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