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package java.lang;
import java.util.Random;
import jdk.internal.math.DoubleConsts;
import jdk.internal.vm.annotation.IntrinsicCandidate;
/**
* The class {@code StrictMath} contains methods for performing basic
* numeric operations such as the elementary exponential, logarithm,
* square root, and trigonometric functions.
*
* <p>To help ensure portability of Java programs, the definitions of
* some of the numeric functions in this package require that they
* produce the same results as certain published algorithms. These
* algorithms are available from the well-known network library
* {@code netlib} as the package "Freely Distributable Math
* Library," <a
* href="https://www.netlib.org/fdlibm/">{@code fdlibm}</a>. These
* algorithms, which are written in the C programming language, are
* then to be understood to be transliterated into Java and executed
* with all floating-point and integer operations following the rules
* of Java arithmetic. The following transformations are used in the
* transliteration:
*
* <ul>
* <li>Extraction and setting of the high and low halves of a 64-bit
* {@code double} in C is expressed using Java platform methods that
* perform bit-wise conversions {@linkplain
* Double#doubleToRawLongBits(double) from {@code double} to {@code
* long}} and {@linkplain Double#longBitsToDouble(long) {@code long}
* to {@code double}}.
*
* <li>Unsigned {@code int} values in C are mapped to signed {@code
* int} values in Java with updates to operations to replicate
* unsigned semantics where the results on the same textual operation
* would differ. For example, {@code >>} shifts on unsigned C values
* are replaced with {@code >>>} shifts on signed Java values. Sized
* comparisons on unsigned C values ({@code <}, {@code <=}, {@code >},
* {@code >=}) are replaced with semantically equivalent calls to
* {@link Integer#compareUnsigned(int, int) compareUnsigned}.
* </ul>
*
* <p>The Java math library is defined with respect to
* {@code fdlibm} version 5.3. Where {@code fdlibm} provides
* more than one definition for a function (such as
* {@code acos}), use the "IEEE 754 core function" version
* (residing in a file whose name begins with the letter
* {@code e}). The methods which require {@code fdlibm}
* semantics are {@code sin}, {@code cos}, {@code tan},
* {@code asin}, {@code acos}, {@code atan},
* {@code exp}, {@code log}, {@code log10},
* {@code cbrt}, {@code atan2}, {@code pow},
* {@code sinh}, {@code cosh}, {@code tanh},
* {@code hypot}, {@code expm1}, and {@code log1p}.
*
* <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 whose names end with
* {@code Exact} throw an {@code ArithmeticException} when the results overflow.
*
* <h2><a id=Ieee754RecommendedOps>IEEE 754 Recommended
* Operations</a></h2>
*
* The {@link java.lang.Math Math} class discusses how the shared
* quality of implementation criteria for selected {@code Math} and
* {@code StrictMath} methods <a
* href="Math.html#Ieee754RecommendedOps">relate to the IEEE 754
* recommended operations</a>.
*
* @spec https://standards.ieee.org/ieee/754/6210/
* IEEE Standard for Floating-Point Arithmetic
*
* @author Joseph D. Darcy
* @since 1.3
*/
public final class StrictMath {
/**
* Don't let anyone instantiate this class.
*/
private StrictMath() {}
/**
* 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 = 2.718281828459045;
/**
* The {@code double} value that is closer than any other to
* <i>pi</i> (&pi;), the ratio of the circumference of a circle to its
* diameter.
*/
public static final double PI = 3.141592653589793;
/**
* The {@code double} value that is closer than any other to
* <i>tau</i> (&tau;), the ratio of the circumference of a circle
* to its radius.
*
* @apiNote
* The value of <i>pi</i> is one half that of <i>tau</i>; in other
* words, <i>tau</i> is double <i>pi</i> .
*
* @since 19
*/
public static final double TAU = 2.0 * PI;
/**
* 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>
*
* @param a an angle, in radians.
* @return the sine of the argument.
*/
public static double sin(double a) {
return FdLibm.Sin.compute(a);
}
/**
* Returns the trigonometric cosine 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 {@code 1.0}.
* </ul>
*
* @param a an angle, in radians.
* @return the cosine of the argument.
*/
public static double cos(double a) {
return FdLibm.Cos.compute(a);
}
/**
* 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>
*
* @param a an angle, in radians.
* @return the tangent of the argument.
*/
public static double tan(double a) {
return FdLibm.Tan.compute(a);
}
/**
* Returns the arc sine of a value; the returned angle is in the
* range &minus;<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>
*
* @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 FdLibm.Asin.compute(a);
}
/**
* 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.
* <li>If the argument is {@code 1.0}, the result is positive zero.
* </ul>
*
* @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 FdLibm.Acos.compute(a);
}
/**
* Returns the arc tangent of a value; the returned angle is in the
* range &minus;<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.
* <li>If the argument is {@linkplain Double#isInfinite infinite},
* then the result is the closest value to <i>pi</i>/2 with the
* same sign as the input.
* </ul>
*
* @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 FdLibm.Atan.compute(a);
}
/**
* 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}
* in radians.
*/
public static double toRadians(double angdeg) {
return Math.toRadians(angdeg);
}
/**
* 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 angrad an angle, in radians
* @return the measurement of the angle {@code angrad}
* in degrees.
*/
public static double toDegrees(double angrad) {
return Math.toDegrees(angrad);
}
/**
* 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.
* <li>If the argument is zero, then the result is {@code 1.0}.
* </ul>
*
* @param a the 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 FdLibm.Exp.compute(a);
}
/**
* 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.
* <li>If the argument is {@code 1.0}, then the result is positive
* zero.
* </ul>
*
* @param a a value
* @return the value ln&nbsp;{@code a}, the natural logarithm of
* {@code a}.
*/
public static double log(double a) {
return FdLibm.Log.compute(a);
}
/**
* 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>. In particular,
* if the argument is {@code 1.0} (10<sup>0</sup>), then the
* result is positive zero.
* </ul>
*
* @param a a value
* @return the base 10 logarithm of {@code a}.
* @since 1.5
*/
public static double log10(double a) {
return FdLibm.Log10.compute(a);
}
/**
* 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 a a value.
* @return the positive square root of {@code a}.
*/
@IntrinsicCandidate
public static double sqrt(double a) {
return FdLibm.Sqrt.compute(a);
}
/**
* 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>
*
* @param a a value.
* @return the cube root of {@code a}.
* @since 1.5
*/
public static double cbrt(double a) {
return FdLibm.Cbrt.compute(a);
}
/**
* Computes the remainder operation on two arguments as prescribed
* by the IEEE 754 standard.
* The remainder value is mathematically equal to
* <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<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 f1 the dividend.
* @param f2 the divisor.
* @return the remainder when {@code f1} is divided by
* {@code f2}.
*/
public static double IEEEremainder(double f1, double f2) {
return FdLibm.IEEEremainder.compute(f1, f2);
}
/**
* 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 StrictMath.ceil(x)} is exactly the
* value of {@code -StrictMath.floor(-x)}.
*
* @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 floorOrCeil(a, -0.0, 1.0, 1.0);
}
/**
* 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 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 floorOrCeil(a, -1.0, 0.0, -1.0);
}
/**
* Internal method to share logic between floor and ceil.
*
* @param a the value to be floored or ceiled
* @param negativeBoundary result for values in (-1, 0)
* @param positiveBoundary result for values in (0, 1)
* @param sign the sign of the result
*/
private static double floorOrCeil(double a,
double negativeBoundary,
double positiveBoundary,
double sign) {
int exponent = Math.getExponent(a);
if (exponent < 0) {
/*
* Absolute value of argument is less than 1.
* floorOrCeil(-0.0) => -0.0
* floorOrCeil(+0.0) => +0.0
*/
return ((a == 0.0) ? a :
( (a < 0.0) ? negativeBoundary : positiveBoundary) );
} else if (exponent >= 52) {
/*
* Infinity, NaN, or a value so large it must be integral.
*/
return a;
}
// Else the argument is either an integral value already XOR it
// has to be rounded to one.
assert exponent >= 0 && exponent <= 51;
long doppel = Double.doubleToRawLongBits(a);
long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
if ( (mask & doppel) == 0L )
return a; // integral value
else {
double result = Double.longBitsToDouble(doppel & (~mask));
if (sign*a > 0.0)
result = result + sign;
return result;
}
}
/**
* 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 to the value of the argument, 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 value.
* @return the closest floating-point value to {@code a} that is
* equal to a mathematical integer.
* @author Joseph D. Darcy
*/
public static double rint(double a) {
/*
* If the absolute value of a is not less than 2^52, it
* is either a finite integer (the double format does not have
* enough significand bits for a number that large to have any
* fractional portion), an infinity, or a NaN. In any of
* these cases, rint of the argument is the argument.
*
* Otherwise, the sum (twoToThe52 + a ) will properly round
* away any fractional portion of a since ulp(twoToThe52) ==
* 1.0; subtracting out twoToThe52 from this sum will then be
* exact and leave the rounded integer portion of a.
*/
double twoToThe52 = (double)(1L << 52); // 2^52
double sign = Math.copySign(1.0, a); // preserve sign info
a = Math.abs(a);
if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
a = ((twoToThe52 + a ) - twoToThe52);
}
return sign * a; // restore original sign
}
/**
* Returns the angle <i>theta</i> from the conversion of rectangular
* coordinates ({@code x},&nbsp;{@code y}) to polar
* coordinates (r,&nbsp;<i>theta</i>).
* This method computes the phase <i>theta</i> by computing an arc tangent
* of {@code y/x} in the range of &minus;<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>
*
* @apiNote
* For <i>y</i> with a positive sign and finite nonzero
* <i>x</i>, the exact mathematical value of {@code atan2} is
* equal to:
* <ul>
* <li>If <i>x</i> {@literal >} 0, atan(abs(<i>y</i>/<i>x</i>))
* <li>If <i>x</i> {@literal <} 0, &pi; - atan(abs(<i>y</i>/<i>x</i>))
* </ul>
*
* @param y the ordinate coordinate
* @param x the abscissa coordinate
* @return the <i>theta</i> component of the point
* (<i>r</i>,&nbsp;<i>theta</i>)
* in polar coordinates that corresponds to the point
* (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
*/
public static double atan2(double y, double x) {
return FdLibm.Atan2.compute(y, x);
}
/**
* 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.)
*
* @apiNote
* The special cases definitions of this method differ from the
* special case definitions of the IEEE 754 recommended {@code
* pow} operation for &plusmn;{@code 1.0} raised to an infinite
* power. This method treats such cases as indeterminate and
* specifies a NaN is returned. The IEEE 754 specification treats
* the infinite power as a large integer (large-magnitude
* floating-point numbers are numerically integers, specifically
* even integers) and therefore specifies {@code 1.0} be returned.
*
* @param a base.
* @param b the exponent.
* @return the value {@code a}<sup>{@code b}</sup>.
*/
public static double pow(double a, double b) {
return FdLibm.Pow.compute(a, b);
}
/**
* 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 a a floating-point value to be rounded to an integer.
* @return the value of the argument rounded to the nearest
* {@code int} value.
* @see java.lang.Integer#MAX_VALUE
* @see java.lang.Integer#MIN_VALUE
*/
public static int round(float a) {
return Math.round(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 a a floating-point value to be rounded to a
* {@code long}.
* @return the value of the argument rounded to the nearest
* {@code long} value.
* @see java.lang.Long#MAX_VALUE
* @see java.lang.Long#MIN_VALUE
*/
public static long round(double a) {
return Math.round(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
* @see Math#addExact(int,int)
* @since 1.8
*/
public static int addExact(int x, int y) {
return Math.addExact(x, y);
}
/**
* 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
* @see Math#addExact(long,long)
* @since 1.8
*/
public static long addExact(long x, long y) {
return Math.addExact(x, y);
}
/**
* 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
* @see Math#subtractExact(int,int)
* @since 1.8
*/
public static int subtractExact(int x, int y) {
return Math.subtractExact(x, y);
}
/**
* 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
* @see Math#subtractExact(long,long)
* @since 1.8
*/
public static long subtractExact(long x, long y) {
return Math.subtractExact(x, y);
}
/**
* 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
* @see Math#multiplyExact(int,int)
* @since 1.8
*/
public static int multiplyExact(int x, int y) {
return Math.multiplyExact(x, y);
}
/**
* 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
* @see Math#multiplyExact(long,int)
* @since 9
*/
public static long multiplyExact(long x, int y) {
return Math.multiplyExact(x, y);
}
/**
* 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
* @see Math#multiplyExact(long,long)
* @since 1.8
*/
public static long multiplyExact(long x, long y) {
return Math.multiplyExact(x, y);
}
/**
* Returns the quotient of the arguments, throwing an exception if the
* result overflows an {@code int}. Such overflow occurs in this method if
* {@code x} is {@link Integer#MIN_VALUE} and {@code y} is {@code -1}.
* In contrast, if {@code Integer.MIN_VALUE / -1} were evaluated directly,
* the result would be {@code Integer.MIN_VALUE} and no exception would be
* thrown.
* <p>
* If {@code y} is zero, an {@code ArithmeticException} is thrown
* (JLS {@jls 15.17.2}).
* <p>
* The built-in remainder operator "{@code %}" is a suitable counterpart
* both for this method and for the built-in division operator "{@code /}".
*
* @param x the dividend
* @param y the divisor
* @return the quotient {@code x / y}
* @throws ArithmeticException if {@code y} is zero or the quotient
* overflows an int
* @jls 15.17.2 Division Operator /
* @see Math#divideExact(int,int)
* @since 18
*/
public static int divideExact(int x, int y) {
return Math.divideExact(x, y);
}
/**
* Returns the quotient of the arguments, throwing an exception if the
* result overflows a {@code long}. Such overflow occurs in this method if
* {@code x} is {@link Long#MIN_VALUE} and {@code y} is {@code -1}.
* In contrast, if {@code Long.MIN_VALUE / -1} were evaluated directly,
* the result would be {@code Long.MIN_VALUE} and no exception would be
* thrown.
* <p>
* If {@code y} is zero, an {@code ArithmeticException} is thrown
* (JLS {@jls 15.17.2}).
* <p>
* The built-in remainder operator "{@code %}" is a suitable counterpart
* both for this method and for the built-in division operator "{@code /}".
*
* @param x the dividend
* @param y the divisor
* @return the quotient {@code x / y}
* @throws ArithmeticException if {@code y} is zero or the quotient
* overflows a long
* @jls 15.17.2 Division Operator /
* @see Math#divideExact(long,long)
* @since 18
*/
public static long divideExact(long x, long y) {
return Math.divideExact(x, y);
}
/**
* Returns the largest (closest to positive infinity)
* {@code int} value that is less than or equal to the algebraic quotient.
* This method is identical to {@link #floorDiv(int,int)} except that it
* throws an {@code ArithmeticException} when the dividend is
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is
* {@code -1} instead of ignoring the integer overflow and returning
* {@code Integer.MIN_VALUE}.
* <p>
* The floor modulus method {@link #floorMod(int,int)} is a suitable
* counterpart both for this method and for the {@link #floorDiv(int,int)}
* method.
* <p>
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @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, or the
* dividend {@code x} is {@code Integer.MIN_VALUE} and the divisor {@code y}
* is {@code -1}.
* @see Math#floorDiv(int, int)
* @since 18
*/
public static int floorDivExact(int x, int y) {
return Math.floorDivExact(x, y);
}
/**
* Returns the largest (closest to positive infinity)
* {@code long} value that is less than or equal to the algebraic quotient.
* This method is identical to {@link #floorDiv(long,long)} except that it
* throws an {@code ArithmeticException} when the dividend is
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is
* {@code -1} instead of ignoring the integer overflow and returning
* {@code Long.MIN_VALUE}.
* <p>
* The floor modulus method {@link #floorMod(long,long)} is a suitable
* counterpart both for this method and for the {@link #floorDiv(long,long)}
* method.
* <p>
* For examples, see {@link Math#floorDiv(int, int) Math.floorDiv}.
*
* @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, or the
* dividend {@code x} is {@code Long.MIN_VALUE} and the divisor {@code y}
* is {@code -1}.
* @see Math#floorDiv(int, int)
* @see Math#floorDiv(long,long)
* @since 18
*/
public static long floorDivExact(long x, long y) {
return Math.floorDivExact(x, y);
}
/**
* Returns the smallest (closest to negative infinity)
* {@code int} value that is greater than or equal to the algebraic quotient.
* This method is identical to {@link #ceilDiv(int,int)} except that it
* throws an {@code ArithmeticException} when the dividend is
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is
* {@code -1} instead of ignoring the integer overflow and returning
* {@code Integer.MIN_VALUE}.
* <p>
* The ceil modulus method {@link #ceilMod(int,int)} is a suitable
* counterpart both for this method and for the {@link #ceilDiv(int,int)}
* method.
* <p>
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to negative infinity)
* {@code int} value that is greater than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero, or the
* dividend {@code x} is {@code Integer.MIN_VALUE} and the divisor {@code y}
* is {@code -1}.
* @see Math#ceilDiv(int, int)
* @since 18
*/
public static int ceilDivExact(int x, int y) {
return Math.ceilDivExact(x, y);
}
/**
* Returns the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* This method is identical to {@link #ceilDiv(long,long)} except that it
* throws an {@code ArithmeticException} when the dividend is
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is
* {@code -1} instead of ignoring the integer overflow and returning
* {@code Long.MIN_VALUE}.
* <p>
* The ceil modulus method {@link #ceilMod(long,long)} is a suitable
* counterpart both for this method and for the {@link #ceilDiv(long,long)}
* method.
* <p>
* For examples, see {@link Math#ceilDiv(int, int) Math.ceilDiv}.
*
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero, or the
* dividend {@code x} is {@code Long.MIN_VALUE} and the divisor {@code y}
* is {@code -1}.
* @see Math#ceilDiv(int, int)
* @see Math#ceilDiv(long,long)
* @since 18
*/
public static long ceilDivExact(long x, long y) {
return Math.ceilDivExact(x, y);
}
/**
* Returns the argument incremented by one,
* throwing an exception if the result overflows an {@code int}.
* The overflow only occurs for {@linkplain Integer#MAX_VALUE the maximum value}.
*
* @param a the value to increment
* @return the result
* @throws ArithmeticException if the result overflows an int
* @see Math#incrementExact(int)
* @since 14
*/
public static int incrementExact(int a) {
return Math.incrementExact(a);
}
/**
* Returns the argument incremented by one,
* throwing an exception if the result overflows a {@code long}.
* The overflow only occurs for {@linkplain Long#MAX_VALUE the maximum value}.
*
* @param a the value to increment
* @return the result
* @throws ArithmeticException if the result overflows a long
* @see Math#incrementExact(long)
* @since 14
*/
public static long incrementExact(long a) {
return Math.incrementExact(a);
}
/**
* Returns the argument decremented by one,
* throwing an exception if the result overflows an {@code int}.
* The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
*
* @param a the value to decrement
* @return the result
* @throws ArithmeticException if the result overflows an int
* @see Math#decrementExact(int)
* @since 14
*/
public static int decrementExact(int a) {
return Math.decrementExact(a);
}
/**
* Returns the argument decremented by one,
* throwing an exception if the result overflows a {@code long}.
* The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
*
* @param a the value to decrement
* @return the result
* @throws ArithmeticException if the result overflows a long
* @see Math#decrementExact(long)
* @since 14
*/
public static long decrementExact(long a) {
return Math.decrementExact(a);
}
/**
* Returns the negation of the argument,
* throwing an exception if the result overflows an {@code int}.
* The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
*
* @param a the value to negate
* @return the result
* @throws ArithmeticException if the result overflows an int
* @see Math#negateExact(int)
* @since 14
*/
public static int negateExact(int a) {
return Math.negateExact(a);
}
/**
* Returns the negation of the argument,
* throwing an exception if the result overflows a {@code long}.
* The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
*
* @param a the value to negate
* @return the result
* @throws ArithmeticException if the result overflows a long
* @see Math#negateExact(long)
* @since 14
*/
public static long negateExact(long a) {
return Math.negateExact(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
* @see Math#toIntExact(long)
* @since 1.8
*/
public static int toIntExact(long value) {
return Math.toIntExact(value);
}
/**
* Returns the exact mathematical product of the arguments.
*
* @param x the first value
* @param y the second value
* @return the result
* @see Math#multiplyFull(int,int)
* @since 9
*/
public static long multiplyFull(int x, int y) {
return Math.multiplyFull(x, y);
}
/**
* Returns as a {@code long} the most significant 64 bits of the 128-bit
* product of two 64-bit factors.
*
* @param x the first value
* @param y the second value
* @return the result
* @see #unsignedMultiplyHigh
* @see Math#multiplyHigh(long,long)
* @since 9
*/
public static long multiplyHigh(long x, long y) {
return Math.multiplyHigh(x, y);
}
/**
* Returns as a {@code long} the most significant 64 bits of the unsigned
* 128-bit product of two unsigned 64-bit factors.
*
* @param x the first value
* @param y the second value
* @return the result
* @see #multiplyHigh
* @see Math#unsignedMultiplyHigh(long,long)
* @since 18
*/
public static long unsignedMultiplyHigh(long x, long y) {
return Math.unsignedMultiplyHigh(x, y);
}
/**
* 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
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Integer.MIN_VALUE}.
* <p>
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @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 Math#floorDiv(int, int)
* @see Math#floor(double)
* @since 1.8
*/
public static int floorDiv(int x, int y) {
return Math.floorDiv(x, y);
}
/**
* 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
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Long.MIN_VALUE}.
* <p>
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @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 Math#floorDiv(long, int)
* @see Math#floor(double)
* @since 9
*/
public static long floorDiv(long x, int y) {
return Math.floorDiv(x, y);
}
/**
* 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
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Long.MIN_VALUE}.
* <p>
* See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @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 Math#floorDiv(long, long)
* @see Math#floor(double)
* @since 1.8
*/
public static long floorDiv(long x, long y) {
return Math.floorDiv(x, y);
}
/**
* Returns the floor modulus of the {@code int} arguments.
* <p>
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
* has the same sign as the divisor {@code y} or is zero, 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}</li>
* </ul>
* <p>
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
* a comparison to the {@code %} operator.
*
* @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 Math#floorMod(int, int)
* @see StrictMath#floorDiv(int, int)
* @since 1.8
*/
public static int floorMod(int x, int y) {
return Math.floorMod(x , y);
}
/**
* Returns the floor modulus of the {@code long} and {@code int} arguments.
* <p>
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
* has the same sign as the divisor {@code y} or is zero, 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}</li>
* </ul>
* <p>
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
* a comparison to the {@code %} operator.
*
* @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 Math#floorMod(long, int)
* @see StrictMath#floorDiv(long, int)
* @since 9
*/
public static int floorMod(long x, int y) {
return Math.floorMod(x , y);
}
/**
* Returns the floor modulus of the {@code long} arguments.
* <p>
* The floor modulus is {@code r = x - (floorDiv(x, y) * y)},
* has the same sign as the divisor {@code y} or is zero, 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}</li>
* </ul>
* <p>
* See {@link Math#floorMod(int, int) Math.floorMod} for examples and
* a comparison to the {@code %} operator.
*
* @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 Math#floorMod(long, long)
* @see StrictMath#floorDiv(long, long)
* @since 1.8
*/
public static long floorMod(long x, long y) {
return Math.floorMod(x, y);
}
/**
* Returns the smallest (closest to negative infinity)
* {@code int} value that is greater than or equal to the algebraic quotient.
* There is one special case: if the dividend is
* {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Integer.MIN_VALUE}.
* <p>
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to negative infinity)
* {@code int} value that is greater than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilDiv(int, int)
* @see Math#ceil(double)
* @since 18
*/
public static int ceilDiv(int x, int y) {
return Math.ceilDiv(x, y);
}
/**
* Returns the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* There is one special case: if the dividend is
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Long.MIN_VALUE}.
* <p>
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilDiv(long, int)
* @see Math#ceil(double)
* @since 18
*/
public static long ceilDiv(long x, int y) {
return Math.ceilDiv(x, y);
}
/**
* Returns the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* There is one special case: if the dividend is
* {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
* then integer overflow occurs and
* the result is equal to {@code Long.MIN_VALUE}.
* <p>
* See {@link Math#ceilDiv(int, int) Math.ceilDiv} for examples and
* a comparison to the integer division {@code /} operator.
*
* @param x the dividend
* @param y the divisor
* @return the smallest (closest to negative infinity)
* {@code long} value that is greater than or equal to the algebraic quotient.
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilDiv(long, long)
* @see Math#ceil(double)
* @since 18
*/
public static long ceilDiv(long x, long y) {
return Math.ceilDiv(x, y);
}
/**
* Returns the ceiling modulus of the {@code int} arguments.
* <p>
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
* has the opposite sign as the divisor {@code y} or is zero, and
* is in the range of {@code -abs(y) < r < +abs(y)}.
*
* <p>
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
* <ul>
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
* </ul>
* <p>
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
* a comparison to the {@code %} operator.
*
* @param x the dividend
* @param y the divisor
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilMod(int, int)
* @see StrictMath#ceilDiv(int, int)
* @since 18
*/
public static int ceilMod(int x, int y) {
return Math.ceilMod(x , y);
}
/**
* Returns the ceiling modulus of the {@code long} and {@code int} arguments.
* <p>
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
* has the opposite sign as the divisor {@code y} or is zero, and
* is in the range of {@code -abs(y) < r < +abs(y)}.
*
* <p>
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
* <ul>
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
* </ul>
* <p>
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
* a comparison to the {@code %} operator.
*
* @param x the dividend
* @param y the divisor
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilMod(long, int)
* @see StrictMath#ceilDiv(long, int)
* @since 18
*/
public static int ceilMod(long x, int y) {
return Math.ceilMod(x , y);
}
/**
* Returns the ceiling modulus of the {@code long} arguments.
* <p>
* The ceiling modulus is {@code r = x - (ceilDiv(x, y) * y)},
* has the opposite sign as the divisor {@code y} or is zero, and
* is in the range of {@code -abs(y) < r < +abs(y)}.
*
* <p>
* The relationship between {@code ceilDiv} and {@code ceilMod} is such that:
* <ul>
* <li>{@code ceilDiv(x, y) * y + ceilMod(x, y) == x}</li>
* </ul>
* <p>
* See {@link Math#ceilMod(int, int) Math.ceilMod} for examples and
* a comparison to the {@code %} operator.
*
* @param x the dividend
* @param y the divisor
* @return the ceiling modulus {@code x - (ceilDiv(x, y) * y)}
* @throws ArithmeticException if the divisor {@code y} is zero
* @see Math#ceilMod(long, long)
* @see StrictMath#ceilDiv(long, long)
* @since 18
*/
public static long ceilMod(long x, long y) {
return Math.ceilMod(x, 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. In
* contrast, the {@link StrictMath#absExact(int)} method throws an
* {@code ArithmeticException} for this value.
*
* @param a the argument whose absolute value is to be determined.
* @return the absolute value of the argument.
* @see Math#absExact(int)
*/
public static int abs(int a) {
return Math.abs(a);
}
/**
* Returns the mathematical absolute value of an {@code int} value
* if it is exactly representable as an {@code int}, throwing
* {@code ArithmeticException} if the result overflows the
* positive {@code int} range.
*
* <p>Since the range of two's complement integers is asymmetric
* with one additional negative value (JLS {@jls 4.2.1}), the
* mathematical absolute value of {@link Integer#MIN_VALUE}
* overflows the positive {@code int} range, so an exception is
* thrown for that argument.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument, unless overflow occurs
* @throws ArithmeticException if the argument is {@link Integer#MIN_VALUE}
* @see Math#abs(int)
* @see Math#absExact(int)
* @since 15
*/
public static int absExact(int a) {
return Math.absExact(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. In
* contrast, the {@link StrictMath#absExact(long)} method throws
* an {@code ArithmeticException} for this value.
*
* @param a the argument whose absolute value is to be determined.
* @return the absolute value of the argument.
* @see Math#absExact(long)
*/
public static long abs(long a) {
return Math.abs(a);
}
/**
* Returns the mathematical absolute value of an {@code long} value
* if it is exactly representable as an {@code long}, throwing
* {@code ArithmeticException} if the result overflows the
* positive {@code long} range.
*
* <p>Since the range of two's complement integers is asymmetric
* with one additional negative value (JLS {@jls 4.2.1}), the
* mathematical absolute value of {@link Long#MIN_VALUE} overflows
* the positive {@code long} range, so an exception is thrown for
* that argument.
*
* @param a the argument whose absolute value is to be determined
* @return the absolute value of the argument, unless overflow occurs
* @throws ArithmeticException if the argument is {@link Long#MIN_VALUE}
* @see Math#abs(long)
* @see Math#absExact(long)
* @since 15
*/
public static long absExact(long a) {
return Math.absExact(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>
*
* @apiNote As implied by the above, one valid implementation of
* this method is given by the expression below which computes a
* {@code float} with the same exponent and significand as the
* argument but with a guaranteed zero sign bit indicating a
* positive value: <br>
* {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
*
* @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 Math.abs(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>
*
* @apiNote As implied by the above, one valid implementation of
* this method is given by the expression below which computes a
* {@code double} with the same exponent and significand as the
* argument but with a guaranteed zero sign bit indicating a
* positive value: <br>
* {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
*
* @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 Math.abs(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 a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
@IntrinsicCandidate
public static int max(int a, int b) {
return Math.max(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 a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
public static long max(long a, long b) {
return Math.max(a, b);
}
/**
* 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 a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
@IntrinsicCandidate
public static float max(float a, float b) {
return Math.max(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 a an argument.
* @param b another argument.
* @return the larger of {@code a} and {@code b}.
*/
@IntrinsicCandidate
public static double max(double a, double b) {
return Math.max(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 a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
@IntrinsicCandidate
public static int min(int a, int b) {
return Math.min(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 a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
public static long min(long a, long b) {
return Math.min(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 a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b.}
*/
@IntrinsicCandidate
public static float min(float a, float b) {
return Math.min(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 a an argument.
* @param b another argument.
* @return the smaller of {@code a} and {@code b}.
*/
@IntrinsicCandidate
public static double min(double a, double b) {
return Math.min(a, b);
}
/**
* Clamps the value to fit between min and max. If the value is less
* than {@code min}, then {@code min} is returned. If the value is greater
* than {@code max}, then {@code max} is returned. Otherwise, the original
* value is returned.
* <p>
* While the original value of type long may not fit into the int type,
* the bounds have the int type, so the result always fits the int type.
* This allows to use method to safely cast long value to int with
* saturation.
*
* @param value value to clamp
* @param min minimal allowed value
* @param max maximal allowed value
* @return a clamped value that fits into {@code min..max} interval
* @throws IllegalArgumentException if {@code min > max}
*
* @since 21
*/
public static int clamp(long value, int min, int max) {
return Math.clamp(value, min, max);
}
/**
* Clamps the value to fit between min and max. If the value is less
* than {@code min}, then {@code min} is returned. If the value is greater
* than {@code max}, then {@code max} is returned. Otherwise, the original
* value is returned.
*
* @param value value to clamp
* @param min minimal allowed value
* @param max maximal allowed value
* @return a clamped value that fits into {@code min..max} interval
* @throws IllegalArgumentException if {@code min > max}
*
* @since 21
*/
public static long clamp(long value, long min, long max) {
return Math.clamp(value, min, max);
}
/**
* Clamps the value to fit between min and max. If the value is less
* than {@code min}, then {@code min} is returned. If the value is greater
* than {@code max}, then {@code max} is returned. Otherwise, the original
* value is returned. If value is NaN, the result is also NaN.
* <p>
* Unlike the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero.
* E.g., {@code clamp(-0.0, 0.0, 1.0)} returns 0.0.
*
* @param value value to clamp
* @param min minimal allowed value
* @param max maximal allowed value
* @return a clamped value that fits into {@code min..max} interval
* @throws IllegalArgumentException if either of {@code min} and {@code max}
* arguments is NaN, or {@code min > max}, or {@code min} is +0.0, and
* {@code max} is -0.0.
*
* @since 21
*/
public static double clamp(double value, double min, double max) {
return Math.clamp(value, min, max);
}
/**
* Clamps the value to fit between min and max. If the value is less
* than {@code min}, then {@code min} is returned. If the value is greater
* than {@code max}, then {@code max} is returned. Otherwise, the original
* value is returned. If value is NaN, the result is also NaN.
* <p>
* Unlike the numerical comparison operators, this method considers
* negative zero to be strictly smaller than positive zero.
* E.g., {@code clamp(-0.0f, 0.0f, 1.0f)} returns 0.0f.
*
* @param value value to clamp
* @param min minimal allowed value
* @param max maximal allowed value
* @return a clamped value that fits into {@code min..max} interval
* @throws IllegalArgumentException if either of {@code min} and {@code max}
* arguments is NaN, or {@code min > max}, or {@code min} is +0.0f, and
* {@code max} is -0.0f.
*
* @since 21
*/
public static float clamp(float value, float min, float max) {
return Math.clamp(value, min, max);
}
/**
* Returns the fused multiply add of the three arguments; that is,
* returns the exact product of the first two arguments summed
* with the third argument and then rounded once to the nearest
* {@code double}.
*
* The rounding is done using the {@linkplain
* java.math.RoundingMode#HALF_EVEN round to nearest even
* rounding mode}.
*
* In contrast, if {@code a * b + c} is evaluated as a regular
* floating-point expression, two rounding errors are involved,
* the first for the multiply operation, the second for the
* addition operation.
*
* <p>Special cases:
* <ul>
* <li> If any argument is NaN, the result is NaN.
*
* <li> If one of the first two arguments is infinite and the
* other is zero, the result is NaN.
*
* <li> If the exact product of the first two arguments is infinite
* (in other words, at least one of the arguments is infinite and
* the other is neither zero nor NaN) and the third argument is an
* infinity of the opposite sign, the result is NaN.
*
* </ul>
*
* <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
* result as ({@code a + c}). However,
* {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
* same result as ({@code a * b}) since
* {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
* ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
* equivalent to ({@code a * b}) however.
*
* @apiNote This method corresponds to the fusedMultiplyAdd
* operation defined in IEEE 754-2008.
*
* @param a a value
* @param b a value
* @param c a value
*
* @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
* computed, as if with unlimited range and precision, and rounded
* once to the nearest {@code double} value
*
* @since 9
*/
public static double fma(double a, double b, double c) {
return Math.fma(a, b, c);
}
/**
* Returns the fused multiply add of the three arguments; that is,
* returns the exact product of the first two arguments summed
* with the third argument and then rounded once to the nearest
* {@code float}.
*
* The rounding is done using the {@linkplain
* java.math.RoundingMode#HALF_EVEN round to nearest even
* rounding mode}.
*
* In contrast, if {@code a * b + c} is evaluated as a regular
* floating-point expression, two rounding errors are involved,
* the first for the multiply operation, the second for the
* addition operation.
*
* <p>Special cases:
* <ul>
* <li> If any argument is NaN, the result is NaN.
*
* <li> If one of the first two arguments is infinite and the
* other is zero, the result is NaN.
*
* <li> If the exact product of the first two arguments is infinite
* (in other words, at least one of the arguments is infinite and
* the other is neither zero nor NaN) and the third argument is an
* infinity of the opposite sign, the result is NaN.
*
* </ul>
*
* <p>Note that {@code fma(a, 1.0f, c)} returns the same
* result as ({@code a + c}). However,
* {@code fma(a, b, +0.0f)} does <em>not</em> always return the
* same result as ({@code a * b}) since
* {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
* ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
* equivalent to ({@code a * b}) however.
*
* @apiNote This method corresponds to the fusedMultiplyAdd
* operation defined in IEEE 754-2008.
*
* @param a a value
* @param b a value
* @param c a value
*
* @return (<i>a</i>&nbsp;&times;&nbsp;<i>b</i>&nbsp;+&nbsp;<i>c</i>)
* computed, as if with unlimited range and precision, and rounded
* once to the nearest {@code float} value
*
* @since 9
*/
public static float fma(float a, float b, float c) {
return Math.fma(a, b, c);
}
/**
* 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 &plusmn;{@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) {
return Math.ulp(d);
}
/**
* 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 &plusmn;{@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) {
return Math.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 Math.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 Math.signum(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>&nbsp;&minus;&nbsp;e<sup>&minus;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>
*
* @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 FdLibm.Sinh.compute(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>&nbsp;+&nbsp;e<sup>&minus;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>
*
* @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 FdLibm.Cosh.compute(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>&nbsp;&minus;&nbsp;e<sup>&minus;x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>&minus;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>
*
* @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 FdLibm.Tanh.compute(x);
}
/**
* Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<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.
*
* <li> If both arguments are zero, the result is positive zero.
* </ul>
*
* @param x a value
* @param y a value
* @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
* without intermediate overflow or underflow
* @since 1.5
*/
public static double hypot(double x, double y) {
return FdLibm.Hypot.compute(x, y);
}
/**
* Returns <i>e</i><sup>x</sup>&nbsp;&minus;1. Note that for values of
* <i>x</i> near 0, the exact sum of
* {@code expm1(x)}&nbsp;+&nbsp;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>
*
* @param x the exponent to raise <i>e</i> to in the computation of
* <i>e</i><sup>{@code x}</sup>&nbsp;&minus;1.
* @return the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
* @since 1.5
*/
public static double expm1(double x) {
return FdLibm.Expm1.compute(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>
*
* @param x a value
* @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
* log of {@code x}&nbsp;+&nbsp;1
* @since 1.5
*/
public static double log1p(double x) {
return FdLibm.Log1p.compute(x);
}
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. For this method, a NaN
* {@code sign} argument is always treated as if it were
* positive.
*
* @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 Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
}
/**
* Returns the first floating-point argument with the sign of the
* second floating-point argument. For this method, a NaN
* {@code sign} argument is always treated as if it were
* positive.
*
* @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 Math.copySign(magnitude, (Float.isNaN(sign)?1.0f: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 Math.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 Math.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
* &plusmn;{@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 &plusmn;
* {@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 Math.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
* &plusmn;{@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 &plusmn;
* {@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 Math.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 Math.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 Math.nextUp(f);
}
/**
* 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) {
return Math.nextDown(d);
}
/**
* 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) {
return Math.nextDown(f);
}
/**
* Returns {@code d} &times; 2<sup>{@code scaleFactor}</sup>
* rounded as if performed by a single correctly rounded
* floating-point multiply. 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} &times; 2<sup>{@code scaleFactor}</sup>
* @since 1.6
*/
public static double scalb(double d, int scaleFactor) {
return Math.scalb(d, scaleFactor);
}
/**
* Returns {@code f} &times; 2<sup>{@code scaleFactor}</sup>
* rounded as if performed by a single correctly rounded
* floating-point multiply. 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} &times; 2<sup>{@code scaleFactor}</sup>
* @since 1.6
*/
public static float scalb(float f, int scaleFactor) {
return Math.scalb(f, scaleFactor);
}
/**
* Returns the product of the unsigned arguments,
* throwing an exception if the result overflows an unsigned {@code int}.
*
* @param x the first unsigned value
* @param y the second unsigned value
* @return the result
* @throws ArithmeticException if the result overflows an unsigned int
* @since 25
*/
public static int unsignedMultiplyExact(int x, int y) {
return Math.unsignedMultiplyExact(x, y);
}
/**
* Returns the product of the unsigned arguments,
* throwing an exception if the result overflows an unsigned {@code long}.
*
* @param x the first unsigned value
* @param y the second unsigned value
* @return the result
* @throws ArithmeticException if the result overflows an unsigned long
* @since 25
*/
public static long unsignedMultiplyExact(long x, int y) {
return Math.unsignedMultiplyExact(x, y);
}
/**
* Returns the product of the unsigned arguments,
* throwing an exception if the result overflows an unsigned {@code long}.
*
* @param x the first unsigned value
* @param y the second unsigned value
* @return the result
* @throws ArithmeticException if the result overflows an unsigned long
* @since 25
*/
public static long unsignedMultiplyExact(long x, long y) {
return Math.unsignedMultiplyExact(x, y);
}
/**
* Returns {@code x} raised to the power of {@code n},
* throwing an exception if the result overflows an {@code int}.
* When {@code n} is 0, the returned value is 1.
*
* @param x the base.
* @param n the exponent.
* @return {@code x} raised to the power of {@code n}.
* @throws ArithmeticException when {@code n} is negative,
* or when the result overflows an int.
* @since 25
*/
public static int powExact(int x, int n) {
return Math.powExact(x, n);
}
/**
* Returns unsigned {@code x} raised to the power of {@code n},
* throwing an exception if the result overflows an unsigned {@code int}.
* When {@code n} is 0, the returned value is 1.
*
* @param x the unsigned base.
* @param n the exponent.
* @return {@code x} raised to the power of {@code n}.
* @throws ArithmeticException when {@code n} is negative,
* or when the result overflows an unsigned int.
* @since 25
*/
public static int unsignedPowExact(int x, int n) {
return Math.unsignedPowExact(x, n);
}
/**
* Returns {@code x} raised to the power of {@code n},
* throwing an exception if the result overflows a {@code long}.
* When {@code n} is 0, the returned value is 1.
*
* @param x the base.
* @param n the exponent.
* @return {@code x} raised to the power of {@code n}.
* @throws ArithmeticException when {@code n} is negative,
* or when the result overflows a long.
* @since 25
*/
public static long powExact(long x, int n) {
return Math.powExact(x, n);
}
/**
* Returns unsigned {@code x} raised to the power of {@code n},
* throwing an exception if the result overflows an unsigned {@code long}.
* When {@code n} is 0, the returned value is 1.
*
* @param x the unsigned base.
* @param n the exponent.
* @return {@code x} raised to the power of {@code n}.
* @throws ArithmeticException when {@code n} is negative,
* or when the result overflows an unsigned long.
* @since 25
*/
public static long unsignedPowExact(long x, int n) {
return Math.unsignedPowExact(x, n);
}
}