1 /*
2 * Copyright (c) 1999, 2015, 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 double pow(double a, double b) {
647 return FdLibm.Pow.compute(a, b);
648 }
649
650 /**
651 * Returns the closest {@code int} to the argument, with ties
652 * rounding to positive infinity.
653 *
654 * <p>Special cases:
655 * <ul><li>If the argument is NaN, the result is 0.
656 * <li>If the argument is negative infinity or any value less than or
657 * equal to the value of {@code Integer.MIN_VALUE}, the result is
658 * equal to the value of {@code Integer.MIN_VALUE}.
659 * <li>If the argument is positive infinity or any value greater than or
660 * equal to the value of {@code Integer.MAX_VALUE}, the result is
661 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
662 *
663 * @param a a floating-point value to be rounded to an integer.
664 * @return the value of the argument rounded to the nearest
665 * {@code int} value.
666 * @see java.lang.Integer#MAX_VALUE
667 * @see java.lang.Integer#MIN_VALUE
668 */
669 public static int round(float a) {
670 return Math.round(a);
671 }
672
673 /**
674 * Returns the closest {@code long} to the argument, with ties
675 * rounding to positive infinity.
676 *
677 * <p>Special cases:
678 * <ul><li>If the argument is NaN, the result is 0.
679 * <li>If the argument is negative infinity or any value less than or
680 * equal to the value of {@code Long.MIN_VALUE}, the result is
681 * equal to the value of {@code Long.MIN_VALUE}.
682 * <li>If the argument is positive infinity or any value greater than or
683 * equal to the value of {@code Long.MAX_VALUE}, the result is
684 * equal to the value of {@code Long.MAX_VALUE}.</ul>
685 *
686 * @param a a floating-point value to be rounded to a
687 * {@code long}.
688 * @return the value of the argument rounded to the nearest
689 * {@code long} value.
690 * @see java.lang.Long#MAX_VALUE
691 * @see java.lang.Long#MIN_VALUE
692 */
693 public static long round(double a) {
694 return Math.round(a);
695 }
696
697 private static final class RandomNumberGeneratorHolder {
698 static final Random randomNumberGenerator = new Random();
699 }
700
701 /**
702 * Returns a {@code double} value with a positive sign, greater
703 * than or equal to {@code 0.0} and less than {@code 1.0}.
704 * Returned values are chosen pseudorandomly with (approximately)
705 * uniform distribution from that range.
706 *
707 * <p>When this method is first called, it creates a single new
708 * pseudorandom-number generator, exactly as if by the expression
709 *
710 * <blockquote>{@code new java.util.Random()}</blockquote>
711 *
712 * This new pseudorandom-number generator is used thereafter for
713 * all calls to this method and is used nowhere else.
714 *
715 * <p>This method is properly synchronized to allow correct use by
716 * more than one thread. However, if many threads need to generate
717 * pseudorandom numbers at a great rate, it may reduce contention
718 * for each thread to have its own pseudorandom-number generator.
719 *
720 * @return a pseudorandom {@code double} greater than or equal
721 * to {@code 0.0} and less than {@code 1.0}.
722 * @see Random#nextDouble()
723 */
724 public static double random() {
725 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
726 }
727
728 /**
729 * Returns the sum of its arguments,
730 * throwing an exception if the result overflows an {@code int}.
731 *
732 * @param x the first value
733 * @param y the second value
734 * @return the result
735 * @throws ArithmeticException if the result overflows an int
736 * @see Math#addExact(int,int)
737 * @since 1.8
738 */
739 public static int addExact(int x, int y) {
740 return Math.addExact(x, y);
741 }
742
743 /**
744 * Returns the sum of its arguments,
745 * throwing an exception if the result overflows a {@code long}.
746 *
747 * @param x the first value
748 * @param y the second value
749 * @return the result
750 * @throws ArithmeticException if the result overflows a long
751 * @see Math#addExact(long,long)
752 * @since 1.8
753 */
754 public static long addExact(long x, long y) {
755 return Math.addExact(x, y);
756 }
757
758 /**
759 * Returns the difference of the arguments,
760 * throwing an exception if the result overflows an {@code int}.
761 *
762 * @param x the first value
763 * @param y the second value to subtract from the first
764 * @return the result
765 * @throws ArithmeticException if the result overflows an int
766 * @see Math#subtractExact(int,int)
767 * @since 1.8
768 */
769 public static int subtractExact(int x, int y) {
770 return Math.subtractExact(x, y);
771 }
772
773 /**
774 * Returns the difference of the arguments,
775 * throwing an exception if the result overflows a {@code long}.
776 *
777 * @param x the first value
778 * @param y the second value to subtract from the first
779 * @return the result
780 * @throws ArithmeticException if the result overflows a long
781 * @see Math#subtractExact(long,long)
782 * @since 1.8
783 */
784 public static long subtractExact(long x, long y) {
785 return Math.subtractExact(x, y);
786 }
787
788 /**
789 * Returns the product of the arguments,
790 * throwing an exception if the result overflows an {@code int}.
791 *
792 * @param x the first value
793 * @param y the second value
794 * @return the result
795 * @throws ArithmeticException if the result overflows an int
796 * @see Math#multiplyExact(int,int)
797 * @since 1.8
798 */
799 public static int multiplyExact(int x, int y) {
800 return Math.multiplyExact(x, y);
801 }
802
803 /**
804 * Returns the product of the arguments,
805 * throwing an exception if the result overflows a {@code long}.
806 *
807 * @param x the first value
808 * @param y the second value
809 * @return the result
810 * @throws ArithmeticException if the result overflows a long
811 * @see Math#multiplyExact(long,long)
812 * @since 1.8
813 */
814 public static long multiplyExact(long x, long y) {
815 return Math.multiplyExact(x, y);
816 }
817
818 /**
819 * Returns the value of the {@code long} argument;
820 * throwing an exception if the value overflows an {@code int}.
821 *
822 * @param value the long value
823 * @return the argument as an int
824 * @throws ArithmeticException if the {@code argument} overflows an int
825 * @see Math#toIntExact(long)
826 * @since 1.8
827 */
828 public static int toIntExact(long value) {
829 return Math.toIntExact(value);
830 }
831
832 /**
833 * Returns the product of the arguments allowing overflowed values within
834 * the range of {@code long}.
835 *
836 * @param x the first value
837 * @param y the second value
838 * @return the result
839 * @see Math#multiplyFull(long,long)
840 * @since 1.9
841 */
842 public static long multiplyFull(int x, int y) {
843 return Math.multiplyFull(x, y);
844 }
845
846 /**
847 * Returns as a {@code long} the most significant 64 bits of the 128-bit
848 * product of two 64-bit factors.
849 *
850 * @param x the first value
851 * @param y the second value
852 * @return the result
853 * @see Math#multiplyHigh(long,long)
854 * @since 1.9
855 */
856 public static long multiplyHigh(long x, long y) {
857 return Math.multiplyHigh(x, y);
858 }
859
860 /**
861 * Returns the largest (closest to positive infinity)
862 * {@code int} value that is less than or equal to the algebraic quotient.
863 * There is one special case, if the dividend is the
864 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
865 * then integer overflow occurs and
866 * the result is equal to the {@code Integer.MIN_VALUE}.
867 * <p>
868 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
869 * a comparison to the integer division {@code /} operator.
870 *
871 * @param x the dividend
872 * @param y the divisor
873 * @return the largest (closest to positive infinity)
874 * {@code int} value that is less than or equal to the algebraic quotient.
875 * @throws ArithmeticException if the divisor {@code y} is zero
876 * @see Math#floorDiv(int, int)
877 * @see Math#floor(double)
878 * @since 1.8
879 */
880 public static int floorDiv(int x, int y) {
881 return Math.floorDiv(x, y);
882 }
883
884 /**
885 * Returns the largest (closest to positive infinity)
886 * {@code long} value that is less than or equal to the algebraic quotient.
887 * There is one special case, if the dividend is the
888 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
889 * then integer overflow occurs and
890 * the result is equal to the {@code Long.MIN_VALUE}.
891 * <p>
892 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
893 * a comparison to the integer division {@code /} operator.
894 *
895 * @param x the dividend
896 * @param y the divisor
897 * @return the largest (closest to positive infinity)
898 * {@code long} value that is less than or equal to the algebraic quotient.
899 * @throws ArithmeticException if the divisor {@code y} is zero
900 * @see Math#floorDiv(long, long)
901 * @see Math#floor(double)
902 * @since 1.8
903 */
904 public static long floorDiv(long x, long y) {
905 return Math.floorDiv(x, y);
906 }
907
908 /**
909 * Returns the floor modulus of the {@code int} arguments.
910 * <p>
911 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
912 * has the same sign as the divisor {@code y}, and
913 * is in the range of {@code -abs(y) < r < +abs(y)}.
914 * <p>
915 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
916 * <ul>
917 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
918 * </ul>
919 * <p>
920 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
921 * a comparison to the {@code %} operator.
922 *
923 * @param x the dividend
924 * @param y the divisor
925 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
926 * @throws ArithmeticException if the divisor {@code y} is zero
927 * @see Math#floorMod(int, int)
928 * @see StrictMath#floorDiv(int, int)
929 * @since 1.8
930 */
931 public static int floorMod(int x, int y) {
932 return Math.floorMod(x , y);
933 }
934 /**
935 * Returns the floor modulus of the {@code long} arguments.
936 * <p>
937 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
938 * has the same sign as the divisor {@code y}, and
939 * is in the range of {@code -abs(y) < r < +abs(y)}.
940 * <p>
941 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
942 * <ul>
943 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
944 * </ul>
945 * <p>
946 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
947 * a comparison to the {@code %} operator.
948 *
949 * @param x the dividend
950 * @param y the divisor
951 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
952 * @throws ArithmeticException if the divisor {@code y} is zero
953 * @see Math#floorMod(long, long)
954 * @see StrictMath#floorDiv(long, long)
955 * @since 1.8
956 */
957 public static long floorMod(long x, long y) {
958 return Math.floorMod(x, y);
959 }
960
961 /**
962 * Returns the absolute value of an {@code int} value.
963 * If the argument is not negative, the argument is returned.
964 * If the argument is negative, the negation of the argument is returned.
965 *
966 * <p>Note that if the argument is equal to the value of
967 * {@link Integer#MIN_VALUE}, the most negative representable
968 * {@code int} value, the result is that same value, which is
969 * negative.
970 *
971 * @param a the argument whose absolute value is to be determined.
972 * @return the absolute value of the argument.
973 */
974 public static int abs(int a) {
975 return Math.abs(a);
976 }
977
978 /**
979 * Returns the absolute value of a {@code long} value.
980 * If the argument is not negative, the argument is returned.
981 * If the argument is negative, the negation of the argument is returned.
982 *
983 * <p>Note that if the argument is equal to the value of
984 * {@link Long#MIN_VALUE}, the most negative representable
985 * {@code long} value, the result is that same value, which
986 * is negative.
987 *
988 * @param a the argument whose absolute value is to be determined.
989 * @return the absolute value of the argument.
990 */
991 public static long abs(long a) {
992 return Math.abs(a);
993 }
994
995 /**
996 * Returns the absolute value of a {@code float} value.
997 * If the argument is not negative, the argument is returned.
998 * If the argument is negative, the negation of the argument is returned.
999 * Special cases:
1000 * <ul><li>If the argument is positive zero or negative zero, the
1001 * result is positive zero.
1002 * <li>If the argument is infinite, the result is positive infinity.
1003 * <li>If the argument is NaN, the result is NaN.</ul>
1004 * In other words, the result is the same as the value of the expression:
1005 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
1006 *
1007 * @param a the argument whose absolute value is to be determined
1008 * @return the absolute value of the argument.
1009 */
1010 public static float abs(float a) {
1011 return Math.abs(a);
1012 }
1013
1014 /**
1015 * Returns the absolute value of a {@code double} value.
1016 * If the argument is not negative, the argument is returned.
1017 * If the argument is negative, the negation of the argument is returned.
1018 * Special cases:
1019 * <ul><li>If the argument is positive zero or negative zero, the result
1020 * is positive zero.
1021 * <li>If the argument is infinite, the result is positive infinity.
1022 * <li>If the argument is NaN, the result is NaN.</ul>
1023 * In other words, the result is the same as the value of the expression:
1024 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
1025 *
1026 * @param a the argument whose absolute value is to be determined
1027 * @return the absolute value of the argument.
1028 */
1029 public static double abs(double a) {
1030 return Math.abs(a);
1031 }
1032
1033 /**
1034 * Returns the greater of two {@code int} values. That is, the
1035 * result is the argument closer to the value of
1036 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1037 * the result is that same value.
1038 *
1039 * @param a an argument.
1040 * @param b another argument.
1041 * @return the larger of {@code a} and {@code b}.
1042 */
1043 @HotSpotIntrinsicCandidate
1044 public static int max(int a, int b) {
1045 return Math.max(a, b);
1046 }
1047
1048 /**
1049 * Returns the greater of two {@code long} values. That is, the
1050 * result is the argument closer to the value of
1051 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1052 * the result is that same value.
1053 *
1054 * @param a an argument.
1055 * @param b another argument.
1056 * @return the larger of {@code a} and {@code b}.
1057 */
1058 public static long max(long a, long b) {
1059 return Math.max(a, b);
1060 }
1061
1062 /**
1063 * Returns the greater of two {@code float} values. That is,
1064 * the result is the argument closer to positive infinity. If the
1065 * arguments have the same value, the result is that same
1066 * value. If either value is NaN, then the result is NaN. Unlike
1067 * the numerical comparison operators, this method considers
1068 * negative zero to be strictly smaller than positive zero. If one
1069 * argument is positive zero and the other negative zero, the
1070 * result is positive zero.
1071 *
1072 * @param a an argument.
1073 * @param b another argument.
1074 * @return the larger of {@code a} and {@code b}.
1075 */
1076 public static float max(float a, float b) {
1077 return Math.max(a, b);
1078 }
1079
1080 /**
1081 * Returns the greater of two {@code double} values. That
1082 * is, the result is the argument closer to positive infinity. If
1083 * the arguments have the same value, the result is that same
1084 * value. If either value is NaN, then the result is NaN. Unlike
1085 * the numerical comparison operators, this method considers
1086 * negative zero to be strictly smaller than positive zero. If one
1087 * argument is positive zero and the other negative zero, the
1088 * result is positive zero.
1089 *
1090 * @param a an argument.
1091 * @param b another argument.
1092 * @return the larger of {@code a} and {@code b}.
1093 */
1094 public static double max(double a, double b) {
1095 return Math.max(a, b);
1096 }
1097
1098 /**
1099 * Returns the smaller of two {@code int} values. That is,
1100 * the result the argument closer to the value of
1101 * {@link Integer#MIN_VALUE}. If the arguments have the same
1102 * value, the result is that same value.
1103 *
1104 * @param a an argument.
1105 * @param b another argument.
1106 * @return the smaller of {@code a} and {@code b}.
1107 */
1108 @HotSpotIntrinsicCandidate
1109 public static int min(int a, int b) {
1110 return Math.min(a, b);
1111 }
1112
1113 /**
1114 * Returns the smaller of two {@code long} values. That is,
1115 * the result is the argument closer to the value of
1116 * {@link Long#MIN_VALUE}. If the arguments have the same
1117 * value, the result is that same value.
1118 *
1119 * @param a an argument.
1120 * @param b another argument.
1121 * @return the smaller of {@code a} and {@code b}.
1122 */
1123 public static long min(long a, long b) {
1124 return Math.min(a, b);
1125 }
1126
1127 /**
1128 * Returns the smaller of two {@code float} values. That is,
1129 * the result is the value closer to negative infinity. If the
1130 * arguments have the same value, the result is that same
1131 * value. If either value is NaN, then the result is NaN. Unlike
1132 * the numerical comparison operators, this method considers
1133 * negative zero to be strictly smaller than positive zero. If
1134 * one argument is positive zero and the other is negative zero,
1135 * the result is negative zero.
1136 *
1137 * @param a an argument.
1138 * @param b another argument.
1139 * @return the smaller of {@code a} and {@code b.}
1140 */
1141 public static float min(float a, float b) {
1142 return Math.min(a, b);
1143 }
1144
1145 /**
1146 * Returns the smaller of two {@code double} values. That
1147 * is, the result is the value closer to negative infinity. If the
1148 * arguments have the same value, the result is that same
1149 * value. If either value is NaN, then the result is NaN. Unlike
1150 * the numerical comparison operators, this method considers
1151 * negative zero to be strictly smaller than positive zero. If one
1152 * argument is positive zero and the other is negative zero, the
1153 * result is negative zero.
1154 *
1155 * @param a an argument.
1156 * @param b another argument.
1157 * @return the smaller of {@code a} and {@code b}.
1158 */
1159 public static double min(double a, double b) {
1160 return Math.min(a, b);
1161 }
1162
1163 /**
1164 * Returns the size of an ulp of the argument. An ulp, unit in
1165 * the last place, of a {@code double} value is the positive
1166 * distance between this floating-point value and the {@code
1167 * double} value next larger in magnitude. Note that for non-NaN
1168 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1169 *
1170 * <p>Special Cases:
1171 * <ul>
1172 * <li> If the argument is NaN, then the result is NaN.
1173 * <li> If the argument is positive or negative infinity, then the
1174 * result is positive infinity.
1175 * <li> If the argument is positive or negative zero, then the result is
1176 * {@code Double.MIN_VALUE}.
1177 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1178 * the result is equal to 2<sup>971</sup>.
1179 * </ul>
1180 *
1181 * @param d the floating-point value whose ulp is to be returned
1182 * @return the size of an ulp of the argument
1183 * @author Joseph D. Darcy
1184 * @since 1.5
1185 */
1186 public static double ulp(double d) {
1187 return Math.ulp(d);
1188 }
1189
1190 /**
1191 * Returns the size of an ulp of the argument. An ulp, unit in
1192 * the last place, of a {@code float} value is the positive
1193 * distance between this floating-point value and the {@code
1194 * float} value next larger in magnitude. Note that for non-NaN
1195 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1196 *
1197 * <p>Special Cases:
1198 * <ul>
1199 * <li> If the argument is NaN, then the result is NaN.
1200 * <li> If the argument is positive or negative infinity, then the
1201 * result is positive infinity.
1202 * <li> If the argument is positive or negative zero, then the result is
1203 * {@code Float.MIN_VALUE}.
1204 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1205 * the result is equal to 2<sup>104</sup>.
1206 * </ul>
1207 *
1208 * @param f the floating-point value whose ulp is to be returned
1209 * @return the size of an ulp of the argument
1210 * @author Joseph D. Darcy
1211 * @since 1.5
1212 */
1213 public static float ulp(float f) {
1214 return Math.ulp(f);
1215 }
1216
1217 /**
1218 * Returns the signum function of the argument; zero if the argument
1219 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1220 * argument is less than zero.
1221 *
1222 * <p>Special Cases:
1223 * <ul>
1224 * <li> If the argument is NaN, then the result is NaN.
1225 * <li> If the argument is positive zero or negative zero, then the
1226 * result is the same as the argument.
1227 * </ul>
1228 *
1229 * @param d the floating-point value whose signum is to be returned
1230 * @return the signum function of the argument
1231 * @author Joseph D. Darcy
1232 * @since 1.5
1233 */
1234 public static double signum(double d) {
1235 return Math.signum(d);
1236 }
1237
1238 /**
1239 * Returns the signum function of the argument; zero if the argument
1240 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1241 * argument is less than zero.
1242 *
1243 * <p>Special Cases:
1244 * <ul>
1245 * <li> If the argument is NaN, then the result is NaN.
1246 * <li> If the argument is positive zero or negative zero, then the
1247 * result is the same as the argument.
1248 * </ul>
1249 *
1250 * @param f the floating-point value whose signum is to be returned
1251 * @return the signum function of the argument
1252 * @author Joseph D. Darcy
1253 * @since 1.5
1254 */
1255 public static float signum(float f) {
1256 return Math.signum(f);
1257 }
1258
1259 /**
1260 * Returns the hyperbolic sine of a {@code double} value.
1261 * The hyperbolic sine of <i>x</i> is defined to be
1262 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1263 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1264 *
1265 * <p>Special cases:
1266 * <ul>
1267 *
1268 * <li>If the argument is NaN, then the result is NaN.
1269 *
1270 * <li>If the argument is infinite, then the result is an infinity
1271 * with the same sign as the argument.
1272 *
1273 * <li>If the argument is zero, then the result is a zero with the
1274 * same sign as the argument.
1275 *
1276 * </ul>
1277 *
1278 * @param x The number whose hyperbolic sine is to be returned.
1279 * @return The hyperbolic sine of {@code x}.
1280 * @since 1.5
1281 */
1282 public static native double sinh(double x);
1283
1284 /**
1285 * Returns the hyperbolic cosine of a {@code double} value.
1286 * The hyperbolic cosine of <i>x</i> is defined to be
1287 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1288 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1289 *
1290 * <p>Special cases:
1291 * <ul>
1292 *
1293 * <li>If the argument is NaN, then the result is NaN.
1294 *
1295 * <li>If the argument is infinite, then the result is positive
1296 * infinity.
1297 *
1298 * <li>If the argument is zero, then the result is {@code 1.0}.
1299 *
1300 * </ul>
1301 *
1302 * @param x The number whose hyperbolic cosine is to be returned.
1303 * @return The hyperbolic cosine of {@code x}.
1304 * @since 1.5
1305 */
1306 public static native double cosh(double x);
1307
1308 /**
1309 * Returns the hyperbolic tangent of a {@code double} value.
1310 * The hyperbolic tangent of <i>x</i> is defined to be
1311 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1312 * in other words, {@linkplain Math#sinh
1313 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1314 * that the absolute value of the exact tanh is always less than
1315 * 1.
1316 *
1317 * <p>Special cases:
1318 * <ul>
1319 *
1320 * <li>If the argument is NaN, then the result is NaN.
1321 *
1322 * <li>If the argument is zero, then the result is a zero with the
1323 * same sign as the argument.
1324 *
1325 * <li>If the argument is positive infinity, then the result is
1326 * {@code +1.0}.
1327 *
1328 * <li>If the argument is negative infinity, then the result is
1329 * {@code -1.0}.
1330 *
1331 * </ul>
1332 *
1333 * @param x The number whose hyperbolic tangent is to be returned.
1334 * @return The hyperbolic tangent of {@code x}.
1335 * @since 1.5
1336 */
1337 public static native double tanh(double x);
1338
1339 /**
1340 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1341 * without intermediate overflow or underflow.
1342 *
1343 * <p>Special cases:
1344 * <ul>
1345 *
1346 * <li> If either argument is infinite, then the result
1347 * is positive infinity.
1348 *
1349 * <li> If either argument is NaN and neither argument is infinite,
1350 * then the result is NaN.
1351 *
1352 * </ul>
1353 *
1354 * @param x a value
1355 * @param y a value
1356 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1357 * without intermediate overflow or underflow
1358 * @since 1.5
1359 */
1360 public static native double hypot(double x, double y);
1361
1362 /**
1363 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1364 * <i>x</i> near 0, the exact sum of
1365 * {@code expm1(x)} + 1 is much closer to the true
1366 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1367 *
1368 * <p>Special cases:
1369 * <ul>
1370 * <li>If the argument is NaN, the result is NaN.
1371 *
1372 * <li>If the argument is positive infinity, then the result is
1373 * positive infinity.
1374 *
1375 * <li>If the argument is negative infinity, then the result is
1376 * -1.0.
1377 *
1378 * <li>If the argument is zero, then the result is a zero with the
1379 * same sign as the argument.
1380 *
1381 * </ul>
1382 *
1383 * @param x the exponent to raise <i>e</i> to in the computation of
1384 * <i>e</i><sup>{@code x}</sup> -1.
1385 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1386 * @since 1.5
1387 */
1388 public static native double expm1(double x);
1389
1390 /**
1391 * Returns the natural logarithm of the sum of the argument and 1.
1392 * Note that for small values {@code x}, the result of
1393 * {@code log1p(x)} is much closer to the true result of ln(1
1394 * + {@code x}) than the floating-point evaluation of
1395 * {@code log(1.0+x)}.
1396 *
1397 * <p>Special cases:
1398 * <ul>
1399 *
1400 * <li>If the argument is NaN or less than -1, then the result is
1401 * NaN.
1402 *
1403 * <li>If the argument is positive infinity, then the result is
1404 * positive infinity.
1405 *
1406 * <li>If the argument is negative one, then the result is
1407 * negative infinity.
1408 *
1409 * <li>If the argument is zero, then the result is a zero with the
1410 * same sign as the argument.
1411 *
1412 * </ul>
1413 *
1414 * @param x a value
1415 * @return the value ln({@code x} + 1), the natural
1416 * log of {@code x} + 1
1417 * @since 1.5
1418 */
1419 public static native double log1p(double x);
1420
1421 /**
1422 * Returns the first floating-point argument with the sign of the
1423 * second floating-point argument. For this method, a NaN
1424 * {@code sign} argument is always treated as if it were
1425 * positive.
1426 *
1427 * @param magnitude the parameter providing the magnitude of the result
1428 * @param sign the parameter providing the sign of the result
1429 * @return a value with the magnitude of {@code magnitude}
1430 * and the sign of {@code sign}.
1431 * @since 1.6
1432 */
1433 public static double copySign(double magnitude, double sign) {
1434 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1435 }
1436
1437 /**
1438 * Returns the first floating-point argument with the sign of the
1439 * second floating-point argument. For this method, a NaN
1440 * {@code sign} argument is always treated as if it were
1441 * positive.
1442 *
1443 * @param magnitude the parameter providing the magnitude of the result
1444 * @param sign the parameter providing the sign of the result
1445 * @return a value with the magnitude of {@code magnitude}
1446 * and the sign of {@code sign}.
1447 * @since 1.6
1448 */
1449 public static float copySign(float magnitude, float sign) {
1450 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1451 }
1452 /**
1453 * Returns the unbiased exponent used in the representation of a
1454 * {@code float}. Special cases:
1455 *
1456 * <ul>
1457 * <li>If the argument is NaN or infinite, then the result is
1458 * {@link Float#MAX_EXPONENT} + 1.
1459 * <li>If the argument is zero or subnormal, then the result is
1460 * {@link Float#MIN_EXPONENT} -1.
1461 * </ul>
1462 * @param f a {@code float} value
1463 * @return the unbiased exponent of the argument
1464 * @since 1.6
1465 */
1466 public static int getExponent(float f) {
1467 return Math.getExponent(f);
1468 }
1469
1470 /**
1471 * Returns the unbiased exponent used in the representation of a
1472 * {@code double}. Special cases:
1473 *
1474 * <ul>
1475 * <li>If the argument is NaN or infinite, then the result is
1476 * {@link Double#MAX_EXPONENT} + 1.
1477 * <li>If the argument is zero or subnormal, then the result is
1478 * {@link Double#MIN_EXPONENT} -1.
1479 * </ul>
1480 * @param d a {@code double} value
1481 * @return the unbiased exponent of the argument
1482 * @since 1.6
1483 */
1484 public static int getExponent(double d) {
1485 return Math.getExponent(d);
1486 }
1487
1488 /**
1489 * Returns the floating-point number adjacent to the first
1490 * argument in the direction of the second argument. If both
1491 * arguments compare as equal the second argument is returned.
1492 *
1493 * <p>Special cases:
1494 * <ul>
1495 * <li> If either argument is a NaN, then NaN is returned.
1496 *
1497 * <li> If both arguments are signed zeros, {@code direction}
1498 * is returned unchanged (as implied by the requirement of
1499 * returning the second argument if the arguments compare as
1500 * equal).
1501 *
1502 * <li> If {@code start} is
1503 * ±{@link Double#MIN_VALUE} and {@code direction}
1504 * has a value such that the result should have a smaller
1505 * magnitude, then a zero with the same sign as {@code start}
1506 * is returned.
1507 *
1508 * <li> If {@code start} is infinite and
1509 * {@code direction} has a value such that the result should
1510 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1511 * same sign as {@code start} is returned.
1512 *
1513 * <li> If {@code start} is equal to ±
1514 * {@link Double#MAX_VALUE} and {@code direction} has a
1515 * value such that the result should have a larger magnitude, an
1516 * infinity with same sign as {@code start} is returned.
1517 * </ul>
1518 *
1519 * @param start starting floating-point value
1520 * @param direction value indicating which of
1521 * {@code start}'s neighbors or {@code start} should
1522 * be returned
1523 * @return The floating-point number adjacent to {@code start} in the
1524 * direction of {@code direction}.
1525 * @since 1.6
1526 */
1527 public static double nextAfter(double start, double direction) {
1528 return Math.nextAfter(start, direction);
1529 }
1530
1531 /**
1532 * Returns the floating-point number adjacent to the first
1533 * argument in the direction of the second argument. If both
1534 * arguments compare as equal a value equivalent to the second argument
1535 * is returned.
1536 *
1537 * <p>Special cases:
1538 * <ul>
1539 * <li> If either argument is a NaN, then NaN is returned.
1540 *
1541 * <li> If both arguments are signed zeros, a value equivalent
1542 * to {@code direction} is returned.
1543 *
1544 * <li> If {@code start} is
1545 * ±{@link Float#MIN_VALUE} and {@code direction}
1546 * has a value such that the result should have a smaller
1547 * magnitude, then a zero with the same sign as {@code start}
1548 * is returned.
1549 *
1550 * <li> If {@code start} is infinite and
1551 * {@code direction} has a value such that the result should
1552 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1553 * same sign as {@code start} is returned.
1554 *
1555 * <li> If {@code start} is equal to ±
1556 * {@link Float#MAX_VALUE} and {@code direction} has a
1557 * value such that the result should have a larger magnitude, an
1558 * infinity with same sign as {@code start} is returned.
1559 * </ul>
1560 *
1561 * @param start starting floating-point value
1562 * @param direction value indicating which of
1563 * {@code start}'s neighbors or {@code start} should
1564 * be returned
1565 * @return The floating-point number adjacent to {@code start} in the
1566 * direction of {@code direction}.
1567 * @since 1.6
1568 */
1569 public static float nextAfter(float start, double direction) {
1570 return Math.nextAfter(start, direction);
1571 }
1572
1573 /**
1574 * Returns the floating-point value adjacent to {@code d} in
1575 * the direction of positive infinity. This method is
1576 * semantically equivalent to {@code nextAfter(d,
1577 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1578 * implementation may run faster than its equivalent
1579 * {@code nextAfter} call.
1580 *
1581 * <p>Special Cases:
1582 * <ul>
1583 * <li> If the argument is NaN, the result is NaN.
1584 *
1585 * <li> If the argument is positive infinity, the result is
1586 * positive infinity.
1587 *
1588 * <li> If the argument is zero, the result is
1589 * {@link Double#MIN_VALUE}
1590 *
1591 * </ul>
1592 *
1593 * @param d starting floating-point value
1594 * @return The adjacent floating-point value closer to positive
1595 * infinity.
1596 * @since 1.6
1597 */
1598 public static double nextUp(double d) {
1599 return Math.nextUp(d);
1600 }
1601
1602 /**
1603 * Returns the floating-point value adjacent to {@code f} in
1604 * the direction of positive infinity. This method is
1605 * semantically equivalent to {@code nextAfter(f,
1606 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1607 * implementation may run faster than its equivalent
1608 * {@code nextAfter} call.
1609 *
1610 * <p>Special Cases:
1611 * <ul>
1612 * <li> If the argument is NaN, the result is NaN.
1613 *
1614 * <li> If the argument is positive infinity, the result is
1615 * positive infinity.
1616 *
1617 * <li> If the argument is zero, the result is
1618 * {@link Float#MIN_VALUE}
1619 *
1620 * </ul>
1621 *
1622 * @param f starting floating-point value
1623 * @return The adjacent floating-point value closer to positive
1624 * infinity.
1625 * @since 1.6
1626 */
1627 public static float nextUp(float f) {
1628 return Math.nextUp(f);
1629 }
1630
1631 /**
1632 * Returns the floating-point value adjacent to {@code d} in
1633 * the direction of negative infinity. This method is
1634 * semantically equivalent to {@code nextAfter(d,
1635 * Double.NEGATIVE_INFINITY)}; however, a
1636 * {@code nextDown} implementation may run faster than its
1637 * equivalent {@code nextAfter} call.
1638 *
1639 * <p>Special Cases:
1640 * <ul>
1641 * <li> If the argument is NaN, the result is NaN.
1642 *
1643 * <li> If the argument is negative infinity, the result is
1644 * negative infinity.
1645 *
1646 * <li> If the argument is zero, the result is
1647 * {@code -Double.MIN_VALUE}
1648 *
1649 * </ul>
1650 *
1651 * @param d starting floating-point value
1652 * @return The adjacent floating-point value closer to negative
1653 * infinity.
1654 * @since 1.8
1655 */
1656 public static double nextDown(double d) {
1657 return Math.nextDown(d);
1658 }
1659
1660 /**
1661 * Returns the floating-point value adjacent to {@code f} in
1662 * the direction of negative infinity. This method is
1663 * semantically equivalent to {@code nextAfter(f,
1664 * Float.NEGATIVE_INFINITY)}; however, a
1665 * {@code nextDown} implementation may run faster than its
1666 * equivalent {@code nextAfter} call.
1667 *
1668 * <p>Special Cases:
1669 * <ul>
1670 * <li> If the argument is NaN, the result is NaN.
1671 *
1672 * <li> If the argument is negative infinity, the result is
1673 * negative infinity.
1674 *
1675 * <li> If the argument is zero, the result is
1676 * {@code -Float.MIN_VALUE}
1677 *
1678 * </ul>
1679 *
1680 * @param f starting floating-point value
1681 * @return The adjacent floating-point value closer to negative
1682 * infinity.
1683 * @since 1.8
1684 */
1685 public static float nextDown(float f) {
1686 return Math.nextDown(f);
1687 }
1688
1689 /**
1690 * Returns {@code d} ×
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 double 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 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1697 * answer is calculated exactly. If the exponent of the result
1698 * would be larger than {@code Double.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 d}.
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 d number to be scaled by a power of two.
1715 * @param scaleFactor power of 2 used to scale {@code d}
1716 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1717 * @since 1.6
1718 */
1719 public static double scalb(double d, int scaleFactor) {
1720 return Math.scalb(d, scaleFactor);
1721 }
1722
1723 /**
1724 * Returns {@code f} ×
1725 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1726 * by a single correctly rounded floating-point multiply to a
1727 * member of the float value set. See the Java
1728 * Language Specification for a discussion of floating-point
1729 * value sets. If the exponent of the result is between {@link
1730 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1731 * answer is calculated exactly. If the exponent of the result
1732 * would be larger than {@code Float.MAX_EXPONENT}, an
1733 * infinity is returned. Note that if the result is subnormal,
1734 * precision may be lost; that is, when {@code scalb(x, n)}
1735 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1736 * <i>x</i>. When the result is non-NaN, the result has the same
1737 * sign as {@code f}.
1738 *
1739 * <p>Special cases:
1740 * <ul>
1741 * <li> If the first argument is NaN, NaN is returned.
1742 * <li> If the first argument is infinite, then an infinity of the
1743 * same sign is returned.
1744 * <li> If the first argument is zero, then a zero of the same
1745 * sign is returned.
1746 * </ul>
1747 *
1748 * @param f number to be scaled by a power of two.
1749 * @param scaleFactor power of 2 used to scale {@code f}
1750 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1751 * @since 1.6
1752 */
1753 public static float scalb(float f, int scaleFactor) {
1754 return Math.scalb(f, scaleFactor);
1755 }
1756 }