content: /*
   * Copyright (c) 1994, 2013, 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 sun.misc.FloatingDecimal;
  import sun.misc.FloatConsts;
  import sun.misc.DoubleConsts;
  
  /**
   * The {@code Float} class wraps a value of primitive type
   * {@code float} in an object. An object of type
   * {@code Float} contains a single field whose type is
   * {@code float}.
   *
   * <p>In addition, this class provides several methods for converting a
   * {@code float} to a {@code String} and a
   * {@code String} to a {@code float}, as well as other
   * constants and methods useful when dealing with a
   * {@code float}.
   *
   * @author  Lee Boynton
   * @author  Arthur van Hoff
   * @author  Joseph D. Darcy
   * @since JDK1.0
   */
  public final class Float extends Number implements Comparable<Float> {
      /**
       * A constant holding the positive infinity of type
       * {@code float}. It is equal to the value returned by
       * {@code Float.intBitsToFloat(0x7f800000)}.
       */
      public static final float POSITIVE_INFINITY = 1.0f / 0.0f;
  
      /**
       * A constant holding the negative infinity of type
       * {@code float}. It is equal to the value returned by
       * {@code Float.intBitsToFloat(0xff800000)}.
       */
      public static final float NEGATIVE_INFINITY = -1.0f / 0.0f;
  
      /**
       * A constant holding a Not-a-Number (NaN) value of type
       * {@code float}.  It is equivalent to the value returned by
       * {@code Float.intBitsToFloat(0x7fc00000)}.
       */
      public static final float NaN = 0.0f / 0.0f;
  
      /**
       * A constant holding the largest positive finite value of type
       * {@code float}, (2-2<sup>-23</sup>)&middot;2<sup>127</sup>.
       * It is equal to the hexadecimal floating-point literal
       * {@code 0x1.fffffeP+127f} and also equal to
       * {@code Float.intBitsToFloat(0x7f7fffff)}.
       */
      public static final float MAX_VALUE = 0x1.fffffeP+127f; // 3.4028235e+38f
  
      /**
       * A constant holding the smallest positive normal value of type
       * {@code float}, 2<sup>-126</sup>.  It is equal to the
       * hexadecimal floating-point literal {@code 0x1.0p-126f} and also
       * equal to {@code Float.intBitsToFloat(0x00800000)}.
       *
       * @since 1.6
       */
      public static final float MIN_NORMAL = 0x1.0p-126f; // 1.17549435E-38f
  
      /**
       * A constant holding the smallest positive nonzero value of type
       * {@code float}, 2<sup>-149</sup>. It is equal to the
       * hexadecimal floating-point literal {@code 0x0.000002P-126f}
       * and also equal to {@code Float.intBitsToFloat(0x1)}.
       */
      public static final float MIN_VALUE = 0x0.000002P-126f; // 1.4e-45f
  
      /**
       * Maximum exponent a finite {@code float} variable may have.  It
       * is equal to the value returned by {@code
       * Math.getExponent(Float.MAX_VALUE)}.
       *
       * @since 1.6
       */
      public static final int MAX_EXPONENT = 127;
  
      /**
       * Minimum exponent a normalized {@code float} variable may have.
       * It is equal to the value returned by {@code
       * Math.getExponent(Float.MIN_NORMAL)}.
       *
       * @since 1.6
       */
      public static final int MIN_EXPONENT = -126;
  
      /**
       * The number of bits used to represent a {@code float} value.
       *
       * @since 1.5
       */
      public static final int SIZE = 32;
  
      /**
       * The number of bytes used to represent a {@code float} value.
       *
       * @since 1.8
       */
      public static final int BYTES = SIZE / Byte.SIZE;
  
      /**
       * The {@code Class} instance representing the primitive type
       * {@code float}.
       *
       * @since JDK1.1
       */
      @SuppressWarnings("unchecked")
      public static final Class<Float> TYPE = (Class<Float>) Class.getPrimitiveClass("float");
  
      /**
       * Returns a string representation of the {@code float}
       * argument. All characters mentioned below are ASCII characters.
       * <ul>
       * <li>If the argument is NaN, the result is the string
       * "{@code NaN}".
       * <li>Otherwise, the result is a string that represents the sign and
       *     magnitude (absolute value) of the argument. If the sign is
       *     negative, the first character of the result is
       *     '{@code -}' ({@code '\u005Cu002D'}); if the sign is
       *     positive, no sign character appears in the result. As for
       *     the magnitude <i>m</i>:
       * <ul>
       * <li>If <i>m</i> is infinity, it is represented by the characters
       *     {@code "Infinity"}; thus, positive infinity produces
       *     the result {@code "Infinity"} and negative infinity
       *     produces the result {@code "-Infinity"}.
       * <li>If <i>m</i> is zero, it is represented by the characters
       *     {@code "0.0"}; thus, negative zero produces the result
       *     {@code "-0.0"} and positive zero produces the result
       *     {@code "0.0"}.
       * <li> If <i>m</i> is greater than or equal to 10<sup>-3</sup> but
       *      less than 10<sup>7</sup>, then it is represented as the
       *      integer part of <i>m</i>, in decimal form with no leading
       *      zeroes, followed by '{@code .}'
       *      ({@code '\u005Cu002E'}), followed by one or more
       *      decimal digits representing the fractional part of
       *      <i>m</i>.
       * <li> If <i>m</i> is less than 10<sup>-3</sup> or greater than or
       *      equal to 10<sup>7</sup>, then it is represented in
       *      so-called "computerized scientific notation." Let <i>n</i>
       *      be the unique integer such that 10<sup><i>n</i> </sup>&le;
       *      <i>m</i> {@literal <} 10<sup><i>n</i>+1</sup>; then let <i>a</i>
       *      be the mathematically exact quotient of <i>m</i> and
       *      10<sup><i>n</i></sup> so that 1 &le; <i>a</i> {@literal <} 10.
       *      The magnitude is then represented as the integer part of
       *      <i>a</i>, as a single decimal digit, followed by
       *      '{@code .}' ({@code '\u005Cu002E'}), followed by
       *      decimal digits representing the fractional part of
       *      <i>a</i>, followed by the letter '{@code E}'
       *      ({@code '\u005Cu0045'}), followed by a representation
       *      of <i>n</i> as a decimal integer, as produced by the
       *      method {@link Integer#toString(int)}.
       *
       * </ul>
       * </ul>
       * How many digits must be printed for the fractional part of
       * <i>m</i> or <i>a</i>? There must be at least one digit
       * to represent the fractional part, and beyond that as many, but
       * only as many, more digits as are needed to uniquely distinguish
       * the argument value from adjacent values of type
       * {@code float}. That is, suppose that <i>x</i> is the
       * exact mathematical value represented by the decimal
       * representation produced by this method for a finite nonzero
       * argument <i>f</i>. Then <i>f</i> must be the {@code float}
       * value nearest to <i>x</i>; or, if two {@code float} values are
       * equally close to <i>x</i>, then <i>f</i> must be one of
       * them and the least significant bit of the significand of
       * <i>f</i> must be {@code 0}.
       *
       * <p>To create localized string representations of a floating-point
       * value, use subclasses of {@link java.text.NumberFormat}.
       *
       * @param   f   the float to be converted.
       * @return a string representation of the argument.
       */
      public static String toString(float f) {
          return FloatingDecimal.toJavaFormatString(f);
      }
  
      /**
       * Returns a hexadecimal string representation of the
       * {@code float} argument. All characters mentioned below are
       * ASCII characters.
       *
       * <ul>
       * <li>If the argument is NaN, the result is the string
       *     "{@code NaN}".
       * <li>Otherwise, the result is a string that represents the sign and
       * magnitude (absolute value) of the argument. If the sign is negative,
       * the first character of the result is '{@code -}'
       * ({@code '\u005Cu002D'}); if the sign is positive, no sign character
       * appears in the result. As for the magnitude <i>m</i>:
       *
       * <ul>
       * <li>If <i>m</i> is infinity, it is represented by the string
       * {@code "Infinity"}; thus, positive infinity produces the
       * result {@code "Infinity"} and negative infinity produces
       * the result {@code "-Infinity"}.
       *
       * <li>If <i>m</i> is zero, it is represented by the string
       * {@code "0x0.0p0"}; thus, negative zero produces the result
       * {@code "-0x0.0p0"} and positive zero produces the result
       * {@code "0x0.0p0"}.
       *
       * <li>If <i>m</i> is a {@code float} value with a
       * normalized representation, substrings are used to represent the
       * significand and exponent fields.  The significand is
       * represented by the characters {@code "0x1."}
       * followed by a lowercase hexadecimal representation of the rest
       * of the significand as a fraction.  Trailing zeros in the
       * hexadecimal representation are removed unless all the digits
       * are zero, in which case a single zero is used. Next, the
       * exponent is represented by {@code "p"} followed
       * by a decimal string of the unbiased exponent as if produced by
       * a call to {@link Integer#toString(int) Integer.toString} on the
       * exponent value.
       *
       * <li>If <i>m</i> is a {@code float} value with a subnormal
       * representation, the significand is represented by the
       * characters {@code "0x0."} followed by a
       * hexadecimal representation of the rest of the significand as a
       * fraction.  Trailing zeros in the hexadecimal representation are
       * removed. Next, the exponent is represented by
       * {@code "p-126"}.  Note that there must be at
       * least one nonzero digit in a subnormal significand.
       *
       * </ul>
       *
       * </ul>
       *
       * <table border>
       * <caption>Examples</caption>
       * <tr><th>Floating-point Value</th><th>Hexadecimal String</th>
       * <tr><td>{@code 1.0}</td> <td>{@code 0x1.0p0}</td>
       * <tr><td>{@code -1.0}</td>        <td>{@code -0x1.0p0}</td>
       * <tr><td>{@code 2.0}</td> <td>{@code 0x1.0p1}</td>
       * <tr><td>{@code 3.0}</td> <td>{@code 0x1.8p1}</td>
       * <tr><td>{@code 0.5}</td> <td>{@code 0x1.0p-1}</td>
       * <tr><td>{@code 0.25}</td>        <td>{@code 0x1.0p-2}</td>
       * <tr><td>{@code Float.MAX_VALUE}</td>
       *     <td>{@code 0x1.fffffep127}</td>
       * <tr><td>{@code Minimum Normal Value}</td>
       *     <td>{@code 0x1.0p-126}</td>
       * <tr><td>{@code Maximum Subnormal Value}</td>
       *     <td>{@code 0x0.fffffep-126}</td>
       * <tr><td>{@code Float.MIN_VALUE}</td>
       *     <td>{@code 0x0.000002p-126}</td>
       * </table>
       * @param   f   the {@code float} to be converted.
       * @return a hex string representation of the argument.
       * @since 1.5
       * @author Joseph D. Darcy
       */
      public static String toHexString(float f) {
          if (Math.abs(f) < FloatConsts.MIN_NORMAL
              &&  f != 0.0f ) {// float subnormal
              // Adjust exponent to create subnormal double, then
              // replace subnormal double exponent with subnormal float
              // exponent
              String s = Double.toHexString(Math.scalb((double)f,
                                                       /* -1022+126 */
                                                       DoubleConsts.MIN_EXPONENT-
                                                       FloatConsts.MIN_EXPONENT));
              return s.replaceFirst("p-1022$", "p-126");
          }
          else // double string will be the same as float string
              return Double.toHexString(f);
      }
  
      /**
       * Returns a {@code Float} object holding the
       * {@code float} value represented by the argument string
       * {@code s}.
       *
       * <p>If {@code s} is {@code null}, then a
       * {@code NullPointerException} is thrown.
       *
       * <p>Leading and trailing whitespace characters in {@code s}
       * are ignored.  Whitespace is removed as if by the {@link
       * String#trim} method; that is, both ASCII space and control
       * characters are removed. The rest of {@code s} should
       * constitute a <i>FloatValue</i> as described by the lexical
       * syntax rules:
       *
       * <blockquote>
       * <dl>
       * <dt><i>FloatValue:</i>
       * <dd><i>Sign<sub>opt</sub></i> {@code NaN}
       * <dd><i>Sign<sub>opt</sub></i> {@code Infinity}
       * <dd><i>Sign<sub>opt</sub> FloatingPointLiteral</i>
       * <dd><i>Sign<sub>opt</sub> HexFloatingPointLiteral</i>
       * <dd><i>SignedInteger</i>
       * </dl>
       *
       * <dl>
       * <dt><i>HexFloatingPointLiteral</i>:
       * <dd> <i>HexSignificand BinaryExponent FloatTypeSuffix<sub>opt</sub></i>
       * </dl>
       *
       * <dl>
       * <dt><i>HexSignificand:</i>
       * <dd><i>HexNumeral</i>
       * <dd><i>HexNumeral</i> {@code .}
       * <dd>{@code 0x} <i>HexDigits<sub>opt</sub>
       *     </i>{@code .}<i> HexDigits</i>
       * <dd>{@code 0X}<i> HexDigits<sub>opt</sub>
       *     </i>{@code .} <i>HexDigits</i>
       * </dl>
       *
       * <dl>
       * <dt><i>BinaryExponent:</i>
       * <dd><i>BinaryExponentIndicator SignedInteger</i>
       * </dl>
       *
       * <dl>
       * <dt><i>BinaryExponentIndicator:</i>
       * <dd>{@code p}
       * <dd>{@code P}
       * </dl>
       *
       * </blockquote>
       *
       * where <i>Sign</i>, <i>FloatingPointLiteral</i>,
       * <i>HexNumeral</i>, <i>HexDigits</i>, <i>SignedInteger</i> and
       * <i>FloatTypeSuffix</i> are as defined in the lexical structure
       * sections of
       * <cite>The Java&trade; Language Specification</cite>,
       * except that underscores are not accepted between digits.
       * If {@code s} does not have the form of
       * a <i>FloatValue</i>, then a {@code NumberFormatException}
       * is thrown. Otherwise, {@code s} is regarded as
       * representing an exact decimal value in the usual
       * "computerized scientific notation" or as an exact
       * hexadecimal value; this exact numerical value is then
       * conceptually converted to an "infinitely precise"
       * binary value that is then rounded to type {@code float}
       * by the usual round-to-nearest rule of IEEE 754 floating-point
       * arithmetic, which includes preserving the sign of a zero
       * value.
       *
       * Note that the round-to-nearest rule also implies overflow and
       * underflow behaviour; if the exact value of {@code s} is large
       * enough in magnitude (greater than or equal to ({@link
       * #MAX_VALUE} + {@link Math#ulp(float) ulp(MAX_VALUE)}/2),
       * rounding to {@code float} will result in an infinity and if the
       * exact value of {@code s} is small enough in magnitude (less
       * than or equal to {@link #MIN_VALUE}/2), rounding to float will
       * result in a zero.
       *
       * Finally, after rounding a {@code Float} object representing
       * this {@code float} value is returned.
       *
       * <p>To interpret localized string representations of a
       * floating-point value, use subclasses of {@link
       * java.text.NumberFormat}.
       *
       * <p>Note that trailing format specifiers, specifiers that
       * determine the type of a floating-point literal
       * ({@code 1.0f} is a {@code float} value;
       * {@code 1.0d} is a {@code double} value), do
       * <em>not</em> influence the results of this method.  In other
       * words, the numerical value of the input string is converted
       * directly to the target floating-point type.  In general, the
       * two-step sequence of conversions, string to {@code double}
       * followed by {@code double} to {@code float}, is
       * <em>not</em> equivalent to converting a string directly to
       * {@code float}.  For example, if first converted to an
       * intermediate {@code double} and then to
       * {@code float}, the string<br>
       * {@code "1.00000017881393421514957253748434595763683319091796875001d"}<br>
       * results in the {@code float} value
       * {@code 1.0000002f}; if the string is converted directly to
       * {@code float}, <code>1.000000<b>1</b>f</code> results.
       *
       * <p>To avoid calling this method on an invalid string and having
       * a {@code NumberFormatException} be thrown, the documentation
       * for {@link Double#valueOf Double.valueOf} lists a regular
       * expression which can be used to screen the input.
       *
       * @param   s   the string to be parsed.
       * @return  a {@code Float} object holding the value
       *          represented by the {@code String} argument.
       * @throws  NumberFormatException  if the string does not contain a
       *          parsable number.
       */
      public static Float valueOf(String s) throws NumberFormatException {
          return new Float(parseFloat(s));
      }
  
      /**
       * Returns a {@code Float} instance representing the specified
       * {@code float} value.
       * If a new {@code Float} instance is not required, this method
       * should generally be used in preference to the constructor
       * {@link #Float(float)}, as this method is likely to yield
       * significantly better space and time performance by caching
       * frequently requested values.
       *
       * @param  f a float value.
       * @return a {@code Float} instance representing {@code f}.
       * @since  1.5
       */
      public static Float valueOf(float f) {
          return new Float(f);
      }
  
      /**
       * Returns a new {@code float} initialized to the value
       * represented by the specified {@code String}, as performed
       * by the {@code valueOf} method of class {@code Float}.
       *
       * @param  s the string to be parsed.
       * @return the {@code float} value represented by the string
       *         argument.
       * @throws NullPointerException  if the string is null
       * @throws NumberFormatException if the string does not contain a
       *               parsable {@code float}.
       * @see    Float#valueOf(String)
       * @since 1.2
       */
      public static float parseFloat(String s) throws NumberFormatException {
          return FloatingDecimal.parseFloat(s);
      }
  
      /**
       * Returns {@code true} if the specified number is a
       * Not-a-Number (NaN) value, {@code false} otherwise.
       *
       * @param   v   the value to be tested.
       * @return  {@code true} if the argument is NaN;
       *          {@code false} otherwise.
       */
      public static boolean isNaN(float v) {
          return (v != v);
      }
  
      /**
       * Returns {@code true} if the specified number is infinitely
       * large in magnitude, {@code false} otherwise.
       *
       * @param   v   the value to be tested.
       * @return  {@code true} if the argument is positive infinity or
       *          negative infinity; {@code false} otherwise.
       */
      public static boolean isInfinite(float v) {
          return (v == POSITIVE_INFINITY) || (v == NEGATIVE_INFINITY);
      }
  
  
      /**
       * Returns {@code true} if the argument is a finite floating-point
       * value; returns {@code false} otherwise (for NaN and infinity
       * arguments).
       *
       * @param f the {@code float} value to be tested
       * @return {@code true} if the argument is a finite
       * floating-point value, {@code false} otherwise.
       * @since 1.8
       */
       public static boolean isFinite(float f) {
          return Math.abs(f) <= FloatConsts.MAX_VALUE;
      }
  
      /**
       * The value of the Float.
       *
       * @serial
       */
      private final float value;
  
      /**
       * Constructs a newly allocated {@code Float} object that
       * represents the primitive {@code float} argument.
       *
       * @param   value   the value to be represented by the {@code Float}.
       */
      public Float(float value) {
          this.value = value;
      }
  
      /**
       * Constructs a newly allocated {@code Float} object that
       * represents the argument converted to type {@code float}.
       *
       * @param   value   the value to be represented by the {@code Float}.
       */
      public Float(double value) {
          this.value = (float)value;
      }
  
      /**
       * Constructs a newly allocated {@code Float} object that
       * represents the floating-point value of type {@code float}
       * represented by the string. The string is converted to a
       * {@code float} value as if by the {@code valueOf} method.
       *
       * @param      s   a string to be converted to a {@code Float}.
       * @throws  NumberFormatException  if the string does not contain a
       *               parsable number.
       * @see        Float#valueOf(String)
       */
      public Float(String s) throws NumberFormatException {
          value = parseFloat(s);
      }
  
      /**
       * Returns {@code true} if this {@code Float} value is a
       * Not-a-Number (NaN), {@code false} otherwise.
       *
       * @return  {@code true} if the value represented by this object is
       *          NaN; {@code false} otherwise.
       */
      public boolean isNaN() {
          return isNaN(value);
      }
  
      /**
       * Returns {@code true} if this {@code Float} value is
       * infinitely large in magnitude, {@code false} otherwise.
       *
       * @return  {@code true} if the value represented by this object is
       *          positive infinity or negative infinity;
       *          {@code false} otherwise.
       */
      public boolean isInfinite() {
          return isInfinite(value);
      }
  
      /**
       * Returns a string representation of this {@code Float} object.
       * The primitive {@code float} value represented by this object
       * is converted to a {@code String} exactly as if by the method
       * {@code toString} of one argument.
       *
       * @return  a {@code String} representation of this object.
       * @see Float#toString(float)
       */
      public String toString() {
          return Float.toString(value);
      }
  
      /**
       * Returns the value of this {@code Float} as a {@code byte} after
       * a narrowing primitive conversion.
       *
       * @return  the {@code float} value represented by this object
       *          converted to type {@code byte}
       * @jls 5.1.3 Narrowing Primitive Conversions
       */
      public byte byteValue() {
          return (byte)value;
      }
  
      /**
       * Returns the value of this {@code Float} as a {@code short}
       * after a narrowing primitive conversion.
       *
       * @return  the {@code float} value represented by this object
       *          converted to type {@code short}
       * @jls 5.1.3 Narrowing Primitive Conversions
       * @since JDK1.1
       */
      public short shortValue() {
          return (short)value;
      }
  
      /**
       * Returns the value of this {@code Float} as an {@code int} after
       * a narrowing primitive conversion.
       *
       * @return  the {@code float} value represented by this object
       *          converted to type {@code int}
       * @jls 5.1.3 Narrowing Primitive Conversions
       */
      public int intValue() {
          return (int)value;
      }
  
      /**
       * Returns value of this {@code Float} as a {@code long} after a
       * narrowing primitive conversion.
       *
       * @return  the {@code float} value represented by this object
       *          converted to type {@code long}
       * @jls 5.1.3 Narrowing Primitive Conversions
       */
      public long longValue() {
          return (long)value;
      }
  
      /**
       * Returns the {@code float} value of this {@code Float} object.
       *
       * @return the {@code float} value represented by this object
       */
      public float floatValue() {
          return value;
      }
  
      /**
       * Returns the value of this {@code Float} as a {@code double}
       * after a widening primitive conversion.
       *
       * @return the {@code float} value represented by this
       *         object converted to type {@code double}
       * @jls 5.1.2 Widening Primitive Conversions
       */
      public double doubleValue() {
          return (double)value;
      }
  
      /**
       * Returns a hash code for this {@code Float} object. The
       * result is the integer bit representation, exactly as produced
       * by the method {@link #floatToIntBits(float)}, of the primitive
       * {@code float} value represented by this {@code Float}
       * object.
       *
       * @return a hash code value for this object.
       */
      @Override
      public int hashCode() {
          return Float.hashCode(value);
      }
  
      /**
       * Returns a hash code for a {@code float} value; compatible with
       * {@code Float.hashCode()}.
       *
       * @param value the value to hash
       * @return a hash code value for a {@code float} value.
       * @since 1.8
       */
      public static int hashCode(float value) {
          return floatToIntBits(value);
      }
  
      /**
  
       * Compares this object against the specified object.  The result
       * is {@code true} if and only if the argument is not
       * {@code null} and is a {@code Float} object that
       * represents a {@code float} with the same value as the
       * {@code float} represented by this object. For this
       * purpose, two {@code float} values are considered to be the
       * same if and only if the method {@link #floatToIntBits(float)}
       * returns the identical {@code int} value when applied to
       * each.
       *
       * <p>Note that in most cases, for two instances of class
       * {@code Float}, {@code f1} and {@code f2}, the value
       * of {@code f1.equals(f2)} is {@code true} if and only if
       *
       * <blockquote><pre>
       *   f1.floatValue() == f2.floatValue()
       * </pre></blockquote>
       *
       * <p>also has the value {@code true}. However, there are two exceptions:
       * <ul>
       * <li>If {@code f1} and {@code f2} both represent
       *     {@code Float.NaN}, then the {@code equals} method returns
       *     {@code true}, even though {@code Float.NaN==Float.NaN}
       *     has the value {@code false}.
       * <li>If {@code f1} represents {@code +0.0f} while
       *     {@code f2} represents {@code -0.0f}, or vice
       *     versa, the {@code equal} test has the value
       *     {@code false}, even though {@code 0.0f==-0.0f}
       *     has the value {@code true}.
       * </ul>
       *
       * This definition allows hash tables to operate properly.
       *
       * @param obj the object to be compared
       * @return  {@code true} if the objects are the same;
       *          {@code false} otherwise.
       * @see Float#floatToIntBits(float)
       */
      public boolean equals(Object obj) {
          return (obj instanceof Float)
                 && (floatToIntBits(((Float)obj).value) == floatToIntBits(value));
      }
  
      /**
       * Returns a representation of the specified floating-point value
       * according to the IEEE 754 floating-point "single format" bit
       * layout.
       *
       * <p>Bit 31 (the bit that is selected by the mask
       * {@code 0x80000000}) represents the sign of the floating-point
       * number.
       * Bits 30-23 (the bits that are selected by the mask
       * {@code 0x7f800000}) represent the exponent.
       * Bits 22-0 (the bits that are selected by the mask
       * {@code 0x007fffff}) represent the significand (sometimes called
       * the mantissa) of the floating-point number.
       *
       * <p>If the argument is positive infinity, the result is
       * {@code 0x7f800000}.
       *
       * <p>If the argument is negative infinity, the result is
       * {@code 0xff800000}.
       *
       * <p>If the argument is NaN, the result is {@code 0x7fc00000}.
       *
       * <p>In all cases, the result is an integer that, when given to the
       * {@link #intBitsToFloat(int)} method, will produce a floating-point
       * value the same as the argument to {@code floatToIntBits}
       * (except all NaN values are collapsed to a single
       * "canonical" NaN value).
       *
       * @param   value   a floating-point number.
       * @return the bits that represent the floating-point number.
       */
      public static int floatToIntBits(float value) {
          int result = floatToRawIntBits(value);
          // Check for NaN based on values of bit fields, maximum
          // exponent and nonzero significand.
          if ( ((result & FloatConsts.EXP_BIT_MASK) ==
                FloatConsts.EXP_BIT_MASK) &&
               (result & FloatConsts.SIGNIF_BIT_MASK) != 0)
              result = 0x7fc00000;
          return result;
      }
  
      /**
       * Returns a representation of the specified floating-point value
       * according to the IEEE 754 floating-point "single format" bit
       * layout, preserving Not-a-Number (NaN) values.
       *
       * <p>Bit 31 (the bit that is selected by the mask
       * {@code 0x80000000}) represents the sign of the floating-point
       * number.
       * Bits 30-23 (the bits that are selected by the mask
       * {@code 0x7f800000}) represent the exponent.
       * Bits 22-0 (the bits that are selected by the mask
       * {@code 0x007fffff}) represent the significand (sometimes called
       * the mantissa) of the floating-point number.
       *
       * <p>If the argument is positive infinity, the result is
       * {@code 0x7f800000}.
       *
       * <p>If the argument is negative infinity, the result is
       * {@code 0xff800000}.
       *
       * <p>If the argument is NaN, the result is the integer representing
       * the actual NaN value.  Unlike the {@code floatToIntBits}
       * method, {@code floatToRawIntBits} does not collapse all the
       * bit patterns encoding a NaN to a single "canonical"
       * NaN value.
       *
       * <p>In all cases, the result is an integer that, when given to the
       * {@link #intBitsToFloat(int)} method, will produce a
       * floating-point value the same as the argument to
       * {@code floatToRawIntBits}.
       *
       * @param   value   a floating-point number.
       * @return the bits that represent the floating-point number.
       * @since 1.3
       */
      public static native int floatToRawIntBits(float value);
  
      /**
       * Returns the {@code float} value corresponding to a given
       * bit representation.
       * The argument is considered to be a representation of a
       * floating-point value according to the IEEE 754 floating-point
       * "single format" bit layout.
       *
       * <p>If the argument is {@code 0x7f800000}, the result is positive
       * infinity.
       *
       * <p>If the argument is {@code 0xff800000}, the result is negative
       * infinity.
       *
       * <p>If the argument is any value in the range
       * {@code 0x7f800001} through {@code 0x7fffffff} or in
       * the range {@code 0xff800001} through
       * {@code 0xffffffff}, the result is a NaN.  No IEEE 754
       * floating-point operation provided by Java can distinguish
       * between two NaN values of the same type with different bit
       * patterns.  Distinct values of NaN are only distinguishable by
       * use of the {@code Float.floatToRawIntBits} method.
       *
       * <p>In all other cases, let <i>s</i>, <i>e</i>, and <i>m</i> be three
       * values that can be computed from the argument:
       *
       * <blockquote><pre>{@code
       * int s = ((bits >> 31) == 0) ? 1 : -1;
       * int e = ((bits >> 23) & 0xff);
       * int m = (e == 0) ?
       *                 (bits & 0x7fffff) << 1 :
       *                 (bits & 0x7fffff) | 0x800000;
       * }</pre></blockquote>
       *
       * Then the floating-point result equals the value of the mathematical
       * expression <i>s</i>&middot;<i>m</i>&middot;2<sup><i>e</i>-150</sup>.
       *
       * <p>Note that this method may not be able to return a
       * {@code float} NaN with exactly same bit pattern as the
       * {@code int} argument.  IEEE 754 distinguishes between two
       * kinds of NaNs, quiet NaNs and <i>signaling NaNs</i>.  The
       * differences between the two kinds of NaN are generally not
       * visible in Java.  Arithmetic operations on signaling NaNs turn
       * them into quiet NaNs with a different, but often similar, bit
       * pattern.  However, on some processors merely copying a
       * signaling NaN also performs that conversion.  In particular,
       * copying a signaling NaN to return it to the calling method may
       * perform this conversion.  So {@code intBitsToFloat} may
       * not be able to return a {@code float} with a signaling NaN
       * bit pattern.  Consequently, for some {@code int} values,
       * {@code floatToRawIntBits(intBitsToFloat(start))} may
       * <i>not</i> equal {@code start}.  Moreover, which
       * particular bit patterns represent signaling NaNs is platform
       * dependent; although all NaN bit patterns, quiet or signaling,
       * must be in the NaN range identified above.
       *
       * @param   bits   an integer.
       * @return  the {@code float} floating-point value with the same bit
       *          pattern.
       */
      public static native float intBitsToFloat(int bits);
  
      /**
       * Compares two {@code Float} objects numerically.  There are
       * two ways in which comparisons performed by this method differ
       * from those performed by the Java language numerical comparison
       * operators ({@code <, <=, ==, >=, >}) when
       * applied to primitive {@code float} values:
       *
       * <ul><li>
       *          {@code Float.NaN} is considered by this method to
       *          be equal to itself and greater than all other
       *          {@code float} values
       *          (including {@code Float.POSITIVE_INFINITY}).
       * <li>
       *          {@code 0.0f} is considered by this method to be greater
       *          than {@code -0.0f}.
       * </ul>
       *
       * This ensures that the <i>natural ordering</i> of {@code Float}
       * objects imposed by this method is <i>consistent with equals</i>.
       *
       * @param   anotherFloat   the {@code Float} to be compared.
       * @return  the value {@code 0} if {@code anotherFloat} is
       *          numerically equal to this {@code Float}; a value
       *          less than {@code 0} if this {@code Float}
       *          is numerically less than {@code anotherFloat};
       *          and a value greater than {@code 0} if this
       *          {@code Float} is numerically greater than
       *          {@code anotherFloat}.
       *
       * @since   1.2
       * @see Comparable#compareTo(Object)
       */
      public int compareTo(Float anotherFloat) {
          return Float.compare(value, anotherFloat.value);
      }
  
      /**
       * Compares the two specified {@code float} values. The sign
       * of the integer value returned is the same as that of the
       * integer that would be returned by the call:
       * <pre>
       *    new Float(f1).compareTo(new Float(f2))
       * </pre>
       *
       * @param   f1        the first {@code float} to compare.
       * @param   f2        the second {@code float} to compare.
       * @return  the value {@code 0} if {@code f1} is
       *          numerically equal to {@code f2}; a value less than
       *          {@code 0} if {@code f1} is numerically less than
       *          {@code f2}; and a value greater than {@code 0}
       *          if {@code f1} is numerically greater than
       *          {@code f2}.
       * @since 1.4
       */
      public static int compare(float f1, float f2) {
          if (f1 < f2)
              return -1;           // Neither val is NaN, thisVal is smaller
          if (f1 > f2)
              return 1;            // Neither val is NaN, thisVal is larger
  
          // Cannot use floatToRawIntBits because of possibility of NaNs.
          int thisBits    = Float.floatToIntBits(f1);
          int anotherBits = Float.floatToIntBits(f2);
  
          return (thisBits == anotherBits ?  0 : // Values are equal
                  (thisBits < anotherBits ? -1 : // (-0.0, 0.0) or (!NaN, NaN)
                   1));                          // (0.0, -0.0) or (NaN, !NaN)
      }
  
      /**
       * Adds two {@code float} values together as per the + operator.
       *
       * @param a the first operand
       * @param b the second operand
       * @return the sum of {@code a} and {@code b}
       * @jls 4.2.4 Floating-Point Operations
       * @see java.util.function.BinaryOperator
       * @since 1.8
       */
      public static float sum(float a, float b) {
          return a + b;
      }
  
      /**
       * Returns the greater of two {@code float} values
       * as if by calling {@link Math#max(float, float) Math.max}.
       *
       * @param a the first operand
       * @param b the second operand
       * @return the greater of {@code a} and {@code b}
       * @see java.util.function.BinaryOperator
       * @since 1.8
       */
      public static float max(float a, float b) {
          return Math.max(a, b);
      }
  
      /**
       * Returns the smaller of two {@code float} values
       * as if by calling {@link Math#min(float, float) Math.min}.
       *
       * @param a the first operand
       * @param b the second operand
       * @return the smaller of {@code a} and {@code b}
       * @see java.util.function.BinaryOperator
       * @since 1.8
       */
      public static float min(float a, float b) {
          return Math.min(a, b);
      }
  
      /** use serialVersionUID from JDK 1.0.2 for interoperability */
      private static final long serialVersionUID = -2671257302660747028L;
  }
  