* @param

aan argument.

* @param

banother argument.

* @return

the larger of {@code a} and {@code b}.

*/

public static long max(long a, long b) {

return (a >= b) ? a : b;

}

// Use raw bit-wise conversions on guaranteed non-NaN arguments.

private static long negativeZeroFloatBits

= Float.floatToRawIntBits(-0.0f);

private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);

/**

* Returns the greater of two {@code 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.

*

* @param

aan argument.

* @param

banother argument.

* @return

the larger of {@code a} and {@code b}.

*/

public static float max(float a, float b) {

if (a != a)

return a;

// a is NaN

if ((a == 0.0f) &&

(b == 0.0f) &&

(Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {

// Raw conversion ok since NaN can't map to -0.0.

return b;

}

return (a >= b) ? a : b;

}

/**

* Returns the greater of two {@code 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.

*

* @param

aan argument.

* @param

banother argument.

* @return

the larger of {@code a} and {@code b}.

*/

public static double max(double a, double b) {

if (a != a)

return a;

// a is NaN

if ((a == 0.0d) &&

(b == 0.0d) &&

(Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {

// Raw conversion ok since NaN can't map to -0.0.

return b;

}

return (a >= b) ? a : b;

}

/**

* Returns the smaller of two {@code int} values. That is,

* the result the argument closer to the value of

* {@link Integer#MIN_VALUE}.

If the arguments have the same

* value, the result is that same value.

*

* @param

aan argument.

* @param

banother argument.

* @return

the smaller of {@code a} and {@code b}.

*/

public static int min(int a, int b) {

return (a <= b) ? a : b;

}

/**

* Returns the smaller of two {@code long} values. That is,

* the result is the argument closer to the value of

* {@link Long#MIN_VALUE}. If the arguments have the same

* value, the result is that same value.

*

* @param

aan argument.

* @param

banother argument.

* @return

the smaller of {@code a} and {@code b}.

*/

public static long min(long a, long b) {

return (a <= b) ? a : b;

}

/**

* Returns the smaller of two {@code 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.

*

* @param

aan argument.

* @param

banother argument.

* @return

the smaller of {@code a} and {@code b}.

*/

public static float min(float a, float b) {

if (a != a)

return a;

// a is NaN

if ((a == 0.0f) &&

(b == 0.0f) &&

(Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {

// Raw conversion ok since NaN can't map to -0.0.

return b;

}

return (a <= b) ? a : b;

}

/**

* Returns the smaller of two {@code 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.

*

* @param

aan argument.

* @param

banother argument.

* @return

the smaller of {@code a} and {@code b}.

*/

public static double min(double a, double b) {

if (a != a)

return a;

// a is NaN

if ((a == 0.0d) &&

(b == 0.0d) &&

(Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {

// Raw conversion ok since NaN can't map to -0.0.

return b;

}

return (a <= b) ? a : b;

}

/**

* Returns the size of an ulp of the argument.

An ulp, unit in

* the last place, of a {@code double} value is the positive

* distance between this floating-point value and the {@code

* double} 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}.

* <li> If the argument is ±{@code Double.MAX_VALUE}, 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) {

int exp = getExponent(d);

switch(exp) {

case DoubleConsts.MAX_EXPONENT+1:

// NaN or infinity

return Math.abs(d);

case DoubleConsts.MIN_EXPONENT-1:

// zero or subnormal

return Double.MIN_VALUE;

default:

assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT;

// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))

exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);

if (exp >= DoubleConsts.MIN_EXPONENT) {

return powerOfTwoD(exp);

}

else {

// return a subnormal result; left shift integer

// representation of Double.MIN_VALUE appropriate

// number of positions

return Double.longBitsToDouble(1L <<

(exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));

}

}

}

/**

* Returns the size of an ulp of the argument.

An ulp, unit in

* the last place, of a {@code float} value is the positive

* distance between this floating-point value and the {@code

* float} 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}.

* <li> If the argument is ±{@code Float.MAX_VALUE}, 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) {

int exp = getExponent(f);

switch(exp) {

case FloatConsts.MAX_EXPONENT+1:

// NaN or infinity

return Math.abs(f);

case FloatConsts.MIN_EXPONENT-1:

// zero or subnormal

return FloatConsts.MIN_VALUE;

default:

assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT;

// ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))

exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);

if (exp >= FloatConsts.MIN_EXPONENT) {

return powerOfTwoF(exp);

}

else {

// return a subnormal result; left shift integer

// representation of FloatConsts.MIN_VALUE appropriate

// number of positions

return Float.intBitsToFloat(1 <<

(exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));

}

}

}

/**

* 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 (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, 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 (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);

}

/**

* Returns the hyperbolic sine of a {@code double} 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}.

* @since 1.5

*/

public static double sinh(double x) {

return StrictMath.sinh(x);

}

/**

* Returns the hyperbolic cosine of a {@code double} 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}.

*

* </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}.

* @since 1.5

*/

public static double cosh(double x) {

return StrictMath.cosh(x);

}

/**

* Returns the hyperbolic tangent of a {@code double} 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}.

*

* <li>If the argument is negative infinity, then the result is

* {@code -1.0}.

*

* </ul>

*

* <p>The computed result must be within 2.5 ulps of the exact result.

* The result of {@code 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 ±{@code 1.0} should

* be returned.

*

* @param

x The number whose hyperbolic tangent is to be returned.

* @return

The hyperbolic tangent of {@code x}.

* @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)} + 1 is much closer to the true

* result of <i>e</i><sup>x</sup> than {@code exp(x)}.

*

* <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} for any finite input must be greater than or

* equal to {@code -1.0}.

Note that once the exact result of

* <i>e</i><sup>{@code x}</sup> - 1 is within 1/2

* ulp of the limit value -1, {@code -1.0} should be

* returned.

*

* @param

xthe exponent to raise <i>e</i> to in the computation of

*

<i>e</i><sup>{@code x}</sup> -1.

* @return

the value <i>e</i><sup>{@code x}</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}, the result of

* {@code log1p(x)} is much closer to the true result of ln(1

* + {@code x}) than the floating-point evaluation of

* {@code log(1.0+x)}.

*

* <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

xa value

* @return the value ln({@code x} + 1), the natural

* log of {@code x} + 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}

* 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}

* and the sign of {@code sign}.

* @since 1.6

*/

public static double copySign(double magnitude, double sign) {

return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &

(DoubleConsts.SIGN_BIT_MASK)) |

(Double.doubleToRawLongBits(magnitude) &

(DoubleConsts.EXP_BIT_MASK |

DoubleConsts.SIGNIF_BIT_MASK)));

}

/**

* 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}

* 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}

* and the sign of {@code sign}.

* @since 1.6

*/

public static float copySign(float magnitude, float sign) {

return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &

(FloatConsts.SIGN_BIT_MASK)) |

(Float.floatToRawIntBits(magnitude) &

(FloatConsts.EXP_BIT_MASK |

FloatConsts.SIGNIF_BIT_MASK)));

}

/**

* 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) {

/*

* Bitwise convert f to integer, mask out exponent bits, shift

* to the right and then subtract out float's bias adjust to

* get true exponent value

*/

return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>

(FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;

}

/**

* 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) {

/*

* Bitwise convert d to long, mask out exponent bits, shift

* to the right and then subtract out double's bias adjust to

* get true exponent value.

*/

return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>

(DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);

}

/**

* 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) {

/*

* The cases:

*

* nextAfter(+infinity, 0)

== MAX_VALUE

* nextAfter(+infinity, +infinity)

== +infinity

* nextAfter(-infinity, 0)

== -MAX_VALUE

* nextAfter(-infinity, -infinity)

== -infinity

*

* are naturally handled without any additional testing

*/

// First check for NaN values

if (Double.isNaN(start) || Double.isNaN(direction)) {

// return a NaN derived from the input NaN(s)

return start + direction;

} else if (start == direction) {

return direction;

} else {

// start > direction or start < direction

// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)

// then bitwise convert start to integer.

long transducer = Double.doubleToRawLongBits(start + 0.0d);

/*

* IEEE 754 floating-point numbers are lexicographically

* ordered if treated as signed- magnitude integers .

* Since Java's integers are two's complement,

* incrementing" the two's complement representation of a

* logically negative floating-point value *decrements*

* the signed-magnitude representation. Therefore, when

* the integer representation of a floating-point values

* is less than zero, the adjustment to the representation

* is in the opposite direction than would be expected at

* first .

*/

if (direction > start) { // Calculate next greater value

transducer = transducer + (transducer >= 0L ? 1L:-1L);

} else

{ // Calculate next lesser value

assert direction < start;

if (transducer > 0L)

--transducer;

else

if (transducer < 0L )

++transducer;

/*

* transducer==0, the result is -MIN_VALUE

*

* The transition from zero (implicitly

* positive) to the smallest negative

* signed magnitude value must be done

* explicitly.

*/

else

transducer = DoubleConsts.SIGN_BIT_MASK | 1L;

}

return Double.longBitsToDouble(transducer);

}

}

/**

* 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) {

/*

* The cases:

*

* nextAfter(+infinity, 0)

== MAX_VALUE

* nextAfter(+infinity, +infinity)

== +infinity

* nextAfter(-infinity, 0)

== -MAX_VALUE

* nextAfter(-infinity, -infinity)

== -infinity

*

* are naturally handled without any additional testing

*/

// First check for NaN values

if (Float.isNaN(start) || Double.isNaN(direction)) {

// return a NaN derived from the input NaN(s)

return start + (float)direction;

} else if (start == direction) {

return (float)direction;

} else {

// start > direction or start < direction

// Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)

// then bitwise convert start to integer.

int transducer = Float.floatToRawIntBits(start + 0.0f);

/*

* IEEE 754 floating-point numbers are lexicographically

* ordered if treated as signed- magnitude integers .

* Since Java's integers are two's complement,

* incrementing" the two's complement representation of a

* logically negative floating-point value *decrements*

* the signed-magnitude representation. Therefore, when

* the integer representation of a floating-point values

* is less than zero, the adjustment to the representation

* is in the opposite direction than would be expected at

* first.

*/

if (direction > start) {// Calculate next greater value

transducer = transducer + (transducer >= 0 ? 1:-1);

} else

{ // Calculate next lesser value

assert direction < start;

if (transducer > 0)

--transducer;

else

if (transducer < 0 )

++transducer;

/*

* transducer==0, the result is -MIN_VALUE

*

* The transition from zero (implicitly

* positive) to the smallest negative

* signed magnitude value must be done

* explicitly.

*/

else

transducer = FloatConsts.SIGN_BIT_MASK | 1;

}

return Float.intBitsToFloat(transducer);

}

}

/**

* 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) {

if( Double.isNaN(d) || d == Double.POSITIVE_INFINITY)

return d;

else {

d += 0.0d;

return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +

((d >= 0.0d)?+1L:-1L));

}

}

/**

* 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) {

if( Float.isNaN(f) || f == FloatConsts.POSITIVE_INFINITY)

return f;

else {

f += 0.0f;

return Float.intBitsToFloat(Float.floatToRawIntBits(f) +

((f >= 0.0f)?+1:-1));

}

}

/**

* Returns the floating-point value adjacent to {@code d} in

* the direction of negative infinity.

This method is

* semantically equivalent to {@code nextAfter(d,

* Double.NEGATIVE_INFINITY)}; however, a

* {@code nextDown} 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 negative infinity, the result is

* negative infinity.

*

* <li> If the argument is zero, the result is

* {@code -Double.MIN_VALUE}

*

* </ul>

*

* @param d

starting floating-point value

* @return The adjacent floating-point value closer to negative

* infinity.

* @since 1.8

*/

public static double nextDown(double d) {

if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)

return d;

else {

if (d == 0.0)

return -Double.MIN_VALUE;

else

return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +

((d > 0.0d)?-1L:+1L));

}

}

/**

* Returns the floating-point value adjacent to {@code f} in

* the direction of negative infinity.

This method is

* semantically equivalent to {@code nextAfter(f,

* Float.NEGATIVE_INFINITY)}; however, a

* {@code nextDown} 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 negative infinity, the result is

* negative infinity.

*

* <li> If the argument is zero, the result is

* {@code -Float.MIN_VALUE}

*

* </ul>

*

* @param f

starting floating-point value

* @return The adjacent floating-point value closer to negative

* infinity.

* @since 1.8

*/

public static float nextDown(float f) {

if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)

return f;

else {

if (f == 0.0f)

return -Float.MIN_VALUE;

else

return Float.intBitsToFloat(Float.floatToRawIntBits(f) +

((f > 0.0f)?-1:+1));

}

}

/**

* Returns {@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) {

/*

* This method does not need to be declared strictfp to

* compute the same correct result on all platforms.

When

* scaling up, it does not matter what order the

* multiply-store operations are done; the result will be

* finite or overflow regardless of the operation ordering.

* However, to get the correct result when scaling down, a

* particular ordering must be used.

*

* When scaling down, the multiply-store operations are

* sequenced so that it is not possible for two consecutive

* multiply-stores to return subnormal results.

If one

* multiply-store result is subnormal, the next multiply will

* round it away to zero.

This is done by first multiplying

* by 2 ^ (scaleFactor % n) and then multiplying several

* times by by 2^n as needed where n is the exponent of number

* that is a covenient power of two.

In this way, at most one

* real rounding error occurs.

If the double value set is

* being used exclusively, the rounding will occur on a

* multiply.

If the double-extended-exponent value set is

* being used, the products will (perhaps) be exact but the

* stores to d are guaranteed to round to the double value

* set.

*

* It is _not_ a valid implementation to first multiply d by

* 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %

* MIN_EXPONENT) since even in a strictfp program double

* rounding on underflow could occur; e.g. if the scaleFactor

* argument was (MIN_EXPONENT - n) and the exponent of d was a

* little less than -(MIN_EXPONENT - n), meaning the final

* result would be subnormal.

*

* Since exact reproducibility of this method can be achieved

* without any undue performance burden, there is no

* compelling reason to allow double rounding on underflow in

* scalb.

*/

// magnitude of a power of two so large that scaling a finite

// nonzero value by it would be guaranteed to over or

// underflow; due to rounding, scaling down takes takes an

// additional power of two which is reflected here

final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT +

DoubleConsts.SIGNIFICAND_WIDTH + 1;

int exp_adjust = 0;

int scale_increment = 0;

double exp_delta = Double.NaN;

// Make sure scaling factor is in a reasonable range

if(scaleFactor < 0) {

scaleFactor = Math.max(scaleFactor, -MAX_SCALE);

scale_increment = -512;

exp_delta = twoToTheDoubleScaleDown;

}

else {

scaleFactor = Math.min(scaleFactor, MAX_SCALE);

scale_increment = 512;

exp_delta = twoToTheDoubleScaleUp;

}

// Calculate (scaleFactor % +/-512), 512 = 2^9, using

// technique from "Hacker's Delight" section 10-2.

int t = (scaleFactor >> 9-1) >>> 32 - 9;

exp_adjust = ((scaleFactor + t) & (512 -1)) - t;

d *= powerOfTwoD(exp_adjust);

scaleFactor -= exp_adjust;

while(scaleFactor != 0) {

d *= exp_delta;

scaleFactor -= scale_increment;

}

return d;

}

/**

* Returns {@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) {

// magnitude of a power of two so large that scaling a finite

// nonzero value by it would be guaranteed to over or

// underflow; due to rounding, scaling down takes takes an

// additional power of two which is reflected here

final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT +

FloatConsts.SIGNIFICAND_WIDTH + 1;

// Make sure scaling factor is in a reasonable range

scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);

/*

* Since + MAX_SCALE for float fits well within the double

* exponent range and + float -> double conversion is exact

* the multiplication below will be exact. Therefore, the

* rounding that occurs when the double product is cast to

* float will be the correctly rounded float result.

Since

* all operations other than the final multiply will be exact,

* it is not necessary to declare this method strictfp.

*/

return (float)((double)f*powerOfTwoD(scaleFactor));

}

// Constants used in scalb

static double twoToTheDoubleScaleUp = powerOfTwoD(512);

static double twoToTheDoubleScaleDown = powerOfTwoD(-512);

/**

* Returns a floating-point power of two in the normal range.

*/

static double powerOfTwoD(int n) {

assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT);

return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<

(DoubleConsts.SIGNIFICAND_WIDTH-1))

& DoubleConsts.EXP_BIT_MASK);

}

/**

* Returns a floating-point power of two in the normal range.

*/

static float powerOfTwoF(int n) {

assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT);

return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<

(FloatConsts.SIGNIFICAND_WIDTH-1))

& FloatConsts.EXP_BIT_MASK);

}

}