/*
- * Copyright (c) 1994, 2013, Oracle and/or its affiliates. All rights reserved.
+ * Copyright (c) 1994, 2017, Oracle and/or its affiliates. All rights reserved.
  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
  *
  * This code is free software; you can redistribute it and/or modify it
  * under the terms of the GNU General Public License version 2 only, as
  * published by the Free Software Foundation.  Oracle designates this
  * particular file as subject to the "Classpath" exception as provided
  * by Oracle in the LICENSE file that accompanied this code.
  *
  * This code is distributed in the hope that it will be useful, but WITHOUT
  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  * version 2 for more details (a copy is included in the LICENSE file that
  * accompanied this code).
  *
  * You should have received a copy of the GNU General Public License version
  * 2 along with this work; if not, write to the Free Software Foundation,
  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  *
  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  * or visit www.oracle.com if you need additional information or have any
  * questions.
  */
 
 package java.lang;
-import java.util.Random;
 
-import sun.misc.FloatConsts;
-import sun.misc.DoubleConsts;
+import java.math.BigDecimal;
+import java.util.Random;
+import jdk.internal.math.FloatConsts;
+import jdk.internal.math.DoubleConsts;
+import jdk.internal.HotSpotIntrinsicCandidate;
 
 /**
  * The class {@code Math} contains methods for performing basic
  * numeric operations such as the elementary exponential, logarithm,
  * square root, and trigonometric functions.
  *
  * <p>Unlike some of the numeric methods of class
  * {@code StrictMath}, all implementations of the equivalent
  * functions of class {@code Math} are not defined to return the
  * bit-for-bit same results.  This relaxation permits
  * better-performing implementations where strict reproducibility is
  * not required.
  *
  * <p>By default many of the {@code Math} methods simply call
  * the equivalent method in {@code StrictMath} for their
  * implementation.  Code generators are encouraged to use
  * platform-specific native libraries or microprocessor instructions,
  * where available, to provide higher-performance implementations of
  * {@code Math} methods.  Such higher-performance
  * implementations still must conform to the specification for
  * {@code Math}.
  *
  * <p>The quality of implementation specifications concern two
  * properties, accuracy of the returned result and monotonicity of the
  * method.  Accuracy of the floating-point {@code Math} methods is
  * measured in terms of <i>ulps</i>, units in the last place.  For a
  * given floating-point format, an {@linkplain #ulp(double) ulp} of a
  * specific real number value is the distance between the two
  * floating-point values bracketing that numerical value.  When
  * discussing the accuracy of a method as a whole rather than at a
  * specific argument, the number of ulps cited is for the worst-case
  * error at any argument.  If a method always has an error less than
  * 0.5 ulps, the method always returns the floating-point number
  * nearest the exact result; such a method is <i>correctly
  * rounded</i>.  A correctly rounded method is generally the best a
  * floating-point approximation can be; however, it is impractical for
  * many floating-point methods to be correctly rounded.  Instead, for
  * the {@code Math} class, a larger error bound of 1 or 2 ulps is
  * allowed for certain methods.  Informally, with a 1 ulp error bound,
  * when the exact result is a representable number, the exact result
  * should be returned as the computed result; otherwise, either of the
  * two floating-point values which bracket the exact result may be
  * returned.  For exact results large in magnitude, one of the
  * endpoints of the bracket may be infinite.  Besides accuracy at
  * individual arguments, maintaining proper relations between the
  * method at different arguments is also important.  Therefore, most
  * methods with more than 0.5 ulp errors are required to be
  * <i>semi-monotonic</i>: whenever the mathematical function is
  * non-decreasing, so is the floating-point approximation, likewise,
  * whenever the mathematical function is non-increasing, so is the
  * floating-point approximation.  Not all approximations that have 1
  * ulp accuracy will automatically meet the monotonicity requirements.
  *
  * <p>
  * The platform uses signed two's complement integer arithmetic with
  * int and long primitive types.  The developer should choose
  * the primitive type to ensure that arithmetic operations consistently
  * produce correct results, which in some cases means the operations
  * will not overflow the range of values of the computation.
  * The best practice is to choose the primitive type and algorithm to avoid
  * overflow. In cases where the size is {@code int} or {@code long} and
  * overflow errors need to be detected, the methods {@code addExact},
  * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
  * throw an {@code ArithmeticException} when the results overflow.
  * For other arithmetic operations such as divide, absolute value,
- * increment, decrement, and negation overflow occurs only with
+ * 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   JDK1.0
+ * @since   1.0
  */
 
 public final class Math {
 
     /**
      * Don't let anyone instantiate this class.
      */
     private Math() {}
 
     /**
      * The {@code double} value that is closer than any other to
      * <i>e</i>, the base of the natural logarithms.
      */
     public static final double E = 2.7182818284590452354;
 
     /**
      * The {@code double} value that is closer than any other to
      * <i>pi</i>, the ratio of the circumference of a circle to its
      * diameter.
      */
     public static final double PI = 3.14159265358979323846;
 
     /**
+     * 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>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   an angle, in radians.
      * @return  the sine of the argument.
      */
+    @HotSpotIntrinsicCandidate
     public static double sin(double a) {
         return StrictMath.sin(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the trigonometric cosine of an angle. Special cases:
      * <ul><li>If the argument is NaN or an infinity, then the
      * result is NaN.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   an angle, in radians.
      * @return  the cosine of the argument.
      */
+    @HotSpotIntrinsicCandidate
     public static double cos(double a) {
         return StrictMath.cos(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the trigonometric tangent of an angle.  Special cases:
      * <ul><li>If the argument is NaN or an infinity, then the result
      * is NaN.
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   an angle, in radians.
      * @return  the tangent of the argument.
      */
+    @HotSpotIntrinsicCandidate
     public static double tan(double a) {
         return StrictMath.tan(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the arc sine of a value; the returned angle is in the
      * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
      * <ul><li>If the argument is NaN or its absolute value is greater
      * than 1, then the result is NaN.
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   the value whose arc sine is to be returned.
      * @return  the arc sine of the argument.
      */
     public static double asin(double a) {
         return StrictMath.asin(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the arc cosine of a value; the returned angle is in the
      * range 0.0 through <i>pi</i>.  Special case:
      * <ul><li>If the argument is NaN or its absolute value is greater
      * than 1, then the result is NaN.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   the value whose arc cosine is to be returned.
      * @return  the arc cosine of the argument.
      */
     public static double acos(double a) {
         return StrictMath.acos(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the arc tangent of a value; the returned angle is in the
      * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
      * <ul><li>If the argument is NaN, then the result is NaN.
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   the value whose arc tangent is to be returned.
      * @return  the arc tangent of the argument.
      */
     public static double atan(double a) {
         return StrictMath.atan(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Converts an angle measured in degrees to an approximately
      * equivalent angle measured in radians.  The conversion from
      * degrees to radians is generally inexact.
      *
      * @param   angdeg   an angle, in degrees
      * @return  the measurement of the angle {@code angdeg}
      *          in radians.
      * @since   1.2
      */
     public static double toRadians(double angdeg) {
-        return angdeg / 180.0 * PI;
+        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.
      * @since   1.2
      */
     public static double toDegrees(double angrad) {
-        return angrad * 180.0 / PI;
+        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>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @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.
      */
+    @HotSpotIntrinsicCandidate
     public static double exp(double a) {
         return StrictMath.exp(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the natural logarithm (base <i>e</i>) of a {@code double}
      * value.  Special cases:
      * <ul><li>If the argument is NaN or less than zero, then the result
      * is NaN.
      * <li>If the argument is positive infinity, then the result is
      * positive infinity.
      * <li>If the argument is positive zero or negative zero, then the
      * result is negative infinity.</ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   a value
      * @return  the value ln&nbsp;{@code a}, the natural logarithm of
      *          {@code a}.
      */
+    @HotSpotIntrinsicCandidate
     public static double log(double a) {
         return StrictMath.log(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the base 10 logarithm of a {@code double} value.
      * Special cases:
      *
      * <ul><li>If the argument is NaN or less than zero, then the result
      * is NaN.
      * <li>If the argument is positive infinity, then the result is
      * positive infinity.
      * <li>If the argument is positive zero or negative zero, then the
      * result is negative infinity.
      * <li> If the argument is equal to 10<sup><i>n</i></sup> for
      * integer <i>n</i>, then the result is <i>n</i>.
      * </ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   a value
      * @return  the base 10 logarithm of  {@code a}.
      * @since 1.5
      */
+    @HotSpotIntrinsicCandidate
     public static double log10(double a) {
         return StrictMath.log10(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the correctly rounded positive square root of a
      * {@code double} value.
      * Special cases:
      * <ul><li>If the argument is NaN or less than zero, then the result
      * is NaN.
      * <li>If the argument is positive infinity, then the result is positive
      * infinity.
      * <li>If the argument is positive zero or negative zero, then the
      * result is the same as the argument.</ul>
      * Otherwise, the result is the {@code double} value closest to
      * the true mathematical square root of the argument value.
      *
      * @param   a   a value.
      * @return  the positive square root of {@code a}.
      *          If the argument is NaN or less than zero, the result is NaN.
      */
+    @HotSpotIntrinsicCandidate
     public static double sqrt(double a) {
         return StrictMath.sqrt(a); // default impl. delegates to StrictMath
                                    // Note that hardware sqrt instructions
                                    // frequently can be directly used by JITs
                                    // and should be much faster than doing
                                    // Math.sqrt in software.
     }
 
 
     /**
      * Returns the cube root of a {@code double} value.  For
      * positive finite {@code x}, {@code cbrt(-x) ==
      * -cbrt(x)}; that is, the cube root of a negative value is
      * the negative of the cube root of that value's magnitude.
      *
      * Special cases:
      *
      * <ul>
      *
      * <li>If the argument is NaN, then the result is NaN.
      *
      * <li>If the argument is infinite, then the result is an infinity
      * with the same sign as the argument.
      *
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.
      *
      * </ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      *
      * @param   a   a value.
      * @return  the cube root of {@code a}.
      * @since 1.5
      */
     public static double cbrt(double a) {
         return StrictMath.cbrt(a);
     }
 
     /**
      * Computes the remainder operation on two arguments as prescribed
      * by the IEEE 754 standard.
      * The remainder value is mathematically equal to
      * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
      * where <i>n</i> is the mathematical integer closest to the exact
      * mathematical value of the quotient {@code f1/f2}, and if two
      * mathematical integers are equally close to {@code f1/f2},
      * then <i>n</i> is the integer that is even. If the remainder is
      * zero, its sign is the same as the sign of the first argument.
      * Special cases:
      * <ul><li>If either argument is NaN, or the first argument is infinite,
      * or the second argument is positive zero or negative zero, then the
      * result is NaN.
      * <li>If the first argument is finite and the second argument is
      * infinite, then the result is the same as the first argument.</ul>
      *
      * @param   f1   the dividend.
      * @param   f2   the divisor.
      * @return  the remainder when {@code f1} is divided by
      *          {@code f2}.
      */
     public static double IEEEremainder(double f1, double f2) {
         return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
     }
 
     /**
      * Returns the smallest (closest to negative infinity)
      * {@code double} value that is greater than or equal to the
      * argument and is equal to a mathematical integer. Special cases:
      * <ul><li>If the argument value is already equal to a
      * mathematical integer, then the result is the same as the
      * argument.  <li>If the argument is NaN or an infinity or
      * positive zero or negative zero, then the result is the same as
      * the argument.  <li>If the argument value is less than zero but
      * greater than -1.0, then the result is negative zero.</ul> Note
      * that the value of {@code Math.ceil(x)} is exactly the
      * value of {@code -Math.floor(-x)}.
      *
      *
      * @param   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 StrictMath.ceil(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the largest (closest to positive infinity)
      * {@code double} value that is less than or equal to the
      * argument and is equal to a mathematical integer. Special cases:
      * <ul><li>If the argument value is already equal to a
      * mathematical integer, then the result is the same as the
      * argument.  <li>If the argument is NaN or an infinity or
      * positive zero or negative zero, then the result is the same as
      * the argument.</ul>
      *
      * @param   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 StrictMath.floor(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the {@code double} value that is closest in value
      * to the argument and is equal to a mathematical integer. If two
      * {@code double} values that are mathematical integers are
      * equally close, the result is the integer value that is
      * even. Special cases:
      * <ul><li>If the argument value is already equal to a mathematical
      * integer, then the result is the same as the argument.
      * <li>If the argument is NaN or an infinity or positive zero or negative
      * zero, then the result is the same as the argument.</ul>
      *
      * @param   a   a {@code double} value.
      * @return  the closest floating-point value to {@code a} that is
      *          equal to a mathematical integer.
      */
     public static double rint(double a) {
         return StrictMath.rint(a); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the angle <i>theta</i> from the conversion of rectangular
      * coordinates ({@code x},&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>
      *
      * <p>The computed result must be within 2 ulps of the exact result.
      * Results must be semi-monotonic.
      *
      * @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.
      */
+    @HotSpotIntrinsicCandidate
     public static double atan2(double y, double x) {
         return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the value of the first argument raised to the power of the
      * second argument. Special cases:
      *
      * <ul><li>If the second argument is positive or negative zero, then the
      * result is 1.0.
      * <li>If the second argument is 1.0, then the result is the same as the
      * first argument.
      * <li>If the second argument is NaN, then the result is NaN.
      * <li>If the first argument is NaN and the second argument is nonzero,
      * then the result is NaN.
      *
      * <li>If
      * <ul>
      * <li>the absolute value of the first argument is greater than 1
      * and the second argument is positive infinity, or
      * <li>the absolute value of the first argument is less than 1 and
      * the second argument is negative infinity,
      * </ul>
      * then the result is positive infinity.
      *
      * <li>If
      * <ul>
      * <li>the absolute value of the first argument is greater than 1 and
      * the second argument is negative infinity, or
      * <li>the absolute value of the
      * first argument is less than 1 and the second argument is positive
      * infinity,
      * </ul>
      * then the result is positive zero.
      *
      * <li>If the absolute value of the first argument equals 1 and the
      * second argument is infinite, then the result is NaN.
      *
      * <li>If
      * <ul>
      * <li>the first argument is positive zero and the second argument
      * is greater than zero, or
      * <li>the first argument is positive infinity and the second
      * argument is less than zero,
      * </ul>
      * then the result is positive zero.
      *
      * <li>If
      * <ul>
      * <li>the first argument is positive zero and the second argument
      * is less than zero, or
      * <li>the first argument is positive infinity and the second
      * argument is greater than zero,
      * </ul>
      * then the result is positive infinity.
      *
      * <li>If
      * <ul>
      * <li>the first argument is negative zero and the second argument
      * is greater than zero but not a finite odd integer, or
      * <li>the first argument is negative infinity and the second
      * argument is less than zero but not a finite odd integer,
      * </ul>
      * then the result is positive zero.
      *
      * <li>If
      * <ul>
      * <li>the first argument is negative zero and the second argument
      * is a positive finite odd integer, or
      * <li>the first argument is negative infinity and the second
      * argument is a negative finite odd integer,
      * </ul>
      * then the result is negative zero.
      *
      * <li>If
      * <ul>
      * <li>the first argument is negative zero and the second argument
      * is less than zero but not a finite odd integer, or
      * <li>the first argument is negative infinity and the second
      * argument is greater than zero but not a finite odd integer,
      * </ul>
      * then the result is positive infinity.
      *
      * <li>If
      * <ul>
      * <li>the first argument is negative zero and the second argument
      * is a negative finite odd integer, or
      * <li>the first argument is negative infinity and the second
      * argument is a positive finite odd integer,
      * </ul>
      * then the result is negative infinity.
      *
      * <li>If the first argument is finite and less than zero
      * <ul>
      * <li> if the second argument is a finite even integer, the
      * result is equal to the result of raising the absolute value of
      * the first argument to the power of the second argument
      *
      * <li>if the second argument is a finite odd integer, the result
      * is equal to the negative of the result of raising the absolute
      * value of the first argument to the power of the second
      * argument
      *
      * <li>if the second argument is finite and not an integer, then
      * the result is NaN.
      * </ul>
      *
      * <li>If both arguments are integers, then the result is exactly equal
      * to the mathematical result of raising the first argument to the power
      * of the second argument if that result can in fact be represented
      * exactly as a {@code double} value.</ul>
      *
      * <p>(In the foregoing descriptions, a floating-point value is
      * considered to be an integer if and only if it is finite and a
      * fixed point of the method {@link #ceil ceil} or,
      * equivalently, a fixed point of the method {@link #floor
      * floor}. A value is a fixed point of a one-argument
      * method if and only if the result of applying the method to the
      * value is equal to the value.)
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   a   the base.
      * @param   b   the exponent.
      * @return  the value {@code a}<sup>{@code b}</sup>.
      */
+    @HotSpotIntrinsicCandidate
     public static double pow(double a, double b) {
         return StrictMath.pow(a, b); // default impl. delegates to StrictMath
     }
 
     /**
      * Returns the closest {@code int} to the argument, with ties
      * rounding to positive infinity.
      *
      * <p>
      * Special cases:
      * <ul><li>If the argument is NaN, the result is 0.
      * <li>If the argument is negative infinity or any value less than or
      * equal to the value of {@code Integer.MIN_VALUE}, the result is
      * equal to the value of {@code Integer.MIN_VALUE}.
      * <li>If the argument is positive infinity or any value greater than or
      * equal to the value of {@code Integer.MAX_VALUE}, the result is
      * equal to the value of {@code Integer.MAX_VALUE}.</ul>
      *
      * @param   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) {
         int intBits = Float.floatToRawIntBits(a);
         int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
                 >> (FloatConsts.SIGNIFICAND_WIDTH - 1);
         int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
                 + FloatConsts.EXP_BIAS) - biasedExp;
         if ((shift & -32) == 0) { // shift >= 0 && shift < 32
             // a is a finite number such that pow(2,-32) <= ulp(a) < 1
             int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
                     | (FloatConsts.SIGNIF_BIT_MASK + 1));
             if (intBits < 0) {
                 r = -r;
             }
             // In the comments below each Java expression evaluates to the value
             // the corresponding mathematical expression:
             // (r) evaluates to a / ulp(a)
             // (r >> shift) evaluates to floor(a * 2)
             // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
             // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
             return ((r >> shift) + 1) >> 1;
         } else {
             // a is either
             // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
             // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
             // - an infinity or NaN
             return (int) a;
         }
     }
 
     /**
      * Returns the closest {@code long} to the argument, with ties
      * rounding to positive infinity.
      *
      * <p>Special cases:
      * <ul><li>If the argument is NaN, the result is 0.
      * <li>If the argument is negative infinity or any value less than or
      * equal to the value of {@code Long.MIN_VALUE}, the result is
      * equal to the value of {@code Long.MIN_VALUE}.
      * <li>If the argument is positive infinity or any value greater than or
      * equal to the value of {@code Long.MAX_VALUE}, the result is
      * equal to the value of {@code Long.MAX_VALUE}.</ul>
      *
      * @param   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) {
         long longBits = Double.doubleToRawLongBits(a);
         long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
                 >> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
         long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
                 + DoubleConsts.EXP_BIAS) - biasedExp;
         if ((shift & -64) == 0) { // shift >= 0 && shift < 64
             // a is a finite number such that pow(2,-64) <= ulp(a) < 1
             long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
                     | (DoubleConsts.SIGNIF_BIT_MASK + 1));
             if (longBits < 0) {
                 r = -r;
             }
             // In the comments below each Java expression evaluates to the value
             // the corresponding mathematical expression:
             // (r) evaluates to a / ulp(a)
             // (r >> shift) evaluates to floor(a * 2)
             // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
             // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
             return ((r >> shift) + 1) >> 1;
         } else {
             // a is either
             // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
             // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
             // - an infinity or NaN
             return (long) a;
         }
     }
 
     private static final class RandomNumberGeneratorHolder {
         static final Random randomNumberGenerator = new Random();
     }
 
     /**
      * Returns a {@code double} value with a positive sign, greater
      * than or equal to {@code 0.0} and less than {@code 1.0}.
      * Returned values are chosen pseudorandomly with (approximately)
      * uniform distribution from that range.
      *
      * <p>When this method is first called, it creates a single new
      * pseudorandom-number generator, exactly as if by the expression
      *
      * <blockquote>{@code new java.util.Random()}</blockquote>
      *
      * This new pseudorandom-number generator is used thereafter for
      * all calls to this method and is used nowhere else.
      *
      * <p>This method is properly synchronized to allow correct use by
      * more than one thread. However, if many threads need to generate
      * pseudorandom numbers at a great rate, it may reduce contention
      * for each thread to have its own pseudorandom-number generator.
      *
+     * @apiNote
+     * As the largest {@code double} value less than {@code 1.0}
+     * is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range
+     * {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements
+     *
+     * <blockquote><pre>{@code
+     * double f = Math.random()/Math.nextDown(1.0);
+     * double x = x1*(1.0 - f) + x2*f;
+     * }</pre></blockquote>
+     *
      * @return  a pseudorandom {@code double} greater than or equal
      * to {@code 0.0} and less than {@code 1.0}.
+     * @see #nextDown(double)
      * @see Random#nextDouble()
      */
     public static double random() {
         return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
     }
 
     /**
      * Returns the sum of its arguments,
      * throwing an exception if the result overflows an {@code int}.
      *
      * @param x the first value
      * @param y the second value
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int addExact(int x, int y) {
         int r = x + y;
         // HD 2-12 Overflow iff both arguments have the opposite sign of the result
         if (((x ^ r) & (y ^ r)) < 0) {
             throw new ArithmeticException("integer overflow");
         }
         return r;
     }
 
     /**
      * Returns the sum of its arguments,
      * throwing an exception if the result overflows a {@code long}.
      *
      * @param x the first value
      * @param y the second value
      * @return the result
      * @throws ArithmeticException if the result overflows a long
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long addExact(long x, long y) {
         long r = x + y;
         // HD 2-12 Overflow iff both arguments have the opposite sign of the result
         if (((x ^ r) & (y ^ r)) < 0) {
             throw new ArithmeticException("long overflow");
         }
         return r;
     }
 
     /**
      * Returns the difference of the arguments,
      * throwing an exception if the result overflows an {@code int}.
      *
      * @param x the first value
      * @param y the second value to subtract from the first
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int subtractExact(int x, int y) {
         int r = x - y;
         // HD 2-12 Overflow iff the arguments have different signs and
-        // the sign of the result is different than the sign of x
+        // the sign of the result is different from the sign of x
         if (((x ^ y) & (x ^ r)) < 0) {
             throw new ArithmeticException("integer overflow");
         }
         return r;
     }
 
     /**
      * Returns the difference of the arguments,
      * throwing an exception if the result overflows a {@code long}.
      *
      * @param x the first value
      * @param y the second value to subtract from the first
      * @return the result
      * @throws ArithmeticException if the result overflows a long
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long subtractExact(long x, long y) {
         long r = x - y;
         // HD 2-12 Overflow iff the arguments have different signs and
-        // the sign of the result is different than the sign of x
+        // the sign of the result is different from the sign of x
         if (((x ^ y) & (x ^ r)) < 0) {
             throw new ArithmeticException("long overflow");
         }
         return r;
     }
 
     /**
      * Returns the product of the arguments,
      * throwing an exception if the result overflows an {@code int}.
      *
      * @param x the first value
      * @param y the second value
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int multiplyExact(int x, int y) {
         long r = (long)x * (long)y;
         if ((int)r != r) {
             throw new ArithmeticException("integer overflow");
         }
         return (int)r;
     }
 
     /**
+     * Returns the product of the arguments, throwing an exception if the result
+     * overflows a {@code long}.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     * @throws ArithmeticException if the result overflows a long
+     * @since 9
+     */
+    public static long multiplyExact(long x, int y) {
+        return multiplyExact(x, (long)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
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long multiplyExact(long x, long y) {
         long r = x * y;
         long ax = Math.abs(x);
         long ay = Math.abs(y);
         if (((ax | ay) >>> 31 != 0)) {
             // Some bits greater than 2^31 that might cause overflow
             // Check the result using the divide operator
             // and check for the special case of Long.MIN_VALUE * -1
            if (((y != 0) && (r / y != x)) ||
                (x == Long.MIN_VALUE && y == -1)) {
                 throw new ArithmeticException("long overflow");
             }
         }
         return r;
     }
 
     /**
      * Returns the argument incremented by one, throwing an exception if the
      * result overflows an {@code int}.
      *
      * @param a the value to increment
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int incrementExact(int a) {
         if (a == Integer.MAX_VALUE) {
             throw new ArithmeticException("integer overflow");
         }
 
         return a + 1;
     }
 
     /**
      * Returns the argument incremented by one, throwing an exception if the
      * result overflows a {@code long}.
      *
      * @param a the value to increment
      * @return the result
      * @throws ArithmeticException if the result overflows a long
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long incrementExact(long a) {
         if (a == Long.MAX_VALUE) {
             throw new ArithmeticException("long overflow");
         }
 
         return a + 1L;
     }
 
     /**
      * Returns the argument decremented by one, throwing an exception if the
      * result overflows an {@code int}.
      *
      * @param a the value to decrement
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int decrementExact(int a) {
         if (a == Integer.MIN_VALUE) {
             throw new ArithmeticException("integer overflow");
         }
 
         return a - 1;
     }
 
     /**
      * Returns the argument decremented by one, throwing an exception if the
      * result overflows a {@code long}.
      *
      * @param a the value to decrement
      * @return the result
      * @throws ArithmeticException if the result overflows a long
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long decrementExact(long a) {
         if (a == Long.MIN_VALUE) {
             throw new ArithmeticException("long overflow");
         }
 
         return a - 1L;
     }
 
     /**
      * Returns the negation of the argument, throwing an exception if the
      * result overflows an {@code int}.
      *
      * @param a the value to negate
      * @return the result
      * @throws ArithmeticException if the result overflows an int
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static int negateExact(int a) {
         if (a == Integer.MIN_VALUE) {
             throw new ArithmeticException("integer overflow");
         }
 
         return -a;
     }
 
     /**
      * Returns the negation of the argument, throwing an exception if the
      * result overflows a {@code long}.
      *
      * @param a the value to negate
      * @return the result
      * @throws ArithmeticException if the result overflows a long
      * @since 1.8
      */
+    @HotSpotIntrinsicCandidate
     public static long negateExact(long a) {
         if (a == Long.MIN_VALUE) {
             throw new ArithmeticException("long overflow");
         }
 
         return -a;
     }
 
     /**
      * Returns the value of the {@code long} argument;
      * throwing an exception if the value overflows an {@code int}.
      *
      * @param value the long value
      * @return the argument as an int
      * @throws ArithmeticException if the {@code argument} overflows an int
      * @since 1.8
      */
     public static int toIntExact(long value) {
         if ((int)value != value) {
             throw new ArithmeticException("integer overflow");
         }
         return (int)value;
     }
 
     /**
+     * Returns the exact mathematical product of the arguments.
+     *
+     * @param x the first value
+     * @param y the second value
+     * @return the result
+     * @since 9
+     */
+    public static long multiplyFull(int x, int y) {
+        return (long)x * (long)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
+     * @since 9
+     */
+    @HotSpotIntrinsicCandidate
+    public static long multiplyHigh(long x, long y) {
+        if (x < 0 || y < 0) {
+            // Use technique from section 8-2 of Henry S. Warren, Jr.,
+            // Hacker's Delight (2nd ed.) (Addison Wesley, 2013), 173-174.
+            long x1 = x >> 32;
+            long x2 = x & 0xFFFFFFFFL;
+            long y1 = y >> 32;
+            long y2 = y & 0xFFFFFFFFL;
+            long z2 = x2 * y2;
+            long t = x1 * y2 + (z2 >>> 32);
+            long z1 = t & 0xFFFFFFFFL;
+            long z0 = t >> 32;
+            z1 += x2 * y1;
+            return x1 * y1 + z0 + (z1 >> 32);
+        } else {
+            // Use Karatsuba technique with two base 2^32 digits.
+            long x1 = x >>> 32;
+            long y1 = y >>> 32;
+            long x2 = x & 0xFFFFFFFFL;
+            long y2 = y & 0xFFFFFFFFL;
+            long A = x1 * y1;
+            long B = x2 * y2;
+            long C = (x1 + x2) * (y1 + y2);
+            long K = C - A - B;
+            return (((B >>> 32) + K) >>> 32) + A;
+        }
+    }
+
+    /**
      * 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}.
+     * the result is equal to {@code Integer.MIN_VALUE}.
      * <p>
      * Normal integer division operates under the round to zero rounding mode
      * (truncation).  This operation instead acts under the round toward
      * negative infinity (floor) rounding mode.
-     * The floor rounding mode gives different results than truncation
+     * The floor rounding mode gives different results from truncation
      * when the exact result is negative.
      * <ul>
      *   <li>If the signs of the arguments are the same, the results of
      *       {@code floorDiv} and the {@code /} operator are the same.  <br>
      *       For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
      *   <li>If the signs of the arguments are different,  the quotient is negative and
      *       {@code floorDiv} returns the integer less than or equal to the quotient
      *       and the {@code /} operator returns the integer closest to zero.<br>
      *       For example, {@code floorDiv(-4, 3) == -2},
      *       whereas {@code (-4 / 3) == -1}.
      *   </li>
      * </ul>
-     * <p>
      *
      * @param x the dividend
      * @param y the divisor
      * @return the largest (closest to positive infinity)
      * {@code int} value that is less than or equal to the algebraic quotient.
      * @throws ArithmeticException if the divisor {@code y} is zero
      * @see #floorMod(int, int)
      * @see #floor(double)
      * @since 1.8
      */
     public static int floorDiv(int x, int y) {
         int r = x / y;
         // if the signs are different and modulo not zero, round down
         if ((x ^ y) < 0 && (r * y != x)) {
             r--;
         }
         return r;
     }
 
     /**
      * Returns the largest (closest to positive infinity)
      * {@code long} value that is less than or equal to the algebraic quotient.
      * There is one special case, if the dividend is the
      * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
      * then integer overflow occurs and
-     * the result is equal to the {@code Long.MIN_VALUE}.
+     * the result is equal to {@code Long.MIN_VALUE}.
      * <p>
      * Normal integer division operates under the round to zero rounding mode
      * (truncation).  This operation instead acts under the round toward
      * negative infinity (floor) rounding mode.
-     * The floor rounding mode gives different results than truncation
+     * The floor rounding mode gives different results from truncation
+     * when the exact result is negative.
+     * <p>
+     * For examples, see {@link #floorDiv(int, int)}.
+     *
+     * @param x the dividend
+     * @param y the divisor
+     * @return the largest (closest to positive infinity)
+     * {@code int} value that is less than or equal to the algebraic quotient.
+     * @throws ArithmeticException if the divisor {@code y} is zero
+     * @see #floorMod(long, int)
+     * @see #floor(double)
+     * @since 9
+     */
+    public static long floorDiv(long x, int y) {
+        return floorDiv(x, (long)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>
+     * Normal integer division operates under the round to zero rounding mode
+     * (truncation).  This operation instead acts under the round toward
+     * negative infinity (floor) rounding mode.
+     * The floor rounding mode gives different results from truncation
      * when the exact result is negative.
      * <p>
      * For examples, see {@link #floorDiv(int, int)}.
      *
      * @param x the dividend
      * @param y the divisor
      * @return the largest (closest to positive infinity)
      * {@code long} value that is less than or equal to the algebraic quotient.
      * @throws ArithmeticException if the divisor {@code y} is zero
      * @see #floorMod(long, long)
      * @see #floor(double)
      * @since 1.8
      */
     public static long floorDiv(long x, long y) {
         long r = x / y;
         // if the signs are different and modulo not zero, round down
         if ((x ^ y) < 0 && (r * y != x)) {
             r--;
         }
         return r;
     }
 
     /**
      * Returns the floor modulus of the {@code int} arguments.
      * <p>
      * The floor modulus is {@code x - (floorDiv(x, y) * y)},
      * has the same sign as the divisor {@code y}, and
      * is in the range of {@code -abs(y) < r < +abs(y)}.
      *
      * <p>
      * The relationship between {@code floorDiv} and {@code floorMod} is such that:
      * <ul>
      *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
      * </ul>
      * <p>
      * The difference in values between {@code floorMod} and
      * the {@code %} operator is due to the difference between
      * {@code floorDiv} that returns the integer less than or equal to the quotient
      * and the {@code /} operator that returns the integer closest to zero.
      * <p>
      * Examples:
      * <ul>
      *   <li>If the signs of the arguments are the same, the results
      *       of {@code floorMod} and the {@code %} operator are the same.  <br>
      *       <ul>
      *       <li>{@code floorMod(4, 3) == 1}; &nbsp; and {@code (4 % 3) == 1}</li>
      *       </ul>
      *   <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br>
      *      <ul>
      *      <li>{@code floorMod(+4, -3) == -2}; &nbsp; and {@code (+4 % -3) == +1} </li>
      *      <li>{@code floorMod(-4, +3) == +2}; &nbsp; and {@code (-4 % +3) == -1} </li>
      *      <li>{@code floorMod(-4, -3) == -1}; &nbsp; and {@code (-4 % -3) == -1 } </li>
      *      </ul>
      *   </li>
      * </ul>
      * <p>
      * If the signs of arguments are unknown and a positive modulus
      * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
      *
      * @param x the dividend
      * @param y the divisor
      * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
      * @throws ArithmeticException if the divisor {@code y} is zero
      * @see #floorDiv(int, int)
      * @since 1.8
      */
     public static int floorMod(int x, int y) {
-        int r = x - floorDiv(x, y) * y;
-        return r;
+        return x - floorDiv(x, y) * 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>
+     * For examples, see {@link #floorMod(int, int)}.
+     *
+     * @param x the dividend
+     * @param y the divisor
+     * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
+     * @throws ArithmeticException if the divisor {@code y} is zero
+     * @see #floorDiv(long, int)
+     * @since 9
+     */
+    public static int floorMod(long x, int y) {
+        // Result cannot overflow the range of int.
+        return (int)(x - floorDiv(x, y) * 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>
      * For examples, see {@link #floorMod(int, int)}.
      *
      * @param x the dividend
      * @param y the divisor
      * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
      * @throws ArithmeticException if the divisor {@code y} is zero
      * @see #floorDiv(long, long)
      * @since 1.8
      */
     public static long floorMod(long x, long y) {
         return x - floorDiv(x, y) * y;
     }
 
     /**
      * Returns the absolute value of an {@code int} value.
      * If the argument is not negative, the argument is returned.
      * If the argument is negative, the negation of the argument is returned.
      *
      * <p>Note that if the argument is equal to the value of
      * {@link Integer#MIN_VALUE}, the most negative representable
      * {@code int} value, the result is that same value, which is
      * negative.
      *
      * @param   a   the argument whose absolute value is to be determined
      * @return  the absolute value of the argument.
      */
     public static int abs(int a) {
         return (a < 0) ? -a : a;
     }
 
     /**
      * Returns the absolute value of a {@code long} value.
      * If the argument is not negative, the argument is returned.
      * If the argument is negative, the negation of the argument is returned.
      *
      * <p>Note that if the argument is equal to the value of
      * {@link Long#MIN_VALUE}, the most negative representable
      * {@code long} value, the result is that same value, which
      * is negative.
      *
      * @param   a   the argument whose absolute value is to be determined
      * @return  the absolute value of the argument.
      */
     public static long abs(long a) {
         return (a < 0) ? -a : a;
     }
 
     /**
      * Returns the absolute value of a {@code float} value.
      * If the argument is not negative, the argument is returned.
      * If the argument is negative, the negation of the argument is returned.
      * Special cases:
      * <ul><li>If the argument is positive zero or negative zero, the
      * result is positive zero.
      * <li>If the argument is infinite, the result is positive infinity.
      * <li>If the argument is NaN, the result is NaN.</ul>
-     * In other words, the result is the same as the value of the expression:
-     * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
+     *
+     * @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 (a <= 0.0F) ? 0.0F - a : a;
     }
 
     /**
      * Returns the absolute value of a {@code double} value.
      * If the argument is not negative, the argument is returned.
      * If the argument is negative, the negation of the argument is returned.
      * Special cases:
      * <ul><li>If the argument is positive zero or negative zero, the result
      * is positive zero.
      * <li>If the argument is infinite, the result is positive infinity.
      * <li>If the argument is NaN, the result is NaN.</ul>
-     * In other words, the result is the same as the value of the expression:
-     * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
+     *
+     * @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.
      */
+    @HotSpotIntrinsicCandidate
     public static double abs(double a) {
         return (a <= 0.0D) ? 0.0D - a : a;
     }
 
     /**
      * Returns the greater of two {@code int} values. That is, the
      * result is the argument closer to the value of
      * {@link Integer#MAX_VALUE}. If the arguments have the same value,
      * the result is that same value.
      *
      * @param   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 (a >= b) ? a : b;
     }
 
     /**
      * Returns the greater of two {@code long} values. That is, the
      * result is the argument closer to the value of
      * {@link Long#MAX_VALUE}. If the arguments have the same value,
      * the result is that same value.
      *
      * @param   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 (a >= b) ? a : b;
     }
 
     // Use raw bit-wise conversions on guaranteed non-NaN arguments.
-    private static long negativeZeroFloatBits  = Float.floatToRawIntBits(-0.0f);
-    private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
+    private static final long negativeZeroFloatBits  = Float.floatToRawIntBits(-0.0f);
+    private static final long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
 
     /**
      * Returns the greater of two {@code float} values.  That is,
      * the result is the argument closer to positive infinity. If the
      * arguments have the same value, the result is that same
      * value. If either value is NaN, then the result is NaN.  Unlike
      * the numerical comparison operators, this method considers
      * negative zero to be strictly smaller than positive zero. If one
      * argument is positive zero and the other negative zero, the
      * result is positive zero.
      *
      * @param   a   an argument.
      * @param   b   another argument.
      * @return  the larger of {@code a} and {@code b}.
      */
     public static float max(float a, float b) {
         if (a != a)
             return a;   // a is NaN
         if ((a == 0.0f) &&
             (b == 0.0f) &&
             (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
             // Raw conversion ok since NaN can't map to -0.0.
             return b;
         }
         return (a >= b) ? a : b;
     }
 
     /**
      * Returns the greater of two {@code double} values.  That
      * is, the result is the argument closer to positive infinity. If
      * the arguments have the same value, the result is that same
      * value. If either value is NaN, then the result is NaN.  Unlike
      * the numerical comparison operators, this method considers
      * negative zero to be strictly smaller than positive zero. If one
      * argument is positive zero and the other negative zero, the
      * result is positive zero.
      *
      * @param   a   an argument.
      * @param   b   another argument.
      * @return  the larger of {@code a} and {@code b}.
      */
     public static double max(double a, double b) {
         if (a != a)
             return a;   // a is NaN
         if ((a == 0.0d) &&
             (b == 0.0d) &&
             (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
             // Raw conversion ok since NaN can't map to -0.0.
             return b;
         }
         return (a >= b) ? a : b;
     }
 
     /**
      * Returns the smaller of two {@code int} values. That is,
      * the result the argument closer to the value of
      * {@link Integer#MIN_VALUE}.  If the arguments have the same
      * value, the result is that same value.
      *
      * @param   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 (a <= b) ? a : b;
     }
 
     /**
      * Returns the smaller of two {@code long} values. That is,
      * the result is the argument closer to the value of
      * {@link Long#MIN_VALUE}. If the arguments have the same
      * value, the result is that same value.
      *
      * @param   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 (a <= b) ? a : b;
     }
 
     /**
      * Returns the smaller of two {@code float} values.  That is,
      * the result is the value closer to negative infinity. If the
      * arguments have the same value, the result is that same
      * value. If either value is NaN, then the result is NaN.  Unlike
      * the numerical comparison operators, this method considers
      * negative zero to be strictly smaller than positive zero.  If
      * one argument is positive zero and the other is negative zero,
      * the result is negative zero.
      *
      * @param   a   an argument.
      * @param   b   another argument.
      * @return  the smaller of {@code a} and {@code b}.
      */
     public static float min(float a, float b) {
         if (a != a)
             return a;   // a is NaN
         if ((a == 0.0f) &&
             (b == 0.0f) &&
             (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
             // Raw conversion ok since NaN can't map to -0.0.
             return b;
         }
         return (a <= b) ? a : b;
     }
 
     /**
      * Returns the smaller of two {@code double} values.  That
      * is, the result is the value closer to negative infinity. If the
      * arguments have the same value, the result is that same
      * value. If either value is NaN, then the result is NaN.  Unlike
      * the numerical comparison operators, this method considers
      * negative zero to be strictly smaller than positive zero. If one
      * argument is positive zero and the other is negative zero, the
      * result is negative zero.
      *
      * @param   a   an argument.
      * @param   b   another argument.
      * @return  the smaller of {@code a} and {@code b}.
      */
     public static double min(double a, double b) {
         if (a != a)
             return a;   // a is NaN
         if ((a == 0.0d) &&
             (b == 0.0d) &&
             (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
             // Raw conversion ok since NaN can't map to -0.0.
             return b;
         }
         return (a <= b) ? a : b;
     }
 
     /**
+     * Returns the 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 fma(a, 1.0, c)} returns the same
+     * result as ({@code a + c}).  However,
+     * {@code fma(a, b, +0.0)} does <em>not</em> always return the
+     * same result as ({@code a * b}) since
+     * {@code fma(-0.0, +0.0, +0.0)} is {@code +0.0} while
+     * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fma(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
+     */
+    @HotSpotIntrinsicCandidate
+    public static double fma(double a, double b, double c) {
+        /*
+         * Infinity and NaN arithmetic is not quite the same with two
+         * roundings as opposed to just one so the simple expression
+         * "a * b + c" cannot always be used to compute the correct
+         * result.  With two roundings, the product can overflow and
+         * if the addend is infinite, a spurious NaN can be produced
+         * if the infinity from the overflow and the infinite addend
+         * have opposite signs.
+         */
+
+        // First, screen for and handle non-finite input values whose
+        // arithmetic is not supported by BigDecimal.
+        if (Double.isNaN(a) || Double.isNaN(b) || Double.isNaN(c)) {
+            return Double.NaN;
+        } else { // All inputs non-NaN
+            boolean infiniteA = Double.isInfinite(a);
+            boolean infiniteB = Double.isInfinite(b);
+            boolean infiniteC = Double.isInfinite(c);
+            double result;
+
+            if (infiniteA || infiniteB || infiniteC) {
+                if (infiniteA && b == 0.0 ||
+                    infiniteB && a == 0.0 ) {
+                    return Double.NaN;
+                }
+                // Store product in a double field to cause an
+                // overflow even if non-strictfp evaluation is being
+                // used.
+                double product = a * b;
+                if (Double.isInfinite(product) && !infiniteA && !infiniteB) {
+                    // Intermediate overflow; might cause a
+                    // spurious NaN if added to infinite c.
+                    assert Double.isInfinite(c);
+                    return c;
+                } else {
+                    result = product + c;
+                    assert !Double.isFinite(result);
+                    return result;
+                }
+            } else { // All inputs finite
+                BigDecimal product = (new BigDecimal(a)).multiply(new BigDecimal(b));
+                if (c == 0.0) { // Positive or negative zero
+                    // If the product is an exact zero, use a
+                    // floating-point expression to compute the sign
+                    // of the zero final result. The product is an
+                    // exact zero if and only if at least one of a and
+                    // b is zero.
+                    if (a == 0.0 || b == 0.0) {
+                        return a * b + c;
+                    } else {
+                        // The sign of a zero addend doesn't matter if
+                        // the product is nonzero. The sign of a zero
+                        // addend is not factored in the result if the
+                        // exact product is nonzero but underflows to
+                        // zero; see IEEE-754 2008 section 6.3 "The
+                        // sign bit".
+                        return product.doubleValue();
+                    }
+                } else {
+                    return product.add(new BigDecimal(c)).doubleValue();
+                }
+            }
+        }
+    }
+
+    /**
+     * 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
+     */
+    @HotSpotIntrinsicCandidate
+    public static float fma(float a, float b, float c) {
+        /*
+         *  Since the double format has more than twice the precision
+         *  of the float format, the multiply of a * b is exact in
+         *  double. The add of c to the product then incurs one
+         *  rounding error. Since the double format moreover has more
+         *  than (2p + 2) precision bits compared to the p bits of the
+         *  float format, the two roundings of (a * b + c), first to
+         *  the double format and then secondarily to the float format,
+         *  are equivalent to rounding the intermediate result directly
+         *  to the float format.
+         *
+         * In terms of strictfp vs default-fp concerns related to
+         * overflow and underflow, since
+         *
+         * (Float.MAX_VALUE * Float.MAX_VALUE) << Double.MAX_VALUE
+         * (Float.MIN_VALUE * Float.MIN_VALUE) >> Double.MIN_VALUE
+         *
+         * neither the multiply nor add will overflow or underflow in
+         * double. Therefore, it is not necessary for this method to
+         * be declared strictfp to have reproducible
+         * behavior. However, it is necessary to explicitly store down
+         * to a float variable to avoid returning a value in the float
+         * extended value set.
+         */
+        float result = (float)(((double) a * (double) b ) + (double) c);
+        return result;
+    }
+
+    /**
      * 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) {
         int exp = getExponent(d);
 
         switch(exp) {
-        case DoubleConsts.MAX_EXPONENT+1:       // NaN or infinity
+        case Double.MAX_EXPONENT + 1:       // NaN or infinity
             return Math.abs(d);
 
-        case DoubleConsts.MIN_EXPONENT-1:       // zero or subnormal
+        case Double.MIN_EXPONENT - 1:       // zero or subnormal
             return Double.MIN_VALUE;
 
         default:
-            assert exp <= DoubleConsts.MAX_EXPONENT && exp >= DoubleConsts.MIN_EXPONENT;
+            assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT;
 
             // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
             exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
-            if (exp >= DoubleConsts.MIN_EXPONENT) {
+            if (exp >= Double.MIN_EXPONENT) {
                 return powerOfTwoD(exp);
             }
             else {
                 // return a subnormal result; left shift integer
                 // representation of Double.MIN_VALUE appropriate
                 // number of positions
                 return Double.longBitsToDouble(1L <<
-                (exp - (DoubleConsts.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
+                (exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
             }
         }
     }
 
     /**
      * Returns the size of an ulp of the argument.  An ulp, unit in
      * the last place, of a {@code float} value is the positive
      * distance between this floating-point value and the {@code
      * float} value next larger in magnitude.  Note that for non-NaN
      * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, then the result is NaN.
      * <li> If the argument is positive or negative infinity, then the
      * result is positive infinity.
      * <li> If the argument is positive or negative zero, then the result is
      * {@code Float.MIN_VALUE}.
      * <li> If the argument is &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) {
         int exp = getExponent(f);
 
         switch(exp) {
-        case FloatConsts.MAX_EXPONENT+1:        // NaN or infinity
+        case Float.MAX_EXPONENT+1:        // NaN or infinity
             return Math.abs(f);
 
-        case FloatConsts.MIN_EXPONENT-1:        // zero or subnormal
-            return FloatConsts.MIN_VALUE;
+        case Float.MIN_EXPONENT-1:        // zero or subnormal
+            return Float.MIN_VALUE;
 
         default:
-            assert exp <= FloatConsts.MAX_EXPONENT && exp >= FloatConsts.MIN_EXPONENT;
+            assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT;
 
             // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
             exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
-            if (exp >= FloatConsts.MIN_EXPONENT) {
+            if (exp >= Float.MIN_EXPONENT) {
                 return powerOfTwoF(exp);
-            }
-            else {
+            } else {
                 // return a subnormal result; left shift integer
                 // representation of FloatConsts.MIN_VALUE appropriate
                 // number of positions
                 return Float.intBitsToFloat(1 <<
-                (exp - (FloatConsts.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
+                (exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
             }
         }
     }
 
     /**
      * Returns the signum function of the argument; zero if the argument
      * is zero, 1.0 if the argument is greater than zero, -1.0 if the
      * argument is less than zero.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, then the result is NaN.
      * <li> If the argument is positive zero or negative zero, then the
      *      result is the same as the argument.
      * </ul>
      *
      * @param d the floating-point value whose signum is to be returned
      * @return the signum function of the argument
      * @author Joseph D. Darcy
      * @since 1.5
      */
     public static double signum(double d) {
         return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d);
     }
 
     /**
      * Returns the signum function of the argument; zero if the argument
      * is zero, 1.0f if the argument is greater than zero, -1.0f if the
      * argument is less than zero.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, then the result is NaN.
      * <li> If the argument is positive zero or negative zero, then the
      *      result is the same as the argument.
      * </ul>
      *
      * @param f the floating-point value whose signum is to be returned
      * @return the signum function of the argument
      * @author Joseph D. Darcy
      * @since 1.5
      */
     public static float signum(float f) {
         return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);
     }
 
     /**
      * Returns the hyperbolic sine of a {@code double} value.
      * The hyperbolic sine of <i>x</i> is defined to be
      * (<i>e<sup>x</sup>&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>
      *
      * <p>The computed result must be within 2.5 ulps of the exact result.
      *
      * @param   x The number whose hyperbolic sine is to be returned.
      * @return  The hyperbolic sine of {@code x}.
      * @since 1.5
      */
     public static double sinh(double x) {
         return StrictMath.sinh(x);
     }
 
     /**
      * Returns the hyperbolic cosine of a {@code double} value.
      * The hyperbolic cosine of <i>x</i> is defined to be
      * (<i>e<sup>x</sup>&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>
      *
      * <p>The computed result must be within 2.5 ulps of the exact result.
      *
      * @param   x The number whose hyperbolic cosine is to be returned.
      * @return  The hyperbolic cosine of {@code x}.
      * @since 1.5
      */
     public static double cosh(double x) {
         return StrictMath.cosh(x);
     }
 
     /**
      * Returns the hyperbolic tangent of a {@code double} value.
      * The hyperbolic tangent of <i>x</i> is defined to be
      * (<i>e<sup>x</sup>&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>
      *
      * <p>The computed result must be within 2.5 ulps of the exact result.
      * The result of {@code tanh} for any finite input must have
      * an absolute value less than or equal to 1.  Note that once the
      * exact result of tanh is within 1/2 of an ulp of the limit value
      * of &plusmn;1, correctly signed &plusmn;{@code 1.0} should
      * be returned.
      *
      * @param   x The number whose hyperbolic tangent is to be returned.
      * @return  The hyperbolic tangent of {@code x}.
      * @since 1.5
      */
     public static double tanh(double x) {
         return StrictMath.tanh(x);
     }
 
     /**
      * Returns sqrt(<i>x</i><sup>2</sup>&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>
      *
      * <p>The computed result must be within 1 ulp of the exact
      * result.  If one parameter is held constant, the results must be
      * semi-monotonic in the other parameter.
      *
      * @param x a value
      * @param y a value
      * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
      * without intermediate overflow or underflow
      * @since 1.5
      */
     public static double hypot(double x, double y) {
         return StrictMath.hypot(x, y);
     }
 
     /**
      * Returns <i>e</i><sup>x</sup>&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>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.  The result of
      * {@code expm1} for any finite input must be greater than or
      * equal to {@code -1.0}.  Note that once the exact result of
      * <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1 is within 1/2
      * ulp of the limit value -1, {@code -1.0} should be
      * returned.
      *
      * @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 double expm1(double x) {
         return StrictMath.expm1(x);
     }
 
     /**
      * Returns the natural logarithm of the sum of the argument and 1.
      * Note that for small values {@code x}, the result of
      * {@code log1p(x)} is much closer to the true result of ln(1
      * + {@code x}) than the floating-point evaluation of
      * {@code log(1.0+x)}.
      *
      * <p>Special cases:
      *
      * <ul>
      *
      * <li>If the argument is NaN or less than -1, then the result is
      * NaN.
      *
      * <li>If the argument is positive infinity, then the result is
      * positive infinity.
      *
      * <li>If the argument is negative one, then the result is
      * negative infinity.
      *
      * <li>If the argument is zero, then the result is a zero with the
      * same sign as the argument.
      *
      * </ul>
      *
      * <p>The computed result must be within 1 ulp of the exact result.
      * Results must be semi-monotonic.
      *
      * @param   x   a value
      * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
      * log of {@code x}&nbsp;+&nbsp;1
      * @since 1.5
      */
     public static double log1p(double x) {
         return StrictMath.log1p(x);
     }
 
     /**
      * Returns the first floating-point argument with the sign of the
      * second floating-point argument.  Note that unlike the {@link
      * StrictMath#copySign(double, double) StrictMath.copySign}
      * method, this method does not require NaN {@code sign}
      * arguments to be treated as positive values; implementations are
      * permitted to treat some NaN arguments as positive and other NaN
      * arguments as negative to allow greater performance.
      *
      * @param magnitude  the parameter providing the magnitude of the result
      * @param sign   the parameter providing the sign of the result
      * @return a value with the magnitude of {@code magnitude}
      * and the sign of {@code sign}.
      * @since 1.6
      */
     public static double copySign(double magnitude, double sign) {
         return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
                                         (DoubleConsts.SIGN_BIT_MASK)) |
                                        (Double.doubleToRawLongBits(magnitude) &
                                         (DoubleConsts.EXP_BIT_MASK |
                                          DoubleConsts.SIGNIF_BIT_MASK)));
     }
 
     /**
      * Returns the first floating-point argument with the sign of the
      * second floating-point argument.  Note that unlike the {@link
      * StrictMath#copySign(float, float) StrictMath.copySign}
      * method, this method does not require NaN {@code sign}
      * arguments to be treated as positive values; implementations are
      * permitted to treat some NaN arguments as positive and other NaN
      * arguments as negative to allow greater performance.
      *
      * @param magnitude  the parameter providing the magnitude of the result
      * @param sign   the parameter providing the sign of the result
      * @return a value with the magnitude of {@code magnitude}
      * and the sign of {@code sign}.
      * @since 1.6
      */
     public static float copySign(float magnitude, float sign) {
         return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
                                      (FloatConsts.SIGN_BIT_MASK)) |
                                     (Float.floatToRawIntBits(magnitude) &
                                      (FloatConsts.EXP_BIT_MASK |
                                       FloatConsts.SIGNIF_BIT_MASK)));
     }
 
     /**
      * Returns the unbiased exponent used in the representation of a
      * {@code float}.  Special cases:
      *
      * <ul>
      * <li>If the argument is NaN or infinite, then the result is
      * {@link Float#MAX_EXPONENT} + 1.
      * <li>If the argument is zero or subnormal, then the result is
      * {@link Float#MIN_EXPONENT} -1.
      * </ul>
      * @param f a {@code float} value
      * @return the unbiased exponent of the argument
      * @since 1.6
      */
     public static int getExponent(float f) {
         /*
          * Bitwise convert f to integer, mask out exponent bits, shift
          * to the right and then subtract out float's bias adjust to
          * get true exponent value
          */
         return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
                 (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
     }
 
     /**
      * Returns the unbiased exponent used in the representation of a
      * {@code double}.  Special cases:
      *
      * <ul>
      * <li>If the argument is NaN or infinite, then the result is
      * {@link Double#MAX_EXPONENT} + 1.
      * <li>If the argument is zero or subnormal, then the result is
      * {@link Double#MIN_EXPONENT} -1.
      * </ul>
      * @param d a {@code double} value
      * @return the unbiased exponent of the argument
      * @since 1.6
      */
     public static int getExponent(double d) {
         /*
          * Bitwise convert d to long, mask out exponent bits, shift
          * to the right and then subtract out double's bias adjust to
          * get true exponent value.
          */
         return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
                       (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
     }
 
     /**
      * Returns the floating-point number adjacent to the first
      * argument in the direction of the second argument.  If both
      * arguments compare as equal the second argument is returned.
      *
      * <p>
      * Special cases:
      * <ul>
      * <li> If either argument is a NaN, then NaN is returned.
      *
      * <li> If both arguments are signed zeros, {@code direction}
      * is returned unchanged (as implied by the requirement of
      * returning the second argument if the arguments compare as
      * equal).
      *
      * <li> If {@code start} is
      * &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) {
         /*
          * The cases:
          *
          * nextAfter(+infinity, 0)  == MAX_VALUE
          * nextAfter(+infinity, +infinity)  == +infinity
          * nextAfter(-infinity, 0)  == -MAX_VALUE
          * nextAfter(-infinity, -infinity)  == -infinity
          *
          * are naturally handled without any additional testing
          */
 
-        // First check for NaN values
-        if (Double.isNaN(start) || Double.isNaN(direction)) {
-            // return a NaN derived from the input NaN(s)
-            return start + direction;
-        } else if (start == direction) {
-            return direction;
-        } else {        // start > direction or start < direction
+        /*
+         * IEEE 754 floating-point numbers are lexicographically
+         * ordered if treated as signed-magnitude integers.
+         * Since Java's integers are two's complement,
+         * incrementing the two's complement representation of a
+         * logically negative floating-point value *decrements*
+         * the signed-magnitude representation. Therefore, when
+         * the integer representation of a floating-point value
+         * is negative, the adjustment to the representation is in
+         * the opposite direction from what would initially be expected.
+         */
+
+        // Branch to descending case first as it is more costly than ascending
+        // case due to start != 0.0d conditional.
+        if (start > direction) { // descending
+            if (start != 0.0d) {
+                final long transducer = Double.doubleToRawLongBits(start);
+                return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L));
+            } else { // start == 0.0d && direction < 0.0d
+                return -Double.MIN_VALUE;
+            }
+        } else if (start < direction) { // ascending
             // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
             // then bitwise convert start to integer.
-            long transducer = Double.doubleToRawLongBits(start + 0.0d);
-
-            /*
-             * IEEE 754 floating-point numbers are lexicographically
-             * ordered if treated as signed- magnitude integers .
-             * Since Java's integers are two's complement,
-             * incrementing" the two's complement representation of a
-             * logically negative floating-point value *decrements*
-             * the signed-magnitude representation. Therefore, when
-             * the integer representation of a floating-point values
-             * is less than zero, the adjustment to the representation
-             * is in the opposite direction than would be expected at
-             * first .
-             */
-            if (direction > start) { // Calculate next greater value
-                transducer = transducer + (transducer >= 0L ? 1L:-1L);
-            } else  { // Calculate next lesser value
-                assert direction < start;
-                if (transducer > 0L)
-                    --transducer;
-                else
-                    if (transducer < 0L )
-                        ++transducer;
-                    /*
-                     * transducer==0, the result is -MIN_VALUE
-                     *
-                     * The transition from zero (implicitly
-                     * positive) to the smallest negative
-                     * signed magnitude value must be done
-                     * explicitly.
-                     */
-                    else
-                        transducer = DoubleConsts.SIGN_BIT_MASK | 1L;
-            }
-
-            return Double.longBitsToDouble(transducer);
+            final long transducer = Double.doubleToRawLongBits(start + 0.0d);
+            return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
+        } else if (start == direction) {
+            return direction;
+        } else { // isNaN(start) || isNaN(direction)
+            return 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) {
         /*
          * The cases:
          *
          * nextAfter(+infinity, 0)  == MAX_VALUE
          * nextAfter(+infinity, +infinity)  == +infinity
          * nextAfter(-infinity, 0)  == -MAX_VALUE
          * nextAfter(-infinity, -infinity)  == -infinity
          *
          * are naturally handled without any additional testing
          */
 
-        // First check for NaN values
-        if (Float.isNaN(start) || Double.isNaN(direction)) {
-            // return a NaN derived from the input NaN(s)
-            return start + (float)direction;
-        } else if (start == direction) {
-            return (float)direction;
-        } else {        // start > direction or start < direction
+        /*
+         * IEEE 754 floating-point numbers are lexicographically
+         * ordered if treated as signed-magnitude integers.
+         * Since Java's integers are two's complement,
+         * incrementing the two's complement representation of a
+         * logically negative floating-point value *decrements*
+         * the signed-magnitude representation. Therefore, when
+         * the integer representation of a floating-point value
+         * is negative, the adjustment to the representation is in
+         * the opposite direction from what would initially be expected.
+         */
+
+        // Branch to descending case first as it is more costly than ascending
+        // case due to start != 0.0f conditional.
+        if (start > direction) { // descending
+            if (start != 0.0f) {
+                final int transducer = Float.floatToRawIntBits(start);
+                return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1));
+            } else { // start == 0.0f && direction < 0.0f
+                return -Float.MIN_VALUE;
+            }
+        } else if (start < direction) { // ascending
             // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
             // then bitwise convert start to integer.
-            int transducer = Float.floatToRawIntBits(start + 0.0f);
-
-            /*
-             * IEEE 754 floating-point numbers are lexicographically
-             * ordered if treated as signed- magnitude integers .
-             * Since Java's integers are two's complement,
-             * incrementing" the two's complement representation of a
-             * logically negative floating-point value *decrements*
-             * the signed-magnitude representation. Therefore, when
-             * the integer representation of a floating-point values
-             * is less than zero, the adjustment to the representation
-             * is in the opposite direction than would be expected at
-             * first.
-             */
-            if (direction > start) {// Calculate next greater value
-                transducer = transducer + (transducer >= 0 ? 1:-1);
-            } else  { // Calculate next lesser value
-                assert direction < start;
-                if (transducer > 0)
-                    --transducer;
-                else
-                    if (transducer < 0 )
-                        ++transducer;
-                    /*
-                     * transducer==0, the result is -MIN_VALUE
-                     *
-                     * The transition from zero (implicitly
-                     * positive) to the smallest negative
-                     * signed magnitude value must be done
-                     * explicitly.
-                     */
-                    else
-                        transducer = FloatConsts.SIGN_BIT_MASK | 1;
-            }
-
-            return Float.intBitsToFloat(transducer);
+            final int transducer = Float.floatToRawIntBits(start + 0.0f);
+            return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
+        } else if (start == direction) {
+            return (float)direction;
+        } else { // isNaN(start) || isNaN(direction)
+            return start + (float)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) {
-        if( Double.isNaN(d) || d == Double.POSITIVE_INFINITY)
+        // Use a single conditional and handle the likely cases first.
+        if (d < Double.POSITIVE_INFINITY) {
+            // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
+            final long transducer = Double.doubleToRawLongBits(d + 0.0D);
+            return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
+        } else { // d is NaN or +Infinity
             return d;
-        else {
-            d += 0.0d;
-            return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
-                                           ((d >= 0.0d)?+1L:-1L));
         }
     }
 
     /**
      * Returns the floating-point value adjacent to {@code f} in
      * the direction of positive infinity.  This method is
      * semantically equivalent to {@code nextAfter(f,
      * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
      * implementation may run faster than its equivalent
      * {@code nextAfter} call.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, the result is NaN.
      *
      * <li> If the argument is positive infinity, the result is
      * positive infinity.
      *
      * <li> If the argument is zero, the result is
      * {@link Float#MIN_VALUE}
      *
      * </ul>
      *
      * @param f starting floating-point value
      * @return The adjacent floating-point value closer to positive
      * infinity.
      * @since 1.6
      */
     public static float nextUp(float f) {
-        if( Float.isNaN(f) || f == FloatConsts.POSITIVE_INFINITY)
+        // Use a single conditional and handle the likely cases first.
+        if (f < Float.POSITIVE_INFINITY) {
+            // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
+            final int transducer = Float.floatToRawIntBits(f + 0.0F);
+            return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
+        } else { // f is NaN or +Infinity
             return f;
-        else {
-            f += 0.0f;
-            return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
-                                        ((f >= 0.0f)?+1:-1));
         }
     }
 
     /**
      * Returns the floating-point value adjacent to {@code d} in
      * the direction of negative infinity.  This method is
      * semantically equivalent to {@code nextAfter(d,
      * Double.NEGATIVE_INFINITY)}; however, a
      * {@code nextDown} implementation may run faster than its
      * equivalent {@code nextAfter} call.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, the result is NaN.
      *
      * <li> If the argument is negative infinity, the result is
      * negative infinity.
      *
      * <li> If the argument is zero, the result is
      * {@code -Double.MIN_VALUE}
      *
      * </ul>
      *
      * @param d  starting floating-point value
      * @return The adjacent floating-point value closer to negative
      * infinity.
      * @since 1.8
      */
     public static double nextDown(double d) {
         if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
             return d;
         else {
             if (d == 0.0)
                 return -Double.MIN_VALUE;
             else
                 return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
                                                ((d > 0.0d)?-1L:+1L));
         }
     }
 
     /**
      * Returns the floating-point value adjacent to {@code f} in
      * the direction of negative infinity.  This method is
      * semantically equivalent to {@code nextAfter(f,
      * Float.NEGATIVE_INFINITY)}; however, a
      * {@code nextDown} implementation may run faster than its
      * equivalent {@code nextAfter} call.
      *
      * <p>Special Cases:
      * <ul>
      * <li> If the argument is NaN, the result is NaN.
      *
      * <li> If the argument is negative infinity, the result is
      * negative infinity.
      *
      * <li> If the argument is zero, the result is
      * {@code -Float.MIN_VALUE}
      *
      * </ul>
      *
      * @param f  starting floating-point value
      * @return The adjacent floating-point value closer to negative
      * infinity.
      * @since 1.8
      */
     public static float nextDown(float f) {
         if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
             return f;
         else {
             if (f == 0.0f)
                 return -Float.MIN_VALUE;
             else
                 return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
                                             ((f > 0.0f)?-1:+1));
         }
     }
 
     /**
      * Returns {@code d} &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) {
         /*
          * This method does not need to be declared strictfp to
          * compute the same correct result on all platforms.  When
          * scaling up, it does not matter what order the
          * multiply-store operations are done; the result will be
          * finite or overflow regardless of the operation ordering.
          * However, to get the correct result when scaling down, a
          * particular ordering must be used.
          *
          * When scaling down, the multiply-store operations are
          * sequenced so that it is not possible for two consecutive
          * multiply-stores to return subnormal results.  If one
          * multiply-store result is subnormal, the next multiply will
          * round it away to zero.  This is done by first multiplying
          * by 2 ^ (scaleFactor % n) and then multiplying several
-         * times by by 2^n as needed where n is the exponent of number
+         * times by 2^n as needed where n is the exponent of number
          * that is a covenient power of two.  In this way, at most one
          * real rounding error occurs.  If the double value set is
          * being used exclusively, the rounding will occur on a
          * multiply.  If the double-extended-exponent value set is
          * being used, the products will (perhaps) be exact but the
          * stores to d are guaranteed to round to the double value
          * set.
          *
          * It is _not_ a valid implementation to first multiply d by
          * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %
          * MIN_EXPONENT) since even in a strictfp program double
          * rounding on underflow could occur; e.g. if the scaleFactor
          * argument was (MIN_EXPONENT - n) and the exponent of d was a
          * little less than -(MIN_EXPONENT - n), meaning the final
          * result would be subnormal.
          *
          * Since exact reproducibility of this method can be achieved
          * without any undue performance burden, there is no
          * compelling reason to allow double rounding on underflow in
          * scalb.
          */
 
         // magnitude of a power of two so large that scaling a finite
         // nonzero value by it would be guaranteed to over or
-        // underflow; due to rounding, scaling down takes takes an
+        // underflow; due to rounding, scaling down takes an
         // additional power of two which is reflected here
-        final int MAX_SCALE = DoubleConsts.MAX_EXPONENT + -DoubleConsts.MIN_EXPONENT +
+        final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT +
                               DoubleConsts.SIGNIFICAND_WIDTH + 1;
         int exp_adjust = 0;
         int scale_increment = 0;
         double exp_delta = Double.NaN;
 
         // Make sure scaling factor is in a reasonable range
 
         if(scaleFactor < 0) {
             scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
             scale_increment = -512;
             exp_delta = twoToTheDoubleScaleDown;
         }
         else {
             scaleFactor = Math.min(scaleFactor, MAX_SCALE);
             scale_increment = 512;
             exp_delta = twoToTheDoubleScaleUp;
         }
 
         // Calculate (scaleFactor % +/-512), 512 = 2^9, using
         // technique from "Hacker's Delight" section 10-2.
         int t = (scaleFactor >> 9-1) >>> 32 - 9;
         exp_adjust = ((scaleFactor + t) & (512 -1)) - t;
 
         d *= powerOfTwoD(exp_adjust);
         scaleFactor -= exp_adjust;
 
         while(scaleFactor != 0) {
             d *= exp_delta;
             scaleFactor -= scale_increment;
         }
         return d;
     }
 
     /**
      * Returns {@code f} &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) {
         // magnitude of a power of two so large that scaling a finite
         // nonzero value by it would be guaranteed to over or
-        // underflow; due to rounding, scaling down takes takes an
+        // underflow; due to rounding, scaling down takes an
         // additional power of two which is reflected here
-        final int MAX_SCALE = FloatConsts.MAX_EXPONENT + -FloatConsts.MIN_EXPONENT +
+        final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT +
                               FloatConsts.SIGNIFICAND_WIDTH + 1;
 
         // Make sure scaling factor is in a reasonable range
         scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);
 
         /*
          * Since + MAX_SCALE for float fits well within the double
          * exponent range and + float -> double conversion is exact
          * the multiplication below will be exact. Therefore, the
          * rounding that occurs when the double product is cast to
          * float will be the correctly rounded float result.  Since
          * all operations other than the final multiply will be exact,
          * it is not necessary to declare this method strictfp.
          */
         return (float)((double)f*powerOfTwoD(scaleFactor));
     }
 
     // Constants used in scalb
     static double twoToTheDoubleScaleUp = powerOfTwoD(512);
     static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
 
     /**
      * Returns a floating-point power of two in the normal range.
      */
     static double powerOfTwoD(int n) {
-        assert(n >= DoubleConsts.MIN_EXPONENT && n <= DoubleConsts.MAX_EXPONENT);
+        assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT);
         return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
                                         (DoubleConsts.SIGNIFICAND_WIDTH-1))
                                        & DoubleConsts.EXP_BIT_MASK);
     }
 
     /**
      * Returns a floating-point power of two in the normal range.
      */
     static float powerOfTwoF(int n) {
-        assert(n >= FloatConsts.MIN_EXPONENT && n <= FloatConsts.MAX_EXPONENT);
+        assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT);
         return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
                                      (FloatConsts.SIGNIFICAND_WIDTH-1))
                                     & FloatConsts.EXP_BIT_MASK);
     }
 }