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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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="https://www.netlib.org/fdlibm/">{@code fdlibm}</a>. These
44 * algorithms, which are written in the C programming language, are
45 * then to be understood as executed with all floating-point
46 * operations following the rules of Java floating-point arithmetic.
47 *
48 * <p>The Java math library is defined with respect to
49 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides
50 * more than one definition for a function (such as
51 * {@code acos}), use the "IEEE 754 core function" version
52 * (residing in a file whose name begins with the letter
53 * {@code e}). The methods which require {@code fdlibm}
54 * semantics are {@code sin}, {@code cos}, {@code tan},
55 * {@code asin}, {@code acos}, {@code atan},
56 * {@code exp}, {@code log}, {@code log10},
57 * {@code cbrt}, {@code atan2}, {@code pow},
58 * {@code sinh}, {@code cosh}, {@code tanh},
59 * {@code hypot}, {@code expm1}, and {@code log1p}.
60 *
61 * <p>
62 * The platform uses signed two's complement integer arithmetic with
63 * int and long primitive types. The developer should choose
64 * the primitive type to ensure that arithmetic operations consistently
65 * produce correct results, which in some cases means the operations
66 * will not overflow the range of values of the computation.
67 * The best practice is to choose the primitive type and algorithm to avoid
68 * overflow. In cases where the size is {@code int} or {@code long} and
69 * overflow errors need to be detected, the methods {@code addExact},
70 * {@code subtractExact}, {@code multiplyExact}, 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 double exp(double a) {
231 return FdLibm.Exp.compute(a);
232 }
233
234 /**
235 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
236 * value. Special cases:
237 * <ul><li>If the argument is NaN or less than zero, then the result
238 * is NaN.
239 * <li>If the argument is positive infinity, then the result is
240 * positive infinity.
241 * <li>If the argument is positive zero or negative zero, then the
242 * result is negative infinity.</ul>
243 *
244 * @param a a value
245 * @return the value ln {@code a}, the natural logarithm of
246 * {@code a}.
247 */
248 public static native double log(double a);
249
250 /**
251 * Returns the base 10 logarithm of a {@code double} value.
252 * Special cases:
253 *
254 * <ul><li>If the argument is NaN or less than zero, then the result
255 * is NaN.
256 * <li>If the argument is positive infinity, then the result is
257 * positive infinity.
258 * <li>If the argument is positive zero or negative zero, then the
259 * result is negative infinity.
260 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
261 * integer <i>n</i>, then the result is <i>n</i>.
262 * </ul>
263 *
264 * @param a a value
265 * @return the base 10 logarithm of {@code a}.
266 * @since 1.5
267 */
268 public static native double log10(double a);
269
270 /**
271 * Returns the correctly rounded positive square root of a
272 * {@code double} value.
273 * Special cases:
274 * <ul><li>If the argument is NaN or less than zero, then the result
275 * is NaN.
276 * <li>If the argument is positive infinity, then the result is positive
277 * infinity.
278 * <li>If the argument is positive zero or negative zero, then the
279 * result is the same as the argument.</ul>
280 * Otherwise, the result is the {@code double} value closest to
281 * the true mathematical square root of the argument value.
282 *
283 * @param a a value.
284 * @return the positive square root of {@code a}.
285 */
286 @HotSpotIntrinsicCandidate
287 public static native double sqrt(double a);
288
289 /**
290 * Returns the cube root of a {@code double} value. For
291 * positive finite {@code x}, {@code cbrt(-x) ==
292 * -cbrt(x)}; that is, the cube root of a negative value is
293 * the negative of the cube root of that value's magnitude.
294 * Special cases:
295 *
296 * <ul>
297 *
298 * <li>If the argument is NaN, then the result is NaN.
299 *
300 * <li>If the argument is infinite, then the result is an infinity
301 * with the same sign as the argument.
302 *
303 * <li>If the argument is zero, then the result is a zero with the
304 * same sign as the argument.
305 *
306 * </ul>
307 *
308 * @param a a value.
309 * @return the cube root of {@code a}.
310 * @since 1.5
311 */
312 public static double cbrt(double a) {
313 return FdLibm.Cbrt.compute(a);
314 }
315
316 /**
317 * Computes the remainder operation on two arguments as prescribed
318 * by the IEEE 754 standard.
319 * The remainder value is mathematically equal to
320 * <code>f1 - f2</code> × <i>n</i>,
321 * where <i>n</i> is the mathematical integer closest to the exact
322 * mathematical value of the quotient {@code f1/f2}, and if two
323 * mathematical integers are equally close to {@code f1/f2},
324 * then <i>n</i> is the integer that is even. If the remainder is
325 * zero, its sign is the same as the sign of the first argument.
326 * Special cases:
327 * <ul><li>If either argument is NaN, or the first argument is infinite,
328 * or the second argument is positive zero or negative zero, then the
329 * result is NaN.
330 * <li>If the first argument is finite and the second argument is
331 * infinite, then the result is the same as the first argument.</ul>
332 *
333 * @param f1 the dividend.
334 * @param f2 the divisor.
335 * @return the remainder when {@code f1} is divided by
336 * {@code f2}.
337 */
338 public static native double IEEEremainder(double f1, double f2);
339
340 /**
341 * Returns the smallest (closest to negative infinity)
342 * {@code double} value that is greater than or equal to the
343 * argument and is equal to a mathematical integer. Special cases:
344 * <ul><li>If the argument value is already equal to a
345 * mathematical integer, then the result is the same as the
346 * argument. <li>If the argument is NaN or an infinity or
347 * positive zero or negative zero, then the result is the same as
348 * the argument. <li>If the argument value is less than zero but
349 * greater than -1.0, then the result is negative zero.</ul> Note
350 * that the value of {@code StrictMath.ceil(x)} is exactly the
351 * value of {@code -StrictMath.floor(-x)}.
352 *
353 * @param a a value.
354 * @return the smallest (closest to negative infinity)
355 * floating-point value that is greater than or equal to
356 * the argument and is equal to a mathematical integer.
357 */
358 public static double ceil(double a) {
359 return floorOrCeil(a, -0.0, 1.0, 1.0);
360 }
361
362 /**
363 * Returns the largest (closest to positive infinity)
364 * {@code double} value that is less than or equal to the
365 * argument and is equal to a mathematical integer. Special cases:
366 * <ul><li>If the argument value is already equal to a
367 * mathematical integer, then the result is the same as the
368 * argument. <li>If the argument is NaN or an infinity or
369 * positive zero or negative zero, then the result is the same as
370 * the argument.</ul>
371 *
372 * @param a a value.
373 * @return the largest (closest to positive infinity)
374 * floating-point value that less than or equal to the argument
375 * and is equal to a mathematical integer.
376 */
377 public static double floor(double a) {
378 return floorOrCeil(a, -1.0, 0.0, -1.0);
379 }
380
381 /**
382 * Internal method to share logic between floor and ceil.
383 *
384 * @param a the value to be floored or ceiled
385 * @param negativeBoundary result for values in (-1, 0)
386 * @param positiveBoundary result for values in (0, 1)
387 * @param increment value to add when the argument is non-integral
388 */
389 private static double floorOrCeil(double a,
390 double negativeBoundary,
391 double positiveBoundary,
392 double sign) {
393 int exponent = Math.getExponent(a);
394
395 if (exponent < 0) {
396 /*
397 * Absolute value of argument is less than 1.
398 * floorOrceil(-0.0) => -0.0
399 * floorOrceil(+0.0) => +0.0
400 */
401 return ((a == 0.0) ? a :
402 ( (a < 0.0) ? negativeBoundary : positiveBoundary) );
403 } else if (exponent >= 52) {
404 /*
405 * Infinity, NaN, or a value so large it must be integral.
406 */
407 return a;
408 }
409 // Else the argument is either an integral value already XOR it
410 // has to be rounded to one.
411 assert exponent >= 0 && exponent <= 51;
412
413 long doppel = Double.doubleToRawLongBits(a);
414 long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent;
415
416 if ( (mask & doppel) == 0L )
417 return a; // integral value
418 else {
419 double result = Double.longBitsToDouble(doppel & (~mask));
420 if (sign*a > 0.0)
421 result = result + sign;
422 return result;
423 }
424 }
425
426 /**
427 * Returns the {@code double} value that is closest in value
428 * to the argument and is equal to a mathematical integer. If two
429 * {@code double} values that are mathematical integers are
430 * equally close to the value of the argument, the result is the
431 * integer value that is even. Special cases:
432 * <ul><li>If the argument value is already equal to a mathematical
433 * integer, then the result is the same as the argument.
434 * <li>If the argument is NaN or an infinity or positive zero or negative
435 * zero, then the result is the same as the argument.</ul>
436 *
437 * @param a a value.
438 * @return the closest floating-point value to {@code a} that is
439 * equal to a mathematical integer.
440 * @author Joseph D. Darcy
441 */
442 public static double rint(double a) {
443 /*
444 * If the absolute value of a is not less than 2^52, it
445 * is either a finite integer (the double format does not have
446 * enough significand bits for a number that large to have any
447 * fractional portion), an infinity, or a NaN. In any of
448 * these cases, rint of the argument is the argument.
449 *
450 * Otherwise, the sum (twoToThe52 + a ) will properly round
451 * away any fractional portion of a since ulp(twoToThe52) ==
452 * 1.0; subtracting out twoToThe52 from this sum will then be
453 * exact and leave the rounded integer portion of a.
454 *
455 * This method does *not* need to be declared strictfp to get
456 * fully reproducible results. Whether or not a method is
457 * declared strictfp can only make a difference in the
458 * returned result if some operation would overflow or
459 * underflow with strictfp semantics. The operation
460 * (twoToThe52 + a ) cannot overflow since large values of a
461 * are screened out; the add cannot underflow since twoToThe52
462 * is too large. The subtraction ((twoToThe52 + a ) -
463 * twoToThe52) will be exact as discussed above and thus
464 * cannot overflow or meaningfully underflow. Finally, the
465 * last multiply in the return statement is by plus or minus
466 * 1.0, which is exact too.
467 */
468 double twoToThe52 = (double)(1L << 52); // 2^52
469 double sign = Math.copySign(1.0, a); // preserve sign info
470 a = Math.abs(a);
471
472 if (a < twoToThe52) { // E_min <= ilogb(a) <= 51
473 a = ((twoToThe52 + a ) - twoToThe52);
474 }
475
476 return sign * a; // restore original sign
477 }
478
479 /**
480 * Returns the angle <i>theta</i> from the conversion of rectangular
481 * coordinates ({@code x}, {@code y}) to polar
482 * coordinates (r, <i>theta</i>).
483 * This method computes the phase <i>theta</i> by computing an arc tangent
484 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
485 * cases:
486 * <ul><li>If either argument is NaN, then the result is NaN.
487 * <li>If the first argument is positive zero and the second argument
488 * is positive, or the first argument is positive and finite and the
489 * second argument is positive infinity, then the result is positive
490 * zero.
491 * <li>If the first argument is negative zero and the second argument
492 * is positive, or the first argument is negative and finite and the
493 * second argument is positive infinity, then the result is negative zero.
494 * <li>If the first argument is positive zero and the second argument
495 * is negative, or the first argument is positive and finite and the
496 * second argument is negative infinity, then the result is the
497 * {@code double} value closest to <i>pi</i>.
498 * <li>If the first argument is negative zero and the second argument
499 * is negative, or the first argument is negative and finite and the
500 * second argument is negative infinity, then the result is the
501 * {@code double} value closest to -<i>pi</i>.
502 * <li>If the first argument is positive and the second argument is
503 * positive zero or negative zero, or the first argument is positive
504 * infinity and the second argument is finite, then the result is the
505 * {@code double} value closest to <i>pi</i>/2.
506 * <li>If the first argument is negative and the second argument is
507 * positive zero or negative zero, or the first argument is negative
508 * infinity and the second argument is finite, then the result is the
509 * {@code double} value closest to -<i>pi</i>/2.
510 * <li>If both arguments are positive infinity, then the result is the
511 * {@code double} value closest to <i>pi</i>/4.
512 * <li>If the first argument is positive infinity and the second argument
513 * is negative infinity, then the result is the {@code double}
514 * value closest to 3*<i>pi</i>/4.
515 * <li>If the first argument is negative infinity and the second argument
516 * is positive infinity, then the result is the {@code double} value
517 * closest to -<i>pi</i>/4.
518 * <li>If both arguments are negative infinity, then the result is the
519 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
520 *
521 * @param y the ordinate coordinate
522 * @param x the abscissa coordinate
523 * @return the <i>theta</i> component of the point
524 * (<i>r</i>, <i>theta</i>)
525 * in polar coordinates that corresponds to the point
526 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
527 */
528 public static native double atan2(double y, double x);
529
530 /**
531 * Returns the value of the first argument raised to the power of the
532 * second argument. Special cases:
533 *
534 * <ul><li>If the second argument is positive or negative zero, then the
535 * result is 1.0.
536 * <li>If the second argument is 1.0, then the result is the same as the
537 * first argument.
538 * <li>If the second argument is NaN, then the result is NaN.
539 * <li>If the first argument is NaN and the second argument is nonzero,
540 * then the result is NaN.
541 *
542 * <li>If
543 * <ul>
544 * <li>the absolute value of the first argument is greater than 1
545 * and the second argument is positive infinity, or
546 * <li>the absolute value of the first argument is less than 1 and
547 * the second argument is negative infinity,
548 * </ul>
549 * then the result is positive infinity.
550 *
551 * <li>If
552 * <ul>
553 * <li>the absolute value of the first argument is greater than 1 and
554 * the second argument is negative infinity, or
555 * <li>the absolute value of the
556 * first argument is less than 1 and the second argument is positive
557 * infinity,
558 * </ul>
559 * then the result is positive zero.
560 *
561 * <li>If the absolute value of the first argument equals 1 and the
562 * second argument is infinite, then the result is NaN.
563 *
564 * <li>If
565 * <ul>
566 * <li>the first argument is positive zero and the second argument
567 * is greater than zero, or
568 * <li>the first argument is positive infinity and the second
569 * argument is less than zero,
570 * </ul>
571 * then the result is positive zero.
572 *
573 * <li>If
574 * <ul>
575 * <li>the first argument is positive zero and the second argument
576 * is less than zero, or
577 * <li>the first argument is positive infinity and the second
578 * argument is greater than zero,
579 * </ul>
580 * then the result is positive infinity.
581 *
582 * <li>If
583 * <ul>
584 * <li>the first argument is negative zero and the second argument
585 * is greater than zero but not a finite odd integer, or
586 * <li>the first argument is negative infinity and the second
587 * argument is less than zero but not a finite odd integer,
588 * </ul>
589 * then the result is positive zero.
590 *
591 * <li>If
592 * <ul>
593 * <li>the first argument is negative zero and the second argument
594 * is a positive finite odd integer, or
595 * <li>the first argument is negative infinity and the second
596 * argument is a negative finite odd integer,
597 * </ul>
598 * then the result is negative zero.
599 *
600 * <li>If
601 * <ul>
602 * <li>the first argument is negative zero and the second argument
603 * is less than zero but not a finite odd integer, or
604 * <li>the first argument is negative infinity and the second
605 * argument is greater than zero but not a finite odd integer,
606 * </ul>
607 * then the result is positive infinity.
608 *
609 * <li>If
610 * <ul>
611 * <li>the first argument is negative zero and the second argument
612 * is a negative finite odd integer, or
613 * <li>the first argument is negative infinity and the second
614 * argument is a positive finite odd integer,
615 * </ul>
616 * then the result is negative infinity.
617 *
618 * <li>If the first argument is finite and less than zero
619 * <ul>
620 * <li> if the second argument is a finite even integer, the
621 * result is equal to the result of raising the absolute value of
622 * the first argument to the power of the second argument
623 *
624 * <li>if the second argument is a finite odd integer, the result
625 * is equal to the negative of the result of raising the absolute
626 * value of the first argument to the power of the second
627 * argument
628 *
629 * <li>if the second argument is finite and not an integer, then
630 * the result is NaN.
631 * </ul>
632 *
633 * <li>If both arguments are integers, then the result is exactly equal
634 * to the mathematical result of raising the first argument to the power
635 * of the second argument if that result can in fact be represented
636 * exactly as a {@code double} value.</ul>
637 *
638 * <p>(In the foregoing descriptions, a floating-point value is
639 * considered to be an integer if and only if it is finite and a
640 * fixed point of the method {@link #ceil ceil} or,
641 * equivalently, a fixed point of the method {@link #floor
642 * floor}. A value is a fixed point of a one-argument
643 * method if and only if the result of applying the method to the
644 * value is equal to the value.)
645 *
646 * @param a base.
647 * @param b the exponent.
648 * @return the value {@code a}<sup>{@code b}</sup>.
649 */
650 public static double pow(double a, double b) {
651 return FdLibm.Pow.compute(a, b);
652 }
653
654 /**
655 * Returns the closest {@code int} to the argument, with ties
656 * rounding to positive infinity.
657 *
658 * <p>Special cases:
659 * <ul><li>If the argument is NaN, the result is 0.
660 * <li>If the argument is negative infinity or any value less than or
661 * equal to the value of {@code Integer.MIN_VALUE}, the result is
662 * equal to the value of {@code Integer.MIN_VALUE}.
663 * <li>If the argument is positive infinity or any value greater than or
664 * equal to the value of {@code Integer.MAX_VALUE}, the result is
665 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
666 *
667 * @param a a floating-point value to be rounded to an integer.
668 * @return the value of the argument rounded to the nearest
669 * {@code int} value.
670 * @see java.lang.Integer#MAX_VALUE
671 * @see java.lang.Integer#MIN_VALUE
672 */
673 public static int round(float a) {
674 return Math.round(a);
675 }
676
677 /**
678 * Returns the closest {@code long} to the argument, with ties
679 * rounding to positive infinity.
680 *
681 * <p>Special cases:
682 * <ul><li>If the argument is NaN, the result is 0.
683 * <li>If the argument is negative infinity or any value less than or
684 * equal to the value of {@code Long.MIN_VALUE}, the result is
685 * equal to the value of {@code Long.MIN_VALUE}.
686 * <li>If the argument is positive infinity or any value greater than or
687 * equal to the value of {@code Long.MAX_VALUE}, the result is
688 * equal to the value of {@code Long.MAX_VALUE}.</ul>
689 *
690 * @param a a floating-point value to be rounded to a
691 * {@code long}.
692 * @return the value of the argument rounded to the nearest
693 * {@code long} value.
694 * @see java.lang.Long#MAX_VALUE
695 * @see java.lang.Long#MIN_VALUE
696 */
697 public static long round(double a) {
698 return Math.round(a);
699 }
700
701 private static final class RandomNumberGeneratorHolder {
702 static final Random randomNumberGenerator = new Random();
703 }
704
705 /**
706 * Returns a {@code double} value with a positive sign, greater
707 * than or equal to {@code 0.0} and less than {@code 1.0}.
708 * Returned values are chosen pseudorandomly with (approximately)
709 * uniform distribution from that range.
710 *
711 * <p>When this method is first called, it creates a single new
712 * pseudorandom-number generator, exactly as if by the expression
713 *
714 * <blockquote>{@code new java.util.Random()}</blockquote>
715 *
716 * This new pseudorandom-number generator is used thereafter for
717 * all calls to this method and is used nowhere else.
718 *
719 * <p>This method is properly synchronized to allow correct use by
720 * more than one thread. However, if many threads need to generate
721 * pseudorandom numbers at a great rate, it may reduce contention
722 * for each thread to have its own pseudorandom-number generator.
723 *
724 * @return a pseudorandom {@code double} greater than or equal
725 * to {@code 0.0} and less than {@code 1.0}.
726 * @see Random#nextDouble()
727 */
728 public static double random() {
729 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
730 }
731
732 /**
733 * Returns the sum of its arguments,
734 * throwing an exception if the result overflows an {@code int}.
735 *
736 * @param x the first value
737 * @param y the second value
738 * @return the result
739 * @throws ArithmeticException if the result overflows an int
740 * @see Math#addExact(int,int)
741 * @since 1.8
742 */
743 public static int addExact(int x, int y) {
744 return Math.addExact(x, y);
745 }
746
747 /**
748 * Returns the sum of its arguments,
749 * throwing an exception if the result overflows a {@code long}.
750 *
751 * @param x the first value
752 * @param y the second value
753 * @return the result
754 * @throws ArithmeticException if the result overflows a long
755 * @see Math#addExact(long,long)
756 * @since 1.8
757 */
758 public static long addExact(long x, long y) {
759 return Math.addExact(x, y);
760 }
761
762 /**
763 * Returns the difference of the arguments,
764 * throwing an exception if the result overflows an {@code int}.
765 *
766 * @param x the first value
767 * @param y the second value to subtract from the first
768 * @return the result
769 * @throws ArithmeticException if the result overflows an int
770 * @see Math#subtractExact(int,int)
771 * @since 1.8
772 */
773 public static int subtractExact(int x, int y) {
774 return Math.subtractExact(x, y);
775 }
776
777 /**
778 * Returns the difference of the arguments,
779 * throwing an exception if the result overflows a {@code long}.
780 *
781 * @param x the first value
782 * @param y the second value to subtract from the first
783 * @return the result
784 * @throws ArithmeticException if the result overflows a long
785 * @see Math#subtractExact(long,long)
786 * @since 1.8
787 */
788 public static long subtractExact(long x, long y) {
789 return Math.subtractExact(x, y);
790 }
791
792 /**
793 * Returns the product of the arguments,
794 * throwing an exception if the result overflows an {@code int}.
795 *
796 * @param x the first value
797 * @param y the second value
798 * @return the result
799 * @throws ArithmeticException if the result overflows an int
800 * @see Math#multiplyExact(int,int)
801 * @since 1.8
802 */
803 public static int multiplyExact(int x, int y) {
804 return Math.multiplyExact(x, y);
805 }
806
807 /**
808 * Returns the product of the arguments, throwing an exception if the result
809 * overflows a {@code long}.
810 *
811 * @param x the first value
812 * @param y the second value
813 * @return the result
814 * @throws ArithmeticException if the result overflows a long
815 * @see Math#multiplyExact(long,int)
816 * @since 9
817 */
818 public static long multiplyExact(long x, int y) {
819 return Math.multiplyExact(x, y);
820 }
821
822 /**
823 * Returns the product of the arguments,
824 * throwing an exception if the result overflows a {@code long}.
825 *
826 * @param x the first value
827 * @param y the second value
828 * @return the result
829 * @throws ArithmeticException if the result overflows a long
830 * @see Math#multiplyExact(long,long)
831 * @since 1.8
832 */
833 public static long multiplyExact(long x, long y) {
834 return Math.multiplyExact(x, y);
835 }
836
837 /**
838 * Returns the value of the {@code long} argument;
839 * throwing an exception if the value overflows an {@code int}.
840 *
841 * @param value the long value
842 * @return the argument as an int
843 * @throws ArithmeticException if the {@code argument} overflows an int
844 * @see Math#toIntExact(long)
845 * @since 1.8
846 */
847 public static int toIntExact(long value) {
848 return Math.toIntExact(value);
849 }
850
851 /**
852 * Returns the exact mathematical product of the arguments.
853 *
854 * @param x the first value
855 * @param y the second value
856 * @return the result
857 * @see Math#multiplyFull(int,int)
858 * @since 9
859 */
860 public static long multiplyFull(int x, int y) {
861 return Math.multiplyFull(x, y);
862 }
863
864 /**
865 * Returns as a {@code long} the most significant 64 bits of the 128-bit
866 * product of two 64-bit factors.
867 *
868 * @param x the first value
869 * @param y the second value
870 * @return the result
871 * @see Math#multiplyHigh(long,long)
872 * @since 9
873 */
874 public static long multiplyHigh(long x, long y) {
875 return Math.multiplyHigh(x, y);
876 }
877
878 /**
879 * Returns the largest (closest to positive infinity)
880 * {@code int} value that is less than or equal to the algebraic quotient.
881 * There is one special case, if the dividend is the
882 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
883 * then integer overflow occurs and
884 * the result is equal to the {@code Integer.MIN_VALUE}.
885 * <p>
886 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
887 * a comparison to the integer division {@code /} operator.
888 *
889 * @param x the dividend
890 * @param y the divisor
891 * @return the largest (closest to positive infinity)
892 * {@code int} value that is less than or equal to the algebraic quotient.
893 * @throws ArithmeticException if the divisor {@code y} is zero
894 * @see Math#floorDiv(int, int)
895 * @see Math#floor(double)
896 * @since 1.8
897 */
898 public static int floorDiv(int x, int y) {
899 return Math.floorDiv(x, y);
900 }
901
902 /**
903 * Returns the largest (closest to positive infinity)
904 * {@code long} value that is less than or equal to the algebraic quotient.
905 * There is one special case, if the dividend is the
906 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
907 * then integer overflow occurs and
908 * the result is equal to {@code Long.MIN_VALUE}.
909 * <p>
910 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
911 * a comparison to the integer division {@code /} operator.
912 *
913 * @param x the dividend
914 * @param y the divisor
915 * @return the largest (closest to positive infinity)
916 * {@code int} value that is less than or equal to the algebraic quotient.
917 * @throws ArithmeticException if the divisor {@code y} is zero
918 * @see Math#floorDiv(long, int)
919 * @see Math#floor(double)
920 * @since 9
921 */
922 public static long floorDiv(long x, int y) {
923 return Math.floorDiv(x, y);
924 }
925
926 /**
927 * Returns the largest (closest to positive infinity)
928 * {@code long} value that is less than or equal to the algebraic quotient.
929 * There is one special case, if the dividend is the
930 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
931 * then integer overflow occurs and
932 * the result is equal to the {@code Long.MIN_VALUE}.
933 * <p>
934 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and
935 * a comparison to the integer division {@code /} operator.
936 *
937 * @param x the dividend
938 * @param y the divisor
939 * @return the largest (closest to positive infinity)
940 * {@code long} value that is less than or equal to the algebraic quotient.
941 * @throws ArithmeticException if the divisor {@code y} is zero
942 * @see Math#floorDiv(long, long)
943 * @see Math#floor(double)
944 * @since 1.8
945 */
946 public static long floorDiv(long x, long y) {
947 return Math.floorDiv(x, y);
948 }
949
950 /**
951 * Returns the floor modulus of the {@code int} arguments.
952 * <p>
953 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
954 * has the same sign as the divisor {@code y}, and
955 * is in the range of {@code -abs(y) < r < +abs(y)}.
956 * <p>
957 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
958 * <ul>
959 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
960 * </ul>
961 * <p>
962 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
963 * a comparison to the {@code %} operator.
964 *
965 * @param x the dividend
966 * @param y the divisor
967 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
968 * @throws ArithmeticException if the divisor {@code y} is zero
969 * @see Math#floorMod(int, int)
970 * @see StrictMath#floorDiv(int, int)
971 * @since 1.8
972 */
973 public static int floorMod(int x, int y) {
974 return Math.floorMod(x , y);
975 }
976
977 /**
978 * Returns the floor modulus of the {@code long} and {@code int} arguments.
979 * <p>
980 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
981 * has the same sign as the divisor {@code y}, and
982 * is in the range of {@code -abs(y) < r < +abs(y)}.
983 *
984 * <p>
985 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
986 * <ul>
987 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
988 * </ul>
989 * <p>
990 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
991 * a comparison to the {@code %} operator.
992 *
993 * @param x the dividend
994 * @param y the divisor
995 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
996 * @throws ArithmeticException if the divisor {@code y} is zero
997 * @see Math#floorMod(long, int)
998 * @see StrictMath#floorDiv(long, int)
999 * @since 9
1000 */
1001 public static int floorMod(long x, int y) {
1002 return Math.floorMod(x , y);
1003 }
1004
1005 /**
1006 * Returns the floor modulus of the {@code long} arguments.
1007 * <p>
1008 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1009 * has the same sign as the divisor {@code y}, and
1010 * is in the range of {@code -abs(y) < r < +abs(y)}.
1011 * <p>
1012 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1013 * <ul>
1014 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1015 * </ul>
1016 * <p>
1017 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and
1018 * a comparison to the {@code %} operator.
1019 *
1020 * @param x the dividend
1021 * @param y the divisor
1022 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1023 * @throws ArithmeticException if the divisor {@code y} is zero
1024 * @see Math#floorMod(long, long)
1025 * @see StrictMath#floorDiv(long, long)
1026 * @since 1.8
1027 */
1028 public static long floorMod(long x, long y) {
1029 return Math.floorMod(x, y);
1030 }
1031
1032 /**
1033 * Returns the absolute value of an {@code int} value.
1034 * If the argument is not negative, the argument is returned.
1035 * If the argument is negative, the negation of the argument is returned.
1036 *
1037 * <p>Note that if the argument is equal to the value of
1038 * {@link Integer#MIN_VALUE}, the most negative representable
1039 * {@code int} value, the result is that same value, which is
1040 * negative.
1041 *
1042 * @param a the argument whose absolute value is to be determined.
1043 * @return the absolute value of the argument.
1044 */
1045 public static int abs(int a) {
1046 return Math.abs(a);
1047 }
1048
1049 /**
1050 * Returns the absolute value of a {@code long} value.
1051 * If the argument is not negative, the argument is returned.
1052 * If the argument is negative, the negation of the argument is returned.
1053 *
1054 * <p>Note that if the argument is equal to the value of
1055 * {@link Long#MIN_VALUE}, the most negative representable
1056 * {@code long} value, the result is that same value, which
1057 * is negative.
1058 *
1059 * @param a the argument whose absolute value is to be determined.
1060 * @return the absolute value of the argument.
1061 */
1062 public static long abs(long a) {
1063 return Math.abs(a);
1064 }
1065
1066 /**
1067 * Returns the absolute value of a {@code float} value.
1068 * If the argument is not negative, the argument is returned.
1069 * If the argument is negative, the negation of the argument is returned.
1070 * Special cases:
1071 * <ul><li>If the argument is positive zero or negative zero, the
1072 * result is positive zero.
1073 * <li>If the argument is infinite, the result is positive infinity.
1074 * <li>If the argument is NaN, the result is NaN.</ul>
1075 *
1076 * @apiNote As implied by the above, one valid implementation of
1077 * this method is given by the expression below which computes a
1078 * {@code float} with the same exponent and significand as the
1079 * argument but with a guaranteed zero sign bit indicating a
1080 * positive value: <br>
1081 * {@code Float.intBitsToFloat(0x7fffffff & Float.floatToRawIntBits(a))}
1082 *
1083 * @param a the argument whose absolute value is to be determined
1084 * @return the absolute value of the argument.
1085 */
1086 public static float abs(float a) {
1087 return Math.abs(a);
1088 }
1089
1090 /**
1091 * Returns the absolute value of a {@code double} value.
1092 * If the argument is not negative, the argument is returned.
1093 * If the argument is negative, the negation of the argument is returned.
1094 * Special cases:
1095 * <ul><li>If the argument is positive zero or negative zero, the result
1096 * is positive zero.
1097 * <li>If the argument is infinite, the result is positive infinity.
1098 * <li>If the argument is NaN, the result is NaN.</ul>
1099 *
1100 * @apiNote As implied by the above, one valid implementation of
1101 * this method is given by the expression below which computes a
1102 * {@code double} with the same exponent and significand as the
1103 * argument but with a guaranteed zero sign bit indicating a
1104 * positive value: <br>
1105 * {@code Double.longBitsToDouble((Double.doubleToRawLongBits(a)<<1)>>>1)}
1106 *
1107 * @param a the argument whose absolute value is to be determined
1108 * @return the absolute value of the argument.
1109 */
1110 public static double abs(double a) {
1111 return Math.abs(a);
1112 }
1113
1114 /**
1115 * Returns the greater of two {@code int} values. That is, the
1116 * result is the argument closer to the value of
1117 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1118 * the result is that same value.
1119 *
1120 * @param a an argument.
1121 * @param b another argument.
1122 * @return the larger of {@code a} and {@code b}.
1123 */
1124 @HotSpotIntrinsicCandidate
1125 public static int max(int a, int b) {
1126 return Math.max(a, b);
1127 }
1128
1129 /**
1130 * Returns the greater of two {@code long} values. That is, the
1131 * result is the argument closer to the value of
1132 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1133 * the result is that same value.
1134 *
1135 * @param a an argument.
1136 * @param b another argument.
1137 * @return the larger of {@code a} and {@code b}.
1138 */
1139 public static long max(long a, long b) {
1140 return Math.max(a, b);
1141 }
1142
1143 /**
1144 * Returns the greater of two {@code float} values. That is,
1145 * the result is the argument closer to positive infinity. If the
1146 * arguments have the same value, the result is that same
1147 * value. If either value is NaN, then the result is NaN. Unlike
1148 * the numerical comparison operators, this method considers
1149 * negative zero to be strictly smaller than positive zero. If one
1150 * argument is positive zero and the other negative zero, the
1151 * result is positive zero.
1152 *
1153 * @param a an argument.
1154 * @param b another argument.
1155 * @return the larger of {@code a} and {@code b}.
1156 */
1157 @HotSpotIntrinsicCandidate
1158 public static float max(float a, float b) {
1159 return Math.max(a, b);
1160 }
1161
1162 /**
1163 * Returns the greater of two {@code double} values. That
1164 * is, the result is the argument closer to positive infinity. If
1165 * the arguments have the same value, the result is that same
1166 * value. If either value is NaN, then the result is NaN. Unlike
1167 * the numerical comparison operators, this method considers
1168 * negative zero to be strictly smaller than positive zero. If one
1169 * argument is positive zero and the other negative zero, the
1170 * result is positive zero.
1171 *
1172 * @param a an argument.
1173 * @param b another argument.
1174 * @return the larger of {@code a} and {@code b}.
1175 */
1176 @HotSpotIntrinsicCandidate
1177 public static double max(double a, double b) {
1178 return Math.max(a, b);
1179 }
1180
1181 /**
1182 * Returns the smaller of two {@code int} values. That is,
1183 * the result the argument closer to the value of
1184 * {@link Integer#MIN_VALUE}. If the arguments have the same
1185 * value, the result is that same value.
1186 *
1187 * @param a an argument.
1188 * @param b another argument.
1189 * @return the smaller of {@code a} and {@code b}.
1190 */
1191 @HotSpotIntrinsicCandidate
1192 public static int min(int a, int b) {
1193 return Math.min(a, b);
1194 }
1195
1196 /**
1197 * Returns the smaller of two {@code long} values. That is,
1198 * the result is the argument closer to the value of
1199 * {@link Long#MIN_VALUE}. If the arguments have the same
1200 * value, the result is that same value.
1201 *
1202 * @param a an argument.
1203 * @param b another argument.
1204 * @return the smaller of {@code a} and {@code b}.
1205 */
1206 public static long min(long a, long b) {
1207 return Math.min(a, b);
1208 }
1209
1210 /**
1211 * Returns the smaller of two {@code float} values. That is,
1212 * the result is the value closer to negative infinity. If the
1213 * arguments have the same value, the result is that same
1214 * value. If either value is NaN, then the result is NaN. Unlike
1215 * the numerical comparison operators, this method considers
1216 * negative zero to be strictly smaller than positive zero. If
1217 * one argument is positive zero and the other is negative zero,
1218 * the result is negative zero.
1219 *
1220 * @param a an argument.
1221 * @param b another argument.
1222 * @return the smaller of {@code a} and {@code b.}
1223 */
1224 @HotSpotIntrinsicCandidate
1225 public static float min(float a, float b) {
1226 return Math.min(a, b);
1227 }
1228
1229 /**
1230 * Returns the smaller of two {@code double} values. That
1231 * is, the result is the value closer to negative infinity. If the
1232 * arguments have the same value, the result is that same
1233 * value. If either value is NaN, then the result is NaN. Unlike
1234 * the numerical comparison operators, this method considers
1235 * negative zero to be strictly smaller than positive zero. If one
1236 * argument is positive zero and the other is negative zero, the
1237 * result is negative zero.
1238 *
1239 * @param a an argument.
1240 * @param b another argument.
1241 * @return the smaller of {@code a} and {@code b}.
1242 */
1243 @HotSpotIntrinsicCandidate
1244 public static double min(double a, double b) {
1245 return Math.min(a, b);
1246 }
1247
1248 /**
1249 * Returns the fused multiply add of the three arguments; that is,
1250 * returns the exact product of the first two arguments summed
1251 * with the third argument and then rounded once to the nearest
1252 * {@code double}.
1253 *
1254 * The rounding is done using the {@linkplain
1255 * java.math.RoundingMode#HALF_EVEN round to nearest even
1256 * rounding mode}.
1257 *
1258 * In contrast, if {@code a * b + c} is evaluated as a regular
1259 * floating-point expression, two rounding errors are involved,
1260 * the first for the multiply operation, the second for the
1261 * addition operation.
1262 *
1263 * <p>Special cases:
1264 * <ul>
1265 * <li> If any argument is NaN, the result is NaN.
1266 *
1267 * <li> If one of the first two arguments is infinite and the
1268 * other is zero, the result is NaN.
1269 *
1270 * <li> If the exact product of the first two arguments is infinite
1271 * (in other words, at least one of the arguments is infinite and
1272 * the other is neither zero nor NaN) and the third argument is an
1273 * infinity of the opposite sign, the result is NaN.
1274 *
1275 * </ul>
1276 *
1277 * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
1278 * result as ({@code a + c}). However,
1279 * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
1280 * same result as ({@code a * b}) since
1281 * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
1282 * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
1283 * equivalent to ({@code a * b}) however.
1284 *
1285 * @apiNote This method corresponds to the fusedMultiplyAdd
1286 * operation defined in IEEE 754-2008.
1287 *
1288 * @param a a value
1289 * @param b a value
1290 * @param c a value
1291 *
1292 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1293 * computed, as if with unlimited range and precision, and rounded
1294 * once to the nearest {@code double} value
1295 *
1296 * @since 9
1297 */
1298 public static double fma(double a, double b, double c) {
1299 return Math.fma(a, b, c);
1300 }
1301
1302 /**
1303 * Returns the fused multiply add of the three arguments; that is,
1304 * returns the exact product of the first two arguments summed
1305 * with the third argument and then rounded once to the nearest
1306 * {@code float}.
1307 *
1308 * The rounding is done using the {@linkplain
1309 * java.math.RoundingMode#HALF_EVEN round to nearest even
1310 * rounding mode}.
1311 *
1312 * In contrast, if {@code a * b + c} is evaluated as a regular
1313 * floating-point expression, two rounding errors are involved,
1314 * the first for the multiply operation, the second for the
1315 * addition operation.
1316 *
1317 * <p>Special cases:
1318 * <ul>
1319 * <li> If any argument is NaN, the result is NaN.
1320 *
1321 * <li> If one of the first two arguments is infinite and the
1322 * other is zero, the result is NaN.
1323 *
1324 * <li> If the exact product of the first two arguments is infinite
1325 * (in other words, at least one of the arguments is infinite and
1326 * the other is neither zero nor NaN) and the third argument is an
1327 * infinity of the opposite sign, the result is NaN.
1328 *
1329 * </ul>
1330 *
1331 * <p>Note that {@code fma(a, 1.0f, c)} returns the same
1332 * result as ({@code a + c}). However,
1333 * {@code fma(a, b, +0.0f)} does <em>not</em> always return the
1334 * same result as ({@code a * b}) since
1335 * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
1336 * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
1337 * equivalent to ({@code a * b}) however.
1338 *
1339 * @apiNote This method corresponds to the fusedMultiplyAdd
1340 * operation defined in IEEE 754-2008.
1341 *
1342 * @param a a value
1343 * @param b a value
1344 * @param c a value
1345 *
1346 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1347 * computed, as if with unlimited range and precision, and rounded
1348 * once to the nearest {@code float} value
1349 *
1350 * @since 9
1351 */
1352 public static float fma(float a, float b, float c) {
1353 return Math.fma(a, b, c);
1354 }
1355
1356 /**
1357 * Returns the size of an ulp of the argument. An ulp, unit in
1358 * the last place, of a {@code double} value is the positive
1359 * distance between this floating-point value and the {@code
1360 * double} value next larger in magnitude. Note that for non-NaN
1361 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1362 *
1363 * <p>Special Cases:
1364 * <ul>
1365 * <li> If the argument is NaN, then the result is NaN.
1366 * <li> If the argument is positive or negative infinity, then the
1367 * result is positive infinity.
1368 * <li> If the argument is positive or negative zero, then the result is
1369 * {@code Double.MIN_VALUE}.
1370 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1371 * the result is equal to 2<sup>971</sup>.
1372 * </ul>
1373 *
1374 * @param d the floating-point value whose ulp is to be returned
1375 * @return the size of an ulp of the argument
1376 * @author Joseph D. Darcy
1377 * @since 1.5
1378 */
1379 public static double ulp(double d) {
1380 return Math.ulp(d);
1381 }
1382
1383 /**
1384 * Returns the size of an ulp of the argument. An ulp, unit in
1385 * the last place, of a {@code float} value is the positive
1386 * distance between this floating-point value and the {@code
1387 * float} value next larger in magnitude. Note that for non-NaN
1388 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1389 *
1390 * <p>Special Cases:
1391 * <ul>
1392 * <li> If the argument is NaN, then the result is NaN.
1393 * <li> If the argument is positive or negative infinity, then the
1394 * result is positive infinity.
1395 * <li> If the argument is positive or negative zero, then the result is
1396 * {@code Float.MIN_VALUE}.
1397 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1398 * the result is equal to 2<sup>104</sup>.
1399 * </ul>
1400 *
1401 * @param f the floating-point value whose ulp is to be returned
1402 * @return the size of an ulp of the argument
1403 * @author Joseph D. Darcy
1404 * @since 1.5
1405 */
1406 public static float ulp(float f) {
1407 return Math.ulp(f);
1408 }
1409
1410 /**
1411 * Returns the signum function of the argument; zero if the argument
1412 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1413 * argument is less than zero.
1414 *
1415 * <p>Special Cases:
1416 * <ul>
1417 * <li> If the argument is NaN, then the result is NaN.
1418 * <li> If the argument is positive zero or negative zero, then the
1419 * result is the same as the argument.
1420 * </ul>
1421 *
1422 * @param d the floating-point value whose signum is to be returned
1423 * @return the signum function of the argument
1424 * @author Joseph D. Darcy
1425 * @since 1.5
1426 */
1427 public static double signum(double d) {
1428 return Math.signum(d);
1429 }
1430
1431 /**
1432 * Returns the signum function of the argument; zero if the argument
1433 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1434 * argument is less than zero.
1435 *
1436 * <p>Special Cases:
1437 * <ul>
1438 * <li> If the argument is NaN, then the result is NaN.
1439 * <li> If the argument is positive zero or negative zero, then the
1440 * result is the same as the argument.
1441 * </ul>
1442 *
1443 * @param f the floating-point value whose signum is to be returned
1444 * @return the signum function of the argument
1445 * @author Joseph D. Darcy
1446 * @since 1.5
1447 */
1448 public static float signum(float f) {
1449 return Math.signum(f);
1450 }
1451
1452 /**
1453 * Returns the hyperbolic sine of a {@code double} value.
1454 * The hyperbolic sine of <i>x</i> is defined to be
1455 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1456 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1457 *
1458 * <p>Special cases:
1459 * <ul>
1460 *
1461 * <li>If the argument is NaN, then the result is NaN.
1462 *
1463 * <li>If the argument is infinite, then the result is an infinity
1464 * with the same sign as the argument.
1465 *
1466 * <li>If the argument is zero, then the result is a zero with the
1467 * same sign as the argument.
1468 *
1469 * </ul>
1470 *
1471 * @param x The number whose hyperbolic sine is to be returned.
1472 * @return The hyperbolic sine of {@code x}.
1473 * @since 1.5
1474 */
1475 public static native double sinh(double x);
1476
1477 /**
1478 * Returns the hyperbolic cosine of a {@code double} value.
1479 * The hyperbolic cosine of <i>x</i> is defined to be
1480 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1481 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1482 *
1483 * <p>Special cases:
1484 * <ul>
1485 *
1486 * <li>If the argument is NaN, then the result is NaN.
1487 *
1488 * <li>If the argument is infinite, then the result is positive
1489 * infinity.
1490 *
1491 * <li>If the argument is zero, then the result is {@code 1.0}.
1492 *
1493 * </ul>
1494 *
1495 * @param x The number whose hyperbolic cosine is to be returned.
1496 * @return The hyperbolic cosine of {@code x}.
1497 * @since 1.5
1498 */
1499 public static native double cosh(double x);
1500
1501 /**
1502 * Returns the hyperbolic tangent of a {@code double} value.
1503 * The hyperbolic tangent of <i>x</i> is defined to be
1504 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1505 * in other words, {@linkplain Math#sinh
1506 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1507 * that the absolute value of the exact tanh is always less than
1508 * 1.
1509 *
1510 * <p>Special cases:
1511 * <ul>
1512 *
1513 * <li>If the argument is NaN, then the result is NaN.
1514 *
1515 * <li>If the argument is zero, then the result is a zero with the
1516 * same sign as the argument.
1517 *
1518 * <li>If the argument is positive infinity, then the result is
1519 * {@code +1.0}.
1520 *
1521 * <li>If the argument is negative infinity, then the result is
1522 * {@code -1.0}.
1523 *
1524 * </ul>
1525 *
1526 * @param x The number whose hyperbolic tangent is to be returned.
1527 * @return The hyperbolic tangent of {@code x}.
1528 * @since 1.5
1529 */
1530 public static native double tanh(double x);
1531
1532 /**
1533 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1534 * without intermediate overflow or underflow.
1535 *
1536 * <p>Special cases:
1537 * <ul>
1538 *
1539 * <li> If either argument is infinite, then the result
1540 * is positive infinity.
1541 *
1542 * <li> If either argument is NaN and neither argument is infinite,
1543 * then the result is NaN.
1544 *
1545 * </ul>
1546 *
1547 * @param x a value
1548 * @param y a value
1549 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1550 * without intermediate overflow or underflow
1551 * @since 1.5
1552 */
1553 public static double hypot(double x, double y) {
1554 return FdLibm.Hypot.compute(x, y);
1555 }
1556
1557 /**
1558 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1559 * <i>x</i> near 0, the exact sum of
1560 * {@code expm1(x)} + 1 is much closer to the true
1561 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1562 *
1563 * <p>Special cases:
1564 * <ul>
1565 * <li>If the argument is NaN, the result is NaN.
1566 *
1567 * <li>If the argument is positive infinity, then the result is
1568 * positive infinity.
1569 *
1570 * <li>If the argument is negative infinity, then the result is
1571 * -1.0.
1572 *
1573 * <li>If the argument is zero, then the result is a zero with the
1574 * same sign as the argument.
1575 *
1576 * </ul>
1577 *
1578 * @param x the exponent to raise <i>e</i> to in the computation of
1579 * <i>e</i><sup>{@code x}</sup> -1.
1580 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1581 * @since 1.5
1582 */
1583 public static native double expm1(double x);
1584
1585 /**
1586 * Returns the natural logarithm of the sum of the argument and 1.
1587 * Note that for small values {@code x}, the result of
1588 * {@code log1p(x)} is much closer to the true result of ln(1
1589 * + {@code x}) than the floating-point evaluation of
1590 * {@code log(1.0+x)}.
1591 *
1592 * <p>Special cases:
1593 * <ul>
1594 *
1595 * <li>If the argument is NaN or less than -1, then the result is
1596 * NaN.
1597 *
1598 * <li>If the argument is positive infinity, then the result is
1599 * positive infinity.
1600 *
1601 * <li>If the argument is negative one, then the result is
1602 * negative infinity.
1603 *
1604 * <li>If the argument is zero, then the result is a zero with the
1605 * same sign as the argument.
1606 *
1607 * </ul>
1608 *
1609 * @param x a value
1610 * @return the value ln({@code x} + 1), the natural
1611 * log of {@code x} + 1
1612 * @since 1.5
1613 */
1614 public static native double log1p(double x);
1615
1616 /**
1617 * Returns the first floating-point argument with the sign of the
1618 * second floating-point argument. For this method, a NaN
1619 * {@code sign} argument is always treated as if it were
1620 * positive.
1621 *
1622 * @param magnitude the parameter providing the magnitude of the result
1623 * @param sign the parameter providing the sign of the result
1624 * @return a value with the magnitude of {@code magnitude}
1625 * and the sign of {@code sign}.
1626 * @since 1.6
1627 */
1628 public static double copySign(double magnitude, double sign) {
1629 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1630 }
1631
1632 /**
1633 * Returns the first floating-point argument with the sign of the
1634 * second floating-point argument. For this method, a NaN
1635 * {@code sign} argument is always treated as if it were
1636 * positive.
1637 *
1638 * @param magnitude the parameter providing the magnitude of the result
1639 * @param sign the parameter providing the sign of the result
1640 * @return a value with the magnitude of {@code magnitude}
1641 * and the sign of {@code sign}.
1642 * @since 1.6
1643 */
1644 public static float copySign(float magnitude, float sign) {
1645 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1646 }
1647 /**
1648 * Returns the unbiased exponent used in the representation of a
1649 * {@code float}. Special cases:
1650 *
1651 * <ul>
1652 * <li>If the argument is NaN or infinite, then the result is
1653 * {@link Float#MAX_EXPONENT} + 1.
1654 * <li>If the argument is zero or subnormal, then the result is
1655 * {@link Float#MIN_EXPONENT} -1.
1656 * </ul>
1657 * @param f a {@code float} value
1658 * @return the unbiased exponent of the argument
1659 * @since 1.6
1660 */
1661 public static int getExponent(float f) {
1662 return Math.getExponent(f);
1663 }
1664
1665 /**
1666 * Returns the unbiased exponent used in the representation of a
1667 * {@code double}. Special cases:
1668 *
1669 * <ul>
1670 * <li>If the argument is NaN or infinite, then the result is
1671 * {@link Double#MAX_EXPONENT} + 1.
1672 * <li>If the argument is zero or subnormal, then the result is
1673 * {@link Double#MIN_EXPONENT} -1.
1674 * </ul>
1675 * @param d a {@code double} value
1676 * @return the unbiased exponent of the argument
1677 * @since 1.6
1678 */
1679 public static int getExponent(double d) {
1680 return Math.getExponent(d);
1681 }
1682
1683 /**
1684 * Returns the floating-point number adjacent to the first
1685 * argument in the direction of the second argument. If both
1686 * arguments compare as equal the second argument is returned.
1687 *
1688 * <p>Special cases:
1689 * <ul>
1690 * <li> If either argument is a NaN, then NaN is returned.
1691 *
1692 * <li> If both arguments are signed zeros, {@code direction}
1693 * is returned unchanged (as implied by the requirement of
1694 * returning the second argument if the arguments compare as
1695 * equal).
1696 *
1697 * <li> If {@code start} is
1698 * ±{@link Double#MIN_VALUE} and {@code direction}
1699 * has a value such that the result should have a smaller
1700 * magnitude, then a zero with the same sign as {@code start}
1701 * is returned.
1702 *
1703 * <li> If {@code start} is infinite and
1704 * {@code direction} has a value such that the result should
1705 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1706 * same sign as {@code start} is returned.
1707 *
1708 * <li> If {@code start} is equal to ±
1709 * {@link Double#MAX_VALUE} and {@code direction} has a
1710 * value such that the result should have a larger magnitude, an
1711 * infinity with same sign as {@code start} is returned.
1712 * </ul>
1713 *
1714 * @param start starting floating-point value
1715 * @param direction value indicating which of
1716 * {@code start}'s neighbors or {@code start} should
1717 * be returned
1718 * @return The floating-point number adjacent to {@code start} in the
1719 * direction of {@code direction}.
1720 * @since 1.6
1721 */
1722 public static double nextAfter(double start, double direction) {
1723 return Math.nextAfter(start, direction);
1724 }
1725
1726 /**
1727 * Returns the floating-point number adjacent to the first
1728 * argument in the direction of the second argument. If both
1729 * arguments compare as equal a value equivalent to the second argument
1730 * is returned.
1731 *
1732 * <p>Special cases:
1733 * <ul>
1734 * <li> If either argument is a NaN, then NaN is returned.
1735 *
1736 * <li> If both arguments are signed zeros, a value equivalent
1737 * to {@code direction} is returned.
1738 *
1739 * <li> If {@code start} is
1740 * ±{@link Float#MIN_VALUE} and {@code direction}
1741 * has a value such that the result should have a smaller
1742 * magnitude, then a zero with the same sign as {@code start}
1743 * is returned.
1744 *
1745 * <li> If {@code start} is infinite and
1746 * {@code direction} has a value such that the result should
1747 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1748 * same sign as {@code start} is returned.
1749 *
1750 * <li> If {@code start} is equal to ±
1751 * {@link Float#MAX_VALUE} and {@code direction} has a
1752 * value such that the result should have a larger magnitude, an
1753 * infinity with same sign as {@code start} is returned.
1754 * </ul>
1755 *
1756 * @param start starting floating-point value
1757 * @param direction value indicating which of
1758 * {@code start}'s neighbors or {@code start} should
1759 * be returned
1760 * @return The floating-point number adjacent to {@code start} in the
1761 * direction of {@code direction}.
1762 * @since 1.6
1763 */
1764 public static float nextAfter(float start, double direction) {
1765 return Math.nextAfter(start, direction);
1766 }
1767
1768 /**
1769 * Returns the floating-point value adjacent to {@code d} in
1770 * the direction of positive infinity. This method is
1771 * semantically equivalent to {@code nextAfter(d,
1772 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1773 * implementation may run faster than its equivalent
1774 * {@code nextAfter} call.
1775 *
1776 * <p>Special Cases:
1777 * <ul>
1778 * <li> If the argument is NaN, the result is NaN.
1779 *
1780 * <li> If the argument is positive infinity, the result is
1781 * positive infinity.
1782 *
1783 * <li> If the argument is zero, the result is
1784 * {@link Double#MIN_VALUE}
1785 *
1786 * </ul>
1787 *
1788 * @param d starting floating-point value
1789 * @return The adjacent floating-point value closer to positive
1790 * infinity.
1791 * @since 1.6
1792 */
1793 public static double nextUp(double d) {
1794 return Math.nextUp(d);
1795 }
1796
1797 /**
1798 * Returns the floating-point value adjacent to {@code f} in
1799 * the direction of positive infinity. This method is
1800 * semantically equivalent to {@code nextAfter(f,
1801 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1802 * implementation may run faster than its equivalent
1803 * {@code nextAfter} call.
1804 *
1805 * <p>Special Cases:
1806 * <ul>
1807 * <li> If the argument is NaN, the result is NaN.
1808 *
1809 * <li> If the argument is positive infinity, the result is
1810 * positive infinity.
1811 *
1812 * <li> If the argument is zero, the result is
1813 * {@link Float#MIN_VALUE}
1814 *
1815 * </ul>
1816 *
1817 * @param f starting floating-point value
1818 * @return The adjacent floating-point value closer to positive
1819 * infinity.
1820 * @since 1.6
1821 */
1822 public static float nextUp(float f) {
1823 return Math.nextUp(f);
1824 }
1825
1826 /**
1827 * Returns the floating-point value adjacent to {@code d} in
1828 * the direction of negative infinity. This method is
1829 * semantically equivalent to {@code nextAfter(d,
1830 * Double.NEGATIVE_INFINITY)}; however, a
1831 * {@code nextDown} implementation may run faster than its
1832 * equivalent {@code nextAfter} call.
1833 *
1834 * <p>Special Cases:
1835 * <ul>
1836 * <li> If the argument is NaN, the result is NaN.
1837 *
1838 * <li> If the argument is negative infinity, the result is
1839 * negative infinity.
1840 *
1841 * <li> If the argument is zero, the result is
1842 * {@code -Double.MIN_VALUE}
1843 *
1844 * </ul>
1845 *
1846 * @param d starting floating-point value
1847 * @return The adjacent floating-point value closer to negative
1848 * infinity.
1849 * @since 1.8
1850 */
1851 public static double nextDown(double d) {
1852 return Math.nextDown(d);
1853 }
1854
1855 /**
1856 * Returns the floating-point value adjacent to {@code f} in
1857 * the direction of negative infinity. This method is
1858 * semantically equivalent to {@code nextAfter(f,
1859 * Float.NEGATIVE_INFINITY)}; however, a
1860 * {@code nextDown} implementation may run faster than its
1861 * equivalent {@code nextAfter} call.
1862 *
1863 * <p>Special Cases:
1864 * <ul>
1865 * <li> If the argument is NaN, the result is NaN.
1866 *
1867 * <li> If the argument is negative infinity, the result is
1868 * negative infinity.
1869 *
1870 * <li> If the argument is zero, the result is
1871 * {@code -Float.MIN_VALUE}
1872 *
1873 * </ul>
1874 *
1875 * @param f starting floating-point value
1876 * @return The adjacent floating-point value closer to negative
1877 * infinity.
1878 * @since 1.8
1879 */
1880 public static float nextDown(float f) {
1881 return Math.nextDown(f);
1882 }
1883
1884 /**
1885 * Returns {@code d} ×
1886 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1887 * by a single correctly rounded floating-point multiply to a
1888 * member of the double value set. See the Java
1889 * Language Specification for a discussion of floating-point
1890 * value sets. If the exponent of the result is between {@link
1891 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1892 * answer is calculated exactly. If the exponent of the result
1893 * would be larger than {@code Double.MAX_EXPONENT}, an
1894 * infinity is returned. Note that if the result is subnormal,
1895 * precision may be lost; that is, when {@code scalb(x, n)}
1896 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1897 * <i>x</i>. When the result is non-NaN, the result has the same
1898 * sign as {@code d}.
1899 *
1900 * <p>Special cases:
1901 * <ul>
1902 * <li> If the first argument is NaN, NaN is returned.
1903 * <li> If the first argument is infinite, then an infinity of the
1904 * same sign is returned.
1905 * <li> If the first argument is zero, then a zero of the same
1906 * sign is returned.
1907 * </ul>
1908 *
1909 * @param d number to be scaled by a power of two.
1910 * @param scaleFactor power of 2 used to scale {@code d}
1911 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1912 * @since 1.6
1913 */
1914 public static double scalb(double d, int scaleFactor) {
1915 return Math.scalb(d, scaleFactor);
1916 }
1917
1918 /**
1919 * Returns {@code f} ×
1920 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1921 * by a single correctly rounded floating-point multiply to a
1922 * member of the float value set. See the Java
1923 * Language Specification for a discussion of floating-point
1924 * value sets. If the exponent of the result is between {@link
1925 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1926 * answer is calculated exactly. If the exponent of the result
1927 * would be larger than {@code Float.MAX_EXPONENT}, an
1928 * infinity is returned. Note that if the result is subnormal,
1929 * precision may be lost; that is, when {@code scalb(x, n)}
1930 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1931 * <i>x</i>. When the result is non-NaN, the result has the same
1932 * sign as {@code f}.
1933 *
1934 * <p>Special cases:
1935 * <ul>
1936 * <li> If the first argument is NaN, NaN is returned.
1937 * <li> If the first argument is infinite, then an infinity of the
1938 * same sign is returned.
1939 * <li> If the first argument is zero, then a zero of the same
1940 * sign is returned.
1941 * </ul>
1942 *
1943 * @param f number to be scaled by a power of two.
1944 * @param scaleFactor power of 2 used to scale {@code f}
1945 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1946 * @since 1.6
1947 */
1948 public static float scalb(float f, int scaleFactor) {
1949 return Math.scalb(f, scaleFactor);
1950 }
1951 }