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   * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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   * This code is free software; you can redistribute it and/or modify it
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   * published by the Free Software Foundation.  Oracle designates this
   * particular file as subject to the "Classpath" exception as provided
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   *
   * 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
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   * 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 sun.misc.DoubleConsts;
  
  /**
   * 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, decrement, and negation overflow occurs only with
   * a specific minimum or maximum value and should be checked against
   * the minimum or maximum as appropriate.
   *
   * @author  unascribed
   * @author  Joseph D. Darcy
   * @since   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;
  
      /**
       * 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 / 180.0 * PI;
      }
  
      /**
       * Converts an angle measured in radians to an approximately
       * equivalent angle measured in degrees.  The conversion from
       * radians to degrees is generally inexact; users should
       * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
       * equal {@code 0.0}.
       *
       * @param   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 * 180.0 / PI;
      }
  
      /**
       * Returns Euler's number <i>e</i> raised to the power of a
       * {@code double} value. Special cases:
       * <ul><li>If the argument is NaN, the result is NaN.
       * <li>If the argument is positive infinity, then the result is
       * positive infinity.
       * <li>If the argument is negative infinity, then the result is
       * positive zero.</ul>
       *
       * @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 native double exp(double 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}.
       */
      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 native double cbrt(double 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 native double pow(double a, double 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     Integer#MAX_VALUE
       * @see     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     Long#MAX_VALUE
       * @see     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,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 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 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} 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>
       * In other words, the result is the same as the value of the expression:
       * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(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>
       * In other words, the result is the same as the value of the expression:
       * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(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}.
       */
      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}.
       */
      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 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 native double hypot(double x, double 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);
      }
  }
  