1 /*
2 * Copyright 1994-2006 Sun Microsystems, Inc. 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. Sun designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
22 * CA 95054 USA or visit www.sun.com if you need additional information or
23 * have any questions.
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
54 * is measured in terms of <i>ulps</i>, units in the last place. For
55 * a given floating-point format, an ulp of a specific real number
56 * value is the distance between the two floating-point values
57 * bracketing that numerical value. When discussing the accuracy of a
58 * method as a whole rather than at a specific argument, the number of
59 * ulps cited is for the worst-case error at any argument. If a
60 * method always has an error less than 0.5 ulps, the method always
61 * returns the floating-point number nearest the exact result; such a
62 * method is <i>correctly rounded</i>. A correctly rounded method is
63 * generally the best a floating-point approximation can be; however,
64 * it is impractical for many floating-point methods to be correctly
65 * rounded. Instead, for the {@code Math} class, a larger error
66 * bound of 1 or 2 ulps is allowed for certain methods. Informally,
67 * with a 1 ulp error bound, when the exact result is a representable
68 * number, the exact result should be returned as the computed result;
69 * otherwise, either of the two floating-point values which bracket
70 * the exact result may be returned. For exact results large in
71 * magnitude, one of the endpoints of the bracket may be infinite.
72 * Besides accuracy at individual arguments, maintaining proper
73 * relations between the method at different arguments is also
74 * important. Therefore, most methods with more than 0.5 ulp errors
75 * are required to be <i>semi-monotonic</i>: whenever the mathematical
76 * function is non-decreasing, so is the floating-point approximation,
77 * likewise, whenever the mathematical function is non-increasing, so
78 * is the floating-point approximation. Not all approximations that
79 * have 1 ulp accuracy will automatically meet the monotonicity
80 * 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. The
631 * result is rounded to an integer by adding 1/2, taking the
632 * floor of the result, and casting the result to type {@code int}.
633 * In other words, the result is equal to the value of the expression:
634 * <p>{@code (int)Math.floor(a + 0.5f)}
635 * <p>
636 * Special cases:
637 * <ul><li>If the argument is NaN, the result is 0.
638 * <li>If the argument is negative infinity or any value less than or
639 * equal to the value of {@code Integer.MIN_VALUE}, the result is
640 * equal to the value of {@code Integer.MIN_VALUE}.
641 * <li>If the argument is positive infinity or any value greater than or
642 * equal to the value of {@code Integer.MAX_VALUE}, the result is
643 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
644 *
645 * @param a a floating-point value to be rounded to an integer.
646 * @return the value of the argument rounded to the nearest
647 * {@code int} value.
648 * @see java.lang.Integer#MAX_VALUE
649 * @see java.lang.Integer#MIN_VALUE
650 */
651 public static int round(float a) {
652 return (int)floor(a + 0.5f);
653 }
654
655 /**
656 * Returns the closest {@code long} to the argument. The result
657 * is rounded to an integer by adding 1/2, taking the floor of the
658 * result, and casting the result to type {@code long}. In other
659 * words, the result is equal to the value of the expression:
660 * <p>{@code (long)Math.floor(a + 0.5d)}
661 * <p>
662 * Special cases:
663 * <ul><li>If the argument is NaN, the result is 0.
664 * <li>If the argument is negative infinity or any value less than or
665 * equal to the value of {@code Long.MIN_VALUE}, the result is
666 * equal to the value of {@code Long.MIN_VALUE}.
667 * <li>If the argument is positive infinity or any value greater than or
668 * equal to the value of {@code Long.MAX_VALUE}, the result is
669 * equal to the value of {@code Long.MAX_VALUE}.</ul>
670 *
671 * @param a a floating-point value to be rounded to a
672 * {@code long}.
673 * @return the value of the argument rounded to the nearest
674 * {@code long} value.
675 * @see java.lang.Long#MAX_VALUE
676 * @see java.lang.Long#MIN_VALUE
677 */
678 public static long round(double a) {
679 return (long)floor(a + 0.5d);
680 }
681
682 private static Random randomNumberGenerator;
683
684 private static synchronized void initRNG() {
685 if (randomNumberGenerator == null)
686 randomNumberGenerator = new Random();
687 }
688
689 /**
690 * Returns a {@code double} value with a positive sign, greater
691 * than or equal to {@code 0.0} and less than {@code 1.0}.
692 * Returned values are chosen pseudorandomly with (approximately)
693 * uniform distribution from that range.
694 *
695 * <p>When this method is first called, it creates a single new
696 * pseudorandom-number generator, exactly as if by the expression
697 * <blockquote>{@code new java.util.Random}</blockquote> This
698 * new pseudorandom-number generator is used thereafter for all
699 * calls to this method and is used nowhere else.
700 *
701 * <p>This method is properly synchronized to allow correct use by
702 * more than one thread. However, if many threads need to generate
703 * pseudorandom numbers at a great rate, it may reduce contention
704 * for each thread to have its own pseudorandom-number generator.
705 *
706 * @return a pseudorandom {@code double} greater than or equal
707 * to {@code 0.0} and less than {@code 1.0}.
708 * @see java.util.Random#nextDouble()
709 */
710 public static double random() {
711 if (randomNumberGenerator == null) initRNG();
712 return randomNumberGenerator.nextDouble();
713 }
714
715 /**
716 * Returns the absolute value of an {@code int} value.
717 * If the argument is not negative, the argument is returned.
718 * If the argument is negative, the negation of the argument is returned.
719 *
720 * <p>Note that if the argument is equal to the value of
721 * {@link Integer#MIN_VALUE}, the most negative representable
722 * {@code int} value, the result is that same value, which is
723 * negative.
724 *
725 * @param a the argument whose absolute value is to be determined
726 * @return the absolute value of the argument.
727 */
728 public static int abs(int a) {
729 return (a < 0) ? -a : a;
730 }
731
732 /**
733 * Returns the absolute value of a {@code long} value.
734 * If the argument is not negative, the argument is returned.
735 * If the argument is negative, the negation of the argument is returned.
736 *
737 * <p>Note that if the argument is equal to the value of
738 * {@link Long#MIN_VALUE}, the most negative representable
739 * {@code long} value, the result is that same value, which
740 * is negative.
741 *
742 * @param a the argument whose absolute value is to be determined
743 * @return the absolute value of the argument.
744 */
745 public static long abs(long a) {
746 return (a < 0) ? -a : a;
747 }
748
749 /**
750 * Returns the absolute value of a {@code float} value.
751 * If the argument is not negative, the argument is returned.
752 * If the argument is negative, the negation of the argument is returned.
753 * Special cases:
754 * <ul><li>If the argument is positive zero or negative zero, the
755 * result is positive zero.
756 * <li>If the argument is infinite, the result is positive infinity.
757 * <li>If the argument is NaN, the result is NaN.</ul>
758 * In other words, the result is the same as the value of the expression:
759 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
760 *
761 * @param a the argument whose absolute value is to be determined
762 * @return the absolute value of the argument.
763 */
764 public static float abs(float a) {
765 return (a <= 0.0F) ? 0.0F - a : a;
766 }
767
768 /**
769 * Returns the absolute value of a {@code double} value.
770 * If the argument is not negative, the argument is returned.
771 * If the argument is negative, the negation of the argument is returned.
772 * Special cases:
773 * <ul><li>If the argument is positive zero or negative zero, the result
774 * is positive zero.
775 * <li>If the argument is infinite, the result is positive infinity.
776 * <li>If the argument is NaN, the result is NaN.</ul>
777 * In other words, the result is the same as the value of the expression:
778 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
779 *
780 * @param a the argument whose absolute value is to be determined
781 * @return the absolute value of the argument.
782 */
783 public static double abs(double a) {
784 return (a <= 0.0D) ? 0.0D - a : a;
785 }
786
787 /**
788 * Returns the greater of two {@code int} values. That is, the
789 * result is the argument closer to the value of
790 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
791 * the result is that same value.
792 *
793 * @param a an argument.
794 * @param b another argument.
795 * @return the larger of {@code a} and {@code b}.
796 */
797 public static int max(int a, int b) {
798 return (a >= b) ? a : b;
799 }
800
801 /**
802 * Returns the greater of two {@code long} values. That is, the
803 * result is the argument closer to the value of
804 * {@link Long#MAX_VALUE}. If the arguments have the same value,
805 * the result is that same value.
806 *
807 * @param a an argument.
808 * @param b another argument.
809 * @return the larger of {@code a} and {@code b}.
810 */
811 public static long max(long a, long b) {
812 return (a >= b) ? a : b;
813 }
814
815 private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
816 private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
817
818 /**
819 * Returns the greater of two {@code float} values. That is,
820 * the result is the argument closer to positive infinity. If the
821 * arguments have the same value, the result is that same
822 * value. If either value is NaN, then the result is NaN. Unlike
823 * the numerical comparison operators, this method considers
824 * negative zero to be strictly smaller than positive zero. If one
825 * argument is positive zero and the other negative zero, the
826 * result is positive zero.
827 *
828 * @param a an argument.
829 * @param b another argument.
830 * @return the larger of {@code a} and {@code b}.
831 */
832 public static float max(float a, float b) {
833 if (a != a) return a; // a is NaN
834 if ((a == 0.0f) && (b == 0.0f)
835 && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
836 return b;
837 }
838 return (a >= b) ? a : b;
839 }
840
841 /**
842 * Returns the greater of two {@code double} values. That
843 * is, the result is the argument closer to positive infinity. If
844 * the arguments have the same value, the result is that same
845 * value. If either value is NaN, then the result is NaN. Unlike
846 * the numerical comparison operators, this method considers
847 * negative zero to be strictly smaller than positive zero. If one
848 * argument is positive zero and the other negative zero, the
849 * result is positive zero.
850 *
851 * @param a an argument.
852 * @param b another argument.
853 * @return the larger of {@code a} and {@code b}.
854 */
855 public static double max(double a, double b) {
856 if (a != a) return a; // a is NaN
857 if ((a == 0.0d) && (b == 0.0d)
858 && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
859 return b;
860 }
861 return (a >= b) ? a : b;
862 }
863
864 /**
865 * Returns the smaller of two {@code int} values. That is,
866 * the result the argument closer to the value of
867 * {@link Integer#MIN_VALUE}. If the arguments have the same
868 * value, the result is that same value.
869 *
870 * @param a an argument.
871 * @param b another argument.
872 * @return the smaller of {@code a} and {@code b}.
873 */
874 public static int min(int a, int b) {
875 return (a <= b) ? a : b;
876 }
877
878 /**
879 * Returns the smaller of two {@code long} values. That is,
880 * the result is the argument closer to the value of
881 * {@link Long#MIN_VALUE}. If the arguments have the same
882 * value, the result is that same value.
883 *
884 * @param a an argument.
885 * @param b another argument.
886 * @return the smaller of {@code a} and {@code b}.
887 */
888 public static long min(long a, long b) {
889 return (a <= b) ? a : b;
890 }
891
892 /**
893 * Returns the smaller of two {@code float} values. That is,
894 * the result is the value closer to negative infinity. If the
895 * arguments have the same value, the result is that same
896 * value. If either value is NaN, then the result is NaN. Unlike
897 * the numerical comparison operators, this method considers
898 * negative zero to be strictly smaller than positive zero. If
899 * one argument is positive zero and the other is negative zero,
900 * the result is negative zero.
901 *
902 * @param a an argument.
903 * @param b another argument.
904 * @return the smaller of {@code a} and {@code b}.
905 */
906 public static float min(float a, float b) {
907 if (a != a) return a; // a is NaN
908 if ((a == 0.0f) && (b == 0.0f)
909 && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
910 return b;
911 }
912 return (a <= b) ? a : b;
913 }
914
915 /**
916 * Returns the smaller of two {@code double} values. That
917 * is, the result is the value closer to negative infinity. If the
918 * arguments have the same value, the result is that same
919 * value. If either value is NaN, then the result is NaN. Unlike
920 * the numerical comparison operators, this method considers
921 * negative zero to be strictly smaller than positive zero. If one
922 * argument is positive zero and the other is negative zero, the
923 * result is negative zero.
924 *
925 * @param a an argument.
926 * @param b another argument.
927 * @return the smaller of {@code a} and {@code b}.
928 */
929 public static double min(double a, double b) {
930 if (a != a) return a; // a is NaN
931 if ((a == 0.0d) && (b == 0.0d)
932 && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
933 return b;
934 }
935 return (a <= b) ? a : b;
936 }
937
938 /**
939 * Returns the size of an ulp of the argument. An ulp of a
940 * {@code double} value is the positive distance between this
941 * floating-point value and the {@code double} value next
942 * larger in magnitude. Note that for non-NaN <i>x</i>,
943 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
944 *
945 * <p>Special Cases:
946 * <ul>
947 * <li> If the argument is NaN, then the result is NaN.
948 * <li> If the argument is positive or negative infinity, then the
949 * result is positive infinity.
950 * <li> If the argument is positive or negative zero, then the result is
951 * {@code Double.MIN_VALUE}.
952 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
953 * the result is equal to 2<sup>971</sup>.
954 * </ul>
955 *
956 * @param d the floating-point value whose ulp is to be returned
957 * @return the size of an ulp of the argument
958 * @author Joseph D. Darcy
959 * @since 1.5
960 */
961 public static double ulp(double d) {
962 return sun.misc.FpUtils.ulp(d);
963 }
964
965 /**
966 * Returns the size of an ulp of the argument. An ulp of a
967 * {@code float} value is the positive distance between this
968 * floating-point value and the {@code float} value next
969 * larger in magnitude. Note that for non-NaN <i>x</i>,
970 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
971 *
972 * <p>Special Cases:
973 * <ul>
974 * <li> If the argument is NaN, then the result is NaN.
975 * <li> If the argument is positive or negative infinity, then the
976 * result is positive infinity.
977 * <li> If the argument is positive or negative zero, then the result is
978 * {@code Float.MIN_VALUE}.
979 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
980 * the result is equal to 2<sup>104</sup>.
981 * </ul>
982 *
983 * @param f the floating-point value whose ulp is to be returned
984 * @return the size of an ulp of the argument
985 * @author Joseph D. Darcy
986 * @since 1.5
987 */
988 public static float ulp(float f) {
989 return sun.misc.FpUtils.ulp(f);
990 }
991
992 /**
993 * Returns the signum function of the argument; zero if the argument
994 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
995 * argument is less than zero.
996 *
997 * <p>Special Cases:
998 * <ul>
999 * <li> If the argument is NaN, then the result is NaN.
1000 * <li> If the argument is positive zero or negative zero, then the
1001 * result is the same as the argument.
1002 * </ul>
1003 *
1004 * @param d the floating-point value whose signum is to be returned
1005 * @return the signum function of the argument
1006 * @author Joseph D. Darcy
1007 * @since 1.5
1008 */
1009 public static double signum(double d) {
1010 return sun.misc.FpUtils.signum(d);
1011 }
1012
1013 /**
1014 * Returns the signum function of the argument; zero if the argument
1015 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1016 * argument is less than zero.
1017 *
1018 * <p>Special Cases:
1019 * <ul>
1020 * <li> If the argument is NaN, then the result is NaN.
1021 * <li> If the argument is positive zero or negative zero, then the
1022 * result is the same as the argument.
1023 * </ul>
1024 *
1025 * @param f the floating-point value whose signum is to be returned
1026 * @return the signum function of the argument
1027 * @author Joseph D. Darcy
1028 * @since 1.5
1029 */
1030 public static float signum(float f) {
1031 return sun.misc.FpUtils.signum(f);
1032 }
1033
1034 /**
1035 * Returns the hyperbolic sine of a {@code double} value.
1036 * The hyperbolic sine of <i>x</i> is defined to be
1037 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1038 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1039 *
1040 * <p>Special cases:
1041 * <ul>
1042 *
1043 * <li>If the argument is NaN, then the result is NaN.
1044 *
1045 * <li>If the argument is infinite, then the result is an infinity
1046 * with the same sign as the argument.
1047 *
1048 * <li>If the argument is zero, then the result is a zero with the
1049 * same sign as the argument.
1050 *
1051 * </ul>
1052 *
1053 * <p>The computed result must be within 2.5 ulps of the exact result.
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 double sinh(double x) {
1060 return StrictMath.sinh(x);
1061 }
1062
1063 /**
1064 * Returns the hyperbolic cosine of a {@code double} value.
1065 * The hyperbolic cosine of <i>x</i> is defined to be
1066 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1067 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1068 *
1069 * <p>Special cases:
1070 * <ul>
1071 *
1072 * <li>If the argument is NaN, then the result is NaN.
1073 *
1074 * <li>If the argument is infinite, then the result is positive
1075 * infinity.
1076 *
1077 * <li>If the argument is zero, then the result is {@code 1.0}.
1078 *
1079 * </ul>
1080 *
1081 * <p>The computed result must be within 2.5 ulps of the exact result.
1082 *
1083 * @param x The number whose hyperbolic cosine is to be returned.
1084 * @return The hyperbolic cosine of {@code x}.
1085 * @since 1.5
1086 */
1087 public static double cosh(double x) {
1088 return StrictMath.cosh(x);
1089 }
1090
1091 /**
1092 * Returns the hyperbolic tangent of a {@code double} value.
1093 * The hyperbolic tangent of <i>x</i> is defined to be
1094 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1095 * in other words, {@linkplain Math#sinh
1096 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1097 * that the absolute value of the exact tanh is always less than
1098 * 1.
1099 *
1100 * <p>Special cases:
1101 * <ul>
1102 *
1103 * <li>If the argument is NaN, then the result is NaN.
1104 *
1105 * <li>If the argument is zero, then the result is a zero with the
1106 * same sign as the argument.
1107 *
1108 * <li>If the argument is positive infinity, then the result is
1109 * {@code +1.0}.
1110 *
1111 * <li>If the argument is negative infinity, then the result is
1112 * {@code -1.0}.
1113 *
1114 * </ul>
1115 *
1116 * <p>The computed result must be within 2.5 ulps of the exact result.
1117 * The result of {@code tanh} for any finite input must have
1118 * an absolute value less than or equal to 1. Note that once the
1119 * exact result of tanh is within 1/2 of an ulp of the limit value
1120 * of ±1, correctly signed ±{@code 1.0} should
1121 * be returned.
1122 *
1123 * @param x The number whose hyperbolic tangent is to be returned.
1124 * @return The hyperbolic tangent of {@code x}.
1125 * @since 1.5
1126 */
1127 public static double tanh(double x) {
1128 return StrictMath.tanh(x);
1129 }
1130
1131 /**
1132 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1133 * without intermediate overflow or underflow.
1134 *
1135 * <p>Special cases:
1136 * <ul>
1137 *
1138 * <li> If either argument is infinite, then the result
1139 * is positive infinity.
1140 *
1141 * <li> If either argument is NaN and neither argument is infinite,
1142 * then the result is NaN.
1143 *
1144 * </ul>
1145 *
1146 * <p>The computed result must be within 1 ulp of the exact
1147 * result. If one parameter is held constant, the results must be
1148 * semi-monotonic in the other parameter.
1149 *
1150 * @param x a value
1151 * @param y a value
1152 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1153 * without intermediate overflow or underflow
1154 * @since 1.5
1155 */
1156 public static double hypot(double x, double y) {
1157 return StrictMath.hypot(x, y);
1158 }
1159
1160 /**
1161 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1162 * <i>x</i> near 0, the exact sum of
1163 * {@code expm1(x)} + 1 is much closer to the true
1164 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1165 *
1166 * <p>Special cases:
1167 * <ul>
1168 * <li>If the argument is NaN, the result is NaN.
1169 *
1170 * <li>If the argument is positive infinity, then the result is
1171 * positive infinity.
1172 *
1173 * <li>If the argument is negative infinity, then the result is
1174 * -1.0.
1175 *
1176 * <li>If the argument is zero, then the result is a zero with the
1177 * same sign as the argument.
1178 *
1179 * </ul>
1180 *
1181 * <p>The computed result must be within 1 ulp of the exact result.
1182 * Results must be semi-monotonic. The result of
1183 * {@code expm1} for any finite input must be greater than or
1184 * equal to {@code -1.0}. Note that once the exact result of
1185 * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
1186 * ulp of the limit value -1, {@code -1.0} should be
1187 * returned.
1188 *
1189 * @param x the exponent to raise <i>e</i> to in the computation of
1190 * <i>e</i><sup>{@code x}</sup> -1.
1191 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1192 * @since 1.5
1193 */
1194 public static double expm1(double x) {
1195 return StrictMath.expm1(x);
1196 }
1197
1198 /**
1199 * Returns the natural logarithm of the sum of the argument and 1.
1200 * Note that for small values {@code x}, the result of
1201 * {@code log1p(x)} is much closer to the true result of ln(1
1202 * + {@code x}) than the floating-point evaluation of
1203 * {@code log(1.0+x)}.
1204 *
1205 * <p>Special cases:
1206 *
1207 * <ul>
1208 *
1209 * <li>If the argument is NaN or less than -1, then the result is
1210 * NaN.
1211 *
1212 * <li>If the argument is positive infinity, then the result is
1213 * positive infinity.
1214 *
1215 * <li>If the argument is negative one, then the result is
1216 * negative infinity.
1217 *
1218 * <li>If the argument is zero, then the result is a zero with the
1219 * same sign as the argument.
1220 *
1221 * </ul>
1222 *
1223 * <p>The computed result must be within 1 ulp of the exact result.
1224 * Results must be semi-monotonic.
1225 *
1226 * @param x a value
1227 * @return the value ln({@code x} + 1), the natural
1228 * log of {@code x} + 1
1229 * @since 1.5
1230 */
1231 public static double log1p(double x) {
1232 return StrictMath.log1p(x);
1233 }
1234
1235 /**
1236 * Returns the first floating-point argument with the sign of the
1237 * second floating-point argument. Note that unlike the {@link
1238 * StrictMath#copySign(double, double) StrictMath.copySign}
1239 * method, this method does not require NaN {@code sign}
1240 * arguments to be treated as positive values; implementations are
1241 * permitted to treat some NaN arguments as positive and other NaN
1242 * arguments as negative to allow greater performance.
1243 *
1244 * @param magnitude the parameter providing the magnitude of the result
1245 * @param sign the parameter providing the sign of the result
1246 * @return a value with the magnitude of {@code magnitude}
1247 * and the sign of {@code sign}.
1248 * @since 1.6
1249 */
1250 public static double copySign(double magnitude, double sign) {
1251 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1252 }
1253
1254 /**
1255 * Returns the first floating-point argument with the sign of the
1256 * second floating-point argument. Note that unlike the {@link
1257 * StrictMath#copySign(float, float) StrictMath.copySign}
1258 * method, this method does not require NaN {@code sign}
1259 * arguments to be treated as positive values; implementations are
1260 * permitted to treat some NaN arguments as positive and other NaN
1261 * arguments as negative to allow greater performance.
1262 *
1263 * @param magnitude the parameter providing the magnitude of the result
1264 * @param sign the parameter providing the sign of the result
1265 * @return a value with the magnitude of {@code magnitude}
1266 * and the sign of {@code sign}.
1267 * @since 1.6
1268 */
1269 public static float copySign(float magnitude, float sign) {
1270 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1271 }
1272
1273 /**
1274 * Returns the unbiased exponent used in the representation of a
1275 * {@code float}. Special cases:
1276 *
1277 * <ul>
1278 * <li>If the argument is NaN or infinite, then the result is
1279 * {@link Float#MAX_EXPONENT} + 1.
1280 * <li>If the argument is zero or subnormal, then the result is
1281 * {@link Float#MIN_EXPONENT} -1.
1282 * </ul>
1283 * @param f a {@code float} value
1284 * @return the unbiased exponent of the argument
1285 * @since 1.6
1286 */
1287 public static int getExponent(float f) {
1288 return sun.misc.FpUtils.getExponent(f);
1289 }
1290
1291 /**
1292 * Returns the unbiased exponent used in the representation of a
1293 * {@code double}. Special cases:
1294 *
1295 * <ul>
1296 * <li>If the argument is NaN or infinite, then the result is
1297 * {@link Double#MAX_EXPONENT} + 1.
1298 * <li>If the argument is zero or subnormal, then the result is
1299 * {@link Double#MIN_EXPONENT} -1.
1300 * </ul>
1301 * @param d a {@code double} value
1302 * @return the unbiased exponent of the argument
1303 * @since 1.6
1304 */
1305 public static int getExponent(double d) {
1306 return sun.misc.FpUtils.getExponent(d);
1307 }
1308
1309 /**
1310 * Returns the floating-point number adjacent to the first
1311 * argument in the direction of the second argument. If both
1312 * arguments compare as equal the second argument is returned.
1313 *
1314 * <p>
1315 * Special cases:
1316 * <ul>
1317 * <li> If either argument is a NaN, then NaN is returned.
1318 *
1319 * <li> If both arguments are signed zeros, {@code direction}
1320 * is returned unchanged (as implied by the requirement of
1321 * returning the second argument if the arguments compare as
1322 * equal).
1323 *
1324 * <li> If {@code start} is
1325 * ±{@link Double#MIN_VALUE} and {@code direction}
1326 * has a value such that the result should have a smaller
1327 * magnitude, then a zero with the same sign as {@code start}
1328 * is returned.
1329 *
1330 * <li> If {@code start} is infinite and
1331 * {@code direction} has a value such that the result should
1332 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1333 * same sign as {@code start} is returned.
1334 *
1335 * <li> If {@code start} is equal to ±
1336 * {@link Double#MAX_VALUE} and {@code direction} has a
1337 * value such that the result should have a larger magnitude, an
1338 * infinity with same sign as {@code start} is returned.
1339 * </ul>
1340 *
1341 * @param start starting floating-point value
1342 * @param direction value indicating which of
1343 * {@code start}'s neighbors or {@code start} should
1344 * be returned
1345 * @return The floating-point number adjacent to {@code start} in the
1346 * direction of {@code direction}.
1347 * @since 1.6
1348 */
1349 public static double nextAfter(double start, double direction) {
1350 return sun.misc.FpUtils.nextAfter(start, direction);
1351 }
1352
1353 /**
1354 * Returns the floating-point number adjacent to the first
1355 * argument in the direction of the second argument. If both
1356 * arguments compare as equal a value equivalent to the second argument
1357 * is returned.
1358 *
1359 * <p>
1360 * Special cases:
1361 * <ul>
1362 * <li> If either argument is a NaN, then NaN is returned.
1363 *
1364 * <li> If both arguments are signed zeros, a value equivalent
1365 * to {@code direction} is returned.
1366 *
1367 * <li> If {@code start} is
1368 * ±{@link Float#MIN_VALUE} and {@code direction}
1369 * has a value such that the result should have a smaller
1370 * magnitude, then a zero with the same sign as {@code start}
1371 * is returned.
1372 *
1373 * <li> If {@code start} is infinite and
1374 * {@code direction} has a value such that the result should
1375 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1376 * same sign as {@code start} is returned.
1377 *
1378 * <li> If {@code start} is equal to ±
1379 * {@link Float#MAX_VALUE} and {@code direction} has a
1380 * value such that the result should have a larger magnitude, an
1381 * infinity with same sign as {@code start} is returned.
1382 * </ul>
1383 *
1384 * @param start starting floating-point value
1385 * @param direction value indicating which of
1386 * {@code start}'s neighbors or {@code start} should
1387 * be returned
1388 * @return The floating-point number adjacent to {@code start} in the
1389 * direction of {@code direction}.
1390 * @since 1.6
1391 */
1392 public static float nextAfter(float start, double direction) {
1393 return sun.misc.FpUtils.nextAfter(start, direction);
1394 }
1395
1396 /**
1397 * Returns the floating-point value adjacent to {@code d} in
1398 * the direction of positive infinity. This method is
1399 * semantically equivalent to {@code nextAfter(d,
1400 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1401 * implementation may run faster than its equivalent
1402 * {@code nextAfter} call.
1403 *
1404 * <p>Special Cases:
1405 * <ul>
1406 * <li> If the argument is NaN, the result is NaN.
1407 *
1408 * <li> If the argument is positive infinity, the result is
1409 * positive infinity.
1410 *
1411 * <li> If the argument is zero, the result is
1412 * {@link Double#MIN_VALUE}
1413 *
1414 * </ul>
1415 *
1416 * @param d starting floating-point value
1417 * @return The adjacent floating-point value closer to positive
1418 * infinity.
1419 * @since 1.6
1420 */
1421 public static double nextUp(double d) {
1422 return sun.misc.FpUtils.nextUp(d);
1423 }
1424
1425 /**
1426 * Returns the floating-point value adjacent to {@code f} in
1427 * the direction of positive infinity. This method is
1428 * semantically equivalent to {@code nextAfter(f,
1429 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1430 * implementation may run faster than its equivalent
1431 * {@code nextAfter} call.
1432 *
1433 * <p>Special Cases:
1434 * <ul>
1435 * <li> If the argument is NaN, the result is NaN.
1436 *
1437 * <li> If the argument is positive infinity, the result is
1438 * positive infinity.
1439 *
1440 * <li> If the argument is zero, the result is
1441 * {@link Float#MIN_VALUE}
1442 *
1443 * </ul>
1444 *
1445 * @param f starting floating-point value
1446 * @return The adjacent floating-point value closer to positive
1447 * infinity.
1448 * @since 1.6
1449 */
1450 public static float nextUp(float f) {
1451 return sun.misc.FpUtils.nextUp(f);
1452 }
1453
1454
1455 /**
1456 * Return {@code d} ×
1457 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1458 * by a single correctly rounded floating-point multiply to a
1459 * member of the double value set. See the Java
1460 * Language Specification for a discussion of floating-point
1461 * value sets. If the exponent of the result is between {@link
1462 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1463 * answer is calculated exactly. If the exponent of the result
1464 * would be larger than {@code Double.MAX_EXPONENT}, an
1465 * infinity is returned. Note that if the result is subnormal,
1466 * precision may be lost; that is, when {@code scalb(x, n)}
1467 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1468 * <i>x</i>. When the result is non-NaN, the result has the same
1469 * sign as {@code d}.
1470 *
1471 * <p>Special cases:
1472 * <ul>
1473 * <li> If the first argument is NaN, NaN is returned.
1474 * <li> If the first argument is infinite, then an infinity of the
1475 * same sign is returned.
1476 * <li> If the first argument is zero, then a zero of the same
1477 * sign is returned.
1478 * </ul>
1479 *
1480 * @param d number to be scaled by a power of two.
1481 * @param scaleFactor power of 2 used to scale {@code d}
1482 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1483 * @since 1.6
1484 */
1485 public static double scalb(double d, int scaleFactor) {
1486 return sun.misc.FpUtils.scalb(d, scaleFactor);
1487 }
1488
1489 /**
1490 * Return {@code f} ×
1491 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1492 * by a single correctly rounded floating-point multiply to a
1493 * member of the float value set. See the Java
1494 * Language Specification for a discussion of floating-point
1495 * value sets. If the exponent of the result is between {@link
1496 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1497 * answer is calculated exactly. If the exponent of the result
1498 * would be larger than {@code Float.MAX_EXPONENT}, an
1499 * infinity is returned. Note that if the result is subnormal,
1500 * precision may be lost; that is, when {@code scalb(x, n)}
1501 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1502 * <i>x</i>. When the result is non-NaN, the result has the same
1503 * sign as {@code f}.
1504 *
1505 * <p>Special cases:
1506 * <ul>
1507 * <li> If the first argument is NaN, NaN is returned.
1508 * <li> If the first argument is infinite, then an infinity of the
1509 * same sign is returned.
1510 * <li> If the first argument is zero, then a zero of the same
1511 * sign is returned.
1512 * </ul>
1513 *
1514 * @param f number to be scaled by a power of two.
1515 * @param scaleFactor power of 2 used to scale {@code f}
1516 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1517 * @since 1.6
1518 */
1519 public static float scalb(float f, int scaleFactor) {
1520 return sun.misc.FpUtils.scalb(f, scaleFactor);
1521 }
1522 }
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