1 /*
2 * Copyright (c) 1994, 2010, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
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7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
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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
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 Random initRNG() {
685 Random rnd = randomNumberGenerator;
686 return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
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 *
698 * <blockquote>{@code new java.util.Random()}</blockquote>
699 *
700 * This new pseudorandom-number generator is used thereafter for
701 * all calls to this method and is used nowhere else.
702 *
703 * <p>This method is properly synchronized to allow correct use by
704 * more than one thread. However, if many threads need to generate
705 * pseudorandom numbers at a great rate, it may reduce contention
706 * for each thread to have its own pseudorandom-number generator.
707 *
708 * @return a pseudorandom {@code double} greater than or equal
709 * to {@code 0.0} and less than {@code 1.0}.
710 * @see Random#nextDouble()
711 */
712 public static double random() {
713 Random rnd = randomNumberGenerator;
714 if (rnd == null) rnd = initRNG();
715 return rnd.nextDouble();
716 }
717
718 /**
719 * Returns the absolute value of an {@code int} value.
720 * If the argument is not negative, the argument is returned.
721 * If the argument is negative, the negation of the argument is returned.
722 *
723 * <p>Note that if the argument is equal to the value of
724 * {@link Integer#MIN_VALUE}, the most negative representable
725 * {@code int} value, the result is that same value, which is
726 * negative.
727 *
728 * @param a the argument whose absolute value is to be determined
729 * @return the absolute value of the argument.
730 */
731 public static int abs(int a) {
732 return (a < 0) ? -a : a;
733 }
734
735 /**
736 * Returns the absolute value of a {@code long} value.
737 * If the argument is not negative, the argument is returned.
738 * If the argument is negative, the negation of the argument is returned.
739 *
740 * <p>Note that if the argument is equal to the value of
741 * {@link Long#MIN_VALUE}, the most negative representable
742 * {@code long} value, the result is that same value, which
743 * is negative.
744 *
745 * @param a the argument whose absolute value is to be determined
746 * @return the absolute value of the argument.
747 */
748 public static long abs(long a) {
749 return (a < 0) ? -a : a;
750 }
751
752 /**
753 * Returns the absolute value of a {@code float} value.
754 * If the argument is not negative, the argument is returned.
755 * If the argument is negative, the negation of the argument is returned.
756 * Special cases:
757 * <ul><li>If the argument is positive zero or negative zero, the
758 * result is positive zero.
759 * <li>If the argument is infinite, the result is positive infinity.
760 * <li>If the argument is NaN, the result is NaN.</ul>
761 * In other words, the result is the same as the value of the expression:
762 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
763 *
764 * @param a the argument whose absolute value is to be determined
765 * @return the absolute value of the argument.
766 */
767 public static float abs(float a) {
768 return (a <= 0.0F) ? 0.0F - a : a;
769 }
770
771 /**
772 * Returns the absolute value of a {@code double} value.
773 * If the argument is not negative, the argument is returned.
774 * If the argument is negative, the negation of the argument is returned.
775 * Special cases:
776 * <ul><li>If the argument is positive zero or negative zero, the result
777 * is positive zero.
778 * <li>If the argument is infinite, the result is positive infinity.
779 * <li>If the argument is NaN, the result is NaN.</ul>
780 * In other words, the result is the same as the value of the expression:
781 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
782 *
783 * @param a the argument whose absolute value is to be determined
784 * @return the absolute value of the argument.
785 */
786 public static double abs(double a) {
787 return (a <= 0.0D) ? 0.0D - a : a;
788 }
789
790 /**
791 * Returns the greater of two {@code int} values. That is, the
792 * result is the argument closer to the value of
793 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
794 * the result is that same value.
795 *
796 * @param a an argument.
797 * @param b another argument.
798 * @return the larger of {@code a} and {@code b}.
799 */
800 public static int max(int a, int b) {
801 return (a >= b) ? a : b;
802 }
803
804 /**
805 * Returns the greater of two {@code long} values. That is, the
806 * result is the argument closer to the value of
807 * {@link Long#MAX_VALUE}. If the arguments have the same value,
808 * the result is that same value.
809 *
810 * @param a an argument.
811 * @param b another argument.
812 * @return the larger of {@code a} and {@code b}.
813 */
814 public static long max(long a, long b) {
815 return (a >= b) ? a : b;
816 }
817
818 private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
819 private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
820
821 /**
822 * Returns the greater of two {@code float} values. That is,
823 * the result is the argument closer to positive infinity. If the
824 * arguments have the same value, the result is that same
825 * value. If either value is NaN, then the result is NaN. Unlike
826 * the numerical comparison operators, this method considers
827 * negative zero to be strictly smaller than positive zero. If one
828 * argument is positive zero and the other negative zero, the
829 * result is positive zero.
830 *
831 * @param a an argument.
832 * @param b another argument.
833 * @return the larger of {@code a} and {@code b}.
834 */
835 public static float max(float a, float b) {
836 if (a != a) return a; // a is NaN
837 if ((a == 0.0f) && (b == 0.0f)
838 && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
839 return b;
840 }
841 return (a >= b) ? a : b;
842 }
843
844 /**
845 * Returns the greater of two {@code double} values. That
846 * is, the result is the argument closer to positive infinity. If
847 * the arguments have the same value, the result is that same
848 * value. If either value is NaN, then the result is NaN. Unlike
849 * the numerical comparison operators, this method considers
850 * negative zero to be strictly smaller than positive zero. If one
851 * argument is positive zero and the other negative zero, the
852 * result is positive zero.
853 *
854 * @param a an argument.
855 * @param b another argument.
856 * @return the larger of {@code a} and {@code b}.
857 */
858 public static double max(double a, double b) {
859 if (a != a) return a; // a is NaN
860 if ((a == 0.0d) && (b == 0.0d)
861 && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
862 return b;
863 }
864 return (a >= b) ? a : b;
865 }
866
867 /**
868 * Returns the smaller of two {@code int} values. That is,
869 * the result the argument closer to the value of
870 * {@link Integer#MIN_VALUE}. If the arguments have the same
871 * value, the result is that same value.
872 *
873 * @param a an argument.
874 * @param b another argument.
875 * @return the smaller of {@code a} and {@code b}.
876 */
877 public static int min(int a, int b) {
878 return (a <= b) ? a : b;
879 }
880
881 /**
882 * Returns the smaller of two {@code long} values. That is,
883 * the result is the argument closer to the value of
884 * {@link Long#MIN_VALUE}. If the arguments have the same
885 * value, the result is that same value.
886 *
887 * @param a an argument.
888 * @param b another argument.
889 * @return the smaller of {@code a} and {@code b}.
890 */
891 public static long min(long a, long b) {
892 return (a <= b) ? a : b;
893 }
894
895 /**
896 * Returns the smaller of two {@code float} values. That is,
897 * the result is the value closer to negative infinity. If the
898 * arguments have the same value, the result is that same
899 * value. If either value is NaN, then the result is NaN. Unlike
900 * the numerical comparison operators, this method considers
901 * negative zero to be strictly smaller than positive zero. If
902 * one argument is positive zero and the other is negative zero,
903 * the result is negative zero.
904 *
905 * @param a an argument.
906 * @param b another argument.
907 * @return the smaller of {@code a} and {@code b}.
908 */
909 public static float min(float a, float b) {
910 if (a != a) return a; // a is NaN
911 if ((a == 0.0f) && (b == 0.0f)
912 && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
913 return b;
914 }
915 return (a <= b) ? a : b;
916 }
917
918 /**
919 * Returns the smaller of two {@code double} values. That
920 * is, the result is the value closer to negative infinity. If the
921 * arguments have the same value, the result is that same
922 * value. If either value is NaN, then the result is NaN. Unlike
923 * the numerical comparison operators, this method considers
924 * negative zero to be strictly smaller than positive zero. If one
925 * argument is positive zero and the other is negative zero, the
926 * result is negative zero.
927 *
928 * @param a an argument.
929 * @param b another argument.
930 * @return the smaller of {@code a} and {@code b}.
931 */
932 public static double min(double a, double b) {
933 if (a != a) return a; // a is NaN
934 if ((a == 0.0d) && (b == 0.0d)
935 && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
936 return b;
937 }
938 return (a <= b) ? a : b;
939 }
940
941 /**
942 * Returns the size of an ulp of the argument. An ulp of a
943 * {@code double} value is the positive distance between this
944 * floating-point value and the {@code double} value next
945 * larger in magnitude. Note that for non-NaN <i>x</i>,
946 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
947 *
948 * <p>Special Cases:
949 * <ul>
950 * <li> If the argument is NaN, then the result is NaN.
951 * <li> If the argument is positive or negative infinity, then the
952 * result is positive infinity.
953 * <li> If the argument is positive or negative zero, then the result is
954 * {@code Double.MIN_VALUE}.
955 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
956 * the result is equal to 2<sup>971</sup>.
957 * </ul>
958 *
959 * @param d the floating-point value whose ulp is to be returned
960 * @return the size of an ulp of the argument
961 * @author Joseph D. Darcy
962 * @since 1.5
963 */
964 public static double ulp(double d) {
965 return sun.misc.FpUtils.ulp(d);
966 }
967
968 /**
969 * Returns the size of an ulp of the argument. An ulp of a
970 * {@code float} value is the positive distance between this
971 * floating-point value and the {@code float} value next
972 * larger in magnitude. Note that for non-NaN <i>x</i>,
973 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
974 *
975 * <p>Special Cases:
976 * <ul>
977 * <li> If the argument is NaN, then the result is NaN.
978 * <li> If the argument is positive or negative infinity, then the
979 * result is positive infinity.
980 * <li> If the argument is positive or negative zero, then the result is
981 * {@code Float.MIN_VALUE}.
982 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
983 * the result is equal to 2<sup>104</sup>.
984 * </ul>
985 *
986 * @param f the floating-point value whose ulp is to be returned
987 * @return the size of an ulp of the argument
988 * @author Joseph D. Darcy
989 * @since 1.5
990 */
991 public static float ulp(float f) {
992 return sun.misc.FpUtils.ulp(f);
993 }
994
995 /**
996 * Returns the signum function of the argument; zero if the argument
997 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
998 * argument is less than zero.
999 *
1000 * <p>Special Cases:
1001 * <ul>
1002 * <li> If the argument is NaN, then the result is NaN.
1003 * <li> If the argument is positive zero or negative zero, then the
1004 * result is the same as the argument.
1005 * </ul>
1006 *
1007 * @param d the floating-point value whose signum is to be returned
1008 * @return the signum function of the argument
1009 * @author Joseph D. Darcy
1010 * @since 1.5
1011 */
1012 public static double signum(double d) {
1013 return sun.misc.FpUtils.signum(d);
1014 }
1015
1016 /**
1017 * Returns the signum function of the argument; zero if the argument
1018 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1019 * argument is less than zero.
1020 *
1021 * <p>Special Cases:
1022 * <ul>
1023 * <li> If the argument is NaN, then the result is NaN.
1024 * <li> If the argument is positive zero or negative zero, then the
1025 * result is the same as the argument.
1026 * </ul>
1027 *
1028 * @param f the floating-point value whose signum is to be returned
1029 * @return the signum function of the argument
1030 * @author Joseph D. Darcy
1031 * @since 1.5
1032 */
1033 public static float signum(float f) {
1034 return sun.misc.FpUtils.signum(f);
1035 }
1036
1037 /**
1038 * Returns the hyperbolic sine of a {@code double} value.
1039 * The hyperbolic sine of <i>x</i> is defined to be
1040 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1041 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1042 *
1043 * <p>Special cases:
1044 * <ul>
1045 *
1046 * <li>If the argument is NaN, then the result is NaN.
1047 *
1048 * <li>If the argument is infinite, then the result is an infinity
1049 * with the same sign as the argument.
1050 *
1051 * <li>If the argument is zero, then the result is a zero with the
1052 * same sign as the argument.
1053 *
1054 * </ul>
1055 *
1056 * <p>The computed result must be within 2.5 ulps of the exact result.
1057 *
1058 * @param x The number whose hyperbolic sine is to be returned.
1059 * @return The hyperbolic sine of {@code x}.
1060 * @since 1.5
1061 */
1062 public static double sinh(double x) {
1063 return StrictMath.sinh(x);
1064 }
1065
1066 /**
1067 * Returns the hyperbolic cosine of a {@code double} value.
1068 * The hyperbolic cosine of <i>x</i> is defined to be
1069 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1070 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1071 *
1072 * <p>Special cases:
1073 * <ul>
1074 *
1075 * <li>If the argument is NaN, then the result is NaN.
1076 *
1077 * <li>If the argument is infinite, then the result is positive
1078 * infinity.
1079 *
1080 * <li>If the argument is zero, then the result is {@code 1.0}.
1081 *
1082 * </ul>
1083 *
1084 * <p>The computed result must be within 2.5 ulps of the exact result.
1085 *
1086 * @param x The number whose hyperbolic cosine is to be returned.
1087 * @return The hyperbolic cosine of {@code x}.
1088 * @since 1.5
1089 */
1090 public static double cosh(double x) {
1091 return StrictMath.cosh(x);
1092 }
1093
1094 /**
1095 * Returns the hyperbolic tangent of a {@code double} value.
1096 * The hyperbolic tangent of <i>x</i> is defined to be
1097 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1098 * in other words, {@linkplain Math#sinh
1099 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1100 * that the absolute value of the exact tanh is always less than
1101 * 1.
1102 *
1103 * <p>Special cases:
1104 * <ul>
1105 *
1106 * <li>If the argument is NaN, then the result is NaN.
1107 *
1108 * <li>If the argument is zero, then the result is a zero with the
1109 * same sign as the argument.
1110 *
1111 * <li>If the argument is positive infinity, then the result is
1112 * {@code +1.0}.
1113 *
1114 * <li>If the argument is negative infinity, then the result is
1115 * {@code -1.0}.
1116 *
1117 * </ul>
1118 *
1119 * <p>The computed result must be within 2.5 ulps of the exact result.
1120 * The result of {@code tanh} for any finite input must have
1121 * an absolute value less than or equal to 1. Note that once the
1122 * exact result of tanh is within 1/2 of an ulp of the limit value
1123 * of ±1, correctly signed ±{@code 1.0} should
1124 * be returned.
1125 *
1126 * @param x The number whose hyperbolic tangent is to be returned.
1127 * @return The hyperbolic tangent of {@code x}.
1128 * @since 1.5
1129 */
1130 public static double tanh(double x) {
1131 return StrictMath.tanh(x);
1132 }
1133
1134 /**
1135 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1136 * without intermediate overflow or underflow.
1137 *
1138 * <p>Special cases:
1139 * <ul>
1140 *
1141 * <li> If either argument is infinite, then the result
1142 * is positive infinity.
1143 *
1144 * <li> If either argument is NaN and neither argument is infinite,
1145 * then the result is NaN.
1146 *
1147 * </ul>
1148 *
1149 * <p>The computed result must be within 1 ulp of the exact
1150 * result. If one parameter is held constant, the results must be
1151 * semi-monotonic in the other parameter.
1152 *
1153 * @param x a value
1154 * @param y a value
1155 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1156 * without intermediate overflow or underflow
1157 * @since 1.5
1158 */
1159 public static double hypot(double x, double y) {
1160 return StrictMath.hypot(x, y);
1161 }
1162
1163 /**
1164 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1165 * <i>x</i> near 0, the exact sum of
1166 * {@code expm1(x)} + 1 is much closer to the true
1167 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1168 *
1169 * <p>Special cases:
1170 * <ul>
1171 * <li>If the argument is NaN, the result is NaN.
1172 *
1173 * <li>If the argument is positive infinity, then the result is
1174 * positive infinity.
1175 *
1176 * <li>If the argument is negative infinity, then the result is
1177 * -1.0.
1178 *
1179 * <li>If the argument is zero, then the result is a zero with the
1180 * same sign as the argument.
1181 *
1182 * </ul>
1183 *
1184 * <p>The computed result must be within 1 ulp of the exact result.
1185 * Results must be semi-monotonic. The result of
1186 * {@code expm1} for any finite input must be greater than or
1187 * equal to {@code -1.0}. Note that once the exact result of
1188 * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
1189 * ulp of the limit value -1, {@code -1.0} should be
1190 * returned.
1191 *
1192 * @param x the exponent to raise <i>e</i> to in the computation of
1193 * <i>e</i><sup>{@code x}</sup> -1.
1194 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1195 * @since 1.5
1196 */
1197 public static double expm1(double x) {
1198 return StrictMath.expm1(x);
1199 }
1200
1201 /**
1202 * Returns the natural logarithm of the sum of the argument and 1.
1203 * Note that for small values {@code x}, the result of
1204 * {@code log1p(x)} is much closer to the true result of ln(1
1205 * + {@code x}) than the floating-point evaluation of
1206 * {@code log(1.0+x)}.
1207 *
1208 * <p>Special cases:
1209 *
1210 * <ul>
1211 *
1212 * <li>If the argument is NaN or less than -1, then the result is
1213 * NaN.
1214 *
1215 * <li>If the argument is positive infinity, then the result is
1216 * positive infinity.
1217 *
1218 * <li>If the argument is negative one, then the result is
1219 * negative infinity.
1220 *
1221 * <li>If the argument is zero, then the result is a zero with the
1222 * same sign as the argument.
1223 *
1224 * </ul>
1225 *
1226 * <p>The computed result must be within 1 ulp of the exact result.
1227 * Results must be semi-monotonic.
1228 *
1229 * @param x a value
1230 * @return the value ln({@code x} + 1), the natural
1231 * log of {@code x} + 1
1232 * @since 1.5
1233 */
1234 public static double log1p(double x) {
1235 return StrictMath.log1p(x);
1236 }
1237
1238 /**
1239 * Returns the first floating-point argument with the sign of the
1240 * second floating-point argument. Note that unlike the {@link
1241 * StrictMath#copySign(double, double) StrictMath.copySign}
1242 * method, this method does not require NaN {@code sign}
1243 * arguments to be treated as positive values; implementations are
1244 * permitted to treat some NaN arguments as positive and other NaN
1245 * arguments as negative to allow greater performance.
1246 *
1247 * @param magnitude the parameter providing the magnitude of the result
1248 * @param sign the parameter providing the sign of the result
1249 * @return a value with the magnitude of {@code magnitude}
1250 * and the sign of {@code sign}.
1251 * @since 1.6
1252 */
1253 public static double copySign(double magnitude, double sign) {
1254 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1255 }
1256
1257 /**
1258 * Returns the first floating-point argument with the sign of the
1259 * second floating-point argument. Note that unlike the {@link
1260 * StrictMath#copySign(float, float) StrictMath.copySign}
1261 * method, this method does not require NaN {@code sign}
1262 * arguments to be treated as positive values; implementations are
1263 * permitted to treat some NaN arguments as positive and other NaN
1264 * arguments as negative to allow greater performance.
1265 *
1266 * @param magnitude the parameter providing the magnitude of the result
1267 * @param sign the parameter providing the sign of the result
1268 * @return a value with the magnitude of {@code magnitude}
1269 * and the sign of {@code sign}.
1270 * @since 1.6
1271 */
1272 public static float copySign(float magnitude, float sign) {
1273 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1274 }
1275
1276 /**
1277 * Returns the unbiased exponent used in the representation of a
1278 * {@code float}. Special cases:
1279 *
1280 * <ul>
1281 * <li>If the argument is NaN or infinite, then the result is
1282 * {@link Float#MAX_EXPONENT} + 1.
1283 * <li>If the argument is zero or subnormal, then the result is
1284 * {@link Float#MIN_EXPONENT} -1.
1285 * </ul>
1286 * @param f a {@code float} value
1287 * @return the unbiased exponent of the argument
1288 * @since 1.6
1289 */
1290 public static int getExponent(float f) {
1291 return sun.misc.FpUtils.getExponent(f);
1292 }
1293
1294 /**
1295 * Returns the unbiased exponent used in the representation of a
1296 * {@code double}. Special cases:
1297 *
1298 * <ul>
1299 * <li>If the argument is NaN or infinite, then the result is
1300 * {@link Double#MAX_EXPONENT} + 1.
1301 * <li>If the argument is zero or subnormal, then the result is
1302 * {@link Double#MIN_EXPONENT} -1.
1303 * </ul>
1304 * @param d a {@code double} value
1305 * @return the unbiased exponent of the argument
1306 * @since 1.6
1307 */
1308 public static int getExponent(double d) {
1309 return sun.misc.FpUtils.getExponent(d);
1310 }
1311
1312 /**
1313 * Returns the floating-point number adjacent to the first
1314 * argument in the direction of the second argument. If both
1315 * arguments compare as equal the second argument is returned.
1316 *
1317 * <p>
1318 * Special cases:
1319 * <ul>
1320 * <li> If either argument is a NaN, then NaN is returned.
1321 *
1322 * <li> If both arguments are signed zeros, {@code direction}
1323 * is returned unchanged (as implied by the requirement of
1324 * returning the second argument if the arguments compare as
1325 * equal).
1326 *
1327 * <li> If {@code start} is
1328 * ±{@link Double#MIN_VALUE} and {@code direction}
1329 * has a value such that the result should have a smaller
1330 * magnitude, then a zero with the same sign as {@code start}
1331 * is returned.
1332 *
1333 * <li> If {@code start} is infinite and
1334 * {@code direction} has a value such that the result should
1335 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1336 * same sign as {@code start} is returned.
1337 *
1338 * <li> If {@code start} is equal to ±
1339 * {@link Double#MAX_VALUE} and {@code direction} has a
1340 * value such that the result should have a larger magnitude, an
1341 * infinity with same sign as {@code start} is returned.
1342 * </ul>
1343 *
1344 * @param start starting floating-point value
1345 * @param direction value indicating which of
1346 * {@code start}'s neighbors or {@code start} should
1347 * be returned
1348 * @return The floating-point number adjacent to {@code start} in the
1349 * direction of {@code direction}.
1350 * @since 1.6
1351 */
1352 public static double nextAfter(double start, double direction) {
1353 return sun.misc.FpUtils.nextAfter(start, direction);
1354 }
1355
1356 /**
1357 * Returns the floating-point number adjacent to the first
1358 * argument in the direction of the second argument. If both
1359 * arguments compare as equal a value equivalent to the second argument
1360 * is returned.
1361 *
1362 * <p>
1363 * Special cases:
1364 * <ul>
1365 * <li> If either argument is a NaN, then NaN is returned.
1366 *
1367 * <li> If both arguments are signed zeros, a value equivalent
1368 * to {@code direction} is returned.
1369 *
1370 * <li> If {@code start} is
1371 * ±{@link Float#MIN_VALUE} and {@code direction}
1372 * has a value such that the result should have a smaller
1373 * magnitude, then a zero with the same sign as {@code start}
1374 * is returned.
1375 *
1376 * <li> If {@code start} is infinite and
1377 * {@code direction} has a value such that the result should
1378 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1379 * same sign as {@code start} is returned.
1380 *
1381 * <li> If {@code start} is equal to ±
1382 * {@link Float#MAX_VALUE} and {@code direction} has a
1383 * value such that the result should have a larger magnitude, an
1384 * infinity with same sign as {@code start} is returned.
1385 * </ul>
1386 *
1387 * @param start starting floating-point value
1388 * @param direction value indicating which of
1389 * {@code start}'s neighbors or {@code start} should
1390 * be returned
1391 * @return The floating-point number adjacent to {@code start} in the
1392 * direction of {@code direction}.
1393 * @since 1.6
1394 */
1395 public static float nextAfter(float start, double direction) {
1396 return sun.misc.FpUtils.nextAfter(start, direction);
1397 }
1398
1399 /**
1400 * Returns the floating-point value adjacent to {@code d} in
1401 * the direction of positive infinity. This method is
1402 * semantically equivalent to {@code nextAfter(d,
1403 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1404 * implementation may run faster than its equivalent
1405 * {@code nextAfter} call.
1406 *
1407 * <p>Special Cases:
1408 * <ul>
1409 * <li> If the argument is NaN, the result is NaN.
1410 *
1411 * <li> If the argument is positive infinity, the result is
1412 * positive infinity.
1413 *
1414 * <li> If the argument is zero, the result is
1415 * {@link Double#MIN_VALUE}
1416 *
1417 * </ul>
1418 *
1419 * @param d starting floating-point value
1420 * @return The adjacent floating-point value closer to positive
1421 * infinity.
1422 * @since 1.6
1423 */
1424 public static double nextUp(double d) {
1425 return sun.misc.FpUtils.nextUp(d);
1426 }
1427
1428 /**
1429 * Returns the floating-point value adjacent to {@code f} in
1430 * the direction of positive infinity. This method is
1431 * semantically equivalent to {@code nextAfter(f,
1432 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1433 * implementation may run faster than its equivalent
1434 * {@code nextAfter} call.
1435 *
1436 * <p>Special Cases:
1437 * <ul>
1438 * <li> If the argument is NaN, the result is NaN.
1439 *
1440 * <li> If the argument is positive infinity, the result is
1441 * positive infinity.
1442 *
1443 * <li> If the argument is zero, the result is
1444 * {@link Float#MIN_VALUE}
1445 *
1446 * </ul>
1447 *
1448 * @param f starting floating-point value
1449 * @return The adjacent floating-point value closer to positive
1450 * infinity.
1451 * @since 1.6
1452 */
1453 public static float nextUp(float f) {
1454 return sun.misc.FpUtils.nextUp(f);
1455 }
1456
1457
1458 /**
1459 * Return {@code d} ×
1460 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1461 * by a single correctly rounded floating-point multiply to a
1462 * member of the double value set. See the Java
1463 * Language Specification for a discussion of floating-point
1464 * value sets. If the exponent of the result is between {@link
1465 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1466 * answer is calculated exactly. If the exponent of the result
1467 * would be larger than {@code Double.MAX_EXPONENT}, an
1468 * infinity is returned. Note that if the result is subnormal,
1469 * precision may be lost; that is, when {@code scalb(x, n)}
1470 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1471 * <i>x</i>. When the result is non-NaN, the result has the same
1472 * sign as {@code d}.
1473 *
1474 * <p>Special cases:
1475 * <ul>
1476 * <li> If the first argument is NaN, NaN is returned.
1477 * <li> If the first argument is infinite, then an infinity of the
1478 * same sign is returned.
1479 * <li> If the first argument is zero, then a zero of the same
1480 * sign is returned.
1481 * </ul>
1482 *
1483 * @param d number to be scaled by a power of two.
1484 * @param scaleFactor power of 2 used to scale {@code d}
1485 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1486 * @since 1.6
1487 */
1488 public static double scalb(double d, int scaleFactor) {
1489 return sun.misc.FpUtils.scalb(d, scaleFactor);
1490 }
1491
1492 /**
1493 * Return {@code f} ×
1494 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1495 * by a single correctly rounded floating-point multiply to a
1496 * member of the float value set. See the Java
1497 * Language Specification for a discussion of floating-point
1498 * value sets. If the exponent of the result is between {@link
1499 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1500 * answer is calculated exactly. If the exponent of the result
1501 * would be larger than {@code Float.MAX_EXPONENT}, an
1502 * infinity is returned. Note that if the result is subnormal,
1503 * precision may be lost; that is, when {@code scalb(x, n)}
1504 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1505 * <i>x</i>. When the result is non-NaN, the result has the same
1506 * sign as {@code f}.
1507 *
1508 * <p>Special cases:
1509 * <ul>
1510 * <li> If the first argument is NaN, NaN is returned.
1511 * <li> If the first argument is infinite, then an infinity of the
1512 * same sign is returned.
1513 * <li> If the first argument is zero, then a zero of the same
1514 * sign is returned.
1515 * </ul>
1516 *
1517 * @param f number to be scaled by a power of two.
1518 * @param scaleFactor power of 2 used to scale {@code f}
1519 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1520 * @since 1.6
1521 */
1522 public static float scalb(float f, int scaleFactor) {
1523 return sun.misc.FpUtils.scalb(f, scaleFactor);
1524 }
1525 }