/*
 * Copyright (c) 1999, 2016, Oracle and/or its affiliates. All rights reserved.
 * ORACLE PROPRIETARY/CONFIDENTIAL. Use is subject to license terms.
 *
 *
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 *
 *
 *
 */

package java.lang;

import java.util.Random;
import jdk.internal.math.DoubleConsts;
import jdk.internal.HotSpotIntrinsicCandidate;

/**
 * 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="ftp://ftp.netlib.org/fdlibm.tar">{@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}, and {@code toIntExact}
 * throw an {@code ArithmeticException} when the results overflow.
 * For other arithmetic operations such as divide, absolute value,
 * increment by one, decrement by one, and negation overflow occurs only with
 * a specific minimum or maximum value and should be checked against
 * the minimum or maximum as appropriate.
 *
 * @author unascribed
 * @author Joseph D. Darcy
 * @since 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.</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.</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.</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 strictfp double toRadians(double angdeg) {
 // Do not delegate to Math.toRadians(angdeg) because
 // this method has the strictfp modifier.
 return angdeg * DEGREES_TO_RADIANS;
 }

 /**
 * 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 strictfp double toDegrees(double angrad) {
 // Do not delegate to Math.toDegrees(angrad) because
 // this method has the strictfp modifier.
 return angrad * RADIANS_TO_DEGREES;
 }

 /**
 * Returns Euler's number <i>e</i> raised to the power of a
 * {@code double} value. Special cases:
 * <ul><li>If the argument is NaN, the result is NaN.
 * <li>If the argument is positive infinity, then the result is
 * positive infinity.
 * <li>If the argument is negative infinity, then the result is
 * positive zero.</ul>
 *
 * @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.</ul>
 *
 * @param a a value
 * @return the value ln&nbsp;{@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>.
 * </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}.
 */
 @HotSpotIntrinsicCandidate
 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&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 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.
 *
 * This method does *not* need to be declared strictfp to get
 * fully reproducible results. Whether or not a method is
 * declared strictfp can only make a difference in the
 * returned result if some operation would overflow or
 * underflow with strictfp semantics. The operation
 * (twoToThe52 + a ) cannot overflow since large values of a
 * are screened out; the add cannot underflow since twoToThe52
 * is too large. The subtraction ((twoToThe52 + a ) -
 * twoToThe52) will be exact as discussed above and thus
 * cannot overflow or meaningfully underflow. Finally, the
 * last multiply in the return statement is by plus or minus
 * 1.0, which is exact too.
 */
 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 -<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>
 *
 * @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 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.)
 *
 * @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 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.
 *
 * @param a the argument whose absolute value is to be determined.
 * @return the absolute value of the argument.
 */
 public static int abs(int a) {
 return Math.abs(a);
 }

 /**
 * Returns the absolute value of a {@code long} value.
 * If the argument is not negative, the argument is returned.
 * If the argument is negative, the negation of the argument is returned.
 *
 * <p>Note that if the argument is equal to the value of
 * {@link Long#MIN_VALUE}, the most negative representable
 * {@code long} value, the result is that same value, which
 * is negative.
 *
 * @param a the argument whose absolute value is to be determined.
 * @return the absolute value of the argument.
 */
 public static long abs(long a) {
 return Math.abs(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}.
 */
 @HotSpotIntrinsicCandidate
 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}.
 */
 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}.
 */
 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}.
 */
 @HotSpotIntrinsicCandidate
 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.}
 */
 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}.
 */
 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>&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;-&nbsp;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>&nbsp;+&nbsp;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>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;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>&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.
 *
 * </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;-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;-1.
 * @return the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;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}&nbsp;+&nbsp;1), the natural
 * log of {@code x}&nbsp;+&nbsp;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
 * &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 to a
 * member of the double value set. See the Java
 * Language Specification for a discussion of floating-point
 * value sets. If the exponent of the result is between {@link
 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
 * answer is calculated exactly. If the exponent of the result
 * would be larger than {@code Double.MAX_EXPONENT}, an
 * infinity is returned. Note that if the result is subnormal,
 * precision may be lost; that is, when {@code scalb(x, n)}
 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
 * <i>x</i>. When the result is non-NaN, the result has the same
 * sign as {@code d}.
 *
 * <p>Special cases:
 * <ul>
 * <li> If the first argument is NaN, NaN is returned.
 * <li> If the first argument is infinite, then an infinity of the
 * same sign is returned.
 * <li> If the first argument is zero, then a zero of the same
 * sign is returned.
 * </ul>
 *
 * @param d number to be scaled by a power of two.
 * @param scaleFactor power of 2 used to scale {@code d}
 * @return {@code d} &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 to a
 * member of the float value set. See the Java
 * Language Specification for a discussion of floating-point
 * value sets. If the exponent of the result is between {@link
 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
 * answer is calculated exactly. If the exponent of the result
 * would be larger than {@code Float.MAX_EXPONENT}, an
 * infinity is returned. Note that if the result is subnormal,
 * precision may be lost; that is, when {@code scalb(x, n)}
 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
 * <i>x</i>. When the result is non-NaN, the result has the same
 * sign as {@code f}.
 *
 * <p>Special cases:
 * <ul>
 * <li> If the first argument is NaN, NaN is returned.
 * <li> If the first argument is infinite, then an infinity of the
 * same sign is returned.
 * <li> If the first argument is zero, then a zero of the same
 * sign is returned.
 * </ul>
 *
 * @param f number to be scaled by a power of two.
 * @param scaleFactor power of 2 used to scale {@code f}
 * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
 * @since 1.6
 */
 public static float scalb(float f, int scaleFactor) {
 return Math.scalb(f, scaleFactor);
 }
}