rev 10702 : 4477961: java.lang.Math.toDegrees(double) could be optimized
Summary: Change toDegrees() and toRadians() to multiplication by a compile-time constant.
Reviewed-by: mduigou, shade

   1 /*
   2  * Copyright (c) 1999, 2013, Oracle and/or its affiliates. All rights reserved.
   3  * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
   4  *
   5  * This code is free software; you can redistribute it and/or modify it
   6  * under the terms of the GNU General Public License version 2 only, as
   7  * published by the Free Software Foundation.  Oracle designates this
   8  * particular file as subject to the "Classpath" exception as provided
   9  * by Oracle in the LICENSE file that accompanied this code.
  10  *
  11  * This code is distributed in the hope that it will be useful, but WITHOUT
  12  * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
  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).
  16  *
  17  * You should have received a copy of the GNU General Public License version
  18  * 2 along with this work; if not, write to the Free Software Foundation,
  19  * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
  20  *
  21  * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
  22  * or visit www.oracle.com if you need additional information or have any
  23  * questions.
  24  */
  25 
  26 package java.lang;
  27 import java.util.Random;
  28 import sun.misc.DoubleConsts;
  29 
  30 /**
  31  * The class {@code StrictMath} contains methods for performing basic
  32  * numeric operations such as the elementary exponential, logarithm,
  33  * square root, and trigonometric functions.
  34  *
  35  * <p>To help ensure portability of Java programs, the definitions of
  36  * some of the numeric functions in this package require that they
  37  * produce the same results as certain published algorithms. These
  38  * algorithms are available from the well-known network library
  39  * {@code netlib} as the package "Freely Distributable Math
  40  * Library," <a
  41  * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
  42  * algorithms, which are written in the C programming language, are
  43  * then to be understood as executed with all floating-point
  44  * operations following the rules of Java floating-point arithmetic.
  45  *
  46  * <p>The Java math library is defined with respect to
  47  * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
  48  * more than one definition for a function (such as
  49  * {@code acos}), use the "IEEE 754 core function" version
  50  * (residing in a file whose name begins with the letter
  51  * {@code e}).  The methods which require {@code fdlibm}
  52  * semantics are {@code sin}, {@code cos}, {@code tan},
  53  * {@code asin}, {@code acos}, {@code atan},
  54  * {@code exp}, {@code log}, {@code log10},
  55  * {@code cbrt}, {@code atan2}, {@code pow},
  56  * {@code sinh}, {@code cosh}, {@code tanh},
  57  * {@code hypot}, {@code expm1}, and {@code log1p}.
  58  *
  59  * <p>
  60  * The platform uses signed two's complement integer arithmetic with
  61  * int and long primitive types.  The developer should choose
  62  * the primitive type to ensure that arithmetic operations consistently
  63  * produce correct results, which in some cases means the operations
  64  * will not overflow the range of values of the computation.
  65  * The best practice is to choose the primitive type and algorithm to avoid
  66  * overflow. In cases where the size is {@code int} or {@code long} and
  67  * overflow errors need to be detected, the methods {@code addExact},
  68  * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
  69  * throw an {@code ArithmeticException} when the results overflow.
  70  * For other arithmetic operations such as divide, absolute value,
  71  * increment, decrement, and negation overflow occurs only with
  72  * a specific minimum or maximum value and should be checked against
  73  * the minimum or maximum as appropriate.
  74  *
  75  * @author  unascribed
  76  * @author  Joseph D. Darcy
  77  * @since   1.3
  78  */
  79 
  80 public final class StrictMath {
  81 
  82     /**
  83      * Don't let anyone instantiate this class.
  84      */
  85     private StrictMath() {}
  86 
  87     /**
  88      * The {@code double} value that is closer than any other to
  89      * <i>e</i>, the base of the natural logarithms.
  90      */
  91     public static final double E = 2.7182818284590452354;
  92 
  93     /**
  94      * The {@code double} value that is closer than any other to
  95      * <i>pi</i>, the ratio of the circumference of a circle to its
  96      * diameter.
  97      */
  98     public static final double PI = 3.14159265358979323846;
  99 
 100     /**
 101      * Constant by which to multiply an angular value in degrees to obtain an
 102      * angular value in radians.
 103      */
 104     private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
 105 
 106     /**
 107      * Constant by which to multiply an angular value in radians to obtain an
 108      * angular value in degrees.
 109      */
 110 
 111     private static final double RADIANS_TO_DEGREES = 57.29577951308232;
 112     /**
 113      * Returns the trigonometric sine of an angle. Special cases:
 114      * <ul><li>If the argument is NaN or an infinity, then the
 115      * result is NaN.
 116      * <li>If the argument is zero, then the result is a zero with the
 117      * same sign as the argument.</ul>
 118      *
 119      * @param   a   an angle, in radians.
 120      * @return  the sine of the argument.
 121      */
 122     public static native double sin(double a);
 123 
 124     /**
 125      * Returns the trigonometric cosine of an angle. Special cases:
 126      * <ul><li>If the argument is NaN or an infinity, then the
 127      * result is NaN.</ul>
 128      *
 129      * @param   a   an angle, in radians.
 130      * @return  the cosine of the argument.
 131      */
 132     public static native double cos(double a);
 133 
 134     /**
 135      * Returns the trigonometric tangent of an angle. Special cases:
 136      * <ul><li>If the argument is NaN or an infinity, then the result
 137      * is NaN.
 138      * <li>If the argument is zero, then the result is a zero with the
 139      * same sign as the argument.</ul>
 140      *
 141      * @param   a   an angle, in radians.
 142      * @return  the tangent of the argument.
 143      */
 144     public static native double tan(double a);
 145 
 146     /**
 147      * Returns the arc sine of a value; the returned angle is in the
 148      * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
 149      * <ul><li>If the argument is NaN or its absolute value is greater
 150      * than 1, then the result is NaN.
 151      * <li>If the argument is zero, then the result is a zero with the
 152      * same sign as the argument.</ul>
 153      *
 154      * @param   a   the value whose arc sine is to be returned.
 155      * @return  the arc sine of the argument.
 156      */
 157     public static native double asin(double a);
 158 
 159     /**
 160      * Returns the arc cosine of a value; the returned angle is in the
 161      * range 0.0 through <i>pi</i>.  Special case:
 162      * <ul><li>If the argument is NaN or its absolute value is greater
 163      * than 1, then the result is NaN.</ul>
 164      *
 165      * @param   a   the value whose arc cosine is to be returned.
 166      * @return  the arc cosine of the argument.
 167      */
 168     public static native double acos(double a);
 169 
 170     /**
 171      * Returns the arc tangent of a value; the returned angle is in the
 172      * range -<i>pi</i>/2 through <i>pi</i>/2.  Special cases:
 173      * <ul><li>If the argument is NaN, then the result is NaN.
 174      * <li>If the argument is zero, then the result is a zero with the
 175      * same sign as the argument.</ul>
 176      *
 177      * @param   a   the value whose arc tangent is to be returned.
 178      * @return  the arc tangent of the argument.
 179      */
 180     public static native double atan(double a);
 181 
 182     /**
 183      * Converts an angle measured in degrees to an approximately
 184      * equivalent angle measured in radians.  The conversion from
 185      * degrees to radians is generally inexact.
 186      *
 187      * @param   angdeg   an angle, in degrees
 188      * @return  the measurement of the angle {@code angdeg}
 189      *          in radians.
 190      */
 191     public static strictfp double toRadians(double angdeg) {
 192         // Do not delegate to Math.toRadians(angdeg) because
 193         // this method has the strictfp modifier.
 194         return angdeg * DEGREES_TO_RADIANS;
 195     }
 196 
 197     /**
 198      * Converts an angle measured in radians to an approximately
 199      * equivalent angle measured in degrees.  The conversion from
 200      * radians to degrees is generally inexact; users should
 201      * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
 202      * equal {@code 0.0}.
 203      *
 204      * @param   angrad   an angle, in radians
 205      * @return  the measurement of the angle {@code angrad}
 206      *          in degrees.
 207      */
 208     public static strictfp double toDegrees(double angrad) {
 209         // Do not delegate to Math.toDegrees(angrad) because
 210         // this method has the strictfp modifier.
 211         return angrad * RADIANS_TO_DEGREES;
 212     }
 213 
 214     /**
 215      * Returns Euler's number <i>e</i> raised to the power of a
 216      * {@code double} value. Special cases:
 217      * <ul><li>If the argument is NaN, the result is NaN.
 218      * <li>If the argument is positive infinity, then the result is
 219      * positive infinity.
 220      * <li>If the argument is negative infinity, then the result is
 221      * positive zero.</ul>
 222      *
 223      * @param   a   the exponent to raise <i>e</i> to.
 224      * @return  the value <i>e</i><sup>{@code a}</sup>,
 225      *          where <i>e</i> is the base of the natural logarithms.
 226      */
 227     public static native double exp(double a);
 228 
 229     /**
 230      * Returns the natural logarithm (base <i>e</i>) of a {@code double}
 231      * value. Special cases:
 232      * <ul><li>If the argument is NaN or less than zero, then the result
 233      * is NaN.
 234      * <li>If the argument is positive infinity, then the result is
 235      * positive infinity.
 236      * <li>If the argument is positive zero or negative zero, then the
 237      * result is negative infinity.</ul>
 238      *
 239      * @param   a   a value
 240      * @return  the value ln&nbsp;{@code a}, the natural logarithm of
 241      *          {@code a}.
 242      */
 243     public static native double log(double a);
 244 
 245 
 246     /**
 247      * Returns the base 10 logarithm of a {@code double} value.
 248      * Special cases:
 249      *
 250      * <ul><li>If the argument is NaN or less than zero, then the result
 251      * is NaN.
 252      * <li>If the argument is positive infinity, then the result is
 253      * positive infinity.
 254      * <li>If the argument is positive zero or negative zero, then the
 255      * result is negative infinity.
 256      * <li> If the argument is equal to 10<sup><i>n</i></sup> for
 257      * integer <i>n</i>, then the result is <i>n</i>.
 258      * </ul>
 259      *
 260      * @param   a   a value
 261      * @return  the base 10 logarithm of  {@code a}.
 262      * @since 1.5
 263      */
 264     public static native double log10(double a);
 265 
 266     /**
 267      * Returns the correctly rounded positive square root of a
 268      * {@code double} value.
 269      * Special cases:
 270      * <ul><li>If the argument is NaN or less than zero, then the result
 271      * is NaN.
 272      * <li>If the argument is positive infinity, then the result is positive
 273      * infinity.
 274      * <li>If the argument is positive zero or negative zero, then the
 275      * result is the same as the argument.</ul>
 276      * Otherwise, the result is the {@code double} value closest to
 277      * the true mathematical square root of the argument value.
 278      *
 279      * @param   a   a value.
 280      * @return  the positive square root of {@code a}.
 281      */
 282     public static native double sqrt(double a);
 283 
 284     /**
 285      * Returns the cube root of a {@code double} value.  For
 286      * positive finite {@code x}, {@code cbrt(-x) ==
 287      * -cbrt(x)}; that is, the cube root of a negative value is
 288      * the negative of the cube root of that value's magnitude.
 289      * Special cases:
 290      *
 291      * <ul>
 292      *
 293      * <li>If the argument is NaN, then the result is NaN.
 294      *
 295      * <li>If the argument is infinite, then the result is an infinity
 296      * with the same sign as the argument.
 297      *
 298      * <li>If the argument is zero, then the result is a zero with the
 299      * same sign as the argument.
 300      *
 301      * </ul>
 302      *
 303      * @param   a   a value.
 304      * @return  the cube root of {@code a}.
 305      * @since 1.5
 306      */
 307     public static native double cbrt(double a);
 308 
 309     /**
 310      * Computes the remainder operation on two arguments as prescribed
 311      * by the IEEE 754 standard.
 312      * The remainder value is mathematically equal to
 313      * <code>f1&nbsp;-&nbsp;f2</code>&nbsp;&times;&nbsp;<i>n</i>,
 314      * where <i>n</i> is the mathematical integer closest to the exact
 315      * mathematical value of the quotient {@code f1/f2}, and if two
 316      * mathematical integers are equally close to {@code f1/f2},
 317      * then <i>n</i> is the integer that is even. If the remainder is
 318      * zero, its sign is the same as the sign of the first argument.
 319      * Special cases:
 320      * <ul><li>If either argument is NaN, or the first argument is infinite,
 321      * or the second argument is positive zero or negative zero, then the
 322      * result is NaN.
 323      * <li>If the first argument is finite and the second argument is
 324      * infinite, then the result is the same as the first argument.</ul>
 325      *
 326      * @param   f1   the dividend.
 327      * @param   f2   the divisor.
 328      * @return  the remainder when {@code f1} is divided by
 329      *          {@code f2}.
 330      */
 331     public static native double IEEEremainder(double f1, double f2);
 332 
 333     /**
 334      * Returns the smallest (closest to negative infinity)
 335      * {@code double} value that is greater than or equal to the
 336      * argument and is equal to a mathematical integer. Special cases:
 337      * <ul><li>If the argument value is already equal to a
 338      * mathematical integer, then the result is the same as the
 339      * argument.  <li>If the argument is NaN or an infinity or
 340      * positive zero or negative zero, then the result is the same as
 341      * the argument.  <li>If the argument value is less than zero but
 342      * greater than -1.0, then the result is negative zero.</ul> Note
 343      * that the value of {@code StrictMath.ceil(x)} is exactly the
 344      * value of {@code -StrictMath.floor(-x)}.
 345      *
 346      * @param   a   a value.
 347      * @return  the smallest (closest to negative infinity)
 348      *          floating-point value that is greater than or equal to
 349      *          the argument and is equal to a mathematical integer.
 350      */
 351     public static double ceil(double a) {
 352         return floorOrCeil(a, -0.0, 1.0, 1.0);
 353     }
 354 
 355     /**
 356      * Returns the largest (closest to positive infinity)
 357      * {@code double} value that is less than or equal to the
 358      * argument and is equal to a mathematical integer. Special cases:
 359      * <ul><li>If the argument value is already equal to a
 360      * mathematical integer, then the result is the same as the
 361      * argument.  <li>If the argument is NaN or an infinity or
 362      * positive zero or negative zero, then the result is the same as
 363      * the argument.</ul>
 364      *
 365      * @param   a   a value.
 366      * @return  the largest (closest to positive infinity)
 367      *          floating-point value that less than or equal to the argument
 368      *          and is equal to a mathematical integer.
 369      */
 370     public static double floor(double a) {
 371         return floorOrCeil(a, -1.0, 0.0, -1.0);
 372     }
 373 
 374     /**
 375      * Internal method to share logic between floor and ceil.
 376      *
 377      * @param a the value to be floored or ceiled
 378      * @param negativeBoundary result for values in (-1, 0)
 379      * @param positiveBoundary result for values in (0, 1)
 380      * @param increment value to add when the argument is non-integral
 381      */
 382     private static double floorOrCeil(double a,
 383                                       double negativeBoundary,
 384                                       double positiveBoundary,
 385                                       double sign) {
 386         int exponent = Math.getExponent(a);
 387 
 388         if (exponent < 0) {
 389             /*
 390              * Absolute value of argument is less than 1.
 391              * floorOrceil(-0.0) => -0.0
 392              * floorOrceil(+0.0) => +0.0
 393              */
 394             return ((a == 0.0) ? a :
 395                     ( (a < 0.0) ?  negativeBoundary : positiveBoundary) );
 396         } else if (exponent >= 52) {
 397             /*
 398              * Infinity, NaN, or a value so large it must be integral.
 399              */
 400             return a;
 401         }
 402         // Else the argument is either an integral value already XOR it
 403         // has to be rounded to one.
 404         assert exponent >= 0 && exponent <= 51;
 405 
 406         long doppel = Double.doubleToRawLongBits(a);
 407         long mask   = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
 408 
 409         if ( (mask & doppel) == 0L )
 410             return a; // integral value
 411         else {
 412             double result = Double.longBitsToDouble(doppel & (~mask));
 413             if (sign*a > 0.0)
 414                 result = result + sign;
 415             return result;
 416         }
 417     }
 418 
 419     /**
 420      * Returns the {@code double} value that is closest in value
 421      * to the argument and is equal to a mathematical integer. If two
 422      * {@code double} values that are mathematical integers are
 423      * equally close to the value of the argument, the result is the
 424      * integer value that is even. Special cases:
 425      * <ul><li>If the argument value is already equal to a mathematical
 426      * integer, then the result is the same as the argument.
 427      * <li>If the argument is NaN or an infinity or positive zero or negative
 428      * zero, then the result is the same as the argument.</ul>
 429      *
 430      * @param   a   a value.
 431      * @return  the closest floating-point value to {@code a} that is
 432      *          equal to a mathematical integer.
 433      * @author Joseph D. Darcy
 434      */
 435     public static double rint(double a) {
 436         /*
 437          * If the absolute value of a is not less than 2^52, it
 438          * is either a finite integer (the double format does not have
 439          * enough significand bits for a number that large to have any
 440          * fractional portion), an infinity, or a NaN.  In any of
 441          * these cases, rint of the argument is the argument.
 442          *
 443          * Otherwise, the sum (twoToThe52 + a ) will properly round
 444          * away any fractional portion of a since ulp(twoToThe52) ==
 445          * 1.0; subtracting out twoToThe52 from this sum will then be
 446          * exact and leave the rounded integer portion of a.
 447          *
 448          * This method does *not* need to be declared strictfp to get
 449          * fully reproducible results.  Whether or not a method is
 450          * declared strictfp can only make a difference in the
 451          * returned result if some operation would overflow or
 452          * underflow with strictfp semantics.  The operation
 453          * (twoToThe52 + a ) cannot overflow since large values of a
 454          * are screened out; the add cannot underflow since twoToThe52
 455          * is too large.  The subtraction ((twoToThe52 + a ) -
 456          * twoToThe52) will be exact as discussed above and thus
 457          * cannot overflow or meaningfully underflow.  Finally, the
 458          * last multiply in the return statement is by plus or minus
 459          * 1.0, which is exact too.
 460          */
 461         double twoToThe52 = (double)(1L << 52); // 2^52
 462         double sign = Math.copySign(1.0, a); // preserve sign info
 463         a = Math.abs(a);
 464 
 465         if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
 466             a = ((twoToThe52 + a ) - twoToThe52);
 467         }
 468 
 469         return sign * a; // restore original sign
 470     }
 471 
 472     /**
 473      * Returns the angle <i>theta</i> from the conversion of rectangular
 474      * coordinates ({@code x},&nbsp;{@code y}) to polar
 475      * coordinates (r,&nbsp;<i>theta</i>).
 476      * This method computes the phase <i>theta</i> by computing an arc tangent
 477      * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
 478      * cases:
 479      * <ul><li>If either argument is NaN, then the result is NaN.
 480      * <li>If the first argument is positive zero and the second argument
 481      * is positive, or the first argument is positive and finite and the
 482      * second argument is positive infinity, then the result is positive
 483      * zero.
 484      * <li>If the first argument is negative zero and the second argument
 485      * is positive, or the first argument is negative and finite and the
 486      * second argument is positive infinity, then the result is negative zero.
 487      * <li>If the first argument is positive zero and the second argument
 488      * is negative, or the first argument is positive and finite and the
 489      * second argument is negative infinity, then the result is the
 490      * {@code double} value closest to <i>pi</i>.
 491      * <li>If the first argument is negative zero and the second argument
 492      * is negative, or the first argument is negative and finite and the
 493      * second argument is negative infinity, then the result is the
 494      * {@code double} value closest to -<i>pi</i>.
 495      * <li>If the first argument is positive and the second argument is
 496      * positive zero or negative zero, or the first argument is positive
 497      * infinity and the second argument is finite, then the result is the
 498      * {@code double} value closest to <i>pi</i>/2.
 499      * <li>If the first argument is negative and the second argument is
 500      * positive zero or negative zero, or the first argument is negative
 501      * infinity and the second argument is finite, then the result is the
 502      * {@code double} value closest to -<i>pi</i>/2.
 503      * <li>If both arguments are positive infinity, then the result is the
 504      * {@code double} value closest to <i>pi</i>/4.
 505      * <li>If the first argument is positive infinity and the second argument
 506      * is negative infinity, then the result is the {@code double}
 507      * value closest to 3*<i>pi</i>/4.
 508      * <li>If the first argument is negative infinity and the second argument
 509      * is positive infinity, then the result is the {@code double} value
 510      * closest to -<i>pi</i>/4.
 511      * <li>If both arguments are negative infinity, then the result is the
 512      * {@code double} value closest to -3*<i>pi</i>/4.</ul>
 513      *
 514      * @param   y   the ordinate coordinate
 515      * @param   x   the abscissa coordinate
 516      * @return  the <i>theta</i> component of the point
 517      *          (<i>r</i>,&nbsp;<i>theta</i>)
 518      *          in polar coordinates that corresponds to the point
 519      *          (<i>x</i>,&nbsp;<i>y</i>) in Cartesian coordinates.
 520      */
 521     public static native double atan2(double y, double x);
 522 
 523 
 524     /**
 525      * Returns the value of the first argument raised to the power of the
 526      * second argument. Special cases:
 527      *
 528      * <ul><li>If the second argument is positive or negative zero, then the
 529      * result is 1.0.
 530      * <li>If the second argument is 1.0, then the result is the same as the
 531      * first argument.
 532      * <li>If the second argument is NaN, then the result is NaN.
 533      * <li>If the first argument is NaN and the second argument is nonzero,
 534      * then the result is NaN.
 535      *
 536      * <li>If
 537      * <ul>
 538      * <li>the absolute value of the first argument is greater than 1
 539      * and the second argument is positive infinity, or
 540      * <li>the absolute value of the first argument is less than 1 and
 541      * the second argument is negative infinity,
 542      * </ul>
 543      * then the result is positive infinity.
 544      *
 545      * <li>If
 546      * <ul>
 547      * <li>the absolute value of the first argument is greater than 1 and
 548      * the second argument is negative infinity, or
 549      * <li>the absolute value of the
 550      * first argument is less than 1 and the second argument is positive
 551      * infinity,
 552      * </ul>
 553      * then the result is positive zero.
 554      *
 555      * <li>If the absolute value of the first argument equals 1 and the
 556      * second argument is infinite, then the result is NaN.
 557      *
 558      * <li>If
 559      * <ul>
 560      * <li>the first argument is positive zero and the second argument
 561      * is greater than zero, or
 562      * <li>the first argument is positive infinity and the second
 563      * argument is less than zero,
 564      * </ul>
 565      * then the result is positive zero.
 566      *
 567      * <li>If
 568      * <ul>
 569      * <li>the first argument is positive zero and the second argument
 570      * is less than zero, or
 571      * <li>the first argument is positive infinity and the second
 572      * argument is greater than zero,
 573      * </ul>
 574      * then the result is positive infinity.
 575      *
 576      * <li>If
 577      * <ul>
 578      * <li>the first argument is negative zero and the second argument
 579      * is greater than zero but not a finite odd integer, or
 580      * <li>the first argument is negative infinity and the second
 581      * argument is less than zero but not a finite odd integer,
 582      * </ul>
 583      * then the result is positive zero.
 584      *
 585      * <li>If
 586      * <ul>
 587      * <li>the first argument is negative zero and the second argument
 588      * is a positive finite odd integer, or
 589      * <li>the first argument is negative infinity and the second
 590      * argument is a negative finite odd integer,
 591      * </ul>
 592      * then the result is negative zero.
 593      *
 594      * <li>If
 595      * <ul>
 596      * <li>the first argument is negative zero and the second argument
 597      * is less than zero but not a finite odd integer, or
 598      * <li>the first argument is negative infinity and the second
 599      * argument is greater than zero but not a finite odd integer,
 600      * </ul>
 601      * then the result is positive infinity.
 602      *
 603      * <li>If
 604      * <ul>
 605      * <li>the first argument is negative zero and the second argument
 606      * is a negative finite odd integer, or
 607      * <li>the first argument is negative infinity and the second
 608      * argument is a positive finite odd integer,
 609      * </ul>
 610      * then the result is negative infinity.
 611      *
 612      * <li>If the first argument is finite and less than zero
 613      * <ul>
 614      * <li> if the second argument is a finite even integer, the
 615      * result is equal to the result of raising the absolute value of
 616      * the first argument to the power of the second argument
 617      *
 618      * <li>if the second argument is a finite odd integer, the result
 619      * is equal to the negative of the result of raising the absolute
 620      * value of the first argument to the power of the second
 621      * argument
 622      *
 623      * <li>if the second argument is finite and not an integer, then
 624      * the result is NaN.
 625      * </ul>
 626      *
 627      * <li>If both arguments are integers, then the result is exactly equal
 628      * to the mathematical result of raising the first argument to the power
 629      * of the second argument if that result can in fact be represented
 630      * exactly as a {@code double} value.</ul>
 631      *
 632      * <p>(In the foregoing descriptions, a floating-point value is
 633      * considered to be an integer if and only if it is finite and a
 634      * fixed point of the method {@link #ceil ceil} or,
 635      * equivalently, a fixed point of the method {@link #floor
 636      * floor}. A value is a fixed point of a one-argument
 637      * method if and only if the result of applying the method to the
 638      * value is equal to the value.)
 639      *
 640      * @param   a   base.
 641      * @param   b   the exponent.
 642      * @return  the value {@code a}<sup>{@code b}</sup>.
 643      */
 644     public static native double pow(double a, double b);
 645 
 646     /**
 647      * Returns the closest {@code int} to the argument, with ties
 648      * rounding to positive infinity.
 649      *
 650      * <p>Special cases:
 651      * <ul><li>If the argument is NaN, the result is 0.
 652      * <li>If the argument is negative infinity or any value less than or
 653      * equal to the value of {@code Integer.MIN_VALUE}, the result is
 654      * equal to the value of {@code Integer.MIN_VALUE}.
 655      * <li>If the argument is positive infinity or any value greater than or
 656      * equal to the value of {@code Integer.MAX_VALUE}, the result is
 657      * equal to the value of {@code Integer.MAX_VALUE}.</ul>
 658      *
 659      * @param   a   a floating-point value to be rounded to an integer.
 660      * @return  the value of the argument rounded to the nearest
 661      *          {@code int} value.
 662      * @see     java.lang.Integer#MAX_VALUE
 663      * @see     java.lang.Integer#MIN_VALUE
 664      */
 665     public static int round(float a) {
 666         return Math.round(a);
 667     }
 668 
 669     /**
 670      * Returns the closest {@code long} to the argument, with ties
 671      * rounding to positive infinity.
 672      *
 673      * <p>Special cases:
 674      * <ul><li>If the argument is NaN, the result is 0.
 675      * <li>If the argument is negative infinity or any value less than or
 676      * equal to the value of {@code Long.MIN_VALUE}, the result is
 677      * equal to the value of {@code Long.MIN_VALUE}.
 678      * <li>If the argument is positive infinity or any value greater than or
 679      * equal to the value of {@code Long.MAX_VALUE}, the result is
 680      * equal to the value of {@code Long.MAX_VALUE}.</ul>
 681      *
 682      * @param   a  a floating-point value to be rounded to a
 683      *          {@code long}.
 684      * @return  the value of the argument rounded to the nearest
 685      *          {@code long} value.
 686      * @see     java.lang.Long#MAX_VALUE
 687      * @see     java.lang.Long#MIN_VALUE
 688      */
 689     public static long round(double a) {
 690         return Math.round(a);
 691     }
 692 
 693     private static final class RandomNumberGeneratorHolder {
 694         static final Random randomNumberGenerator = new Random();
 695     }
 696 
 697     /**
 698      * Returns a {@code double} value with a positive sign, greater
 699      * than or equal to {@code 0.0} and less than {@code 1.0}.
 700      * Returned values are chosen pseudorandomly with (approximately)
 701      * uniform distribution from that range.
 702      *
 703      * <p>When this method is first called, it creates a single new
 704      * pseudorandom-number generator, exactly as if by the expression
 705      *
 706      * <blockquote>{@code new java.util.Random()}</blockquote>
 707      *
 708      * This new pseudorandom-number generator is used thereafter for
 709      * all calls to this method and is used nowhere else.
 710      *
 711      * <p>This method is properly synchronized to allow correct use by
 712      * more than one thread. However, if many threads need to generate
 713      * pseudorandom numbers at a great rate, it may reduce contention
 714      * for each thread to have its own pseudorandom-number generator.
 715      *
 716      * @return  a pseudorandom {@code double} greater than or equal
 717      * to {@code 0.0} and less than {@code 1.0}.
 718      * @see Random#nextDouble()
 719      */
 720     public static double random() {
 721         return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
 722     }
 723 
 724     /**
 725      * Returns the sum of its arguments,
 726      * throwing an exception if the result overflows an {@code int}.
 727      *
 728      * @param x the first value
 729      * @param y the second value
 730      * @return the result
 731      * @throws ArithmeticException if the result overflows an int
 732      * @see Math#addExact(int,int)
 733      * @since 1.8
 734      */
 735     public static int addExact(int x, int y) {
 736         return Math.addExact(x, y);
 737     }
 738 
 739     /**
 740      * Returns the sum of its arguments,
 741      * throwing an exception if the result overflows a {@code long}.
 742      *
 743      * @param x the first value
 744      * @param y the second value
 745      * @return the result
 746      * @throws ArithmeticException if the result overflows a long
 747      * @see Math#addExact(long,long)
 748      * @since 1.8
 749      */
 750     public static long addExact(long x, long y) {
 751         return Math.addExact(x, y);
 752     }
 753 
 754     /**
 755      * Returns the difference of the arguments,
 756      * throwing an exception if the result overflows an {@code int}.
 757      *
 758      * @param x the first value
 759      * @param y the second value to subtract from the first
 760      * @return the result
 761      * @throws ArithmeticException if the result overflows an int
 762      * @see Math#subtractExact(int,int)
 763      * @since 1.8
 764      */
 765     public static int subtractExact(int x, int y) {
 766         return Math.subtractExact(x, y);
 767     }
 768 
 769     /**
 770      * Returns the difference of the arguments,
 771      * throwing an exception if the result overflows a {@code long}.
 772      *
 773      * @param x the first value
 774      * @param y the second value to subtract from the first
 775      * @return the result
 776      * @throws ArithmeticException if the result overflows a long
 777      * @see Math#subtractExact(long,long)
 778      * @since 1.8
 779      */
 780     public static long subtractExact(long x, long y) {
 781         return Math.subtractExact(x, y);
 782     }
 783 
 784     /**
 785      * Returns the product of the arguments,
 786      * throwing an exception if the result overflows an {@code int}.
 787      *
 788      * @param x the first value
 789      * @param y the second value
 790      * @return the result
 791      * @throws ArithmeticException if the result overflows an int
 792      * @see Math#multiplyExact(int,int)
 793      * @since 1.8
 794      */
 795     public static int multiplyExact(int x, int y) {
 796         return Math.multiplyExact(x, y);
 797     }
 798 
 799     /**
 800      * Returns the product of the arguments,
 801      * throwing an exception if the result overflows a {@code long}.
 802      *
 803      * @param x the first value
 804      * @param y the second value
 805      * @return the result
 806      * @throws ArithmeticException if the result overflows a long
 807      * @see Math#multiplyExact(long,long)
 808      * @since 1.8
 809      */
 810     public static long multiplyExact(long x, long y) {
 811         return Math.multiplyExact(x, y);
 812     }
 813 
 814     /**
 815      * Returns the value of the {@code long} argument;
 816      * throwing an exception if the value overflows an {@code int}.
 817      *
 818      * @param value the long value
 819      * @return the argument as an int
 820      * @throws ArithmeticException if the {@code argument} overflows an int
 821      * @see Math#toIntExact(long)
 822      * @since 1.8
 823      */
 824     public static int toIntExact(long value) {
 825         return Math.toIntExact(value);
 826     }
 827 
 828     /**
 829      * Returns the largest (closest to positive infinity)
 830      * {@code int} value that is less than or equal to the algebraic quotient.
 831      * There is one special case, if the dividend is the
 832      * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
 833      * then integer overflow occurs and
 834      * the result is equal to the {@code Integer.MIN_VALUE}.
 835      * <p>
 836      * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
 837      * a comparison to the integer division {@code /} operator.
 838      *
 839      * @param x the dividend
 840      * @param y the divisor
 841      * @return the largest (closest to positive infinity)
 842      * {@code int} value that is less than or equal to the algebraic quotient.
 843      * @throws ArithmeticException if the divisor {@code y} is zero
 844      * @see Math#floorDiv(int, int)
 845      * @see Math#floor(double)
 846      * @since 1.8
 847      */
 848     public static int floorDiv(int x, int y) {
 849         return Math.floorDiv(x, y);
 850     }
 851 
 852     /**
 853      * Returns the largest (closest to positive infinity)
 854      * {@code long} value that is less than or equal to the algebraic quotient.
 855      * There is one special case, if the dividend is the
 856      * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
 857      * then integer overflow occurs and
 858      * the result is equal to the {@code Long.MIN_VALUE}.
 859      * <p>
 860      * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
 861      * a comparison to the integer division {@code /} operator.
 862      *
 863      * @param x the dividend
 864      * @param y the divisor
 865      * @return the largest (closest to positive infinity)
 866      * {@code long} value that is less than or equal to the algebraic quotient.
 867      * @throws ArithmeticException if the divisor {@code y} is zero
 868      * @see Math#floorDiv(long, long)
 869      * @see Math#floor(double)
 870      * @since 1.8
 871      */
 872     public static long floorDiv(long x, long y) {
 873         return Math.floorDiv(x, y);
 874     }
 875 
 876     /**
 877      * Returns the floor modulus of the {@code int} arguments.
 878      * <p>
 879      * The floor modulus is {@code x - (floorDiv(x, y) * y)},
 880      * has the same sign as the divisor {@code y}, and
 881      * is in the range of {@code -abs(y) < r < +abs(y)}.
 882      * <p>
 883      * The relationship between {@code floorDiv} and {@code floorMod} is such that:
 884      * <ul>
 885      *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
 886      * </ul>
 887      * <p>
 888      * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
 889      * a comparison to the {@code %} operator.
 890      *
 891      * @param x the dividend
 892      * @param y the divisor
 893      * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
 894      * @throws ArithmeticException if the divisor {@code y} is zero
 895      * @see Math#floorMod(int, int)
 896      * @see StrictMath#floorDiv(int, int)
 897      * @since 1.8
 898      */
 899     public static int floorMod(int x, int y) {
 900         return Math.floorMod(x , y);
 901     }
 902     /**
 903      * Returns the floor modulus of the {@code long} arguments.
 904      * <p>
 905      * The floor modulus is {@code x - (floorDiv(x, y) * y)},
 906      * has the same sign as the divisor {@code y}, and
 907      * is in the range of {@code -abs(y) < r < +abs(y)}.
 908      * <p>
 909      * The relationship between {@code floorDiv} and {@code floorMod} is such that:
 910      * <ul>
 911      *   <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
 912      * </ul>
 913      * <p>
 914      * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
 915      * a comparison to the {@code %} operator.
 916      *
 917      * @param x the dividend
 918      * @param y the divisor
 919      * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
 920      * @throws ArithmeticException if the divisor {@code y} is zero
 921      * @see Math#floorMod(long, long)
 922      * @see StrictMath#floorDiv(long, long)
 923      * @since 1.8
 924      */
 925     public static long floorMod(long x, long y) {
 926         return Math.floorMod(x, y);
 927     }
 928 
 929     /**
 930      * Returns the absolute value of an {@code int} value.
 931      * If the argument is not negative, the argument is returned.
 932      * If the argument is negative, the negation of the argument is returned.
 933      *
 934      * <p>Note that if the argument is equal to the value of
 935      * {@link Integer#MIN_VALUE}, the most negative representable
 936      * {@code int} value, the result is that same value, which is
 937      * negative.
 938      *
 939      * @param   a   the  argument whose absolute value is to be determined.
 940      * @return  the absolute value of the argument.
 941      */
 942     public static int abs(int a) {
 943         return Math.abs(a);
 944     }
 945 
 946     /**
 947      * Returns the absolute value of a {@code long} value.
 948      * If the argument is not negative, the argument is returned.
 949      * If the argument is negative, the negation of the argument is returned.
 950      *
 951      * <p>Note that if the argument is equal to the value of
 952      * {@link Long#MIN_VALUE}, the most negative representable
 953      * {@code long} value, the result is that same value, which
 954      * is negative.
 955      *
 956      * @param   a   the  argument whose absolute value is to be determined.
 957      * @return  the absolute value of the argument.
 958      */
 959     public static long abs(long a) {
 960         return Math.abs(a);
 961     }
 962 
 963     /**
 964      * Returns the absolute value of a {@code float} value.
 965      * If the argument is not negative, the argument is returned.
 966      * If the argument is negative, the negation of the argument is returned.
 967      * Special cases:
 968      * <ul><li>If the argument is positive zero or negative zero, the
 969      * result is positive zero.
 970      * <li>If the argument is infinite, the result is positive infinity.
 971      * <li>If the argument is NaN, the result is NaN.</ul>
 972      * In other words, the result is the same as the value of the expression:
 973      * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
 974      *
 975      * @param   a   the argument whose absolute value is to be determined
 976      * @return  the absolute value of the argument.
 977      */
 978     public static float abs(float a) {
 979         return Math.abs(a);
 980     }
 981 
 982     /**
 983      * Returns the absolute value of a {@code double} value.
 984      * If the argument is not negative, the argument is returned.
 985      * If the argument is negative, the negation of the argument is returned.
 986      * Special cases:
 987      * <ul><li>If the argument is positive zero or negative zero, the result
 988      * is positive zero.
 989      * <li>If the argument is infinite, the result is positive infinity.
 990      * <li>If the argument is NaN, the result is NaN.</ul>
 991      * In other words, the result is the same as the value of the expression:
 992      * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
 993      *
 994      * @param   a   the argument whose absolute value is to be determined
 995      * @return  the absolute value of the argument.
 996      */
 997     public static double abs(double a) {
 998         return Math.abs(a);
 999     }
1000 
1001     /**
1002      * Returns the greater of two {@code int} values. That is, the
1003      * result is the argument closer to the value of
1004      * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1005      * the result is that same value.
1006      *
1007      * @param   a   an argument.
1008      * @param   b   another argument.
1009      * @return  the larger of {@code a} and {@code b}.
1010      */
1011     public static int max(int a, int b) {
1012         return Math.max(a, b);
1013     }
1014 
1015     /**
1016      * Returns the greater of two {@code long} values. That is, the
1017      * result is the argument closer to the value of
1018      * {@link Long#MAX_VALUE}. If the arguments have the same value,
1019      * the result is that same value.
1020      *
1021      * @param   a   an argument.
1022      * @param   b   another argument.
1023      * @return  the larger of {@code a} and {@code b}.
1024         */
1025     public static long max(long a, long b) {
1026         return Math.max(a, b);
1027     }
1028 
1029     /**
1030      * Returns the greater of two {@code float} values.  That is,
1031      * the result is the argument closer to positive infinity. If the
1032      * arguments have the same value, the result is that same
1033      * value. If either value is NaN, then the result is NaN.  Unlike
1034      * the numerical comparison operators, this method considers
1035      * negative zero to be strictly smaller than positive zero. If one
1036      * argument is positive zero and the other negative zero, the
1037      * result is positive zero.
1038      *
1039      * @param   a   an argument.
1040      * @param   b   another argument.
1041      * @return  the larger of {@code a} and {@code b}.
1042      */
1043     public static float max(float a, float b) {
1044         return Math.max(a, b);
1045     }
1046 
1047     /**
1048      * Returns the greater of two {@code double} values.  That
1049      * is, the result is the argument closer to positive infinity. If
1050      * the arguments have the same value, the result is that same
1051      * value. If either value is NaN, then the result is NaN.  Unlike
1052      * the numerical comparison operators, this method considers
1053      * negative zero to be strictly smaller than positive zero. If one
1054      * argument is positive zero and the other negative zero, the
1055      * result is positive zero.
1056      *
1057      * @param   a   an argument.
1058      * @param   b   another argument.
1059      * @return  the larger of {@code a} and {@code b}.
1060      */
1061     public static double max(double a, double b) {
1062         return Math.max(a, b);
1063     }
1064 
1065     /**
1066      * Returns the smaller of two {@code int} values. That is,
1067      * the result the argument closer to the value of
1068      * {@link Integer#MIN_VALUE}.  If the arguments have the same
1069      * value, the result is that same value.
1070      *
1071      * @param   a   an argument.
1072      * @param   b   another argument.
1073      * @return  the smaller of {@code a} and {@code b}.
1074      */
1075     public static int min(int a, int b) {
1076         return Math.min(a, b);
1077     }
1078 
1079     /**
1080      * Returns the smaller of two {@code long} values. That is,
1081      * the result is the argument closer to the value of
1082      * {@link Long#MIN_VALUE}. If the arguments have the same
1083      * value, the result is that same value.
1084      *
1085      * @param   a   an argument.
1086      * @param   b   another argument.
1087      * @return  the smaller of {@code a} and {@code b}.
1088      */
1089     public static long min(long a, long b) {
1090         return Math.min(a, b);
1091     }
1092 
1093     /**
1094      * Returns the smaller of two {@code float} values.  That is,
1095      * the result is the value closer to negative infinity. If the
1096      * arguments have the same value, the result is that same
1097      * value. If either value is NaN, then the result is NaN.  Unlike
1098      * the numerical comparison operators, this method considers
1099      * negative zero to be strictly smaller than positive zero.  If
1100      * one argument is positive zero and the other is negative zero,
1101      * the result is negative zero.
1102      *
1103      * @param   a   an argument.
1104      * @param   b   another argument.
1105      * @return  the smaller of {@code a} and {@code b.}
1106      */
1107     public static float min(float a, float b) {
1108         return Math.min(a, b);
1109     }
1110 
1111     /**
1112      * Returns the smaller of two {@code double} values.  That
1113      * is, the result is the value closer to negative infinity. If the
1114      * arguments have the same value, the result is that same
1115      * value. If either value is NaN, then the result is NaN.  Unlike
1116      * the numerical comparison operators, this method considers
1117      * negative zero to be strictly smaller than positive zero. If one
1118      * argument is positive zero and the other is negative zero, the
1119      * result is negative zero.
1120      *
1121      * @param   a   an argument.
1122      * @param   b   another argument.
1123      * @return  the smaller of {@code a} and {@code b}.
1124      */
1125     public static double min(double a, double b) {
1126         return Math.min(a, b);
1127     }
1128 
1129     /**
1130      * Returns the size of an ulp of the argument.  An ulp, unit in
1131      * the last place, of a {@code double} value is the positive
1132      * distance between this floating-point value and the {@code
1133      * double} value next larger in magnitude.  Note that for non-NaN
1134      * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1135      *
1136      * <p>Special Cases:
1137      * <ul>
1138      * <li> If the argument is NaN, then the result is NaN.
1139      * <li> If the argument is positive or negative infinity, then the
1140      * result is positive infinity.
1141      * <li> If the argument is positive or negative zero, then the result is
1142      * {@code Double.MIN_VALUE}.
1143      * <li> If the argument is &plusmn;{@code Double.MAX_VALUE}, then
1144      * the result is equal to 2<sup>971</sup>.
1145      * </ul>
1146      *
1147      * @param d the floating-point value whose ulp is to be returned
1148      * @return the size of an ulp of the argument
1149      * @author Joseph D. Darcy
1150      * @since 1.5
1151      */
1152     public static double ulp(double d) {
1153         return Math.ulp(d);
1154     }
1155 
1156     /**
1157      * Returns the size of an ulp of the argument.  An ulp, unit in
1158      * the last place, of a {@code float} value is the positive
1159      * distance between this floating-point value and the {@code
1160      * float} value next larger in magnitude.  Note that for non-NaN
1161      * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1162      *
1163      * <p>Special Cases:
1164      * <ul>
1165      * <li> If the argument is NaN, then the result is NaN.
1166      * <li> If the argument is positive or negative infinity, then the
1167      * result is positive infinity.
1168      * <li> If the argument is positive or negative zero, then the result is
1169      * {@code Float.MIN_VALUE}.
1170      * <li> If the argument is &plusmn;{@code Float.MAX_VALUE}, then
1171      * the result is equal to 2<sup>104</sup>.
1172      * </ul>
1173      *
1174      * @param f the floating-point value whose ulp is to be returned
1175      * @return the size of an ulp of the argument
1176      * @author Joseph D. Darcy
1177      * @since 1.5
1178      */
1179     public static float ulp(float f) {
1180         return Math.ulp(f);
1181     }
1182 
1183     /**
1184      * Returns the signum function of the argument; zero if the argument
1185      * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1186      * argument is less than zero.
1187      *
1188      * <p>Special Cases:
1189      * <ul>
1190      * <li> If the argument is NaN, then the result is NaN.
1191      * <li> If the argument is positive zero or negative zero, then the
1192      *      result is the same as the argument.
1193      * </ul>
1194      *
1195      * @param d the floating-point value whose signum is to be returned
1196      * @return the signum function of the argument
1197      * @author Joseph D. Darcy
1198      * @since 1.5
1199      */
1200     public static double signum(double d) {
1201         return Math.signum(d);
1202     }
1203 
1204     /**
1205      * Returns the signum function of the argument; zero if the argument
1206      * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1207      * argument is less than zero.
1208      *
1209      * <p>Special Cases:
1210      * <ul>
1211      * <li> If the argument is NaN, then the result is NaN.
1212      * <li> If the argument is positive zero or negative zero, then the
1213      *      result is the same as the argument.
1214      * </ul>
1215      *
1216      * @param f the floating-point value whose signum is to be returned
1217      * @return the signum function of the argument
1218      * @author Joseph D. Darcy
1219      * @since 1.5
1220      */
1221     public static float signum(float f) {
1222         return Math.signum(f);
1223     }
1224 
1225     /**
1226      * Returns the hyperbolic sine of a {@code double} value.
1227      * The hyperbolic sine of <i>x</i> is defined to be
1228      * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/2
1229      * where <i>e</i> is {@linkplain Math#E Euler's number}.
1230      *
1231      * <p>Special cases:
1232      * <ul>
1233      *
1234      * <li>If the argument is NaN, then the result is NaN.
1235      *
1236      * <li>If the argument is infinite, then the result is an infinity
1237      * with the same sign as the argument.
1238      *
1239      * <li>If the argument is zero, then the result is a zero with the
1240      * same sign as the argument.
1241      *
1242      * </ul>
1243      *
1244      * @param   x The number whose hyperbolic sine is to be returned.
1245      * @return  The hyperbolic sine of {@code x}.
1246      * @since 1.5
1247      */
1248     public static native double sinh(double x);
1249 
1250     /**
1251      * Returns the hyperbolic cosine of a {@code double} value.
1252      * The hyperbolic cosine of <i>x</i> is defined to be
1253      * (<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>)/2
1254      * where <i>e</i> is {@linkplain Math#E Euler's number}.
1255      *
1256      * <p>Special cases:
1257      * <ul>
1258      *
1259      * <li>If the argument is NaN, then the result is NaN.
1260      *
1261      * <li>If the argument is infinite, then the result is positive
1262      * infinity.
1263      *
1264      * <li>If the argument is zero, then the result is {@code 1.0}.
1265      *
1266      * </ul>
1267      *
1268      * @param   x The number whose hyperbolic cosine is to be returned.
1269      * @return  The hyperbolic cosine of {@code x}.
1270      * @since 1.5
1271      */
1272     public static native double cosh(double x);
1273 
1274     /**
1275      * Returns the hyperbolic tangent of a {@code double} value.
1276      * The hyperbolic tangent of <i>x</i> is defined to be
1277      * (<i>e<sup>x</sup>&nbsp;-&nbsp;e<sup>-x</sup></i>)/(<i>e<sup>x</sup>&nbsp;+&nbsp;e<sup>-x</sup></i>),
1278      * in other words, {@linkplain Math#sinh
1279      * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}.  Note
1280      * that the absolute value of the exact tanh is always less than
1281      * 1.
1282      *
1283      * <p>Special cases:
1284      * <ul>
1285      *
1286      * <li>If the argument is NaN, then the result is NaN.
1287      *
1288      * <li>If the argument is zero, then the result is a zero with the
1289      * same sign as the argument.
1290      *
1291      * <li>If the argument is positive infinity, then the result is
1292      * {@code +1.0}.
1293      *
1294      * <li>If the argument is negative infinity, then the result is
1295      * {@code -1.0}.
1296      *
1297      * </ul>
1298      *
1299      * @param   x The number whose hyperbolic tangent is to be returned.
1300      * @return  The hyperbolic tangent of {@code x}.
1301      * @since 1.5
1302      */
1303     public static native double tanh(double x);
1304 
1305     /**
1306      * Returns sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
1307      * without intermediate overflow or underflow.
1308      *
1309      * <p>Special cases:
1310      * <ul>
1311      *
1312      * <li> If either argument is infinite, then the result
1313      * is positive infinity.
1314      *
1315      * <li> If either argument is NaN and neither argument is infinite,
1316      * then the result is NaN.
1317      *
1318      * </ul>
1319      *
1320      * @param x a value
1321      * @param y a value
1322      * @return sqrt(<i>x</i><sup>2</sup>&nbsp;+<i>y</i><sup>2</sup>)
1323      * without intermediate overflow or underflow
1324      * @since 1.5
1325      */
1326     public static native double hypot(double x, double y);
1327 
1328     /**
1329      * Returns <i>e</i><sup>x</sup>&nbsp;-1.  Note that for values of
1330      * <i>x</i> near 0, the exact sum of
1331      * {@code expm1(x)}&nbsp;+&nbsp;1 is much closer to the true
1332      * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1333      *
1334      * <p>Special cases:
1335      * <ul>
1336      * <li>If the argument is NaN, the result is NaN.
1337      *
1338      * <li>If the argument is positive infinity, then the result is
1339      * positive infinity.
1340      *
1341      * <li>If the argument is negative infinity, then the result is
1342      * -1.0.
1343      *
1344      * <li>If the argument is zero, then the result is a zero with the
1345      * same sign as the argument.
1346      *
1347      * </ul>
1348      *
1349      * @param   x   the exponent to raise <i>e</i> to in the computation of
1350      *              <i>e</i><sup>{@code x}</sup>&nbsp;-1.
1351      * @return  the value <i>e</i><sup>{@code x}</sup>&nbsp;-&nbsp;1.
1352      * @since 1.5
1353      */
1354     public static native double expm1(double x);
1355 
1356     /**
1357      * Returns the natural logarithm of the sum of the argument and 1.
1358      * Note that for small values {@code x}, the result of
1359      * {@code log1p(x)} is much closer to the true result of ln(1
1360      * + {@code x}) than the floating-point evaluation of
1361      * {@code log(1.0+x)}.
1362      *
1363      * <p>Special cases:
1364      * <ul>
1365      *
1366      * <li>If the argument is NaN or less than -1, then the result is
1367      * NaN.
1368      *
1369      * <li>If the argument is positive infinity, then the result is
1370      * positive infinity.
1371      *
1372      * <li>If the argument is negative one, then the result is
1373      * negative infinity.
1374      *
1375      * <li>If the argument is zero, then the result is a zero with the
1376      * same sign as the argument.
1377      *
1378      * </ul>
1379      *
1380      * @param   x   a value
1381      * @return the value ln({@code x}&nbsp;+&nbsp;1), the natural
1382      * log of {@code x}&nbsp;+&nbsp;1
1383      * @since 1.5
1384      */
1385     public static native double log1p(double x);
1386 
1387     /**
1388      * Returns the first floating-point argument with the sign of the
1389      * second floating-point argument.  For this method, a NaN
1390      * {@code sign} argument is always treated as if it were
1391      * positive.
1392      *
1393      * @param magnitude  the parameter providing the magnitude of the result
1394      * @param sign   the parameter providing the sign of the result
1395      * @return a value with the magnitude of {@code magnitude}
1396      * and the sign of {@code sign}.
1397      * @since 1.6
1398      */
1399     public static double copySign(double magnitude, double sign) {
1400         return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1401     }
1402 
1403     /**
1404      * Returns the first floating-point argument with the sign of the
1405      * second floating-point argument.  For this method, a NaN
1406      * {@code sign} argument is always treated as if it were
1407      * positive.
1408      *
1409      * @param magnitude  the parameter providing the magnitude of the result
1410      * @param sign   the parameter providing the sign of the result
1411      * @return a value with the magnitude of {@code magnitude}
1412      * and the sign of {@code sign}.
1413      * @since 1.6
1414      */
1415     public static float copySign(float magnitude, float sign) {
1416         return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1417     }
1418     /**
1419      * Returns the unbiased exponent used in the representation of a
1420      * {@code float}.  Special cases:
1421      *
1422      * <ul>
1423      * <li>If the argument is NaN or infinite, then the result is
1424      * {@link Float#MAX_EXPONENT} + 1.
1425      * <li>If the argument is zero or subnormal, then the result is
1426      * {@link Float#MIN_EXPONENT} -1.
1427      * </ul>
1428      * @param f a {@code float} value
1429      * @return the unbiased exponent of the argument
1430      * @since 1.6
1431      */
1432     public static int getExponent(float f) {
1433         return Math.getExponent(f);
1434     }
1435 
1436     /**
1437      * Returns the unbiased exponent used in the representation of a
1438      * {@code double}.  Special cases:
1439      *
1440      * <ul>
1441      * <li>If the argument is NaN or infinite, then the result is
1442      * {@link Double#MAX_EXPONENT} + 1.
1443      * <li>If the argument is zero or subnormal, then the result is
1444      * {@link Double#MIN_EXPONENT} -1.
1445      * </ul>
1446      * @param d a {@code double} value
1447      * @return the unbiased exponent of the argument
1448      * @since 1.6
1449      */
1450     public static int getExponent(double d) {
1451         return Math.getExponent(d);
1452     }
1453 
1454     /**
1455      * Returns the floating-point number adjacent to the first
1456      * argument in the direction of the second argument.  If both
1457      * arguments compare as equal the second argument is returned.
1458      *
1459      * <p>Special cases:
1460      * <ul>
1461      * <li> If either argument is a NaN, then NaN is returned.
1462      *
1463      * <li> If both arguments are signed zeros, {@code direction}
1464      * is returned unchanged (as implied by the requirement of
1465      * returning the second argument if the arguments compare as
1466      * equal).
1467      *
1468      * <li> If {@code start} is
1469      * &plusmn;{@link Double#MIN_VALUE} and {@code direction}
1470      * has a value such that the result should have a smaller
1471      * magnitude, then a zero with the same sign as {@code start}
1472      * is returned.
1473      *
1474      * <li> If {@code start} is infinite and
1475      * {@code direction} has a value such that the result should
1476      * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1477      * same sign as {@code start} is returned.
1478      *
1479      * <li> If {@code start} is equal to &plusmn;
1480      * {@link Double#MAX_VALUE} and {@code direction} has a
1481      * value such that the result should have a larger magnitude, an
1482      * infinity with same sign as {@code start} is returned.
1483      * </ul>
1484      *
1485      * @param start  starting floating-point value
1486      * @param direction value indicating which of
1487      * {@code start}'s neighbors or {@code start} should
1488      * be returned
1489      * @return The floating-point number adjacent to {@code start} in the
1490      * direction of {@code direction}.
1491      * @since 1.6
1492      */
1493     public static double nextAfter(double start, double direction) {
1494         return Math.nextAfter(start, direction);
1495     }
1496 
1497     /**
1498      * Returns the floating-point number adjacent to the first
1499      * argument in the direction of the second argument.  If both
1500      * arguments compare as equal a value equivalent to the second argument
1501      * is returned.
1502      *
1503      * <p>Special cases:
1504      * <ul>
1505      * <li> If either argument is a NaN, then NaN is returned.
1506      *
1507      * <li> If both arguments are signed zeros, a value equivalent
1508      * to {@code direction} is returned.
1509      *
1510      * <li> If {@code start} is
1511      * &plusmn;{@link Float#MIN_VALUE} and {@code direction}
1512      * has a value such that the result should have a smaller
1513      * magnitude, then a zero with the same sign as {@code start}
1514      * is returned.
1515      *
1516      * <li> If {@code start} is infinite and
1517      * {@code direction} has a value such that the result should
1518      * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1519      * same sign as {@code start} is returned.
1520      *
1521      * <li> If {@code start} is equal to &plusmn;
1522      * {@link Float#MAX_VALUE} and {@code direction} has a
1523      * value such that the result should have a larger magnitude, an
1524      * infinity with same sign as {@code start} is returned.
1525      * </ul>
1526      *
1527      * @param start  starting floating-point value
1528      * @param direction value indicating which of
1529      * {@code start}'s neighbors or {@code start} should
1530      * be returned
1531      * @return The floating-point number adjacent to {@code start} in the
1532      * direction of {@code direction}.
1533      * @since 1.6
1534      */
1535     public static float nextAfter(float start, double direction) {
1536         return Math.nextAfter(start, direction);
1537     }
1538 
1539     /**
1540      * Returns the floating-point value adjacent to {@code d} in
1541      * the direction of positive infinity.  This method is
1542      * semantically equivalent to {@code nextAfter(d,
1543      * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1544      * implementation may run faster than its equivalent
1545      * {@code nextAfter} call.
1546      *
1547      * <p>Special Cases:
1548      * <ul>
1549      * <li> If the argument is NaN, the result is NaN.
1550      *
1551      * <li> If the argument is positive infinity, the result is
1552      * positive infinity.
1553      *
1554      * <li> If the argument is zero, the result is
1555      * {@link Double#MIN_VALUE}
1556      *
1557      * </ul>
1558      *
1559      * @param d starting floating-point value
1560      * @return The adjacent floating-point value closer to positive
1561      * infinity.
1562      * @since 1.6
1563      */
1564     public static double nextUp(double d) {
1565         return Math.nextUp(d);
1566     }
1567 
1568     /**
1569      * Returns the floating-point value adjacent to {@code f} in
1570      * the direction of positive infinity.  This method is
1571      * semantically equivalent to {@code nextAfter(f,
1572      * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1573      * implementation may run faster than its equivalent
1574      * {@code nextAfter} call.
1575      *
1576      * <p>Special Cases:
1577      * <ul>
1578      * <li> If the argument is NaN, the result is NaN.
1579      *
1580      * <li> If the argument is positive infinity, the result is
1581      * positive infinity.
1582      *
1583      * <li> If the argument is zero, the result is
1584      * {@link Float#MIN_VALUE}
1585      *
1586      * </ul>
1587      *
1588      * @param f starting floating-point value
1589      * @return The adjacent floating-point value closer to positive
1590      * infinity.
1591      * @since 1.6
1592      */
1593     public static float nextUp(float f) {
1594         return Math.nextUp(f);
1595     }
1596 
1597     /**
1598      * Returns the floating-point value adjacent to {@code d} in
1599      * the direction of negative infinity.  This method is
1600      * semantically equivalent to {@code nextAfter(d,
1601      * Double.NEGATIVE_INFINITY)}; however, a
1602      * {@code nextDown} implementation may run faster than its
1603      * equivalent {@code nextAfter} call.
1604      *
1605      * <p>Special Cases:
1606      * <ul>
1607      * <li> If the argument is NaN, the result is NaN.
1608      *
1609      * <li> If the argument is negative infinity, the result is
1610      * negative infinity.
1611      *
1612      * <li> If the argument is zero, the result is
1613      * {@code -Double.MIN_VALUE}
1614      *
1615      * </ul>
1616      *
1617      * @param d  starting floating-point value
1618      * @return The adjacent floating-point value closer to negative
1619      * infinity.
1620      * @since 1.8
1621      */
1622     public static double nextDown(double d) {
1623         return Math.nextDown(d);
1624     }
1625 
1626     /**
1627      * Returns the floating-point value adjacent to {@code f} in
1628      * the direction of negative infinity.  This method is
1629      * semantically equivalent to {@code nextAfter(f,
1630      * Float.NEGATIVE_INFINITY)}; however, a
1631      * {@code nextDown} implementation may run faster than its
1632      * equivalent {@code nextAfter} call.
1633      *
1634      * <p>Special Cases:
1635      * <ul>
1636      * <li> If the argument is NaN, the result is NaN.
1637      *
1638      * <li> If the argument is negative infinity, the result is
1639      * negative infinity.
1640      *
1641      * <li> If the argument is zero, the result is
1642      * {@code -Float.MIN_VALUE}
1643      *
1644      * </ul>
1645      *
1646      * @param f  starting floating-point value
1647      * @return The adjacent floating-point value closer to negative
1648      * infinity.
1649      * @since 1.8
1650      */
1651     public static float nextDown(float f) {
1652         return Math.nextDown(f);
1653     }
1654 
1655     /**
1656      * Returns {@code d} &times;
1657      * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1658      * by a single correctly rounded floating-point multiply to a
1659      * member of the double value set.  See the Java
1660      * Language Specification for a discussion of floating-point
1661      * value sets.  If the exponent of the result is between {@link
1662      * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1663      * answer is calculated exactly.  If the exponent of the result
1664      * would be larger than {@code Double.MAX_EXPONENT}, an
1665      * infinity is returned.  Note that if the result is subnormal,
1666      * precision may be lost; that is, when {@code scalb(x, n)}
1667      * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1668      * <i>x</i>.  When the result is non-NaN, the result has the same
1669      * sign as {@code d}.
1670      *
1671      * <p>Special cases:
1672      * <ul>
1673      * <li> If the first argument is NaN, NaN is returned.
1674      * <li> If the first argument is infinite, then an infinity of the
1675      * same sign is returned.
1676      * <li> If the first argument is zero, then a zero of the same
1677      * sign is returned.
1678      * </ul>
1679      *
1680      * @param d number to be scaled by a power of two.
1681      * @param scaleFactor power of 2 used to scale {@code d}
1682      * @return {@code d} &times; 2<sup>{@code scaleFactor}</sup>
1683      * @since 1.6
1684      */
1685     public static double scalb(double d, int scaleFactor) {
1686         return Math.scalb(d, scaleFactor);
1687     }
1688 
1689     /**
1690      * Returns {@code f} &times;
1691      * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1692      * by a single correctly rounded floating-point multiply to a
1693      * member of the float value set.  See the Java
1694      * Language Specification for a discussion of floating-point
1695      * value sets.  If the exponent of the result is between {@link
1696      * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1697      * answer is calculated exactly.  If the exponent of the result
1698      * would be larger than {@code Float.MAX_EXPONENT}, an
1699      * infinity is returned.  Note that if the result is subnormal,
1700      * precision may be lost; that is, when {@code scalb(x, n)}
1701      * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1702      * <i>x</i>.  When the result is non-NaN, the result has the same
1703      * sign as {@code f}.
1704      *
1705      * <p>Special cases:
1706      * <ul>
1707      * <li> If the first argument is NaN, NaN is returned.
1708      * <li> If the first argument is infinite, then an infinity of the
1709      * same sign is returned.
1710      * <li> If the first argument is zero, then a zero of the same
1711      * sign is returned.
1712      * </ul>
1713      *
1714      * @param f number to be scaled by a power of two.
1715      * @param scaleFactor power of 2 used to scale {@code f}
1716      * @return {@code f} &times; 2<sup>{@code scaleFactor}</sup>
1717      * @since 1.6
1718      */
1719     public static float scalb(float f, int scaleFactor) {
1720         return Math.scalb(f, scaleFactor);
1721     }
1722 }
--- EOF ---