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	/*
	* Copyright (c) 1999, 2021, Oracle and/or its affiliates. All rights reserved.
	* 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
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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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 as executed with all floating-point
	* operations following the rules of Java floating-point arithmetic.
	*
	* <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 {@code addExact},
	* {@code subtractExact}, {@code multiplyExact}, {@code toIntExact},
	* {@code incrementExact}, {@code decrementExact} and {@code negateExact}
	* throw an {@code ArithmeticException} when the results overflow.
	* For the arithmetic operations divide and absolute value, overflow
	* occurs only with a specific minimum or maximum value and
	* should be checked against the minimum or maximum as appropriate.
	*
	* <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>.
	*
	* @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 = 2.7182818284590452354;

	/**
	* 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;

	/**
	* Constant by which to multiply an angular value in degrees to obtain an
	* angular value in radians.
	*/
	private static final double DEGREES_TO_RADIANS = 0.017453292519943295;

	/**
	* Constant by which to multiply an angular value in radians to obtain an
	* angular value in degrees.
	*/

	private static final double RADIANS_TO_DEGREES = 57.29577951308232;

	/**
	* 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 native double sin(double 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 native double cos(double 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 native double tan(double a);

	/**
	* 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>
	*
	* @param a the value whose arc sine is to be returned.
	* @return the arc sine of the argument.
	*/
	public static native double asin(double 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 native double acos(double a);

	/**
	* 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.
	* <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 native double atan(double 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 {@code a}, the natural logarithm of
	* {@code a}.
	*/
	public static native double log(double 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 native double log10(double 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 native double sqrt(double 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 - 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 f1 the dividend.
	* @param f2 the divisor.
	* @return the remainder when {@code f1} is divided by
	* {@code f2}.
	*/
	public static native double IEEEremainder(double f1, double 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 increment value to add when the argument is non-integral
	*/
	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}, {@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>
	*
	* @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, π - 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>, <i>theta</i>)
	* in polar coordinates that corresponds to the point
	* (<i>x</i>, <i>y</i>) in Cartesian coordinates.
	*/
	public static native double atan2(double y, double 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 ±{@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 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 Math#multiplyHigh(long,long)
	* @since 9
	*/
	public static long multiplyHigh(long x, long y) {
	return Math.multiplyHigh(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 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>
	* 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 the
	* {@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 int} 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 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>
	* 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 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>
	* 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 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>
	* 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 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>
	* 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 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);
	}

	/**
	* 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> × <i>b</i> + <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> × <i>b</i> + <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 ±{@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 ±{@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> - 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>
	*
	* @param x The number whose hyperbolic sine is to be returned.
	* @return The hyperbolic sine of {@code x}.
	* @since 1.5
	*/
	public static native double sinh(double 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>
	*
	* @param x The number whose hyperbolic cosine is to be returned.
	* @return The hyperbolic cosine of {@code x}.
	* @since 1.5
	*/
	public static native double cosh(double 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>
	*
	* @param x The number whose hyperbolic tangent is to be returned.
	* @return The hyperbolic tangent of {@code x}.
	* @since 1.5
	*/
	public static native double tanh(double 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.
	*
	* <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> +<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> -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>
	*
	* @param x the 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 native double expm1(double 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} + 1), the natural
	* log of {@code x} + 1
	* @since 1.5
	*/
	public static native double log1p(double 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
	* ±{@link Double#MIN_VALUE} and {@code direction}
	* has a value such that the result should have a smaller
	* magnitude, then a zero with the same sign as {@code start}
	* is returned.
	*
	* <li> If {@code start} is infinite and
	* {@code direction} has a value such that the result should
	* have a smaller magnitude, {@link Double#MAX_VALUE} with the
	* same sign as {@code start} is returned.
	*
	* <li> If {@code start} is equal to ±
	* {@link Double#MAX_VALUE} and {@code direction} has a
	* value such that the result should have a larger magnitude, an
	* infinity with same sign as {@code start} is returned.
	* </ul>
	*
	* @param start starting floating-point value
	* @param direction value indicating which of
	* {@code start}'s neighbors or {@code start} should
	* be returned
	* @return The floating-point number adjacent to {@code start} in the
	* direction of {@code direction}.
	* @since 1.6
	*/
	public static double nextAfter(double start, double direction) {
	return 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
	* ±{@link Float#MIN_VALUE} and {@code direction}
	* has a value such that the result should have a smaller
	* magnitude, then a zero with the same sign as {@code start}
	* is returned.
	*
	* <li> If {@code start} is infinite and
	* {@code direction} has a value such that the result should
	* have a smaller magnitude, {@link Float#MAX_VALUE} with the
	* same sign as {@code start} is returned.
	*
	* <li> If {@code start} is equal to ±
	* {@link Float#MAX_VALUE} and {@code direction} has a
	* value such that the result should have a larger magnitude, an
	* infinity with same sign as {@code start} is returned.
	* </ul>
	*
	* @param start starting floating-point value
	* @param direction value indicating which of
	* {@code start}'s neighbors or {@code start} should
	* be returned
	* @return The floating-point number adjacent to {@code start} in the
	* direction of {@code direction}.
	* @since 1.6
	*/
	public static float nextAfter(float start, double direction) {
	return 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} × 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} × 2<sup>{@code scaleFactor}</sup>
	* @since 1.6
	*/
	public static double scalb(double d, int scaleFactor) {
	return Math.scalb(d, scaleFactor);
	}

	/**
	* Returns {@code f} × 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} × 2<sup>{@code scaleFactor}</sup>
	* @since 1.6
	*/
	public static float scalb(float f, int scaleFactor) {
	return Math.scalb(f, scaleFactor);
	}
	}

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