1 /*
2 * Copyright (c) 1999, 2020, 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 jdk.internal.math.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="https://www.netlib.org/fdlibm/">{@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}, {@code toIntExact},
71 * {@code incrementExact}, {@code decrementExact} and {@code negateExact}
72 * throw an {@code ArithmeticException} when the results overflow.
73 * For the arithmetic operations divide and absolute value, overflow
74 * occurs only with a specific minimum or maximum value and
75 * should be checked against 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 double exp(double a) {
231 return FdLibm.Exp.compute(a);
232 }
233
234 /**
235 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
236 * value. Special cases:
237 * <ul><li>If the argument is NaN or less than zero, then the result
238 * is NaN.
239 * <li>If the argument is positive infinity, then the result is
240 * positive infinity.
241 * <li>If the argument is positive zero or negative zero, then the
242 * result is negative infinity.</ul>
243 *
244 * @param a a value
245 * @return the value ln {@code a}, the natural logarithm of
246 * {@code a}.
247 */
248 public static native double log(double a);
249
250 /**
251 * Returns the base 10 logarithm of a {@code double} value.
252 * Special cases:
253 *
254 * <ul><li>If the argument is NaN or less than zero, then the result
255 * is NaN.
256 * <li>If the argument is positive infinity, then the result is
257 * positive infinity.
258 * <li>If the argument is positive zero or negative zero, then the
259 * result is negative infinity.
260 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
261 * integer <i>n</i>, then the result is <i>n</i>.
262 * </ul>
263 *
264 * @param a a value
265 * @return the base 10 logarithm of {@code a}.
266 * @since 1.5
267 */
268 public static native double log10(double a);
269
270 /**
271 * Returns the correctly rounded positive square root of a
272 * {@code double} value.
273 * Special cases:
274 * <ul><li>If the argument is NaN or less than zero, then the result
275 * is NaN.
276 * <li>If the argument is positive infinity, then the result is positive
277 * infinity.
278 * <li>If the argument is positive zero or negative zero, then the
279 * result is the same as the argument.</ul>
280 * Otherwise, the result is the {@code double} value closest to
281 * the true mathematical square root of the argument value.
282 *
283 * @param a a value.
284 * @return the positive square root of {@code a}.
285 */
286 @HotSpotIntrinsicCandidate
287 public static native double sqrt(double a);
288
289 /**
290 * Returns the cube root of a {@code double} value. For
291 * positive finite {@code x}, {@code cbrt(-x) ==
292 * -cbrt(x)}; that is, the cube root of a negative value is
293 * the negative of the cube root of that value's magnitude.
294 * Special cases:
295 *
296 * <ul>
297 *
298 * <li>If the argument is NaN, then the result is NaN.
299 *
300 * <li>If the argument is infinite, then the result is an infinity
301 * with the same sign as the argument.
302 *
303 * <li>If the argument is zero, then the result is a zero with the
304 * same sign as the argument.
305 *
306 * </ul>
307 *
308 * @param a a value.
309 * @return the cube root of {@code a}.
310 * @since 1.5
311 */
312 public static double cbrt(double a) {
313 return FdLibm.Cbrt.compute(a);
314 }
315
316 /**
317 * Computes the remainder operation on two arguments as prescribed
318 * by the IEEE 754 standard.
319 * The remainder value is mathematically equal to
320 * <code>f1 - f2</code> × <i>n</i>,
321 * where <i>n</i> is the mathematical integer closest to the exact
322 * mathematical value of the quotient {@code f1/f2}, and if two
323 * mathematical integers are equally close to {@code f1/f2},
324 * then <i>n</i> is the integer that is even. If the remainder is
325 * zero, its sign is the same as the sign of the first argument.
326 * Special cases:
327 * <ul><li>If either argument is NaN, or the first argument is infinite,
328 * or the second argument is positive zero or negative zero, then the
329 * result is NaN.
330 * <li>If the first argument is finite and the second argument is
331 * infinite, then the result is the same as the first argument.</ul>
332 *
333 * @param f1 the dividend.
334 * @param f2 the divisor.
335 * @return the remainder when {@code f1} is divided by
336 * {@code f2}.
337 */
338 public static native double IEEEremainder(double f1, double f2);
339
340 /**
341 * Returns the smallest (closest to negative infinity)
342 * {@code double} value that is greater than or equal to the
343 * argument and is equal to a mathematical integer. Special cases:
344 * <ul><li>If the argument value is already equal to a
345 * mathematical integer, then the result is the same as the
346 * argument. <li>If the argument is NaN or an infinity or
347 * positive zero or negative zero, then the result is the same as
348 * the argument. <li>If the argument value is less than zero but
349 * greater than -1.0, then the result is negative zero.</ul> Note
350 * that the value of {@code StrictMath.ceil(x)} is exactly the
351 * value of {@code -StrictMath.floor(-x)}.
352 *
353 * @param a a value.
354 * @return the smallest (closest to negative infinity)
355 * floating-point value that is greater than or equal to
356 * the argument and is equal to a mathematical integer.
357 */
358 public static double ceil(double a) {
359 return floorOrCeil(a, -0.0, 1.0, 1.0);
360 }
361
362 /**
363 * Returns the largest (closest to positive infinity)
364 * {@code double} value that is less than or equal to the
365 * argument and is equal to a mathematical integer. Special cases:
366 * <ul><li>If the argument value is already equal to a
367 * mathematical integer, then the result is the same as the
368 * argument. <li>If the argument is NaN or an infinity or
369 * positive zero or negative zero, then the result is the same as
370 * the argument.</ul>
371 *
372 * @param a a value.
373 * @return the largest (closest to positive infinity)
374 * floating-point value that less than or equal to the argument
375 * and is equal to a mathematical integer.
376 */
377 public static double floor(double a) {
378 return floorOrCeil(a, -1.0, 0.0, -1.0);
379 }
380
381 /**
382 * Internal method to share logic between floor and ceil.
383 *
384 * @param a the value to be floored or ceiled
385 * @param negativeBoundary result for values in (-1, 0)
386 * @param positiveBoundary result for values in (0, 1)
387 * @param increment value to add when the argument is non-integral
388 */
389 private static double floorOrCeil(double a,
390 double negativeBoundary,
391 double positiveBoundary,
392 double sign) {
393 int exponent = Math.getExponent(a);
394
395 if (exponent < 0) {
396 /*
397 * Absolute value of argument is less than 1.
398 * floorOrceil(-0.0) => -0.0
399 * floorOrceil(+0.0) => +0.0
400 */
401 return ((a == 0.0) ? a :
402 ( (a < 0.0) ? negativeBoundary : positiveBoundary) );
403 } else if (exponent >= 52) {
404 /*
405 * Infinity, NaN, or a value so large it must be integral.
406 */
407 return a;
408 }
409 // Else the argument is either an integral value already XOR it
410 // has to be rounded to one.
411 assert exponent >= 0 && exponent <= 51;
412
413 long doppel = Double.doubleToRawLongBits(a);
414 long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
415
416 if ( (mask & doppel) == 0L )
417 return a; // integral value
418 else {
419 double result = Double.longBitsToDouble(doppel & (~mask));
420 if (sign*a > 0.0)
421 result = result + sign;
422 return result;
423 }
424 }
425
426 /**
427 * Returns the {@code double} value that is closest in value
428 * to the argument and is equal to a mathematical integer. If two
429 * {@code double} values that are mathematical integers are
430 * equally close to the value of the argument, the result is the
431 * integer value that is even. Special cases:
432 * <ul><li>If the argument value is already equal to a mathematical
433 * integer, then the result is the same as the argument.
434 * <li>If the argument is NaN or an infinity or positive zero or negative
435 * zero, then the result is the same as the argument.</ul>
436 *
437 * @param a a value.
438 * @return the closest floating-point value to {@code a} that is
439 * equal to a mathematical integer.
440 * @author Joseph D. Darcy
441 */
442 public static double rint(double a) {
443 /*
444 * If the absolute value of a is not less than 2^52, it
445 * is either a finite integer (the double format does not have
446 * enough significand bits for a number that large to have any
447 * fractional portion), an infinity, or a NaN. In any of
448 * these cases, rint of the argument is the argument.
449 *
450 * Otherwise, the sum (twoToThe52 + a ) will properly round
451 * away any fractional portion of a since ulp(twoToThe52) ==
452 * 1.0; subtracting out twoToThe52 from this sum will then be
453 * exact and leave the rounded integer portion of a.
454 *
455 * This method does *not* need to be declared strictfp to get
456 * fully reproducible results. Whether or not a method is
457 * declared strictfp can only make a difference in the
458 * returned result if some operation would overflow or
459 * underflow with strictfp semantics. The operation
460 * (twoToThe52 + a ) cannot overflow since large values of a
461 * are screened out; the add cannot underflow since twoToThe52
462 * is too large. The subtraction ((twoToThe52 + a ) -
463 * twoToThe52) will be exact as discussed above and thus
464 * cannot overflow or meaningfully underflow. Finally, the
465 * last multiply in the return statement is by plus or minus
466 * 1.0, which is exact too.
467 */
468 double twoToThe52 = (double)(1L << 52); // 2^52
469 double sign = Math.copySign(1.0, a); // preserve sign info
470 a = Math.abs(a);
471
472 if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
473 a = ((twoToThe52 + a ) - twoToThe52);
474 }
475
476 return sign * a; // restore original sign
477 }
478
479 /**
480 * Returns the angle <i>theta</i> from the conversion of rectangular
481 * coordinates ({@code x}, {@code y}) to polar
482 * coordinates (r, <i>theta</i>).
483 * This method computes the phase <i>theta</i> by computing an arc tangent
484 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
485 * cases:
486 * <ul><li>If either argument is NaN, then the result is NaN.
487 * <li>If the first argument is positive zero and the second argument
488 * is positive, or the first argument is positive and finite and the
489 * second argument is positive infinity, then the result is positive
490 * zero.
491 * <li>If the first argument is negative zero and the second argument
492 * is positive, or the first argument is negative and finite and the
493 * second argument is positive infinity, then the result is negative zero.
494 * <li>If the first argument is positive zero and the second argument
495 * is negative, or the first argument is positive 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 negative zero and the second argument
499 * is negative, or the first argument is negative and finite and the
500 * second argument is negative infinity, then the result is the
501 * {@code double} value closest to -<i>pi</i>.
502 * <li>If the first argument is positive and the second argument is
503 * positive zero or negative zero, or the first argument is positive
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 the first argument is negative and the second argument is
507 * positive zero or negative zero, or the first argument is negative
508 * infinity and the second argument is finite, then the result is the
509 * {@code double} value closest to -<i>pi</i>/2.
510 * <li>If both arguments are positive infinity, then the result is the
511 * {@code double} value closest to <i>pi</i>/4.
512 * <li>If the first argument is positive infinity and the second argument
513 * is negative infinity, then the result is the {@code double}
514 * value closest to 3*<i>pi</i>/4.
515 * <li>If the first argument is negative infinity and the second argument
516 * is positive infinity, then the result is the {@code double} value
517 * closest to -<i>pi</i>/4.
518 * <li>If both arguments are negative infinity, then the result is the
519 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
520 *
521 * @param y the ordinate coordinate
522 * @param x the abscissa coordinate
523 * @return the <i>theta</i> component of the point
524 * (<i>r</i>, <i>theta</i>)
525 * in polar coordinates that corresponds to the point
526 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
527 */
528 public static native double atan2(double y, double x);
529
530 /**
531 * Returns the value of the first argument raised to the power of the
532 * second argument. Special cases:
533 *
534 * <ul><li>If the second argument is positive or negative zero, then the
535 * result is 1.0.
536 * <li>If the second argument is 1.0, then the result is the same as the
537 * first argument.
538 * <li>If the second argument is NaN, then the result is NaN.
539 * <li>If the first argument is NaN and the second argument is nonzero,
540 * then the result is NaN.
541 *
542 * <li>If
543 * <ul>
544 * <li>the absolute value of the first argument is greater than 1
545 * and the second argument is positive infinity, or
546 * <li>the absolute value of the first argument is less than 1 and
547 * the second argument is negative infinity,
548 * </ul>
549 * then the result is positive infinity.
550 *
551 * <li>If
552 * <ul>
553 * <li>the absolute value of the first argument is greater than 1 and
554 * the second argument is negative infinity, or
555 * <li>the absolute value of the
556 * first argument is less than 1 and the second argument is positive
557 * infinity,
558 * </ul>
559 * then the result is positive zero.
560 *
561 * <li>If the absolute value of the first argument equals 1 and the
562 * second argument is infinite, then the result is NaN.
563 *
564 * <li>If
565 * <ul>
566 * <li>the first argument is positive zero and the second argument
567 * is greater than zero, or
568 * <li>the first argument is positive infinity and the second
569 * argument is less than zero,
570 * </ul>
571 * then the result is positive zero.
572 *
573 * <li>If
574 * <ul>
575 * <li>the first argument is positive zero and the second argument
576 * is less than zero, or
577 * <li>the first argument is positive infinity and the second
578 * argument is greater than zero,
579 * </ul>
580 * then the result is positive infinity.
581 *
582 * <li>If
583 * <ul>
584 * <li>the first argument is negative zero and the second argument
585 * is greater than zero but not a finite odd integer, or
586 * <li>the first argument is negative infinity and the second
587 * argument is less than zero but not a finite odd integer,
588 * </ul>
589 * then the result is positive zero.
590 *
591 * <li>If
592 * <ul>
593 * <li>the first argument is negative zero and the second argument
594 * is a positive finite odd integer, or
595 * <li>the first argument is negative infinity and the second
596 * argument is a negative finite odd integer,
597 * </ul>
598 * then the result is negative zero.
599 *
600 * <li>If
601 * <ul>
602 * <li>the first argument is negative zero and the second argument
603 * is less than zero but not a finite odd integer, or
604 * <li>the first argument is negative infinity and the second
605 * argument is greater than zero but not a finite odd integer,
606 * </ul>
607 * then the result is positive infinity.
608 *
609 * <li>If
610 * <ul>
611 * <li>the first argument is negative zero and the second argument
612 * is a negative finite odd integer, or
613 * <li>the first argument is negative infinity and the second
614 * argument is a positive finite odd integer,
615 * </ul>
616 * then the result is negative infinity.
617 *
618 * <li>If the first argument is finite and less than zero
619 * <ul>
620 * <li> if the second argument is a finite even integer, the
621 * result is equal to the result of raising the absolute value of
622 * the first argument to the power of the second argument
623 *
624 * <li>if the second argument is a finite odd integer, the result
625 * is equal to the negative of the result of raising the absolute
626 * value of the first argument to the power of the second
627 * argument
628 *
629 * <li>if the second argument is finite and not an integer, then
630 * the result is NaN.
631 * </ul>
632 *
633 * <li>If both arguments are integers, then the result is exactly equal
634 * to the mathematical result of raising the first argument to the power
635 * of the second argument if that result can in fact be represented
636 * exactly as a {@code double} value.</ul>
637 *
638 * <p>(In the foregoing descriptions, a floating-point value is
639 * considered to be an integer if and only if it is finite and a
640 * fixed point of the method {@link #ceil ceil} or,
641 * equivalently, a fixed point of the method {@link #floor
642 * floor}. A value is a fixed point of a one-argument
643 * method if and only if the result of applying the method to the
644 * value is equal to the value.)
645 *
646 * @param a base.
647 * @param b the exponent.
648 * @return the value {@code a}<sup>{@code b}</sup>.
649 */
650 public static double pow(double a, double b) {
651 return FdLibm.Pow.compute(a, b);
652 }
653
654 /**
655 * Returns the closest {@code int} to the argument, with ties
656 * rounding to positive infinity.
657 *
658 * <p>Special cases:
659 * <ul><li>If the argument is NaN, the result is 0.
660 * <li>If the argument is negative infinity or any value less than or
661 * equal to the value of {@code Integer.MIN_VALUE}, the result is
662 * equal to the value of {@code Integer.MIN_VALUE}.
663 * <li>If the argument is positive infinity or any value greater than or
664 * equal to the value of {@code Integer.MAX_VALUE}, the result is
665 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
666 *
667 * @param a a floating-point value to be rounded to an integer.
668 * @return the value of the argument rounded to the nearest
669 * {@code int} value.
670 * @see java.lang.Integer#MAX_VALUE
671 * @see java.lang.Integer#MIN_VALUE
672 */
673 public static int round(float a) {
674 return Math.round(a);
675 }
676
677 /**
678 * Returns the closest {@code long} to the argument, with ties
679 * rounding to positive infinity.
680 *
681 * <p>Special cases:
682 * <ul><li>If the argument is NaN, the result is 0.
683 * <li>If the argument is negative infinity or any value less than or
684 * equal to the value of {@code Long.MIN_VALUE}, the result is
685 * equal to the value of {@code Long.MIN_VALUE}.
686 * <li>If the argument is positive infinity or any value greater than or
687 * equal to the value of {@code Long.MAX_VALUE}, the result is
688 * equal to the value of {@code Long.MAX_VALUE}.</ul>
689 *
690 * @param a a floating-point value to be rounded to a
691 * {@code long}.
692 * @return the value of the argument rounded to the nearest
693 * {@code long} value.
694 * @see java.lang.Long#MAX_VALUE
695 * @see java.lang.Long#MIN_VALUE
696 */
697 public static long round(double a) {
698 return Math.round(a);
699 }
700
701 private static final class RandomNumberGeneratorHolder {
702 static final Random randomNumberGenerator = new Random();
703 }
704
705 /**
706 * Returns a {@code double} value with a positive sign, greater
707 * than or equal to {@code 0.0} and less than {@code 1.0}.
708 * Returned values are chosen pseudorandomly with (approximately)
709 * uniform distribution from that range.
710 *
711 * <p>When this method is first called, it creates a single new
712 * pseudorandom-number generator, exactly as if by the expression
713 *
714 * <blockquote>{@code new java.util.Random()}</blockquote>
715 *
716 * This new pseudorandom-number generator is used thereafter for
717 * all calls to this method and is used nowhere else.
718 *
719 * <p>This method is properly synchronized to allow correct use by
720 * more than one thread. However, if many threads need to generate
721 * pseudorandom numbers at a great rate, it may reduce contention
722 * for each thread to have its own pseudorandom-number generator.
723 *
724 * @return a pseudorandom {@code double} greater than or equal
725 * to {@code 0.0} and less than {@code 1.0}.
726 * @see Random#nextDouble()
727 */
728 public static double random() {
729 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
730 }
731
732 /**
733 * Returns the sum of its arguments,
734 * throwing an exception if the result overflows an {@code int}.
735 *
736 * @param x the first value
737 * @param y the second value
738 * @return the result
739 * @throws ArithmeticException if the result overflows an int
740 * @see Math#addExact(int,int)
741 * @since 1.8
742 */
743 public static int addExact(int x, int y) {
744 return Math.addExact(x, y);
745 }
746
747 /**
748 * Returns the sum of its arguments,
749 * throwing an exception if the result overflows a {@code long}.
750 *
751 * @param x the first value
752 * @param y the second value
753 * @return the result
754 * @throws ArithmeticException if the result overflows a long
755 * @see Math#addExact(long,long)
756 * @since 1.8
757 */
758 public static long addExact(long x, long y) {
759 return Math.addExact(x, y);
760 }
761
762 /**
763 * Returns the difference of the arguments,
764 * throwing an exception if the result overflows an {@code int}.
765 *
766 * @param x the first value
767 * @param y the second value to subtract from the first
768 * @return the result
769 * @throws ArithmeticException if the result overflows an int
770 * @see Math#subtractExact(int,int)
771 * @since 1.8
772 */
773 public static int subtractExact(int x, int y) {
774 return Math.subtractExact(x, y);
775 }
776
777 /**
778 * Returns the difference of the arguments,
779 * throwing an exception if the result overflows a {@code long}.
780 *
781 * @param x the first value
782 * @param y the second value to subtract from the first
783 * @return the result
784 * @throws ArithmeticException if the result overflows a long
785 * @see Math#subtractExact(long,long)
786 * @since 1.8
787 */
788 public static long subtractExact(long x, long y) {
789 return Math.subtractExact(x, y);
790 }
791
792 /**
793 * Returns the product of the arguments,
794 * throwing an exception if the result overflows an {@code int}.
795 *
796 * @param x the first value
797 * @param y the second value
798 * @return the result
799 * @throws ArithmeticException if the result overflows an int
800 * @see Math#multiplyExact(int,int)
801 * @since 1.8
802 */
803 public static int multiplyExact(int x, int y) {
804 return Math.multiplyExact(x, y);
805 }
806
807 /**
808 * Returns the product of the arguments, throwing an exception if the result
809 * overflows a {@code long}.
810 *
811 * @param x the first value
812 * @param y the second value
813 * @return the result
814 * @throws ArithmeticException if the result overflows a long
815 * @see Math#multiplyExact(long,int)
816 * @since 9
817 */
818 public static long multiplyExact(long x, int y) {
819 return Math.multiplyExact(x, y);
820 }
821
822 /**
823 * Returns the product of the arguments,
824 * throwing an exception if the result overflows a {@code long}.
825 *
826 * @param x the first value
827 * @param y the second value
828 * @return the result
829 * @throws ArithmeticException if the result overflows a long
830 * @see Math#multiplyExact(long,long)
831 * @since 1.8
832 */
833 public static long multiplyExact(long x, long y) {
834 return Math.multiplyExact(x, y);
835 }
836
837 /**
838 * Returns the argument incremented by one,
839 * throwing an exception if the result overflows an {@code int}.
840 * The overflow only occurs for {@linkplain Integer#MAX_VALUE the maximum value}.
841 *
842 * @param a the value to increment
843 * @return the result
844 * @throws ArithmeticException if the result overflows an int
845 * @see Math#incrementExact(int)
846 * @since 14
847 */
848 public static int incrementExact(int a) {
849 return Math.incrementExact(a);
850 }
851
852 /**
853 * Returns the argument incremented by one,
854 * throwing an exception if the result overflows a {@code long}.
855 * The overflow only occurs for {@linkplain Long#MAX_VALUE the maximum value}.
856 *
857 * @param a the value to increment
858 * @return the result
859 * @throws ArithmeticException if the result overflows a long
860 * @see Math#incrementExact(long)
861 * @since 14
862 */
863 public static long incrementExact(long a) {
864 return Math.incrementExact(a);
865 }
866
867 /**
868 * Returns the argument decremented by one,
869 * throwing an exception if the result overflows an {@code int}.
870 * The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
871 *
872 * @param a the value to decrement
873 * @return the result
874 * @throws ArithmeticException if the result overflows an int
875 * @see Math#decrementExact(int)
876 * @since 14
877 */
878 public static int decrementExact(int a) {
879 return Math.decrementExact(a);
880 }
881
882 /**
883 * Returns the argument decremented by one,
884 * throwing an exception if the result overflows a {@code long}.
885 * The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
886 *
887 * @param a the value to decrement
888 * @return the result
889 * @throws ArithmeticException if the result overflows a long
890 * @see Math#decrementExact(long)
891 * @since 14
892 */
893 public static long decrementExact(long a) {
894 return Math.decrementExact(a);
895 }
896
897 /**
898 * Returns the negation of the argument,
899 * throwing an exception if the result overflows an {@code int}.
900 * The overflow only occurs for {@linkplain Integer#MIN_VALUE the minimum value}.
901 *
902 * @param a the value to negate
903 * @return the result
904 * @throws ArithmeticException if the result overflows an int
905 * @see Math#negateExact(int)
906 * @since 14
907 */
908 public static int negateExact(int a) {
909 return Math.negateExact(a);
910 }
911
912 /**
913 * Returns the negation of the argument,
914 * throwing an exception if the result overflows a {@code long}.
915 * The overflow only occurs for {@linkplain Long#MIN_VALUE the minimum value}.
916 *
917 * @param a the value to negate
918 * @return the result
919 * @throws ArithmeticException if the result overflows a long
920 * @see Math#negateExact(long)
921 * @since 14
922 */
923 public static long negateExact(long a) {
924 return Math.negateExact(a);
925 }
926
927 /**
928 * Returns the value of the {@code long} argument, throwing an exception
929 * if the value overflows an {@code int}.
930 *
931 * @param value the long value
932 * @return the argument as an int
933 * @throws ArithmeticException if the {@code argument} overflows an int
934 * @see Math#toIntExact(long)
935 * @since 1.8
936 */
937 public static int toIntExact(long value) {
938 return Math.toIntExact(value);
939 }
940
941 /**
942 * Returns the exact mathematical product of the arguments.
943 *
944 * @param x the first value
945 * @param y the second value
946 * @return the result
947 * @see Math#multiplyFull(int,int)
948 * @since 9
949 */
950 public static long multiplyFull(int x, int y) {
951 return Math.multiplyFull(x, y);
952 }
953
954 /**
955 * Returns as a {@code long} the most significant 64 bits of the 128-bit
956 * product of two 64-bit factors.
957 *
958 * @param x the first value
959 * @param y the second value
960 * @return the result
961 * @see Math#multiplyHigh(long,long)
962 * @since 9
963 */
964 public static long multiplyHigh(long x, long y) {
965 return Math.multiplyHigh(x, y);
966 }
967
968 /**
969 * Returns the largest (closest to positive infinity)
970 * {@code int} value that is less than or equal to the algebraic quotient.
971 * There is one special case, if the dividend is the
972 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
973 * then integer overflow occurs and
974 * the result is equal to the {@code Integer.MIN_VALUE}.
975 * <p>
976 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
977 * a comparison to the integer division {@code /} operator.
978 *
979 * @param x the dividend
980 * @param y the divisor
981 * @return the largest (closest to positive infinity)
982 * {@code int} value that is less than or equal to the algebraic quotient.
983 * @throws ArithmeticException if the divisor {@code y} is zero
984 * @see Math#floorDiv(int, int)
985 * @see Math#floor(double)
986 * @since 1.8
987 */
988 public static int floorDiv(int x, int y) {
989 return Math.floorDiv(x, y);
990 }
991
992 /**
993 * Returns the largest (closest to positive infinity)
994 * {@code long} value that is less than or equal to the algebraic quotient.
995 * There is one special case, if the dividend is the
996 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
997 * then integer overflow occurs and
998 * the result is equal to {@code Long.MIN_VALUE}.
999 * <p>
1000 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
1001 * a comparison to the integer division {@code /} operator.
1002 *
1003 * @param x the dividend
1004 * @param y the divisor
1005 * @return the largest (closest to positive infinity)
1006 * {@code int} value that is less than or equal to the algebraic quotient.
1007 * @throws ArithmeticException if the divisor {@code y} is zero
1008 * @see Math#floorDiv(long, int)
1009 * @see Math#floor(double)
1010 * @since 9
1011 */
1012 public static long floorDiv(long x, int y) {
1013 return Math.floorDiv(x, y);
1014 }
1015
1016 /**
1017 * Returns the largest (closest to positive infinity)
1018 * {@code long} value that is less than or equal to the algebraic quotient.
1019 * There is one special case, if the dividend is the
1020 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
1021 * then integer overflow occurs and
1022 * the result is equal to the {@code Long.MIN_VALUE}.
1023 * <p>
1024 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
1025 * a comparison to the integer division {@code /} operator.
1026 *
1027 * @param x the dividend
1028 * @param y the divisor
1029 * @return the largest (closest to positive infinity)
1030 * {@code long} value that is less than or equal to the algebraic quotient.
1031 * @throws ArithmeticException if the divisor {@code y} is zero
1032 * @see Math#floorDiv(long, long)
1033 * @see Math#floor(double)
1034 * @since 1.8
1035 */
1036 public static long floorDiv(long x, long y) {
1037 return Math.floorDiv(x, y);
1038 }
1039
1040 /**
1041 * Returns the floor modulus of the {@code int} arguments.
1042 * <p>
1043 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1044 * has the same sign as the divisor {@code y}, and
1045 * is in the range of {@code -abs(y) < r < +abs(y)}.
1046 * <p>
1047 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1048 * <ul>
1049 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1050 * </ul>
1051 * <p>
1052 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
1053 * a comparison to the {@code %} operator.
1054 *
1055 * @param x the dividend
1056 * @param y the divisor
1057 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1058 * @throws ArithmeticException if the divisor {@code y} is zero
1059 * @see Math#floorMod(int, int)
1060 * @see StrictMath#floorDiv(int, int)
1061 * @since 1.8
1062 */
1063 public static int floorMod(int x, int y) {
1064 return Math.floorMod(x , y);
1065 }
1066
1067 /**
1068 * Returns the floor modulus of the {@code long} and {@code int} arguments.
1069 * <p>
1070 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1071 * has the same sign as the divisor {@code y}, and
1072 * is in the range of {@code -abs(y) < r < +abs(y)}.
1073 *
1074 * <p>
1075 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1076 * <ul>
1077 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1078 * </ul>
1079 * <p>
1080 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
1081 * a comparison to the {@code %} operator.
1082 *
1083 * @param x the dividend
1084 * @param y the divisor
1085 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1086 * @throws ArithmeticException if the divisor {@code y} is zero
1087 * @see Math#floorMod(long, int)
1088 * @see StrictMath#floorDiv(long, int)
1089 * @since 9
1090 */
1091 public static int floorMod(long x, int y) {
1092 return Math.floorMod(x , y);
1093 }
1094
1095 /**
1096 * Returns the floor modulus of the {@code long} arguments.
1097 * <p>
1098 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1099 * has the same sign as the divisor {@code y}, and
1100 * is in the range of {@code -abs(y) < r < +abs(y)}.
1101 * <p>
1102 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1103 * <ul>
1104 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1105 * </ul>
1106 * <p>
1107 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
1108 * a comparison to the {@code %} operator.
1109 *
1110 * @param x the dividend
1111 * @param y the divisor
1112 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1113 * @throws ArithmeticException if the divisor {@code y} is zero
1114 * @see Math#floorMod(long, long)
1115 * @see StrictMath#floorDiv(long, long)
1116 * @since 1.8
1117 */
1118 public static long floorMod(long x, long y) {
1119 return Math.floorMod(x, y);
1120 }
1121
1122 /**
1123 * Returns the absolute value of an {@code int} value.
1124 * If the argument is not negative, the argument is returned.
1125 * If the argument is negative, the negation of the argument is returned.
1126 *
1127 * <p>Note that if the argument is equal to the value of
1128 * {@link Integer#MIN_VALUE}, the most negative representable
1129 * {@code int} value, the result is that same value, which is
1130 * negative.
1131 * In contrast, the {@link StrictMath#absExact(int)} method throws an
1132 * {@code ArithmeticException} for this value.
1133 *
1134 * @param a the argument whose absolute value is to be determined.
1135 * @return the absolute value of the argument.
1136 * @see Math#absExact(int)
1137 */
1138 public static int abs(int a) {
1139 return Math.abs(a);
1140 }
1141
1142 /**
1143 * Returns the mathematical absolute value of an {@code int} value
1144 * if it is exactly representable as an {@code int}, throwing
1145 * {@code ArithmeticException} if the result overflows the
1146 * positive {@code int} range.
1147 *
1148 * <p>Since the range of two's complement integers is asymmetric
1149 * with one additional negative value (JLS {@jls 4.2.1}), the
1150 * mathematical absolute value of {@link Integer#MIN_VALUE}
1151 * overflows the positive {@code int} range, so an exception is
1152 * thrown for that argument.
1153 *
1154 * @param a the argument whose absolute value is to be determined
1155 * @return the absolute value of the argument, unless overflow occurs
1156 * @throws ArithmeticException if the argument is {@link Integer#MIN_VALUE}
1157 * @see Math#abs(int)
1158 * @see Math#absExact(int)
1159 * @since 15
1160 */
1161 public static int absExact(int a) {
1162 return Math.absExact(a);
1163 }
1164
1165 /**
1166 * Returns the absolute value of a {@code long} value.
1167 * If the argument is not negative, the argument is returned.
1168 * If the argument is negative, the negation of the argument is returned.
1169 *
1170 * <p>Note that if the argument is equal to the value of
1171 * {@link Long#MIN_VALUE}, the most negative representable
1172 * {@code long} value, the result is that same value, which
1173 * is negative.
1174 * In contrast, the {@link StrictMath#absExact(long)} method throws an
1175 * {@code ArithmeticException} for this value.
1176 *
1177 * @param a the argument whose absolute value is to be determined.
1178 * @return the absolute value of the argument.
1179 * @see Math#absExact(long)
1180 */
1181 public static long abs(long a) {
1182 return Math.abs(a);
1183 }
1184
1185 /**
1186 * Returns the mathematical absolute value of an {@code long} value
1187 * if it is exactly representable as an {@code long}, throwing
1188 * {@code ArithmeticException} if the result overflows the
1189 * positive {@code long} range.
1190 *
1191 * <p>Since the range of two's complement integers is asymmetric
1192 * with one additional negative value (JLS {@jls 4.2.1}), the
1193 * mathematical absolute value of {@link Long#MIN_VALUE} overflows
1194 * the positive {@code long} range, so an exception is thrown for
1195 * that argument.
1196 *
1197 * @param a the argument whose absolute value is to be determined
1198 * @return the absolute value of the argument, unless overflow occurs
1199 * @throws ArithmeticException if the argument is {@link Long#MIN_VALUE}
1200 * @see Math#abs(long)
1201 * @see Math#absExact(long)
1202 * @since 15
1203 */
1204 public static long absExact(long a) {
1205 return Math.absExact(a);
1206 }
1207
1208 /**
1209 * Returns the absolute value of a {@code float} value.
1210 * If the argument is not negative, the argument is returned.
1211 * If the argument is negative, the negation of the argument is returned.
1212 * Special cases:
1213 * <ul><li>If the argument is positive zero or negative zero, the
1214 * result is positive zero.
1215 * <li>If the argument is infinite, the result is positive infinity.
1216 * <li>If the argument is NaN, the result is NaN.</ul>
1217 *
1218 * @apiNote As implied by the above, one valid implementation of
1219 * this method is given by the expression below which computes a
1220 * {@code float} with the same exponent and significand as the
1221 * argument but with a guaranteed zero sign bit indicating a
1222 * positive value: <br>
1223 * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
1224 *
1225 * @param a the argument whose absolute value is to be determined
1226 * @return the absolute value of the argument.
1227 */
1228 public static float abs(float a) {
1229 return Math.abs(a);
1230 }
1231
1232 /**
1233 * Returns the absolute value of a {@code double} value.
1234 * If the argument is not negative, the argument is returned.
1235 * If the argument is negative, the negation of the argument is returned.
1236 * Special cases:
1237 * <ul><li>If the argument is positive zero or negative zero, the result
1238 * is positive zero.
1239 * <li>If the argument is infinite, the result is positive infinity.
1240 * <li>If the argument is NaN, the result is NaN.</ul>
1241 *
1242 * @apiNote As implied by the above, one valid implementation of
1243 * this method is given by the expression below which computes a
1244 * {@code double} with the same exponent and significand as the
1245 * argument but with a guaranteed zero sign bit indicating a
1246 * positive value: <br>
1247 * {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
1248 *
1249 * @param a the argument whose absolute value is to be determined
1250 * @return the absolute value of the argument.
1251 */
1252 public static double abs(double a) {
1253 return Math.abs(a);
1254 }
1255
1256 /**
1257 * Returns the greater of two {@code int} values. That is, the
1258 * result is the argument closer to the value of
1259 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1260 * the result is that same value.
1261 *
1262 * @param a an argument.
1263 * @param b another argument.
1264 * @return the larger of {@code a} and {@code b}.
1265 */
1266 @HotSpotIntrinsicCandidate
1267 public static int max(int a, int b) {
1268 return Math.max(a, b);
1269 }
1270
1271 /**
1272 * Returns the greater of two {@code long} values. That is, the
1273 * result is the argument closer to the value of
1274 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1275 * the result is that same value.
1276 *
1277 * @param a an argument.
1278 * @param b another argument.
1279 * @return the larger of {@code a} and {@code b}.
1280 */
1281 public static long max(long a, long b) {
1282 return Math.max(a, b);
1283 }
1284
1285 /**
1286 * Returns the greater of two {@code float} values. That is,
1287 * the result is the argument closer to positive infinity. If the
1288 * arguments have the same value, the result is that same
1289 * value. If either value is NaN, then the result is NaN. Unlike
1290 * the numerical comparison operators, this method considers
1291 * negative zero to be strictly smaller than positive zero. If one
1292 * argument is positive zero and the other negative zero, the
1293 * result is positive zero.
1294 *
1295 * @param a an argument.
1296 * @param b another argument.
1297 * @return the larger of {@code a} and {@code b}.
1298 */
1299 @HotSpotIntrinsicCandidate
1300 public static float max(float a, float b) {
1301 return Math.max(a, b);
1302 }
1303
1304 /**
1305 * Returns the greater of two {@code double} values. That
1306 * is, the result is the argument closer to positive infinity. If
1307 * the arguments have the same value, the result is that same
1308 * value. If either value is NaN, then the result is NaN. Unlike
1309 * the numerical comparison operators, this method considers
1310 * negative zero to be strictly smaller than positive zero. If one
1311 * argument is positive zero and the other negative zero, the
1312 * result is positive zero.
1313 *
1314 * @param a an argument.
1315 * @param b another argument.
1316 * @return the larger of {@code a} and {@code b}.
1317 */
1318 @HotSpotIntrinsicCandidate
1319 public static double max(double a, double b) {
1320 return Math.max(a, b);
1321 }
1322
1323 /**
1324 * Returns the smaller of two {@code int} values. That is,
1325 * the result the argument closer to the value of
1326 * {@link Integer#MIN_VALUE}. If the arguments have the same
1327 * value, the result is that same value.
1328 *
1329 * @param a an argument.
1330 * @param b another argument.
1331 * @return the smaller of {@code a} and {@code b}.
1332 */
1333 @HotSpotIntrinsicCandidate
1334 public static int min(int a, int b) {
1335 return Math.min(a, b);
1336 }
1337
1338 /**
1339 * Returns the smaller of two {@code long} values. That is,
1340 * the result is the argument closer to the value of
1341 * {@link Long#MIN_VALUE}. If the arguments have the same
1342 * value, the result is that same value.
1343 *
1344 * @param a an argument.
1345 * @param b another argument.
1346 * @return the smaller of {@code a} and {@code b}.
1347 */
1348 public static long min(long a, long b) {
1349 return Math.min(a, b);
1350 }
1351
1352 /**
1353 * Returns the smaller of two {@code float} values. That is,
1354 * the result is the value closer to negative infinity. If the
1355 * arguments have the same value, the result is that same
1356 * value. If either value is NaN, then the result is NaN. Unlike
1357 * the numerical comparison operators, this method considers
1358 * negative zero to be strictly smaller than positive zero. If
1359 * one argument is positive zero and the other is negative zero,
1360 * the result is negative zero.
1361 *
1362 * @param a an argument.
1363 * @param b another argument.
1364 * @return the smaller of {@code a} and {@code b.}
1365 */
1366 @HotSpotIntrinsicCandidate
1367 public static float min(float a, float b) {
1368 return Math.min(a, b);
1369 }
1370
1371 /**
1372 * Returns the smaller of two {@code double} values. That
1373 * is, the result is the value closer to negative infinity. If the
1374 * arguments have the same value, the result is that same
1375 * value. If either value is NaN, then the result is NaN. Unlike
1376 * the numerical comparison operators, this method considers
1377 * negative zero to be strictly smaller than positive zero. If one
1378 * argument is positive zero and the other is negative zero, the
1379 * result is negative zero.
1380 *
1381 * @param a an argument.
1382 * @param b another argument.
1383 * @return the smaller of {@code a} and {@code b}.
1384 */
1385 @HotSpotIntrinsicCandidate
1386 public static double min(double a, double b) {
1387 return Math.min(a, b);
1388 }
1389
1390 /**
1391 * Returns the fused multiply add of the three arguments; that is,
1392 * returns the exact product of the first two arguments summed
1393 * with the third argument and then rounded once to the nearest
1394 * {@code double}.
1395 *
1396 * The rounding is done using the {@linkplain
1397 * java.math.RoundingMode#HALF_EVEN round to nearest even
1398 * rounding mode}.
1399 *
1400 * In contrast, if {@code a * b + c} is evaluated as a regular
1401 * floating-point expression, two rounding errors are involved,
1402 * the first for the multiply operation, the second for the
1403 * addition operation.
1404 *
1405 * <p>Special cases:
1406 * <ul>
1407 * <li> If any argument is NaN, the result is NaN.
1408 *
1409 * <li> If one of the first two arguments is infinite and the
1410 * other is zero, the result is NaN.
1411 *
1412 * <li> If the exact product of the first two arguments is infinite
1413 * (in other words, at least one of the arguments is infinite and
1414 * the other is neither zero nor NaN) and the third argument is an
1415 * infinity of the opposite sign, the result is NaN.
1416 *
1417 * </ul>
1418 *
1419 * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
1420 * result as ({@code a + c}). However,
1421 * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
1422 * same result as ({@code a * b}) since
1423 * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
1424 * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
1425 * equivalent to ({@code a * b}) however.
1426 *
1427 * @apiNote This method corresponds to the fusedMultiplyAdd
1428 * operation defined in IEEE 754-2008.
1429 *
1430 * @param a a value
1431 * @param b a value
1432 * @param c a value
1433 *
1434 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1435 * computed, as if with unlimited range and precision, and rounded
1436 * once to the nearest {@code double} value
1437 *
1438 * @since 9
1439 */
1440 public static double fma(double a, double b, double c) {
1441 return Math.fma(a, b, c);
1442 }
1443
1444 /**
1445 * Returns the fused multiply add of the three arguments; that is,
1446 * returns the exact product of the first two arguments summed
1447 * with the third argument and then rounded once to the nearest
1448 * {@code float}.
1449 *
1450 * The rounding is done using the {@linkplain
1451 * java.math.RoundingMode#HALF_EVEN round to nearest even
1452 * rounding mode}.
1453 *
1454 * In contrast, if {@code a * b + c} is evaluated as a regular
1455 * floating-point expression, two rounding errors are involved,
1456 * the first for the multiply operation, the second for the
1457 * addition operation.
1458 *
1459 * <p>Special cases:
1460 * <ul>
1461 * <li> If any argument is NaN, the result is NaN.
1462 *
1463 * <li> If one of the first two arguments is infinite and the
1464 * other is zero, the result is NaN.
1465 *
1466 * <li> If the exact product of the first two arguments is infinite
1467 * (in other words, at least one of the arguments is infinite and
1468 * the other is neither zero nor NaN) and the third argument is an
1469 * infinity of the opposite sign, the result is NaN.
1470 *
1471 * </ul>
1472 *
1473 * <p>Note that {@code fma(a, 1.0f, c)} returns the same
1474 * result as ({@code a + c}). However,
1475 * {@code fma(a, b, +0.0f)} does <em>not</em> always return the
1476 * same result as ({@code a * b}) since
1477 * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
1478 * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
1479 * equivalent to ({@code a * b}) however.
1480 *
1481 * @apiNote This method corresponds to the fusedMultiplyAdd
1482 * operation defined in IEEE 754-2008.
1483 *
1484 * @param a a value
1485 * @param b a value
1486 * @param c a value
1487 *
1488 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1489 * computed, as if with unlimited range and precision, and rounded
1490 * once to the nearest {@code float} value
1491 *
1492 * @since 9
1493 */
1494 public static float fma(float a, float b, float c) {
1495 return Math.fma(a, b, c);
1496 }
1497
1498 /**
1499 * Returns the size of an ulp of the argument. An ulp, unit in
1500 * the last place, of a {@code double} value is the positive
1501 * distance between this floating-point value and the {@code
1502 * double} value next larger in magnitude. Note that for non-NaN
1503 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1504 *
1505 * <p>Special Cases:
1506 * <ul>
1507 * <li> If the argument is NaN, then the result is NaN.
1508 * <li> If the argument is positive or negative infinity, then the
1509 * result is positive infinity.
1510 * <li> If the argument is positive or negative zero, then the result is
1511 * {@code Double.MIN_VALUE}.
1512 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1513 * the result is equal to 2<sup>971</sup>.
1514 * </ul>
1515 *
1516 * @param d the floating-point value whose ulp is to be returned
1517 * @return the size of an ulp of the argument
1518 * @author Joseph D. Darcy
1519 * @since 1.5
1520 */
1521 public static double ulp(double d) {
1522 return Math.ulp(d);
1523 }
1524
1525 /**
1526 * Returns the size of an ulp of the argument. An ulp, unit in
1527 * the last place, of a {@code float} value is the positive
1528 * distance between this floating-point value and the {@code
1529 * float} value next larger in magnitude. Note that for non-NaN
1530 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1531 *
1532 * <p>Special Cases:
1533 * <ul>
1534 * <li> If the argument is NaN, then the result is NaN.
1535 * <li> If the argument is positive or negative infinity, then the
1536 * result is positive infinity.
1537 * <li> If the argument is positive or negative zero, then the result is
1538 * {@code Float.MIN_VALUE}.
1539 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1540 * the result is equal to 2<sup>104</sup>.
1541 * </ul>
1542 *
1543 * @param f the floating-point value whose ulp is to be returned
1544 * @return the size of an ulp of the argument
1545 * @author Joseph D. Darcy
1546 * @since 1.5
1547 */
1548 public static float ulp(float f) {
1549 return Math.ulp(f);
1550 }
1551
1552 /**
1553 * Returns the signum function of the argument; zero if the argument
1554 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1555 * argument is less than zero.
1556 *
1557 * <p>Special Cases:
1558 * <ul>
1559 * <li> If the argument is NaN, then the result is NaN.
1560 * <li> If the argument is positive zero or negative zero, then the
1561 * result is the same as the argument.
1562 * </ul>
1563 *
1564 * @param d the floating-point value whose signum is to be returned
1565 * @return the signum function of the argument
1566 * @author Joseph D. Darcy
1567 * @since 1.5
1568 */
1569 public static double signum(double d) {
1570 return Math.signum(d);
1571 }
1572
1573 /**
1574 * Returns the signum function of the argument; zero if the argument
1575 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1576 * argument is less than zero.
1577 *
1578 * <p>Special Cases:
1579 * <ul>
1580 * <li> If the argument is NaN, then the result is NaN.
1581 * <li> If the argument is positive zero or negative zero, then the
1582 * result is the same as the argument.
1583 * </ul>
1584 *
1585 * @param f the floating-point value whose signum is to be returned
1586 * @return the signum function of the argument
1587 * @author Joseph D. Darcy
1588 * @since 1.5
1589 */
1590 public static float signum(float f) {
1591 return Math.signum(f);
1592 }
1593
1594 /**
1595 * Returns the hyperbolic sine of a {@code double} value.
1596 * The hyperbolic sine of <i>x</i> is defined to be
1597 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1598 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1599 *
1600 * <p>Special cases:
1601 * <ul>
1602 *
1603 * <li>If the argument is NaN, then the result is NaN.
1604 *
1605 * <li>If the argument is infinite, then the result is an infinity
1606 * with the same sign as the argument.
1607 *
1608 * <li>If the argument is zero, then the result is a zero with the
1609 * same sign as the argument.
1610 *
1611 * </ul>
1612 *
1613 * @param x The number whose hyperbolic sine is to be returned.
1614 * @return The hyperbolic sine of {@code x}.
1615 * @since 1.5
1616 */
1617 public static native double sinh(double x);
1618
1619 /**
1620 * Returns the hyperbolic cosine of a {@code double} value.
1621 * The hyperbolic cosine of <i>x</i> is defined to be
1622 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1623 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1624 *
1625 * <p>Special cases:
1626 * <ul>
1627 *
1628 * <li>If the argument is NaN, then the result is NaN.
1629 *
1630 * <li>If the argument is infinite, then the result is positive
1631 * infinity.
1632 *
1633 * <li>If the argument is zero, then the result is {@code 1.0}.
1634 *
1635 * </ul>
1636 *
1637 * @param x The number whose hyperbolic cosine is to be returned.
1638 * @return The hyperbolic cosine of {@code x}.
1639 * @since 1.5
1640 */
1641 public static native double cosh(double x);
1642
1643 /**
1644 * Returns the hyperbolic tangent of a {@code double} value.
1645 * The hyperbolic tangent of <i>x</i> is defined to be
1646 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1647 * in other words, {@linkplain Math#sinh
1648 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1649 * that the absolute value of the exact tanh is always less than
1650 * 1.
1651 *
1652 * <p>Special cases:
1653 * <ul>
1654 *
1655 * <li>If the argument is NaN, then the result is NaN.
1656 *
1657 * <li>If the argument is zero, then the result is a zero with the
1658 * same sign as the argument.
1659 *
1660 * <li>If the argument is positive infinity, then the result is
1661 * {@code +1.0}.
1662 *
1663 * <li>If the argument is negative infinity, then the result is
1664 * {@code -1.0}.
1665 *
1666 * </ul>
1667 *
1668 * @param x The number whose hyperbolic tangent is to be returned.
1669 * @return The hyperbolic tangent of {@code x}.
1670 * @since 1.5
1671 */
1672 public static native double tanh(double x);
1673
1674 /**
1675 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1676 * without intermediate overflow or underflow.
1677 *
1678 * <p>Special cases:
1679 * <ul>
1680 *
1681 * <li> If either argument is infinite, then the result
1682 * is positive infinity.
1683 *
1684 * <li> If either argument is NaN and neither argument is infinite,
1685 * then the result is NaN.
1686 *
1687 * </ul>
1688 *
1689 * @param x a value
1690 * @param y a value
1691 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1692 * without intermediate overflow or underflow
1693 * @since 1.5
1694 */
1695 public static double hypot(double x, double y) {
1696 return FdLibm.Hypot.compute(x, y);
1697 }
1698
1699 /**
1700 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1701 * <i>x</i> near 0, the exact sum of
1702 * {@code expm1(x)} + 1 is much closer to the true
1703 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1704 *
1705 * <p>Special cases:
1706 * <ul>
1707 * <li>If the argument is NaN, the result is NaN.
1708 *
1709 * <li>If the argument is positive infinity, then the result is
1710 * positive infinity.
1711 *
1712 * <li>If the argument is negative infinity, then the result is
1713 * -1.0.
1714 *
1715 * <li>If the argument is zero, then the result is a zero with the
1716 * same sign as the argument.
1717 *
1718 * </ul>
1719 *
1720 * @param x the exponent to raise <i>e</i> to in the computation of
1721 * <i>e</i><sup>{@code x}</sup> -1.
1722 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1723 * @since 1.5
1724 */
1725 public static native double expm1(double x);
1726
1727 /**
1728 * Returns the natural logarithm of the sum of the argument and 1.
1729 * Note that for small values {@code x}, the result of
1730 * {@code log1p(x)} is much closer to the true result of ln(1
1731 * + {@code x}) than the floating-point evaluation of
1732 * {@code log(1.0+x)}.
1733 *
1734 * <p>Special cases:
1735 * <ul>
1736 *
1737 * <li>If the argument is NaN or less than -1, then the result is
1738 * NaN.
1739 *
1740 * <li>If the argument is positive infinity, then the result is
1741 * positive infinity.
1742 *
1743 * <li>If the argument is negative one, then the result is
1744 * negative infinity.
1745 *
1746 * <li>If the argument is zero, then the result is a zero with the
1747 * same sign as the argument.
1748 *
1749 * </ul>
1750 *
1751 * @param x a value
1752 * @return the value ln({@code x} + 1), the natural
1753 * log of {@code x} + 1
1754 * @since 1.5
1755 */
1756 public static native double log1p(double x);
1757
1758 /**
1759 * Returns the first floating-point argument with the sign of the
1760 * second floating-point argument. For this method, a NaN
1761 * {@code sign} argument is always treated as if it were
1762 * positive.
1763 *
1764 * @param magnitude the parameter providing the magnitude of the result
1765 * @param sign the parameter providing the sign of the result
1766 * @return a value with the magnitude of {@code magnitude}
1767 * and the sign of {@code sign}.
1768 * @since 1.6
1769 */
1770 public static double copySign(double magnitude, double sign) {
1771 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1772 }
1773
1774 /**
1775 * Returns the first floating-point argument with the sign of the
1776 * second floating-point argument. For this method, a NaN
1777 * {@code sign} argument is always treated as if it were
1778 * positive.
1779 *
1780 * @param magnitude the parameter providing the magnitude of the result
1781 * @param sign the parameter providing the sign of the result
1782 * @return a value with the magnitude of {@code magnitude}
1783 * and the sign of {@code sign}.
1784 * @since 1.6
1785 */
1786 public static float copySign(float magnitude, float sign) {
1787 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1788 }
1789 /**
1790 * Returns the unbiased exponent used in the representation of a
1791 * {@code float}. Special cases:
1792 *
1793 * <ul>
1794 * <li>If the argument is NaN or infinite, then the result is
1795 * {@link Float#MAX_EXPONENT} + 1.
1796 * <li>If the argument is zero or subnormal, then the result is
1797 * {@link Float#MIN_EXPONENT} -1.
1798 * </ul>
1799 * @param f a {@code float} value
1800 * @return the unbiased exponent of the argument
1801 * @since 1.6
1802 */
1803 public static int getExponent(float f) {
1804 return Math.getExponent(f);
1805 }
1806
1807 /**
1808 * Returns the unbiased exponent used in the representation of a
1809 * {@code double}. Special cases:
1810 *
1811 * <ul>
1812 * <li>If the argument is NaN or infinite, then the result is
1813 * {@link Double#MAX_EXPONENT} + 1.
1814 * <li>If the argument is zero or subnormal, then the result is
1815 * {@link Double#MIN_EXPONENT} -1.
1816 * </ul>
1817 * @param d a {@code double} value
1818 * @return the unbiased exponent of the argument
1819 * @since 1.6
1820 */
1821 public static int getExponent(double d) {
1822 return Math.getExponent(d);
1823 }
1824
1825 /**
1826 * Returns the floating-point number adjacent to the first
1827 * argument in the direction of the second argument. If both
1828 * arguments compare as equal the second argument is returned.
1829 *
1830 * <p>Special cases:
1831 * <ul>
1832 * <li> If either argument is a NaN, then NaN is returned.
1833 *
1834 * <li> If both arguments are signed zeros, {@code direction}
1835 * is returned unchanged (as implied by the requirement of
1836 * returning the second argument if the arguments compare as
1837 * equal).
1838 *
1839 * <li> If {@code start} is
1840 * ±{@link Double#MIN_VALUE} and {@code direction}
1841 * has a value such that the result should have a smaller
1842 * magnitude, then a zero with the same sign as {@code start}
1843 * is returned.
1844 *
1845 * <li> If {@code start} is infinite and
1846 * {@code direction} has a value such that the result should
1847 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1848 * same sign as {@code start} is returned.
1849 *
1850 * <li> If {@code start} is equal to ±
1851 * {@link Double#MAX_VALUE} and {@code direction} has a
1852 * value such that the result should have a larger magnitude, an
1853 * infinity with same sign as {@code start} is returned.
1854 * </ul>
1855 *
1856 * @param start starting floating-point value
1857 * @param direction value indicating which of
1858 * {@code start}'s neighbors or {@code start} should
1859 * be returned
1860 * @return The floating-point number adjacent to {@code start} in the
1861 * direction of {@code direction}.
1862 * @since 1.6
1863 */
1864 public static double nextAfter(double start, double direction) {
1865 return Math.nextAfter(start, direction);
1866 }
1867
1868 /**
1869 * Returns the floating-point number adjacent to the first
1870 * argument in the direction of the second argument. If both
1871 * arguments compare as equal a value equivalent to the second argument
1872 * is returned.
1873 *
1874 * <p>Special cases:
1875 * <ul>
1876 * <li> If either argument is a NaN, then NaN is returned.
1877 *
1878 * <li> If both arguments are signed zeros, a value equivalent
1879 * to {@code direction} is returned.
1880 *
1881 * <li> If {@code start} is
1882 * ±{@link Float#MIN_VALUE} and {@code direction}
1883 * has a value such that the result should have a smaller
1884 * magnitude, then a zero with the same sign as {@code start}
1885 * is returned.
1886 *
1887 * <li> If {@code start} is infinite and
1888 * {@code direction} has a value such that the result should
1889 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1890 * same sign as {@code start} is returned.
1891 *
1892 * <li> If {@code start} is equal to ±
1893 * {@link Float#MAX_VALUE} and {@code direction} has a
1894 * value such that the result should have a larger magnitude, an
1895 * infinity with same sign as {@code start} is returned.
1896 * </ul>
1897 *
1898 * @param start starting floating-point value
1899 * @param direction value indicating which of
1900 * {@code start}'s neighbors or {@code start} should
1901 * be returned
1902 * @return The floating-point number adjacent to {@code start} in the
1903 * direction of {@code direction}.
1904 * @since 1.6
1905 */
1906 public static float nextAfter(float start, double direction) {
1907 return Math.nextAfter(start, direction);
1908 }
1909
1910 /**
1911 * Returns the floating-point value adjacent to {@code d} in
1912 * the direction of positive infinity. This method is
1913 * semantically equivalent to {@code nextAfter(d,
1914 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1915 * implementation may run faster than its equivalent
1916 * {@code nextAfter} call.
1917 *
1918 * <p>Special Cases:
1919 * <ul>
1920 * <li> If the argument is NaN, the result is NaN.
1921 *
1922 * <li> If the argument is positive infinity, the result is
1923 * positive infinity.
1924 *
1925 * <li> If the argument is zero, the result is
1926 * {@link Double#MIN_VALUE}
1927 *
1928 * </ul>
1929 *
1930 * @param d starting floating-point value
1931 * @return The adjacent floating-point value closer to positive
1932 * infinity.
1933 * @since 1.6
1934 */
1935 public static double nextUp(double d) {
1936 return Math.nextUp(d);
1937 }
1938
1939 /**
1940 * Returns the floating-point value adjacent to {@code f} in
1941 * the direction of positive infinity. This method is
1942 * semantically equivalent to {@code nextAfter(f,
1943 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1944 * implementation may run faster than its equivalent
1945 * {@code nextAfter} call.
1946 *
1947 * <p>Special Cases:
1948 * <ul>
1949 * <li> If the argument is NaN, the result is NaN.
1950 *
1951 * <li> If the argument is positive infinity, the result is
1952 * positive infinity.
1953 *
1954 * <li> If the argument is zero, the result is
1955 * {@link Float#MIN_VALUE}
1956 *
1957 * </ul>
1958 *
1959 * @param f starting floating-point value
1960 * @return The adjacent floating-point value closer to positive
1961 * infinity.
1962 * @since 1.6
1963 */
1964 public static float nextUp(float f) {
1965 return Math.nextUp(f);
1966 }
1967
1968 /**
1969 * Returns the floating-point value adjacent to {@code d} in
1970 * the direction of negative infinity. This method is
1971 * semantically equivalent to {@code nextAfter(d,
1972 * Double.NEGATIVE_INFINITY)}; however, a
1973 * {@code nextDown} implementation may run faster than its
1974 * equivalent {@code nextAfter} call.
1975 *
1976 * <p>Special Cases:
1977 * <ul>
1978 * <li> If the argument is NaN, the result is NaN.
1979 *
1980 * <li> If the argument is negative infinity, the result is
1981 * negative infinity.
1982 *
1983 * <li> If the argument is zero, the result is
1984 * {@code -Double.MIN_VALUE}
1985 *
1986 * </ul>
1987 *
1988 * @param d starting floating-point value
1989 * @return The adjacent floating-point value closer to negative
1990 * infinity.
1991 * @since 1.8
1992 */
1993 public static double nextDown(double d) {
1994 return Math.nextDown(d);
1995 }
1996
1997 /**
1998 * Returns the floating-point value adjacent to {@code f} in
1999 * the direction of negative infinity. This method is
2000 * semantically equivalent to {@code nextAfter(f,
2001 * Float.NEGATIVE_INFINITY)}; however, a
2002 * {@code nextDown} implementation may run faster than its
2003 * equivalent {@code nextAfter} call.
2004 *
2005 * <p>Special Cases:
2006 * <ul>
2007 * <li> If the argument is NaN, the result is NaN.
2008 *
2009 * <li> If the argument is negative infinity, the result is
2010 * negative infinity.
2011 *
2012 * <li> If the argument is zero, the result is
2013 * {@code -Float.MIN_VALUE}
2014 *
2015 * </ul>
2016 *
2017 * @param f starting floating-point value
2018 * @return The adjacent floating-point value closer to negative
2019 * infinity.
2020 * @since 1.8
2021 */
2022 public static float nextDown(float f) {
2023 return Math.nextDown(f);
2024 }
2025
2026 /**
2027 * Returns {@code d} ×
2028 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
2029 * by a single correctly rounded floating-point multiply to a
2030 * member of the double value set. See the Java
2031 * Language Specification for a discussion of floating-point
2032 * value sets. If the exponent of the result is between {@link
2033 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
2034 * answer is calculated exactly. If the exponent of the result
2035 * would be larger than {@code Double.MAX_EXPONENT}, an
2036 * infinity is returned. Note that if the result is subnormal,
2037 * precision may be lost; that is, when {@code scalb(x, n)}
2038 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
2039 * <i>x</i>. When the result is non-NaN, the result has the same
2040 * sign as {@code d}.
2041 *
2042 * <p>Special cases:
2043 * <ul>
2044 * <li> If the first argument is NaN, NaN is returned.
2045 * <li> If the first argument is infinite, then an infinity of the
2046 * same sign is returned.
2047 * <li> If the first argument is zero, then a zero of the same
2048 * sign is returned.
2049 * </ul>
2050 *
2051 * @param d number to be scaled by a power of two.
2052 * @param scaleFactor power of 2 used to scale {@code d}
2053 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
2054 * @since 1.6
2055 */
2056 public static double scalb(double d, int scaleFactor) {
2057 return Math.scalb(d, scaleFactor);
2058 }
2059
2060 /**
2061 * Returns {@code f} ×
2062 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
2063 * by a single correctly rounded floating-point multiply to a
2064 * member of the float value set. See the Java
2065 * Language Specification for a discussion of floating-point
2066 * value sets. If the exponent of the result is between {@link
2067 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
2068 * answer is calculated exactly. If the exponent of the result
2069 * would be larger than {@code Float.MAX_EXPONENT}, an
2070 * infinity is returned. Note that if the result is subnormal,
2071 * precision may be lost; that is, when {@code scalb(x, n)}
2072 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
2073 * <i>x</i>. When the result is non-NaN, the result has the same
2074 * sign as {@code f}.
2075 *
2076 * <p>Special cases:
2077 * <ul>
2078 * <li> If the first argument is NaN, NaN is returned.
2079 * <li> If the first argument is infinite, then an infinity of the
2080 * same sign is returned.
2081 * <li> If the first argument is zero, then a zero of the same
2082 * sign is returned.
2083 * </ul>
2084 *
2085 * @param f number to be scaled by a power of two.
2086 * @param scaleFactor power of 2 used to scale {@code f}
2087 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
2088 * @since 1.6
2089 */
2090 public static float scalb(float f, int scaleFactor) {
2091 return Math.scalb(f, scaleFactor);
2092 }
2093 }