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28 import org.apidesign.bck2brwsr.core.JavaScriptBody;
32 * The class {@code Math} contains methods for performing basic
33 * numeric operations such as the elementary exponential, logarithm,
34 * square root, and trigonometric functions.
36 * <p>Unlike some of the numeric methods of class
37 * {@code StrictMath}, all implementations of the equivalent
38 * functions of class {@code Math} are not defined to return the
39 * bit-for-bit same results. This relaxation permits
40 * better-performing implementations where strict reproducibility is
43 * <p>By default many of the {@code Math} methods simply call
44 * the equivalent method in {@code StrictMath} for their
45 * implementation. Code generators are encouraged to use
46 * platform-specific native libraries or microprocessor instructions,
47 * where available, to provide higher-performance implementations of
48 * {@code Math} methods. Such higher-performance
49 * implementations still must conform to the specification for
52 * <p>The quality of implementation specifications concern two
53 * properties, accuracy of the returned result and monotonicity of the
54 * method. Accuracy of the floating-point {@code Math} methods
55 * is measured in terms of <i>ulps</i>, units in the last place. For
56 * a given floating-point format, an ulp of a specific real number
57 * value is the distance between the two floating-point values
58 * bracketing that numerical value. When discussing the accuracy of a
59 * method as a whole rather than at a specific argument, the number of
60 * ulps cited is for the worst-case error at any argument. If a
61 * method always has an error less than 0.5 ulps, the method always
62 * returns the floating-point number nearest the exact result; such a
63 * method is <i>correctly rounded</i>. A correctly rounded method is
64 * generally the best a floating-point approximation can be; however,
65 * it is impractical for many floating-point methods to be correctly
66 * rounded. Instead, for the {@code Math} class, a larger error
67 * bound of 1 or 2 ulps is allowed for certain methods. Informally,
68 * with a 1 ulp error bound, when the exact result is a representable
69 * number, the exact result should be returned as the computed result;
70 * otherwise, either of the two floating-point values which bracket
71 * the exact result may be returned. For exact results large in
72 * magnitude, one of the endpoints of the bracket may be infinite.
73 * Besides accuracy at individual arguments, maintaining proper
74 * relations between the method at different arguments is also
75 * important. Therefore, most methods with more than 0.5 ulp errors
76 * are required to be <i>semi-monotonic</i>: whenever the mathematical
77 * function is non-decreasing, so is the floating-point approximation,
78 * likewise, whenever the mathematical function is non-increasing, so
79 * is the floating-point approximation. Not all approximations that
80 * have 1 ulp accuracy will automatically meet the monotonicity
84 * @author Joseph D. Darcy
88 public final class Math {
91 * Don't let anyone instantiate this class.
96 * The {@code double} value that is closer than any other to
97 * <i>e</i>, the base of the natural logarithms.
99 public static final double E = 2.7182818284590452354;
102 * The {@code double} value that is closer than any other to
103 * <i>pi</i>, the ratio of the circumference of a circle to its
106 public static final double PI = 3.14159265358979323846;
109 * Returns the trigonometric sine of an angle. Special cases:
110 * <ul><li>If the argument is NaN or an infinity, then the
112 * <li>If the argument is zero, then the result is a zero with the
113 * same sign as the argument.</ul>
115 * <p>The computed result must be within 1 ulp of the exact result.
116 * Results must be semi-monotonic.
118 * @param a an angle, in radians.
119 * @return the sine of the argument.
121 @JavaScriptBody(args="a", body="return Math.sin(a);")
122 public static double sin(double a) {
123 throw new UnsupportedOperationException();
127 * Returns the trigonometric cosine of an angle. Special cases:
128 * <ul><li>If the argument is NaN or an infinity, then the
129 * result is NaN.</ul>
131 * <p>The computed result must be within 1 ulp of the exact result.
132 * Results must be semi-monotonic.
134 * @param a an angle, in radians.
135 * @return the cosine of the argument.
137 @JavaScriptBody(args="a", body="return Math.cos(a);")
138 public static double cos(double a) {
139 throw new UnsupportedOperationException();
143 * Returns the trigonometric tangent of an angle. Special cases:
144 * <ul><li>If the argument is NaN or an infinity, then the result
146 * <li>If the argument is zero, then the result is a zero with the
147 * same sign as the argument.</ul>
149 * <p>The computed result must be within 1 ulp of the exact result.
150 * Results must be semi-monotonic.
152 * @param a an angle, in radians.
153 * @return the tangent of the argument.
155 @JavaScriptBody(args="a", body="return Math.tan(a);")
156 public static double tan(double a) {
157 throw new UnsupportedOperationException();
161 * Returns the arc sine of a value; the returned angle is in the
162 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
163 * <ul><li>If the argument is NaN or its absolute value is greater
164 * than 1, then the result is NaN.
165 * <li>If the argument is zero, then the result is a zero with the
166 * same sign as the argument.</ul>
168 * <p>The computed result must be within 1 ulp of the exact result.
169 * Results must be semi-monotonic.
171 * @param a the value whose arc sine is to be returned.
172 * @return the arc sine of the argument.
174 @JavaScriptBody(args="a", body="return Math.asin(a);")
175 public static double asin(double a) {
176 throw new UnsupportedOperationException();
180 * Returns the arc cosine of a value; the returned angle is in the
181 * range 0.0 through <i>pi</i>. Special case:
182 * <ul><li>If the argument is NaN or its absolute value is greater
183 * than 1, then the result is NaN.</ul>
185 * <p>The computed result must be within 1 ulp of the exact result.
186 * Results must be semi-monotonic.
188 * @param a the value whose arc cosine is to be returned.
189 * @return the arc cosine of the argument.
191 @JavaScriptBody(args="a", body="return Math.acos(a);")
192 public static double acos(double a) {
193 throw new UnsupportedOperationException();
197 * Returns the arc tangent of a value; the returned angle is in the
198 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
199 * <ul><li>If the argument is NaN, then the result is NaN.
200 * <li>If the argument is zero, then the result is a zero with the
201 * same sign as the argument.</ul>
203 * <p>The computed result must be within 1 ulp of the exact result.
204 * Results must be semi-monotonic.
206 * @param a the value whose arc tangent is to be returned.
207 * @return the arc tangent of the argument.
209 @JavaScriptBody(args="a", body="return Math.atan(a);")
210 public static double atan(double a) {
211 throw new UnsupportedOperationException();
215 * Converts an angle measured in degrees to an approximately
216 * equivalent angle measured in radians. The conversion from
217 * degrees to radians is generally inexact.
219 * @param angdeg an angle, in degrees
220 * @return the measurement of the angle {@code angdeg}
224 public static double toRadians(double angdeg) {
225 return angdeg / 180.0 * PI;
229 * Converts an angle measured in radians to an approximately
230 * equivalent angle measured in degrees. The conversion from
231 * radians to degrees is generally inexact; users should
232 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
235 * @param angrad an angle, in radians
236 * @return the measurement of the angle {@code angrad}
240 public static double toDegrees(double angrad) {
241 return angrad * 180.0 / PI;
245 * Returns Euler's number <i>e</i> raised to the power of a
246 * {@code double} value. Special cases:
247 * <ul><li>If the argument is NaN, the result is NaN.
248 * <li>If the argument is positive infinity, then the result is
250 * <li>If the argument is negative infinity, then the result is
251 * positive zero.</ul>
253 * <p>The computed result must be within 1 ulp of the exact result.
254 * Results must be semi-monotonic.
256 * @param a the exponent to raise <i>e</i> to.
257 * @return the value <i>e</i><sup>{@code a}</sup>,
258 * where <i>e</i> is the base of the natural logarithms.
260 @JavaScriptBody(args="a", body="return Math.exp(a);")
261 public static double exp(double a) {
262 throw new UnsupportedOperationException();
266 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
267 * value. Special cases:
268 * <ul><li>If the argument is NaN or less than zero, then the result
270 * <li>If the argument is positive infinity, then the result is
272 * <li>If the argument is positive zero or negative zero, then the
273 * result is negative infinity.</ul>
275 * <p>The computed result must be within 1 ulp of the exact result.
276 * Results must be semi-monotonic.
279 * @return the value ln {@code a}, the natural logarithm of
282 @JavaScriptBody(args="a", body="return Math.log(a);")
283 public static double log(double a) {
284 throw new UnsupportedOperationException();
288 * Returns the base 10 logarithm of a {@code double} value.
291 * <ul><li>If the argument is NaN or less than zero, then the result
293 * <li>If the argument is positive infinity, then the result is
295 * <li>If the argument is positive zero or negative zero, then the
296 * result is negative infinity.
297 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
298 * integer <i>n</i>, then the result is <i>n</i>.
301 * <p>The computed result must be within 1 ulp of the exact result.
302 * Results must be semi-monotonic.
305 * @return the base 10 logarithm of {@code a}.
308 @JavaScriptBody(args="a", body="return Math.log(a) / Math.LN10;")
309 public static double log10(double a) {
310 throw new UnsupportedOperationException();
314 * Returns the correctly rounded positive square root of a
315 * {@code double} value.
317 * <ul><li>If the argument is NaN or less than zero, then the result
319 * <li>If the argument is positive infinity, then the result is positive
321 * <li>If the argument is positive zero or negative zero, then the
322 * result is the same as the argument.</ul>
323 * Otherwise, the result is the {@code double} value closest to
324 * the true mathematical square root of the argument value.
327 * @return the positive square root of {@code a}.
328 * If the argument is NaN or less than zero, the result is NaN.
330 @JavaScriptBody(args="a", body="return Math.sqrt(a);")
331 public static double sqrt(double a) {
332 throw new UnsupportedOperationException();
336 * Returns the smallest (closest to negative infinity)
337 * {@code double} value that is greater than or equal to the
338 * argument and is equal to a mathematical integer. Special cases:
339 * <ul><li>If the argument value is already equal to a
340 * mathematical integer, then the result is the same as the
341 * argument. <li>If the argument is NaN or an infinity or
342 * positive zero or negative zero, then the result is the same as
343 * the argument. <li>If the argument value is less than zero but
344 * greater than -1.0, then the result is negative zero.</ul> Note
345 * that the value of {@code Math.ceil(x)} is exactly the
346 * value of {@code -Math.floor(-x)}.
350 * @return the smallest (closest to negative infinity)
351 * floating-point value that is greater than or equal to
352 * the argument and is equal to a mathematical integer.
354 @JavaScriptBody(args="a", body="return Math.ceil(a);")
355 public static double ceil(double a) {
356 throw new UnsupportedOperationException();
360 * Returns the largest (closest to positive infinity)
361 * {@code double} value that is less than or equal to the
362 * argument and is equal to a mathematical integer. Special cases:
363 * <ul><li>If the argument value is already equal to a
364 * mathematical integer, then the result is the same as the
365 * argument. <li>If the argument is NaN or an infinity or
366 * positive zero or negative zero, then the result is the same as
370 * @return the largest (closest to positive infinity)
371 * floating-point value that less than or equal to the argument
372 * and is equal to a mathematical integer.
374 @JavaScriptBody(args="a", body="return Math.floor(a);")
375 public static double floor(double a) {
376 throw new UnsupportedOperationException();
379 * Computes the remainder operation on two arguments as prescribed
380 * by the IEEE 754 standard.
381 * The remainder value is mathematically equal to
382 * <code>f1 - f2</code> × <i>n</i>,
383 * where <i>n</i> is the mathematical integer closest to the exact
384 * mathematical value of the quotient {@code f1/f2}, and if two
385 * mathematical integers are equally close to {@code f1/f2},
386 * then <i>n</i> is the integer that is even. If the remainder is
387 * zero, its sign is the same as the sign of the first argument.
389 * <ul><li>If either argument is NaN, or the first argument is infinite,
390 * or the second argument is positive zero or negative zero, then the
392 * <li>If the first argument is finite and the second argument is
393 * infinite, then the result is the same as the first argument.</ul>
395 * @param f1 the dividend.
396 * @param f2 the divisor.
397 * @return the remainder when {@code f1} is divided by
400 public static double IEEEremainder(double f1, double f2) {
401 return f1 - (f2 * Math.round(f1 / f2));
405 * Returns the {@code double} value that is closest in value
406 * to the argument and is equal to a mathematical integer. If two
407 * {@code double} values that are mathematical integers are
408 * equally close, the result is the integer value that is
409 * even. Special cases:
410 * <ul><li>If the argument value is already equal to a mathematical
411 * integer, then the result is the same as the argument.
412 * <li>If the argument is NaN or an infinity or positive zero or negative
413 * zero, then the result is the same as the argument.</ul>
415 * @param a a {@code double} value.
416 * @return the closest floating-point value to {@code a} that is
417 * equal to a mathematical integer.
419 public static double rint(double a) {
420 double ceil = ceil(a);
421 double floor = floor(a);
423 double dc = ceil - a;
424 double df = a - floor;
428 } else if (dc > df) {
432 int tenC = (int) (ceil % 10.0);
442 * Returns the angle <i>theta</i> from the conversion of rectangular
443 * coordinates ({@code x}, {@code y}) to polar
444 * coordinates (r, <i>theta</i>).
445 * This method computes the phase <i>theta</i> by computing an arc tangent
446 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
448 * <ul><li>If either argument is NaN, then the result is NaN.
449 * <li>If the first argument is positive zero and the second argument
450 * is positive, or the first argument is positive and finite and the
451 * second argument is positive infinity, then the result is positive
453 * <li>If the first argument is negative zero and the second argument
454 * is positive, or the first argument is negative and finite and the
455 * second argument is positive infinity, then the result is negative zero.
456 * <li>If the first argument is positive zero and the second argument
457 * is negative, or the first argument is positive and finite and the
458 * second argument is negative infinity, then the result is the
459 * {@code double} value closest to <i>pi</i>.
460 * <li>If the first argument is negative zero and the second argument
461 * is negative, or the first argument is negative and finite and the
462 * second argument is negative infinity, then the result is the
463 * {@code double} value closest to -<i>pi</i>.
464 * <li>If the first argument is positive and the second argument is
465 * positive zero or negative zero, or the first argument is positive
466 * infinity and the second argument is finite, then the result is the
467 * {@code double} value closest to <i>pi</i>/2.
468 * <li>If the first argument is negative and the second argument is
469 * positive zero or negative zero, or the first argument is negative
470 * infinity and the second argument is finite, then the result is the
471 * {@code double} value closest to -<i>pi</i>/2.
472 * <li>If both arguments are positive infinity, then the result is the
473 * {@code double} value closest to <i>pi</i>/4.
474 * <li>If the first argument is positive infinity and the second argument
475 * is negative infinity, then the result is the {@code double}
476 * value closest to 3*<i>pi</i>/4.
477 * <li>If the first argument is negative infinity and the second argument
478 * is positive infinity, then the result is the {@code double} value
479 * closest to -<i>pi</i>/4.
480 * <li>If both arguments are negative infinity, then the result is the
481 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
483 * <p>The computed result must be within 2 ulps of the exact result.
484 * Results must be semi-monotonic.
486 * @param y the ordinate coordinate
487 * @param x the abscissa coordinate
488 * @return the <i>theta</i> component of the point
489 * (<i>r</i>, <i>theta</i>)
490 * in polar coordinates that corresponds to the point
491 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
493 @JavaScriptBody(args={"y", "x"}, body="return Math.atan2(y, x);")
494 public static double atan2(double y, double x) {
495 throw new UnsupportedOperationException();
499 * Returns the value of the first argument raised to the power of the
500 * second argument. Special cases:
502 * <ul><li>If the second argument is positive or negative zero, then the
504 * <li>If the second argument is 1.0, then the result is the same as the
506 * <li>If the second argument is NaN, then the result is NaN.
507 * <li>If the first argument is NaN and the second argument is nonzero,
508 * then the result is NaN.
512 * <li>the absolute value of the first argument is greater than 1
513 * and the second argument is positive infinity, or
514 * <li>the absolute value of the first argument is less than 1 and
515 * the second argument is negative infinity,
517 * then the result is positive infinity.
521 * <li>the absolute value of the first argument is greater than 1 and
522 * the second argument is negative infinity, or
523 * <li>the absolute value of the
524 * first argument is less than 1 and the second argument is positive
527 * then the result is positive zero.
529 * <li>If the absolute value of the first argument equals 1 and the
530 * second argument is infinite, then the result is NaN.
534 * <li>the first argument is positive zero and the second argument
535 * is greater than zero, or
536 * <li>the first argument is positive infinity and the second
537 * argument is less than zero,
539 * then the result is positive zero.
543 * <li>the first argument is positive zero and the second argument
544 * is less than zero, or
545 * <li>the first argument is positive infinity and the second
546 * argument is greater than zero,
548 * then the result is positive infinity.
552 * <li>the first argument is negative zero and the second argument
553 * is greater than zero but not a finite odd integer, or
554 * <li>the first argument is negative infinity and the second
555 * argument is less than zero but not a finite odd integer,
557 * then the result is positive zero.
561 * <li>the first argument is negative zero and the second argument
562 * is a positive finite odd integer, or
563 * <li>the first argument is negative infinity and the second
564 * argument is a negative finite odd integer,
566 * then the result is negative zero.
570 * <li>the first argument is negative zero and the second argument
571 * is less than zero but not a finite odd integer, or
572 * <li>the first argument is negative infinity and the second
573 * argument is greater than zero but not a finite odd integer,
575 * then the result is positive infinity.
579 * <li>the first argument is negative zero and the second argument
580 * is a negative finite odd integer, or
581 * <li>the first argument is negative infinity and the second
582 * argument is a positive finite odd integer,
584 * then the result is negative infinity.
586 * <li>If the first argument is finite and less than zero
588 * <li> if the second argument is a finite even integer, the
589 * result is equal to the result of raising the absolute value of
590 * the first argument to the power of the second argument
592 * <li>if the second argument is a finite odd integer, the result
593 * is equal to the negative of the result of raising the absolute
594 * value of the first argument to the power of the second
597 * <li>if the second argument is finite and not an integer, then
601 * <li>If both arguments are integers, then the result is exactly equal
602 * to the mathematical result of raising the first argument to the power
603 * of the second argument if that result can in fact be represented
604 * exactly as a {@code double} value.</ul>
606 * <p>(In the foregoing descriptions, a floating-point value is
607 * considered to be an integer if and only if it is finite and a
608 * fixed point of the method {@link #ceil ceil} or,
609 * equivalently, a fixed point of the method {@link #floor
610 * floor}. A value is a fixed point of a one-argument
611 * method if and only if the result of applying the method to the
612 * value is equal to the value.)
614 * <p>The computed result must be within 1 ulp of the exact result.
615 * Results must be semi-monotonic.
618 * @param b the exponent.
619 * @return the value {@code a}<sup>{@code b}</sup>.
621 @JavaScriptBody(args={"a", "b"}, body="return Math.pow(a, b);")
622 public static double pow(double a, double b) {
623 throw new UnsupportedOperationException();
627 * Returns the closest {@code int} to the argument, with ties
632 * <ul><li>If the argument is NaN, the result is 0.
633 * <li>If the argument is negative infinity or any value less than or
634 * equal to the value of {@code Integer.MIN_VALUE}, the result is
635 * equal to the value of {@code Integer.MIN_VALUE}.
636 * <li>If the argument is positive infinity or any value greater than or
637 * equal to the value of {@code Integer.MAX_VALUE}, the result is
638 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
640 * @param a a floating-point value to be rounded to an integer.
641 * @return the value of the argument rounded to the nearest
643 * @see java.lang.Integer#MAX_VALUE
644 * @see java.lang.Integer#MIN_VALUE
646 @JavaScriptBody(args="a", body="return Math.round(a);")
647 public static int round(float a) {
648 throw new UnsupportedOperationException();
652 * Returns the closest {@code long} to the argument, with ties
656 * <ul><li>If the argument is NaN, the result is 0.
657 * <li>If the argument is negative infinity or any value less than or
658 * equal to the value of {@code Long.MIN_VALUE}, the result is
659 * equal to the value of {@code Long.MIN_VALUE}.
660 * <li>If the argument is positive infinity or any value greater than or
661 * equal to the value of {@code Long.MAX_VALUE}, the result is
662 * equal to the value of {@code Long.MAX_VALUE}.</ul>
664 * @param a a floating-point value to be rounded to a
666 * @return the value of the argument rounded to the nearest
667 * {@code long} value.
668 * @see java.lang.Long#MAX_VALUE
669 * @see java.lang.Long#MIN_VALUE
671 @JavaScriptBody(args="a", body="return Math.round(a);")
672 public static long round(double a) {
673 throw new UnsupportedOperationException();
676 // private static Random randomNumberGenerator;
678 // private static synchronized Random initRNG() {
679 // Random rnd = randomNumberGenerator;
680 // return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd;
684 * Returns a {@code double} value with a positive sign, greater
685 * than or equal to {@code 0.0} and less than {@code 1.0}.
686 * Returned values are chosen pseudorandomly with (approximately)
687 * uniform distribution from that range.
689 * <p>When this method is first called, it creates a single new
690 * pseudorandom-number generator, exactly as if by the expression
692 * <blockquote>{@code new java.util.Random()}</blockquote>
694 * This new pseudorandom-number generator is used thereafter for
695 * all calls to this method and is used nowhere else.
697 * <p>This method is properly synchronized to allow correct use by
698 * more than one thread. However, if many threads need to generate
699 * pseudorandom numbers at a great rate, it may reduce contention
700 * for each thread to have its own pseudorandom-number generator.
702 * @return a pseudorandom {@code double} greater than or equal
703 * to {@code 0.0} and less than {@code 1.0}.
704 * @see Random#nextDouble()
706 @JavaScriptBody(args={}, body="return Math.random();")
707 public static double random() {
708 throw new UnsupportedOperationException();
712 * Returns the absolute value of an {@code int} value.
713 * If the argument is not negative, the argument is returned.
714 * If the argument is negative, the negation of the argument is returned.
716 * <p>Note that if the argument is equal to the value of
717 * {@link Integer#MIN_VALUE}, the most negative representable
718 * {@code int} value, the result is that same value, which is
721 * @param a the argument whose absolute value is to be determined
722 * @return the absolute value of the argument.
724 public static int abs(int a) {
725 return (a < 0) ? -a : a;
729 * Returns the absolute value of a {@code long} value.
730 * If the argument is not negative, the argument is returned.
731 * If the argument is negative, the negation of the argument is returned.
733 * <p>Note that if the argument is equal to the value of
734 * {@link Long#MIN_VALUE}, the most negative representable
735 * {@code long} value, the result is that same value, which
738 * @param a the argument whose absolute value is to be determined
739 * @return the absolute value of the argument.
741 public static long abs(long a) {
742 return (a < 0) ? -a : a;
746 * Returns the absolute value of a {@code float} value.
747 * If the argument is not negative, the argument is returned.
748 * If the argument is negative, the negation of the argument is returned.
750 * <ul><li>If the argument is positive zero or negative zero, the
751 * result is positive zero.
752 * <li>If the argument is infinite, the result is positive infinity.
753 * <li>If the argument is NaN, the result is NaN.</ul>
754 * In other words, the result is the same as the value of the expression:
755 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
757 * @param a the argument whose absolute value is to be determined
758 * @return the absolute value of the argument.
760 public static float abs(float a) {
761 return (a <= 0.0F) ? 0.0F - a : a;
765 * Returns the absolute value of a {@code double} value.
766 * If the argument is not negative, the argument is returned.
767 * If the argument is negative, the negation of the argument is returned.
769 * <ul><li>If the argument is positive zero or negative zero, the result
771 * <li>If the argument is infinite, the result is positive infinity.
772 * <li>If the argument is NaN, the result is NaN.</ul>
773 * In other words, the result is the same as the value of the expression:
774 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
776 * @param a the argument whose absolute value is to be determined
777 * @return the absolute value of the argument.
779 public static double abs(double a) {
780 return (a <= 0.0D) ? 0.0D - a : a;
784 * Returns the greater of two {@code int} values. That is, the
785 * result is the argument closer to the value of
786 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
787 * the result is that same value.
789 * @param a an argument.
790 * @param b another argument.
791 * @return the larger of {@code a} and {@code b}.
793 public static int max(int a, int b) {
794 return (a >= b) ? a : b;
798 * Returns the greater of two {@code long} values. That is, the
799 * result is the argument closer to the value of
800 * {@link Long#MAX_VALUE}. If the arguments have the same value,
801 * the result is that same value.
803 * @param a an argument.
804 * @param b another argument.
805 * @return the larger of {@code a} and {@code b}.
807 public static long max(long a, long b) {
808 return (a >= b) ? a : b;
812 * Returns the greater of two {@code float} values. That is,
813 * the result is the argument closer to positive infinity. If the
814 * arguments have the same value, the result is that same
815 * value. If either value is NaN, then the result is NaN. Unlike
816 * the numerical comparison operators, this method considers
817 * negative zero to be strictly smaller than positive zero. If one
818 * argument is positive zero and the other negative zero, the
819 * result is positive zero.
821 * @param a an argument.
822 * @param b another argument.
823 * @return the larger of {@code a} and {@code b}.
825 @JavaScriptBody(args={"a", "b"},
826 body="return Math.max(a,b);"
828 public static float max(float a, float b) {
829 throw new UnsupportedOperationException();
833 * Returns the greater of two {@code double} values. That
834 * is, the result is the argument closer to positive infinity. If
835 * the arguments have the same value, the result is that same
836 * value. If either value is NaN, then the result is NaN. Unlike
837 * the numerical comparison operators, this method considers
838 * negative zero to be strictly smaller than positive zero. If one
839 * argument is positive zero and the other negative zero, the
840 * result is positive zero.
842 * @param a an argument.
843 * @param b another argument.
844 * @return the larger of {@code a} and {@code b}.
846 @JavaScriptBody(args={"a", "b"},
847 body="return Math.max(a,b);"
849 public static double max(double a, double b) {
850 throw new UnsupportedOperationException();
854 * Returns the smaller of two {@code int} values. That is,
855 * the result the argument closer to the value of
856 * {@link Integer#MIN_VALUE}. If the arguments have the same
857 * value, the result is that same value.
859 * @param a an argument.
860 * @param b another argument.
861 * @return the smaller of {@code a} and {@code b}.
863 public static int min(int a, int b) {
864 return (a <= b) ? a : b;
868 * Returns the smaller of two {@code long} values. That is,
869 * the result is the argument closer to the value of
870 * {@link Long#MIN_VALUE}. If the arguments have the same
871 * value, the result is that same value.
873 * @param a an argument.
874 * @param b another argument.
875 * @return the smaller of {@code a} and {@code b}.
877 public static long min(long a, long b) {
878 return (a <= b) ? a : b;
882 * Returns the smaller of two {@code float} values. That is,
883 * the result is the value closer to negative infinity. If the
884 * arguments have the same value, the result is that same
885 * value. If either value is NaN, then the result is NaN. Unlike
886 * the numerical comparison operators, this method considers
887 * negative zero to be strictly smaller than positive zero. If
888 * one argument is positive zero and the other is negative zero,
889 * the result is negative zero.
891 * @param a an argument.
892 * @param b another argument.
893 * @return the smaller of {@code a} and {@code b}.
895 @JavaScriptBody(args={"a", "b"},
896 body="return Math.min(a,b);"
898 public static float min(float a, float b) {
899 throw new UnsupportedOperationException();
903 * Returns the smaller of two {@code double} values. That
904 * is, the result is the value closer to negative infinity. If the
905 * arguments have the same value, the result is that same
906 * value. If either value is NaN, then the result is NaN. Unlike
907 * the numerical comparison operators, this method considers
908 * negative zero to be strictly smaller than positive zero. If one
909 * argument is positive zero and the other is negative zero, the
910 * result is negative zero.
912 * @param a an argument.
913 * @param b another argument.
914 * @return the smaller of {@code a} and {@code b}.
916 @JavaScriptBody(args={"a", "b"},
917 body="return Math.min(a,b);"
919 public static double min(double a, double b) {
920 throw new UnsupportedOperationException();
924 * Returns the size of an ulp of the argument. An ulp of a
925 * {@code double} value is the positive distance between this
926 * floating-point value and the {@code double} value next
927 * larger in magnitude. Note that for non-NaN <i>x</i>,
928 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
932 * <li> If the argument is NaN, then the result is NaN.
933 * <li> If the argument is positive or negative infinity, then the
934 * result is positive infinity.
935 * <li> If the argument is positive or negative zero, then the result is
936 * {@code Double.MIN_VALUE}.
937 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
938 * the result is equal to 2<sup>971</sup>.
941 * @param d the floating-point value whose ulp is to be returned
942 * @return the size of an ulp of the argument
943 * @author Joseph D. Darcy
946 // public static double ulp(double d) {
947 // return sun.misc.FpUtils.ulp(d);
951 * Returns the size of an ulp of the argument. An ulp of a
952 * {@code float} value is the positive distance between this
953 * floating-point value and the {@code float} value next
954 * larger in magnitude. Note that for non-NaN <i>x</i>,
955 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
959 * <li> If the argument is NaN, then the result is NaN.
960 * <li> If the argument is positive or negative infinity, then the
961 * result is positive infinity.
962 * <li> If the argument is positive or negative zero, then the result is
963 * {@code Float.MIN_VALUE}.
964 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
965 * the result is equal to 2<sup>104</sup>.
968 * @param f the floating-point value whose ulp is to be returned
969 * @return the size of an ulp of the argument
970 * @author Joseph D. Darcy
973 // public static float ulp(float f) {
974 // return sun.misc.FpUtils.ulp(f);
978 * Returns the signum function of the argument; zero if the argument
979 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
980 * argument is less than zero.
984 * <li> If the argument is NaN, then the result is NaN.
985 * <li> If the argument is positive zero or negative zero, then the
986 * result is the same as the argument.
989 * @param d the floating-point value whose signum is to be returned
990 * @return the signum function of the argument
991 * @author Joseph D. Darcy
994 public static double signum(double d) {
995 if (d < 0.0) { return -1.0; }
996 if (d > 0.0) { return 1.0; }
1001 * Returns the signum function of the argument; zero if the argument
1002 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
1003 * argument is less than zero.
1007 * <li> If the argument is NaN, then the result is NaN.
1008 * <li> If the argument is positive zero or negative zero, then the
1009 * result is the same as the argument.
1012 * @param f the floating-point value whose signum is to be returned
1013 * @return the signum function of the argument
1014 * @author Joseph D. Darcy
1017 public static float signum(float f) {
1018 if (f < 0.0f) { return -1.0f; }
1019 if (f > 0.0f) { return 1.0f; }
1024 * Returns the first floating-point argument with the sign of the
1025 * second floating-point argument. Note that unlike the {@link
1026 * StrictMath#copySign(double, double) StrictMath.copySign}
1027 * method, this method does not require NaN {@code sign}
1028 * arguments to be treated as positive values; implementations are
1029 * permitted to treat some NaN arguments as positive and other NaN
1030 * arguments as negative to allow greater performance.
1032 * @param magnitude the parameter providing the magnitude of the result
1033 * @param sign the parameter providing the sign of the result
1034 * @return a value with the magnitude of {@code magnitude}
1035 * and the sign of {@code sign}.
1038 // public static double copySign(double magnitude, double sign) {
1039 // return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1043 * Returns the first floating-point argument with the sign of the
1044 * second floating-point argument. Note that unlike the {@link
1045 * StrictMath#copySign(float, float) StrictMath.copySign}
1046 * method, this method does not require NaN {@code sign}
1047 * arguments to be treated as positive values; implementations are
1048 * permitted to treat some NaN arguments as positive and other NaN
1049 * arguments as negative to allow greater performance.
1051 * @param magnitude the parameter providing the magnitude of the result
1052 * @param sign the parameter providing the sign of the result
1053 * @return a value with the magnitude of {@code magnitude}
1054 * and the sign of {@code sign}.
1057 // public static float copySign(float magnitude, float sign) {
1058 // return sun.misc.FpUtils.rawCopySign(magnitude, sign);
1062 * Returns the unbiased exponent used in the representation of a
1063 * {@code float}. Special cases:
1066 * <li>If the argument is NaN or infinite, then the result is
1067 * {@link Float#MAX_EXPONENT} + 1.
1068 * <li>If the argument is zero or subnormal, then the result is
1069 * {@link Float#MIN_EXPONENT} -1.
1071 * @param f a {@code float} value
1072 * @return the unbiased exponent of the argument
1075 // public static int getExponent(float f) {
1076 // return sun.misc.FpUtils.getExponent(f);
1080 * Returns the unbiased exponent used in the representation of a
1081 * {@code double}. Special cases:
1084 * <li>If the argument is NaN or infinite, then the result is
1085 * {@link Double#MAX_EXPONENT} + 1.
1086 * <li>If the argument is zero or subnormal, then the result is
1087 * {@link Double#MIN_EXPONENT} -1.
1089 * @param d a {@code double} value
1090 * @return the unbiased exponent of the argument
1093 // public static int getExponent(double d) {
1094 // return sun.misc.FpUtils.getExponent(d);
1098 * Returns the floating-point number adjacent to the first
1099 * argument in the direction of the second argument. If both
1100 * arguments compare as equal the second argument is returned.
1105 * <li> If either argument is a NaN, then NaN is returned.
1107 * <li> If both arguments are signed zeros, {@code direction}
1108 * is returned unchanged (as implied by the requirement of
1109 * returning the second argument if the arguments compare as
1112 * <li> If {@code start} is
1113 * ±{@link Double#MIN_VALUE} and {@code direction}
1114 * has a value such that the result should have a smaller
1115 * magnitude, then a zero with the same sign as {@code start}
1118 * <li> If {@code start} is infinite and
1119 * {@code direction} has a value such that the result should
1120 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
1121 * same sign as {@code start} is returned.
1123 * <li> If {@code start} is equal to ±
1124 * {@link Double#MAX_VALUE} and {@code direction} has a
1125 * value such that the result should have a larger magnitude, an
1126 * infinity with same sign as {@code start} is returned.
1129 * @param start starting floating-point value
1130 * @param direction value indicating which of
1131 * {@code start}'s neighbors or {@code start} should
1133 * @return The floating-point number adjacent to {@code start} in the
1134 * direction of {@code direction}.
1137 // public static double nextAfter(double start, double direction) {
1138 // return sun.misc.FpUtils.nextAfter(start, direction);
1142 * Returns the floating-point number adjacent to the first
1143 * argument in the direction of the second argument. If both
1144 * arguments compare as equal a value equivalent to the second argument
1150 * <li> If either argument is a NaN, then NaN is returned.
1152 * <li> If both arguments are signed zeros, a value equivalent
1153 * to {@code direction} is returned.
1155 * <li> If {@code start} is
1156 * ±{@link Float#MIN_VALUE} and {@code direction}
1157 * has a value such that the result should have a smaller
1158 * magnitude, then a zero with the same sign as {@code start}
1161 * <li> If {@code start} is infinite and
1162 * {@code direction} has a value such that the result should
1163 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
1164 * same sign as {@code start} is returned.
1166 * <li> If {@code start} is equal to ±
1167 * {@link Float#MAX_VALUE} and {@code direction} has a
1168 * value such that the result should have a larger magnitude, an
1169 * infinity with same sign as {@code start} is returned.
1172 * @param start starting floating-point value
1173 * @param direction value indicating which of
1174 * {@code start}'s neighbors or {@code start} should
1176 * @return The floating-point number adjacent to {@code start} in the
1177 * direction of {@code direction}.
1180 // public static float nextAfter(float start, double direction) {
1181 // return sun.misc.FpUtils.nextAfter(start, direction);
1185 * Returns the floating-point value adjacent to {@code d} in
1186 * the direction of positive infinity. This method is
1187 * semantically equivalent to {@code nextAfter(d,
1188 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
1189 * implementation may run faster than its equivalent
1190 * {@code nextAfter} call.
1194 * <li> If the argument is NaN, the result is NaN.
1196 * <li> If the argument is positive infinity, the result is
1197 * positive infinity.
1199 * <li> If the argument is zero, the result is
1200 * {@link Double#MIN_VALUE}
1204 * @param d starting floating-point value
1205 * @return The adjacent floating-point value closer to positive
1209 // public static double nextUp(double d) {
1210 // return sun.misc.FpUtils.nextUp(d);
1214 * Returns the floating-point value adjacent to {@code f} in
1215 * the direction of positive infinity. This method is
1216 * semantically equivalent to {@code nextAfter(f,
1217 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
1218 * implementation may run faster than its equivalent
1219 * {@code nextAfter} call.
1223 * <li> If the argument is NaN, the result is NaN.
1225 * <li> If the argument is positive infinity, the result is
1226 * positive infinity.
1228 * <li> If the argument is zero, the result is
1229 * {@link Float#MIN_VALUE}
1233 * @param f starting floating-point value
1234 * @return The adjacent floating-point value closer to positive
1238 // public static float nextUp(float f) {
1239 // return sun.misc.FpUtils.nextUp(f);
1244 * Return {@code d} ×
1245 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1246 * by a single correctly rounded floating-point multiply to a
1247 * member of the double value set. See the Java
1248 * Language Specification for a discussion of floating-point
1249 * value sets. If the exponent of the result is between {@link
1250 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
1251 * answer is calculated exactly. If the exponent of the result
1252 * would be larger than {@code Double.MAX_EXPONENT}, an
1253 * infinity is returned. Note that if the result is subnormal,
1254 * precision may be lost; that is, when {@code scalb(x, n)}
1255 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1256 * <i>x</i>. When the result is non-NaN, the result has the same
1257 * sign as {@code d}.
1261 * <li> If the first argument is NaN, NaN is returned.
1262 * <li> If the first argument is infinite, then an infinity of the
1263 * same sign is returned.
1264 * <li> If the first argument is zero, then a zero of the same
1268 * @param d number to be scaled by a power of two.
1269 * @param scaleFactor power of 2 used to scale {@code d}
1270 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
1273 // public static double scalb(double d, int scaleFactor) {
1274 // return sun.misc.FpUtils.scalb(d, scaleFactor);
1278 * Return {@code f} ×
1279 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
1280 * by a single correctly rounded floating-point multiply to a
1281 * member of the float value set. See the Java
1282 * Language Specification for a discussion of floating-point
1283 * value sets. If the exponent of the result is between {@link
1284 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
1285 * answer is calculated exactly. If the exponent of the result
1286 * would be larger than {@code Float.MAX_EXPONENT}, an
1287 * infinity is returned. Note that if the result is subnormal,
1288 * precision may be lost; that is, when {@code scalb(x, n)}
1289 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
1290 * <i>x</i>. When the result is non-NaN, the result has the same
1291 * sign as {@code f}.
1295 * <li> If the first argument is NaN, NaN is returned.
1296 * <li> If the first argument is infinite, then an infinity of the
1297 * same sign is returned.
1298 * <li> If the first argument is zero, then a zero of the same
1302 * @param f number to be scaled by a power of two.
1303 * @param scaleFactor power of 2 used to scale {@code f}
1304 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
1307 // public static float scalb(float f, int scaleFactor) {
1308 // return sun.misc.FpUtils.scalb(f, scaleFactor);