1 /*
2 * Copyright (c) 1999, 2015, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
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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
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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, decrement, and negation overflow occurs only with
74 * a specific minimum or maximum value and should be checked against
75 * the minimum or maximum as appropriate.
76 *
77 * @author unascribed
78 * @author Joseph D. Darcy
79 * @since 1.3
80 */
81
82 public final class StrictMath {
83
84 /**
85 * Don't let anyone instantiate this class.
86 */
87 private StrictMath() {}
88
89 /**
90 * The {@code double} value that is closer than any other to
91 * <i>e</i>, the base of the natural logarithms.
92 */
93 public static final double E = 2.7182818284590452354;
94
95 /**
96 * The {@code double} value that is closer than any other to
97 * <i>pi</i>, the ratio of the circumference of a circle to its
98 * diameter.
99 */
100 public static final double PI = 3.14159265358979323846;
101
102 /**
103 * Constant by which to multiply an angular value in degrees to obtain an
104 * angular value in radians.
105 */
106 private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
107
108 /**
109 * Constant by which to multiply an angular value in radians to obtain an
110 * angular value in degrees.
111 */
112
113 private static final double RADIANS_TO_DEGREES = 57.29577951308232;
114
115 /**
116 * Returns the trigonometric sine of an angle. Special cases:
117 * <ul><li>If the argument is NaN or an infinity, then the
118 * result is NaN.
119 * <li>If the argument is zero, then the result is a zero with the
120 * same sign as the argument.</ul>
121 *
122 * @param a an angle, in radians.
123 * @return the sine of the argument.
124 */
125 public static native double sin(double a);
126
127 /**
128 * Returns the trigonometric cosine of an angle. Special cases:
129 * <ul><li>If the argument is NaN or an infinity, then the
130 * result is NaN.</ul>
131 *
132 * @param a an angle, in radians.
133 * @return the cosine of the argument.
134 */
135 public static native double cos(double a);
136
137 /**
138 * Returns the trigonometric tangent of an angle. Special cases:
139 * <ul><li>If the argument is NaN or an infinity, then the result
140 * is NaN.
141 * <li>If the argument is zero, then the result is a zero with the
142 * same sign as the argument.</ul>
143 *
144 * @param a an angle, in radians.
145 * @return the tangent of the argument.
146 */
147 public static native double tan(double a);
148
149 /**
150 * Returns the arc sine of a value; the returned angle is in the
151 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
152 * <ul><li>If the argument is NaN or its absolute value is greater
153 * than 1, then the result is NaN.
154 * <li>If the argument is zero, then the result is a zero with the
155 * same sign as the argument.</ul>
156 *
157 * @param a the value whose arc sine is to be returned.
158 * @return the arc sine of the argument.
159 */
160 public static native double asin(double a);
161
162 /**
163 * Returns the arc cosine of a value; the returned angle is in the
164 * range 0.0 through <i>pi</i>. Special case:
165 * <ul><li>If the argument is NaN or its absolute value is greater
166 * than 1, then the result is NaN.</ul>
167 *
168 * @param a the value whose arc cosine is to be returned.
169 * @return the arc cosine of the argument.
170 */
171 public static native double acos(double a);
172
173 /**
174 * Returns the arc tangent of a value; the returned angle is in the
175 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
176 * <ul><li>If the argument is NaN, then the result is NaN.
177 * <li>If the argument is zero, then the result is a zero with the
178 * same sign as the argument.</ul>
179 *
180 * @param a the value whose arc tangent is to be returned.
181 * @return the arc tangent of the argument.
182 */
183 public static native double atan(double a);
184
185 /**
186 * Converts an angle measured in degrees to an approximately
187 * equivalent angle measured in radians. The conversion from
188 * degrees to radians is generally inexact.
189 *
190 * @param angdeg an angle, in degrees
191 * @return the measurement of the angle {@code angdeg}
192 * in radians.
193 */
194 public static strictfp double toRadians(double angdeg) {
195 // Do not delegate to Math.toRadians(angdeg) because
196 // this method has the strictfp modifier.
197 return angdeg * DEGREES_TO_RADIANS;
198 }
199
200 /**
201 * Converts an angle measured in radians to an approximately
202 * equivalent angle measured in degrees. The conversion from
203 * radians to degrees is generally inexact; users should
204 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
205 * equal {@code 0.0}.
206 *
207 * @param angrad an angle, in radians
208 * @return the measurement of the angle {@code angrad}
209 * in degrees.
210 */
211 public static strictfp double toDegrees(double angrad) {
212 // Do not delegate to Math.toDegrees(angrad) because
213 // this method has the strictfp modifier.
214 return angrad * RADIANS_TO_DEGREES;
215 }
216
217 /**
218 * Returns Euler's number <i>e</i> raised to the power of a
219 * {@code double} value. Special cases:
220 * <ul><li>If the argument is NaN, the result is NaN.
221 * <li>If the argument is positive infinity, then the result is
222 * positive infinity.
223 * <li>If the argument is negative infinity, then the result is
224 * positive zero.</ul>
225 *
226 * @param a the exponent to raise <i>e</i> to.
227 * @return the value <i>e</i><sup>{@code a}</sup>,
228 * where <i>e</i> is the base of the natural logarithms.
229 */
230 public static native double exp(double a);
231
232 /**
233 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
234 * value. Special cases:
235 * <ul><li>If the argument is NaN or less than zero, then the result
236 * is NaN.
237 * <li>If the argument is positive infinity, then the result is
238 * positive infinity.
239 * <li>If the argument is positive zero or negative zero, then the
240 * result is negative infinity.</ul>
241 *
242 * @param a a value
243 * @return the value ln {@code a}, the natural logarithm of
244 * {@code a}.
245 */
246 public static native double log(double a);
247
248 /**
249 * Returns the base 10 logarithm of a {@code double} value.
250 * Special cases:
251 *
252 * <ul><li>If the argument is NaN or less than zero, then the result
253 * is NaN.
254 * <li>If the argument is positive infinity, then the result is
255 * positive infinity.
256 * <li>If the argument is positive zero or negative zero, then the
257 * result is negative infinity.
258 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
259 * integer <i>n</i>, then the result is <i>n</i>.
260 * </ul>
261 *
262 * @param a a value
263 * @return the base 10 logarithm of {@code a}.
264 * @since 1.5
265 */
266 public static native double log10(double a);
267
268 /**
269 * Returns the correctly rounded positive square root of a
270 * {@code double} value.
271 * Special cases:
272 * <ul><li>If the argument is NaN or less than zero, then the result
273 * is NaN.
274 * <li>If the argument is positive infinity, then the result is positive
275 * infinity.
276 * <li>If the argument is positive zero or negative zero, then the
277 * result is the same as the argument.</ul>
278 * Otherwise, the result is the {@code double} value closest to
279 * the true mathematical square root of the argument value.
280 *
281 * @param a a value.
282 * @return the positive square root of {@code a}.
283 */
284 @HotSpotIntrinsicCandidate
285 public static native double sqrt(double a);
286
287 /**
288 * Returns the cube root of a {@code double} value. For
289 * positive finite {@code x}, {@code cbrt(-x) ==
290 * -cbrt(x)}; that is, the cube root of a negative value is
291 * the negative of the cube root of that value's magnitude.
292 * Special cases:
293 *
294 * <ul>
295 *
296 * <li>If the argument is NaN, then the result is NaN.
297 *
298 * <li>If the argument is infinite, then the result is an infinity
299 * with the same sign as the argument.
300 *
301 * <li>If the argument is zero, then the result is a zero with the
302 * same sign as the argument.
303 *
304 * </ul>
305 *
306 * @param a a value.
307 * @return the cube root of {@code a}.
308 * @since 1.5
309 */
310 public static 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,
807 * throwing an exception if the result 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,long)
814 * @since 1.8
815 */
816 public static long multiplyExact(long x, long y) {
817 return Math.multiplyExact(x, y);
818 }
819
820 /**
821 * Returns the value of the {@code long} argument;
822 * throwing an exception if the value overflows an {@code int}.
823 *
824 * @param value the long value
825 * @return the argument as an int
826 * @throws ArithmeticException if the {@code argument} overflows an int
827 * @see Math#toIntExact(long)
828 * @since 1.8
829 */
830 public static int toIntExact(long value) {
831 return Math.toIntExact(value);
832 }
833
834 /**
835 * Returns the largest (closest to positive infinity)
836 * {@code int} value that is less than or equal to the algebraic quotient.
837 * There is one special case, if the dividend is the
838 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
839 * then integer overflow occurs and
840 * the result is equal to the {@code Integer.MIN_VALUE}.
841 * <p>
842 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
843 * a comparison to the integer division {@code /} operator.
844 *
845 * @param x the dividend
846 * @param y the divisor
847 * @return the largest (closest to positive infinity)
848 * {@code int} value that is less than or equal to the algebraic quotient.
849 * @throws ArithmeticException if the divisor {@code y} is zero
850 * @see Math#floorDiv(int, int)
851 * @see Math#floor(double)
852 * @since 1.8
853 */
854 public static int floorDiv(int x, int y) {
855 return Math.floorDiv(x, y);
856 }
857
858 /**
859 * Returns the largest (closest to positive infinity)
860 * {@code long} value that is less than or equal to the algebraic quotient.
861 * There is one special case, if the dividend is the
862 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
863 * then integer overflow occurs and
864 * the result is equal to the {@code Long.MIN_VALUE}.
865 * <p>
866 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
867 * a comparison to the integer division {@code /} operator.
868 *
869 * @param x the dividend
870 * @param y the divisor
871 * @return the largest (closest to positive infinity)
872 * {@code long} value that is less than or equal to the algebraic quotient.
873 * @throws ArithmeticException if the divisor {@code y} is zero
874 * @see Math#floorDiv(long, long)
875 * @see Math#floor(double)
876 * @since 1.8
877 */
878 public static long floorDiv(long x, long y) {
879 return Math.floorDiv(x, y);
880 }
881
882 /**
883 * Returns the floor modulus of the {@code int} arguments.
884 * <p>
885 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
886 * has the same sign as the divisor {@code y}, and
887 * is in the range of {@code -abs(y) < r < +abs(y)}.
888 * <p>
889 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
890 * <ul>
891 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
892 * </ul>
893 * <p>
894 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
895 * a comparison to the {@code %} operator.
896 *
897 * @param x the dividend
898 * @param y the divisor
899 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
900 * @throws ArithmeticException if the divisor {@code y} is zero
901 * @see Math#floorMod(int, int)
902 * @see StrictMath#floorDiv(int, int)
903 * @since 1.8
904 */
905 public static int floorMod(int x, int y) {
906 return Math.floorMod(x , y);
907 }
908 /**
909 * Returns the floor modulus of the {@code long} arguments.
910 * <p>
911 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
912 * has the same sign as the divisor {@code y}, and
913 * is in the range of {@code -abs(y) < r < +abs(y)}.
914 * <p>
915 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
916 * <ul>
917 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
918 * </ul>
919 * <p>
920 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
921 * a comparison to the {@code %} operator.
922 *
923 * @param x the dividend
924 * @param y the divisor
925 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
926 * @throws ArithmeticException if the divisor {@code y} is zero
927 * @see Math#floorMod(long, long)
928 * @see StrictMath#floorDiv(long, long)
929 * @since 1.8
930 */
931 public static long floorMod(long x, long y) {
932 return Math.floorMod(x, y);
933 }
934
935 /**
936 * Returns the absolute value of an {@code int} value.
937 * If the argument is not negative, the argument is returned.
938 * If the argument is negative, the negation of the argument is returned.
939 *
940 * <p>Note that if the argument is equal to the value of
941 * {@link Integer#MIN_VALUE}, the most negative representable
942 * {@code int} value, the result is that same value, which is
943 * negative.
944 *
945 * @param a the argument whose absolute value is to be determined.
946 * @return the absolute value of the argument.
947 */
948 public static int abs(int a) {
949 return Math.abs(a);
950 }
951
952 /**
953 * Returns the absolute value of a {@code long} value.
954 * If the argument is not negative, the argument is returned.
955 * If the argument is negative, the negation of the argument is returned.
956 *
957 * <p>Note that if the argument is equal to the value of
958 * {@link Long#MIN_VALUE}, the most negative representable
959 * {@code long} value, the result is that same value, which
960 * is negative.
961 *
962 * @param a the argument whose absolute value is to be determined.
963 * @return the absolute value of the argument.
964 */
965 public static long abs(long a) {
966 return Math.abs(a);
967 }
968
969 /**
970 * Returns the absolute value of a {@code float} value.
971 * If the argument is not negative, the argument is returned.
972 * If the argument is negative, the negation of the argument is returned.
973 * Special cases:
974 * <ul><li>If the argument is positive zero or negative zero, the
975 * result is positive zero.
976 * <li>If the argument is infinite, the result is positive infinity.
977 * <li>If the argument is NaN, the result is NaN.</ul>
978 * In other words, the result is the same as the value of the expression:
979 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
980 *
981 * @param a the argument whose absolute value is to be determined
982 * @return the absolute value of the argument.
983 */
984 public static float abs(float a) {
985 return Math.abs(a);
986 }
987
988 /**
989 * Returns the absolute value of a {@code double} value.
990 * If the argument is not negative, the argument is returned.
991 * If the argument is negative, the negation of the argument is returned.
992 * Special cases:
993 * <ul><li>If the argument is positive zero or negative zero, the result
994 * is positive zero.
995 * <li>If the argument is infinite, the result is positive infinity.
996 * <li>If the argument is NaN, the result is NaN.</ul>
997 * In other words, the result is the same as the value of the expression:
998 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
999 *
1000 * @param a the argument whose absolute value is to be determined
1001 * @return the absolute value of the argument.
1002 */
1003 public static double abs(double a) {
1004 return Math.abs(a);
1005 }
1006
1007 /**
1008 * Returns the greater of two {@code int} values. That is, the
1009 * result is the argument closer to the value of
1010 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1011 * the result is that same value.
1012 *
1013 * @param a an argument.
1014 * @param b another argument.
1015 * @return the larger of {@code a} and {@code b}.
1016 */
1017 @HotSpotIntrinsicCandidate
1018 public static int max(int a, int b) {
1019 return Math.max(a, b);
1020 }
1021
1022 /**
1023 * Returns the greater of two {@code long} values. That is, the
1024 * result is the argument closer to the value of
1025 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1026 * the result is that same value.
1027 *
1028 * @param a an argument.
1029 * @param b another argument.
1030 * @return the larger of {@code a} and {@code b}.
1031 */
1032 public static long max(long a, long b) {
1033 return Math.max(a, b);
1034 }
1035
1036 /**
1037 * Returns the greater of two {@code float} values. That is,
1038 * the result is the argument closer to positive infinity. If the
1039 * arguments have the same value, the result is that same
1040 * value. If either value is NaN, then the result is NaN. Unlike
1041 * the numerical comparison operators, this method considers
1042 * negative zero to be strictly smaller than positive zero. If one
1043 * argument is positive zero and the other negative zero, the
1044 * result is positive zero.
1045 *
1046 * @param a an argument.
1047 * @param b another argument.
1048 * @return the larger of {@code a} and {@code b}.
1049 */
1050 public static float max(float a, float b) {
1051 return Math.max(a, b);
1052 }
1053
1054 /**
1055 * Returns the greater of two {@code double} values. That
1056 * is, the result is the argument closer to positive infinity. If
1057 * the arguments have the same value, the result is that same
1058 * value. If either value is NaN, then the result is NaN. Unlike
1059 * the numerical comparison operators, this method considers
1060 * negative zero to be strictly smaller than positive zero. If one
1061 * argument is positive zero and the other negative zero, the
1062 * result is positive zero.
1063 *
1064 * @param a an argument.
1065 * @param b another argument.
1066 * @return the larger of {@code a} and {@code b}.
1067 */
1068 public static double max(double a, double b) {
1069 return Math.max(a, b);
1070 }
1071
1072 /**
1073 * Returns the smaller of two {@code int} values. That is,
1074 * the result the argument closer to the value of
1075 * {@link Integer#MIN_VALUE}. If the arguments have the same
1076 * value, the result is that same value.
1077 *
1078 * @param a an argument.
1079 * @param b another argument.
1080 * @return the smaller of {@code a} and {@code b}.
1081 */
1082 @HotSpotIntrinsicCandidate
1083 public static int min(int a, int b) {
1084 return Math.min(a, b);
1085 }
1086
1087 /**
1088 * Returns the smaller of two {@code long} values. That is,
1089 * the result is the argument closer to the value of
1090 * {@link Long#MIN_VALUE}. If the arguments have the same
1091 * value, the result is that same value.
1092 *
1093 * @param a an argument.
1094 * @param b another argument.
1095 * @return the smaller of {@code a} and {@code b}.
1096 */
1097 public static long min(long a, long b) {
1098 return Math.min(a, b);
1099 }
1100
1101 /**
1102 * Returns the smaller of two {@code float} values. That is,
1103 * the result is the value closer to negative infinity. If the
1104 * arguments have the same value, the result is that same
1105 * value. If either value is NaN, then the result is NaN. Unlike
1106 * the numerical comparison operators, this method considers
1107 * negative zero to be strictly smaller than positive zero. If
1108 * one argument is positive zero and the other is negative zero,
1109 * the result is negative zero.
1110 *
1111 * @param a an argument.
1112 * @param b another argument.
1113 * @return the smaller of {@code a} and {@code b.}
1114 */
1115 public static float min(float a, float b) {
1116 return Math.min(a, b);
1117 }
1118
1119 /**
1120 * Returns the smaller of two {@code double} values. That
1121 * is, the result is the value closer to negative infinity. If the
1122 * arguments have the same value, the result is that same
1123 * value. If either value is NaN, then the result is NaN. Unlike
1124 * the numerical comparison operators, this method considers
1125 * negative zero to be strictly smaller than positive zero. If one
1126 * argument is positive zero and the other is negative zero, the
1127 * result is negative zero.
1128 *
1129 * @param a an argument.
1130 * @param b another argument.
1131 * @return the smaller of {@code a} and {@code b}.
1132 */
1133 public static double min(double a, double b) {
1134 return Math.min(a, b);
1135 }
1136
1137 /**
1138 * Returns the fused multiply-accumulate of the three arguments;
1139 * that is, returns the exact product of the first two arguments
1140 * summed with the third argument and then rounded once to the
1141 * nearest {@code double}.
1142 *
1143 * The rounding is done using the {@linkplain
1144 * java.math.RoundingMode#HALF_EVEN round to nearest even
1145 * rounding mode}.
1146 *
1147 * In contrast, if {@code a * b + c} is evaluated as a regular
1148 * floating-point expression, two rounding errors are involved,
1149 * the first for the multiply operation, the second for the
1150 * addition operation.
1151 *
1152 * <p>Special cases:
1153 * <ul>
1154 * <li> If any argument is NaN, the result is NaN.
1155 *
1156 * <li> If one of the first two arguments is infinite and the
1157 * other is zero, the result is NaN.
1158 *
1159 * <li> If the exact product of the first two arguments is infinite
1160 * (in other words, at least one of the arguments is infinite and
1161 * the other is neither zero nor NaN) and the third argument is an
1162 * infinity of the opposite sign, the result is NaN.
1163 *
1164 * </ul>
1165 *
1166 * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
1167 * result as ({@code a + c}). However,
1168 * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
1169 * same result as ({@code a * b}) since
1170 * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
1171 * ({@code 0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
1172 * equivalent to ({@code a * b}) however.
1173 *
1174 * @param a a value
1175 * @param b a value
1176 * @param c a value
1177 *
1178 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1179 * computed, as if with unlimited range and precision, and rounded
1180 * once to the nearest {@code double} value
1181 */
1182 public static double fusedMac(double a, double b, double c) {
1183 return Math.fusedMac(a, b, c);
1184 }
1185
1186 /**
1187 * Returns the fused multiply-accumulate of the three arguments;
1188 * that is, returns the exact product of the first two arguments
1189 * summed with the third argument and then rounded once to the
1190 * nearest {@code float}.
1191 *
1192 * The rounding is done using the {@linkplain
1193 * java.math.RoundingMode#HALF_EVEN round to nearest even
1194 * rounding mode}.
1195 *
1196 * In contrast, if {@code a * b + c} is evaluated as a regular
1197 * floating-point expression, two rounding errors are involved,
1198 * the first for the multiply operation, the second for the
1199 * addition operation.
1200 *
1201 * <p>Special cases:
1202 * <ul>
1203 * <li> If any argument is NaN, the result is NaN.
1204 *
1205 * <li> If one of the first two arguments is infinite and the
1206 * other is zero, the result is NaN.
1207 *
1208 * <li> If the exact product of the first two arguments is infinite
1209 * (in other words, at least one of the arguments is infinite and
1210 * the other is neither zero nor NaN) and the third argument is an
1211 * infinity of the opposite sign, the result is NaN.
1212 *
1213 * </ul>
1214 *
1215 * <p>Note that {@code fusedMac(a, 1.0f, c)} returns the same
1216 * result as ({@code a + c}). However,
1217 * {@code fusedMac(a, b, +0.0f)} does <em>not</em> always return the
1218 * same result as ({@code a * b}) since
1219 * {@code fusedMac(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
1220 * ({@code 0.0f * +0.0f}) is {@code -0.0f}; {@code fusedMac(a, b, -0.0f)} is
1221 * equivalent to ({@code a * b}) however.
1222 *
1223 * @param a a value
1224 * @param b a value
1225 * @param c a value
1226 *
1227 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1228 * computed, as if with unlimited range and precision, and rounded
1229 * once to the nearest {@code float} value
1230 */
1231 public static float fusedMac(float a, float b, float c) {
1232 return Math.fusedMac(a, b, c);
1233 }
1234
1235 /**
1236 * Returns the size of an ulp of the argument. An ulp, unit in
1237 * the last place, of a {@code double} value is the positive
1238 * distance between this floating-point value and the {@code
1239 * double} value next larger in magnitude. Note that for non-NaN
1240 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1241 *
1242 * <p>Special Cases:
1243 * <ul>
1244 * <li> If the argument is NaN, then the result is NaN.
1245 * <li> If the argument is positive or negative infinity, then the
1246 * result is positive infinity.
1247 * <li> If the argument is positive or negative zero, then the result is
1248 * {@code Double.MIN_VALUE}.
1249 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1250 * the result is equal to 2<sup>971</sup>.
1251 * </ul>
1252 *
1253 * @param d the floating-point value whose ulp is to be returned
1254 * @return the size of an ulp of the argument
1255 * @author Joseph D. Darcy
1256 * @since 1.5
1257 */
1258 public static double ulp(double d) {
1259 return Math.ulp(d);
1260 }
1261
1262 /**
1263 * Returns the size of an ulp of the argument. An ulp, unit in
1264 * the last place, of a {@code float} value is the positive
1265 * distance between this floating-point value and the {@code
1266 * float} value next larger in magnitude. Note that for non-NaN
1267 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1268 *
1269 * <p>Special Cases:
1270 * <ul>
1271 * <li> If the argument is NaN, then the result is NaN.
1272 * <li> If the argument is positive or negative infinity, then the
1273 * result is positive infinity.
1274 * <li> If the argument is positive or negative zero, then the result is
1275 * {@code Float.MIN_VALUE}.
1276 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1277 * the result is equal to 2<sup>104</sup>.
1278 * </ul>
1279 *
1280 * @param f the floating-point value whose ulp is to be returned
1281 * @return the size of an ulp of the argument
1282 * @author Joseph D. Darcy
1283 * @since 1.5
1284 */
1285 public static float ulp(float f) {
1286 return Math.ulp(f);
1287 }
1288
1289 /**
1290 * Returns the signum function of the argument; zero if the argument
1291 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1292 * argument is less than zero.
1293 *
1294 * <p>Special Cases:
1295 * <ul>
1296 * <li> If the argument is NaN, then the result is NaN.
1297 * <li> If the argument is positive zero or negative zero, then the
1298 * result is the same as the argument.
1299 * </ul>
1300 *
1301 * @param d the floating-point value whose signum is to be returned
1302 * @return the signum function of the argument
1303 * @author Joseph D. Darcy
1304 * @since 1.5
1305 */
1306 public static double signum(double d) {
1307 return Math.signum(d);
1308 }
1309
1310 /**
1311 * Returns the signum function of the argument; zero if the argument
1312 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1313 * argument is less than zero.
1314 *
1315 * <p>Special Cases:
1316 * <ul>
1317 * <li> If the argument is NaN, then the result is NaN.
1318 * <li> If the argument is positive zero or negative zero, then the
1319 * result is the same as the argument.
1320 * </ul>
1321 *
1322 * @param f the floating-point value whose signum is to be returned
1323 * @return the signum function of the argument
1324 * @author Joseph D. Darcy
1325 * @since 1.5
1326 */
1327 public static float signum(float f) {
1328 return Math.signum(f);
1329 }
1330
1331 /**
1332 * Returns the hyperbolic sine of a {@code double} value.
1333 * The hyperbolic sine of <i>x</i> is defined to be
1334 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1335 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1336 *
1337 * <p>Special cases:
1338 * <ul>
1339 *
1340 * <li>If the argument is NaN, then the result is NaN.
1341 *
1342 * <li>If the argument is infinite, then the result is an infinity
1343 * with the same sign as the argument.
1344 *
1345 * <li>If the argument is zero, then the result is a zero with the
1346 * same sign as the argument.
1347 *
1348 * </ul>
1349 *
1350 * @param x The number whose hyperbolic sine is to be returned.
1351 * @return The hyperbolic sine of {@code x}.
1352 * @since 1.5
1353 */
1354 public static native double sinh(double x);
1355
1356 /**
1357 * Returns the hyperbolic cosine of a {@code double} value.
1358 * The hyperbolic cosine of <i>x</i> is defined to be
1359 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1360 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1361 *
1362 * <p>Special cases:
1363 * <ul>
1364 *
1365 * <li>If the argument is NaN, then the result is NaN.
1366 *
1367 * <li>If the argument is infinite, then the result is positive
1368 * infinity.
1369 *
1370 * <li>If the argument is zero, then the result is {@code 1.0}.
1371 *
1372 * </ul>
1373 *
1374 * @param x The number whose hyperbolic cosine is to be returned.
1375 * @return The hyperbolic cosine of {@code x}.
1376 * @since 1.5
1377 */
1378 public static native double cosh(double x);
1379
1380 /**
1381 * Returns the hyperbolic tangent of a {@code double} value.
1382 * The hyperbolic tangent of <i>x</i> is defined to be
1383 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1384 * in other words, {@linkplain Math#sinh
1385 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1386 * that the absolute value of the exact tanh is always less than
1387 * 1.
1388 *
1389 * <p>Special cases:
1390 * <ul>
1391 *
1392 * <li>If the argument is NaN, then the result is NaN.
1393 *
1394 * <li>If the argument is zero, then the result is a zero with the
1395 * same sign as the argument.
1396 *
1397 * <li>If the argument is positive infinity, then the result is
1398 * {@code +1.0}.
1399 *
1400 * <li>If the argument is negative infinity, then the result is
1401 * {@code -1.0}.
1402 *
1403 * </ul>
1404 *
1405 * @param x The number whose hyperbolic tangent is to be returned.
1406 * @return The hyperbolic tangent of {@code x}.
1407 * @since 1.5
1408 */
1409 public static native double tanh(double x);
1410
1411 /**
1412 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1413 * without intermediate overflow or underflow.
1414 *
1415 * <p>Special cases:
1416 * <ul>
1417 *
1418 * <li> If either argument is infinite, then the result
1419 * is positive infinity.
1420 *
1421 * <li> If either argument is NaN and neither argument is infinite,
1422 * then the result is NaN.
1423 *
1424 * </ul>
1425 *
1426 * @param x a value
1427 * @param y a value
1428 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1429 * without intermediate overflow or underflow
1430 * @since 1.5
1431 */
1432 public static double hypot(double x, double y) {
1433 return FdLibm.Hypot.compute(x, y);
1434 }
1435
1436 /**
1437 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1438 * <i>x</i> near 0, the exact sum of
1439 * {@code expm1(x)} + 1 is much closer to the true
1440 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1441 *
1442 * <p>Special cases:
1443 * <ul>
1444 * <li>If the argument is NaN, the result is NaN.
1445 *
1446 * <li>If the argument is positive infinity, then the result is
1447 * positive infinity.
1448 *
1449 * <li>If the argument is negative infinity, then the result is
1450 * -1.0.
1451 *
1452 * <li>If the argument is zero, then the result is a zero with the
1453 * same sign as the argument.
1454 *
1455 * </ul>
1456 *
1457 * @param x the exponent to raise <i>e</i> to in the computation of
1458 * <i>e</i><sup>{@code x}</sup> -1.
1459 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1460 * @since 1.5
1461 */
1462 public static native double expm1(double x);
1463
1464 /**
1465 * Returns the natural logarithm of the sum of the argument and 1.
1466 * Note that for small values {@code x}, the result of
1467 * {@code log1p(x)} is much closer to the true result of ln(1
1468 * + {@code x}) than the floating-point evaluation of
1469 * {@code log(1.0+x)}.
1470 *
1471 * <p>Special cases:
1472 * <ul>
1473 *
1474 * <li>If the argument is NaN or less than -1, then the result is
1475 * NaN.
1476 *
1477 * <li>If the argument is positive infinity, then the result is
1478 * positive infinity.
1479 *
1480 * <li>If the argument is negative one, then the result is
1481 * negative infinity.
1482 *
1483 * <li>If the argument is zero, then the result is a zero with the
1484 * same sign as the argument.
1485 *
1486 * </ul>
1487 *
1488 * @param x a value
1489 * @return the value ln({@code x} + 1), the natural
1490 * log of {@code x} + 1
1491 * @since 1.5
1492 */
1493 public static native double log1p(double x);
1494
1495 /**
1496 * Returns the first floating-point argument with the sign of the
1497 * second floating-point argument. For this method, a NaN
1498 * {@code sign} argument is always treated as if it were
1499 * positive.
1500 *
1501 * @param magnitude the parameter providing the magnitude of the result
1502 * @param sign the parameter providing the sign of the result
1503 * @return a value with the magnitude of {@code magnitude}
1504 * and the sign of {@code sign}.
1505 * @since 1.6
1506 */
1507 public static double copySign(double magnitude, double sign) {
1508 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1509 }
1510
1511 /**
1512 * Returns the first floating-point argument with the sign of the
1513 * second floating-point argument. For this method, a NaN
1514 * {@code sign} argument is always treated as if it were
1515 * positive.
1516 *
1517 * @param magnitude the parameter providing the magnitude of the result
1518 * @param sign the parameter providing the sign of the result
1519 * @return a value with the magnitude of {@code magnitude}
1520 * and the sign of {@code sign}.
1521 * @since 1.6
1522 */
1523 public static float copySign(float magnitude, float sign) {
1524 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1525 }
1526 /**
1527 * Returns the unbiased exponent used in the representation of a
1528 * {@code float}. Special cases:
1529 *
1530 * <ul>
1531 * <li>If the argument is NaN or infinite, then the result is
1532 * {@link Float#MAX_EXPONENT} + 1.
1533 * <li>If the argument is zero or subnormal, then the result is
1534 * {@link Float#MIN_EXPONENT} -1.
1535 * </ul>
1536 * @param f a {@code float} value
1537 * @return the unbiased exponent of the argument
1538 * @since 1.6
1539 */
1540 public static int getExponent(float f) {
1541 return Math.getExponent(f);
1542 }
1543
1544 /**
1545 * Returns the unbiased exponent used in the representation of a
1546 * {@code double}. Special cases:
1547 *
1548 * <ul>
1549 * <li>If the argument is NaN or infinite, then the result is
1550 * {@link Double#MAX_EXPONENT} + 1.
1551 * <li>If the argument is zero or subnormal, then the result is
1552 * {@link Double#MIN_EXPONENT} -1.
1553 * </ul>
1554 * @param d a {@code double} value
1555 * @return the unbiased exponent of the argument
1556 * @since 1.6
1557 */
1558 public static int getExponent(double d) {
1559 return Math.getExponent(d);
1560 }
1561
1562 /**
1563 * Returns the floating-point number adjacent to the first
1564 * argument in the direction of the second argument. If both
1565 * arguments compare as equal the second argument is returned.
1566 *
1567 * <p>Special cases:
1568 * <ul>
1569 * <li> If either argument is a NaN, then NaN is returned.
1570 *
1571 * <li> If both arguments are signed zeros, {@code direction}
1572 * is returned unchanged (as implied by the requirement of
1573 * returning the second argument if the arguments compare as
1574 * equal).
1575 *
1576 * <li> If {@code start} is
1577 * ±{@link Double#MIN_VALUE} and {@code direction}
1578 * has a value such that the result should have a smaller
1579 * magnitude, then a zero with the same sign as {@code start}
1580 * is returned.
1581 *
1582 * <li> If {@code start} is infinite and
1583 * {@code direction} has a value such that the result should
1584 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1585 * same sign as {@code start} is returned.
1586 *
1587 * <li> If {@code start} is equal to ±
1588 * {@link Double#MAX_VALUE} and {@code direction} has a
1589 * value such that the result should have a larger magnitude, an
1590 * infinity with same sign as {@code start} is returned.
1591 * </ul>
1592 *
1593 * @param start starting floating-point value
1594 * @param direction value indicating which of
1595 * {@code start}'s neighbors or {@code start} should
1596 * be returned
1597 * @return The floating-point number adjacent to {@code start} in the
1598 * direction of {@code direction}.
1599 * @since 1.6
1600 */
1601 public static double nextAfter(double start, double direction) {
1602 return Math.nextAfter(start, direction);
1603 }
1604
1605 /**
1606 * Returns the floating-point number adjacent to the first
1607 * argument in the direction of the second argument. If both
1608 * arguments compare as equal a value equivalent to the second argument
1609 * is returned.
1610 *
1611 * <p>Special cases:
1612 * <ul>
1613 * <li> If either argument is a NaN, then NaN is returned.
1614 *
1615 * <li> If both arguments are signed zeros, a value equivalent
1616 * to {@code direction} is returned.
1617 *
1618 * <li> If {@code start} is
1619 * ±{@link Float#MIN_VALUE} and {@code direction}
1620 * has a value such that the result should have a smaller
1621 * magnitude, then a zero with the same sign as {@code start}
1622 * is returned.
1623 *
1624 * <li> If {@code start} is infinite and
1625 * {@code direction} has a value such that the result should
1626 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1627 * same sign as {@code start} is returned.
1628 *
1629 * <li> If {@code start} is equal to ±
1630 * {@link Float#MAX_VALUE} and {@code direction} has a
1631 * value such that the result should have a larger magnitude, an
1632 * infinity with same sign as {@code start} is returned.
1633 * </ul>
1634 *
1635 * @param start starting floating-point value
1636 * @param direction value indicating which of
1637 * {@code start}'s neighbors or {@code start} should
1638 * be returned
1639 * @return The floating-point number adjacent to {@code start} in the
1640 * direction of {@code direction}.
1641 * @since 1.6
1642 */
1643 public static float nextAfter(float start, double direction) {
1644 return Math.nextAfter(start, direction);
1645 }
1646
1647 /**
1648 * Returns the floating-point value adjacent to {@code d} in
1649 * the direction of positive infinity. This method is
1650 * semantically equivalent to {@code nextAfter(d,
1651 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1652 * implementation may run faster than its equivalent
1653 * {@code nextAfter} call.
1654 *
1655 * <p>Special Cases:
1656 * <ul>
1657 * <li> If the argument is NaN, the result is NaN.
1658 *
1659 * <li> If the argument is positive infinity, the result is
1660 * positive infinity.
1661 *
1662 * <li> If the argument is zero, the result is
1663 * {@link Double#MIN_VALUE}
1664 *
1665 * </ul>
1666 *
1667 * @param d starting floating-point value
1668 * @return The adjacent floating-point value closer to positive
1669 * infinity.
1670 * @since 1.6
1671 */
1672 public static double nextUp(double d) {
1673 return Math.nextUp(d);
1674 }
1675
1676 /**
1677 * Returns the floating-point value adjacent to {@code f} in
1678 * the direction of positive infinity. This method is
1679 * semantically equivalent to {@code nextAfter(f,
1680 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1681 * implementation may run faster than its equivalent
1682 * {@code nextAfter} call.
1683 *
1684 * <p>Special Cases:
1685 * <ul>
1686 * <li> If the argument is NaN, the result is NaN.
1687 *
1688 * <li> If the argument is positive infinity, the result is
1689 * positive infinity.
1690 *
1691 * <li> If the argument is zero, the result is
1692 * {@link Float#MIN_VALUE}
1693 *
1694 * </ul>
1695 *
1696 * @param f starting floating-point value
1697 * @return The adjacent floating-point value closer to positive
1698 * infinity.
1699 * @since 1.6
1700 */
1701 public static float nextUp(float f) {
1702 return Math.nextUp(f);
1703 }
1704
1705 /**
1706 * Returns the floating-point value adjacent to {@code d} in
1707 * the direction of negative infinity. This method is
1708 * semantically equivalent to {@code nextAfter(d,
1709 * Double.NEGATIVE_INFINITY)}; however, a
1710 * {@code nextDown} implementation may run faster than its
1711 * equivalent {@code nextAfter} call.
1712 *
1713 * <p>Special Cases:
1714 * <ul>
1715 * <li> If the argument is NaN, the result is NaN.
1716 *
1717 * <li> If the argument is negative infinity, the result is
1718 * negative infinity.
1719 *
1720 * <li> If the argument is zero, the result is
1721 * {@code -Double.MIN_VALUE}
1722 *
1723 * </ul>
1724 *
1725 * @param d starting floating-point value
1726 * @return The adjacent floating-point value closer to negative
1727 * infinity.
1728 * @since 1.8
1729 */
1730 public static double nextDown(double d) {
1731 return Math.nextDown(d);
1732 }
1733
1734 /**
1735 * Returns the floating-point value adjacent to {@code f} in
1736 * the direction of negative infinity. This method is
1737 * semantically equivalent to {@code nextAfter(f,
1738 * Float.NEGATIVE_INFINITY)}; however, a
1739 * {@code nextDown} implementation may run faster than its
1740 * equivalent {@code nextAfter} call.
1741 *
1742 * <p>Special Cases:
1743 * <ul>
1744 * <li> If the argument is NaN, the result is NaN.
1745 *
1746 * <li> If the argument is negative infinity, the result is
1747 * negative infinity.
1748 *
1749 * <li> If the argument is zero, the result is
1750 * {@code -Float.MIN_VALUE}
1751 *
1752 * </ul>
1753 *
1754 * @param f starting floating-point value
1755 * @return The adjacent floating-point value closer to negative
1756 * infinity.
1757 * @since 1.8
1758 */
1759 public static float nextDown(float f) {
1760 return Math.nextDown(f);
1761 }
1762
1763 /**
1764 * Returns {@code d} ×
1765 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1766 * by a single correctly rounded floating-point multiply to a
1767 * member of the double value set. See the Java
1768 * Language Specification for a discussion of floating-point
1769 * value sets. If the exponent of the result is between {@link
1770 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1771 * answer is calculated exactly. If the exponent of the result
1772 * would be larger than {@code Double.MAX_EXPONENT}, an
1773 * infinity is returned. Note that if the result is subnormal,
1774 * precision may be lost; that is, when {@code scalb(x, n)}
1775 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1776 * <i>x</i>. When the result is non-NaN, the result has the same
1777 * sign as {@code d}.
1778 *
1779 * <p>Special cases:
1780 * <ul>
1781 * <li> If the first argument is NaN, NaN is returned.
1782 * <li> If the first argument is infinite, then an infinity of the
1783 * same sign is returned.
1784 * <li> If the first argument is zero, then a zero of the same
1785 * sign is returned.
1786 * </ul>
1787 *
1788 * @param d number to be scaled by a power of two.
1789 * @param scaleFactor power of 2 used to scale {@code d}
1790 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1791 * @since 1.6
1792 */
1793 public static double scalb(double d, int scaleFactor) {
1794 return Math.scalb(d, scaleFactor);
1795 }
1796
1797 /**
1798 * Returns {@code f} ×
1799 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1800 * by a single correctly rounded floating-point multiply to a
1801 * member of the float value set. See the Java
1802 * Language Specification for a discussion of floating-point
1803 * value sets. If the exponent of the result is between {@link
1804 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1805 * answer is calculated exactly. If the exponent of the result
1806 * would be larger than {@code Float.MAX_EXPONENT}, an
1807 * infinity is returned. Note that if the result is subnormal,
1808 * precision may be lost; that is, when {@code scalb(x, n)}
1809 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1810 * <i>x</i>. When the result is non-NaN, the result has the same
1811 * sign as {@code f}.
1812 *
1813 * <p>Special cases:
1814 * <ul>
1815 * <li> If the first argument is NaN, NaN is returned.
1816 * <li> If the first argument is infinite, then an infinity of the
1817 * same sign is returned.
1818 * <li> If the first argument is zero, then a zero of the same
1819 * sign is returned.
1820 * </ul>
1821 *
1822 * @param f number to be scaled by a power of two.
1823 * @param scaleFactor power of 2 used to scale {@code f}
1824 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1825 * @since 1.6
1826 */
1827 public static float scalb(float f, int scaleFactor) {
1828 return Math.scalb(f, scaleFactor);
1829 }
1830 }