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