1 /*
2 * Copyright (c) 1999, 2010, 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.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 {@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 - f2</code> × <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}, {@code y}) to polar
444 * coordinates (r, <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>, <i>theta</i>)
487 * in polar coordinates that corresponds to the point
488 * (<i>x</i>, <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. The
617 * result is rounded to an integer by adding 1/2, taking the
618 * floor of the result, and casting the result to type {@code int}.
619 * In other words, the result is equal to the value of the expression:
620 * <p>{@code (int)Math.floor(a + 0.5f)}
621 *
622 * <p>Special cases:
623 * <ul><li>If the argument is NaN, the result is 0.
624 * <li>If the argument is negative infinity or any value less than or
625 * equal to the value of {@code Integer.MIN_VALUE}, the result is
626 * equal to the value of {@code Integer.MIN_VALUE}.
627 * <li>If the argument is positive infinity or any value greater than or
628 * equal to the value of {@code Integer.MAX_VALUE}, the result is
629 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
630 *
631 * @param a a floating-point value to be rounded to an integer.
632 * @return the value of the argument rounded to the nearest
633 * {@code int} value.
634 * @see java.lang.Integer#MAX_VALUE
635 * @see java.lang.Integer#MIN_VALUE
636 */
637 public static int round(float a) {
638 return (int)floor(a + 0.5f);
639 }
640
641 /**
642 * Returns the closest {@code long} to the argument. The result
643 * is rounded to an integer by adding 1/2, taking the floor of the
644 * result, and casting the result to type {@code long}. In other
645 * words, the result is equal to the value of the expression:
646 * <p>{@code (long)Math.floor(a + 0.5d)}
647 *
648 * <p>Special cases:
649 * <ul><li>If the argument is NaN, the result is 0.
650 * <li>If the argument is negative infinity or any value less than or
651 * equal to the value of {@code Long.MIN_VALUE}, the result is
652 * equal to the value of {@code Long.MIN_VALUE}.
653 * <li>If the argument is positive infinity or any value greater than or
654 * equal to the value of {@code Long.MAX_VALUE}, the result is
655 * equal to the value of {@code Long.MAX_VALUE}.</ul>
656 *
657 * @param a a floating-point value to be rounded to a
658 * {@code long}.
659 * @return the value of the argument rounded to the nearest
660 * {@code long} value.
661 * @see java.lang.Long#MAX_VALUE
662 * @see java.lang.Long#MIN_VALUE
663 */
664 public static long round(double a) {
665 return (long)floor(a + 0.5d);
666 }
667
668 private static Random randomNumberGenerator;
669
670 private static synchronized Random initRNG() {
671 Random rnd = randomNumberGenerator;
672 return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
673 }
674
675 /**
676 * Returns a {@code double} value with a positive sign, greater
677 * than or equal to {@code 0.0} and less than {@code 1.0}.
678 * Returned values are chosen pseudorandomly with (approximately)
679 * uniform distribution from that range.
680 *
681 * <p>When this method is first called, it creates a single new
682 * pseudorandom-number generator, exactly as if by the expression
683 *
684 * <blockquote>{@code new java.util.Random()}</blockquote>
685 *
686 * This new pseudorandom-number generator is used thereafter for
687 * all calls to this method and is used nowhere else.
688 *
689 * <p>This method is properly synchronized to allow correct use by
690 * more than one thread. However, if many threads need to generate
691 * pseudorandom numbers at a great rate, it may reduce contention
692 * for each thread to have its own pseudorandom number generator.
693 *
694 * @return a pseudorandom {@code double} greater than or equal
695 * to {@code 0.0} and less than {@code 1.0}.
696 * @see Random#nextDouble()
697 */
698 public static double random() {
699 Random rnd = randomNumberGenerator;
700 if (rnd == null) rnd = initRNG();
701 return rnd.nextDouble();
702 }
703
704 /**
705 * Returns the absolute value of an {@code int} value..
706 * If the argument is not negative, the argument is returned.
707 * If the argument is negative, the negation of the argument is returned.
708 *
709 * <p>Note that if the argument is equal to the value of
710 * {@link Integer#MIN_VALUE}, the most negative representable
711 * {@code int} value, the result is that same value, which is
712 * negative.
713 *
714 * @param a the argument whose absolute value is to be determined.
715 * @return the absolute value of the argument.
716 */
717 public static int abs(int a) {
718 return (a < 0) ? -a : a;
719 }
720
721 /**
722 * Returns the absolute value of a {@code long} value.
723 * If the argument is not negative, the argument is returned.
724 * If the argument is negative, the negation of the argument is returned.
725 *
726 * <p>Note that if the argument is equal to the value of
727 * {@link Long#MIN_VALUE}, the most negative representable
728 * {@code long} value, the result is that same value, which
729 * is negative.
730 *
731 * @param a the argument whose absolute value is to be determined.
732 * @return the absolute value of the argument.
733 */
734 public static long abs(long a) {
735 return (a < 0) ? -a : a;
736 }
737
738 /**
739 * Returns the absolute value of a {@code float} value.
740 * If the argument is not negative, the argument is returned.
741 * If the argument is negative, the negation of the argument is returned.
742 * Special cases:
743 * <ul><li>If the argument is positive zero or negative zero, the
744 * result is positive zero.
745 * <li>If the argument is infinite, the result is positive infinity.
746 * <li>If the argument is NaN, the result is NaN.</ul>
747 * In other words, the result is the same as the value of the expression:
748 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
749 *
750 * @param a the argument whose absolute value is to be determined
751 * @return the absolute value of the argument.
752 */
753 public static float abs(float a) {
754 return (a <= 0.0F) ? 0.0F - a : a;
755 }
756
757 /**
758 * Returns the absolute value of a {@code double} value.
759 * If the argument is not negative, the argument is returned.
760 * If the argument is negative, the negation of the argument is returned.
761 * Special cases:
762 * <ul><li>If the argument is positive zero or negative zero, the result
763 * is positive zero.
764 * <li>If the argument is infinite, the result is positive infinity.
765 * <li>If the argument is NaN, the result is NaN.</ul>
766 * In other words, the result is the same as the value of the expression:
767 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
768 *
769 * @param a the argument whose absolute value is to be determined
770 * @return the absolute value of the argument.
771 */
772 public static double abs(double a) {
773 return (a <= 0.0D) ? 0.0D - a : a;
774 }
775
776 /**
777 * Returns the greater of two {@code int} values. That is, the
778 * result is the argument closer to the value of
779 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
780 * the result is that same value.
781 *
782 * @param a an argument.
783 * @param b another argument.
784 * @return the larger of {@code a} and {@code b}.
785 */
786 public static int max(int a, int b) {
787 return (a >= b) ? a : b;
788 }
789
790 /**
791 * Returns the greater of two {@code long} values. That is, the
792 * result is the argument closer to the value of
793 * {@link Long#MAX_VALUE}. If the arguments have the same value,
794 * the result is that same value.
795 *
796 * @param a an argument.
797 * @param b another argument.
798 * @return the larger of {@code a} and {@code b}.
799 */
800 public static long max(long a, long b) {
801 return (a >= b) ? a : b;
802 }
803
804 // Use raw bit-wise conversions on guaranteed non-NaN arguments.
805 private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
806 private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
807
808 /**
809 * Returns the greater of two {@code float} values. That is,
810 * the result is the argument closer to positive infinity. If the
811 * arguments have the same value, the result is that same
812 * value. If either value is NaN, then the result is NaN. Unlike
813 * the numerical comparison operators, this method considers
814 * negative zero to be strictly smaller than positive zero. If one
815 * argument is positive zero and the other negative zero, the
816 * result is positive zero.
817 *
818 * @param a an argument.
819 * @param b another argument.
820 * @return the larger of {@code a} and {@code b}.
821 */
822 public static float max(float a, float b) {
823 if (a != a)
824 return a; // a is NaN
825 if ((a == 0.0f) &&
826 (b == 0.0f) &&
827 (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
828 // Raw conversion ok since NaN can't map to -0.0.
829 return b;
830 }
831 return (a >= b) ? a : b;
832 }
833
834 /**
835 * Returns the greater of two {@code double} values. That
836 * is, the result is the argument closer to positive infinity. If
837 * the arguments have the same value, the result is that same
838 * value. If either value is NaN, then the result is NaN. Unlike
839 * the numerical comparison operators, this method considers
840 * negative zero to be strictly smaller than positive zero. If one
841 * argument is positive zero and the other negative zero, the
842 * result is positive zero.
843 *
844 * @param a an argument.
845 * @param b another argument.
846 * @return the larger of {@code a} and {@code b}.
847 */
848 public static double max(double a, double b) {
849 if (a != a)
850 return a; // a is NaN
851 if ((a == 0.0d) &&
852 (b == 0.0d) &&
853 (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
854 // Raw conversion ok since NaN can't map to -0.0.
855 return b;
856 }
857 return (a >= b) ? a : b;
858 }
859
860 /**
861 * Returns the smaller of two {@code int} values. That is,
862 * the result the argument closer to the value of
863 * {@link Integer#MIN_VALUE}. If the arguments have the same
864 * value, the result is that same value.
865 *
866 * @param a an argument.
867 * @param b another argument.
868 * @return the smaller of {@code a} and {@code b}.
869 */
870 public static int min(int a, int b) {
871 return (a <= b) ? a : b;
872 }
873
874 /**
875 * Returns the smaller of two {@code long} values. That is,
876 * the result is the argument closer to the value of
877 * {@link Long#MIN_VALUE}. If the arguments have the same
878 * value, the result is that same value.
879 *
880 * @param a an argument.
881 * @param b another argument.
882 * @return the smaller of {@code a} and {@code b}.
883 */
884 public static long min(long a, long b) {
885 return (a <= b) ? a : b;
886 }
887
888 /**
889 * Returns the smaller of two {@code float} values. That is,
890 * the result is the value closer to negative infinity. If the
891 * arguments have the same value, the result is that same
892 * value. If either value is NaN, then the result is NaN. Unlike
893 * the numerical comparison operators, this method considers
894 * negative zero to be strictly smaller than positive zero. If
895 * one argument is positive zero and the other is negative zero,
896 * the result is negative zero.
897 *
898 * @param a an argument.
899 * @param b another argument.
900 * @return the smaller of {@code a} and {@code b.}
901 */
902 public static float min(float a, float b) {
903 if (a != a)
904 return a; // a is NaN
905 if ((a == 0.0f) &&
906 (b == 0.0f) &&
907 (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
908 // Raw conversion ok since NaN can't map to -0.0.
909 return b;
910 }
911 return (a <= b) ? a : b;
912 }
913
914 /**
915 * Returns the smaller of two {@code double} values. That
916 * is, the result is the value closer to negative infinity. If the
917 * arguments have the same value, the result is that same
918 * value. If either value is NaN, then the result is NaN. Unlike
919 * the numerical comparison operators, this method considers
920 * negative zero to be strictly smaller than positive zero. If one
921 * argument is positive zero and the other is negative zero, the
922 * result is negative zero.
923 *
924 * @param a an argument.
925 * @param b another argument.
926 * @return the smaller of {@code a} and {@code b}.
927 */
928 public static double min(double a, double b) {
929 if (a != a)
930 return a; // a is NaN
931 if ((a == 0.0d) &&
932 (b == 0.0d) &&
933 (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
934 // Raw conversion ok since NaN can't map to -0.0.
935 return b;
936 }
937 return (a <= b) ? a : b;
938 }
939
940 /**
941 * Returns the size of an ulp of the argument. An ulp of a
942 * {@code double} value is the positive distance between this
943 * floating-point value and the {@code double} value next
944 * larger in magnitude. Note that for non-NaN <i>x</i>,
945 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
946 *
947 * <p>Special Cases:
948 * <ul>
949 * <li> If the argument is NaN, then the result is NaN.
950 * <li> If the argument is positive or negative infinity, then the
951 * result is positive infinity.
952 * <li> If the argument is positive or negative zero, then the result is
953 * {@code Double.MIN_VALUE}.
954 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
955 * the result is equal to 2<sup>971</sup>.
956 * </ul>
957 *
958 * @param d the floating-point value whose ulp is to be returned
959 * @return the size of an ulp of the argument
960 * @author Joseph D. Darcy
961 * @since 1.5
962 */
963 public static double ulp(double d) {
964 return sun.misc.FpUtils.ulp(d);
965 }
966
967 /**
968 * Returns the size of an ulp of the argument. An ulp of a
969 * {@code float} value is the positive distance between this
970 * floating-point value and the {@code float} value next
971 * larger in magnitude. Note that for non-NaN <i>x</i>,
972 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
973 *
974 * <p>Special Cases:
975 * <ul>
976 * <li> If the argument is NaN, then the result is NaN.
977 * <li> If the argument is positive or negative infinity, then the
978 * result is positive infinity.
979 * <li> If the argument is positive or negative zero, then the result is
980 * {@code Float.MIN_VALUE}.
981 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
982 * the result is equal to 2<sup>104</sup>.
983 * </ul>
984 *
985 * @param f the floating-point value whose ulp is to be returned
986 * @return the size of an ulp of the argument
987 * @author Joseph D. Darcy
988 * @since 1.5
989 */
990 public static float ulp(float f) {
991 return sun.misc.FpUtils.ulp(f);
992 }
993
994 /**
995 * Returns the signum function of the argument; zero if the argument
996 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
997 * argument is less than zero.
998 *
999 * <p>Special Cases:
1000 * <ul>
1001 * <li> If the argument is NaN, then the result is NaN.
1002 * <li> If the argument is positive zero or negative zero, then the
1003 * result is the same as the argument.
1004 * </ul>
1005 *
1006 * @param d the floating-point value whose signum is to be returned
1007 * @return the signum function of the argument
1008 * @author Joseph D. Darcy
1009 * @since 1.5
1010 */
1011 public static double signum(double d) {
1012 return sun.misc.FpUtils.signum(d);
1013 }
1014
1015 /**
1016 * Returns the signum function of the argument; zero if the argument
1017 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1018 * argument is less than zero.
1019 *
1020 * <p>Special Cases:
1021 * <ul>
1022 * <li> If the argument is NaN, then the result is NaN.
1023 * <li> If the argument is positive zero or negative zero, then the
1024 * result is the same as the argument.
1025 * </ul>
1026 *
1027 * @param f the floating-point value whose signum is to be returned
1028 * @return the signum function of the argument
1029 * @author Joseph D. Darcy
1030 * @since 1.5
1031 */
1032 public static float signum(float f) {
1033 return sun.misc.FpUtils.signum(f);
1034 }
1035
1036 /**
1037 * Returns the hyperbolic sine of a {@code double} value.
1038 * The hyperbolic sine of <i>x</i> is defined to be
1039 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1040 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1041 *
1042 * <p>Special cases:
1043 * <ul>
1044 *
1045 * <li>If the argument is NaN, then the result is NaN.
1046 *
1047 * <li>If the argument is infinite, then the result is an infinity
1048 * with the same sign as the argument.
1049 *
1050 * <li>If the argument is zero, then the result is a zero with the
1051 * same sign as the argument.
1052 *
1053 * </ul>
1054 *
1055 * @param x The number whose hyperbolic sine is to be returned.
1056 * @return The hyperbolic sine of {@code x}.
1057 * @since 1.5
1058 */
1059 public static native double sinh(double x);
1060
1061 /**
1062 * Returns the hyperbolic cosine of a {@code double} value.
1063 * The hyperbolic cosine of <i>x</i> is defined to be
1064 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1065 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1066 *
1067 * <p>Special cases:
1068 * <ul>
1069 *
1070 * <li>If the argument is NaN, then the result is NaN.
1071 *
1072 * <li>If the argument is infinite, then the result is positive
1073 * infinity.
1074 *
1075 * <li>If the argument is zero, then the result is {@code 1.0}.
1076 *
1077 * </ul>
1078 *
1079 * @param x The number whose hyperbolic cosine is to be returned.
1080 * @return The hyperbolic cosine of {@code x}.
1081 * @since 1.5
1082 */
1083 public static native double cosh(double x);
1084
1085 /**
1086 * Returns the hyperbolic tangent of a {@code double} value.
1087 * The hyperbolic tangent of <i>x</i> is defined to be
1088 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1089 * in other words, {@linkplain Math#sinh
1090 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1091 * that the absolute value of the exact tanh is always less than
1092 * 1.
1093 *
1094 * <p>Special cases:
1095 * <ul>
1096 *
1097 * <li>If the argument is NaN, then the result is NaN.
1098 *
1099 * <li>If the argument is zero, then the result is a zero with the
1100 * same sign as the argument.
1101 *
1102 * <li>If the argument is positive infinity, then the result is
1103 * {@code +1.0}.
1104 *
1105 * <li>If the argument is negative infinity, then the result is
1106 * {@code -1.0}.
1107 *
1108 * </ul>
1109 *
1110 * @param x The number whose hyperbolic tangent is to be returned.
1111 * @return The hyperbolic tangent of {@code x}.
1112 * @since 1.5
1113 */
1114 public static native double tanh(double x);
1115
1116 /**
1117 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1118 * without intermediate overflow or underflow.
1119 *
1120 * <p>Special cases:
1121 * <ul>
1122 *
1123 * <li> If either argument is infinite, then the result
1124 * is positive infinity.
1125 *
1126 * <li> If either argument is NaN and neither argument is infinite,
1127 * then the result is NaN.
1128 *
1129 * </ul>
1130 *
1131 * @param x a value
1132 * @param y a value
1133 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1134 * without intermediate overflow or underflow
1135 * @since 1.5
1136 */
1137 public static native double hypot(double x, double y);
1138
1139 /**
1140 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1141 * <i>x</i> near 0, the exact sum of
1142 * {@code expm1(x)} + 1 is much closer to the true
1143 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1144 *
1145 * <p>Special cases:
1146 * <ul>
1147 * <li>If the argument is NaN, the result is NaN.
1148 *
1149 * <li>If the argument is positive infinity, then the result is
1150 * positive infinity.
1151 *
1152 * <li>If the argument is negative infinity, then the result is
1153 * -1.0.
1154 *
1155 * <li>If the argument is zero, then the result is a zero with the
1156 * same sign as the argument.
1157 *
1158 * </ul>
1159 *
1160 * @param x the exponent to raise <i>e</i> to in the computation of
1161 * <i>e</i><sup>{@code x}</sup> -1.
1162 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1163 * @since 1.5
1164 */
1165 public static native double expm1(double x);
1166
1167 /**
1168 * Returns the natural logarithm of the sum of the argument and 1.
1169 * Note that for small values {@code x}, the result of
1170 * {@code log1p(x)} is much closer to the true result of ln(1
1171 * + {@code x}) than the floating-point evaluation of
1172 * {@code log(1.0+x)}.
1173 *
1174 * <p>Special cases:
1175 * <ul>
1176 *
1177 * <li>If the argument is NaN or less than -1, then the result is
1178 * NaN.
1179 *
1180 * <li>If the argument is positive infinity, then the result is
1181 * positive infinity.
1182 *
1183 * <li>If the argument is negative one, then the result is
1184 * negative infinity.
1185 *
1186 * <li>If the argument is zero, then the result is a zero with the
1187 * same sign as the argument.
1188 *
1189 * </ul>
1190 *
1191 * @param x a value
1192 * @return the value ln({@code x} + 1), the natural
1193 * log of {@code x} + 1
1194 * @since 1.5
1195 */
1196 public static native double log1p(double x);
1197
1198 /**
1199 * Returns the first floating-point argument with the sign of the
1200 * second floating-point argument. For this method, a NaN
1201 * {@code sign} argument is always treated as if it were
1202 * positive.
1203 *
1204 * @param magnitude the parameter providing the magnitude of the result
1205 * @param sign the parameter providing the sign of the result
1206 * @return a value with the magnitude of {@code magnitude}
1207 * and the sign of {@code sign}.
1208 * @since 1.6
1209 */
1210 public static double copySign(double magnitude, double sign) {
1211 return sun.misc.FpUtils.copySign(magnitude, sign);
1212 }
1213
1214 /**
1215 * Returns the first floating-point argument with the sign of the
1216 * second floating-point argument. For this method, a NaN
1217 * {@code sign} argument is always treated as if it were
1218 * positive.
1219 *
1220 * @param magnitude the parameter providing the magnitude of the result
1221 * @param sign the parameter providing the sign of the result
1222 * @return a value with the magnitude of {@code magnitude}
1223 * and the sign of {@code sign}.
1224 * @since 1.6
1225 */
1226 public static float copySign(float magnitude, float sign) {
1227 return sun.misc.FpUtils.copySign(magnitude, sign);
1228 }
1229 /**
1230 * Returns the unbiased exponent used in the representation of a
1231 * {@code float}. Special cases:
1232 *
1233 * <ul>
1234 * <li>If the argument is NaN or infinite, then the result is
1235 * {@link Float#MAX_EXPONENT} + 1.
1236 * <li>If the argument is zero or subnormal, then the result is
1237 * {@link Float#MIN_EXPONENT} -1.
1238 * </ul>
1239 * @param f a {@code float} value
1240 * @since 1.6
1241 */
1242 public static int getExponent(float f) {
1243 return sun.misc.FpUtils.getExponent(f);
1244 }
1245
1246 /**
1247 * Returns the unbiased exponent used in the representation of a
1248 * {@code double}. Special cases:
1249 *
1250 * <ul>
1251 * <li>If the argument is NaN or infinite, then the result is
1252 * {@link Double#MAX_EXPONENT} + 1.
1253 * <li>If the argument is zero or subnormal, then the result is
1254 * {@link Double#MIN_EXPONENT} -1.
1255 * </ul>
1256 * @param d a {@code double} value
1257 * @since 1.6
1258 */
1259 public static int getExponent(double d) {
1260 return sun.misc.FpUtils.getExponent(d);
1261 }
1262
1263 /**
1264 * Returns the floating-point number adjacent to the first
1265 * argument in the direction of the second argument. If both
1266 * arguments compare as equal the second argument is returned.
1267 *
1268 * <p>Special cases:
1269 * <ul>
1270 * <li> If either argument is a NaN, then NaN is returned.
1271 *
1272 * <li> If both arguments are signed zeros, {@code direction}
1273 * is returned unchanged (as implied by the requirement of
1274 * returning the second argument if the arguments compare as
1275 * equal).
1276 *
1277 * <li> If {@code start} is
1278 * ±{@link Double#MIN_VALUE} and {@code direction}
1279 * has a value such that the result should have a smaller
1280 * magnitude, then a zero with the same sign as {@code start}
1281 * is returned.
1282 *
1283 * <li> If {@code start} is infinite and
1284 * {@code direction} has a value such that the result should
1285 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1286 * same sign as {@code start} is returned.
1287 *
1288 * <li> If {@code start} is equal to ±
1289 * {@link Double#MAX_VALUE} and {@code direction} has a
1290 * value such that the result should have a larger magnitude, an
1291 * infinity with same sign as {@code start} is returned.
1292 * </ul>
1293 *
1294 * @param start starting floating-point value
1295 * @param direction value indicating which of
1296 * {@code start}'s neighbors or {@code start} should
1297 * be returned
1298 * @return The floating-point number adjacent to {@code start} in the
1299 * direction of {@code direction}.
1300 * @since 1.6
1301 */
1302 public static double nextAfter(double start, double direction) {
1303 return sun.misc.FpUtils.nextAfter(start, direction);
1304 }
1305
1306 /**
1307 * Returns the floating-point number adjacent to the first
1308 * argument in the direction of the second argument. If both
1309 * arguments compare as equal a value equivalent to the second argument
1310 * is returned.
1311 *
1312 * <p>Special cases:
1313 * <ul>
1314 * <li> If either argument is a NaN, then NaN is returned.
1315 *
1316 * <li> If both arguments are signed zeros, a value equivalent
1317 * to {@code direction} is returned.
1318 *
1319 * <li> If {@code start} is
1320 * ±{@link Float#MIN_VALUE} and {@code direction}
1321 * has a value such that the result should have a smaller
1322 * magnitude, then a zero with the same sign as {@code start}
1323 * is returned.
1324 *
1325 * <li> If {@code start} is infinite and
1326 * {@code direction} has a value such that the result should
1327 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1328 * same sign as {@code start} is returned.
1329 *
1330 * <li> If {@code start} is equal to ±
1331 * {@link Float#MAX_VALUE} and {@code direction} has a
1332 * value such that the result should have a larger magnitude, an
1333 * infinity with same sign as {@code start} is returned.
1334 * </ul>
1335 *
1336 * @param start starting floating-point value
1337 * @param direction value indicating which of
1338 * {@code start}'s neighbors or {@code start} should
1339 * be returned
1340 * @return The floating-point number adjacent to {@code start} in the
1341 * direction of {@code direction}.
1342 * @since 1.6
1343 */
1344 public static float nextAfter(float start, double direction) {
1345 return sun.misc.FpUtils.nextAfter(start, direction);
1346 }
1347
1348 /**
1349 * Returns the floating-point value adjacent to {@code d} in
1350 * the direction of positive infinity. This method is
1351 * semantically equivalent to {@code nextAfter(d,
1352 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1353 * implementation may run faster than its equivalent
1354 * {@code nextAfter} call.
1355 *
1356 * <p>Special Cases:
1357 * <ul>
1358 * <li> If the argument is NaN, the result is NaN.
1359 *
1360 * <li> If the argument is positive infinity, the result is
1361 * positive infinity.
1362 *
1363 * <li> If the argument is zero, the result is
1364 * {@link Double#MIN_VALUE}
1365 *
1366 * </ul>
1367 *
1368 * @param d starting floating-point value
1369 * @return The adjacent floating-point value closer to positive
1370 * infinity.
1371 * @since 1.6
1372 */
1373 public static double nextUp(double d) {
1374 return sun.misc.FpUtils.nextUp(d);
1375 }
1376
1377 /**
1378 * Returns the floating-point value adjacent to {@code f} in
1379 * the direction of positive infinity. This method is
1380 * semantically equivalent to {@code nextAfter(f,
1381 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1382 * implementation may run faster than its equivalent
1383 * {@code nextAfter} call.
1384 *
1385 * <p>Special Cases:
1386 * <ul>
1387 * <li> If the argument is NaN, the result is NaN.
1388 *
1389 * <li> If the argument is positive infinity, the result is
1390 * positive infinity.
1391 *
1392 * <li> If the argument is zero, the result is
1393 * {@link Float#MIN_VALUE}
1394 *
1395 * </ul>
1396 *
1397 * @param f starting floating-point value
1398 * @return The adjacent floating-point value closer to positive
1399 * infinity.
1400 * @since 1.6
1401 */
1402 public static float nextUp(float f) {
1403 return sun.misc.FpUtils.nextUp(f);
1404 }
1405
1406
1407 /**
1408 * Return {@code d} ×
1409 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1410 * by a single correctly rounded floating-point multiply to a
1411 * member of the double value set. See the Java
1412 * Language Specification for a discussion of floating-point
1413 * value sets. If the exponent of the result is between {@link
1414 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1415 * answer is calculated exactly. If the exponent of the result
1416 * would be larger than {@code Double.MAX_EXPONENT}, an
1417 * infinity is returned. Note that if the result is subnormal,
1418 * precision may be lost; that is, when {@code scalb(x, n)}
1419 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1420 * <i>x</i>. When the result is non-NaN, the result has the same
1421 * sign as {@code d}.
1422 *
1423 * <p>Special cases:
1424 * <ul>
1425 * <li> If the first argument is NaN, NaN is returned.
1426 * <li> If the first argument is infinite, then an infinity of the
1427 * same sign is returned.
1428 * <li> If the first argument is zero, then a zero of the same
1429 * sign is returned.
1430 * </ul>
1431 *
1432 * @param d number to be scaled by a power of two.
1433 * @param scaleFactor power of 2 used to scale {@code d}
1434 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1435 * @since 1.6
1436 */
1437 public static double scalb(double d, int scaleFactor) {
1438 return sun.misc.FpUtils.scalb(d, scaleFactor);
1439 }
1440
1441 /**
1442 * Return {@code f} ×
1443 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1444 * by a single correctly rounded floating-point multiply to a
1445 * member of the float value set. See the Java
1446 * Language Specification for a discussion of floating-point
1447 * value sets. If the exponent of the result is between {@link
1448 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1449 * answer is calculated exactly. If the exponent of the result
1450 * would be larger than {@code Float.MAX_EXPONENT}, an
1451 * infinity is returned. Note that if the result is subnormal,
1452 * precision may be lost; that is, when {@code scalb(x, n)}
1453 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1454 * <i>x</i>. When the result is non-NaN, the result has the same
1455 * sign as {@code f}.
1456 *
1457 * <p>Special cases:
1458 * <ul>
1459 * <li> If the first argument is NaN, NaN is returned.
1460 * <li> If the first argument is infinite, then an infinity of the
1461 * same sign is returned.
1462 * <li> If the first argument is zero, then a zero of the same
1463 * sign is returned.
1464 * </ul>
1465 *
1466 * @param f number to be scaled by a power of two.
1467 * @param scaleFactor power of 2 used to scale {@code f}
1468 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1469 * @since 1.6
1470 */
1471 public static float scalb(float f, int scaleFactor) {
1472 return sun.misc.FpUtils.scalb(f, scaleFactor);
1473 }
1474 }