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 public static float max(float a, float b) {
1158 return Math.max(a, b);
1159 }
1160
1161 /**
1162 * Returns the greater of two {@code double} values. That
1163 * is, the result is the argument closer to positive infinity. If
1164 * the arguments have the same value, the result is that same
1165 * value. If either value is NaN, then the result is NaN. Unlike
1166 * the numerical comparison operators, this method considers
1167 * negative zero to be strictly smaller than positive zero. If one
1168 * argument is positive zero and the other negative zero, the
1169 * result is positive zero.
1170 *
1171 * @param a an argument.
1172 * @param b another argument.
1173 * @return the larger of {@code a} and {@code b}.
1174 */
1175 public static double max(double a, double b) {
1176 return Math.max(a, b);
1177 }
1178
1179 /**
1180 * Returns the smaller of two {@code int} values. That is,
1181 * the result the argument closer to the value of
1182 * {@link Integer#MIN_VALUE}. If the arguments have the same
1183 * value, the result is that same value.
1184 *
1185 * @param a an argument.
1186 * @param b another argument.
1187 * @return the smaller of {@code a} and {@code b}.
1188 */
1189 @HotSpotIntrinsicCandidate
1190 public static int min(int a, int b) {
1191 return Math.min(a, b);
1192 }
1193
1194 /**
1195 * Returns the smaller of two {@code long} values. That is,
1196 * the result is the argument closer to the value of
1197 * {@link Long#MIN_VALUE}. If the arguments have the same
1198 * value, the result is that same value.
1199 *
1200 * @param a an argument.
1201 * @param b another argument.
1202 * @return the smaller of {@code a} and {@code b}.
1203 */
1204 public static long min(long a, long b) {
1205 return Math.min(a, b);
1206 }
1207
1208 /**
1209 * Returns the smaller of two {@code float} values. That is,
1210 * the result is the value closer to negative infinity. If the
1211 * arguments have the same value, the result is that same
1212 * value. If either value is NaN, then the result is NaN. Unlike
1213 * the numerical comparison operators, this method considers
1214 * negative zero to be strictly smaller than positive zero. If
1215 * one argument is positive zero and the other is negative zero,
1216 * the result is negative zero.
1217 *
1218 * @param a an argument.
1219 * @param b another argument.
1220 * @return the smaller of {@code a} and {@code b.}
1221 */
1222 public static float min(float a, float b) {
1223 return Math.min(a, b);
1224 }
1225
1226 /**
1227 * Returns the smaller of two {@code double} values. That
1228 * is, the result is the value closer to negative infinity. If the
1229 * arguments have the same value, the result is that same
1230 * value. If either value is NaN, then the result is NaN. Unlike
1231 * the numerical comparison operators, this method considers
1232 * negative zero to be strictly smaller than positive zero. If one
1233 * argument is positive zero and the other is negative zero, the
1234 * result is negative zero.
1235 *
1236 * @param a an argument.
1237 * @param b another argument.
1238 * @return the smaller of {@code a} and {@code b}.
1239 */
1240 public static double min(double a, double b) {
1241 return Math.min(a, b);
1242 }
1243
1244 /**
1245 * Returns the fused multiply add of the three arguments; that is,
1246 * returns the exact product of the first two arguments summed
1247 * with the third argument and then rounded once to the nearest
1248 * {@code double}.
1249 *
1250 * The rounding is done using the {@linkplain
1251 * java.math.RoundingMode#HALF_EVEN round to nearest even
1252 * rounding mode}.
1253 *
1254 * In contrast, if {@code a * b + c} is evaluated as a regular
1255 * floating-point expression, two rounding errors are involved,
1256 * the first for the multiply operation, the second for the
1257 * addition operation.
1258 *
1259 * <p>Special cases:
1260 * <ul>
1261 * <li> If any argument is NaN, the result is NaN.
1262 *
1263 * <li> If one of the first two arguments is infinite and the
1264 * other is zero, the result is NaN.
1265 *
1266 * <li> If the exact product of the first two arguments is infinite
1267 * (in other words, at least one of the arguments is infinite and
1268 * the other is neither zero nor NaN) and the third argument is an
1269 * infinity of the opposite sign, the result is NaN.
1270 *
1271 * </ul>
1272 *
1273 * <p>Note that {@code fusedMac(a, 1.0, c)} returns the same
1274 * result as ({@code a + c}). However,
1275 * {@code fusedMac(a, b, +0.0)} does <em>not</em> always return the
1276 * same result as ({@code a * b}) since
1277 * {@code fusedMac(-0.0, +0.0, +0.0)} is {@code +0.0} while
1278 * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fusedMac(a, b, -0.0)} is
1279 * equivalent to ({@code a * b}) however.
1280 *
1281 * @apiNote This method corresponds to the fusedMultiplyAdd
1282 * operation defined in IEEE 754-2008.
1283 *
1284 * @param a a value
1285 * @param b a value
1286 * @param c a value
1287 *
1288 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1289 * computed, as if with unlimited range and precision, and rounded
1290 * once to the nearest {@code double} value
1291 *
1292 * @since 9
1293 */
1294 public static double fma(double a, double b, double c) {
1295 return Math.fma(a, b, c);
1296 }
1297
1298 /**
1299 * Returns the fused multiply add of the three arguments; that is,
1300 * returns the exact product of the first two arguments summed
1301 * with the third argument and then rounded once to the nearest
1302 * {@code float}.
1303 *
1304 * The rounding is done using the {@linkplain
1305 * java.math.RoundingMode#HALF_EVEN round to nearest even
1306 * rounding mode}.
1307 *
1308 * In contrast, if {@code a * b + c} is evaluated as a regular
1309 * floating-point expression, two rounding errors are involved,
1310 * the first for the multiply operation, the second for the
1311 * addition operation.
1312 *
1313 * <p>Special cases:
1314 * <ul>
1315 * <li> If any argument is NaN, the result is NaN.
1316 *
1317 * <li> If one of the first two arguments is infinite and the
1318 * other is zero, the result is NaN.
1319 *
1320 * <li> If the exact product of the first two arguments is infinite
1321 * (in other words, at least one of the arguments is infinite and
1322 * the other is neither zero nor NaN) and the third argument is an
1323 * infinity of the opposite sign, the result is NaN.
1324 *
1325 * </ul>
1326 *
1327 * <p>Note that {@code fma(a, 1.0f, c)} returns the same
1328 * result as ({@code a + c}). However,
1329 * {@code fma(a, b, +0.0f)} does <em>not</em> always return the
1330 * same result as ({@code a * b}) since
1331 * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
1332 * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
1333 * equivalent to ({@code a * b}) however.
1334 *
1335 * @apiNote This method corresponds to the fusedMultiplyAdd
1336 * operation defined in IEEE 754-2008.
1337 *
1338 * @param a a value
1339 * @param b a value
1340 * @param c a value
1341 *
1342 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1343 * computed, as if with unlimited range and precision, and rounded
1344 * once to the nearest {@code float} value
1345 *
1346 * @since 9
1347 */
1348 public static float fma(float a, float b, float c) {
1349 return Math.fma(a, b, c);
1350 }
1351
1352 /**
1353 * Returns the size of an ulp of the argument. An ulp, unit in
1354 * the last place, of a {@code double} value is the positive
1355 * distance between this floating-point value and the {@code
1356 * double} value next larger in magnitude. Note that for non-NaN
1357 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1358 *
1359 * <p>Special Cases:
1360 * <ul>
1361 * <li> If the argument is NaN, then the result is NaN.
1362 * <li> If the argument is positive or negative infinity, then the
1363 * result is positive infinity.
1364 * <li> If the argument is positive or negative zero, then the result is
1365 * {@code Double.MIN_VALUE}.
1366 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1367 * the result is equal to 2<sup>971</sup>.
1368 * </ul>
1369 *
1370 * @param d the floating-point value whose ulp is to be returned
1371 * @return the size of an ulp of the argument
1372 * @author Joseph D. Darcy
1373 * @since 1.5
1374 */
1375 public static double ulp(double d) {
1376 return Math.ulp(d);
1377 }
1378
1379 /**
1380 * Returns the size of an ulp of the argument. An ulp, unit in
1381 * the last place, of a {@code float} value is the positive
1382 * distance between this floating-point value and the {@code
1383 * float} value next larger in magnitude. Note that for non-NaN
1384 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1385 *
1386 * <p>Special Cases:
1387 * <ul>
1388 * <li> If the argument is NaN, then the result is NaN.
1389 * <li> If the argument is positive or negative infinity, then the
1390 * result is positive infinity.
1391 * <li> If the argument is positive or negative zero, then the result is
1392 * {@code Float.MIN_VALUE}.
1393 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1394 * the result is equal to 2<sup>104</sup>.
1395 * </ul>
1396 *
1397 * @param f the floating-point value whose ulp is to be returned
1398 * @return the size of an ulp of the argument
1399 * @author Joseph D. Darcy
1400 * @since 1.5
1401 */
1402 public static float ulp(float f) {
1403 return Math.ulp(f);
1404 }
1405
1406 /**
1407 * Returns the signum function of the argument; zero if the argument
1408 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1409 * argument is less than zero.
1410 *
1411 * <p>Special Cases:
1412 * <ul>
1413 * <li> If the argument is NaN, then the result is NaN.
1414 * <li> If the argument is positive zero or negative zero, then the
1415 * result is the same as the argument.
1416 * </ul>
1417 *
1418 * @param d the floating-point value whose signum is to be returned
1419 * @return the signum function of the argument
1420 * @author Joseph D. Darcy
1421 * @since 1.5
1422 */
1423 public static double signum(double d) {
1424 return Math.signum(d);
1425 }
1426
1427 /**
1428 * Returns the signum function of the argument; zero if the argument
1429 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1430 * argument is less than zero.
1431 *
1432 * <p>Special Cases:
1433 * <ul>
1434 * <li> If the argument is NaN, then the result is NaN.
1435 * <li> If the argument is positive zero or negative zero, then the
1436 * result is the same as the argument.
1437 * </ul>
1438 *
1439 * @param f the floating-point value whose signum is to be returned
1440 * @return the signum function of the argument
1441 * @author Joseph D. Darcy
1442 * @since 1.5
1443 */
1444 public static float signum(float f) {
1445 return Math.signum(f);
1446 }
1447
1448 /**
1449 * Returns the hyperbolic sine of a {@code double} value.
1450 * The hyperbolic sine of <i>x</i> is defined to be
1451 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1452 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1453 *
1454 * <p>Special cases:
1455 * <ul>
1456 *
1457 * <li>If the argument is NaN, then the result is NaN.
1458 *
1459 * <li>If the argument is infinite, then the result is an infinity
1460 * with the same sign as the argument.
1461 *
1462 * <li>If the argument is zero, then the result is a zero with the
1463 * same sign as the argument.
1464 *
1465 * </ul>
1466 *
1467 * @param x The number whose hyperbolic sine is to be returned.
1468 * @return The hyperbolic sine of {@code x}.
1469 * @since 1.5
1470 */
1471 public static native double sinh(double x);
1472
1473 /**
1474 * Returns the hyperbolic cosine of a {@code double} value.
1475 * The hyperbolic cosine of <i>x</i> is defined to be
1476 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1477 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1478 *
1479 * <p>Special cases:
1480 * <ul>
1481 *
1482 * <li>If the argument is NaN, then the result is NaN.
1483 *
1484 * <li>If the argument is infinite, then the result is positive
1485 * infinity.
1486 *
1487 * <li>If the argument is zero, then the result is {@code 1.0}.
1488 *
1489 * </ul>
1490 *
1491 * @param x The number whose hyperbolic cosine is to be returned.
1492 * @return The hyperbolic cosine of {@code x}.
1493 * @since 1.5
1494 */
1495 public static native double cosh(double x);
1496
1497 /**
1498 * Returns the hyperbolic tangent of a {@code double} value.
1499 * The hyperbolic tangent of <i>x</i> is defined to be
1500 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1501 * in other words, {@linkplain Math#sinh
1502 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1503 * that the absolute value of the exact tanh is always less than
1504 * 1.
1505 *
1506 * <p>Special cases:
1507 * <ul>
1508 *
1509 * <li>If the argument is NaN, then the result is NaN.
1510 *
1511 * <li>If the argument is zero, then the result is a zero with the
1512 * same sign as the argument.
1513 *
1514 * <li>If the argument is positive infinity, then the result is
1515 * {@code +1.0}.
1516 *
1517 * <li>If the argument is negative infinity, then the result is
1518 * {@code -1.0}.
1519 *
1520 * </ul>
1521 *
1522 * @param x The number whose hyperbolic tangent is to be returned.
1523 * @return The hyperbolic tangent of {@code x}.
1524 * @since 1.5
1525 */
1526 public static native double tanh(double x);
1527
1528 /**
1529 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1530 * without intermediate overflow or underflow.
1531 *
1532 * <p>Special cases:
1533 * <ul>
1534 *
1535 * <li> If either argument is infinite, then the result
1536 * is positive infinity.
1537 *
1538 * <li> If either argument is NaN and neither argument is infinite,
1539 * then the result is NaN.
1540 *
1541 * </ul>
1542 *
1543 * @param x a value
1544 * @param y a value
1545 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1546 * without intermediate overflow or underflow
1547 * @since 1.5
1548 */
1549 public static double hypot(double x, double y) {
1550 return FdLibm.Hypot.compute(x, y);
1551 }
1552
1553 /**
1554 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1555 * <i>x</i> near 0, the exact sum of
1556 * {@code expm1(x)} + 1 is much closer to the true
1557 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1558 *
1559 * <p>Special cases:
1560 * <ul>
1561 * <li>If the argument is NaN, the result is NaN.
1562 *
1563 * <li>If the argument is positive infinity, then the result is
1564 * positive infinity.
1565 *
1566 * <li>If the argument is negative infinity, then the result is
1567 * -1.0.
1568 *
1569 * <li>If the argument is zero, then the result is a zero with the
1570 * same sign as the argument.
1571 *
1572 * </ul>
1573 *
1574 * @param x the exponent to raise <i>e</i> to in the computation of
1575 * <i>e</i><sup>{@code x}</sup> -1.
1576 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1577 * @since 1.5
1578 */
1579 public static native double expm1(double x);
1580
1581 /**
1582 * Returns the natural logarithm of the sum of the argument and 1.
1583 * Note that for small values {@code x}, the result of
1584 * {@code log1p(x)} is much closer to the true result of ln(1
1585 * + {@code x}) than the floating-point evaluation of
1586 * {@code log(1.0+x)}.
1587 *
1588 * <p>Special cases:
1589 * <ul>
1590 *
1591 * <li>If the argument is NaN or less than -1, then the result is
1592 * NaN.
1593 *
1594 * <li>If the argument is positive infinity, then the result is
1595 * positive infinity.
1596 *
1597 * <li>If the argument is negative one, then the result is
1598 * negative infinity.
1599 *
1600 * <li>If the argument is zero, then the result is a zero with the
1601 * same sign as the argument.
1602 *
1603 * </ul>
1604 *
1605 * @param x a value
1606 * @return the value ln({@code x} + 1), the natural
1607 * log of {@code x} + 1
1608 * @since 1.5
1609 */
1610 public static native double log1p(double x);
1611
1612 /**
1613 * Returns the first floating-point argument with the sign of the
1614 * second floating-point argument. For this method, a NaN
1615 * {@code sign} argument is always treated as if it were
1616 * positive.
1617 *
1618 * @param magnitude the parameter providing the magnitude of the result
1619 * @param sign the parameter providing the sign of the result
1620 * @return a value with the magnitude of {@code magnitude}
1621 * and the sign of {@code sign}.
1622 * @since 1.6
1623 */
1624 public static double copySign(double magnitude, double sign) {
1625 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign));
1626 }
1627
1628 /**
1629 * Returns the first floating-point argument with the sign of the
1630 * second floating-point argument. For this method, a NaN
1631 * {@code sign} argument is always treated as if it were
1632 * positive.
1633 *
1634 * @param magnitude the parameter providing the magnitude of the result
1635 * @param sign the parameter providing the sign of the result
1636 * @return a value with the magnitude of {@code magnitude}
1637 * and the sign of {@code sign}.
1638 * @since 1.6
1639 */
1640 public static float copySign(float magnitude, float sign) {
1641 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign));
1642 }
1643 /**
1644 * Returns the unbiased exponent used in the representation of a
1645 * {@code float}. Special cases:
1646 *
1647 * <ul>
1648 * <li>If the argument is NaN or infinite, then the result is
1649 * {@link Float#MAX_EXPONENT} + 1.
1650 * <li>If the argument is zero or subnormal, then the result is
1651 * {@link Float#MIN_EXPONENT} -1.
1652 * </ul>
1653 * @param f a {@code float} value
1654 * @return the unbiased exponent of the argument
1655 * @since 1.6
1656 */
1657 public static int getExponent(float f) {
1658 return Math.getExponent(f);
1659 }
1660
1661 /**
1662 * Returns the unbiased exponent used in the representation of a
1663 * {@code double}. Special cases:
1664 *
1665 * <ul>
1666 * <li>If the argument is NaN or infinite, then the result is
1667 * {@link Double#MAX_EXPONENT} + 1.
1668 * <li>If the argument is zero or subnormal, then the result is
1669 * {@link Double#MIN_EXPONENT} -1.
1670 * </ul>
1671 * @param d a {@code double} value
1672 * @return the unbiased exponent of the argument
1673 * @since 1.6
1674 */
1675 public static int getExponent(double d) {
1676 return Math.getExponent(d);
1677 }
1678
1679 /**
1680 * Returns the floating-point number adjacent to the first
1681 * argument in the direction of the second argument. If both
1682 * arguments compare as equal the second argument is returned.
1683 *
1684 * <p>Special cases:
1685 * <ul>
1686 * <li> If either argument is a NaN, then NaN is returned.
1687 *
1688 * <li> If both arguments are signed zeros, {@code direction}
1689 * is returned unchanged (as implied by the requirement of
1690 * returning the second argument if the arguments compare as
1691 * equal).
1692 *
1693 * <li> If {@code start} is
1694 * ±{@link Double#MIN_VALUE} and {@code direction}
1695 * has a value such that the result should have a smaller
1696 * magnitude, then a zero with the same sign as {@code start}
1697 * is returned.
1698 *
1699 * <li> If {@code start} is infinite and
1700 * {@code direction} has a value such that the result should
1701 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1702 * same sign as {@code start} is returned.
1703 *
1704 * <li> If {@code start} is equal to ±
1705 * {@link Double#MAX_VALUE} and {@code direction} has a
1706 * value such that the result should have a larger magnitude, an
1707 * infinity with same sign as {@code start} is returned.
1708 * </ul>
1709 *
1710 * @param start starting floating-point value
1711 * @param direction value indicating which of
1712 * {@code start}'s neighbors or {@code start} should
1713 * be returned
1714 * @return The floating-point number adjacent to {@code start} in the
1715 * direction of {@code direction}.
1716 * @since 1.6
1717 */
1718 public static double nextAfter(double start, double direction) {
1719 return Math.nextAfter(start, direction);
1720 }
1721
1722 /**
1723 * Returns the floating-point number adjacent to the first
1724 * argument in the direction of the second argument. If both
1725 * arguments compare as equal a value equivalent to the second argument
1726 * is returned.
1727 *
1728 * <p>Special cases:
1729 * <ul>
1730 * <li> If either argument is a NaN, then NaN is returned.
1731 *
1732 * <li> If both arguments are signed zeros, a value equivalent
1733 * to {@code direction} is returned.
1734 *
1735 * <li> If {@code start} is
1736 * ±{@link Float#MIN_VALUE} and {@code direction}
1737 * has a value such that the result should have a smaller
1738 * magnitude, then a zero with the same sign as {@code start}
1739 * is returned.
1740 *
1741 * <li> If {@code start} is infinite and
1742 * {@code direction} has a value such that the result should
1743 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1744 * same sign as {@code start} is returned.
1745 *
1746 * <li> If {@code start} is equal to ±
1747 * {@link Float#MAX_VALUE} and {@code direction} has a
1748 * value such that the result should have a larger magnitude, an
1749 * infinity with same sign as {@code start} is returned.
1750 * </ul>
1751 *
1752 * @param start starting floating-point value
1753 * @param direction value indicating which of
1754 * {@code start}'s neighbors or {@code start} should
1755 * be returned
1756 * @return The floating-point number adjacent to {@code start} in the
1757 * direction of {@code direction}.
1758 * @since 1.6
1759 */
1760 public static float nextAfter(float start, double direction) {
1761 return Math.nextAfter(start, direction);
1762 }
1763
1764 /**
1765 * Returns the floating-point value adjacent to {@code d} in
1766 * the direction of positive infinity. This method is
1767 * semantically equivalent to {@code nextAfter(d,
1768 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1769 * implementation may run faster than its equivalent
1770 * {@code nextAfter} call.
1771 *
1772 * <p>Special Cases:
1773 * <ul>
1774 * <li> If the argument is NaN, the result is NaN.
1775 *
1776 * <li> If the argument is positive infinity, the result is
1777 * positive infinity.
1778 *
1779 * <li> If the argument is zero, the result is
1780 * {@link Double#MIN_VALUE}
1781 *
1782 * </ul>
1783 *
1784 * @param d starting floating-point value
1785 * @return The adjacent floating-point value closer to positive
1786 * infinity.
1787 * @since 1.6
1788 */
1789 public static double nextUp(double d) {
1790 return Math.nextUp(d);
1791 }
1792
1793 /**
1794 * Returns the floating-point value adjacent to {@code f} in
1795 * the direction of positive infinity. This method is
1796 * semantically equivalent to {@code nextAfter(f,
1797 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1798 * implementation may run faster than its equivalent
1799 * {@code nextAfter} call.
1800 *
1801 * <p>Special Cases:
1802 * <ul>
1803 * <li> If the argument is NaN, the result is NaN.
1804 *
1805 * <li> If the argument is positive infinity, the result is
1806 * positive infinity.
1807 *
1808 * <li> If the argument is zero, the result is
1809 * {@link Float#MIN_VALUE}
1810 *
1811 * </ul>
1812 *
1813 * @param f starting floating-point value
1814 * @return The adjacent floating-point value closer to positive
1815 * infinity.
1816 * @since 1.6
1817 */
1818 public static float nextUp(float f) {
1819 return Math.nextUp(f);
1820 }
1821
1822 /**
1823 * Returns the floating-point value adjacent to {@code d} in
1824 * the direction of negative infinity. This method is
1825 * semantically equivalent to {@code nextAfter(d,
1826 * Double.NEGATIVE_INFINITY)}; however, a
1827 * {@code nextDown} implementation may run faster than its
1828 * equivalent {@code nextAfter} call.
1829 *
1830 * <p>Special Cases:
1831 * <ul>
1832 * <li> If the argument is NaN, the result is NaN.
1833 *
1834 * <li> If the argument is negative infinity, the result is
1835 * negative infinity.
1836 *
1837 * <li> If the argument is zero, the result is
1838 * {@code -Double.MIN_VALUE}
1839 *
1840 * </ul>
1841 *
1842 * @param d starting floating-point value
1843 * @return The adjacent floating-point value closer to negative
1844 * infinity.
1845 * @since 1.8
1846 */
1847 public static double nextDown(double d) {
1848 return Math.nextDown(d);
1849 }
1850
1851 /**
1852 * Returns the floating-point value adjacent to {@code f} in
1853 * the direction of negative infinity. This method is
1854 * semantically equivalent to {@code nextAfter(f,
1855 * Float.NEGATIVE_INFINITY)}; however, a
1856 * {@code nextDown} implementation may run faster than its
1857 * equivalent {@code nextAfter} call.
1858 *
1859 * <p>Special Cases:
1860 * <ul>
1861 * <li> If the argument is NaN, the result is NaN.
1862 *
1863 * <li> If the argument is negative infinity, the result is
1864 * negative infinity.
1865 *
1866 * <li> If the argument is zero, the result is
1867 * {@code -Float.MIN_VALUE}
1868 *
1869 * </ul>
1870 *
1871 * @param f starting floating-point value
1872 * @return The adjacent floating-point value closer to negative
1873 * infinity.
1874 * @since 1.8
1875 */
1876 public static float nextDown(float f) {
1877 return Math.nextDown(f);
1878 }
1879
1880 /**
1881 * Returns {@code d} ×
1882 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1883 * by a single correctly rounded floating-point multiply to a
1884 * member of the double value set. See the Java
1885 * Language Specification for a discussion of floating-point
1886 * value sets. If the exponent of the result is between {@link
1887 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1888 * answer is calculated exactly. If the exponent of the result
1889 * would be larger than {@code Double.MAX_EXPONENT}, an
1890 * infinity is returned. Note that if the result is subnormal,
1891 * precision may be lost; that is, when {@code scalb(x, n)}
1892 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1893 * <i>x</i>. When the result is non-NaN, the result has the same
1894 * sign as {@code d}.
1895 *
1896 * <p>Special cases:
1897 * <ul>
1898 * <li> If the first argument is NaN, NaN is returned.
1899 * <li> If the first argument is infinite, then an infinity of the
1900 * same sign is returned.
1901 * <li> If the first argument is zero, then a zero of the same
1902 * sign is returned.
1903 * </ul>
1904 *
1905 * @param d number to be scaled by a power of two.
1906 * @param scaleFactor power of 2 used to scale {@code d}
1907 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1908 * @since 1.6
1909 */
1910 public static double scalb(double d, int scaleFactor) {
1911 return Math.scalb(d, scaleFactor);
1912 }
1913
1914 /**
1915 * Returns {@code f} ×
1916 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1917 * by a single correctly rounded floating-point multiply to a
1918 * member of the float value set. See the Java
1919 * Language Specification for a discussion of floating-point
1920 * value sets. If the exponent of the result is between {@link
1921 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1922 * answer is calculated exactly. If the exponent of the result
1923 * would be larger than {@code Float.MAX_EXPONENT}, an
1924 * infinity is returned. Note that if the result is subnormal,
1925 * precision may be lost; that is, when {@code scalb(x, n)}
1926 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1927 * <i>x</i>. When the result is non-NaN, the result has the same
1928 * sign as {@code f}.
1929 *
1930 * <p>Special cases:
1931 * <ul>
1932 * <li> If the first argument is NaN, NaN is returned.
1933 * <li> If the first argument is infinite, then an infinity of the
1934 * same sign is returned.
1935 * <li> If the first argument is zero, then a zero of the same
1936 * sign is returned.
1937 * </ul>
1938 *
1939 * @param f number to be scaled by a power of two.
1940 * @param scaleFactor power of 2 used to scale {@code f}
1941 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1942 * @since 1.6
1943 */
1944 public static float scalb(float f, int scaleFactor) {
1945 return Math.scalb(f, scaleFactor);
1946 }
1947 }