1 /*
2 * Copyright (c) 1994, 2011, 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 *
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24 */
25
26 package java.lang;
27 import java.util.Random;
28
29
30 /**
31 * The class {@code Math} contains methods for performing basic
32 * numeric operations such as the elementary exponential, logarithm,
33 * square root, and trigonometric functions.
34 *
35 * <p>Unlike some of the numeric methods of class
36 * {@code StrictMath}, all implementations of the equivalent
37 * functions of class {@code Math} are not defined to return the
38 * bit-for-bit same results. This relaxation permits
39 * better-performing implementations where strict reproducibility is
40 * not required.
41 *
42 * <p>By default many of the {@code Math} methods simply call
43 * the equivalent method in {@code StrictMath} for their
44 * implementation. Code generators are encouraged to use
45 * platform-specific native libraries or microprocessor instructions,
46 * where available, to provide higher-performance implementations of
47 * {@code Math} methods. Such higher-performance
48 * implementations still must conform to the specification for
49 * {@code Math}.
50 *
51 * <p>The quality of implementation specifications concern two
52 * properties, accuracy of the returned result and monotonicity of the
53 * method. Accuracy of the floating-point {@code Math} methods is
54 * measured in terms of <i>ulps</i>, units in the last place. For a
55 * given floating-point format, an {@linkplain #ulp(double) ulp} of a
56 * specific real number value is the distance between the two
57 * floating-point values bracketing that numerical value. When
58 * discussing the accuracy of a method as a whole rather than at a
59 * specific argument, the number of ulps cited is for the worst-case
60 * error at any argument. If a method always has an error less than
61 * 0.5 ulps, the method always returns the floating-point number
62 * nearest the exact result; such a method is <i>correctly
63 * rounded</i>. A correctly rounded method is generally the best a
64 * floating-point approximation can be; however, it is impractical for
65 * many floating-point methods to be correctly rounded. Instead, for
66 * the {@code Math} class, a larger error bound of 1 or 2 ulps is
67 * allowed for certain methods. Informally, with a 1 ulp error bound,
68 * when the exact result is a representable number, the exact result
69 * should be returned as the computed result; otherwise, either of the
70 * two floating-point values which bracket the exact result may be
71 * returned. For exact results large in magnitude, one of the
72 * endpoints of the bracket may be infinite. Besides accuracy at
73 * individual arguments, maintaining proper relations between the
74 * method at different arguments is also important. Therefore, most
75 * methods with more than 0.5 ulp errors are required to be
76 * <i>semi-monotonic</i>: whenever the mathematical function is
77 * non-decreasing, so is the floating-point approximation, likewise,
78 * whenever the mathematical function is non-increasing, so is the
79 * floating-point approximation. Not all approximations that have 1
80 * ulp accuracy will automatically meet the monotonicity requirements.
81 *
82 * @author unascribed
83 * @author Joseph D. Darcy
84 * @since JDK1.0
85 */
86
87 public final class Math {
88
89 /**
90 * Don't let anyone instantiate this class.
91 */
92 private Math() {}
93
94 /**
95 * The {@code double} value that is closer than any other to
96 * <i>e</i>, the base of the natural logarithms.
97 */
98 public static final double E = 2.7182818284590452354;
99
100 /**
101 * The {@code double} value that is closer than any other to
102 * <i>pi</i>, the ratio of the circumference of a circle to its
103 * diameter.
104 */
105 public static final double PI = 3.14159265358979323846;
106
107 /**
108 * Returns the trigonometric sine of an angle. Special cases:
109 * <ul><li>If the argument is NaN or an infinity, then the
110 * result 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 * <p>The computed result must be within 1 ulp of the exact result.
115 * Results must be semi-monotonic.
116 *
117 * @param a an angle, in radians.
118 * @return the sine of the argument.
119 */
120 public static double sin(double a) {
121 return StrictMath.sin(a); // default impl. delegates to StrictMath
122 }
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 * <p>The computed result must be within 1 ulp of the exact result.
130 * Results must be semi-monotonic.
131 *
132 * @param a an angle, in radians.
133 * @return the cosine of the argument.
134 */
135 public static double cos(double a) {
136 return StrictMath.cos(a); // default impl. delegates to StrictMath
137 }
138
139 /**
140 * Returns the trigonometric tangent of an angle. Special cases:
141 * <ul><li>If the argument is NaN or an infinity, then the result
142 * is NaN.
143 * <li>If the argument is zero, then the result is a zero with the
144 * same sign as the argument.</ul>
145 *
146 * <p>The computed result must be within 1 ulp of the exact result.
147 * Results must be semi-monotonic.
148 *
149 * @param a an angle, in radians.
150 * @return the tangent of the argument.
151 */
152 public static double tan(double a) {
153 return StrictMath.tan(a); // default impl. delegates to StrictMath
154 }
155
156 /**
157 * Returns the arc sine of a value; the returned angle is in the
158 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
159 * <ul><li>If the argument is NaN or its absolute value is greater
160 * than 1, then the result is NaN.
161 * <li>If the argument is zero, then the result is a zero with the
162 * same sign as the argument.</ul>
163 *
164 * <p>The computed result must be within 1 ulp of the exact result.
165 * Results must be semi-monotonic.
166 *
167 * @param a the value whose arc sine is to be returned.
168 * @return the arc sine of the argument.
169 */
170 public static double asin(double a) {
171 return StrictMath.asin(a); // default impl. delegates to StrictMath
172 }
173
174 /**
175 * Returns the arc cosine of a value; the returned angle is in the
176 * range 0.0 through <i>pi</i>. Special case:
177 * <ul><li>If the argument is NaN or its absolute value is greater
178 * than 1, then the result is NaN.</ul>
179 *
180 * <p>The computed result must be within 1 ulp of the exact result.
181 * Results must be semi-monotonic.
182 *
183 * @param a the value whose arc cosine is to be returned.
184 * @return the arc cosine of the argument.
185 */
186 public static double acos(double a) {
187 return StrictMath.acos(a); // default impl. delegates to StrictMath
188 }
189
190 /**
191 * Returns the arc tangent of a value; the returned angle is in the
192 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
193 * <ul><li>If the argument is NaN, then the result is NaN.
194 * <li>If the argument is zero, then the result is a zero with the
195 * same sign as the argument.</ul>
196 *
197 * <p>The computed result must be within 1 ulp of the exact result.
198 * Results must be semi-monotonic.
199 *
200 * @param a the value whose arc tangent is to be returned.
201 * @return the arc tangent of the argument.
202 */
203 public static double atan(double a) {
204 return StrictMath.atan(a); // default impl. delegates to StrictMath
205 }
206
207 /**
208 * Converts an angle measured in degrees to an approximately
209 * equivalent angle measured in radians. The conversion from
210 * degrees to radians is generally inexact.
211 *
212 * @param angdeg an angle, in degrees
213 * @return the measurement of the angle {@code angdeg}
214 * in radians.
215 * @since 1.2
216 */
217 public static double toRadians(double angdeg) {
218 return angdeg / 180.0 * PI;
219 }
220
221 /**
222 * Converts an angle measured in radians to an approximately
223 * equivalent angle measured in degrees. The conversion from
224 * radians to degrees is generally inexact; users should
225 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
226 * equal {@code 0.0}.
227 *
228 * @param angrad an angle, in radians
229 * @return the measurement of the angle {@code angrad}
230 * in degrees.
231 * @since 1.2
232 */
233 public static double toDegrees(double angrad) {
234 return angrad * 180.0 / PI;
235 }
236
237 /**
238 * Returns Euler's number <i>e</i> raised to the power of a
239 * {@code double} value. Special cases:
240 * <ul><li>If the argument is NaN, the result is NaN.
241 * <li>If the argument is positive infinity, then the result is
242 * positive infinity.
243 * <li>If the argument is negative infinity, then the result is
244 * positive zero.</ul>
245 *
246 * <p>The computed result must be within 1 ulp of the exact result.
247 * Results must be semi-monotonic.
248 *
249 * @param a the exponent to raise <i>e</i> to.
250 * @return the value <i>e</i><sup>{@code a}</sup>,
251 * where <i>e</i> is the base of the natural logarithms.
252 */
253 public static double exp(double a) {
254 return StrictMath.exp(a); // default impl. delegates to StrictMath
255 }
256
257 /**
258 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
259 * value. Special cases:
260 * <ul><li>If the argument is NaN or less than zero, then the result
261 * is NaN.
262 * <li>If the argument is positive infinity, then the result is
263 * positive infinity.
264 * <li>If the argument is positive zero or negative zero, then the
265 * result is negative infinity.</ul>
266 *
267 * <p>The computed result must be within 1 ulp of the exact result.
268 * Results must be semi-monotonic.
269 *
270 * @param a a value
271 * @return the value ln {@code a}, the natural logarithm of
272 * {@code a}.
273 */
274 public static double log(double a) {
275 return StrictMath.log(a); // default impl. delegates to StrictMath
276 }
277
278 /**
279 * Returns the base 10 logarithm of a {@code double} value.
280 * Special cases:
281 *
282 * <ul><li>If the argument is NaN or less than zero, then the result
283 * is NaN.
284 * <li>If the argument is positive infinity, then the result is
285 * positive infinity.
286 * <li>If the argument is positive zero or negative zero, then the
287 * result is negative infinity.
288 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
289 * integer <i>n</i>, then the result is <i>n</i>.
290 * </ul>
291 *
292 * <p>The computed result must be within 1 ulp of the exact result.
293 * Results must be semi-monotonic.
294 *
295 * @param a a value
296 * @return the base 10 logarithm of {@code a}.
297 * @since 1.5
298 */
299 public static double log10(double a) {
300 return StrictMath.log10(a); // default impl. delegates to StrictMath
301 }
302
303 /**
304 * Returns the correctly rounded positive square root of a
305 * {@code double} value.
306 * Special cases:
307 * <ul><li>If the argument is NaN or less than zero, then the result
308 * is NaN.
309 * <li>If the argument is positive infinity, then the result is positive
310 * infinity.
311 * <li>If the argument is positive zero or negative zero, then the
312 * result is the same as the argument.</ul>
313 * Otherwise, the result is the {@code double} value closest to
314 * the true mathematical square root of the argument value.
315 *
316 * @param a a value.
317 * @return the positive square root of {@code a}.
318 * If the argument is NaN or less than zero, the result is NaN.
319 */
320 public static double sqrt(double a) {
321 return StrictMath.sqrt(a); // default impl. delegates to StrictMath
322 // Note that hardware sqrt instructions
323 // frequently can be directly used by JITs
324 // and should be much faster than doing
325 // Math.sqrt in software.
326 }
327
328
329 /**
330 * Returns the cube root of a {@code double} value. For
331 * positive finite {@code x}, {@code cbrt(-x) ==
332 * -cbrt(x)}; that is, the cube root of a negative value is
333 * the negative of the cube root of that value's magnitude.
334 *
335 * Special cases:
336 *
337 * <ul>
338 *
339 * <li>If the argument is NaN, then the result is NaN.
340 *
341 * <li>If the argument is infinite, then the result is an infinity
342 * with the same sign as the argument.
343 *
344 * <li>If the argument is zero, then the result is a zero with the
345 * same sign as the argument.
346 *
347 * </ul>
348 *
349 * <p>The computed result must be within 1 ulp of the exact result.
350 *
351 * @param a a value.
352 * @return the cube root of {@code a}.
353 * @since 1.5
354 */
355 public static double cbrt(double a) {
356 return StrictMath.cbrt(a);
357 }
358
359 /**
360 * Computes the remainder operation on two arguments as prescribed
361 * by the IEEE 754 standard.
362 * The remainder value is mathematically equal to
363 * <code>f1 - f2</code> × <i>n</i>,
364 * where <i>n</i> is the mathematical integer closest to the exact
365 * mathematical value of the quotient {@code f1/f2}, and if two
366 * mathematical integers are equally close to {@code f1/f2},
367 * then <i>n</i> is the integer that is even. If the remainder is
368 * zero, its sign is the same as the sign of the first argument.
369 * Special cases:
370 * <ul><li>If either argument is NaN, or the first argument is infinite,
371 * or the second argument is positive zero or negative zero, then the
372 * result is NaN.
373 * <li>If the first argument is finite and the second argument is
374 * infinite, then the result is the same as the first argument.</ul>
375 *
376 * @param f1 the dividend.
377 * @param f2 the divisor.
378 * @return the remainder when {@code f1} is divided by
379 * {@code f2}.
380 */
381 public static double IEEEremainder(double f1, double f2) {
382 return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
383 }
384
385 /**
386 * Returns the smallest (closest to negative infinity)
387 * {@code double} value that is greater than or equal to the
388 * argument and is equal to a mathematical integer. Special cases:
389 * <ul><li>If the argument value is already equal to a
390 * mathematical integer, then the result is the same as the
391 * argument. <li>If the argument is NaN or an infinity or
392 * positive zero or negative zero, then the result is the same as
393 * the argument. <li>If the argument value is less than zero but
394 * greater than -1.0, then the result is negative zero.</ul> Note
395 * that the value of {@code Math.ceil(x)} is exactly the
396 * value of {@code -Math.floor(-x)}.
397 *
398 *
399 * @param a a value.
400 * @return the smallest (closest to negative infinity)
401 * floating-point value that is greater than or equal to
402 * the argument and is equal to a mathematical integer.
403 */
404 public static double ceil(double a) {
405 return StrictMath.ceil(a); // default impl. delegates to StrictMath
406 }
407
408 /**
409 * Returns the largest (closest to positive infinity)
410 * {@code double} value that is less than or equal to the
411 * argument and is equal to a mathematical integer. Special cases:
412 * <ul><li>If the argument value is already equal to a
413 * mathematical integer, then the result is the same as the
414 * argument. <li>If the argument is NaN or an infinity or
415 * positive zero or negative zero, then the result is the same as
416 * the argument.</ul>
417 *
418 * @param a a value.
419 * @return the largest (closest to positive infinity)
420 * floating-point value that less than or equal to the argument
421 * and is equal to a mathematical integer.
422 */
423 public static double floor(double a) {
424 return StrictMath.floor(a); // default impl. delegates to StrictMath
425 }
426
427 /**
428 * Returns the {@code double} value that is closest in value
429 * to the argument and is equal to a mathematical integer. If two
430 * {@code double} values that are mathematical integers are
431 * equally close, the result is the integer value that is
432 * even. Special cases:
433 * <ul><li>If the argument value is already equal to a mathematical
434 * integer, then the result is the same as the argument.
435 * <li>If the argument is NaN or an infinity or positive zero or negative
436 * zero, then the result is the same as the argument.</ul>
437 *
438 * @param a a {@code double} value.
439 * @return the closest floating-point value to {@code a} that is
440 * equal to a mathematical integer.
441 */
442 public static double rint(double a) {
443 return StrictMath.rint(a); // default impl. delegates to StrictMath
444 }
445
446 /**
447 * Returns the angle <i>theta</i> from the conversion of rectangular
448 * coordinates ({@code x}, {@code y}) to polar
449 * coordinates (r, <i>theta</i>).
450 * This method computes the phase <i>theta</i> by computing an arc tangent
451 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
452 * cases:
453 * <ul><li>If either argument is NaN, then the result is NaN.
454 * <li>If the first argument is positive zero and the second argument
455 * is positive, or the first argument is positive and finite and the
456 * second argument is positive infinity, then the result is positive
457 * zero.
458 * <li>If the first argument is negative zero and the second argument
459 * is positive, or the first argument is negative and finite and the
460 * second argument is positive infinity, then the result is negative zero.
461 * <li>If the first argument is positive zero and the second argument
462 * is negative, or the first argument is positive and finite and the
463 * second argument is negative infinity, then the result is the
464 * {@code double} value closest to <i>pi</i>.
465 * <li>If the first argument is negative zero and the second argument
466 * is negative, or the first argument is negative and finite and the
467 * second argument is negative infinity, then the result is the
468 * {@code double} value closest to -<i>pi</i>.
469 * <li>If the first argument is positive and the second argument is
470 * positive zero or negative zero, or the first argument is positive
471 * infinity and the second argument is finite, then the result is the
472 * {@code double} value closest to <i>pi</i>/2.
473 * <li>If the first argument is negative and the second argument is
474 * positive zero or negative zero, or the first argument is negative
475 * infinity and the second argument is finite, then the result is the
476 * {@code double} value closest to -<i>pi</i>/2.
477 * <li>If both arguments are positive infinity, then the result is the
478 * {@code double} value closest to <i>pi</i>/4.
479 * <li>If the first argument is positive infinity and the second argument
480 * is negative infinity, then the result is the {@code double}
481 * value closest to 3*<i>pi</i>/4.
482 * <li>If the first argument is negative infinity and the second argument
483 * is positive infinity, then the result is the {@code double} value
484 * closest to -<i>pi</i>/4.
485 * <li>If both arguments are negative infinity, then the result is the
486 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
487 *
488 * <p>The computed result must be within 2 ulps of the exact result.
489 * Results must be semi-monotonic.
490 *
491 * @param y the ordinate coordinate
492 * @param x the abscissa coordinate
493 * @return the <i>theta</i> component of the point
494 * (<i>r</i>, <i>theta</i>)
495 * in polar coordinates that corresponds to the point
496 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
497 */
498 public static double atan2(double y, double x) {
499 return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
500 }
501
502 /**
503 * Returns the value of the first argument raised to the power of the
504 * second argument. Special cases:
505 *
506 * <ul><li>If the second argument is positive or negative zero, then the
507 * result is 1.0.
508 * <li>If the second argument is 1.0, then the result is the same as the
509 * first argument.
510 * <li>If the second argument is NaN, then the result is NaN.
511 * <li>If the first argument is NaN and the second argument is nonzero,
512 * then the result is NaN.
513 *
514 * <li>If
515 * <ul>
516 * <li>the absolute value of the first argument is greater than 1
517 * and the second argument is positive infinity, or
518 * <li>the absolute value of the first argument is less than 1 and
519 * the second argument is negative infinity,
520 * </ul>
521 * then the result is positive infinity.
522 *
523 * <li>If
524 * <ul>
525 * <li>the absolute value of the first argument is greater than 1 and
526 * the second argument is negative infinity, or
527 * <li>the absolute value of the
528 * first argument is less than 1 and the second argument is positive
529 * infinity,
530 * </ul>
531 * then the result is positive zero.
532 *
533 * <li>If the absolute value of the first argument equals 1 and the
534 * second argument is infinite, then the result is NaN.
535 *
536 * <li>If
537 * <ul>
538 * <li>the first argument is positive zero and the second argument
539 * is greater than zero, or
540 * <li>the first argument is positive infinity and the second
541 * argument is less than zero,
542 * </ul>
543 * then the result is positive zero.
544 *
545 * <li>If
546 * <ul>
547 * <li>the first argument is positive zero and the second argument
548 * is less than zero, or
549 * <li>the first argument is positive infinity and the second
550 * argument is greater than zero,
551 * </ul>
552 * then the result is positive infinity.
553 *
554 * <li>If
555 * <ul>
556 * <li>the first argument is negative zero and the second argument
557 * is greater than zero but not a finite odd integer, or
558 * <li>the first argument is negative infinity and the second
559 * argument is less than zero but not a finite odd integer,
560 * </ul>
561 * then the result is positive zero.
562 *
563 * <li>If
564 * <ul>
565 * <li>the first argument is negative zero and the second argument
566 * is a positive finite odd integer, or
567 * <li>the first argument is negative infinity and the second
568 * argument is a negative finite odd integer,
569 * </ul>
570 * then the result is negative zero.
571 *
572 * <li>If
573 * <ul>
574 * <li>the first argument is negative zero and the second argument
575 * is less than zero but not a finite odd integer, or
576 * <li>the first argument is negative infinity and the second
577 * argument is greater than zero but not a finite odd integer,
578 * </ul>
579 * then the result is positive infinity.
580 *
581 * <li>If
582 * <ul>
583 * <li>the first argument is negative zero and the second argument
584 * is a negative finite odd integer, or
585 * <li>the first argument is negative infinity and the second
586 * argument is a positive finite odd integer,
587 * </ul>
588 * then the result is negative infinity.
589 *
590 * <li>If the first argument is finite and less than zero
591 * <ul>
592 * <li> if the second argument is a finite even integer, the
593 * result is equal to the result of raising the absolute value of
594 * the first argument to the power of the second argument
595 *
596 * <li>if the second argument is a finite odd integer, the result
597 * is equal to the negative of the result of raising the absolute
598 * value of the first argument to the power of the second
599 * argument
600 *
601 * <li>if the second argument is finite and not an integer, then
602 * the result is NaN.
603 * </ul>
604 *
605 * <li>If both arguments are integers, then the result is exactly equal
606 * to the mathematical result of raising the first argument to the power
607 * of the second argument if that result can in fact be represented
608 * exactly as a {@code double} value.</ul>
609 *
610 * <p>(In the foregoing descriptions, a floating-point value is
611 * considered to be an integer if and only if it is finite and a
612 * fixed point of the method {@link #ceil ceil} or,
613 * equivalently, a fixed point of the method {@link #floor
614 * floor}. A value is a fixed point of a one-argument
615 * method if and only if the result of applying the method to the
616 * value is equal to the value.)
617 *
618 * <p>The computed result must be within 1 ulp of the exact result.
619 * Results must be semi-monotonic.
620 *
621 * @param a the base.
622 * @param b the exponent.
623 * @return the value {@code a}<sup>{@code b}</sup>.
624 */
625 public static double pow(double a, double b) {
626 return StrictMath.pow(a, b); // default impl. delegates to StrictMath
627 }
628
629 /**
630 * Returns the closest {@code int} to the argument, with ties
631 * rounding up.
632 *
633 * <p>
634 * Special cases:
635 * <ul><li>If the argument is NaN, the result is 0.
636 * <li>If the argument is negative infinity or any value less than or
637 * equal to the value of {@code Integer.MIN_VALUE}, the result is
638 * equal to the value of {@code Integer.MIN_VALUE}.
639 * <li>If the argument is positive infinity or any value greater than or
640 * equal to the value of {@code Integer.MAX_VALUE}, the result is
641 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
642 *
643 * @param a a floating-point value to be rounded to an integer.
644 * @return the value of the argument rounded to the nearest
645 * {@code int} value.
646 * @see java.lang.Integer#MAX_VALUE
647 * @see java.lang.Integer#MIN_VALUE
648 */
649 public static int round(float a) {
650 if (a != 0x1.fffffep-2f) // greatest float value less than 0.5
651 return (int)floor(a + 0.5f);
652 else
653 return 0;
654 }
655
656 /**
657 * Returns the closest {@code long} to the argument, with ties
658 * rounding up.
659 *
660 * <p>Special cases:
661 * <ul><li>If the argument is NaN, the result is 0.
662 * <li>If the argument is negative infinity or any value less than or
663 * equal to the value of {@code Long.MIN_VALUE}, the result is
664 * equal to the value of {@code Long.MIN_VALUE}.
665 * <li>If the argument is positive infinity or any value greater than or
666 * equal to the value of {@code Long.MAX_VALUE}, the result is
667 * equal to the value of {@code Long.MAX_VALUE}.</ul>
668 *
669 * @param a a floating-point value to be rounded to a
670 * {@code long}.
671 * @return the value of the argument rounded to the nearest
672 * {@code long} value.
673 * @see java.lang.Long#MAX_VALUE
674 * @see java.lang.Long#MIN_VALUE
675 */
676 public static long round(double a) {
677 if (a != 0x1.fffffffffffffp-2) // greatest double value less than 0.5
678 return (long)floor(a + 0.5d);
679 else
680 return 0;
681 }
682
683 private static Random randomNumberGenerator;
684
685 private static synchronized Random initRNG() {
686 Random rnd = randomNumberGenerator;
687 return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
688 }
689
690 /**
691 * Returns a {@code double} value with a positive sign, greater
692 * than or equal to {@code 0.0} and less than {@code 1.0}.
693 * Returned values are chosen pseudorandomly with (approximately)
694 * uniform distribution from that range.
695 *
696 * <p>When this method is first called, it creates a single new
697 * pseudorandom-number generator, exactly as if by the expression
698 *
699 * <blockquote>{@code new java.util.Random()}</blockquote>
700 *
701 * This new pseudorandom-number generator is used thereafter for
702 * all calls to this method and is used nowhere else.
703 *
704 * <p>This method is properly synchronized to allow correct use by
705 * more than one thread. However, if many threads need to generate
706 * pseudorandom numbers at a great rate, it may reduce contention
707 * for each thread to have its own pseudorandom-number generator.
708 *
709 * @return a pseudorandom {@code double} greater than or equal
710 * to {@code 0.0} and less than {@code 1.0}.
711 * @see Random#nextDouble()
712 */
713 public static double random() {
714 Random rnd = randomNumberGenerator;
715 if (rnd == null) rnd = initRNG();
716 return rnd.nextDouble();
717 }
718
719 /**
720 * Returns the absolute value of an {@code int} value.
721 * If the argument is not negative, the argument is returned.
722 * If the argument is negative, the negation of the argument is returned.
723 *
724 * <p>Note that if the argument is equal to the value of
725 * {@link Integer#MIN_VALUE}, the most negative representable
726 * {@code int} value, the result is that same value, which is
727 * negative.
728 *
729 * @param a the argument whose absolute value is to be determined
730 * @return the absolute value of the argument.
731 */
732 public static int abs(int a) {
733 return (a < 0) ? -a : a;
734 }
735
736 /**
737 * Returns the absolute value of a {@code long} value.
738 * If the argument is not negative, the argument is returned.
739 * If the argument is negative, the negation of the argument is returned.
740 *
741 * <p>Note that if the argument is equal to the value of
742 * {@link Long#MIN_VALUE}, the most negative representable
743 * {@code long} value, the result is that same value, which
744 * is negative.
745 *
746 * @param a the argument whose absolute value is to be determined
747 * @return the absolute value of the argument.
748 */
749 public static long abs(long a) {
750 return (a < 0) ? -a : a;
751 }
752
753 /**
754 * Returns the absolute value of a {@code float} value.
755 * If the argument is not negative, the argument is returned.
756 * If the argument is negative, the negation of the argument is returned.
757 * Special cases:
758 * <ul><li>If the argument is positive zero or negative zero, the
759 * result is positive zero.
760 * <li>If the argument is infinite, the result is positive infinity.
761 * <li>If the argument is NaN, the result is NaN.</ul>
762 * In other words, the result is the same as the value of the expression:
763 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
764 *
765 * @param a the argument whose absolute value is to be determined
766 * @return the absolute value of the argument.
767 */
768 public static float abs(float a) {
769 return (a <= 0.0F) ? 0.0F - a : a;
770 }
771
772 /**
773 * Returns the absolute value of a {@code double} value.
774 * If the argument is not negative, the argument is returned.
775 * If the argument is negative, the negation of the argument is returned.
776 * Special cases:
777 * <ul><li>If the argument is positive zero or negative zero, the result
778 * is positive zero.
779 * <li>If the argument is infinite, the result is positive infinity.
780 * <li>If the argument is NaN, the result is NaN.</ul>
781 * In other words, the result is the same as the value of the expression:
782 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
783 *
784 * @param a the argument whose absolute value is to be determined
785 * @return the absolute value of the argument.
786 */
787 public static double abs(double a) {
788 return (a <= 0.0D) ? 0.0D - a : a;
789 }
790
791 /**
792 * Returns the greater of two {@code int} values. That is, the
793 * result is the argument closer to the value of
794 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
795 * the result is that same value.
796 *
797 * @param a an argument.
798 * @param b another argument.
799 * @return the larger of {@code a} and {@code b}.
800 */
801 public static int max(int a, int b) {
802 return (a >= b) ? a : b;
803 }
804
805 /**
806 * Returns the greater of two {@code long} values. That is, the
807 * result is the argument closer to the value of
808 * {@link Long#MAX_VALUE}. If the arguments have the same value,
809 * the result is that same value.
810 *
811 * @param a an argument.
812 * @param b another argument.
813 * @return the larger of {@code a} and {@code b}.
814 */
815 public static long max(long a, long b) {
816 return (a >= b) ? a : b;
817 }
818
819 private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
820 private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
821
822 /**
823 * Returns the greater of two {@code float} values. That is,
824 * the result is the argument closer to positive infinity. If the
825 * arguments have the same value, the result is that same
826 * value. If either value is NaN, then the result is NaN. Unlike
827 * the numerical comparison operators, this method considers
828 * negative zero to be strictly smaller than positive zero. If one
829 * argument is positive zero and the other negative zero, the
830 * result is positive zero.
831 *
832 * @param a an argument.
833 * @param b another argument.
834 * @return the larger of {@code a} and {@code b}.
835 */
836 public static float max(float a, float b) {
837 if (a != a) return a; // a is NaN
838 if ((a == 0.0f) && (b == 0.0f)
839 && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
840 return b;
841 }
842 return (a >= b) ? a : b;
843 }
844
845 /**
846 * Returns the greater of two {@code double} values. That
847 * is, the result is the argument closer to positive infinity. If
848 * the arguments have the same value, the result is that same
849 * value. If either value is NaN, then the result is NaN. Unlike
850 * the numerical comparison operators, this method considers
851 * negative zero to be strictly smaller than positive zero. If one
852 * argument is positive zero and the other negative zero, the
853 * result is positive zero.
854 *
855 * @param a an argument.
856 * @param b another argument.
857 * @return the larger of {@code a} and {@code b}.
858 */
859 public static double max(double a, double b) {
860 if (a != a) return a; // a is NaN
861 if ((a == 0.0d) && (b == 0.0d)
862 && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
863 return b;
864 }
865 return (a >= b) ? a : b;
866 }
867
868 /**
869 * Returns the smaller of two {@code int} values. That is,
870 * the result the argument closer to the value of
871 * {@link Integer#MIN_VALUE}. If the arguments have the same
872 * value, the result is that same value.
873 *
874 * @param a an argument.
875 * @param b another argument.
876 * @return the smaller of {@code a} and {@code b}.
877 */
878 public static int min(int a, int b) {
879 return (a <= b) ? a : b;
880 }
881
882 /**
883 * Returns the smaller of two {@code long} values. That is,
884 * the result is the argument closer to the value of
885 * {@link Long#MIN_VALUE}. If the arguments have the same
886 * value, the result is that same value.
887 *
888 * @param a an argument.
889 * @param b another argument.
890 * @return the smaller of {@code a} and {@code b}.
891 */
892 public static long min(long a, long b) {
893 return (a <= b) ? a : b;
894 }
895
896 /**
897 * Returns the smaller of two {@code float} values. That is,
898 * the result is the value closer to negative infinity. If the
899 * arguments have the same value, the result is that same
900 * value. If either value is NaN, then the result is NaN. Unlike
901 * the numerical comparison operators, this method considers
902 * negative zero to be strictly smaller than positive zero. If
903 * one argument is positive zero and the other is negative zero,
904 * the result is negative zero.
905 *
906 * @param a an argument.
907 * @param b another argument.
908 * @return the smaller of {@code a} and {@code b}.
909 */
910 public static float min(float a, float b) {
911 if (a != a) return a; // a is NaN
912 if ((a == 0.0f) && (b == 0.0f)
913 && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
914 return b;
915 }
916 return (a <= b) ? a : b;
917 }
918
919 /**
920 * Returns the smaller of two {@code double} values. That
921 * is, the result is the value closer to negative infinity. If the
922 * arguments have the same value, the result is that same
923 * value. If either value is NaN, then the result is NaN. Unlike
924 * the numerical comparison operators, this method considers
925 * negative zero to be strictly smaller than positive zero. If one
926 * argument is positive zero and the other is negative zero, the
927 * result is negative zero.
928 *
929 * @param a an argument.
930 * @param b another argument.
931 * @return the smaller of {@code a} and {@code b}.
932 */
933 public static double min(double a, double b) {
934 if (a != a) return a; // a is NaN
935 if ((a == 0.0d) && (b == 0.0d)
936 && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
937 return b;
938 }
939 return (a <= b) ? a : b;
940 }
941
942 /**
943 * Returns the size of an ulp of the argument. An ulp, unit in
944 * the last place, of a {@code double} value is the positive
945 * distance between this floating-point value and the {@code
946 * double} value next larger in magnitude. Note that for non-NaN
947 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
948 *
949 * <p>Special Cases:
950 * <ul>
951 * <li> If the argument is NaN, then the result is NaN.
952 * <li> If the argument is positive or negative infinity, then the
953 * result is positive infinity.
954 * <li> If the argument is positive or negative zero, then the result is
955 * {@code Double.MIN_VALUE}.
956 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
957 * the result is equal to 2<sup>971</sup>.
958 * </ul>
959 *
960 * @param d the floating-point value whose ulp is to be returned
961 * @return the size of an ulp of the argument
962 * @author Joseph D. Darcy
963 * @since 1.5
964 */
965 public static double ulp(double d) {
966 return sun.misc.FpUtils.ulp(d);
967 }
968
969 /**
970 * Returns the size of an ulp of the argument. An ulp, unit in
971 * the last place, of a {@code float} value is the positive
972 * distance between this floating-point value and the {@code
973 * float} value next larger in magnitude. Note that for non-NaN
974 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
975 *
976 * <p>Special Cases:
977 * <ul>
978 * <li> If the argument is NaN, then the result is NaN.
979 * <li> If the argument is positive or negative infinity, then the
980 * result is positive infinity.
981 * <li> If the argument is positive or negative zero, then the result is
982 * {@code Float.MIN_VALUE}.
983 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
984 * the result is equal to 2<sup>104</sup>.
985 * </ul>
986 *
987 * @param f the floating-point value whose ulp is to be returned
988 * @return the size of an ulp of the argument
989 * @author Joseph D. Darcy
990 * @since 1.5
991 */
992 public static float ulp(float f) {
993 return sun.misc.FpUtils.ulp(f);
994 }
995
996 /**
997 * Returns the signum function of the argument; zero if the argument
998 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
999 * argument is less than zero.
1000 *
1001 * <p>Special Cases:
1002 * <ul>
1003 * <li> If the argument is NaN, then the result is NaN.
1004 * <li> If the argument is positive zero or negative zero, then the
1005 * result is the same as the argument.
1006 * </ul>
1007 *
1008 * @param d the floating-point value whose signum is to be returned
1009 * @return the signum function of the argument
1010 * @author Joseph D. Darcy
1011 * @since 1.5
1012 */
1013 public static double signum(double d) {
1014 return sun.misc.FpUtils.signum(d);
1015 }
1016
1017 /**
1018 * Returns the signum function of the argument; zero if the argument
1019 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1020 * argument is less than zero.
1021 *
1022 * <p>Special Cases:
1023 * <ul>
1024 * <li> If the argument is NaN, then the result is NaN.
1025 * <li> If the argument is positive zero or negative zero, then the
1026 * result is the same as the argument.
1027 * </ul>
1028 *
1029 * @param f the floating-point value whose signum is to be returned
1030 * @return the signum function of the argument
1031 * @author Joseph D. Darcy
1032 * @since 1.5
1033 */
1034 public static float signum(float f) {
1035 return sun.misc.FpUtils.signum(f);
1036 }
1037
1038 /**
1039 * Returns the hyperbolic sine of a {@code double} value.
1040 * The hyperbolic sine of <i>x</i> is defined to be
1041 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1042 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1043 *
1044 * <p>Special cases:
1045 * <ul>
1046 *
1047 * <li>If the argument is NaN, then the result is NaN.
1048 *
1049 * <li>If the argument is infinite, then the result is an infinity
1050 * with the same sign as the argument.
1051 *
1052 * <li>If the argument is zero, then the result is a zero with the
1053 * same sign as the argument.
1054 *
1055 * </ul>
1056 *
1057 * <p>The computed result must be within 2.5 ulps of the exact result.
1058 *
1059 * @param x The number whose hyperbolic sine is to be returned.
1060 * @return The hyperbolic sine of {@code x}.
1061 * @since 1.5
1062 */
1063 public static double sinh(double x) {
1064 return StrictMath.sinh(x);
1065 }
1066
1067 /**
1068 * Returns the hyperbolic cosine of a {@code double} value.
1069 * The hyperbolic cosine of <i>x</i> is defined to be
1070 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1071 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1072 *
1073 * <p>Special cases:
1074 * <ul>
1075 *
1076 * <li>If the argument is NaN, then the result is NaN.
1077 *
1078 * <li>If the argument is infinite, then the result is positive
1079 * infinity.
1080 *
1081 * <li>If the argument is zero, then the result is {@code 1.0}.
1082 *
1083 * </ul>
1084 *
1085 * <p>The computed result must be within 2.5 ulps of the exact result.
1086 *
1087 * @param x The number whose hyperbolic cosine is to be returned.
1088 * @return The hyperbolic cosine of {@code x}.
1089 * @since 1.5
1090 */
1091 public static double cosh(double x) {
1092 return StrictMath.cosh(x);
1093 }
1094
1095 /**
1096 * Returns the hyperbolic tangent of a {@code double} value.
1097 * The hyperbolic tangent of <i>x</i> is defined to be
1098 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1099 * in other words, {@linkplain Math#sinh
1100 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1101 * that the absolute value of the exact tanh is always less than
1102 * 1.
1103 *
1104 * <p>Special cases:
1105 * <ul>
1106 *
1107 * <li>If the argument is NaN, then the result is NaN.
1108 *
1109 * <li>If the argument is zero, then the result is a zero with the
1110 * same sign as the argument.
1111 *
1112 * <li>If the argument is positive infinity, then the result is
1113 * {@code +1.0}.
1114 *
1115 * <li>If the argument is negative infinity, then the result is
1116 * {@code -1.0}.
1117 *
1118 * </ul>
1119 *
1120 * <p>The computed result must be within 2.5 ulps of the exact result.
1121 * The result of {@code tanh} for any finite input must have
1122 * an absolute value less than or equal to 1. Note that once the
1123 * exact result of tanh is within 1/2 of an ulp of the limit value
1124 * of ±1, correctly signed ±{@code 1.0} should
1125 * be returned.
1126 *
1127 * @param x The number whose hyperbolic tangent is to be returned.
1128 * @return The hyperbolic tangent of {@code x}.
1129 * @since 1.5
1130 */
1131 public static double tanh(double x) {
1132 return StrictMath.tanh(x);
1133 }
1134
1135 /**
1136 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1137 * without intermediate overflow or underflow.
1138 *
1139 * <p>Special cases:
1140 * <ul>
1141 *
1142 * <li> If either argument is infinite, then the result
1143 * is positive infinity.
1144 *
1145 * <li> If either argument is NaN and neither argument is infinite,
1146 * then the result is NaN.
1147 *
1148 * </ul>
1149 *
1150 * <p>The computed result must be within 1 ulp of the exact
1151 * result. If one parameter is held constant, the results must be
1152 * semi-monotonic in the other parameter.
1153 *
1154 * @param x a value
1155 * @param y a value
1156 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1157 * without intermediate overflow or underflow
1158 * @since 1.5
1159 */
1160 public static double hypot(double x, double y) {
1161 return StrictMath.hypot(x, y);
1162 }
1163
1164 /**
1165 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1166 * <i>x</i> near 0, the exact sum of
1167 * {@code expm1(x)} + 1 is much closer to the true
1168 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1169 *
1170 * <p>Special cases:
1171 * <ul>
1172 * <li>If the argument is NaN, the result is NaN.
1173 *
1174 * <li>If the argument is positive infinity, then the result is
1175 * positive infinity.
1176 *
1177 * <li>If the argument is negative infinity, then the result is
1178 * -1.0.
1179 *
1180 * <li>If the argument is zero, then the result is a zero with the
1181 * same sign as the argument.
1182 *
1183 * </ul>
1184 *
1185 * <p>The computed result must be within 1 ulp of the exact result.
1186 * Results must be semi-monotonic. The result of
1187 * {@code expm1} for any finite input must be greater than or
1188 * equal to {@code -1.0}. Note that once the exact result of
1189 * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
1190 * ulp of the limit value -1, {@code -1.0} should be
1191 * returned.
1192 *
1193 * @param x the exponent to raise <i>e</i> to in the computation of
1194 * <i>e</i><sup>{@code x}</sup> -1.
1195 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1196 * @since 1.5
1197 */
1198 public static double expm1(double x) {
1199 return StrictMath.expm1(x);
1200 }
1201
1202 /**
1203 * Returns the natural logarithm of the sum of the argument and 1.
1204 * Note that for small values {@code x}, the result of
1205 * {@code log1p(x)} is much closer to the true result of ln(1
1206 * + {@code x}) than the floating-point evaluation of
1207 * {@code log(1.0+x)}.
1208 *
1209 * <p>Special cases:
1210 *
1211 * <ul>
1212 *
1213 * <li>If the argument is NaN or less than -1, then the result is
1214 * NaN.
1215 *
1216 * <li>If the argument is positive infinity, then the result is
1217 * positive infinity.
1218 *
1219 * <li>If the argument is negative one, then the result is
1220 * negative infinity.
1221 *
1222 * <li>If the argument is zero, then the result is a zero with the
1223 * same sign as the argument.
1224 *
1225 * </ul>
1226 *
1227 * <p>The computed result must be within 1 ulp of the exact result.
1228 * Results must be semi-monotonic.
1229 *
1230 * @param x a value
1231 * @return the value ln({@code x} + 1), the natural
1232 * log of {@code x} + 1
1233 * @since 1.5
1234 */
1235 public static double log1p(double x) {
1236 return StrictMath.log1p(x);
1237 }
1238
1239 /**
1240 * Returns the first floating-point argument with the sign of the
1241 * second floating-point argument. Note that unlike the {@link
1242 * StrictMath#copySign(double, double) StrictMath.copySign}
1243 * method, this method does not require NaN {@code sign}
1244 * arguments to be treated as positive values; implementations are
1245 * permitted to treat some NaN arguments as positive and other NaN
1246 * arguments as negative to allow greater performance.
1247 *
1248 * @param magnitude the parameter providing the magnitude of the result
1249 * @param sign the parameter providing the sign of the result
1250 * @return a value with the magnitude of {@code magnitude}
1251 * and the sign of {@code sign}.
1252 * @since 1.6
1253 */
1254 public static double copySign(double magnitude, double sign) {
1255 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1256 }
1257
1258 /**
1259 * Returns the first floating-point argument with the sign of the
1260 * second floating-point argument. Note that unlike the {@link
1261 * StrictMath#copySign(float, float) StrictMath.copySign}
1262 * method, this method does not require NaN {@code sign}
1263 * arguments to be treated as positive values; implementations are
1264 * permitted to treat some NaN arguments as positive and other NaN
1265 * arguments as negative to allow greater performance.
1266 *
1267 * @param magnitude the parameter providing the magnitude of the result
1268 * @param sign the parameter providing the sign of the result
1269 * @return a value with the magnitude of {@code magnitude}
1270 * and the sign of {@code sign}.
1271 * @since 1.6
1272 */
1273 public static float copySign(float magnitude, float sign) {
1274 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1275 }
1276
1277 /**
1278 * Returns the unbiased exponent used in the representation of a
1279 * {@code float}. Special cases:
1280 *
1281 * <ul>
1282 * <li>If the argument is NaN or infinite, then the result is
1283 * {@link Float#MAX_EXPONENT} + 1.
1284 * <li>If the argument is zero or subnormal, then the result is
1285 * {@link Float#MIN_EXPONENT} -1.
1286 * </ul>
1287 * @param f a {@code float} value
1288 * @return the unbiased exponent of the argument
1289 * @since 1.6
1290 */
1291 public static int getExponent(float f) {
1292 return sun.misc.FpUtils.getExponent(f);
1293 }
1294
1295 /**
1296 * Returns the unbiased exponent used in the representation of a
1297 * {@code double}. Special cases:
1298 *
1299 * <ul>
1300 * <li>If the argument is NaN or infinite, then the result is
1301 * {@link Double#MAX_EXPONENT} + 1.
1302 * <li>If the argument is zero or subnormal, then the result is
1303 * {@link Double#MIN_EXPONENT} -1.
1304 * </ul>
1305 * @param d a {@code double} value
1306 * @return the unbiased exponent of the argument
1307 * @since 1.6
1308 */
1309 public static int getExponent(double d) {
1310 return sun.misc.FpUtils.getExponent(d);
1311 }
1312
1313 /**
1314 * Returns the floating-point number adjacent to the first
1315 * argument in the direction of the second argument. If both
1316 * arguments compare as equal the second argument is returned.
1317 *
1318 * <p>
1319 * Special cases:
1320 * <ul>
1321 * <li> If either argument is a NaN, then NaN is returned.
1322 *
1323 * <li> If both arguments are signed zeros, {@code direction}
1324 * is returned unchanged (as implied by the requirement of
1325 * returning the second argument if the arguments compare as
1326 * equal).
1327 *
1328 * <li> If {@code start} is
1329 * ±{@link Double#MIN_VALUE} and {@code direction}
1330 * has a value such that the result should have a smaller
1331 * magnitude, then a zero with the same sign as {@code start}
1332 * is returned.
1333 *
1334 * <li> If {@code start} is infinite and
1335 * {@code direction} has a value such that the result should
1336 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1337 * same sign as {@code start} is returned.
1338 *
1339 * <li> If {@code start} is equal to ±
1340 * {@link Double#MAX_VALUE} and {@code direction} has a
1341 * value such that the result should have a larger magnitude, an
1342 * infinity with same sign as {@code start} is returned.
1343 * </ul>
1344 *
1345 * @param start starting floating-point value
1346 * @param direction value indicating which of
1347 * {@code start}'s neighbors or {@code start} should
1348 * be returned
1349 * @return The floating-point number adjacent to {@code start} in the
1350 * direction of {@code direction}.
1351 * @since 1.6
1352 */
1353 public static double nextAfter(double start, double direction) {
1354 return sun.misc.FpUtils.nextAfter(start, direction);
1355 }
1356
1357 /**
1358 * Returns the floating-point number adjacent to the first
1359 * argument in the direction of the second argument. If both
1360 * arguments compare as equal a value equivalent to the second argument
1361 * is returned.
1362 *
1363 * <p>
1364 * Special cases:
1365 * <ul>
1366 * <li> If either argument is a NaN, then NaN is returned.
1367 *
1368 * <li> If both arguments are signed zeros, a value equivalent
1369 * to {@code direction} is returned.
1370 *
1371 * <li> If {@code start} is
1372 * ±{@link Float#MIN_VALUE} and {@code direction}
1373 * has a value such that the result should have a smaller
1374 * magnitude, then a zero with the same sign as {@code start}
1375 * is returned.
1376 *
1377 * <li> If {@code start} is infinite and
1378 * {@code direction} has a value such that the result should
1379 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1380 * same sign as {@code start} is returned.
1381 *
1382 * <li> If {@code start} is equal to ±
1383 * {@link Float#MAX_VALUE} and {@code direction} has a
1384 * value such that the result should have a larger magnitude, an
1385 * infinity with same sign as {@code start} is returned.
1386 * </ul>
1387 *
1388 * @param start starting floating-point value
1389 * @param direction value indicating which of
1390 * {@code start}'s neighbors or {@code start} should
1391 * be returned
1392 * @return The floating-point number adjacent to {@code start} in the
1393 * direction of {@code direction}.
1394 * @since 1.6
1395 */
1396 public static float nextAfter(float start, double direction) {
1397 return sun.misc.FpUtils.nextAfter(start, direction);
1398 }
1399
1400 /**
1401 * Returns the floating-point value adjacent to {@code d} in
1402 * the direction of positive infinity. This method is
1403 * semantically equivalent to {@code nextAfter(d,
1404 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1405 * implementation may run faster than its equivalent
1406 * {@code nextAfter} call.
1407 *
1408 * <p>Special Cases:
1409 * <ul>
1410 * <li> If the argument is NaN, the result is NaN.
1411 *
1412 * <li> If the argument is positive infinity, the result is
1413 * positive infinity.
1414 *
1415 * <li> If the argument is zero, the result is
1416 * {@link Double#MIN_VALUE}
1417 *
1418 * </ul>
1419 *
1420 * @param d starting floating-point value
1421 * @return The adjacent floating-point value closer to positive
1422 * infinity.
1423 * @since 1.6
1424 */
1425 public static double nextUp(double d) {
1426 return sun.misc.FpUtils.nextUp(d);
1427 }
1428
1429 /**
1430 * Returns the floating-point value adjacent to {@code f} in
1431 * the direction of positive infinity. This method is
1432 * semantically equivalent to {@code nextAfter(f,
1433 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1434 * implementation may run faster than its equivalent
1435 * {@code nextAfter} call.
1436 *
1437 * <p>Special Cases:
1438 * <ul>
1439 * <li> If the argument is NaN, the result is NaN.
1440 *
1441 * <li> If the argument is positive infinity, the result is
1442 * positive infinity.
1443 *
1444 * <li> If the argument is zero, the result is
1445 * {@link Float#MIN_VALUE}
1446 *
1447 * </ul>
1448 *
1449 * @param f starting floating-point value
1450 * @return The adjacent floating-point value closer to positive
1451 * infinity.
1452 * @since 1.6
1453 */
1454 public static float nextUp(float f) {
1455 return sun.misc.FpUtils.nextUp(f);
1456 }
1457
1458
1459 /**
1460 * Return {@code d} ×
1461 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1462 * by a single correctly rounded floating-point multiply to a
1463 * member of the double value set. See the Java
1464 * Language Specification for a discussion of floating-point
1465 * value sets. If the exponent of the result is between {@link
1466 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1467 * answer is calculated exactly. If the exponent of the result
1468 * would be larger than {@code Double.MAX_EXPONENT}, an
1469 * infinity is returned. Note that if the result is subnormal,
1470 * precision may be lost; that is, when {@code scalb(x, n)}
1471 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1472 * <i>x</i>. When the result is non-NaN, the result has the same
1473 * sign as {@code d}.
1474 *
1475 * <p>Special cases:
1476 * <ul>
1477 * <li> If the first argument is NaN, NaN is returned.
1478 * <li> If the first argument is infinite, then an infinity of the
1479 * same sign is returned.
1480 * <li> If the first argument is zero, then a zero of the same
1481 * sign is returned.
1482 * </ul>
1483 *
1484 * @param d number to be scaled by a power of two.
1485 * @param scaleFactor power of 2 used to scale {@code d}
1486 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1487 * @since 1.6
1488 */
1489 public static double scalb(double d, int scaleFactor) {
1490 return sun.misc.FpUtils.scalb(d, scaleFactor);
1491 }
1492
1493 /**
1494 * Return {@code f} ×
1495 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1496 * by a single correctly rounded floating-point multiply to a
1497 * member of the float value set. See the Java
1498 * Language Specification for a discussion of floating-point
1499 * value sets. If the exponent of the result is between {@link
1500 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1501 * answer is calculated exactly. If the exponent of the result
1502 * would be larger than {@code Float.MAX_EXPONENT}, an
1503 * infinity is returned. Note that if the result is subnormal,
1504 * precision may be lost; that is, when {@code scalb(x, n)}
1505 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1506 * <i>x</i>. When the result is non-NaN, the result has the same
1507 * sign as {@code f}.
1508 *
1509 * <p>Special cases:
1510 * <ul>
1511 * <li> If the first argument is NaN, NaN is returned.
1512 * <li> If the first argument is infinite, then an infinity of the
1513 * same sign is returned.
1514 * <li> If the first argument is zero, then a zero of the same
1515 * sign is returned.
1516 * </ul>
1517 *
1518 * @param f number to be scaled by a power of two.
1519 * @param scaleFactor power of 2 used to scale {@code f}
1520 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1521 * @since 1.6
1522 */
1523 public static float scalb(float f, int scaleFactor) {
1524 return sun.misc.FpUtils.scalb(f, scaleFactor);
1525 }
1526 }