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    2    * Copyright (c) 1999, 2011, Oracle and/or its affiliates. All rights reserved.
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    4    *
    5    * This code is free software; you can redistribute it and/or modify it
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    8    * particular file as subject to the "Classpath" exception as provided
    9    * by Oracle in the LICENSE file that accompanied this code.
   10    *
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   13    * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
   14    * version 2 for more details (a copy is included in the LICENSE file that
   15    * accompanied this code).
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   25   
   26   package java.lang;
   27   import java.util.Random;
   28   import sun.misc.FpUtils;
   29   import sun.misc.DoubleConsts;
   30   
   31   /**
   32    * The class {@code StrictMath} contains methods for performing basic
   33    * numeric operations such as the elementary exponential, logarithm,
   34    * square root, and trigonometric functions.
   35    *
   36    * <p>To help ensure portability of Java programs, the definitions of
   37    * some of the numeric functions in this package require that they
   38    * produce the same results as certain published algorithms. These
   39    * algorithms are available from the well-known network library
   40    * {@code netlib} as the package "Freely Distributable Math
   41    * Library," <a
   42    * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
   43    * algorithms, which are written in the C programming language, are
   44    * then to be understood as executed with all floating-point
   45    * operations following the rules of Java floating-point arithmetic.
   46    *
   47    * <p>The Java math library is defined with respect to
   48    * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
   49    * more than one definition for a function (such as
   50    * {@code acos}), use the "IEEE 754 core function" version
   51    * (residing in a file whose name begins with the letter
   52    * {@code e}).  The methods which require {@code fdlibm}
   53    * semantics are {@code sin}, {@code cos}, {@code tan},
   54    * {@code asin}, {@code acos}, {@code atan},
   55    * {@code exp}, {@code log}, {@code log10},
   56    * {@code cbrt}, {@code atan2}, {@code pow},
   57    * {@code sinh}, {@code cosh}, {@code tanh},
   58    * {@code hypot}, {@code expm1}, and {@code log1p}.
   59    *
   60    * @author  unascribed
   61    * @author  Joseph D. Darcy
   62    * @since   1.3
   63    */
   64   
   65   public final class StrictMath {
   66   
   67       /**
   68        * Don't let anyone instantiate this class.
   69        */
   70       private StrictMath() {}
   71   
   72       /**
   73        * The {@code double} value that is closer than any other to
   74        * <i>e</i>, the base of the natural logarithms.
   75        */
   76       public static final double E = 2.7182818284590452354;
   77   
   78       /**
   79        * The {@code double} value that is closer than any other to
   80        * <i>pi</i>, the ratio of the circumference of a circle to its
   81        * diameter.
   82        */
   83       public static final double PI = 3.14159265358979323846;
   84   
   85       /**
   86        * Returns the trigonometric sine of an angle. Special cases:
   87        * <ul><li>If the argument is NaN or an infinity, then the
   88        * result is NaN.
   89        * <li>If the argument is zero, then the result is a zero with the
   90        * same sign as the argument.</ul>
   91        *
   92        * @param   a   an angle, in radians.
   93        * @return  the sine of the argument.
   94        */
   95       public static native double sin(double a);
   96   
   97       /**
   98        * Returns the trigonometric cosine of an angle. Special cases:
   99        * <ul><li>If the argument is NaN or an infinity, then the
  100        * result is NaN.</ul>
  101        *
  102        * @param   a   an angle, in radians.
  103        * @return  the cosine of the argument.
  104        */
  105       public static native double cos(double a);
  106   
  107       /**
  108        * Returns the trigonometric tangent of an angle. Special cases:
  109        * <ul><li>If the argument is NaN or an infinity, then the result
  110        * is NaN.
  111        * <li>If the argument is zero, then the result is a zero with the
  112        * same sign as the argument.</ul>
  113        *
  114        * @param   a   an angle, in radians.
  115        * @return  the tangent of the argument.
  116        */
  117       public static native double tan(double a);
  118   
  119       /**
  120        * Returns the arc sine of a value; the returned angle is in the
  121        * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
  122        * <ul><li>If the argument is NaN or its absolute value is greater
  123        * than 1, then the result is NaN.
  124        * <li>If the argument is zero, then the result is a zero with the
  125        * same sign as the argument.</ul>
  126        *
  127        * @param   a   the value whose arc sine is to be returned.
  128        * @return  the arc sine of the argument.
  129        */
  130       public static native double asin(double a);
  131   
  132       /**
  133        * Returns the arc cosine of a value; the returned angle is in the
  134        * range 0.0 through <i>pi</i>.  Special case:
  135        * <ul><li>If the argument is NaN or its absolute value is greater
  136        * than 1, then the result is NaN.</ul>
  137        *
  138        * @param   a   the value whose arc cosine is to be returned.
  139        * @return  the arc cosine of the argument.
  140        */
  141       public static native double acos(double a);
  142   
  143       /**
  144        * Returns the arc tangent of a value; the returned angle is in the
  145        * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
  146        * <ul><li>If the argument is NaN, then the result is NaN.
  147        * <li>If the argument is zero, then the result is a zero with the
  148        * same sign as the argument.</ul>
  149        *
  150        * @param   a   the value whose arc tangent is to be returned.
  151        * @return  the arc tangent of the argument.
  152        */
  153       public static native double atan(double a);
  154   
  155       /**
  156        * Converts an angle measured in degrees to an approximately
  157        * equivalent angle measured in radians.  The conversion from
  158        * degrees to radians is generally inexact.
  159        *
  160        * @param   angdeg   an angle, in degrees
  161        * @return  the measurement of the angle {@code angdeg}
  162        *          in radians.
  163        */
  164       public static strictfp double toRadians(double angdeg) {
  165           return angdeg / 180.0 * PI;
  166       }
  167   
  168       /**
  169        * Converts an angle measured in radians to an approximately
  170        * equivalent angle measured in degrees.  The conversion from
  171        * radians to degrees is generally inexact; users should
  172        * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
  173        * equal {@code 0.0}.
  174        *
  175        * @param   angrad   an angle, in radians
  176        * @return  the measurement of the angle {@code angrad}
  177        *          in degrees.
  178        */
  179       public static strictfp double toDegrees(double angrad) {
  180           return angrad * 180.0 / PI;
  181       }
  182   
  183       /**
  184        * Returns Euler's number <i>e</i> raised to the power of a
  185        * {@code double} value. Special cases:
  186        * <ul><li>If the argument is NaN, the result is NaN.
  187        * <li>If the argument is positive infinity, then the result is
  188        * positive infinity.
  189        * <li>If the argument is negative infinity, then the result is
  190        * positive zero.</ul>
  191        *
  192        * @param   a   the exponent to raise <i>e</i> to.
  193        * @return  the value <i>e</i><sup>{@code a}</sup>,
  194        *          where <i>e</i> is the base of the natural logarithms.
  195        */
  196       public static native double exp(double a);
  197   
  198       /**
  199        * Returns the natural logarithm (base <i>e</i>) of a {@code double}
  200        * value. Special cases:
  201        * <ul><li>If the argument is NaN or less than zero, then the result
  202        * is NaN.
  203        * <li>If the argument is positive infinity, then the result is
  204        * positive infinity.
  205        * <li>If the argument is positive zero or negative zero, then the
  206        * result is negative infinity.</ul>
  207        *
  208        * @param   a   a value
  209        * @return  the value ln&nbsp;{@code a}, the natural logarithm of
  210        *          {@code a}.
  211        */
  212       public static native double log(double a);
  213   
  214   
  215       /**
  216        * Returns the base 10 logarithm of a {@code double} value.
  217        * Special cases:
  218        *
  219        * <ul><li>If the argument is NaN or less than zero, then the result
  220        * is NaN.
  221        * <li>If the argument is positive infinity, then the result is
  222        * positive infinity.
  223        * <li>If the argument is positive zero or negative zero, then the
  224        * result is negative infinity.
  225        * <li> If the argument is equal to 10<sup><i>n</i></sup> for
  226        * integer <i>n</i>, then the result is <i>n</i>.
  227        * </ul>
  228        *
  229        * @param   a   a value
  230        * @return  the base 10 logarithm of  {@code a}.
  231        * @since 1.5
  232        */
  233       public static native double log10(double a);
  234   
  235       /**
  236        * Returns the correctly rounded positive square root of a
  237        * {@code double} value.
  238        * Special cases:
  239        * <ul><li>If the argument is NaN or less than zero, then the result
  240        * is NaN.
  241        * <li>If the argument is positive infinity, then the result is positive
  242        * infinity.
  243        * <li>If the argument is positive zero or negative zero, then the
  244        * result is the same as the argument.</ul>
  245        * Otherwise, the result is the {@code double} value closest to
  246        * the true mathematical square root of the argument value.
  247        *
  248        * @param   a   a value.
  249        * @return  the positive square root of {@code a}.
  250        */
  251       public static native double sqrt(double a);
  252   
  253       /**
  254        * Returns the cube root of a {@code double} value.  For
  255        * positive finite {@code x}, {@code cbrt(-x) ==
  256        * -cbrt(x)}; that is, the cube root of a negative value is
  257        * the negative of the cube root of that value's magnitude.
  258        * Special cases:
  259        *
  260        * <ul>
  261        *
  262        * <li>If the argument is NaN, then the result is NaN.
  263        *
  264        * <li>If the argument is infinite, then the result is an infinity
  265        * with the same sign as the argument.
  266        *
  267        * <li>If the argument is zero, then the result is a zero with the
  268        * same sign as the argument.
  269        *
  270        * </ul>
  271        *
  272        * @param   a   a value.
  273        * @return  the cube root of {@code a}.
  274        * @since 1.5
  275        */
  276       public static native double cbrt(double a);
  277   
  278       /**
  279        * Computes the remainder operation on two arguments as prescribed
  280        * by the IEEE 754 standard.
  281        * The remainder value is mathematically equal to
  282        * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
  283        * where <i>n</i> is the mathematical integer closest to the exact
  284        * mathematical value of the quotient {@code f1/f2}, and if two
  285        * mathematical integers are equally close to {@code f1/f2},
  286        * then <i>n</i> is the integer that is even. If the remainder is
  287        * zero, its sign is the same as the sign of the first argument.
  288        * Special cases:
  289        * <ul><li>If either argument is NaN, or the first argument is infinite,
  290        * or the second argument is positive zero or negative zero, then the
  291        * result is NaN.
  292        * <li>If the first argument is finite and the second argument is
  293        * infinite, then the result is the same as the first argument.</ul>
  294        *
  295        * @param   f1   the dividend.
  296        * @param   f2   the divisor.
  297        * @return  the remainder when {@code f1} is divided by
  298        *          {@code f2}.
  299        */
  300       public static native double IEEEremainder(double f1, double f2);
  301   
  302       /**
  303        * Returns the smallest (closest to negative infinity)
  304        * {@code double} value that is greater than or equal to the
  305        * argument and is equal to a mathematical integer. Special cases:
  306        * <ul><li>If the argument value is already equal to a
  307        * mathematical integer, then the result is the same as the
  308        * argument.  <li>If the argument is NaN or an infinity or
  309        * positive zero or negative zero, then the result is the same as
  310        * the argument.  <li>If the argument value is less than zero but
  311        * greater than -1.0, then the result is negative zero.</ul> Note
  312        * that the value of {@code StrictMath.ceil(x)} is exactly the
  313        * value of {@code -StrictMath.floor(-x)}.
  314        *
  315        * @param   a   a value.
  316        * @return  the smallest (closest to negative infinity)
  317        *          floating-point value that is greater than or equal to
  318        *          the argument and is equal to a mathematical integer.
  319        */
  320       public static double ceil(double a) {
  321           return floorOrCeil(a, -0.0, 1.0, 1.0);
  322       }
  323   
  324       /**
  325        * Returns the largest (closest to positive infinity)
  326        * {@code double} value that is less than or equal to the
  327        * argument and is equal to a mathematical integer. Special cases:
  328        * <ul><li>If the argument value is already equal to a
  329        * mathematical integer, then the result is the same as the
  330        * argument.  <li>If the argument is NaN or an infinity or
  331        * positive zero or negative zero, then the result is the same as
  332        * the argument.</ul>
  333        *
  334        * @param   a   a value.
  335        * @return  the largest (closest to positive infinity)
  336        *          floating-point value that less than or equal to the argument
  337        *          and is equal to a mathematical integer.
  338        */
  339       public static double floor(double a) {
  340           return floorOrCeil(a, -1.0, 0.0, -1.0);
  341       }
  342   
  343       /**
  344        * Internal method to share logic between floor and ceil.
  345        *
  346        * @param a the value to be floored or ceiled
  347        * @param negativeBoundary result for values in (-1, 0)
  348        * @param positiveBoundary result for values in (0, 1)
  349        * @param increment value to add when the argument is non-integral
  350        */
  351       private static double floorOrCeil(double a,
  352                                         double negativeBoundary,
  353                                         double positiveBoundary,
  354                                         double sign) {
  355           int exponent = Math.getExponent(a);
  356   
  357           if (exponent < 0) {
  358               /*
  359                * Absolute value of argument is less than 1.
  360                * floorOrceil(-0.0) => -0.0
  361                * floorOrceil(+0.0) => +0.0
  362                */
  363               return ((a == 0.0) ? a :
  364                       ( (a < 0.0) ?  negativeBoundary : positiveBoundary) );
  365           } else if (exponent >= 52) {
  366               /*
  367                * Infinity, NaN, or a value so large it must be integral.
  368                */
  369               return a;
  370           }
  371           // Else the argument is either an integral value already XOR it
  372           // has to be rounded to one.
  373           assert exponent >= 0 && exponent <= 51;
  374   
  375           long doppel = Double.doubleToRawLongBits(a);
  376           long mask   = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
  377   
  378           if ( (mask & doppel) == 0L )
  379               return a; // integral value
  380           else {
  381               double result = Double.longBitsToDouble(doppel & (~mask));
  382               if (sign*a > 0.0)
  383                   result = result + sign;
  384               return result;
  385           }
  386       }
  387   
  388       /**
  389        * Returns the {@code double} value that is closest in value
  390        * to the argument and is equal to a mathematical integer. If two
  391        * {@code double} values that are mathematical integers are
  392        * equally close to the value of the argument, the result is the
  393        * integer value that is even. Special cases:
  394        * <ul><li>If the argument value is already equal to a mathematical
  395        * integer, then the result is the same as the argument.
  396        * <li>If the argument is NaN or an infinity or positive zero or negative
  397        * zero, then the result is the same as the argument.</ul>
  398        *
  399        * @param   a   a value.
  400        * @return  the closest floating-point value to {@code a} that is
  401        *          equal to a mathematical integer.
  402        * @author Joseph D. Darcy
  403        */
  404       public static double rint(double a) {
  405           /*
  406            * If the absolute value of a is not less than 2^52, it
  407            * is either a finite integer (the double format does not have
  408            * enough significand bits for a number that large to have any
  409            * fractional portion), an infinity, or a NaN.  In any of
  410            * these cases, rint of the argument is the argument.
  411            *
  412            * Otherwise, the sum (twoToThe52 + a ) will properly round
  413            * away any fractional portion of a since ulp(twoToThe52) ==
  414            * 1.0; subtracting out twoToThe52 from this sum will then be
  415            * exact and leave the rounded integer portion of a.
  416            *
  417            * This method does *not* need to be declared strictfp to get
  418            * fully reproducible results.  Whether or not a method is
  419            * declared strictfp can only make a difference in the
  420            * returned result if some operation would overflow or
  421            * underflow with strictfp semantics.  The operation
  422            * (twoToThe52 + a ) cannot overflow since large values of a
  423            * are screened out; the add cannot underflow since twoToThe52
  424            * is too large.  The subtraction ((twoToThe52 + a ) -
  425            * twoToThe52) will be exact as discussed above and thus
  426            * cannot overflow or meaningfully underflow.  Finally, the
  427            * last multiply in the return statement is by plus or minus
  428            * 1.0, which is exact too.
  429            */
  430           double twoToThe52 = (double)(1L << 52); // 2^52
  431           double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info
  432           a = Math.abs(a);
  433   
  434           if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
  435               a = ((twoToThe52 + a ) - twoToThe52);
  436           }
  437   
  438           return sign * a; // restore original sign
  439       }
  440   
  441       /**
  442        * Returns the angle <i>theta</i> from the conversion of rectangular
  443        * coordinates ({@code x},&nbsp;{@code y}) to polar
  444        * coordinates (r,&nbsp;<i>theta</i>).
  445        * This method computes the phase <i>theta</i> by computing an arc tangent
  446        * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
  447        * cases:
  448        * <ul><li>If either argument is NaN, then the result is NaN.
  449        * <li>If the first argument is positive zero and the second argument
  450        * is positive, or the first argument is positive and finite and the
  451        * second argument is positive infinity, then the result is positive
  452        * zero.
  453        * <li>If the first argument is negative zero and the second argument
  454        * is positive, or the first argument is negative and finite and the
  455        * second argument is positive infinity, then the result is negative zero.
  456        * <li>If the first argument is positive zero and the second argument
  457        * is negative, or the first argument is positive and finite and the
  458        * second argument is negative infinity, then the result is the
  459        * {@code double} value closest to <i>pi</i>.
  460        * <li>If the first argument is negative zero and the second argument
  461        * is negative, or the first argument is negative and finite and the
  462        * second argument is negative infinity, then the result is the
  463        * {@code double} value closest to -<i>pi</i>.
  464        * <li>If the first argument is positive and the second argument is
  465        * positive zero or negative zero, or the first argument is positive
  466        * infinity and the second argument is finite, then the result is the
  467        * {@code double} value closest to <i>pi</i>/2.
  468        * <li>If the first argument is negative and the second argument is
  469        * positive zero or negative zero, or the first argument is negative
  470        * infinity and the second argument is finite, then the result is the
  471        * {@code double} value closest to -<i>pi</i>/2.
  472        * <li>If both arguments are positive infinity, then the result is the
  473        * {@code double} value closest to <i>pi</i>/4.
  474        * <li>If the first argument is positive infinity and the second argument
  475        * is negative infinity, then the result is the {@code double}
  476        * value closest to 3*<i>pi</i>/4.
  477        * <li>If the first argument is negative infinity and the second argument
  478        * is positive infinity, then the result is the {@code double} value
  479        * closest to -<i>pi</i>/4.
  480        * <li>If both arguments are negative infinity, then the result is the
  481        * {@code double} value closest to -3*<i>pi</i>/4.</ul>
  482        *
  483        * @param   y   the ordinate coordinate
  484        * @param   x   the abscissa coordinate
  485        * @return  the <i>theta</i> component of the point
  486        *          (<i>r</i>,&nbsp;<i>theta</i>)
  487        *          in polar coordinates that corresponds to the point
  488        *          (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
  489        */
  490       public static native double atan2(double y, double x);
  491   
  492   
  493       /**
  494        * Returns the value of the first argument raised to the power of the
  495        * second argument. Special cases:
  496        *
  497        * <ul><li>If the second argument is positive or negative zero, then the
  498        * result is 1.0.
  499        * <li>If the second argument is 1.0, then the result is the same as the
  500        * first argument.
  501        * <li>If the second argument is NaN, then the result is NaN.
  502        * <li>If the first argument is NaN and the second argument is nonzero,
  503        * then the result is NaN.
  504        *
  505        * <li>If
  506        * <ul>
  507        * <li>the absolute value of the first argument is greater than 1
  508        * and the second argument is positive infinity, or
  509        * <li>the absolute value of the first argument is less than 1 and
  510        * the second argument is negative infinity,
  511        * </ul>
  512        * then the result is positive infinity.
  513        *
  514        * <li>If
  515        * <ul>
  516        * <li>the absolute value of the first argument is greater than 1 and
  517        * the second argument is negative infinity, or
  518        * <li>the absolute value of the
  519        * first argument is less than 1 and the second argument is positive
  520        * infinity,
  521        * </ul>
  522        * then the result is positive zero.
  523        *
  524        * <li>If the absolute value of the first argument equals 1 and the
  525        * second argument is infinite, then the result is NaN.
  526        *
  527        * <li>If
  528        * <ul>
  529        * <li>the first argument is positive zero and the second argument
  530        * is greater than zero, or
  531        * <li>the first argument is positive infinity and the second
  532        * argument is less than zero,
  533        * </ul>
  534        * then the result is positive zero.
  535        *
  536        * <li>If
  537        * <ul>
  538        * <li>the first argument is positive zero and the second argument
  539        * is less than zero, or
  540        * <li>the first argument is positive infinity and the second
  541        * argument is greater than zero,
  542        * </ul>
  543        * then the result is positive infinity.
  544        *
  545        * <li>If
  546        * <ul>
  547        * <li>the first argument is negative zero and the second argument
  548        * is greater than zero but not a finite odd integer, or
  549        * <li>the first argument is negative infinity and the second
  550        * argument is less than zero but not a finite odd integer,
  551        * </ul>
  552        * then the result is positive zero.
  553        *
  554        * <li>If
  555        * <ul>
  556        * <li>the first argument is negative zero and the second argument
  557        * is a positive finite odd integer, or
  558        * <li>the first argument is negative infinity and the second
  559        * argument is a negative finite odd integer,
  560        * </ul>
  561        * then the result is negative zero.
  562        *
  563        * <li>If
  564        * <ul>
  565        * <li>the first argument is negative zero and the second argument
  566        * is less than zero but not a finite odd integer, or
  567        * <li>the first argument is negative infinity and the second
  568        * argument is greater than zero but not a finite odd integer,
  569        * </ul>
  570        * then the result is positive infinity.
  571        *
  572        * <li>If
  573        * <ul>
  574        * <li>the first argument is negative zero and the second argument
  575        * is a negative finite odd integer, or
  576        * <li>the first argument is negative infinity and the second
  577        * argument is a positive finite odd integer,
  578        * </ul>
  579        * then the result is negative infinity.
  580        *
  581        * <li>If the first argument is finite and less than zero
  582        * <ul>
  583        * <li> if the second argument is a finite even integer, the
  584        * result is equal to the result of raising the absolute value of
  585        * the first argument to the power of the second argument
  586        *
  587        * <li>if the second argument is a finite odd integer, the result
  588        * is equal to the negative of the result of raising the absolute
  589        * value of the first argument to the power of the second
  590        * argument
  591        *
  592        * <li>if the second argument is finite and not an integer, then
  593        * the result is NaN.
  594        * </ul>
  595        *
  596        * <li>If both arguments are integers, then the result is exactly equal
  597        * to the mathematical result of raising the first argument to the power
  598        * of the second argument if that result can in fact be represented
  599        * exactly as a {@code double} value.</ul>
  600        *
  601        * <p>(In the foregoing descriptions, a floating-point value is
  602        * considered to be an integer if and only if it is finite and a
  603        * fixed point of the method {@link #ceil ceil} or,
  604        * equivalently, a fixed point of the method {@link #floor
  605        * floor}. A value is a fixed point of a one-argument
  606        * method if and only if the result of applying the method to the
  607        * value is equal to the value.)
  608        *
  609        * @param   a   base.
  610        * @param   b   the exponent.
  611        * @return  the value {@code a}<sup>{@code b}</sup>.
  612        */
  613       public static native double pow(double a, double b);
  614   
  615       /**
  616        * Returns the closest {@code int} to the argument, with ties
  617        * rounding up.
  618        *
  619        * <p>Special cases:
  620        * <ul><li>If the argument is NaN, the result is 0.
  621        * <li>If the argument is negative infinity or any value less than or
  622        * equal to the value of {@code Integer.MIN_VALUE}, the result is
  623        * equal to the value of {@code Integer.MIN_VALUE}.
  624        * <li>If the argument is positive infinity or any value greater than or
  625        * equal to the value of {@code Integer.MAX_VALUE}, the result is
  626        * equal to the value of {@code Integer.MAX_VALUE}.</ul>
  627        *
  628        * @param   a   a floating-point value to be rounded to an integer.
  629        * @return  the value of the argument rounded to the nearest
  630        *          {@code int} value.
  631        * @see     java.lang.Integer#MAX_VALUE
  632        * @see     java.lang.Integer#MIN_VALUE
  633        */
  634       public static int round(float a) {
  635           return Math.round(a);
  636       }
  637   
  638       /**
  639        * Returns the closest {@code long} to the argument, with ties
  640        * rounding up.
  641        *
  642        * <p>Special cases:
  643        * <ul><li>If the argument is NaN, the result is 0.
  644        * <li>If the argument is negative infinity or any value less than or
  645        * equal to the value of {@code Long.MIN_VALUE}, the result is
  646        * equal to the value of {@code Long.MIN_VALUE}.
  647        * <li>If the argument is positive infinity or any value greater than or
  648        * equal to the value of {@code Long.MAX_VALUE}, the result is
  649        * equal to the value of {@code Long.MAX_VALUE}.</ul>
  650        *
  651        * @param   a  a floating-point value to be rounded to a
  652        *          {@code long}.
  653        * @return  the value of the argument rounded to the nearest
  654        *          {@code long} value.
  655        * @see     java.lang.Long#MAX_VALUE
  656        * @see     java.lang.Long#MIN_VALUE
  657        */
  658       public static long round(double a) {
  659           return Math.round(a);
  660       }
  661   
  662       private static Random randomNumberGenerator;
  663   
  664       private static synchronized Random initRNG() {
  665           Random rnd = randomNumberGenerator;
  666           return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
  667       }
  668   
  669       /**
  670        * Returns a {@code double} value with a positive sign, greater
  671        * than or equal to {@code 0.0} and less than {@code 1.0}.
  672        * Returned values are chosen pseudorandomly with (approximately)
  673        * uniform distribution from that range.
  674        *
  675        * <p>When this method is first called, it creates a single new
  676        * pseudorandom-number generator, exactly as if by the expression
  677        *
  678        * <blockquote>{@code new java.util.Random()}</blockquote>
  679        *
  680        * This new pseudorandom-number generator is used thereafter for
  681        * all calls to this method and is used nowhere else.
  682        *
  683        * <p>This method is properly synchronized to allow correct use by
  684        * more than one thread. However, if many threads need to generate
  685        * pseudorandom numbers at a great rate, it may reduce contention
  686        * for each thread to have its own pseudorandom number generator.
  687        *
  688        * @return  a pseudorandom {@code double} greater than or equal
  689        * to {@code 0.0} and less than {@code 1.0}.
  690        * @see Random#nextDouble()
  691        */
  692       public static double random() {
  693           Random rnd = randomNumberGenerator;
  694           if (rnd == null) rnd = initRNG();
  695           return rnd.nextDouble();
  696       }
  697   
  698       /**
  699        * Returns the absolute value of an {@code int} value..
  700        * If the argument is not negative, the argument is returned.
  701        * If the argument is negative, the negation of the argument is returned.
  702        *
  703        * <p>Note that if the argument is equal to the value of
  704        * {@link Integer#MIN_VALUE}, the most negative representable
  705        * {@code int} value, the result is that same value, which is
  706        * negative.
  707        *
  708        * @param   a   the  argument whose absolute value is to be determined.
  709        * @return  the absolute value of the argument.
  710        */
  711       public static int abs(int a) {
  712           return (a < 0) ? -a : a;
  713       }
  714   
  715       /**
  716        * Returns the absolute value of a {@code long} value.
  717        * If the argument is not negative, the argument is returned.
  718        * If the argument is negative, the negation of the argument is returned.
  719        *
  720        * <p>Note that if the argument is equal to the value of
  721        * {@link Long#MIN_VALUE}, the most negative representable
  722        * {@code long} value, the result is that same value, which
  723        * is negative.
  724        *
  725        * @param   a   the  argument whose absolute value is to be determined.
  726        * @return  the absolute value of the argument.
  727        */
  728       public static long abs(long a) {
  729           return (a < 0) ? -a : a;
  730       }
  731   
  732       /**
  733        * Returns the absolute value of a {@code float} value.
  734        * If the argument is not negative, the argument is returned.
  735        * If the argument is negative, the negation of the argument is returned.
  736        * Special cases:
  737        * <ul><li>If the argument is positive zero or negative zero, the
  738        * result is positive zero.
  739        * <li>If the argument is infinite, the result is positive infinity.
  740        * <li>If the argument is NaN, the result is NaN.</ul>
  741        * In other words, the result is the same as the value of the expression:
  742        * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
  743        *
  744        * @param   a   the argument whose absolute value is to be determined
  745        * @return  the absolute value of the argument.
  746        */
  747       public static float abs(float a) {
  748           return (a <= 0.0F) ? 0.0F - a : a;
  749       }
  750   
  751       /**
  752        * Returns the absolute value of a {@code double} value.
  753        * If the argument is not negative, the argument is returned.
  754        * If the argument is negative, the negation of the argument is returned.
  755        * Special cases:
  756        * <ul><li>If the argument is positive zero or negative zero, the result
  757        * is positive zero.
  758        * <li>If the argument is infinite, the result is positive infinity.
  759        * <li>If the argument is NaN, the result is NaN.</ul>
  760        * In other words, the result is the same as the value of the expression:
  761        * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
  762        *
  763        * @param   a   the argument whose absolute value is to be determined
  764        * @return  the absolute value of the argument.
  765        */
  766       public static double abs(double a) {
  767           return (a <= 0.0D) ? 0.0D - a : a;
  768       }
  769   
  770       /**
  771        * Returns the greater of two {@code int} values. That is, the
  772        * result is the argument closer to the value of
  773        * {@link Integer#MAX_VALUE}. If the arguments have the same value,
  774        * the result is that same value.
  775        *
  776        * @param   a   an argument.
  777        * @param   b   another argument.
  778        * @return  the larger of {@code a} and {@code b}.
  779        */
  780       public static int max(int a, int b) {
  781           return (a >= b) ? a : b;
  782       }
  783   
  784       /**
  785        * Returns the greater of two {@code long} values. That is, the
  786        * result is the argument closer to the value of
  787        * {@link Long#MAX_VALUE}. If the arguments have the same value,
  788        * the result is that same value.
  789        *
  790        * @param   a   an argument.
  791        * @param   b   another argument.
  792        * @return  the larger of {@code a} and {@code b}.
  793           */
  794       public static long max(long a, long b) {
  795           return (a >= b) ? a : b;
  796       }
  797   
  798       // Use raw bit-wise conversions on guaranteed non-NaN arguments.
  799       private static long negativeZeroFloatBits  = Float.floatToRawIntBits(-0.0f);
  800       private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
  801   
  802       /**
  803        * Returns the greater of two {@code float} values.  That is,
  804        * the result is the argument closer to positive infinity. If the
  805        * arguments have the same value, the result is that same
  806        * value. If either value is NaN, then the result is NaN.  Unlike
  807        * the numerical comparison operators, this method considers
  808        * negative zero to be strictly smaller than positive zero. If one
  809        * argument is positive zero and the other negative zero, the
  810        * result is positive zero.
  811        *
  812        * @param   a   an argument.
  813        * @param   b   another argument.
  814        * @return  the larger of {@code a} and {@code b}.
  815        */
  816       public static float max(float a, float b) {
  817           if (a != a)
  818               return a;   // a is NaN
  819           if ((a == 0.0f) &&
  820               (b == 0.0f) &&
  821               (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
  822               // Raw conversion ok since NaN can't map to -0.0.
  823               return b;
  824           }
  825           return (a >= b) ? a : b;
  826       }
  827   
  828       /**
  829        * Returns the greater of two {@code double} values.  That
  830        * is, the result is the argument closer to positive infinity. If
  831        * the arguments have the same value, the result is that same
  832        * value. If either value is NaN, then the result is NaN.  Unlike
  833        * the numerical comparison operators, this method considers
  834        * negative zero to be strictly smaller than positive zero. If one
  835        * argument is positive zero and the other negative zero, the
  836        * result is positive zero.
  837        *
  838        * @param   a   an argument.
  839        * @param   b   another argument.
  840        * @return  the larger of {@code a} and {@code b}.
  841        */
  842       public static double max(double a, double b) {
  843           if (a != a)
  844               return a;   // a is NaN
  845           if ((a == 0.0d) &&
  846               (b == 0.0d) &&
  847               (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
  848               // Raw conversion ok since NaN can't map to -0.0.
  849               return b;
  850           }
  851           return (a >= b) ? a : b;
  852       }
  853   
  854       /**
  855        * Returns the smaller of two {@code int} values. That is,
  856        * the result the argument closer to the value of
  857        * {@link Integer#MIN_VALUE}.  If the arguments have the same
  858        * value, the result is that same value.
  859        *
  860        * @param   a   an argument.
  861        * @param   b   another argument.
  862        * @return  the smaller of {@code a} and {@code b}.
  863        */
  864       public static int min(int a, int b) {
  865           return (a <= b) ? a : b;
  866       }
  867   
  868       /**
  869        * Returns the smaller of two {@code long} values. That is,
  870        * the result is the argument closer to the value of
  871        * {@link Long#MIN_VALUE}. If the arguments have the same
  872        * value, the result is that same value.
  873        *
  874        * @param   a   an argument.
  875        * @param   b   another argument.
  876        * @return  the smaller of {@code a} and {@code b}.
  877        */
  878       public static long min(long a, long b) {
  879           return (a <= b) ? a : b;
  880       }
  881   
  882       /**
  883        * Returns the smaller of two {@code float} values.  That is,
  884        * the result is the value closer to negative infinity. If the
  885        * arguments have the same value, the result is that same
  886        * value. If either value is NaN, then the result is NaN.  Unlike
  887        * the numerical comparison operators, this method considers
  888        * negative zero to be strictly smaller than positive zero.  If
  889        * one argument is positive zero and the other is negative zero,
  890        * the result is negative zero.
  891        *
  892        * @param   a   an argument.
  893        * @param   b   another argument.
  894        * @return  the smaller of {@code a} and {@code b.}
  895        */
  896       public static float min(float a, float b) {
  897           if (a != a)
  898               return a;   // a is NaN
  899           if ((a == 0.0f) &&
  900               (b == 0.0f) &&
  901               (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
  902               // Raw conversion ok since NaN can't map to -0.0.
  903               return b;
  904           }
  905           return (a <= b) ? a : b;
  906       }
  907   
  908       /**
  909        * Returns the smaller of two {@code double} values.  That
  910        * is, the result is the value closer to negative infinity. If the
  911        * arguments have the same value, the result is that same
  912        * value. If either value is NaN, then the result is NaN.  Unlike
  913        * the numerical comparison operators, this method considers
  914        * negative zero to be strictly smaller than positive zero. If one
  915        * argument is positive zero and the other is negative zero, the
  916        * result is negative zero.
  917        *
  918        * @param   a   an argument.
  919        * @param   b   another argument.
  920        * @return  the smaller of {@code a} and {@code b}.
  921        */
  922       public static double min(double a, double b) {
  923           if (a != a)
  924               return a;   // a is NaN
  925           if ((a == 0.0d) &&
  926               (b == 0.0d) &&
  927               (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
  928               // Raw conversion ok since NaN can't map to -0.0.
  929               return b;
  930           }
  931           return (a <= b) ? a : b;
  932       }
  933   
  934       /**
  935        * Returns the size of an ulp of the argument.  An ulp of a
  936        * {@code double} value is the positive distance between this
  937        * floating-point value and the {@code double} value next
  938        * larger in magnitude.  Note that for non-NaN <i>x</i>,
  939        * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
  940        *
  941        * <p>Special Cases:
  942        * <ul>
  943        * <li> If the argument is NaN, then the result is NaN.
  944        * <li> If the argument is positive or negative infinity, then the
  945        * result is positive infinity.
  946        * <li> If the argument is positive or negative zero, then the result is
  947        * {@code Double.MIN_VALUE}.
  948        * <li> If the argument is &plusmn;{@code Double.MAX_VALUE}, then
  949        * the result is equal to 2<sup>971</sup>.
  950        * </ul>
  951        *
  952        * @param d the floating-point value whose ulp is to be returned
  953        * @return the size of an ulp of the argument
  954        * @author Joseph D. Darcy
  955        * @since 1.5
  956        */
  957       public static double ulp(double d) {
  958           return sun.misc.FpUtils.ulp(d);
  959       }
  960   
  961       /**
  962        * Returns the size of an ulp of the argument.  An ulp of a
  963        * {@code float} value is the positive distance between this
  964        * floating-point value and the {@code float} value next
  965        * larger in magnitude.  Note that for non-NaN <i>x</i>,
  966        * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
  967        *
  968        * <p>Special Cases:
  969        * <ul>
  970        * <li> If the argument is NaN, then the result is NaN.
  971        * <li> If the argument is positive or negative infinity, then the
  972        * result is positive infinity.
  973        * <li> If the argument is positive or negative zero, then the result is
  974        * {@code Float.MIN_VALUE}.
  975        * <li> If the argument is &plusmn;{@code Float.MAX_VALUE}, then
  976        * the result is equal to 2<sup>104</sup>.
  977        * </ul>
  978        *
  979        * @param f the floating-point value whose ulp is to be returned
  980        * @return the size of an ulp of the argument
  981        * @author Joseph D. Darcy
  982        * @since 1.5
  983        */
  984       public static float ulp(float f) {
  985           return sun.misc.FpUtils.ulp(f);
  986       }
  987   
  988       /**
  989        * Returns the signum function of the argument; zero if the argument
  990        * is zero, 1.0 if the argument is greater than zero, -1.0 if the
  991        * argument is less than zero.
  992        *
  993        * <p>Special Cases:
  994        * <ul>
  995        * <li> If the argument is NaN, then the result is NaN.
  996        * <li> If the argument is positive zero or negative zero, then the
  997        *      result is the same as the argument.
  998        * </ul>
  999        *
 1000        * @param d the floating-point value whose signum is to be returned
 1001        * @return the signum function of the argument
 1002        * @author Joseph D. Darcy
 1003        * @since 1.5
 1004        */
 1005       public static double signum(double d) {
 1006           return sun.misc.FpUtils.signum(d);
 1007       }
 1008   
 1009       /**
 1010        * Returns the signum function of the argument; zero if the argument
 1011        * is zero, 1.0f if the argument is greater than zero, -1.0f if the
 1012        * argument is less than zero.
 1013        *
 1014        * <p>Special Cases:
 1015        * <ul>
 1016        * <li> If the argument is NaN, then the result is NaN.
 1017        * <li> If the argument is positive zero or negative zero, then the
 1018        *      result is the same as the argument.
 1019        * </ul>
 1020        *
 1021        * @param f the floating-point value whose signum is to be returned
 1022        * @return the signum function of the argument
 1023        * @author Joseph D. Darcy
 1024        * @since 1.5
 1025        */
 1026       public static float signum(float f) {
 1027           return sun.misc.FpUtils.signum(f);
 1028       }
 1029   
 1030       /**
 1031        * Returns the hyperbolic sine of a {@code double} value.
 1032        * The hyperbolic sine of <i>x</i> is defined to be
 1033        * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
 1034        * where <i>e</i> is {@linkplain Math#E Euler's number}.
 1035        *
 1036        * <p>Special cases:
 1037        * <ul>
 1038        *
 1039        * <li>If the argument is NaN, then the result is NaN.
 1040        *
 1041        * <li>If the argument is infinite, then the result is an infinity
 1042        * with the same sign as the argument.
 1043        *
 1044        * <li>If the argument is zero, then the result is a zero with the
 1045        * same sign as the argument.
 1046        *
 1047        * </ul>
 1048        *
 1049        * @param   x The number whose hyperbolic sine is to be returned.
 1050        * @return  The hyperbolic sine of {@code x}.
 1051        * @since 1.5
 1052        */
 1053       public static native double sinh(double x);
 1054   
 1055       /**
 1056        * Returns the hyperbolic cosine of a {@code double} value.
 1057        * The hyperbolic cosine of <i>x</i> is defined to be
 1058        * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2
 1059        * where <i>e</i> is {@linkplain Math#E Euler's number}.
 1060        *
 1061        * <p>Special cases:
 1062        * <ul>
 1063        *
 1064        * <li>If the argument is NaN, then the result is NaN.
 1065        *
 1066        * <li>If the argument is infinite, then the result is positive
 1067        * infinity.
 1068        *
 1069        * <li>If the argument is zero, then the result is {@code 1.0}.
 1070        *
 1071        * </ul>
 1072        *
 1073        * @param   x The number whose hyperbolic cosine is to be returned.
 1074        * @return  The hyperbolic cosine of {@code x}.
 1075        * @since 1.5
 1076        */
 1077       public static native double cosh(double x);
 1078   
 1079       /**
 1080        * Returns the hyperbolic tangent of a {@code double} value.
 1081        * The hyperbolic tangent of <i>x</i> is defined to be
 1082        * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
 1083        * in other words, {@linkplain Math#sinh
 1084        * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}.  Note
 1085        * that the absolute value of the exact tanh is always less than
 1086        * 1.
 1087        *
 1088        * <p>Special cases:
 1089        * <ul>
 1090        *
 1091        * <li>If the argument is NaN, then the result is NaN.
 1092        *
 1093        * <li>If the argument is zero, then the result is a zero with the
 1094        * same sign as the argument.
 1095        *
 1096        * <li>If the argument is positive infinity, then the result is
 1097        * {@code +1.0}.
 1098        *
 1099        * <li>If the argument is negative infinity, then the result is
 1100        * {@code -1.0}.
 1101        *
 1102        * </ul>
 1103        *
 1104        * @param   x The number whose hyperbolic tangent is to be returned.
 1105        * @return  The hyperbolic tangent of {@code x}.
 1106        * @since 1.5
 1107        */
 1108       public static native double tanh(double x);
 1109   
 1110       /**
 1111        * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
 1112        * without intermediate overflow or underflow.
 1113        *
 1114        * <p>Special cases:
 1115        * <ul>
 1116        *
 1117        * <li> If either argument is infinite, then the result
 1118        * is positive infinity.
 1119        *
 1120        * <li> If either argument is NaN and neither argument is infinite,
 1121        * then the result is NaN.
 1122        *
 1123        * </ul>
 1124        *
 1125        * @param x a value
 1126        * @param y a value
 1127        * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
 1128        * without intermediate overflow or underflow
 1129        * @since 1.5
 1130        */
 1131       public static native double hypot(double x, double y);
 1132   
 1133       /**
 1134        * Returns <i>e</i><sup>x</sup>&nbsp;-1.  Note that for values of
 1135        * <i>x</i> near 0, the exact sum of
 1136        * {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
 1137        * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
 1138        *
 1139        * <p>Special cases:
 1140        * <ul>
 1141        * <li>If the argument is NaN, the result is NaN.
 1142        *
 1143        * <li>If the argument is positive infinity, then the result is
 1144        * positive infinity.
 1145        *
 1146        * <li>If the argument is negative infinity, then the result is
 1147        * -1.0.
 1148        *
 1149        * <li>If the argument is zero, then the result is a zero with the
 1150        * same sign as the argument.
 1151        *
 1152        * </ul>
 1153        *
 1154        * @param   x   the exponent to raise <i>e</i> to in the computation of
 1155        *              <i>e</i><sup>{@code x}</sup>&nbsp;-1.
 1156        * @return  the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
 1157        * @since 1.5
 1158        */
 1159       public static native double expm1(double x);
 1160   
 1161       /**
 1162        * Returns the natural logarithm of the sum of the argument and 1.
 1163        * Note that for small values {@code x}, the result of
 1164        * {@code log1p(x)} is much closer to the true result of ln(1
 1165        * + {@code x}) than the floating-point evaluation of
 1166        * {@code log(1.0+x)}.
 1167        *
 1168        * <p>Special cases:
 1169        * <ul>
 1170        *
 1171        * <li>If the argument is NaN or less than -1, then the result is
 1172        * NaN.
 1173        *
 1174        * <li>If the argument is positive infinity, then the result is
 1175        * positive infinity.
 1176        *
 1177        * <li>If the argument is negative one, then the result is
 1178        * negative infinity.
 1179        *
 1180        * <li>If the argument is zero, then the result is a zero with the
 1181        * same sign as the argument.
 1182        *
 1183        * </ul>
 1184        *
 1185        * @param   x   a value
 1186        * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
 1187        * log of {@code x}&nbsp;+&nbsp;1
 1188        * @since 1.5
 1189        */
 1190       public static native double log1p(double x);
 1191   
 1192       /**
 1193        * Returns the first floating-point argument with the sign of the
 1194        * second floating-point argument.  For this method, a NaN
 1195        * {@code sign} argument is always treated as if it were
 1196        * positive.
 1197        *
 1198        * @param magnitude  the parameter providing the magnitude of the result
 1199        * @param sign   the parameter providing the sign of the result
 1200        * @return a value with the magnitude of {@code magnitude}
 1201        * and the sign of {@code sign}.
 1202        * @since 1.6
 1203        */
 1204       public static double copySign(double magnitude, double sign) {
 1205           return sun.misc.FpUtils.copySign(magnitude, sign);
 1206       }
 1207   
 1208       /**
 1209        * Returns the first floating-point argument with the sign of the
 1210        * second floating-point argument.  For this method, a NaN
 1211        * {@code sign} argument is always treated as if it were
 1212        * positive.
 1213        *
 1214        * @param magnitude  the parameter providing the magnitude of the result
 1215        * @param sign   the parameter providing the sign of the result
 1216        * @return a value with the magnitude of {@code magnitude}
 1217        * and the sign of {@code sign}.
 1218        * @since 1.6
 1219        */
 1220       public static float copySign(float magnitude, float sign) {
 1221           return sun.misc.FpUtils.copySign(magnitude, sign);
 1222       }
 1223       /**
 1224        * Returns the unbiased exponent used in the representation of a
 1225        * {@code float}.  Special cases:
 1226        *
 1227        * <ul>
 1228        * <li>If the argument is NaN or infinite, then the result is
 1229        * {@link Float#MAX_EXPONENT} + 1.
 1230        * <li>If the argument is zero or subnormal, then the result is
 1231        * {@link Float#MIN_EXPONENT} -1.
 1232        * </ul>
 1233        * @param f a {@code float} value
 1234        * @since 1.6
 1235        */
 1236       public static int getExponent(float f) {
 1237           return sun.misc.FpUtils.getExponent(f);
 1238       }
 1239   
 1240       /**
 1241        * Returns the unbiased exponent used in the representation of a
 1242        * {@code double}.  Special cases:
 1243        *
 1244        * <ul>
 1245        * <li>If the argument is NaN or infinite, then the result is
 1246        * {@link Double#MAX_EXPONENT} + 1.
 1247        * <li>If the argument is zero or subnormal, then the result is
 1248        * {@link Double#MIN_EXPONENT} -1.
 1249        * </ul>
 1250        * @param d a {@code double} value
 1251        * @since 1.6
 1252        */
 1253       public static int getExponent(double d) {
 1254           return sun.misc.FpUtils.getExponent(d);
 1255       }
 1256   
 1257       /**
 1258        * Returns the floating-point number adjacent to the first
 1259        * argument in the direction of the second argument.  If both
 1260        * arguments compare as equal the second argument is returned.
 1261        *
 1262        * <p>Special cases:
 1263        * <ul>
 1264        * <li> If either argument is a NaN, then NaN is returned.
 1265        *
 1266        * <li> If both arguments are signed zeros, {@code direction}
 1267        * is returned unchanged (as implied by the requirement of
 1268        * returning the second argument if the arguments compare as
 1269        * equal).
 1270        *
 1271        * <li> If {@code start} is
 1272        * &plusmn;{@link Double#MIN_VALUE} and {@code direction}
 1273        * has a value such that the result should have a smaller
 1274        * magnitude, then a zero with the same sign as {@code start}
 1275        * is returned.
 1276        *
 1277        * <li> If {@code start} is infinite and
 1278        * {@code direction} has a value such that the result should
 1279        * have a smaller magnitude, {@link Double#MAX_VALUE} with the
 1280        * same sign as {@code start} is returned.
 1281        *
 1282        * <li> If {@code start} is equal to &plusmn;
 1283        * {@link Double#MAX_VALUE} and {@code direction} has a
 1284        * value such that the result should have a larger magnitude, an
 1285        * infinity with same sign as {@code start} is returned.
 1286        * </ul>
 1287        *
 1288        * @param start  starting floating-point value
 1289        * @param direction value indicating which of
 1290        * {@code start}'s neighbors or {@code start} should
 1291        * be returned
 1292        * @return The floating-point number adjacent to {@code start} in the
 1293        * direction of {@code direction}.
 1294        * @since 1.6
 1295        */
 1296       public static double nextAfter(double start, double direction) {
 1297           return sun.misc.FpUtils.nextAfter(start, direction);
 1298       }
 1299   
 1300       /**
 1301        * Returns the floating-point number adjacent to the first
 1302        * argument in the direction of the second argument.  If both
 1303        * arguments compare as equal a value equivalent to the second argument
 1304        * is returned.
 1305        *
 1306        * <p>Special cases:
 1307        * <ul>
 1308        * <li> If either argument is a NaN, then NaN is returned.
 1309        *
 1310        * <li> If both arguments are signed zeros, a value equivalent
 1311        * to {@code direction} is returned.
 1312        *
 1313        * <li> If {@code start} is
 1314        * &plusmn;{@link Float#MIN_VALUE} and {@code direction}
 1315        * has a value such that the result should have a smaller
 1316        * magnitude, then a zero with the same sign as {@code start}
 1317        * is returned.
 1318        *
 1319        * <li> If {@code start} is infinite and
 1320        * {@code direction} has a value such that the result should
 1321        * have a smaller magnitude, {@link Float#MAX_VALUE} with the
 1322        * same sign as {@code start} is returned.
 1323        *
 1324        * <li> If {@code start} is equal to &plusmn;
 1325        * {@link Float#MAX_VALUE} and {@code direction} has a
 1326        * value such that the result should have a larger magnitude, an
 1327        * infinity with same sign as {@code start} is returned.
 1328        * </ul>
 1329        *
 1330        * @param start  starting floating-point value
 1331        * @param direction value indicating which of
 1332        * {@code start}'s neighbors or {@code start} should
 1333        * be returned
 1334        * @return The floating-point number adjacent to {@code start} in the
 1335        * direction of {@code direction}.
 1336        * @since 1.6
 1337        */
 1338       public static float nextAfter(float start, double direction) {
 1339           return sun.misc.FpUtils.nextAfter(start, direction);
 1340       }
 1341   
 1342       /**
 1343        * Returns the floating-point value adjacent to {@code d} in
 1344        * the direction of positive infinity.  This method is
 1345        * semantically equivalent to {@code nextAfter(d,
 1346        * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
 1347        * implementation may run faster than its equivalent
 1348        * {@code nextAfter} call.
 1349        *
 1350        * <p>Special Cases:
 1351        * <ul>
 1352        * <li> If the argument is NaN, the result is NaN.
 1353        *
 1354        * <li> If the argument is positive infinity, the result is
 1355        * positive infinity.
 1356        *
 1357        * <li> If the argument is zero, the result is
 1358        * {@link Double#MIN_VALUE}
 1359        *
 1360        * </ul>
 1361        *
 1362        * @param d starting floating-point value
 1363        * @return The adjacent floating-point value closer to positive
 1364        * infinity.
 1365        * @since 1.6
 1366        */
 1367       public static double nextUp(double d) {
 1368           return sun.misc.FpUtils.nextUp(d);
 1369       }
 1370   
 1371       /**
 1372        * Returns the floating-point value adjacent to {@code f} in
 1373        * the direction of positive infinity.  This method is
 1374        * semantically equivalent to {@code nextAfter(f,
 1375        * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
 1376        * implementation may run faster than its equivalent
 1377        * {@code nextAfter} call.
 1378        *
 1379        * <p>Special Cases:
 1380        * <ul>
 1381        * <li> If the argument is NaN, the result is NaN.
 1382        *
 1383        * <li> If the argument is positive infinity, the result is
 1384        * positive infinity.
 1385        *
 1386        * <li> If the argument is zero, the result is
 1387        * {@link Float#MIN_VALUE}
 1388        *
 1389        * </ul>
 1390        *
 1391        * @param f starting floating-point value
 1392        * @return The adjacent floating-point value closer to positive
 1393        * infinity.
 1394        * @since 1.6
 1395        */
 1396       public static float nextUp(float f) {
 1397           return sun.misc.FpUtils.nextUp(f);
 1398       }
 1399   
 1400   
 1401       /**
 1402        * Return {@code d} &times;
 1403        * 2<sup>{@code scaleFactor}</sup> rounded as if performed
 1404        * by a single correctly rounded floating-point multiply to a
 1405        * member of the double value set.  See the Java
 1406        * Language Specification for a discussion of floating-point
 1407        * value sets.  If the exponent of the result is between {@link
 1408        * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
 1409        * answer is calculated exactly.  If the exponent of the result
 1410        * would be larger than {@code Double.MAX_EXPONENT}, an
 1411        * infinity is returned.  Note that if the result is subnormal,
 1412        * precision may be lost; that is, when {@code scalb(x, n)}
 1413        * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
 1414        * <i>x</i>.  When the result is non-NaN, the result has the same
 1415        * sign as {@code d}.
 1416        *
 1417        * <p>Special cases:
 1418        * <ul>
 1419        * <li> If the first argument is NaN, NaN is returned.
 1420        * <li> If the first argument is infinite, then an infinity of the
 1421        * same sign is returned.
 1422        * <li> If the first argument is zero, then a zero of the same
 1423        * sign is returned.
 1424        * </ul>
 1425        *
 1426        * @param d number to be scaled by a power of two.
 1427        * @param scaleFactor power of 2 used to scale {@code d}
 1428        * @return {@code d} &times; 2<sup>{@code scaleFactor}</sup>
 1429        * @since 1.6
 1430        */
 1431       public static double scalb(double d, int scaleFactor) {
 1432           return sun.misc.FpUtils.scalb(d, scaleFactor);
 1433       }
 1434   
 1435       /**
 1436        * Return {@code f} &times;
 1437        * 2<sup>{@code scaleFactor}</sup> rounded as if performed
 1438        * by a single correctly rounded floating-point multiply to a
 1439        * member of the float value set.  See the Java
 1440        * Language Specification for a discussion of floating-point
 1441        * value sets.  If the exponent of the result is between {@link
 1442        * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
 1443        * answer is calculated exactly.  If the exponent of the result
 1444        * would be larger than {@code Float.MAX_EXPONENT}, an
 1445        * infinity is returned.  Note that if the result is subnormal,
 1446        * precision may be lost; that is, when {@code scalb(x, n)}
 1447        * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
 1448        * <i>x</i>.  When the result is non-NaN, the result has the same
 1449        * sign as {@code f}.
 1450        *
 1451        * <p>Special cases:
 1452        * <ul>
 1453        * <li> If the first argument is NaN, NaN is returned.
 1454        * <li> If the first argument is infinite, then an infinity of the
 1455        * same sign is returned.
 1456        * <li> If the first argument is zero, then a zero of the same
 1457        * sign is returned.
 1458        * </ul>
 1459        *
 1460        * @param f number to be scaled by a power of two.
 1461        * @param scaleFactor power of 2 used to scale {@code f}
 1462        * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
 1463        * @since 1.6
 1464        */
 1465       public static float scalb(float f, int scaleFactor) {
 1466           return sun.misc.FpUtils.scalb(f, scaleFactor);
 1467       }
 1468   }

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