1 /*
2 * Copyright (c) 1999, 2013, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 package java.lang;
27
28 import java.util.Random;
29 import sun.misc.DoubleConsts;
30 import jdk.internal.HotSpotIntrinsicCandidate;
31
32 /**
33 * The class {@code StrictMath} contains methods for performing basic
34 * numeric operations such as the elementary exponential, logarithm,
35 * square root, and trigonometric functions.
36 *
37 * <p>To help ensure portability of Java programs, the definitions of
38 * some of the numeric functions in this package require that they
39 * produce the same results as certain published algorithms. These
40 * algorithms are available from the well-known network library
41 * {@code netlib} as the package "Freely Distributable Math
42 * Library," <a
43 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These
44 * algorithms, which are written in the C programming language, are
45 * then to be understood as executed with all floating-point
46 * operations following the rules of Java floating-point arithmetic.
47 *
48 * <p>The Java math library is defined with respect to
49 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
50 * more than one definition for a function (such as
51 * {@code acos}), use the "IEEE 754 core function" version
52 * (residing in a file whose name begins with the letter
53 * {@code e}). The methods which require {@code fdlibm}
54 * semantics are {@code sin}, {@code cos}, {@code tan},
55 * {@code asin}, {@code acos}, {@code atan},
56 * {@code exp}, {@code log}, {@code log10},
57 * {@code cbrt}, {@code atan2}, {@code pow},
58 * {@code sinh}, {@code cosh}, {@code tanh},
59 * {@code hypot}, {@code expm1}, and {@code log1p}.
60 *
61 * <p>
62 * The platform uses signed two's complement integer arithmetic with
63 * int and long primitive types. The developer should choose
64 * the primitive type to ensure that arithmetic operations consistently
65 * produce correct results, which in some cases means the operations
66 * will not overflow the range of values of the computation.
67 * The best practice is to choose the primitive type and algorithm to avoid
68 * overflow. In cases where the size is {@code int} or {@code long} and
69 * overflow errors need to be detected, the methods {@code addExact},
70 * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
71 * throw an {@code ArithmeticException} when the results overflow.
72 * For other arithmetic operations such as divide, absolute value,
73 * increment, decrement, and negation overflow occurs only with
74 * a specific minimum or maximum value and should be checked against
75 * the minimum or maximum as appropriate.
76 *
77 * @author unascribed
78 * @author Joseph D. Darcy
79 * @since 1.3
80 */
81
82 public final class StrictMath {
83
84 /**
85 * Don't let anyone instantiate this class.
86 */
87 private StrictMath() {}
88
89 /**
90 * The {@code double} value that is closer than any other to
91 * <i>e</i>, the base of the natural logarithms.
92 */
93 public static final double E = 2.7182818284590452354;
94
95 /**
96 * The {@code double} value that is closer than any other to
97 * <i>pi</i>, the ratio of the circumference of a circle to its
98 * diameter.
99 */
100 public static final double PI = 3.14159265358979323846;
101
102 /**
103 * Constant by which to multiply an angular value in degrees to obtain an
104 * angular value in radians.
105 */
106 private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
107
108 /**
109 * Constant by which to multiply an angular value in radians to obtain an
110 * angular value in degrees.
111 */
112
113 private static final double RADIANS_TO_DEGREES = 57.29577951308232;
114
115 /**
116 * Returns the trigonometric sine of an angle. Special cases:
117 * <ul><li>If the argument is NaN or an infinity, then the
118 * result is NaN.
119 * <li>If the argument is zero, then the result is a zero with the
120 * same sign as the argument.</ul>
121 *
122 * @param a an angle, in radians.
123 * @return the sine of the argument.
124 */
125 public static native double sin(double a);
126
127 /**
128 * Returns the trigonometric cosine of an angle. Special cases:
129 * <ul><li>If the argument is NaN or an infinity, then the
130 * result is NaN.</ul>
131 *
132 * @param a an angle, in radians.
133 * @return the cosine of the argument.
134 */
135 public static native double cos(double a);
136
137 /**
138 * Returns the trigonometric tangent of an angle. Special cases:
139 * <ul><li>If the argument is NaN or an infinity, then the result
140 * is NaN.
141 * <li>If the argument is zero, then the result is a zero with the
142 * same sign as the argument.</ul>
143 *
144 * @param a an angle, in radians.
145 * @return the tangent of the argument.
146 */
147 public static native double tan(double a);
148
149 /**
150 * Returns the arc sine of a value; the returned angle is in the
151 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
152 * <ul><li>If the argument is NaN or its absolute value is greater
153 * than 1, then the result is NaN.
154 * <li>If the argument is zero, then the result is a zero with the
155 * same sign as the argument.</ul>
156 *
157 * @param a the value whose arc sine is to be returned.
158 * @return the arc sine of the argument.
159 */
160 public static native double asin(double a);
161
162 /**
163 * Returns the arc cosine of a value; the returned angle is in the
164 * range 0.0 through <i>pi</i>. Special case:
165 * <ul><li>If the argument is NaN or its absolute value is greater
166 * than 1, then the result is NaN.</ul>
167 *
168 * @param a the value whose arc cosine is to be returned.
169 * @return the arc cosine of the argument.
170 */
171 public static native double acos(double a);
172
173 /**
174 * Returns the arc tangent of a value; the returned angle is in the
175 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
176 * <ul><li>If the argument is NaN, then the result is NaN.
177 * <li>If the argument is zero, then the result is a zero with the
178 * same sign as the argument.</ul>
179 *
180 * @param a the value whose arc tangent is to be returned.
181 * @return the arc tangent of the argument.
182 */
183 public static native double atan(double a);
184
185 /**
186 * Converts an angle measured in degrees to an approximately
187 * equivalent angle measured in radians. The conversion from
188 * degrees to radians is generally inexact.
189 *
190 * @param angdeg an angle, in degrees
191 * @return the measurement of the angle {@code angdeg}
192 * in radians.
193 */
194 public static strictfp double toRadians(double angdeg) {
195 // Do not delegate to Math.toRadians(angdeg) because
196 // this method has the strictfp modifier.
197 return angdeg * DEGREES_TO_RADIANS;
198 }
199
200 /**
201 * Converts an angle measured in radians to an approximately
202 * equivalent angle measured in degrees. The conversion from
203 * radians to degrees is generally inexact; users should
204 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
205 * equal {@code 0.0}.
206 *
207 * @param angrad an angle, in radians
208 * @return the measurement of the angle {@code angrad}
209 * in degrees.
210 */
211 public static strictfp double toDegrees(double angrad) {
212 // Do not delegate to Math.toDegrees(angrad) because
213 // this method has the strictfp modifier.
214 return angrad * RADIANS_TO_DEGREES;
215 }
216
217 /**
218 * Returns Euler's number <i>e</i> raised to the power of a
219 * {@code double} value. Special cases:
220 * <ul><li>If the argument is NaN, the result is NaN.
221 * <li>If the argument is positive infinity, then the result is
222 * positive infinity.
223 * <li>If the argument is negative infinity, then the result is
224 * positive zero.</ul>
225 *
226 * @param a the exponent to raise <i>e</i> to.
227 * @return the value <i>e</i><sup>{@code a}</sup>,
228 * where <i>e</i> is the base of the natural logarithms.
229 */
230 public static native double exp(double a);
231
232 /**
233 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
234 * value. Special cases:
235 * <ul><li>If the argument is NaN or less than zero, then the result
236 * is NaN.
237 * <li>If the argument is positive infinity, then the result is
238 * positive infinity.
239 * <li>If the argument is positive zero or negative zero, then the
240 * result is negative infinity.</ul>
241 *
242 * @param a a value
243 * @return the value ln {@code a}, the natural logarithm of
244 * {@code a}.
245 */
246 public static native double log(double a);
247
248 /**
249 * Returns the base 10 logarithm of a {@code double} value.
250 * Special cases:
251 *
252 * <ul><li>If the argument is NaN or less than zero, then the result
253 * is NaN.
254 * <li>If the argument is positive infinity, then the result is
255 * positive infinity.
256 * <li>If the argument is positive zero or negative zero, then the
257 * result is negative infinity.
258 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
259 * integer <i>n</i>, then the result is <i>n</i>.
260 * </ul>
261 *
262 * @param a a value
263 * @return the base 10 logarithm of {@code a}.
264 * @since 1.5
265 */
266 public static native double log10(double a);
267
268 /**
269 * Returns the correctly rounded positive square root of a
270 * {@code double} value.
271 * Special cases:
272 * <ul><li>If the argument is NaN or less than zero, then the result
273 * is NaN.
274 * <li>If the argument is positive infinity, then the result is positive
275 * infinity.
276 * <li>If the argument is positive zero or negative zero, then the
277 * result is the same as the argument.</ul>
278 * Otherwise, the result is the {@code double} value closest to
279 * the true mathematical square root of the argument value.
280 *
281 * @param a a value.
282 * @return the positive square root of {@code a}.
283 */
284 @HotSpotIntrinsicCandidate
285 public static native double sqrt(double a);
286
287 /**
288 * Returns the cube root of a {@code double} value. For
289 * positive finite {@code x}, {@code cbrt(-x) ==
290 * -cbrt(x)}; that is, the cube root of a negative value is
291 * the negative of the cube root of that value's magnitude.
292 * Special cases:
293 *
294 * <ul>
295 *
296 * <li>If the argument is NaN, then the result is NaN.
297 *
298 * <li>If the argument is infinite, then the result is an infinity
299 * with the same sign as the argument.
300 *
301 * <li>If the argument is zero, then the result is a zero with the
302 * same sign as the argument.
303 *
304 * </ul>
305 *
306 * @param a a value.
307 * @return the cube root of {@code a}.
308 * @since 1.5
309 */
310 public static native double cbrt(double a);
311
312 /**
313 * Computes the remainder operation on two arguments as prescribed
314 * by the IEEE 754 standard.
315 * The remainder value is mathematically equal to
316 * <code>f1 - f2</code> × <i>n</i>,
317 * where <i>n</i> is the mathematical integer closest to the exact
318 * mathematical value of the quotient {@code f1/f2}, and if two
319 * mathematical integers are equally close to {@code f1/f2},
320 * then <i>n</i> is the integer that is even. If the remainder is
321 * zero, its sign is the same as the sign of the first argument.
322 * Special cases:
323 * <ul><li>If either argument is NaN, or the first argument is infinite,
324 * or the second argument is positive zero or negative zero, then the
325 * result is NaN.
326 * <li>If the first argument is finite and the second argument is
327 * infinite, then the result is the same as the first argument.</ul>
328 *
329 * @param f1 the dividend.
330 * @param f2 the divisor.
331 * @return the remainder when {@code f1} is divided by
332 * {@code f2}.
333 */
334 public static native double IEEEremainder(double f1, double f2);
335
336 /**
337 * Returns the smallest (closest to negative infinity)
338 * {@code double} value that is greater than or equal to the
339 * argument and is equal to a mathematical integer. Special cases:
340 * <ul><li>If the argument value is already equal to a
341 * mathematical integer, then the result is the same as the
342 * argument. <li>If the argument is NaN or an infinity or
343 * positive zero or negative zero, then the result is the same as
344 * the argument. <li>If the argument value is less than zero but
345 * greater than -1.0, then the result is negative zero.</ul> Note
346 * that the value of {@code StrictMath.ceil(x)} is exactly the
347 * value of {@code -StrictMath.floor(-x)}.
348 *
349 * @param a a value.
350 * @return the smallest (closest to negative infinity)
351 * floating-point value that is greater than or equal to
352 * the argument and is equal to a mathematical integer.
353 */
354 public static double ceil(double a) {
355 return floorOrCeil(a, -0.0, 1.0, 1.0);
356 }
357
358 /**
359 * Returns the largest (closest to positive infinity)
360 * {@code double} value that is less than or equal to the
361 * argument and is equal to a mathematical integer. Special cases:
362 * <ul><li>If the argument value is already equal to a
363 * mathematical integer, then the result is the same as the
364 * argument. <li>If the argument is NaN or an infinity or
365 * positive zero or negative zero, then the result is the same as
366 * the argument.</ul>
367 *
368 * @param a a value.
369 * @return the largest (closest to positive infinity)
370 * floating-point value that less than or equal to the argument
371 * and is equal to a mathematical integer.
372 */
373 public static double floor(double a) {
374 return floorOrCeil(a, -1.0, 0.0, -1.0);
375 }
376
377 /**
378 * Internal method to share logic between floor and ceil.
379 *
380 * @param a the value to be floored or ceiled
381 * @param negativeBoundary result for values in (-1, 0)
382 * @param positiveBoundary result for values in (0, 1)
383 * @param increment value to add when the argument is non-integral
384 */
385 private static double floorOrCeil(double a,
386 double negativeBoundary,
387 double positiveBoundary,
388 double sign) {
389 int exponent = Math.getExponent(a);
390
391 if (exponent < 0) {
392 /*
393 * Absolute value of argument is less than 1.
394 * floorOrceil(-0.0) => -0.0
395 * floorOrceil(+0.0) => +0.0
396 */
397 return ((a == 0.0) ? a :
398 ( (a < 0.0) ? negativeBoundary : positiveBoundary) );
399 } else if (exponent >= 52) {
400 /*
401 * Infinity, NaN, or a value so large it must be integral.
402 */
403 return a;
404 }
405 // Else the argument is either an integral value already XOR it
406 // has to be rounded to one.
407 assert exponent >= 0 && exponent <= 51;
408
409 long doppel = Double.doubleToRawLongBits(a);
410 long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
411
412 if ( (mask & doppel) == 0L )
413 return a; // integral value
414 else {
415 double result = Double.longBitsToDouble(doppel & (~mask));
416 if (sign*a > 0.0)
417 result = result + sign;
418 return result;
419 }
420 }
421
422 /**
423 * Returns the {@code double} value that is closest in value
424 * to the argument and is equal to a mathematical integer. If two
425 * {@code double} values that are mathematical integers are
426 * equally close to the value of the argument, the result is the
427 * integer value that is even. Special cases:
428 * <ul><li>If the argument value is already equal to a mathematical
429 * integer, then the result is the same as the argument.
430 * <li>If the argument is NaN or an infinity or positive zero or negative
431 * zero, then the result is the same as the argument.</ul>
432 *
433 * @param a a value.
434 * @return the closest floating-point value to {@code a} that is
435 * equal to a mathematical integer.
436 * @author Joseph D. Darcy
437 */
438 public static double rint(double a) {
439 /*
440 * If the absolute value of a is not less than 2^52, it
441 * is either a finite integer (the double format does not have
442 * enough significand bits for a number that large to have any
443 * fractional portion), an infinity, or a NaN. In any of
444 * these cases, rint of the argument is the argument.
445 *
446 * Otherwise, the sum (twoToThe52 + a ) will properly round
447 * away any fractional portion of a since ulp(twoToThe52) ==
448 * 1.0; subtracting out twoToThe52 from this sum will then be
449 * exact and leave the rounded integer portion of a.
450 *
451 * This method does *not* need to be declared strictfp to get
452 * fully reproducible results. Whether or not a method is
453 * declared strictfp can only make a difference in the
454 * returned result if some operation would overflow or
455 * underflow with strictfp semantics. The operation
456 * (twoToThe52 + a ) cannot overflow since large values of a
457 * are screened out; the add cannot underflow since twoToThe52
458 * is too large. The subtraction ((twoToThe52 + a ) -
459 * twoToThe52) will be exact as discussed above and thus
460 * cannot overflow or meaningfully underflow. Finally, the
461 * last multiply in the return statement is by plus or minus
462 * 1.0, which is exact too.
463 */
464 double twoToThe52 = (double)(1L << 52); // 2^52
465 double sign = Math.copySign(1.0, a); // preserve sign info
466 a = Math.abs(a);
467
468 if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
469 a = ((twoToThe52 + a ) - twoToThe52);
470 }
471
472 return sign * a; // restore original sign
473 }
474
475 /**
476 * Returns the angle <i>theta</i> from the conversion of rectangular
477 * coordinates ({@code x}, {@code y}) to polar
478 * coordinates (r, <i>theta</i>).
479 * This method computes the phase <i>theta</i> by computing an arc tangent
480 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
481 * cases:
482 * <ul><li>If either argument is NaN, then the result is NaN.
483 * <li>If the first argument is positive zero and the second argument
484 * is positive, or the first argument is positive and finite and the
485 * second argument is positive infinity, then the result is positive
486 * zero.
487 * <li>If the first argument is negative zero and the second argument
488 * is positive, or the first argument is negative and finite and the
489 * second argument is positive infinity, then the result is negative zero.
490 * <li>If the first argument is positive zero and the second argument
491 * is negative, or the first argument is positive and finite and the
492 * second argument is negative infinity, then the result is the
493 * {@code double} value closest to <i>pi</i>.
494 * <li>If the first argument is negative zero and the second argument
495 * is negative, or the first argument is negative and finite and the
496 * second argument is negative infinity, then the result is the
497 * {@code double} value closest to -<i>pi</i>.
498 * <li>If the first argument is positive and the second argument is
499 * positive zero or negative zero, or the first argument is positive
500 * infinity and the second argument is finite, then the result is the
501 * {@code double} value closest to <i>pi</i>/2.
502 * <li>If the first argument is negative and the second argument is
503 * positive zero or negative zero, or the first argument is negative
504 * infinity and the second argument is finite, then the result is the
505 * {@code double} value closest to -<i>pi</i>/2.
506 * <li>If both arguments are positive infinity, then the result is the
507 * {@code double} value closest to <i>pi</i>/4.
508 * <li>If the first argument is positive infinity and the second argument
509 * is negative infinity, then the result is the {@code double}
510 * value closest to 3*<i>pi</i>/4.
511 * <li>If the first argument is negative infinity and the second argument
512 * is positive infinity, then the result is the {@code double} value
513 * closest to -<i>pi</i>/4.
514 * <li>If both arguments are negative infinity, then the result is the
515 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
516 *
517 * @param y the ordinate coordinate
518 * @param x the abscissa coordinate
519 * @return the <i>theta</i> component of the point
520 * (<i>r</i>, <i>theta</i>)
521 * in polar coordinates that corresponds to the point
522 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
523 */
524 public static native double atan2(double y, double x);
525
526 /**
527 * Returns the value of the first argument raised to the power of the
528 * second argument. Special cases:
529 *
530 * <ul><li>If the second argument is positive or negative zero, then the
531 * result is 1.0.
532 * <li>If the second argument is 1.0, then the result is the same as the
533 * first argument.
534 * <li>If the second argument is NaN, then the result is NaN.
535 * <li>If the first argument is NaN and the second argument is nonzero,
536 * then the result is NaN.
537 *
538 * <li>If
539 * <ul>
540 * <li>the absolute value of the first argument is greater than 1
541 * and the second argument is positive infinity, or
542 * <li>the absolute value of the first argument is less than 1 and
543 * the second argument is negative infinity,
544 * </ul>
545 * then the result is positive infinity.
546 *
547 * <li>If
548 * <ul>
549 * <li>the absolute value of the first argument is greater than 1 and
550 * the second argument is negative infinity, or
551 * <li>the absolute value of the
552 * first argument is less than 1 and the second argument is positive
553 * infinity,
554 * </ul>
555 * then the result is positive zero.
556 *
557 * <li>If the absolute value of the first argument equals 1 and the
558 * second argument is infinite, then the result is NaN.
559 *
560 * <li>If
561 * <ul>
562 * <li>the first argument is positive zero and the second argument
563 * is greater than zero, or
564 * <li>the first argument is positive infinity and the second
565 * argument is less than zero,
566 * </ul>
567 * then the result is positive zero.
568 *
569 * <li>If
570 * <ul>
571 * <li>the first argument is positive zero and the second argument
572 * is less than zero, or
573 * <li>the first argument is positive infinity and the second
574 * argument is greater than zero,
575 * </ul>
576 * then the result is positive infinity.
577 *
578 * <li>If
579 * <ul>
580 * <li>the first argument is negative zero and the second argument
581 * is greater than zero but not a finite odd integer, or
582 * <li>the first argument is negative infinity and the second
583 * argument is less than zero but not a finite odd integer,
584 * </ul>
585 * then the result is positive zero.
586 *
587 * <li>If
588 * <ul>
589 * <li>the first argument is negative zero and the second argument
590 * is a positive finite odd integer, or
591 * <li>the first argument is negative infinity and the second
592 * argument is a negative finite odd integer,
593 * </ul>
594 * then the result is negative zero.
595 *
596 * <li>If
597 * <ul>
598 * <li>the first argument is negative zero and the second argument
599 * is less than zero but not a finite odd integer, or
600 * <li>the first argument is negative infinity and the second
601 * argument is greater than zero but not a finite odd integer,
602 * </ul>
603 * then the result is positive infinity.
604 *
605 * <li>If
606 * <ul>
607 * <li>the first argument is negative zero and the second argument
608 * is a negative finite odd integer, or
609 * <li>the first argument is negative infinity and the second
610 * argument is a positive finite odd integer,
611 * </ul>
612 * then the result is negative infinity.
613 *
614 * <li>If the first argument is finite and less than zero
615 * <ul>
616 * <li> if the second argument is a finite even integer, the
617 * result is equal to the result of raising the absolute value of
618 * the first argument to the power of the second argument
619 *
620 * <li>if the second argument is a finite odd integer, the result
621 * is equal to the negative of the result of raising the absolute
622 * value of the first argument to the power of the second
623 * argument
624 *
625 * <li>if the second argument is finite and not an integer, then
626 * the result is NaN.
627 * </ul>
628 *
629 * <li>If both arguments are integers, then the result is exactly equal
630 * to the mathematical result of raising the first argument to the power
631 * of the second argument if that result can in fact be represented
632 * exactly as a {@code double} value.</ul>
633 *
634 * <p>(In the foregoing descriptions, a floating-point value is
635 * considered to be an integer if and only if it is finite and a
636 * fixed point of the method {@link #ceil ceil} or,
637 * equivalently, a fixed point of the method {@link #floor
638 * floor}. A value is a fixed point of a one-argument
639 * method if and only if the result of applying the method to the
640 * value is equal to the value.)
641 *
642 * @param a base.
643 * @param b the exponent.
644 * @return the value {@code a}<sup>{@code b}</sup>.
645 */
646 public static native double pow(double a, double b);
647
648 /**
649 * Returns the closest {@code int} to the argument, with ties
650 * rounding to positive infinity.
651 *
652 * <p>Special cases:
653 * <ul><li>If the argument is NaN, the result is 0.
654 * <li>If the argument is negative infinity or any value less than or
655 * equal to the value of {@code Integer.MIN_VALUE}, the result is
656 * equal to the value of {@code Integer.MIN_VALUE}.
657 * <li>If the argument is positive infinity or any value greater than or
658 * equal to the value of {@code Integer.MAX_VALUE}, the result is
659 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
660 *
661 * @param a a floating-point value to be rounded to an integer.
662 * @return the value of the argument rounded to the nearest
663 * {@code int} value.
664 * @see java.lang.Integer#MAX_VALUE
665 * @see java.lang.Integer#MIN_VALUE
666 */
667 public static int round(float a) {
668 return Math.round(a);
669 }
670
671 /**
672 * Returns the closest {@code long} to the argument, with ties
673 * rounding to positive infinity.
674 *
675 * <p>Special cases:
676 * <ul><li>If the argument is NaN, the result is 0.
677 * <li>If the argument is negative infinity or any value less than or
678 * equal to the value of {@code Long.MIN_VALUE}, the result is
679 * equal to the value of {@code Long.MIN_VALUE}.
680 * <li>If the argument is positive infinity or any value greater than or
681 * equal to the value of {@code Long.MAX_VALUE}, the result is
682 * equal to the value of {@code Long.MAX_VALUE}.</ul>
683 *
684 * @param a a floating-point value to be rounded to a
685 * {@code long}.
686 * @return the value of the argument rounded to the nearest
687 * {@code long} value.
688 * @see java.lang.Long#MAX_VALUE
689 * @see java.lang.Long#MIN_VALUE
690 */
691 public static long round(double a) {
692 return Math.round(a);
693 }
694
695 private static final class RandomNumberGeneratorHolder {
696 static final Random randomNumberGenerator = new Random();
697 }
698
699 /**
700 * Returns a {@code double} value with a positive sign, greater
701 * than or equal to {@code 0.0} and less than {@code 1.0}.
702 * Returned values are chosen pseudorandomly with (approximately)
703 * uniform distribution from that range.
704 *
705 * <p>When this method is first called, it creates a single new
706 * pseudorandom-number generator, exactly as if by the expression
707 *
708 * <blockquote>{@code new java.util.Random()}</blockquote>
709 *
710 * This new pseudorandom-number generator is used thereafter for
711 * all calls to this method and is used nowhere else.
712 *
713 * <p>This method is properly synchronized to allow correct use by
714 * more than one thread. However, if many threads need to generate
715 * pseudorandom numbers at a great rate, it may reduce contention
716 * for each thread to have its own pseudorandom-number generator.
717 *
718 * @return a pseudorandom {@code double} greater than or equal
719 * to {@code 0.0} and less than {@code 1.0}.
720 * @see Random#nextDouble()
721 */
722 public static double random() {
723 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
724 }
725
726 /**
727 * Returns the sum of its arguments,
728 * throwing an exception if the result overflows an {@code int}.
729 *
730 * @param x the first value
731 * @param y the second value
732 * @return the result
733 * @throws ArithmeticException if the result overflows an int
734 * @see Math#addExact(int,int)
735 * @since 1.8
736 */
737 public static int addExact(int x, int y) {
738 return Math.addExact(x, y);
739 }
740
741 /**
742 * Returns the sum of its arguments,
743 * throwing an exception if the result overflows a {@code long}.
744 *
745 * @param x the first value
746 * @param y the second value
747 * @return the result
748 * @throws ArithmeticException if the result overflows a long
749 * @see Math#addExact(long,long)
750 * @since 1.8
751 */
752 public static long addExact(long x, long y) {
753 return Math.addExact(x, y);
754 }
755
756 /**
757 * Returns the difference of the arguments,
758 * throwing an exception if the result overflows an {@code int}.
759 *
760 * @param x the first value
761 * @param y the second value to subtract from the first
762 * @return the result
763 * @throws ArithmeticException if the result overflows an int
764 * @see Math#subtractExact(int,int)
765 * @since 1.8
766 */
767 public static int subtractExact(int x, int y) {
768 return Math.subtractExact(x, y);
769 }
770
771 /**
772 * Returns the difference of the arguments,
773 * throwing an exception if the result overflows a {@code long}.
774 *
775 * @param x the first value
776 * @param y the second value to subtract from the first
777 * @return the result
778 * @throws ArithmeticException if the result overflows a long
779 * @see Math#subtractExact(long,long)
780 * @since 1.8
781 */
782 public static long subtractExact(long x, long y) {
783 return Math.subtractExact(x, y);
784 }
785
786 /**
787 * Returns the product of the arguments,
788 * throwing an exception if the result overflows an {@code int}.
789 *
790 * @param x the first value
791 * @param y the second value
792 * @return the result
793 * @throws ArithmeticException if the result overflows an int
794 * @see Math#multiplyExact(int,int)
795 * @since 1.8
796 */
797 public static int multiplyExact(int x, int y) {
798 return Math.multiplyExact(x, y);
799 }
800
801 /**
802 * Returns the product of the arguments,
803 * throwing an exception if the result overflows a {@code long}.
804 *
805 * @param x the first value
806 * @param y the second value
807 * @return the result
808 * @throws ArithmeticException if the result overflows a long
809 * @see Math#multiplyExact(long,long)
810 * @since 1.8
811 */
812 public static long multiplyExact(long x, long y) {
813 return Math.multiplyExact(x, y);
814 }
815
816 /**
817 * Returns the value of the {@code long} argument;
818 * throwing an exception if the value overflows an {@code int}.
819 *
820 * @param value the long value
821 * @return the argument as an int
822 * @throws ArithmeticException if the {@code argument} overflows an int
823 * @see Math#toIntExact(long)
824 * @since 1.8
825 */
826 public static int toIntExact(long value) {
827 return Math.toIntExact(value);
828 }
829
830 /**
831 * Returns the largest (closest to positive infinity)
832 * {@code int} value that is less than or equal to the algebraic quotient.
833 * There is one special case, if the dividend is the
834 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
835 * then integer overflow occurs and
836 * the result is equal to the {@code Integer.MIN_VALUE}.
837 * <p>
838 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
839 * a comparison to the integer division {@code /} operator.
840 *
841 * @param x the dividend
842 * @param y the divisor
843 * @return the largest (closest to positive infinity)
844 * {@code int} value that is less than or equal to the algebraic quotient.
845 * @throws ArithmeticException if the divisor {@code y} is zero
846 * @see Math#floorDiv(int, int)
847 * @see Math#floor(double)
848 * @since 1.8
849 */
850 public static int floorDiv(int x, int y) {
851 return Math.floorDiv(x, y);
852 }
853
854 /**
855 * Returns the largest (closest to positive infinity)
856 * {@code long} value that is less than or equal to the algebraic quotient.
857 * There is one special case, if the dividend is the
858 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
859 * then integer overflow occurs and
860 * the result is equal to the {@code Long.MIN_VALUE}.
861 * <p>
862 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
863 * a comparison to the integer division {@code /} operator.
864 *
865 * @param x the dividend
866 * @param y the divisor
867 * @return the largest (closest to positive infinity)
868 * {@code long} value that is less than or equal to the algebraic quotient.
869 * @throws ArithmeticException if the divisor {@code y} is zero
870 * @see Math#floorDiv(long, long)
871 * @see Math#floor(double)
872 * @since 1.8
873 */
874 public static long floorDiv(long x, long y) {
875 return Math.floorDiv(x, y);
876 }
877
878 /**
879 * Returns the floor modulus of the {@code int} arguments.
880 * <p>
881 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
882 * has the same sign as the divisor {@code y}, and
883 * is in the range of {@code -abs(y) < r < +abs(y)}.
884 * <p>
885 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
886 * <ul>
887 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
888 * </ul>
889 * <p>
890 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
891 * a comparison to the {@code %} operator.
892 *
893 * @param x the dividend
894 * @param y the divisor
895 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
896 * @throws ArithmeticException if the divisor {@code y} is zero
897 * @see Math#floorMod(int, int)
898 * @see StrictMath#floorDiv(int, int)
899 * @since 1.8
900 */
901 public static int floorMod(int x, int y) {
902 return Math.floorMod(x , y);
903 }
904 /**
905 * Returns the floor modulus of the {@code long} arguments.
906 * <p>
907 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
908 * has the same sign as the divisor {@code y}, and
909 * is in the range of {@code -abs(y) < r < +abs(y)}.
910 * <p>
911 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
912 * <ul>
913 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
914 * </ul>
915 * <p>
916 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
917 * a comparison to the {@code %} operator.
918 *
919 * @param x the dividend
920 * @param y the divisor
921 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
922 * @throws ArithmeticException if the divisor {@code y} is zero
923 * @see Math#floorMod(long, long)
924 * @see StrictMath#floorDiv(long, long)
925 * @since 1.8
926 */
927 public static long floorMod(long x, long y) {
928 return Math.floorMod(x, y);
929 }
930
931 /**
932 * Returns the absolute value of an {@code int} value.
933 * If the argument is not negative, the argument is returned.
934 * If the argument is negative, the negation of the argument is returned.
935 *
936 * <p>Note that if the argument is equal to the value of
937 * {@link Integer#MIN_VALUE}, the most negative representable
938 * {@code int} value, the result is that same value, which is
939 * negative.
940 *
941 * @param a the argument whose absolute value is to be determined.
942 * @return the absolute value of the argument.
943 */
944 public static int abs(int a) {
945 return Math.abs(a);
946 }
947
948 /**
949 * Returns the absolute value of a {@code long} value.
950 * If the argument is not negative, the argument is returned.
951 * If the argument is negative, the negation of the argument is returned.
952 *
953 * <p>Note that if the argument is equal to the value of
954 * {@link Long#MIN_VALUE}, the most negative representable
955 * {@code long} value, the result is that same value, which
956 * is negative.
957 *
958 * @param a the argument whose absolute value is to be determined.
959 * @return the absolute value of the argument.
960 */
961 public static long abs(long a) {
962 return Math.abs(a);
963 }
964
965 /**
966 * Returns the absolute value of a {@code float} value.
967 * If the argument is not negative, the argument is returned.
968 * If the argument is negative, the negation of the argument is returned.
969 * Special cases:
970 * <ul><li>If the argument is positive zero or negative zero, the
971 * result is positive zero.
972 * <li>If the argument is infinite, the result is positive infinity.
973 * <li>If the argument is NaN, the result is NaN.</ul>
974 * In other words, the result is the same as the value of the expression:
975 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
976 *
977 * @param a the argument whose absolute value is to be determined
978 * @return the absolute value of the argument.
979 */
980 public static float abs(float a) {
981 return Math.abs(a);
982 }
983
984 /**
985 * Returns the absolute value of a {@code double} value.
986 * If the argument is not negative, the argument is returned.
987 * If the argument is negative, the negation of the argument is returned.
988 * Special cases:
989 * <ul><li>If the argument is positive zero or negative zero, the result
990 * is positive zero.
991 * <li>If the argument is infinite, the result is positive infinity.
992 * <li>If the argument is NaN, the result is NaN.</ul>
993 * In other words, the result is the same as the value of the expression:
994 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
995 *
996 * @param a the argument whose absolute value is to be determined
997 * @return the absolute value of the argument.
998 */
999 public static double abs(double a) {
1000 return Math.abs(a);
1001 }
1002
1003 /**
1004 * Returns the greater of two {@code int} values. That is, the
1005 * result is the argument closer to the value of
1006 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1007 * the result is that same value.
1008 *
1009 * @param a an argument.
1010 * @param b another argument.
1011 * @return the larger of {@code a} and {@code b}.
1012 */
1013 @HotSpotIntrinsicCandidate
1014 public static int max(int a, int b) {
1015 return Math.max(a, b);
1016 }
1017
1018 /**
1019 * Returns the greater of two {@code long} values. That is, the
1020 * result is the argument closer to the value of
1021 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1022 * the result is that same value.
1023 *
1024 * @param a an argument.
1025 * @param b another argument.
1026 * @return the larger of {@code a} and {@code b}.
1027 */
1028 public static long max(long a, long b) {
1029 return Math.max(a, b);
1030 }
1031
1032 /**
1033 * Returns the greater of two {@code float} values. That is,
1034 * the result is the argument closer to positive infinity. If the
1035 * arguments have the same value, the result is that same
1036 * value. If either value is NaN, then the result is NaN. Unlike
1037 * the numerical comparison operators, this method considers
1038 * negative zero to be strictly smaller than positive zero. If one
1039 * argument is positive zero and the other negative zero, the
1040 * result is positive zero.
1041 *
1042 * @param a an argument.
1043 * @param b another argument.
1044 * @return the larger of {@code a} and {@code b}.
1045 */
1046 public static float max(float a, float b) {
1047 return Math.max(a, b);
1048 }
1049
1050 /**
1051 * Returns the greater of two {@code double} values. That
1052 * is, the result is the argument closer to positive infinity. If
1053 * the arguments have the same value, the result is that same
1054 * value. If either value is NaN, then the result is NaN. Unlike
1055 * the numerical comparison operators, this method considers
1056 * negative zero to be strictly smaller than positive zero. If one
1057 * argument is positive zero and the other negative zero, the
1058 * result is positive zero.
1059 *
1060 * @param a an argument.
1061 * @param b another argument.
1062 * @return the larger of {@code a} and {@code b}.
1063 */
1064 public static double max(double a, double b) {
1065 return Math.max(a, b);
1066 }
1067
1068 /**
1069 * Returns the smaller of two {@code int} values. That is,
1070 * the result the argument closer to the value of
1071 * {@link Integer#MIN_VALUE}. If the arguments have the same
1072 * value, the result is that same value.
1073 *
1074 * @param a an argument.
1075 * @param b another argument.
1076 * @return the smaller of {@code a} and {@code b}.
1077 */
1078 @HotSpotIntrinsicCandidate
1079 public static int min(int a, int b) {
1080 return Math.min(a, b);
1081 }
1082
1083 /**
1084 * Returns the smaller of two {@code long} values. That is,
1085 * the result is the argument closer to the value of
1086 * {@link Long#MIN_VALUE}. If the arguments have the same
1087 * value, the result is that same value.
1088 *
1089 * @param a an argument.
1090 * @param b another argument.
1091 * @return the smaller of {@code a} and {@code b}.
1092 */
1093 public static long min(long a, long b) {
1094 return Math.min(a, b);
1095 }
1096
1097 /**
1098 * Returns the smaller of two {@code float} values. That is,
1099 * the result is the value closer to negative infinity. If the
1100 * arguments have the same value, the result is that same
1101 * value. If either value is NaN, then the result is NaN. Unlike
1102 * the numerical comparison operators, this method considers
1103 * negative zero to be strictly smaller than positive zero. If
1104 * one argument is positive zero and the other is negative zero,
1105 * the result is negative zero.
1106 *
1107 * @param a an argument.
1108 * @param b another argument.
1109 * @return the smaller of {@code a} and {@code b.}
1110 */
1111 public static float min(float a, float b) {
1112 return Math.min(a, b);
1113 }
1114
1115 /**
1116 * Returns the smaller of two {@code double} values. That
1117 * is, the result is the value closer to negative infinity. If the
1118 * arguments have the same value, the result is that same
1119 * value. If either value is NaN, then the result is NaN. Unlike
1120 * the numerical comparison operators, this method considers
1121 * negative zero to be strictly smaller than positive zero. If one
1122 * argument is positive zero and the other is negative zero, the
1123 * result is negative zero.
1124 *
1125 * @param a an argument.
1126 * @param b another argument.
1127 * @return the smaller of {@code a} and {@code b}.
1128 */
1129 public static double min(double a, double b) {
1130 return Math.min(a, b);
1131 }
1132
1133 /**
1134 * Returns the size of an ulp of the argument. An ulp, unit in
1135 * the last place, of a {@code double} value is the positive
1136 * distance between this floating-point value and the {@code
1137 * double} value next larger in magnitude. Note that for non-NaN
1138 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1139 *
1140 * <p>Special Cases:
1141 * <ul>
1142 * <li> If the argument is NaN, then the result is NaN.
1143 * <li> If the argument is positive or negative infinity, then the
1144 * result is positive infinity.
1145 * <li> If the argument is positive or negative zero, then the result is
1146 * {@code Double.MIN_VALUE}.
1147 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1148 * the result is equal to 2<sup>971</sup>.
1149 * </ul>
1150 *
1151 * @param d the floating-point value whose ulp is to be returned
1152 * @return the size of an ulp of the argument
1153 * @author Joseph D. Darcy
1154 * @since 1.5
1155 */
1156 public static double ulp(double d) {
1157 return Math.ulp(d);
1158 }
1159
1160 /**
1161 * Returns the size of an ulp of the argument. An ulp, unit in
1162 * the last place, of a {@code float} value is the positive
1163 * distance between this floating-point value and the {@code
1164 * float} value next larger in magnitude. Note that for non-NaN
1165 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1166 *
1167 * <p>Special Cases:
1168 * <ul>
1169 * <li> If the argument is NaN, then the result is NaN.
1170 * <li> If the argument is positive or negative infinity, then the
1171 * result is positive infinity.
1172 * <li> If the argument is positive or negative zero, then the result is
1173 * {@code Float.MIN_VALUE}.
1174 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1175 * the result is equal to 2<sup>104</sup>.
1176 * </ul>
1177 *
1178 * @param f the floating-point value whose ulp is to be returned
1179 * @return the size of an ulp of the argument
1180 * @author Joseph D. Darcy
1181 * @since 1.5
1182 */
1183 public static float ulp(float f) {
1184 return Math.ulp(f);
1185 }
1186
1187 /**
1188 * Returns the signum function of the argument; zero if the argument
1189 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1190 * argument is less than zero.
1191 *
1192 * <p>Special Cases:
1193 * <ul>
1194 * <li> If the argument is NaN, then the result is NaN.
1195 * <li> If the argument is positive zero or negative zero, then the
1196 * result is the same as the argument.
1197 * </ul>
1198 *
1199 * @param d the floating-point value whose signum is to be returned
1200 * @return the signum function of the argument
1201 * @author Joseph D. Darcy
1202 * @since 1.5
1203 */
1204 public static double signum(double d) {
1205 return Math.signum(d);
1206 }
1207
1208 /**
1209 * Returns the signum function of the argument; zero if the argument
1210 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1211 * argument is less than zero.
1212 *
1213 * <p>Special Cases:
1214 * <ul>
1215 * <li> If the argument is NaN, then the result is NaN.
1216 * <li> If the argument is positive zero or negative zero, then the
1217 * result is the same as the argument.
1218 * </ul>
1219 *
1220 * @param f the floating-point value whose signum is to be returned
1221 * @return the signum function of the argument
1222 * @author Joseph D. Darcy
1223 * @since 1.5
1224 */
1225 public static float signum(float f) {
1226 return Math.signum(f);
1227 }
1228
1229 /**
1230 * Returns the hyperbolic sine of a {@code double} value.
1231 * The hyperbolic sine of <i>x</i> is defined to be
1232 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1233 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1234 *
1235 * <p>Special cases:
1236 * <ul>
1237 *
1238 * <li>If the argument is NaN, then the result is NaN.
1239 *
1240 * <li>If the argument is infinite, then the result is an infinity
1241 * with the same sign as the argument.
1242 *
1243 * <li>If the argument is zero, then the result is a zero with the
1244 * same sign as the argument.
1245 *
1246 * </ul>
1247 *
1248 * @param x The number whose hyperbolic sine is to be returned.
1249 * @return The hyperbolic sine of {@code x}.
1250 * @since 1.5
1251 */
1252 public static native double sinh(double x);
1253
1254 /**
1255 * Returns the hyperbolic cosine of a {@code double} value.
1256 * The hyperbolic cosine of <i>x</i> is defined to be
1257 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1258 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1259 *
1260 * <p>Special cases:
1261 * <ul>
1262 *
1263 * <li>If the argument is NaN, then the result is NaN.
1264 *
1265 * <li>If the argument is infinite, then the result is positive
1266 * infinity.
1267 *
1268 * <li>If the argument is zero, then the result is {@code 1.0}.
1269 *
1270 * </ul>
1271 *
1272 * @param x The number whose hyperbolic cosine is to be returned.
1273 * @return The hyperbolic cosine of {@code x}.
1274 * @since 1.5
1275 */
1276 public static native double cosh(double x);
1277
1278 /**
1279 * Returns the hyperbolic tangent of a {@code double} value.
1280 * The hyperbolic tangent of <i>x</i> is defined to be
1281 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1282 * in other words, {@linkplain Math#sinh
1283 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1284 * that the absolute value of the exact tanh is always less than
1285 * 1.
1286 *
1287 * <p>Special cases:
1288 * <ul>
1289 *
1290 * <li>If the argument is NaN, then the result is NaN.
1291 *
1292 * <li>If the argument is zero, then the result is a zero with the
1293 * same sign as the argument.
1294 *
1295 * <li>If the argument is positive infinity, then the result is
1296 * {@code +1.0}.
1297 *
1298 * <li>If the argument is negative infinity, then the result is
1299 * {@code -1.0}.
1300 *
1301 * </ul>
1302 *
1303 * @param x The number whose hyperbolic tangent is to be returned.
1304 * @return The hyperbolic tangent of {@code x}.
1305 * @since 1.5
1306 */
1307 public static native double tanh(double x);
1308
1309 /**
1310 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1311 * without intermediate overflow or underflow.
1312 *
1313 * <p>Special cases:
1314 * <ul>
1315 *
1316 * <li> If either argument is infinite, then the result
1317 * is positive infinity.
1318 *
1319 * <li> If either argument is NaN and neither argument is infinite,
1320 * then the result is NaN.
1321 *
1322 * </ul>
1323 *
1324 * @param x a value
1325 * @param y a value
1326 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1327 * without intermediate overflow or underflow
1328 * @since 1.5
1329 */
1330 public static native double hypot(double x, double y);
1331
1332 /**
1333 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1334 * <i>x</i> near 0, the exact sum of
1335 * {@code expm1(x)} + 1 is much closer to the true
1336 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1337 *
1338 * <p>Special cases:
1339 * <ul>
1340 * <li>If the argument is NaN, the result is NaN.
1341 *
1342 * <li>If the argument is positive infinity, then the result is
1343 * positive infinity.
1344 *
1345 * <li>If the argument is negative infinity, then the result is
1346 * -1.0.
1347 *
1348 * <li>If the argument is zero, then the result is a zero with the
1349 * same sign as the argument.
1350 *
1351 * </ul>
1352 *
1353 * @param x the exponent to raise <i>e</i> to in the computation of
1354 * <i>e</i><sup>{@code x}</sup> -1.
1355 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1356 * @since 1.5
1357 */
1358 public static native double expm1(double x);
1359
1360 /**
1361 * Returns the natural logarithm of the sum of the argument and 1.
1362 * Note that for small values {@code x}, the result of
1363 * {@code log1p(x)} is much closer to the true result of ln(1
1364 * + {@code x}) than the floating-point evaluation of
1365 * {@code log(1.0+x)}.
1366 *
1367 * <p>Special cases:
1368 * <ul>
1369 *
1370 * <li>If the argument is NaN or less than -1, then the result is
1371 * NaN.
1372 *
1373 * <li>If the argument is positive infinity, then the result is
1374 * positive infinity.
1375 *
1376 * <li>If the argument is negative one, then the result is
1377 * negative infinity.
1378 *
1379 * <li>If the argument is zero, then the result is a zero with the
1380 * same sign as the argument.
1381 *
1382 * </ul>
1383 *
1384 * @param x a value
1385 * @return the value ln({@code x} + 1), the natural
1386 * log of {@code x} + 1
1387 * @since 1.5
1388 */
1389 public static native double log1p(double x);
1390
1391 /**
1392 * Returns the first floating-point argument with the sign of the
1393 * second floating-point argument. For this method, a NaN
1394 * {@code sign} argument is always treated as if it were
1395 * positive.
1396 *
1397 * @param magnitude the parameter providing the magnitude of the result
1398 * @param sign the parameter providing the sign of the result
1399 * @return a value with the magnitude of {@code magnitude}
1400 * and the sign of {@code sign}.
1401 * @since 1.6
1402 */
1403 public static double copySign(double magnitude, double sign) {
1404 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1405 }
1406
1407 /**
1408 * Returns the first floating-point argument with the sign of the
1409 * second floating-point argument. For this method, a NaN
1410 * {@code sign} argument is always treated as if it were
1411 * positive.
1412 *
1413 * @param magnitude the parameter providing the magnitude of the result
1414 * @param sign the parameter providing the sign of the result
1415 * @return a value with the magnitude of {@code magnitude}
1416 * and the sign of {@code sign}.
1417 * @since 1.6
1418 */
1419 public static float copySign(float magnitude, float sign) {
1420 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1421 }
1422 /**
1423 * Returns the unbiased exponent used in the representation of a
1424 * {@code float}. Special cases:
1425 *
1426 * <ul>
1427 * <li>If the argument is NaN or infinite, then the result is
1428 * {@link Float#MAX_EXPONENT} + 1.
1429 * <li>If the argument is zero or subnormal, then the result is
1430 * {@link Float#MIN_EXPONENT} -1.
1431 * </ul>
1432 * @param f a {@code float} value
1433 * @return the unbiased exponent of the argument
1434 * @since 1.6
1435 */
1436 public static int getExponent(float f) {
1437 return Math.getExponent(f);
1438 }
1439
1440 /**
1441 * Returns the unbiased exponent used in the representation of a
1442 * {@code double}. Special cases:
1443 *
1444 * <ul>
1445 * <li>If the argument is NaN or infinite, then the result is
1446 * {@link Double#MAX_EXPONENT} + 1.
1447 * <li>If the argument is zero or subnormal, then the result is
1448 * {@link Double#MIN_EXPONENT} -1.
1449 * </ul>
1450 * @param d a {@code double} value
1451 * @return the unbiased exponent of the argument
1452 * @since 1.6
1453 */
1454 public static int getExponent(double d) {
1455 return Math.getExponent(d);
1456 }
1457
1458 /**
1459 * Returns the floating-point number adjacent to the first
1460 * argument in the direction of the second argument. If both
1461 * arguments compare as equal the second argument is returned.
1462 *
1463 * <p>Special cases:
1464 * <ul>
1465 * <li> If either argument is a NaN, then NaN is returned.
1466 *
1467 * <li> If both arguments are signed zeros, {@code direction}
1468 * is returned unchanged (as implied by the requirement of
1469 * returning the second argument if the arguments compare as
1470 * equal).
1471 *
1472 * <li> If {@code start} is
1473 * ±{@link Double#MIN_VALUE} and {@code direction}
1474 * has a value such that the result should have a smaller
1475 * magnitude, then a zero with the same sign as {@code start}
1476 * is returned.
1477 *
1478 * <li> If {@code start} is infinite and
1479 * {@code direction} has a value such that the result should
1480 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1481 * same sign as {@code start} is returned.
1482 *
1483 * <li> If {@code start} is equal to ±
1484 * {@link Double#MAX_VALUE} and {@code direction} has a
1485 * value such that the result should have a larger magnitude, an
1486 * infinity with same sign as {@code start} is returned.
1487 * </ul>
1488 *
1489 * @param start starting floating-point value
1490 * @param direction value indicating which of
1491 * {@code start}'s neighbors or {@code start} should
1492 * be returned
1493 * @return The floating-point number adjacent to {@code start} in the
1494 * direction of {@code direction}.
1495 * @since 1.6
1496 */
1497 public static double nextAfter(double start, double direction) {
1498 return Math.nextAfter(start, direction);
1499 }
1500
1501 /**
1502 * Returns the floating-point number adjacent to the first
1503 * argument in the direction of the second argument. If both
1504 * arguments compare as equal a value equivalent to the second argument
1505 * is returned.
1506 *
1507 * <p>Special cases:
1508 * <ul>
1509 * <li> If either argument is a NaN, then NaN is returned.
1510 *
1511 * <li> If both arguments are signed zeros, a value equivalent
1512 * to {@code direction} is returned.
1513 *
1514 * <li> If {@code start} is
1515 * ±{@link Float#MIN_VALUE} and {@code direction}
1516 * has a value such that the result should have a smaller
1517 * magnitude, then a zero with the same sign as {@code start}
1518 * is returned.
1519 *
1520 * <li> If {@code start} is infinite and
1521 * {@code direction} has a value such that the result should
1522 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1523 * same sign as {@code start} is returned.
1524 *
1525 * <li> If {@code start} is equal to ±
1526 * {@link Float#MAX_VALUE} and {@code direction} has a
1527 * value such that the result should have a larger magnitude, an
1528 * infinity with same sign as {@code start} is returned.
1529 * </ul>
1530 *
1531 * @param start starting floating-point value
1532 * @param direction value indicating which of
1533 * {@code start}'s neighbors or {@code start} should
1534 * be returned
1535 * @return The floating-point number adjacent to {@code start} in the
1536 * direction of {@code direction}.
1537 * @since 1.6
1538 */
1539 public static float nextAfter(float start, double direction) {
1540 return Math.nextAfter(start, direction);
1541 }
1542
1543 /**
1544 * Returns the floating-point value adjacent to {@code d} in
1545 * the direction of positive infinity. This method is
1546 * semantically equivalent to {@code nextAfter(d,
1547 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1548 * implementation may run faster than its equivalent
1549 * {@code nextAfter} call.
1550 *
1551 * <p>Special Cases:
1552 * <ul>
1553 * <li> If the argument is NaN, the result is NaN.
1554 *
1555 * <li> If the argument is positive infinity, the result is
1556 * positive infinity.
1557 *
1558 * <li> If the argument is zero, the result is
1559 * {@link Double#MIN_VALUE}
1560 *
1561 * </ul>
1562 *
1563 * @param d starting floating-point value
1564 * @return The adjacent floating-point value closer to positive
1565 * infinity.
1566 * @since 1.6
1567 */
1568 public static double nextUp(double d) {
1569 return Math.nextUp(d);
1570 }
1571
1572 /**
1573 * Returns the floating-point value adjacent to {@code f} in
1574 * the direction of positive infinity. This method is
1575 * semantically equivalent to {@code nextAfter(f,
1576 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1577 * implementation may run faster than its equivalent
1578 * {@code nextAfter} call.
1579 *
1580 * <p>Special Cases:
1581 * <ul>
1582 * <li> If the argument is NaN, the result is NaN.
1583 *
1584 * <li> If the argument is positive infinity, the result is
1585 * positive infinity.
1586 *
1587 * <li> If the argument is zero, the result is
1588 * {@link Float#MIN_VALUE}
1589 *
1590 * </ul>
1591 *
1592 * @param f starting floating-point value
1593 * @return The adjacent floating-point value closer to positive
1594 * infinity.
1595 * @since 1.6
1596 */
1597 public static float nextUp(float f) {
1598 return Math.nextUp(f);
1599 }
1600
1601 /**
1602 * Returns the floating-point value adjacent to {@code d} in
1603 * the direction of negative infinity. This method is
1604 * semantically equivalent to {@code nextAfter(d,
1605 * Double.NEGATIVE_INFINITY)}; however, a
1606 * {@code nextDown} implementation may run faster than its
1607 * equivalent {@code nextAfter} call.
1608 *
1609 * <p>Special Cases:
1610 * <ul>
1611 * <li> If the argument is NaN, the result is NaN.
1612 *
1613 * <li> If the argument is negative infinity, the result is
1614 * negative infinity.
1615 *
1616 * <li> If the argument is zero, the result is
1617 * {@code -Double.MIN_VALUE}
1618 *
1619 * </ul>
1620 *
1621 * @param d starting floating-point value
1622 * @return The adjacent floating-point value closer to negative
1623 * infinity.
1624 * @since 1.8
1625 */
1626 public static double nextDown(double d) {
1627 return Math.nextDown(d);
1628 }
1629
1630 /**
1631 * Returns the floating-point value adjacent to {@code f} in
1632 * the direction of negative infinity. This method is
1633 * semantically equivalent to {@code nextAfter(f,
1634 * Float.NEGATIVE_INFINITY)}; however, a
1635 * {@code nextDown} implementation may run faster than its
1636 * equivalent {@code nextAfter} call.
1637 *
1638 * <p>Special Cases:
1639 * <ul>
1640 * <li> If the argument is NaN, the result is NaN.
1641 *
1642 * <li> If the argument is negative infinity, the result is
1643 * negative infinity.
1644 *
1645 * <li> If the argument is zero, the result is
1646 * {@code -Float.MIN_VALUE}
1647 *
1648 * </ul>
1649 *
1650 * @param f starting floating-point value
1651 * @return The adjacent floating-point value closer to negative
1652 * infinity.
1653 * @since 1.8
1654 */
1655 public static float nextDown(float f) {
1656 return Math.nextDown(f);
1657 }
1658
1659 /**
1660 * Returns {@code d} ×
1661 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1662 * by a single correctly rounded floating-point multiply to a
1663 * member of the double value set. See the Java
1664 * Language Specification for a discussion of floating-point
1665 * value sets. If the exponent of the result is between {@link
1666 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1667 * answer is calculated exactly. If the exponent of the result
1668 * would be larger than {@code Double.MAX_EXPONENT}, an
1669 * infinity is returned. Note that if the result is subnormal,
1670 * precision may be lost; that is, when {@code scalb(x, n)}
1671 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1672 * <i>x</i>. When the result is non-NaN, the result has the same
1673 * sign as {@code d}.
1674 *
1675 * <p>Special cases:
1676 * <ul>
1677 * <li> If the first argument is NaN, NaN is returned.
1678 * <li> If the first argument is infinite, then an infinity of the
1679 * same sign is returned.
1680 * <li> If the first argument is zero, then a zero of the same
1681 * sign is returned.
1682 * </ul>
1683 *
1684 * @param d number to be scaled by a power of two.
1685 * @param scaleFactor power of 2 used to scale {@code d}
1686 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1687 * @since 1.6
1688 */
1689 public static double scalb(double d, int scaleFactor) {
1690 return Math.scalb(d, scaleFactor);
1691 }
1692
1693 /**
1694 * Returns {@code f} ×
1695 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1696 * by a single correctly rounded floating-point multiply to a
1697 * member of the float value set. See the Java
1698 * Language Specification for a discussion of floating-point
1699 * value sets. If the exponent of the result is between {@link
1700 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1701 * answer is calculated exactly. If the exponent of the result
1702 * would be larger than {@code Float.MAX_EXPONENT}, an
1703 * infinity is returned. Note that if the result is subnormal,
1704 * precision may be lost; that is, when {@code scalb(x, n)}
1705 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1706 * <i>x</i>. When the result is non-NaN, the result has the same
1707 * sign as {@code f}.
1708 *
1709 * <p>Special cases:
1710 * <ul>
1711 * <li> If the first argument is NaN, NaN is returned.
1712 * <li> If the first argument is infinite, then an infinity of the
1713 * same sign is returned.
1714 * <li> If the first argument is zero, then a zero of the same
1715 * sign is returned.
1716 * </ul>
1717 *
1718 * @param f number to be scaled by a power of two.
1719 * @param scaleFactor power of 2 used to scale {@code f}
1720 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1721 * @since 1.6
1722 */
1723 public static float scalb(float f, int scaleFactor) {
1724 return Math.scalb(f, scaleFactor);
1725 }
1726 }