1 /*
2 * Copyright (c) 1994, 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
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26 package java.lang;
27
28 import java.math.BigDecimal;
29 import java.util.Random;
30 import jdk.internal.math.FloatConsts;
31 import jdk.internal.math.DoubleConsts;
32 import jdk.internal.HotSpotIntrinsicCandidate;
33
34 /**
35 * The class {@code Math} contains methods for performing basic
36 * numeric operations such as the elementary exponential, logarithm,
37 * square root, and trigonometric functions.
38 *
39 * <p>Unlike some of the numeric methods of class
40 * {@code StrictMath}, all implementations of the equivalent
41 * functions of class {@code Math} are not defined to return the
42 * bit-for-bit same results. This relaxation permits
43 * better-performing implementations where strict reproducibility is
44 * not required.
45 *
46 * <p>By default many of the {@code Math} methods simply call
47 * the equivalent method in {@code StrictMath} for their
48 * implementation. Code generators are encouraged to use
49 * platform-specific native libraries or microprocessor instructions,
50 * where available, to provide higher-performance implementations of
51 * {@code Math} methods. Such higher-performance
52 * implementations still must conform to the specification for
53 * {@code Math}.
54 *
55 * <p>The quality of implementation specifications concern two
56 * properties, accuracy of the returned result and monotonicity of the
57 * method. Accuracy of the floating-point {@code Math} methods is
58 * measured in terms of <i>ulps</i>, units in the last place. For a
59 * given floating-point format, an {@linkplain #ulp(double) ulp} of a
60 * specific real number value is the distance between the two
61 * floating-point values bracketing that numerical value. When
62 * discussing the accuracy of a method as a whole rather than at a
63 * specific argument, the number of ulps cited is for the worst-case
64 * error at any argument. If a method always has an error less than
65 * 0.5 ulps, the method always returns the floating-point number
66 * nearest the exact result; such a method is <i>correctly
67 * rounded</i>. A correctly rounded method is generally the best a
68 * floating-point approximation can be; however, it is impractical for
69 * many floating-point methods to be correctly rounded. Instead, for
70 * the {@code Math} class, a larger error bound of 1 or 2 ulps is
71 * allowed for certain methods. Informally, with a 1 ulp error bound,
72 * when the exact result is a representable number, the exact result
73 * should be returned as the computed result; otherwise, either of the
74 * two floating-point values which bracket the exact result may be
75 * returned. For exact results large in magnitude, one of the
76 * endpoints of the bracket may be infinite. Besides accuracy at
77 * individual arguments, maintaining proper relations between the
78 * method at different arguments is also important. Therefore, most
79 * methods with more than 0.5 ulp errors are required to be
80 * <i>semi-monotonic</i>: whenever the mathematical function is
81 * non-decreasing, so is the floating-point approximation, likewise,
82 * whenever the mathematical function is non-increasing, so is the
83 * floating-point approximation. Not all approximations that have 1
84 * ulp accuracy will automatically meet the monotonicity requirements.
85 *
86 * <p>
87 * The platform uses signed two's complement integer arithmetic with
88 * int and long primitive types. The developer should choose
89 * the primitive type to ensure that arithmetic operations consistently
90 * produce correct results, which in some cases means the operations
91 * will not overflow the range of values of the computation.
92 * The best practice is to choose the primitive type and algorithm to avoid
93 * overflow. In cases where the size is {@code int} or {@code long} and
94 * overflow errors need to be detected, the methods {@code addExact},
95 * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact}
96 * throw an {@code ArithmeticException} when the results overflow.
97 * For other arithmetic operations such as divide, absolute value,
98 * increment, decrement, and negation overflow occurs only with
99 * a specific minimum or maximum value and should be checked against
100 * the minimum or maximum as appropriate.
101 *
102 * @author unascribed
103 * @author Joseph D. Darcy
104 * @since 1.0
105 */
106
107 public final class Math {
108
109 /**
110 * Don't let anyone instantiate this class.
111 */
112 private Math() {}
113
114 /**
115 * The {@code double} value that is closer than any other to
116 * <i>e</i>, the base of the natural logarithms.
117 */
118 public static final double E = 2.7182818284590452354;
119
120 /**
121 * The {@code double} value that is closer than any other to
122 * <i>pi</i>, the ratio of the circumference of a circle to its
123 * diameter.
124 */
125 public static final double PI = 3.14159265358979323846;
126
127 /**
128 * Constant by which to multiply an angular value in degrees to obtain an
129 * angular value in radians.
130 */
131 private static final double DEGREES_TO_RADIANS = 0.017453292519943295;
132
133 /**
134 * Constant by which to multiply an angular value in radians to obtain an
135 * angular value in degrees.
136 */
137 private static final double RADIANS_TO_DEGREES = 57.29577951308232;
138
139 /**
140 * Returns the trigonometric sine of an angle. Special cases:
141 * <ul><li>If the argument is NaN or an infinity, then the
142 * result is NaN.
143 * <li>If the argument is zero, then the result is a zero with the
144 * same sign as the argument.</ul>
145 *
146 * <p>The computed result must be within 1 ulp of the exact result.
147 * Results must be semi-monotonic.
148 *
149 * @param a an angle, in radians.
150 * @return the sine of the argument.
151 */
152 @HotSpotIntrinsicCandidate
153 public static double sin(double a) {
154 return StrictMath.sin(a); // default impl. delegates to StrictMath
155 }
156
157 /**
158 * Returns the trigonometric cosine of an angle. Special cases:
159 * <ul><li>If the argument is NaN or an infinity, then the
160 * result is NaN.</ul>
161 *
162 * <p>The computed result must be within 1 ulp of the exact result.
163 * Results must be semi-monotonic.
164 *
165 * @param a an angle, in radians.
166 * @return the cosine of the argument.
167 */
168 @HotSpotIntrinsicCandidate
169 public static double cos(double a) {
170 return StrictMath.cos(a); // default impl. delegates to StrictMath
171 }
172
173 /**
174 * Returns the trigonometric tangent of an angle. Special cases:
175 * <ul><li>If the argument is NaN or an infinity, then the result
176 * 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 * <p>The computed result must be within 1 ulp of the exact result.
181 * Results must be semi-monotonic.
182 *
183 * @param a an angle, in radians.
184 * @return the tangent of the argument.
185 */
186 @HotSpotIntrinsicCandidate
187 public static double tan(double a) {
188 return StrictMath.tan(a); // default impl. delegates to StrictMath
189 }
190
191 /**
192 * Returns the arc sine of a value; the returned angle is in the
193 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
194 * <ul><li>If the argument is NaN or its absolute value is greater
195 * than 1, then the result is NaN.
196 * <li>If the argument is zero, then the result is a zero with the
197 * same sign as the argument.</ul>
198 *
199 * <p>The computed result must be within 1 ulp of the exact result.
200 * Results must be semi-monotonic.
201 *
202 * @param a the value whose arc sine is to be returned.
203 * @return the arc sine of the argument.
204 */
205 public static double asin(double a) {
206 return StrictMath.asin(a); // default impl. delegates to StrictMath
207 }
208
209 /**
210 * Returns the arc cosine of a value; the returned angle is in the
211 * range 0.0 through <i>pi</i>. Special case:
212 * <ul><li>If the argument is NaN or its absolute value is greater
213 * than 1, then the result is NaN.</ul>
214 *
215 * <p>The computed result must be within 1 ulp of the exact result.
216 * Results must be semi-monotonic.
217 *
218 * @param a the value whose arc cosine is to be returned.
219 * @return the arc cosine of the argument.
220 */
221 public static double acos(double a) {
222 return StrictMath.acos(a); // default impl. delegates to StrictMath
223 }
224
225 /**
226 * Returns the arc tangent of a value; the returned angle is in the
227 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
228 * <ul><li>If the argument is NaN, then the result is NaN.
229 * <li>If the argument is zero, then the result is a zero with the
230 * same sign as the argument.</ul>
231 *
232 * <p>The computed result must be within 1 ulp of the exact result.
233 * Results must be semi-monotonic.
234 *
235 * @param a the value whose arc tangent is to be returned.
236 * @return the arc tangent of the argument.
237 */
238 public static double atan(double a) {
239 return StrictMath.atan(a); // default impl. delegates to StrictMath
240 }
241
242 /**
243 * Converts an angle measured in degrees to an approximately
244 * equivalent angle measured in radians. The conversion from
245 * degrees to radians is generally inexact.
246 *
247 * @param angdeg an angle, in degrees
248 * @return the measurement of the angle {@code angdeg}
249 * in radians.
250 * @since 1.2
251 */
252 public static double toRadians(double angdeg) {
253 return angdeg * DEGREES_TO_RADIANS;
254 }
255
256 /**
257 * Converts an angle measured in radians to an approximately
258 * equivalent angle measured in degrees. The conversion from
259 * radians to degrees is generally inexact; users should
260 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
261 * equal {@code 0.0}.
262 *
263 * @param angrad an angle, in radians
264 * @return the measurement of the angle {@code angrad}
265 * in degrees.
266 * @since 1.2
267 */
268 public static double toDegrees(double angrad) {
269 return angrad * RADIANS_TO_DEGREES;
270 }
271
272 /**
273 * Returns Euler's number <i>e</i> raised to the power of a
274 * {@code double} value. Special cases:
275 * <ul><li>If the argument is NaN, the result is NaN.
276 * <li>If the argument is positive infinity, then the result is
277 * positive infinity.
278 * <li>If the argument is negative infinity, then the result is
279 * positive zero.</ul>
280 *
281 * <p>The computed result must be within 1 ulp of the exact result.
282 * Results must be semi-monotonic.
283 *
284 * @param a the exponent to raise <i>e</i> to.
285 * @return the value <i>e</i><sup>{@code a}</sup>,
286 * where <i>e</i> is the base of the natural logarithms.
287 */
288 @HotSpotIntrinsicCandidate
289 public static double exp(double a) {
290 return StrictMath.exp(a); // default impl. delegates to StrictMath
291 }
292
293 /**
294 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
295 * value. Special cases:
296 * <ul><li>If the argument is NaN or less than zero, then the result
297 * is NaN.
298 * <li>If the argument is positive infinity, then the result is
299 * positive infinity.
300 * <li>If the argument is positive zero or negative zero, then the
301 * result is negative infinity.</ul>
302 *
303 * <p>The computed result must be within 1 ulp of the exact result.
304 * Results must be semi-monotonic.
305 *
306 * @param a a value
307 * @return the value ln {@code a}, the natural logarithm of
308 * {@code a}.
309 */
310 @HotSpotIntrinsicCandidate
311 public static double log(double a) {
312 return StrictMath.log(a); // default impl. delegates to StrictMath
313 }
314
315 /**
316 * Returns the base 10 logarithm of a {@code double} value.
317 * Special cases:
318 *
319 * <ul><li>If the argument is NaN or less than zero, then the result
320 * is NaN.
321 * <li>If the argument is positive infinity, then the result is
322 * positive infinity.
323 * <li>If the argument is positive zero or negative zero, then the
324 * result is negative infinity.
325 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
326 * integer <i>n</i>, then the result is <i>n</i>.
327 * </ul>
328 *
329 * <p>The computed result must be within 1 ulp of the exact result.
330 * Results must be semi-monotonic.
331 *
332 * @param a a value
333 * @return the base 10 logarithm of {@code a}.
334 * @since 1.5
335 */
336 @HotSpotIntrinsicCandidate
337 public static double log10(double a) {
338 return StrictMath.log10(a); // default impl. delegates to StrictMath
339 }
340
341 /**
342 * Returns the correctly rounded positive square root of a
343 * {@code double} value.
344 * Special cases:
345 * <ul><li>If the argument is NaN or less than zero, then the result
346 * is NaN.
347 * <li>If the argument is positive infinity, then the result is positive
348 * infinity.
349 * <li>If the argument is positive zero or negative zero, then the
350 * result is the same as the argument.</ul>
351 * Otherwise, the result is the {@code double} value closest to
352 * the true mathematical square root of the argument value.
353 *
354 * @param a a value.
355 * @return the positive square root of {@code a}.
356 * If the argument is NaN or less than zero, the result is NaN.
357 */
358 @HotSpotIntrinsicCandidate
359 public static double sqrt(double a) {
360 return StrictMath.sqrt(a); // default impl. delegates to StrictMath
361 // Note that hardware sqrt instructions
362 // frequently can be directly used by JITs
363 // and should be much faster than doing
364 // Math.sqrt in software.
365 }
366
367
368 /**
369 * Returns the cube root of a {@code double} value. For
370 * positive finite {@code x}, {@code cbrt(-x) ==
371 * -cbrt(x)}; that is, the cube root of a negative value is
372 * the negative of the cube root of that value's magnitude.
373 *
374 * Special cases:
375 *
376 * <ul>
377 *
378 * <li>If the argument is NaN, then the result is NaN.
379 *
380 * <li>If the argument is infinite, then the result is an infinity
381 * with the same sign as the argument.
382 *
383 * <li>If the argument is zero, then the result is a zero with the
384 * same sign as the argument.
385 *
386 * </ul>
387 *
388 * <p>The computed result must be within 1 ulp of the exact result.
389 *
390 * @param a a value.
391 * @return the cube root of {@code a}.
392 * @since 1.5
393 */
394 public static double cbrt(double a) {
395 return StrictMath.cbrt(a);
396 }
397
398 /**
399 * Computes the remainder operation on two arguments as prescribed
400 * by the IEEE 754 standard.
401 * The remainder value is mathematically equal to
402 * <code>f1 - f2</code> × <i>n</i>,
403 * where <i>n</i> is the mathematical integer closest to the exact
404 * mathematical value of the quotient {@code f1/f2}, and if two
405 * mathematical integers are equally close to {@code f1/f2},
406 * then <i>n</i> is the integer that is even. If the remainder is
407 * zero, its sign is the same as the sign of the first argument.
408 * Special cases:
409 * <ul><li>If either argument is NaN, or the first argument is infinite,
410 * or the second argument is positive zero or negative zero, then the
411 * result is NaN.
412 * <li>If the first argument is finite and the second argument is
413 * infinite, then the result is the same as the first argument.</ul>
414 *
415 * @param f1 the dividend.
416 * @param f2 the divisor.
417 * @return the remainder when {@code f1} is divided by
418 * {@code f2}.
419 */
420 public static double IEEEremainder(double f1, double f2) {
421 return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
422 }
423
424 /**
425 * Returns the smallest (closest to negative infinity)
426 * {@code double} value that is greater than or equal to the
427 * argument and is equal to a mathematical integer. Special cases:
428 * <ul><li>If the argument value is already equal to a
429 * mathematical integer, then the result is the same as the
430 * argument. <li>If the argument is NaN or an infinity or
431 * positive zero or negative zero, then the result is the same as
432 * the argument. <li>If the argument value is less than zero but
433 * greater than -1.0, then the result is negative zero.</ul> Note
434 * that the value of {@code Math.ceil(x)} is exactly the
435 * value of {@code -Math.floor(-x)}.
436 *
437 *
438 * @param a a value.
439 * @return the smallest (closest to negative infinity)
440 * floating-point value that is greater than or equal to
441 * the argument and is equal to a mathematical integer.
442 */
443 public static double ceil(double a) {
444 return StrictMath.ceil(a); // default impl. delegates to StrictMath
445 }
446
447 /**
448 * Returns the largest (closest to positive infinity)
449 * {@code double} value that is less than or equal to the
450 * argument and is equal to a mathematical integer. Special cases:
451 * <ul><li>If the argument value is already equal to a
452 * mathematical integer, then the result is the same as the
453 * argument. <li>If the argument is NaN or an infinity or
454 * positive zero or negative zero, then the result is the same as
455 * the argument.</ul>
456 *
457 * @param a a value.
458 * @return the largest (closest to positive infinity)
459 * floating-point value that less than or equal to the argument
460 * and is equal to a mathematical integer.
461 */
462 public static double floor(double a) {
463 return StrictMath.floor(a); // default impl. delegates to StrictMath
464 }
465
466 /**
467 * Returns the {@code double} value that is closest in value
468 * to the argument and is equal to a mathematical integer. If two
469 * {@code double} values that are mathematical integers are
470 * equally close, the result is the integer value that is
471 * even. Special cases:
472 * <ul><li>If the argument value is already equal to a mathematical
473 * integer, then the result is the same as the argument.
474 * <li>If the argument is NaN or an infinity or positive zero or negative
475 * zero, then the result is the same as the argument.</ul>
476 *
477 * @param a a {@code double} value.
478 * @return the closest floating-point value to {@code a} that is
479 * equal to a mathematical integer.
480 */
481 public static double rint(double a) {
482 return StrictMath.rint(a); // default impl. delegates to StrictMath
483 }
484
485 /**
486 * Returns the angle <i>theta</i> from the conversion of rectangular
487 * coordinates ({@code x}, {@code y}) to polar
488 * coordinates (r, <i>theta</i>).
489 * This method computes the phase <i>theta</i> by computing an arc tangent
490 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
491 * cases:
492 * <ul><li>If either argument is NaN, then the result is NaN.
493 * <li>If the first argument is positive zero and the second argument
494 * is positive, or the first argument is positive and finite and the
495 * second argument is positive infinity, then the result is positive
496 * zero.
497 * <li>If the first argument is negative zero and the second argument
498 * is positive, or the first argument is negative and finite and the
499 * second argument is positive infinity, then the result is negative zero.
500 * <li>If the first argument is positive zero and the second argument
501 * is negative, or the first argument is positive and finite and the
502 * second argument is negative infinity, then the result is the
503 * {@code double} value closest to <i>pi</i>.
504 * <li>If the first argument is negative zero and the second argument
505 * is negative, or the first argument is negative and finite and the
506 * second argument is negative infinity, then the result is the
507 * {@code double} value closest to -<i>pi</i>.
508 * <li>If the first argument is positive and the second argument is
509 * positive zero or negative zero, or the first argument is positive
510 * infinity and the second argument is finite, then the result is the
511 * {@code double} value closest to <i>pi</i>/2.
512 * <li>If the first argument is negative and the second argument is
513 * positive zero or negative zero, or the first argument is negative
514 * infinity and the second argument is finite, then the result is the
515 * {@code double} value closest to -<i>pi</i>/2.
516 * <li>If both arguments are positive infinity, then the result is the
517 * {@code double} value closest to <i>pi</i>/4.
518 * <li>If the first argument is positive infinity and the second argument
519 * is negative infinity, then the result is the {@code double}
520 * value closest to 3*<i>pi</i>/4.
521 * <li>If the first argument is negative infinity and the second argument
522 * is positive infinity, then the result is the {@code double} value
523 * closest to -<i>pi</i>/4.
524 * <li>If both arguments are negative infinity, then the result is the
525 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
526 *
527 * <p>The computed result must be within 2 ulps of the exact result.
528 * Results must be semi-monotonic.
529 *
530 * @param y the ordinate coordinate
531 * @param x the abscissa coordinate
532 * @return the <i>theta</i> component of the point
533 * (<i>r</i>, <i>theta</i>)
534 * in polar coordinates that corresponds to the point
535 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
536 */
537 @HotSpotIntrinsicCandidate
538 public static double atan2(double y, double x) {
539 return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
540 }
541
542 /**
543 * Returns the value of the first argument raised to the power of the
544 * second argument. Special cases:
545 *
546 * <ul><li>If the second argument is positive or negative zero, then the
547 * result is 1.0.
548 * <li>If the second argument is 1.0, then the result is the same as the
549 * first argument.
550 * <li>If the second argument is NaN, then the result is NaN.
551 * <li>If the first argument is NaN and the second argument is nonzero,
552 * then the result is NaN.
553 *
554 * <li>If
555 * <ul>
556 * <li>the absolute value of the first argument is greater than 1
557 * and the second argument is positive infinity, or
558 * <li>the absolute value of the first argument is less than 1 and
559 * the second argument is negative infinity,
560 * </ul>
561 * then the result is positive infinity.
562 *
563 * <li>If
564 * <ul>
565 * <li>the absolute value of the first argument is greater than 1 and
566 * the second argument is negative infinity, or
567 * <li>the absolute value of the
568 * first argument is less than 1 and the second argument is positive
569 * infinity,
570 * </ul>
571 * then the result is positive zero.
572 *
573 * <li>If the absolute value of the first argument equals 1 and the
574 * second argument is infinite, then the result is NaN.
575 *
576 * <li>If
577 * <ul>
578 * <li>the first argument is positive zero and the second argument
579 * is greater than zero, or
580 * <li>the first argument is positive infinity and the second
581 * argument is less than zero,
582 * </ul>
583 * then the result is positive zero.
584 *
585 * <li>If
586 * <ul>
587 * <li>the first argument is positive zero and the second argument
588 * is less than zero, or
589 * <li>the first argument is positive infinity and the second
590 * argument is greater than zero,
591 * </ul>
592 * then the result is positive infinity.
593 *
594 * <li>If
595 * <ul>
596 * <li>the first argument is negative zero and the second argument
597 * is greater than zero but not a finite odd integer, or
598 * <li>the first argument is negative infinity and the second
599 * argument is less than zero but not a finite odd integer,
600 * </ul>
601 * then the result is positive zero.
602 *
603 * <li>If
604 * <ul>
605 * <li>the first argument is negative zero and the second argument
606 * is a positive finite odd integer, or
607 * <li>the first argument is negative infinity and the second
608 * argument is a negative finite odd integer,
609 * </ul>
610 * then the result is negative zero.
611 *
612 * <li>If
613 * <ul>
614 * <li>the first argument is negative zero and the second argument
615 * is less than zero but not a finite odd integer, or
616 * <li>the first argument is negative infinity and the second
617 * argument is greater than zero but not a finite odd integer,
618 * </ul>
619 * then the result is positive infinity.
620 *
621 * <li>If
622 * <ul>
623 * <li>the first argument is negative zero and the second argument
624 * is a negative finite odd integer, or
625 * <li>the first argument is negative infinity and the second
626 * argument is a positive finite odd integer,
627 * </ul>
628 * then the result is negative infinity.
629 *
630 * <li>If the first argument is finite and less than zero
631 * <ul>
632 * <li> if the second argument is a finite even integer, the
633 * result is equal to the result of raising the absolute value of
634 * the first argument to the power of the second argument
635 *
636 * <li>if the second argument is a finite odd integer, the result
637 * is equal to the negative of the result of raising the absolute
638 * value of the first argument to the power of the second
639 * argument
640 *
641 * <li>if the second argument is finite and not an integer, then
642 * the result is NaN.
643 * </ul>
644 *
645 * <li>If both arguments are integers, then the result is exactly equal
646 * to the mathematical result of raising the first argument to the power
647 * of the second argument if that result can in fact be represented
648 * exactly as a {@code double} value.</ul>
649 *
650 * <p>(In the foregoing descriptions, a floating-point value is
651 * considered to be an integer if and only if it is finite and a
652 * fixed point of the method {@link #ceil ceil} or,
653 * equivalently, a fixed point of the method {@link #floor
654 * floor}. A value is a fixed point of a one-argument
655 * method if and only if the result of applying the method to the
656 * value is equal to the value.)
657 *
658 * <p>The computed result must be within 1 ulp of the exact result.
659 * Results must be semi-monotonic.
660 *
661 * @param a the base.
662 * @param b the exponent.
663 * @return the value {@code a}<sup>{@code b}</sup>.
664 */
665 @HotSpotIntrinsicCandidate
666 public static double pow(double a, double b) {
667 return StrictMath.pow(a, b); // default impl. delegates to StrictMath
668 }
669
670 /**
671 * Returns the closest {@code int} to the argument, with ties
672 * rounding to positive infinity.
673 *
674 * <p>
675 * Special cases:
676 * <ul><li>If the argument is NaN, the result is 0.
677 * <li>If the argument is negative infinity or any value less than or
678 * equal to the value of {@code Integer.MIN_VALUE}, the result is
679 * equal to the value of {@code Integer.MIN_VALUE}.
680 * <li>If the argument is positive infinity or any value greater than or
681 * equal to the value of {@code Integer.MAX_VALUE}, the result is
682 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
683 *
684 * @param a a floating-point value to be rounded to an integer.
685 * @return the value of the argument rounded to the nearest
686 * {@code int} value.
687 * @see java.lang.Integer#MAX_VALUE
688 * @see java.lang.Integer#MIN_VALUE
689 */
690 public static int round(float a) {
691 int intBits = Float.floatToRawIntBits(a);
692 int biasedExp = (intBits & FloatConsts.EXP_BIT_MASK)
693 >> (FloatConsts.SIGNIFICAND_WIDTH - 1);
694 int shift = (FloatConsts.SIGNIFICAND_WIDTH - 2
695 + FloatConsts.EXP_BIAS) - biasedExp;
696 if ((shift & -32) == 0) { // shift >= 0 && shift < 32
697 // a is a finite number such that pow(2,-32) <= ulp(a) < 1
698 int r = ((intBits & FloatConsts.SIGNIF_BIT_MASK)
699 | (FloatConsts.SIGNIF_BIT_MASK + 1));
700 if (intBits < 0) {
701 r = -r;
702 }
703 // In the comments below each Java expression evaluates to the value
704 // the corresponding mathematical expression:
705 // (r) evaluates to a / ulp(a)
706 // (r >> shift) evaluates to floor(a * 2)
707 // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
708 // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
709 return ((r >> shift) + 1) >> 1;
710 } else {
711 // a is either
712 // - a finite number with abs(a) < exp(2,FloatConsts.SIGNIFICAND_WIDTH-32) < 1/2
713 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
714 // - an infinity or NaN
715 return (int) a;
716 }
717 }
718
719 /**
720 * Returns the closest {@code long} to the argument, with ties
721 * rounding to positive infinity.
722 *
723 * <p>Special cases:
724 * <ul><li>If the argument is NaN, the result is 0.
725 * <li>If the argument is negative infinity or any value less than or
726 * equal to the value of {@code Long.MIN_VALUE}, the result is
727 * equal to the value of {@code Long.MIN_VALUE}.
728 * <li>If the argument is positive infinity or any value greater than or
729 * equal to the value of {@code Long.MAX_VALUE}, the result is
730 * equal to the value of {@code Long.MAX_VALUE}.</ul>
731 *
732 * @param a a floating-point value to be rounded to a
733 * {@code long}.
734 * @return the value of the argument rounded to the nearest
735 * {@code long} value.
736 * @see java.lang.Long#MAX_VALUE
737 * @see java.lang.Long#MIN_VALUE
738 */
739 public static long round(double a) {
740 long longBits = Double.doubleToRawLongBits(a);
741 long biasedExp = (longBits & DoubleConsts.EXP_BIT_MASK)
742 >> (DoubleConsts.SIGNIFICAND_WIDTH - 1);
743 long shift = (DoubleConsts.SIGNIFICAND_WIDTH - 2
744 + DoubleConsts.EXP_BIAS) - biasedExp;
745 if ((shift & -64) == 0) { // shift >= 0 && shift < 64
746 // a is a finite number such that pow(2,-64) <= ulp(a) < 1
747 long r = ((longBits & DoubleConsts.SIGNIF_BIT_MASK)
748 | (DoubleConsts.SIGNIF_BIT_MASK + 1));
749 if (longBits < 0) {
750 r = -r;
751 }
752 // In the comments below each Java expression evaluates to the value
753 // the corresponding mathematical expression:
754 // (r) evaluates to a / ulp(a)
755 // (r >> shift) evaluates to floor(a * 2)
756 // ((r >> shift) + 1) evaluates to floor((a + 1/2) * 2)
757 // (((r >> shift) + 1) >> 1) evaluates to floor(a + 1/2)
758 return ((r >> shift) + 1) >> 1;
759 } else {
760 // a is either
761 // - a finite number with abs(a) < exp(2,DoubleConsts.SIGNIFICAND_WIDTH-64) < 1/2
762 // - a finite number with ulp(a) >= 1 and hence a is a mathematical integer
763 // - an infinity or NaN
764 return (long) a;
765 }
766 }
767
768 private static final class RandomNumberGeneratorHolder {
769 static final Random randomNumberGenerator = new Random();
770 }
771
772 /**
773 * Returns a {@code double} value with a positive sign, greater
774 * than or equal to {@code 0.0} and less than {@code 1.0}.
775 * Returned values are chosen pseudorandomly with (approximately)
776 * uniform distribution from that range.
777 *
778 * <p>When this method is first called, it creates a single new
779 * pseudorandom-number generator, exactly as if by the expression
780 *
781 * <blockquote>{@code new java.util.Random()}</blockquote>
782 *
783 * This new pseudorandom-number generator is used thereafter for
784 * all calls to this method and is used nowhere else.
785 *
786 * <p>This method is properly synchronized to allow correct use by
787 * more than one thread. However, if many threads need to generate
788 * pseudorandom numbers at a great rate, it may reduce contention
789 * for each thread to have its own pseudorandom-number generator.
790 *
791 * @apiNote
792 * As the largest {@code double} value less than {@code 1.0}
793 * is {@code Math.nextDown(1.0)}, a value {@code x} in the closed range
794 * {@code [x1,x2]} where {@code x1<=x2} may be defined by the statements
795 *
796 * <blockquote><pre>{@code
797 * double f = Math.random()/Math.nextDown(1.0);
798 * double x = x1*(1.0 - f) + x2*f;
799 * }</pre></blockquote>
800 *
801 * @return a pseudorandom {@code double} greater than or equal
802 * to {@code 0.0} and less than {@code 1.0}.
803 * @see #nextDown(double)
804 * @see Random#nextDouble()
805 */
806 public static double random() {
807 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble();
808 }
809
810 /**
811 * Returns the sum of its arguments,
812 * throwing an exception if the result overflows an {@code int}.
813 *
814 * @param x the first value
815 * @param y the second value
816 * @return the result
817 * @throws ArithmeticException if the result overflows an int
818 * @since 1.8
819 */
820 @HotSpotIntrinsicCandidate
821 public static int addExact(int x, int y) {
822 int r = x + y;
823 // HD 2-12 Overflow iff both arguments have the opposite sign of the result
824 if (((x ^ r) & (y ^ r)) < 0) {
825 throw new ArithmeticException("integer overflow");
826 }
827 return r;
828 }
829
830 /**
831 * Returns the sum of its arguments,
832 * throwing an exception if the result overflows a {@code long}.
833 *
834 * @param x the first value
835 * @param y the second value
836 * @return the result
837 * @throws ArithmeticException if the result overflows a long
838 * @since 1.8
839 */
840 @HotSpotIntrinsicCandidate
841 public static long addExact(long x, long y) {
842 long r = x + y;
843 // HD 2-12 Overflow iff both arguments have the opposite sign of the result
844 if (((x ^ r) & (y ^ r)) < 0) {
845 throw new ArithmeticException("long overflow");
846 }
847 return r;
848 }
849
850 /**
851 * Returns the difference of the arguments,
852 * throwing an exception if the result overflows an {@code int}.
853 *
854 * @param x the first value
855 * @param y the second value to subtract from the first
856 * @return the result
857 * @throws ArithmeticException if the result overflows an int
858 * @since 1.8
859 */
860 @HotSpotIntrinsicCandidate
861 public static int subtractExact(int x, int y) {
862 int r = x - y;
863 // HD 2-12 Overflow iff the arguments have different signs and
864 // the sign of the result is different than the sign of x
865 if (((x ^ y) & (x ^ r)) < 0) {
866 throw new ArithmeticException("integer overflow");
867 }
868 return r;
869 }
870
871 /**
872 * Returns the difference of the arguments,
873 * throwing an exception if the result overflows a {@code long}.
874 *
875 * @param x the first value
876 * @param y the second value to subtract from the first
877 * @return the result
878 * @throws ArithmeticException if the result overflows a long
879 * @since 1.8
880 */
881 @HotSpotIntrinsicCandidate
882 public static long subtractExact(long x, long y) {
883 long r = x - y;
884 // HD 2-12 Overflow iff the arguments have different signs and
885 // the sign of the result is different than the sign of x
886 if (((x ^ y) & (x ^ r)) < 0) {
887 throw new ArithmeticException("long overflow");
888 }
889 return r;
890 }
891
892 /**
893 * Returns the product of the arguments,
894 * throwing an exception if the result overflows an {@code int}.
895 *
896 * @param x the first value
897 * @param y the second value
898 * @return the result
899 * @throws ArithmeticException if the result overflows an int
900 * @since 1.8
901 */
902 @HotSpotIntrinsicCandidate
903 public static int multiplyExact(int x, int y) {
904 long r = (long)x * (long)y;
905 if ((int)r != r) {
906 throw new ArithmeticException("integer overflow");
907 }
908 return (int)r;
909 }
910
911 /**
912 * Returns the product of the arguments,
913 * throwing an exception if the result overflows a {@code long}.
914 *
915 * @param x the first value
916 * @param y the second value
917 * @return the result
918 * @throws ArithmeticException if the result overflows a long
919 * @since 1.8
920 */
921 @HotSpotIntrinsicCandidate
922 public static long multiplyExact(long x, long y) {
923 long r = x * y;
924 long ax = Math.abs(x);
925 long ay = Math.abs(y);
926 if (((ax | ay) >>> 31 != 0)) {
927 // Some bits greater than 2^31 that might cause overflow
928 // Check the result using the divide operator
929 // and check for the special case of Long.MIN_VALUE * -1
930 if (((y != 0) && (r / y != x)) ||
931 (x == Long.MIN_VALUE && y == -1)) {
932 throw new ArithmeticException("long overflow");
933 }
934 }
935 return r;
936 }
937
938 /**
939 * Returns the argument incremented by one, throwing an exception if the
940 * result overflows an {@code int}.
941 *
942 * @param a the value to increment
943 * @return the result
944 * @throws ArithmeticException if the result overflows an int
945 * @since 1.8
946 */
947 @HotSpotIntrinsicCandidate
948 public static int incrementExact(int a) {
949 if (a == Integer.MAX_VALUE) {
950 throw new ArithmeticException("integer overflow");
951 }
952
953 return a + 1;
954 }
955
956 /**
957 * Returns the argument incremented by one, throwing an exception if the
958 * result overflows a {@code long}.
959 *
960 * @param a the value to increment
961 * @return the result
962 * @throws ArithmeticException if the result overflows a long
963 * @since 1.8
964 */
965 @HotSpotIntrinsicCandidate
966 public static long incrementExact(long a) {
967 if (a == Long.MAX_VALUE) {
968 throw new ArithmeticException("long overflow");
969 }
970
971 return a + 1L;
972 }
973
974 /**
975 * Returns the argument decremented by one, throwing an exception if the
976 * result overflows an {@code int}.
977 *
978 * @param a the value to decrement
979 * @return the result
980 * @throws ArithmeticException if the result overflows an int
981 * @since 1.8
982 */
983 @HotSpotIntrinsicCandidate
984 public static int decrementExact(int a) {
985 if (a == Integer.MIN_VALUE) {
986 throw new ArithmeticException("integer overflow");
987 }
988
989 return a - 1;
990 }
991
992 /**
993 * Returns the argument decremented by one, throwing an exception if the
994 * result overflows a {@code long}.
995 *
996 * @param a the value to decrement
997 * @return the result
998 * @throws ArithmeticException if the result overflows a long
999 * @since 1.8
1000 */
1001 @HotSpotIntrinsicCandidate
1002 public static long decrementExact(long a) {
1003 if (a == Long.MIN_VALUE) {
1004 throw new ArithmeticException("long overflow");
1005 }
1006
1007 return a - 1L;
1008 }
1009
1010 /**
1011 * Returns the negation of the argument, throwing an exception if the
1012 * result overflows an {@code int}.
1013 *
1014 * @param a the value to negate
1015 * @return the result
1016 * @throws ArithmeticException if the result overflows an int
1017 * @since 1.8
1018 */
1019 @HotSpotIntrinsicCandidate
1020 public static int negateExact(int a) {
1021 if (a == Integer.MIN_VALUE) {
1022 throw new ArithmeticException("integer overflow");
1023 }
1024
1025 return -a;
1026 }
1027
1028 /**
1029 * Returns the negation of the argument, throwing an exception if the
1030 * result overflows a {@code long}.
1031 *
1032 * @param a the value to negate
1033 * @return the result
1034 * @throws ArithmeticException if the result overflows a long
1035 * @since 1.8
1036 */
1037 @HotSpotIntrinsicCandidate
1038 public static long negateExact(long a) {
1039 if (a == Long.MIN_VALUE) {
1040 throw new ArithmeticException("long overflow");
1041 }
1042
1043 return -a;
1044 }
1045
1046 /**
1047 * Returns the value of the {@code long} argument;
1048 * throwing an exception if the value overflows an {@code int}.
1049 *
1050 * @param value the long value
1051 * @return the argument as an int
1052 * @throws ArithmeticException if the {@code argument} overflows an int
1053 * @since 1.8
1054 */
1055 public static int toIntExact(long value) {
1056 if ((int)value != value) {
1057 throw new ArithmeticException("integer overflow");
1058 }
1059 return (int)value;
1060 }
1061
1062 /**
1063 * Returns the largest (closest to positive infinity)
1064 * {@code int} value that is less than or equal to the algebraic quotient.
1065 * There is one special case, if the dividend is the
1066 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1},
1067 * then integer overflow occurs and
1068 * the result is equal to the {@code Integer.MIN_VALUE}.
1069 * <p>
1070 * Normal integer division operates under the round to zero rounding mode
1071 * (truncation). This operation instead acts under the round toward
1072 * negative infinity (floor) rounding mode.
1073 * The floor rounding mode gives different results than truncation
1074 * when the exact result is negative.
1075 * <ul>
1076 * <li>If the signs of the arguments are the same, the results of
1077 * {@code floorDiv} and the {@code /} operator are the same. <br>
1078 * For example, {@code floorDiv(4, 3) == 1} and {@code (4 / 3) == 1}.</li>
1079 * <li>If the signs of the arguments are different, the quotient is negative and
1080 * {@code floorDiv} returns the integer less than or equal to the quotient
1081 * and the {@code /} operator returns the integer closest to zero.<br>
1082 * For example, {@code floorDiv(-4, 3) == -2},
1083 * whereas {@code (-4 / 3) == -1}.
1084 * </li>
1085 * </ul>
1086 *
1087 * @param x the dividend
1088 * @param y the divisor
1089 * @return the largest (closest to positive infinity)
1090 * {@code int} value that is less than or equal to the algebraic quotient.
1091 * @throws ArithmeticException if the divisor {@code y} is zero
1092 * @see #floorMod(int, int)
1093 * @see #floor(double)
1094 * @since 1.8
1095 */
1096 public static int floorDiv(int x, int y) {
1097 int r = x / y;
1098 // if the signs are different and modulo not zero, round down
1099 if ((x ^ y) < 0 && (r * y != x)) {
1100 r--;
1101 }
1102 return r;
1103 }
1104
1105 /**
1106 * Returns the largest (closest to positive infinity)
1107 * {@code long} value that is less than or equal to the algebraic quotient.
1108 * There is one special case, if the dividend is the
1109 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1},
1110 * then integer overflow occurs and
1111 * the result is equal to the {@code Long.MIN_VALUE}.
1112 * <p>
1113 * Normal integer division operates under the round to zero rounding mode
1114 * (truncation). This operation instead acts under the round toward
1115 * negative infinity (floor) rounding mode.
1116 * The floor rounding mode gives different results than truncation
1117 * when the exact result is negative.
1118 * <p>
1119 * For examples, see {@link #floorDiv(int, int)}.
1120 *
1121 * @param x the dividend
1122 * @param y the divisor
1123 * @return the largest (closest to positive infinity)
1124 * {@code long} value that is less than or equal to the algebraic quotient.
1125 * @throws ArithmeticException if the divisor {@code y} is zero
1126 * @see #floorMod(long, long)
1127 * @see #floor(double)
1128 * @since 1.8
1129 */
1130 public static long floorDiv(long x, long y) {
1131 long r = x / y;
1132 // if the signs are different and modulo not zero, round down
1133 if ((x ^ y) < 0 && (r * y != x)) {
1134 r--;
1135 }
1136 return r;
1137 }
1138
1139 /**
1140 * Returns the floor modulus of the {@code int} arguments.
1141 * <p>
1142 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1143 * has the same sign as the divisor {@code y}, and
1144 * is in the range of {@code -abs(y) < r < +abs(y)}.
1145 *
1146 * <p>
1147 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1148 * <ul>
1149 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1150 * </ul>
1151 * <p>
1152 * The difference in values between {@code floorMod} and
1153 * the {@code %} operator is due to the difference between
1154 * {@code floorDiv} that returns the integer less than or equal to the quotient
1155 * and the {@code /} operator that returns the integer closest to zero.
1156 * <p>
1157 * Examples:
1158 * <ul>
1159 * <li>If the signs of the arguments are the same, the results
1160 * of {@code floorMod} and the {@code %} operator are the same. <br>
1161 * <ul>
1162 * <li>{@code floorMod(4, 3) == 1}; and {@code (4 % 3) == 1}</li>
1163 * </ul>
1164 * <li>If the signs of the arguments are different, the results differ from the {@code %} operator.<br>
1165 * <ul>
1166 * <li>{@code floorMod(+4, -3) == -2}; and {@code (+4 % -3) == +1} </li>
1167 * <li>{@code floorMod(-4, +3) == +2}; and {@code (-4 % +3) == -1} </li>
1168 * <li>{@code floorMod(-4, -3) == -1}; and {@code (-4 % -3) == -1 } </li>
1169 * </ul>
1170 * </li>
1171 * </ul>
1172 * <p>
1173 * If the signs of arguments are unknown and a positive modulus
1174 * is needed it can be computed as {@code (floorMod(x, y) + abs(y)) % abs(y)}.
1175 *
1176 * @param x the dividend
1177 * @param y the divisor
1178 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1179 * @throws ArithmeticException if the divisor {@code y} is zero
1180 * @see #floorDiv(int, int)
1181 * @since 1.8
1182 */
1183 public static int floorMod(int x, int y) {
1184 int r = x - floorDiv(x, y) * y;
1185 return r;
1186 }
1187
1188 /**
1189 * Returns the floor modulus of the {@code long} arguments.
1190 * <p>
1191 * The floor modulus is {@code x - (floorDiv(x, y) * y)},
1192 * has the same sign as the divisor {@code y}, and
1193 * is in the range of {@code -abs(y) < r < +abs(y)}.
1194 *
1195 * <p>
1196 * The relationship between {@code floorDiv} and {@code floorMod} is such that:
1197 * <ul>
1198 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x}
1199 * </ul>
1200 * <p>
1201 * For examples, see {@link #floorMod(int, int)}.
1202 *
1203 * @param x the dividend
1204 * @param y the divisor
1205 * @return the floor modulus {@code x - (floorDiv(x, y) * y)}
1206 * @throws ArithmeticException if the divisor {@code y} is zero
1207 * @see #floorDiv(long, long)
1208 * @since 1.8
1209 */
1210 public static long floorMod(long x, long y) {
1211 return x - floorDiv(x, y) * y;
1212 }
1213
1214 /**
1215 * Returns the absolute value of an {@code int} value.
1216 * If the argument is not negative, the argument is returned.
1217 * If the argument is negative, the negation of the argument is returned.
1218 *
1219 * <p>Note that if the argument is equal to the value of
1220 * {@link Integer#MIN_VALUE}, the most negative representable
1221 * {@code int} value, the result is that same value, which is
1222 * negative.
1223 *
1224 * @param a the argument whose absolute value is to be determined
1225 * @return the absolute value of the argument.
1226 */
1227 public static int abs(int a) {
1228 return (a < 0) ? -a : a;
1229 }
1230
1231 /**
1232 * Returns the absolute value of a {@code long} value.
1233 * If the argument is not negative, the argument is returned.
1234 * If the argument is negative, the negation of the argument is returned.
1235 *
1236 * <p>Note that if the argument is equal to the value of
1237 * {@link Long#MIN_VALUE}, the most negative representable
1238 * {@code long} value, the result is that same value, which
1239 * is negative.
1240 *
1241 * @param a the argument whose absolute value is to be determined
1242 * @return the absolute value of the argument.
1243 */
1244 public static long abs(long a) {
1245 return (a < 0) ? -a : a;
1246 }
1247
1248 /**
1249 * Returns the absolute value of a {@code float} value.
1250 * If the argument is not negative, the argument is returned.
1251 * If the argument is negative, the negation of the argument is returned.
1252 * Special cases:
1253 * <ul><li>If the argument is positive zero or negative zero, the
1254 * result is positive zero.
1255 * <li>If the argument is infinite, the result is positive infinity.
1256 * <li>If the argument is NaN, the result is NaN.</ul>
1257 * In other words, the result is the same as the value of the expression:
1258 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
1259 *
1260 * @param a the argument whose absolute value is to be determined
1261 * @return the absolute value of the argument.
1262 */
1263 public static float abs(float a) {
1264 return (a <= 0.0F) ? 0.0F - a : a;
1265 }
1266
1267 /**
1268 * Returns the absolute value of a {@code double} value.
1269 * If the argument is not negative, the argument is returned.
1270 * If the argument is negative, the negation of the argument is returned.
1271 * Special cases:
1272 * <ul><li>If the argument is positive zero or negative zero, the result
1273 * is positive zero.
1274 * <li>If the argument is infinite, the result is positive infinity.
1275 * <li>If the argument is NaN, the result is NaN.</ul>
1276 * In other words, the result is the same as the value of the expression:
1277 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
1278 *
1279 * @param a the argument whose absolute value is to be determined
1280 * @return the absolute value of the argument.
1281 */
1282 @HotSpotIntrinsicCandidate
1283 public static double abs(double a) {
1284 return (a <= 0.0D) ? 0.0D - a : a;
1285 }
1286
1287 /**
1288 * Returns the greater of two {@code int} values. That is, the
1289 * result is the argument closer to the value of
1290 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
1291 * the result is that same value.
1292 *
1293 * @param a an argument.
1294 * @param b another argument.
1295 * @return the larger of {@code a} and {@code b}.
1296 */
1297 @HotSpotIntrinsicCandidate
1298 public static int max(int a, int b) {
1299 return (a >= b) ? a : b;
1300 }
1301
1302 /**
1303 * Returns the greater of two {@code long} values. That is, the
1304 * result is the argument closer to the value of
1305 * {@link Long#MAX_VALUE}. If the arguments have the same value,
1306 * the result is that same value.
1307 *
1308 * @param a an argument.
1309 * @param b another argument.
1310 * @return the larger of {@code a} and {@code b}.
1311 */
1312 public static long max(long a, long b) {
1313 return (a >= b) ? a : b;
1314 }
1315
1316 // Use raw bit-wise conversions on guaranteed non-NaN arguments.
1317 private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f);
1318 private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d);
1319
1320 /**
1321 * Returns the greater of two {@code float} values. That is,
1322 * the result is the argument closer to positive infinity. If the
1323 * arguments have the same value, the result is that same
1324 * value. If either value is NaN, then the result is NaN. Unlike
1325 * the numerical comparison operators, this method considers
1326 * negative zero to be strictly smaller than positive zero. If one
1327 * argument is positive zero and the other negative zero, the
1328 * result is positive zero.
1329 *
1330 * @param a an argument.
1331 * @param b another argument.
1332 * @return the larger of {@code a} and {@code b}.
1333 */
1334 public static float max(float a, float b) {
1335 if (a != a)
1336 return a; // a is NaN
1337 if ((a == 0.0f) &&
1338 (b == 0.0f) &&
1339 (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) {
1340 // Raw conversion ok since NaN can't map to -0.0.
1341 return b;
1342 }
1343 return (a >= b) ? a : b;
1344 }
1345
1346 /**
1347 * Returns the greater of two {@code double} values. That
1348 * is, the result is the argument closer to positive infinity. If
1349 * the arguments have the same value, the result is that same
1350 * value. If either value is NaN, then the result is NaN. Unlike
1351 * the numerical comparison operators, this method considers
1352 * negative zero to be strictly smaller than positive zero. If one
1353 * argument is positive zero and the other negative zero, the
1354 * result is positive zero.
1355 *
1356 * @param a an argument.
1357 * @param b another argument.
1358 * @return the larger of {@code a} and {@code b}.
1359 */
1360 public static double max(double a, double b) {
1361 if (a != a)
1362 return a; // a is NaN
1363 if ((a == 0.0d) &&
1364 (b == 0.0d) &&
1365 (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) {
1366 // Raw conversion ok since NaN can't map to -0.0.
1367 return b;
1368 }
1369 return (a >= b) ? a : b;
1370 }
1371
1372 /**
1373 * Returns the smaller of two {@code int} values. That is,
1374 * the result the argument closer to the value of
1375 * {@link Integer#MIN_VALUE}. If the arguments have the same
1376 * value, the result is that same value.
1377 *
1378 * @param a an argument.
1379 * @param b another argument.
1380 * @return the smaller of {@code a} and {@code b}.
1381 */
1382 @HotSpotIntrinsicCandidate
1383 public static int min(int a, int b) {
1384 return (a <= b) ? a : b;
1385 }
1386
1387 /**
1388 * Returns the smaller of two {@code long} values. That is,
1389 * the result is the argument closer to the value of
1390 * {@link Long#MIN_VALUE}. If the arguments have the same
1391 * value, the result is that same value.
1392 *
1393 * @param a an argument.
1394 * @param b another argument.
1395 * @return the smaller of {@code a} and {@code b}.
1396 */
1397 public static long min(long a, long b) {
1398 return (a <= b) ? a : b;
1399 }
1400
1401 /**
1402 * Returns the smaller of two {@code float} values. That is,
1403 * the result is the value closer to negative infinity. If the
1404 * arguments have the same value, the result is that same
1405 * value. If either value is NaN, then the result is NaN. Unlike
1406 * the numerical comparison operators, this method considers
1407 * negative zero to be strictly smaller than positive zero. If
1408 * one argument is positive zero and the other is negative zero,
1409 * the result is negative zero.
1410 *
1411 * @param a an argument.
1412 * @param b another argument.
1413 * @return the smaller of {@code a} and {@code b}.
1414 */
1415 public static float min(float a, float b) {
1416 if (a != a)
1417 return a; // a is NaN
1418 if ((a == 0.0f) &&
1419 (b == 0.0f) &&
1420 (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) {
1421 // Raw conversion ok since NaN can't map to -0.0.
1422 return b;
1423 }
1424 return (a <= b) ? a : b;
1425 }
1426
1427 /**
1428 * Returns the smaller of two {@code double} values. That
1429 * is, the result is the value closer to negative infinity. If the
1430 * arguments have the same value, the result is that same
1431 * value. If either value is NaN, then the result is NaN. Unlike
1432 * the numerical comparison operators, this method considers
1433 * negative zero to be strictly smaller than positive zero. If one
1434 * argument is positive zero and the other is negative zero, the
1435 * result is negative zero.
1436 *
1437 * @param a an argument.
1438 * @param b another argument.
1439 * @return the smaller of {@code a} and {@code b}.
1440 */
1441 public static double min(double a, double b) {
1442 if (a != a)
1443 return a; // a is NaN
1444 if ((a == 0.0d) &&
1445 (b == 0.0d) &&
1446 (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) {
1447 // Raw conversion ok since NaN can't map to -0.0.
1448 return b;
1449 }
1450 return (a <= b) ? a : b;
1451 }
1452
1453 /**
1454 * Returns the fused multiply add of the three arguments; that is,
1455 * returns the exact product of the first two arguments summed
1456 * with the third argument and then rounded once to the nearest
1457 * {@code double}.
1458 *
1459 * The rounding is done using the {@linkplain
1460 * java.math.RoundingMode#HALF_EVEN round to nearest even
1461 * rounding mode}.
1462 *
1463 * In contrast, if {@code a * b + c} is evaluated as a regular
1464 * floating-point expression, two rounding errors are involved,
1465 * the first for the multiply operation, the second for the
1466 * addition operation.
1467 *
1468 * <p>Special cases:
1469 * <ul>
1470 * <li> If any argument is NaN, the result is NaN.
1471 *
1472 * <li> If one of the first two arguments is infinite and the
1473 * other is zero, the result is NaN.
1474 *
1475 * <li> If the exact product of the first two arguments is infinite
1476 * (in other words, at least one of the arguments is infinite and
1477 * the other is neither zero nor NaN) and the third argument is an
1478 * infinity of the opposite sign, the result is NaN.
1479 *
1480 * </ul>
1481 *
1482 * <p>Note that {@code fma(a, 1.0, c)} returns the same
1483 * result as ({@code a + c}). However,
1484 * {@code fma(a, b, +0.0)} does <em>not</em> always return the
1485 * same result as ({@code a * b}) since
1486 * {@code fma(-0.0, +0.0, +0.0)} is {@code +0.0} while
1487 * ({@code -0.0 * +0.0}) is {@code -0.0}; {@code fma(a, b, -0.0)} is
1488 * equivalent to ({@code a * b}) however.
1489 *
1490 * @apiNote This method corresponds to the fusedMultiplyAdd
1491 * operation defined in IEEE 754-2008.
1492 *
1493 * @param a a value
1494 * @param b a value
1495 * @param c a value
1496 *
1497 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1498 * computed, as if with unlimited range and precision, and rounded
1499 * once to the nearest {@code double} value
1500 */
1501 // @HotSpotIntrinsicCandidate
1502 public static double fma(double a, double b, double c) {
1503 /*
1504 * Infinity and NaN arithmetic is not quite the same with two
1505 * roundings as opposed to just one so the simple expression
1506 * "a * b + c" cannot always be used to compute the correct
1507 * result. With two roundings, the product can overflow and
1508 * if the addend is infinite, a spurious NaN can be produced
1509 * if the infinity from the overflow and the infinite addend
1510 * have opposite signs.
1511 */
1512
1513 // First, screen for and handle non-finite input values whose
1514 // arithmetic is not supported by BigDecimal.
1515 if (Double.isNaN(a) || Double.isNaN(b) || Double.isNaN(c)) {
1516 return Double.NaN;
1517 } else { // All inputs non-NaN
1518 boolean infiniteA = Double.isInfinite(a);
1519 boolean infiniteB = Double.isInfinite(b);
1520 boolean infiniteC = Double.isInfinite(c);
1521 double result;
1522
1523 if (infiniteA || infiniteB || infiniteC) {
1524 if (infiniteA && b == 0.0 ||
1525 infiniteB && a == 0.0 ) {
1526 return Double.NaN;
1527 }
1528 // Store product in a double field to cause an
1529 // overflow even if non-strictfp evaluation is being
1530 // used.
1531 double product = a * b;
1532 if (Double.isInfinite(product) && !infiniteA && !infiniteB) {
1533 // Intermediate overflow; might cause a
1534 // spurious NaN if added to infinite c.
1535 assert Double.isInfinite(c);
1536 return c;
1537 } else {
1538 result = product + c;
1539 assert !Double.isFinite(result);
1540 return result;
1541 }
1542 } else { // All inputs finite
1543 BigDecimal product = (new BigDecimal(a)).multiply(new BigDecimal(b));
1544 if (c == 0.0) { // Positive or negative zero
1545 // If the product is an exact zero, use a
1546 // floating-point expression to compute the sign
1547 // of the zero final result. The product is an
1548 // exact zero if and only if at least one of a and
1549 // b is zero.
1550 if (a == 0.0 || b == 0.0) {
1551 return a * b + c;
1552 } else {
1553 // The sign of a zero addend doesn't matter if
1554 // the product is nonzero. The sign of a zero
1555 // addend is not factored in the result if the
1556 // exact product is nonzero but underflows to
1557 // zero; see IEEE-754 2008 section 6.3 "The
1558 // sign bit".
1559 return product.doubleValue();
1560 }
1561 } else {
1562 return product.add(new BigDecimal(c)).doubleValue();
1563 }
1564 }
1565 }
1566 }
1567
1568 /**
1569 * Returns the fused multiply add of the three arguments; that is,
1570 * returns the exact product of the first two arguments summed
1571 * with the third argument and then rounded once to the nearest
1572 * {@code float}.
1573 *
1574 * The rounding is done using the {@linkplain
1575 * java.math.RoundingMode#HALF_EVEN round to nearest even
1576 * rounding mode}.
1577 *
1578 * In contrast, if {@code a * b + c} is evaluated as a regular
1579 * floating-point expression, two rounding errors are involved,
1580 * the first for the multiply operation, the second for the
1581 * addition operation.
1582 *
1583 * <p>Special cases:
1584 * <ul>
1585 * <li> If any argument is NaN, the result is NaN.
1586 *
1587 * <li> If one of the first two arguments is infinite and the
1588 * other is zero, the result is NaN.
1589 *
1590 * <li> If the exact product of the first two arguments is infinite
1591 * (in other words, at least one of the arguments is infinite and
1592 * the other is neither zero nor NaN) and the third argument is an
1593 * infinity of the opposite sign, the result is NaN.
1594 *
1595 * </ul>
1596 *
1597 * <p>Note that {@code fma(a, 1.0f, c)} returns the same
1598 * result as ({@code a + c}). However,
1599 * {@code fma(a, b, +0.0f)} does <em>not</em> always return the
1600 * same result as ({@code a * b}) since
1601 * {@code fma(-0.0f, +0.0f, +0.0f)} is {@code +0.0f} while
1602 * ({@code -0.0f * +0.0f}) is {@code -0.0f}; {@code fma(a, b, -0.0f)} is
1603 * equivalent to ({@code a * b}) however.
1604 *
1605 * @apiNote This method corresponds to the fusedMultiplyAdd
1606 * operation defined in IEEE 754-2008.
1607 *
1608 * @param a a value
1609 * @param b a value
1610 * @param c a value
1611 *
1612 * @return (<i>a</i> × <i>b</i> + <i>c</i>)
1613 * computed, as if with unlimited range and precision, and rounded
1614 * once to the nearest {@code float} value
1615 */
1616 // @HotSpotIntrinsicCandidate
1617 public static float fma(float a, float b, float c) {
1618 /*
1619 * Since the double format has more than twice the precision
1620 * of the float format, the multiply of a * b is exact in
1621 * double. The add of c to the product then incurs one
1622 * rounding error. Since the double format moreover has more
1623 * than (2p + 2) precision bits compared to the p bits of the
1624 * float format, the two roundings of (a * b + c), first to
1625 * the double format and then secondarily to the float format,
1626 * are equivalent to rounding the intermediate result directly
1627 * to the float format.
1628 *
1629 * In terms of strictfp vs default-fp concerns related to
1630 * overflow and underflow, since
1631 *
1632 * (Float.MAX_VALUE * Float.MAX_VALUE) << Double.MAX_VALUE
1633 * (Float.MIN_VALUE * Float.MIN_VALUE) >> Double.MIN_VALUE
1634 *
1635 * neither the multiply nor add will overflow or underflow in
1636 * double. Therefore, it is not necessary for this method to
1637 * be declared strictfp to have reproducible
1638 * behavior. However, it is necessary to explicitly store down
1639 * to a float variable to avoid returning a value in the float
1640 * extended value set.
1641 */
1642 float result = (float)(((double) a * (double) b ) + (double) c);
1643 return result;
1644 }
1645
1646 /**
1647 * Returns the size of an ulp of the argument. An ulp, unit in
1648 * the last place, of a {@code double} value is the positive
1649 * distance between this floating-point value and the {@code
1650 * double} value next larger in magnitude. Note that for non-NaN
1651 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1652 *
1653 * <p>Special Cases:
1654 * <ul>
1655 * <li> If the argument is NaN, then the result is NaN.
1656 * <li> If the argument is positive or negative infinity, then the
1657 * result is positive infinity.
1658 * <li> If the argument is positive or negative zero, then the result is
1659 * {@code Double.MIN_VALUE}.
1660 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
1661 * the result is equal to 2<sup>971</sup>.
1662 * </ul>
1663 *
1664 * @param d the floating-point value whose ulp is to be returned
1665 * @return the size of an ulp of the argument
1666 * @author Joseph D. Darcy
1667 * @since 1.5
1668 */
1669 public static double ulp(double d) {
1670 int exp = getExponent(d);
1671
1672 switch(exp) {
1673 case Double.MAX_EXPONENT + 1: // NaN or infinity
1674 return Math.abs(d);
1675
1676 case Double.MIN_EXPONENT - 1: // zero or subnormal
1677 return Double.MIN_VALUE;
1678
1679 default:
1680 assert exp <= Double.MAX_EXPONENT && exp >= Double.MIN_EXPONENT;
1681
1682 // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
1683 exp = exp - (DoubleConsts.SIGNIFICAND_WIDTH-1);
1684 if (exp >= Double.MIN_EXPONENT) {
1685 return powerOfTwoD(exp);
1686 }
1687 else {
1688 // return a subnormal result; left shift integer
1689 // representation of Double.MIN_VALUE appropriate
1690 // number of positions
1691 return Double.longBitsToDouble(1L <<
1692 (exp - (Double.MIN_EXPONENT - (DoubleConsts.SIGNIFICAND_WIDTH-1)) ));
1693 }
1694 }
1695 }
1696
1697 /**
1698 * Returns the size of an ulp of the argument. An ulp, unit in
1699 * the last place, of a {@code float} value is the positive
1700 * distance between this floating-point value and the {@code
1701 * float} value next larger in magnitude. Note that for non-NaN
1702 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
1703 *
1704 * <p>Special Cases:
1705 * <ul>
1706 * <li> If the argument is NaN, then the result is NaN.
1707 * <li> If the argument is positive or negative infinity, then the
1708 * result is positive infinity.
1709 * <li> If the argument is positive or negative zero, then the result is
1710 * {@code Float.MIN_VALUE}.
1711 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
1712 * the result is equal to 2<sup>104</sup>.
1713 * </ul>
1714 *
1715 * @param f the floating-point value whose ulp is to be returned
1716 * @return the size of an ulp of the argument
1717 * @author Joseph D. Darcy
1718 * @since 1.5
1719 */
1720 public static float ulp(float f) {
1721 int exp = getExponent(f);
1722
1723 switch(exp) {
1724 case Float.MAX_EXPONENT+1: // NaN or infinity
1725 return Math.abs(f);
1726
1727 case Float.MIN_EXPONENT-1: // zero or subnormal
1728 return Float.MIN_VALUE;
1729
1730 default:
1731 assert exp <= Float.MAX_EXPONENT && exp >= Float.MIN_EXPONENT;
1732
1733 // ulp(x) is usually 2^(SIGNIFICAND_WIDTH-1)*(2^ilogb(x))
1734 exp = exp - (FloatConsts.SIGNIFICAND_WIDTH-1);
1735 if (exp >= Float.MIN_EXPONENT) {
1736 return powerOfTwoF(exp);
1737 } else {
1738 // return a subnormal result; left shift integer
1739 // representation of FloatConsts.MIN_VALUE appropriate
1740 // number of positions
1741 return Float.intBitsToFloat(1 <<
1742 (exp - (Float.MIN_EXPONENT - (FloatConsts.SIGNIFICAND_WIDTH-1)) ));
1743 }
1744 }
1745 }
1746
1747 /**
1748 * Returns the signum function of the argument; zero if the argument
1749 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
1750 * argument is less than zero.
1751 *
1752 * <p>Special Cases:
1753 * <ul>
1754 * <li> If the argument is NaN, then the result is NaN.
1755 * <li> If the argument is positive zero or negative zero, then the
1756 * result is the same as the argument.
1757 * </ul>
1758 *
1759 * @param d the floating-point value whose signum is to be returned
1760 * @return the signum function of the argument
1761 * @author Joseph D. Darcy
1762 * @since 1.5
1763 */
1764 public static double signum(double d) {
1765 return (d == 0.0 || Double.isNaN(d))?d:copySign(1.0, d);
1766 }
1767
1768 /**
1769 * Returns the signum function of the argument; zero if the argument
1770 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1771 * argument is less than zero.
1772 *
1773 * <p>Special Cases:
1774 * <ul>
1775 * <li> If the argument is NaN, then the result is NaN.
1776 * <li> If the argument is positive zero or negative zero, then the
1777 * result is the same as the argument.
1778 * </ul>
1779 *
1780 * @param f the floating-point value whose signum is to be returned
1781 * @return the signum function of the argument
1782 * @author Joseph D. Darcy
1783 * @since 1.5
1784 */
1785 public static float signum(float f) {
1786 return (f == 0.0f || Float.isNaN(f))?f:copySign(1.0f, f);
1787 }
1788
1789 /**
1790 * Returns the hyperbolic sine of a {@code double} value.
1791 * The hyperbolic sine of <i>x</i> is defined to be
1792 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
1793 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1794 *
1795 * <p>Special cases:
1796 * <ul>
1797 *
1798 * <li>If the argument is NaN, then the result is NaN.
1799 *
1800 * <li>If the argument is infinite, then the result is an infinity
1801 * with the same sign as the argument.
1802 *
1803 * <li>If the argument is zero, then the result is a zero with the
1804 * same sign as the argument.
1805 *
1806 * </ul>
1807 *
1808 * <p>The computed result must be within 2.5 ulps of the exact result.
1809 *
1810 * @param x The number whose hyperbolic sine is to be returned.
1811 * @return The hyperbolic sine of {@code x}.
1812 * @since 1.5
1813 */
1814 public static double sinh(double x) {
1815 return StrictMath.sinh(x);
1816 }
1817
1818 /**
1819 * Returns the hyperbolic cosine of a {@code double} value.
1820 * The hyperbolic cosine of <i>x</i> is defined to be
1821 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
1822 * where <i>e</i> is {@linkplain Math#E Euler's number}.
1823 *
1824 * <p>Special cases:
1825 * <ul>
1826 *
1827 * <li>If the argument is NaN, then the result is NaN.
1828 *
1829 * <li>If the argument is infinite, then the result is positive
1830 * infinity.
1831 *
1832 * <li>If the argument is zero, then the result is {@code 1.0}.
1833 *
1834 * </ul>
1835 *
1836 * <p>The computed result must be within 2.5 ulps of the exact result.
1837 *
1838 * @param x The number whose hyperbolic cosine is to be returned.
1839 * @return The hyperbolic cosine of {@code x}.
1840 * @since 1.5
1841 */
1842 public static double cosh(double x) {
1843 return StrictMath.cosh(x);
1844 }
1845
1846 /**
1847 * Returns the hyperbolic tangent of a {@code double} value.
1848 * The hyperbolic tangent of <i>x</i> is defined to be
1849 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
1850 * in other words, {@linkplain Math#sinh
1851 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
1852 * that the absolute value of the exact tanh is always less than
1853 * 1.
1854 *
1855 * <p>Special cases:
1856 * <ul>
1857 *
1858 * <li>If the argument is NaN, then the result is NaN.
1859 *
1860 * <li>If the argument is zero, then the result is a zero with the
1861 * same sign as the argument.
1862 *
1863 * <li>If the argument is positive infinity, then the result is
1864 * {@code +1.0}.
1865 *
1866 * <li>If the argument is negative infinity, then the result is
1867 * {@code -1.0}.
1868 *
1869 * </ul>
1870 *
1871 * <p>The computed result must be within 2.5 ulps of the exact result.
1872 * The result of {@code tanh} for any finite input must have
1873 * an absolute value less than or equal to 1. Note that once the
1874 * exact result of tanh is within 1/2 of an ulp of the limit value
1875 * of ±1, correctly signed ±{@code 1.0} should
1876 * be returned.
1877 *
1878 * @param x The number whose hyperbolic tangent is to be returned.
1879 * @return The hyperbolic tangent of {@code x}.
1880 * @since 1.5
1881 */
1882 public static double tanh(double x) {
1883 return StrictMath.tanh(x);
1884 }
1885
1886 /**
1887 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1888 * without intermediate overflow or underflow.
1889 *
1890 * <p>Special cases:
1891 * <ul>
1892 *
1893 * <li> If either argument is infinite, then the result
1894 * is positive infinity.
1895 *
1896 * <li> If either argument is NaN and neither argument is infinite,
1897 * then the result is NaN.
1898 *
1899 * </ul>
1900 *
1901 * <p>The computed result must be within 1 ulp of the exact
1902 * result. If one parameter is held constant, the results must be
1903 * semi-monotonic in the other parameter.
1904 *
1905 * @param x a value
1906 * @param y a value
1907 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
1908 * without intermediate overflow or underflow
1909 * @since 1.5
1910 */
1911 public static double hypot(double x, double y) {
1912 return StrictMath.hypot(x, y);
1913 }
1914
1915 /**
1916 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
1917 * <i>x</i> near 0, the exact sum of
1918 * {@code expm1(x)} + 1 is much closer to the true
1919 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
1920 *
1921 * <p>Special cases:
1922 * <ul>
1923 * <li>If the argument is NaN, the result is NaN.
1924 *
1925 * <li>If the argument is positive infinity, then the result is
1926 * positive infinity.
1927 *
1928 * <li>If the argument is negative infinity, then the result is
1929 * -1.0.
1930 *
1931 * <li>If the argument is zero, then the result is a zero with the
1932 * same sign as the argument.
1933 *
1934 * </ul>
1935 *
1936 * <p>The computed result must be within 1 ulp of the exact result.
1937 * Results must be semi-monotonic. The result of
1938 * {@code expm1} for any finite input must be greater than or
1939 * equal to {@code -1.0}. Note that once the exact result of
1940 * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
1941 * ulp of the limit value -1, {@code -1.0} should be
1942 * returned.
1943 *
1944 * @param x the exponent to raise <i>e</i> to in the computation of
1945 * <i>e</i><sup>{@code x}</sup> -1.
1946 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
1947 * @since 1.5
1948 */
1949 public static double expm1(double x) {
1950 return StrictMath.expm1(x);
1951 }
1952
1953 /**
1954 * Returns the natural logarithm of the sum of the argument and 1.
1955 * Note that for small values {@code x}, the result of
1956 * {@code log1p(x)} is much closer to the true result of ln(1
1957 * + {@code x}) than the floating-point evaluation of
1958 * {@code log(1.0+x)}.
1959 *
1960 * <p>Special cases:
1961 *
1962 * <ul>
1963 *
1964 * <li>If the argument is NaN or less than -1, then the result is
1965 * NaN.
1966 *
1967 * <li>If the argument is positive infinity, then the result is
1968 * positive infinity.
1969 *
1970 * <li>If the argument is negative one, then the result is
1971 * negative infinity.
1972 *
1973 * <li>If the argument is zero, then the result is a zero with the
1974 * same sign as the argument.
1975 *
1976 * </ul>
1977 *
1978 * <p>The computed result must be within 1 ulp of the exact result.
1979 * Results must be semi-monotonic.
1980 *
1981 * @param x a value
1982 * @return the value ln({@code x} + 1), the natural
1983 * log of {@code x} + 1
1984 * @since 1.5
1985 */
1986 public static double log1p(double x) {
1987 return StrictMath.log1p(x);
1988 }
1989
1990 /**
1991 * Returns the first floating-point argument with the sign of the
1992 * second floating-point argument. Note that unlike the {@link
1993 * StrictMath#copySign(double, double) StrictMath.copySign}
1994 * method, this method does not require NaN {@code sign}
1995 * arguments to be treated as positive values; implementations are
1996 * permitted to treat some NaN arguments as positive and other NaN
1997 * arguments as negative to allow greater performance.
1998 *
1999 * @param magnitude the parameter providing the magnitude of the result
2000 * @param sign the parameter providing the sign of the result
2001 * @return a value with the magnitude of {@code magnitude}
2002 * and the sign of {@code sign}.
2003 * @since 1.6
2004 */
2005 public static double copySign(double magnitude, double sign) {
2006 return Double.longBitsToDouble((Double.doubleToRawLongBits(sign) &
2007 (DoubleConsts.SIGN_BIT_MASK)) |
2008 (Double.doubleToRawLongBits(magnitude) &
2009 (DoubleConsts.EXP_BIT_MASK |
2010 DoubleConsts.SIGNIF_BIT_MASK)));
2011 }
2012
2013 /**
2014 * Returns the first floating-point argument with the sign of the
2015 * second floating-point argument. Note that unlike the {@link
2016 * StrictMath#copySign(float, float) StrictMath.copySign}
2017 * method, this method does not require NaN {@code sign}
2018 * arguments to be treated as positive values; implementations are
2019 * permitted to treat some NaN arguments as positive and other NaN
2020 * arguments as negative to allow greater performance.
2021 *
2022 * @param magnitude the parameter providing the magnitude of the result
2023 * @param sign the parameter providing the sign of the result
2024 * @return a value with the magnitude of {@code magnitude}
2025 * and the sign of {@code sign}.
2026 * @since 1.6
2027 */
2028 public static float copySign(float magnitude, float sign) {
2029 return Float.intBitsToFloat((Float.floatToRawIntBits(sign) &
2030 (FloatConsts.SIGN_BIT_MASK)) |
2031 (Float.floatToRawIntBits(magnitude) &
2032 (FloatConsts.EXP_BIT_MASK |
2033 FloatConsts.SIGNIF_BIT_MASK)));
2034 }
2035
2036 /**
2037 * Returns the unbiased exponent used in the representation of a
2038 * {@code float}. Special cases:
2039 *
2040 * <ul>
2041 * <li>If the argument is NaN or infinite, then the result is
2042 * {@link Float#MAX_EXPONENT} + 1.
2043 * <li>If the argument is zero or subnormal, then the result is
2044 * {@link Float#MIN_EXPONENT} -1.
2045 * </ul>
2046 * @param f a {@code float} value
2047 * @return the unbiased exponent of the argument
2048 * @since 1.6
2049 */
2050 public static int getExponent(float f) {
2051 /*
2052 * Bitwise convert f to integer, mask out exponent bits, shift
2053 * to the right and then subtract out float's bias adjust to
2054 * get true exponent value
2055 */
2056 return ((Float.floatToRawIntBits(f) & FloatConsts.EXP_BIT_MASK) >>
2057 (FloatConsts.SIGNIFICAND_WIDTH - 1)) - FloatConsts.EXP_BIAS;
2058 }
2059
2060 /**
2061 * Returns the unbiased exponent used in the representation of a
2062 * {@code double}. Special cases:
2063 *
2064 * <ul>
2065 * <li>If the argument is NaN or infinite, then the result is
2066 * {@link Double#MAX_EXPONENT} + 1.
2067 * <li>If the argument is zero or subnormal, then the result is
2068 * {@link Double#MIN_EXPONENT} -1.
2069 * </ul>
2070 * @param d a {@code double} value
2071 * @return the unbiased exponent of the argument
2072 * @since 1.6
2073 */
2074 public static int getExponent(double d) {
2075 /*
2076 * Bitwise convert d to long, mask out exponent bits, shift
2077 * to the right and then subtract out double's bias adjust to
2078 * get true exponent value.
2079 */
2080 return (int)(((Double.doubleToRawLongBits(d) & DoubleConsts.EXP_BIT_MASK) >>
2081 (DoubleConsts.SIGNIFICAND_WIDTH - 1)) - DoubleConsts.EXP_BIAS);
2082 }
2083
2084 /**
2085 * Returns the floating-point number adjacent to the first
2086 * argument in the direction of the second argument. If both
2087 * arguments compare as equal the second argument is returned.
2088 *
2089 * <p>
2090 * Special cases:
2091 * <ul>
2092 * <li> If either argument is a NaN, then NaN is returned.
2093 *
2094 * <li> If both arguments are signed zeros, {@code direction}
2095 * is returned unchanged (as implied by the requirement of
2096 * returning the second argument if the arguments compare as
2097 * equal).
2098 *
2099 * <li> If {@code start} is
2100 * ±{@link Double#MIN_VALUE} and {@code direction}
2101 * has a value such that the result should have a smaller
2102 * magnitude, then a zero with the same sign as {@code start}
2103 * is returned.
2104 *
2105 * <li> If {@code start} is infinite and
2106 * {@code direction} has a value such that the result should
2107 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
2108 * same sign as {@code start} is returned.
2109 *
2110 * <li> If {@code start} is equal to ±
2111 * {@link Double#MAX_VALUE} and {@code direction} has a
2112 * value such that the result should have a larger magnitude, an
2113 * infinity with same sign as {@code start} is returned.
2114 * </ul>
2115 *
2116 * @param start starting floating-point value
2117 * @param direction value indicating which of
2118 * {@code start}'s neighbors or {@code start} should
2119 * be returned
2120 * @return The floating-point number adjacent to {@code start} in the
2121 * direction of {@code direction}.
2122 * @since 1.6
2123 */
2124 public static double nextAfter(double start, double direction) {
2125 /*
2126 * The cases:
2127 *
2128 * nextAfter(+infinity, 0) == MAX_VALUE
2129 * nextAfter(+infinity, +infinity) == +infinity
2130 * nextAfter(-infinity, 0) == -MAX_VALUE
2131 * nextAfter(-infinity, -infinity) == -infinity
2132 *
2133 * are naturally handled without any additional testing
2134 */
2135
2136 /*
2137 * IEEE 754 floating-point numbers are lexicographically
2138 * ordered if treated as signed-magnitude integers.
2139 * Since Java's integers are two's complement,
2140 * incrementing the two's complement representation of a
2141 * logically negative floating-point value *decrements*
2142 * the signed-magnitude representation. Therefore, when
2143 * the integer representation of a floating-point value
2144 * is negative, the adjustment to the representation is in
2145 * the opposite direction from what would initially be expected.
2146 */
2147
2148 // Branch to descending case first as it is more costly than ascending
2149 // case due to start != 0.0d conditional.
2150 if (start > direction) { // descending
2151 if (start != 0.0d) {
2152 final long transducer = Double.doubleToRawLongBits(start);
2153 return Double.longBitsToDouble(transducer + ((transducer > 0L) ? -1L : 1L));
2154 } else { // start == 0.0d && direction < 0.0d
2155 return -Double.MIN_VALUE;
2156 }
2157 } else if (start < direction) { // ascending
2158 // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
2159 // then bitwise convert start to integer.
2160 final long transducer = Double.doubleToRawLongBits(start + 0.0d);
2161 return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
2162 } else if (start == direction) {
2163 return direction;
2164 } else { // isNaN(start) || isNaN(direction)
2165 return start + direction;
2166 }
2167 }
2168
2169 /**
2170 * Returns the floating-point number adjacent to the first
2171 * argument in the direction of the second argument. If both
2172 * arguments compare as equal a value equivalent to the second argument
2173 * is returned.
2174 *
2175 * <p>
2176 * Special cases:
2177 * <ul>
2178 * <li> If either argument is a NaN, then NaN is returned.
2179 *
2180 * <li> If both arguments are signed zeros, a value equivalent
2181 * to {@code direction} is returned.
2182 *
2183 * <li> If {@code start} is
2184 * ±{@link Float#MIN_VALUE} and {@code direction}
2185 * has a value such that the result should have a smaller
2186 * magnitude, then a zero with the same sign as {@code start}
2187 * is returned.
2188 *
2189 * <li> If {@code start} is infinite and
2190 * {@code direction} has a value such that the result should
2191 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
2192 * same sign as {@code start} is returned.
2193 *
2194 * <li> If {@code start} is equal to ±
2195 * {@link Float#MAX_VALUE} and {@code direction} has a
2196 * value such that the result should have a larger magnitude, an
2197 * infinity with same sign as {@code start} is returned.
2198 * </ul>
2199 *
2200 * @param start starting floating-point value
2201 * @param direction value indicating which of
2202 * {@code start}'s neighbors or {@code start} should
2203 * be returned
2204 * @return The floating-point number adjacent to {@code start} in the
2205 * direction of {@code direction}.
2206 * @since 1.6
2207 */
2208 public static float nextAfter(float start, double direction) {
2209 /*
2210 * The cases:
2211 *
2212 * nextAfter(+infinity, 0) == MAX_VALUE
2213 * nextAfter(+infinity, +infinity) == +infinity
2214 * nextAfter(-infinity, 0) == -MAX_VALUE
2215 * nextAfter(-infinity, -infinity) == -infinity
2216 *
2217 * are naturally handled without any additional testing
2218 */
2219
2220 /*
2221 * IEEE 754 floating-point numbers are lexicographically
2222 * ordered if treated as signed-magnitude integers.
2223 * Since Java's integers are two's complement,
2224 * incrementing the two's complement representation of a
2225 * logically negative floating-point value *decrements*
2226 * the signed-magnitude representation. Therefore, when
2227 * the integer representation of a floating-point value
2228 * is negative, the adjustment to the representation is in
2229 * the opposite direction from what would initially be expected.
2230 */
2231
2232 // Branch to descending case first as it is more costly than ascending
2233 // case due to start != 0.0f conditional.
2234 if (start > direction) { // descending
2235 if (start != 0.0f) {
2236 final int transducer = Float.floatToRawIntBits(start);
2237 return Float.intBitsToFloat(transducer + ((transducer > 0) ? -1 : 1));
2238 } else { // start == 0.0f && direction < 0.0f
2239 return -Float.MIN_VALUE;
2240 }
2241 } else if (start < direction) { // ascending
2242 // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0)
2243 // then bitwise convert start to integer.
2244 final int transducer = Float.floatToRawIntBits(start + 0.0f);
2245 return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
2246 } else if (start == direction) {
2247 return (float)direction;
2248 } else { // isNaN(start) || isNaN(direction)
2249 return start + (float)direction;
2250 }
2251 }
2252
2253 /**
2254 * Returns the floating-point value adjacent to {@code d} in
2255 * the direction of positive infinity. This method is
2256 * semantically equivalent to {@code nextAfter(d,
2257 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
2258 * implementation may run faster than its equivalent
2259 * {@code nextAfter} call.
2260 *
2261 * <p>Special Cases:
2262 * <ul>
2263 * <li> If the argument is NaN, the result is NaN.
2264 *
2265 * <li> If the argument is positive infinity, the result is
2266 * positive infinity.
2267 *
2268 * <li> If the argument is zero, the result is
2269 * {@link Double#MIN_VALUE}
2270 *
2271 * </ul>
2272 *
2273 * @param d starting floating-point value
2274 * @return The adjacent floating-point value closer to positive
2275 * infinity.
2276 * @since 1.6
2277 */
2278 public static double nextUp(double d) {
2279 // Use a single conditional and handle the likely cases first.
2280 if (d < Double.POSITIVE_INFINITY) {
2281 // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
2282 final long transducer = Double.doubleToRawLongBits(d + 0.0D);
2283 return Double.longBitsToDouble(transducer + ((transducer >= 0L) ? 1L : -1L));
2284 } else { // d is NaN or +Infinity
2285 return d;
2286 }
2287 }
2288
2289 /**
2290 * Returns the floating-point value adjacent to {@code f} in
2291 * the direction of positive infinity. This method is
2292 * semantically equivalent to {@code nextAfter(f,
2293 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
2294 * implementation may run faster than its equivalent
2295 * {@code nextAfter} call.
2296 *
2297 * <p>Special Cases:
2298 * <ul>
2299 * <li> If the argument is NaN, the result is NaN.
2300 *
2301 * <li> If the argument is positive infinity, the result is
2302 * positive infinity.
2303 *
2304 * <li> If the argument is zero, the result is
2305 * {@link Float#MIN_VALUE}
2306 *
2307 * </ul>
2308 *
2309 * @param f starting floating-point value
2310 * @return The adjacent floating-point value closer to positive
2311 * infinity.
2312 * @since 1.6
2313 */
2314 public static float nextUp(float f) {
2315 // Use a single conditional and handle the likely cases first.
2316 if (f < Float.POSITIVE_INFINITY) {
2317 // Add +0.0 to get rid of a -0.0 (+0.0 + -0.0 => +0.0).
2318 final int transducer = Float.floatToRawIntBits(f + 0.0F);
2319 return Float.intBitsToFloat(transducer + ((transducer >= 0) ? 1 : -1));
2320 } else { // f is NaN or +Infinity
2321 return f;
2322 }
2323 }
2324
2325 /**
2326 * Returns the floating-point value adjacent to {@code d} in
2327 * the direction of negative infinity. This method is
2328 * semantically equivalent to {@code nextAfter(d,
2329 * Double.NEGATIVE_INFINITY)}; however, a
2330 * {@code nextDown} implementation may run faster than its
2331 * equivalent {@code nextAfter} call.
2332 *
2333 * <p>Special Cases:
2334 * <ul>
2335 * <li> If the argument is NaN, the result is NaN.
2336 *
2337 * <li> If the argument is negative infinity, the result is
2338 * negative infinity.
2339 *
2340 * <li> If the argument is zero, the result is
2341 * {@code -Double.MIN_VALUE}
2342 *
2343 * </ul>
2344 *
2345 * @param d starting floating-point value
2346 * @return The adjacent floating-point value closer to negative
2347 * infinity.
2348 * @since 1.8
2349 */
2350 public static double nextDown(double d) {
2351 if (Double.isNaN(d) || d == Double.NEGATIVE_INFINITY)
2352 return d;
2353 else {
2354 if (d == 0.0)
2355 return -Double.MIN_VALUE;
2356 else
2357 return Double.longBitsToDouble(Double.doubleToRawLongBits(d) +
2358 ((d > 0.0d)?-1L:+1L));
2359 }
2360 }
2361
2362 /**
2363 * Returns the floating-point value adjacent to {@code f} in
2364 * the direction of negative infinity. This method is
2365 * semantically equivalent to {@code nextAfter(f,
2366 * Float.NEGATIVE_INFINITY)}; however, a
2367 * {@code nextDown} implementation may run faster than its
2368 * equivalent {@code nextAfter} call.
2369 *
2370 * <p>Special Cases:
2371 * <ul>
2372 * <li> If the argument is NaN, the result is NaN.
2373 *
2374 * <li> If the argument is negative infinity, the result is
2375 * negative infinity.
2376 *
2377 * <li> If the argument is zero, the result is
2378 * {@code -Float.MIN_VALUE}
2379 *
2380 * </ul>
2381 *
2382 * @param f starting floating-point value
2383 * @return The adjacent floating-point value closer to negative
2384 * infinity.
2385 * @since 1.8
2386 */
2387 public static float nextDown(float f) {
2388 if (Float.isNaN(f) || f == Float.NEGATIVE_INFINITY)
2389 return f;
2390 else {
2391 if (f == 0.0f)
2392 return -Float.MIN_VALUE;
2393 else
2394 return Float.intBitsToFloat(Float.floatToRawIntBits(f) +
2395 ((f > 0.0f)?-1:+1));
2396 }
2397 }
2398
2399 /**
2400 * Returns {@code d} ×
2401 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
2402 * by a single correctly rounded floating-point multiply to a
2403 * member of the double value set. See the Java
2404 * Language Specification for a discussion of floating-point
2405 * value sets. If the exponent of the result is between {@link
2406 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
2407 * answer is calculated exactly. If the exponent of the result
2408 * would be larger than {@code Double.MAX_EXPONENT}, an
2409 * infinity is returned. Note that if the result is subnormal,
2410 * precision may be lost; that is, when {@code scalb(x, n)}
2411 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
2412 * <i>x</i>. When the result is non-NaN, the result has the same
2413 * sign as {@code d}.
2414 *
2415 * <p>Special cases:
2416 * <ul>
2417 * <li> If the first argument is NaN, NaN is returned.
2418 * <li> If the first argument is infinite, then an infinity of the
2419 * same sign is returned.
2420 * <li> If the first argument is zero, then a zero of the same
2421 * sign is returned.
2422 * </ul>
2423 *
2424 * @param d number to be scaled by a power of two.
2425 * @param scaleFactor power of 2 used to scale {@code d}
2426 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
2427 * @since 1.6
2428 */
2429 public static double scalb(double d, int scaleFactor) {
2430 /*
2431 * This method does not need to be declared strictfp to
2432 * compute the same correct result on all platforms. When
2433 * scaling up, it does not matter what order the
2434 * multiply-store operations are done; the result will be
2435 * finite or overflow regardless of the operation ordering.
2436 * However, to get the correct result when scaling down, a
2437 * particular ordering must be used.
2438 *
2439 * When scaling down, the multiply-store operations are
2440 * sequenced so that it is not possible for two consecutive
2441 * multiply-stores to return subnormal results. If one
2442 * multiply-store result is subnormal, the next multiply will
2443 * round it away to zero. This is done by first multiplying
2444 * by 2 ^ (scaleFactor % n) and then multiplying several
2445 * times by 2^n as needed where n is the exponent of number
2446 * that is a covenient power of two. In this way, at most one
2447 * real rounding error occurs. If the double value set is
2448 * being used exclusively, the rounding will occur on a
2449 * multiply. If the double-extended-exponent value set is
2450 * being used, the products will (perhaps) be exact but the
2451 * stores to d are guaranteed to round to the double value
2452 * set.
2453 *
2454 * It is _not_ a valid implementation to first multiply d by
2455 * 2^MIN_EXPONENT and then by 2 ^ (scaleFactor %
2456 * MIN_EXPONENT) since even in a strictfp program double
2457 * rounding on underflow could occur; e.g. if the scaleFactor
2458 * argument was (MIN_EXPONENT - n) and the exponent of d was a
2459 * little less than -(MIN_EXPONENT - n), meaning the final
2460 * result would be subnormal.
2461 *
2462 * Since exact reproducibility of this method can be achieved
2463 * without any undue performance burden, there is no
2464 * compelling reason to allow double rounding on underflow in
2465 * scalb.
2466 */
2467
2468 // magnitude of a power of two so large that scaling a finite
2469 // nonzero value by it would be guaranteed to over or
2470 // underflow; due to rounding, scaling down takes an
2471 // additional power of two which is reflected here
2472 final int MAX_SCALE = Double.MAX_EXPONENT + -Double.MIN_EXPONENT +
2473 DoubleConsts.SIGNIFICAND_WIDTH + 1;
2474 int exp_adjust = 0;
2475 int scale_increment = 0;
2476 double exp_delta = Double.NaN;
2477
2478 // Make sure scaling factor is in a reasonable range
2479
2480 if(scaleFactor < 0) {
2481 scaleFactor = Math.max(scaleFactor, -MAX_SCALE);
2482 scale_increment = -512;
2483 exp_delta = twoToTheDoubleScaleDown;
2484 }
2485 else {
2486 scaleFactor = Math.min(scaleFactor, MAX_SCALE);
2487 scale_increment = 512;
2488 exp_delta = twoToTheDoubleScaleUp;
2489 }
2490
2491 // Calculate (scaleFactor % +/-512), 512 = 2^9, using
2492 // technique from "Hacker's Delight" section 10-2.
2493 int t = (scaleFactor >> 9-1) >>> 32 - 9;
2494 exp_adjust = ((scaleFactor + t) & (512 -1)) - t;
2495
2496 d *= powerOfTwoD(exp_adjust);
2497 scaleFactor -= exp_adjust;
2498
2499 while(scaleFactor != 0) {
2500 d *= exp_delta;
2501 scaleFactor -= scale_increment;
2502 }
2503 return d;
2504 }
2505
2506 /**
2507 * Returns {@code f} ×
2508 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
2509 * by a single correctly rounded floating-point multiply to a
2510 * member of the float value set. See the Java
2511 * Language Specification for a discussion of floating-point
2512 * value sets. If the exponent of the result is between {@link
2513 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
2514 * answer is calculated exactly. If the exponent of the result
2515 * would be larger than {@code Float.MAX_EXPONENT}, an
2516 * infinity is returned. Note that if the result is subnormal,
2517 * precision may be lost; that is, when {@code scalb(x, n)}
2518 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
2519 * <i>x</i>. When the result is non-NaN, the result has the same
2520 * sign as {@code f}.
2521 *
2522 * <p>Special cases:
2523 * <ul>
2524 * <li> If the first argument is NaN, NaN is returned.
2525 * <li> If the first argument is infinite, then an infinity of the
2526 * same sign is returned.
2527 * <li> If the first argument is zero, then a zero of the same
2528 * sign is returned.
2529 * </ul>
2530 *
2531 * @param f number to be scaled by a power of two.
2532 * @param scaleFactor power of 2 used to scale {@code f}
2533 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
2534 * @since 1.6
2535 */
2536 public static float scalb(float f, int scaleFactor) {
2537 // magnitude of a power of two so large that scaling a finite
2538 // nonzero value by it would be guaranteed to over or
2539 // underflow; due to rounding, scaling down takes an
2540 // additional power of two which is reflected here
2541 final int MAX_SCALE = Float.MAX_EXPONENT + -Float.MIN_EXPONENT +
2542 FloatConsts.SIGNIFICAND_WIDTH + 1;
2543
2544 // Make sure scaling factor is in a reasonable range
2545 scaleFactor = Math.max(Math.min(scaleFactor, MAX_SCALE), -MAX_SCALE);
2546
2547 /*
2548 * Since + MAX_SCALE for float fits well within the double
2549 * exponent range and + float -> double conversion is exact
2550 * the multiplication below will be exact. Therefore, the
2551 * rounding that occurs when the double product is cast to
2552 * float will be the correctly rounded float result. Since
2553 * all operations other than the final multiply will be exact,
2554 * it is not necessary to declare this method strictfp.
2555 */
2556 return (float)((double)f*powerOfTwoD(scaleFactor));
2557 }
2558
2559 // Constants used in scalb
2560 static double twoToTheDoubleScaleUp = powerOfTwoD(512);
2561 static double twoToTheDoubleScaleDown = powerOfTwoD(-512);
2562
2563 /**
2564 * Returns a floating-point power of two in the normal range.
2565 */
2566 static double powerOfTwoD(int n) {
2567 assert(n >= Double.MIN_EXPONENT && n <= Double.MAX_EXPONENT);
2568 return Double.longBitsToDouble((((long)n + (long)DoubleConsts.EXP_BIAS) <<
2569 (DoubleConsts.SIGNIFICAND_WIDTH-1))
2570 & DoubleConsts.EXP_BIT_MASK);
2571 }
2572
2573 /**
2574 * Returns a floating-point power of two in the normal range.
2575 */
2576 static float powerOfTwoF(int n) {
2577 assert(n >= Float.MIN_EXPONENT && n <= Float.MAX_EXPONENT);
2578 return Float.intBitsToFloat(((n + FloatConsts.EXP_BIAS) <<
2579 (FloatConsts.SIGNIFICAND_WIDTH-1))
2580 & FloatConsts.EXP_BIT_MASK);
2581 }
2582 }