2
+ − 1 /*
+ − 2 * Copyright 1994-2006 Sun Microsystems, Inc. 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. Sun designates this
+ − 8 * particular file as subject to the "Classpath" exception as provided
+ − 9 * by Sun 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 Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
+ − 22 * CA 95054 USA or visit www.sun.com if you need additional information or
+ − 23 * have any questions.
+ − 24 */
+ − 25
+ − 26 package java.lang;
+ − 27 import java.util.Random;
+ − 28
+ − 29
+ − 30 /**
+ − 31 * The class {@code Math} contains methods for performing basic
+ − 32 * numeric operations such as the elementary exponential, logarithm,
+ − 33 * square root, and trigonometric functions.
+ − 34 *
+ − 35 * <p>Unlike some of the numeric methods of class
+ − 36 * {@code StrictMath}, all implementations of the equivalent
+ − 37 * functions of class {@code Math} are not defined to return the
+ − 38 * bit-for-bit same results. This relaxation permits
+ − 39 * better-performing implementations where strict reproducibility is
+ − 40 * not required.
+ − 41 *
+ − 42 * <p>By default many of the {@code Math} methods simply call
+ − 43 * the equivalent method in {@code StrictMath} for their
+ − 44 * implementation. Code generators are encouraged to use
+ − 45 * platform-specific native libraries or microprocessor instructions,
+ − 46 * where available, to provide higher-performance implementations of
+ − 47 * {@code Math} methods. Such higher-performance
+ − 48 * implementations still must conform to the specification for
+ − 49 * {@code Math}.
+ − 50 *
+ − 51 * <p>The quality of implementation specifications concern two
+ − 52 * properties, accuracy of the returned result and monotonicity of the
+ − 53 * method. Accuracy of the floating-point {@code Math} methods
+ − 54 * is measured in terms of <i>ulps</i>, units in the last place. For
+ − 55 * a given floating-point format, an ulp of a specific real number
+ − 56 * value is the distance between the two floating-point values
+ − 57 * bracketing that numerical value. When discussing the accuracy of a
+ − 58 * method as a whole rather than at a specific argument, the number of
+ − 59 * ulps cited is for the worst-case error at any argument. If a
+ − 60 * method always has an error less than 0.5 ulps, the method always
+ − 61 * returns the floating-point number nearest the exact result; such a
+ − 62 * method is <i>correctly rounded</i>. A correctly rounded method is
+ − 63 * generally the best a floating-point approximation can be; however,
+ − 64 * it is impractical for many floating-point methods to be correctly
+ − 65 * rounded. Instead, for the {@code Math} class, a larger error
+ − 66 * bound of 1 or 2 ulps is allowed for certain methods. Informally,
+ − 67 * with a 1 ulp error bound, when the exact result is a representable
+ − 68 * number, the exact result should be returned as the computed result;
+ − 69 * otherwise, either of the two floating-point values which bracket
+ − 70 * the exact result may be returned. For exact results large in
+ − 71 * magnitude, one of the endpoints of the bracket may be infinite.
+ − 72 * Besides accuracy at individual arguments, maintaining proper
+ − 73 * relations between the method at different arguments is also
+ − 74 * important. Therefore, most methods with more than 0.5 ulp errors
+ − 75 * are required to be <i>semi-monotonic</i>: whenever the mathematical
+ − 76 * function is non-decreasing, so is the floating-point approximation,
+ − 77 * likewise, whenever the mathematical function is non-increasing, so
+ − 78 * is the floating-point approximation. Not all approximations that
+ − 79 * have 1 ulp accuracy will automatically meet the monotonicity
+ − 80 * requirements.
+ − 81 *
+ − 82 * @author unascribed
+ − 83 * @author Joseph D. Darcy
+ − 84 * @since JDK1.0
+ − 85 */
+ − 86
+ − 87 public final class Math {
+ − 88
+ − 89 /**
+ − 90 * Don't let anyone instantiate this class.
+ − 91 */
+ − 92 private Math() {}
+ − 93
+ − 94 /**
+ − 95 * The {@code double} value that is closer than any other to
+ − 96 * <i>e</i>, the base of the natural logarithms.
+ − 97 */
+ − 98 public static final double E = 2.7182818284590452354;
+ − 99
+ − 100 /**
+ − 101 * The {@code double} value that is closer than any other to
+ − 102 * <i>pi</i>, the ratio of the circumference of a circle to its
+ − 103 * diameter.
+ − 104 */
+ − 105 public static final double PI = 3.14159265358979323846;
+ − 106
+ − 107 /**
+ − 108 * Returns the trigonometric sine of an angle. Special cases:
+ − 109 * <ul><li>If the argument is NaN or an infinity, then the
+ − 110 * result is NaN.
+ − 111 * <li>If the argument is zero, then the result is a zero with the
+ − 112 * same sign as the argument.</ul>
+ − 113 *
+ − 114 * <p>The computed result must be within 1 ulp of the exact result.
+ − 115 * Results must be semi-monotonic.
+ − 116 *
+ − 117 * @param a an angle, in radians.
+ − 118 * @return the sine of the argument.
+ − 119 */
+ − 120 public static double sin(double a) {
+ − 121 return StrictMath.sin(a); // default impl. delegates to StrictMath
+ − 122 }
+ − 123
+ − 124 /**
+ − 125 * Returns the trigonometric cosine of an angle. Special cases:
+ − 126 * <ul><li>If the argument is NaN or an infinity, then the
+ − 127 * result is NaN.</ul>
+ − 128 *
+ − 129 * <p>The computed result must be within 1 ulp of the exact result.
+ − 130 * Results must be semi-monotonic.
+ − 131 *
+ − 132 * @param a an angle, in radians.
+ − 133 * @return the cosine of the argument.
+ − 134 */
+ − 135 public static double cos(double a) {
+ − 136 return StrictMath.cos(a); // default impl. delegates to StrictMath
+ − 137 }
+ − 138
+ − 139 /**
+ − 140 * Returns the trigonometric tangent of an angle. Special cases:
+ − 141 * <ul><li>If the argument is NaN or an infinity, then the result
+ − 142 * 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 tangent of the argument.
+ − 151 */
+ − 152 public static double tan(double a) {
+ − 153 return StrictMath.tan(a); // default impl. delegates to StrictMath
+ − 154 }
+ − 155
+ − 156 /**
+ − 157 * Returns the arc sine of a value; the returned angle is in the
+ − 158 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
+ − 159 * <ul><li>If the argument is NaN or its absolute value is greater
+ − 160 * than 1, then the result is NaN.
+ − 161 * <li>If the argument is zero, then the result is a zero with the
+ − 162 * same sign as the argument.</ul>
+ − 163 *
+ − 164 * <p>The computed result must be within 1 ulp of the exact result.
+ − 165 * Results must be semi-monotonic.
+ − 166 *
+ − 167 * @param a the value whose arc sine is to be returned.
+ − 168 * @return the arc sine of the argument.
+ − 169 */
+ − 170 public static double asin(double a) {
+ − 171 return StrictMath.asin(a); // default impl. delegates to StrictMath
+ − 172 }
+ − 173
+ − 174 /**
+ − 175 * Returns the arc cosine of a value; the returned angle is in the
+ − 176 * range 0.0 through <i>pi</i>. Special case:
+ − 177 * <ul><li>If the argument is NaN or its absolute value is greater
+ − 178 * than 1, then the result is NaN.</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 the value whose arc cosine is to be returned.
+ − 184 * @return the arc cosine of the argument.
+ − 185 */
+ − 186 public static double acos(double a) {
+ − 187 return StrictMath.acos(a); // default impl. delegates to StrictMath
+ − 188 }
+ − 189
+ − 190 /**
+ − 191 * Returns the arc tangent of a value; the returned angle is in the
+ − 192 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases:
+ − 193 * <ul><li>If the argument is NaN, then the result is NaN.
+ − 194 * <li>If the argument is zero, then the result is a zero with the
+ − 195 * same sign as the argument.</ul>
+ − 196 *
+ − 197 * <p>The computed result must be within 1 ulp of the exact result.
+ − 198 * Results must be semi-monotonic.
+ − 199 *
+ − 200 * @param a the value whose arc tangent is to be returned.
+ − 201 * @return the arc tangent of the argument.
+ − 202 */
+ − 203 public static double atan(double a) {
+ − 204 return StrictMath.atan(a); // default impl. delegates to StrictMath
+ − 205 }
+ − 206
+ − 207 /**
+ − 208 * Converts an angle measured in degrees to an approximately
+ − 209 * equivalent angle measured in radians. The conversion from
+ − 210 * degrees to radians is generally inexact.
+ − 211 *
+ − 212 * @param angdeg an angle, in degrees
+ − 213 * @return the measurement of the angle {@code angdeg}
+ − 214 * in radians.
+ − 215 * @since 1.2
+ − 216 */
+ − 217 public static double toRadians(double angdeg) {
+ − 218 return angdeg / 180.0 * PI;
+ − 219 }
+ − 220
+ − 221 /**
+ − 222 * Converts an angle measured in radians to an approximately
+ − 223 * equivalent angle measured in degrees. The conversion from
+ − 224 * radians to degrees is generally inexact; users should
+ − 225 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly
+ − 226 * equal {@code 0.0}.
+ − 227 *
+ − 228 * @param angrad an angle, in radians
+ − 229 * @return the measurement of the angle {@code angrad}
+ − 230 * in degrees.
+ − 231 * @since 1.2
+ − 232 */
+ − 233 public static double toDegrees(double angrad) {
+ − 234 return angrad * 180.0 / PI;
+ − 235 }
+ − 236
+ − 237 /**
+ − 238 * Returns Euler's number <i>e</i> raised to the power of a
+ − 239 * {@code double} value. Special cases:
+ − 240 * <ul><li>If the argument is NaN, the result is NaN.
+ − 241 * <li>If the argument is positive infinity, then the result is
+ − 242 * positive infinity.
+ − 243 * <li>If the argument is negative infinity, then the result is
+ − 244 * positive zero.</ul>
+ − 245 *
+ − 246 * <p>The computed result must be within 1 ulp of the exact result.
+ − 247 * Results must be semi-monotonic.
+ − 248 *
+ − 249 * @param a the exponent to raise <i>e</i> to.
+ − 250 * @return the value <i>e</i><sup>{@code a}</sup>,
+ − 251 * where <i>e</i> is the base of the natural logarithms.
+ − 252 */
+ − 253 public static double exp(double a) {
+ − 254 return StrictMath.exp(a); // default impl. delegates to StrictMath
+ − 255 }
+ − 256
+ − 257 /**
+ − 258 * Returns the natural logarithm (base <i>e</i>) of a {@code double}
+ − 259 * value. Special cases:
+ − 260 * <ul><li>If the argument is NaN or less than zero, then the result
+ − 261 * is NaN.
+ − 262 * <li>If the argument is positive infinity, then the result is
+ − 263 * positive infinity.
+ − 264 * <li>If the argument is positive zero or negative zero, then the
+ − 265 * result is negative infinity.</ul>
+ − 266 *
+ − 267 * <p>The computed result must be within 1 ulp of the exact result.
+ − 268 * Results must be semi-monotonic.
+ − 269 *
+ − 270 * @param a a value
+ − 271 * @return the value ln {@code a}, the natural logarithm of
+ − 272 * {@code a}.
+ − 273 */
+ − 274 public static double log(double a) {
+ − 275 return StrictMath.log(a); // default impl. delegates to StrictMath
+ − 276 }
+ − 277
+ − 278 /**
+ − 279 * Returns the base 10 logarithm of a {@code double} value.
+ − 280 * Special cases:
+ − 281 *
+ − 282 * <ul><li>If the argument is NaN or less than zero, then the result
+ − 283 * is NaN.
+ − 284 * <li>If the argument is positive infinity, then the result is
+ − 285 * positive infinity.
+ − 286 * <li>If the argument is positive zero or negative zero, then the
+ − 287 * result is negative infinity.
+ − 288 * <li> If the argument is equal to 10<sup><i>n</i></sup> for
+ − 289 * integer <i>n</i>, then the result is <i>n</i>.
+ − 290 * </ul>
+ − 291 *
+ − 292 * <p>The computed result must be within 1 ulp of the exact result.
+ − 293 * Results must be semi-monotonic.
+ − 294 *
+ − 295 * @param a a value
+ − 296 * @return the base 10 logarithm of {@code a}.
+ − 297 * @since 1.5
+ − 298 */
+ − 299 public static double log10(double a) {
+ − 300 return StrictMath.log10(a); // default impl. delegates to StrictMath
+ − 301 }
+ − 302
+ − 303 /**
+ − 304 * Returns the correctly rounded positive square root of a
+ − 305 * {@code double} value.
+ − 306 * Special cases:
+ − 307 * <ul><li>If the argument is NaN or less than zero, then the result
+ − 308 * is NaN.
+ − 309 * <li>If the argument is positive infinity, then the result is positive
+ − 310 * infinity.
+ − 311 * <li>If the argument is positive zero or negative zero, then the
+ − 312 * result is the same as the argument.</ul>
+ − 313 * Otherwise, the result is the {@code double} value closest to
+ − 314 * the true mathematical square root of the argument value.
+ − 315 *
+ − 316 * @param a a value.
+ − 317 * @return the positive square root of {@code a}.
+ − 318 * If the argument is NaN or less than zero, the result is NaN.
+ − 319 */
+ − 320 public static double sqrt(double a) {
+ − 321 return StrictMath.sqrt(a); // default impl. delegates to StrictMath
+ − 322 // Note that hardware sqrt instructions
+ − 323 // frequently can be directly used by JITs
+ − 324 // and should be much faster than doing
+ − 325 // Math.sqrt in software.
+ − 326 }
+ − 327
+ − 328
+ − 329 /**
+ − 330 * Returns the cube root of a {@code double} value. For
+ − 331 * positive finite {@code x}, {@code cbrt(-x) ==
+ − 332 * -cbrt(x)}; that is, the cube root of a negative value is
+ − 333 * the negative of the cube root of that value's magnitude.
+ − 334 *
+ − 335 * Special cases:
+ − 336 *
+ − 337 * <ul>
+ − 338 *
+ − 339 * <li>If the argument is NaN, then the result is NaN.
+ − 340 *
+ − 341 * <li>If the argument is infinite, then the result is an infinity
+ − 342 * with the same sign as the argument.
+ − 343 *
+ − 344 * <li>If the argument is zero, then the result is a zero with the
+ − 345 * same sign as the argument.
+ − 346 *
+ − 347 * </ul>
+ − 348 *
+ − 349 * <p>The computed result must be within 1 ulp of the exact result.
+ − 350 *
+ − 351 * @param a a value.
+ − 352 * @return the cube root of {@code a}.
+ − 353 * @since 1.5
+ − 354 */
+ − 355 public static double cbrt(double a) {
+ − 356 return StrictMath.cbrt(a);
+ − 357 }
+ − 358
+ − 359 /**
+ − 360 * Computes the remainder operation on two arguments as prescribed
+ − 361 * by the IEEE 754 standard.
+ − 362 * The remainder value is mathematically equal to
+ − 363 * <code>f1 - f2</code> × <i>n</i>,
+ − 364 * where <i>n</i> is the mathematical integer closest to the exact
+ − 365 * mathematical value of the quotient {@code f1/f2}, and if two
+ − 366 * mathematical integers are equally close to {@code f1/f2},
+ − 367 * then <i>n</i> is the integer that is even. If the remainder is
+ − 368 * zero, its sign is the same as the sign of the first argument.
+ − 369 * Special cases:
+ − 370 * <ul><li>If either argument is NaN, or the first argument is infinite,
+ − 371 * or the second argument is positive zero or negative zero, then the
+ − 372 * result is NaN.
+ − 373 * <li>If the first argument is finite and the second argument is
+ − 374 * infinite, then the result is the same as the first argument.</ul>
+ − 375 *
+ − 376 * @param f1 the dividend.
+ − 377 * @param f2 the divisor.
+ − 378 * @return the remainder when {@code f1} is divided by
+ − 379 * {@code f2}.
+ − 380 */
+ − 381 public static double IEEEremainder(double f1, double f2) {
+ − 382 return StrictMath.IEEEremainder(f1, f2); // delegate to StrictMath
+ − 383 }
+ − 384
+ − 385 /**
+ − 386 * Returns the smallest (closest to negative infinity)
+ − 387 * {@code double} value that is greater than or equal to the
+ − 388 * argument and is equal to a mathematical integer. Special cases:
+ − 389 * <ul><li>If the argument value is already equal to a
+ − 390 * mathematical integer, then the result is the same as the
+ − 391 * argument. <li>If the argument is NaN or an infinity or
+ − 392 * positive zero or negative zero, then the result is the same as
+ − 393 * the argument. <li>If the argument value is less than zero but
+ − 394 * greater than -1.0, then the result is negative zero.</ul> Note
+ − 395 * that the value of {@code Math.ceil(x)} is exactly the
+ − 396 * value of {@code -Math.floor(-x)}.
+ − 397 *
+ − 398 *
+ − 399 * @param a a value.
+ − 400 * @return the smallest (closest to negative infinity)
+ − 401 * floating-point value that is greater than or equal to
+ − 402 * the argument and is equal to a mathematical integer.
+ − 403 */
+ − 404 public static double ceil(double a) {
+ − 405 return StrictMath.ceil(a); // default impl. delegates to StrictMath
+ − 406 }
+ − 407
+ − 408 /**
+ − 409 * Returns the largest (closest to positive infinity)
+ − 410 * {@code double} value that is less than or equal to the
+ − 411 * argument and is equal to a mathematical integer. Special cases:
+ − 412 * <ul><li>If the argument value is already equal to a
+ − 413 * mathematical integer, then the result is the same as the
+ − 414 * argument. <li>If the argument is NaN or an infinity or
+ − 415 * positive zero or negative zero, then the result is the same as
+ − 416 * the argument.</ul>
+ − 417 *
+ − 418 * @param a a value.
+ − 419 * @return the largest (closest to positive infinity)
+ − 420 * floating-point value that less than or equal to the argument
+ − 421 * and is equal to a mathematical integer.
+ − 422 */
+ − 423 public static double floor(double a) {
+ − 424 return StrictMath.floor(a); // default impl. delegates to StrictMath
+ − 425 }
+ − 426
+ − 427 /**
+ − 428 * Returns the {@code double} value that is closest in value
+ − 429 * to the argument and is equal to a mathematical integer. If two
+ − 430 * {@code double} values that are mathematical integers are
+ − 431 * equally close, the result is the integer value that is
+ − 432 * even. Special cases:
+ − 433 * <ul><li>If the argument value is already equal to a mathematical
+ − 434 * integer, then the result is the same as the argument.
+ − 435 * <li>If the argument is NaN or an infinity or positive zero or negative
+ − 436 * zero, then the result is the same as the argument.</ul>
+ − 437 *
+ − 438 * @param a a {@code double} value.
+ − 439 * @return the closest floating-point value to {@code a} that is
+ − 440 * equal to a mathematical integer.
+ − 441 */
+ − 442 public static double rint(double a) {
+ − 443 return StrictMath.rint(a); // default impl. delegates to StrictMath
+ − 444 }
+ − 445
+ − 446 /**
+ − 447 * Returns the angle <i>theta</i> from the conversion of rectangular
+ − 448 * coordinates ({@code x}, {@code y}) to polar
+ − 449 * coordinates (r, <i>theta</i>).
+ − 450 * This method computes the phase <i>theta</i> by computing an arc tangent
+ − 451 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special
+ − 452 * cases:
+ − 453 * <ul><li>If either argument is NaN, then the result is NaN.
+ − 454 * <li>If the first argument is positive zero and the second argument
+ − 455 * is positive, or the first argument is positive and finite and the
+ − 456 * second argument is positive infinity, then the result is positive
+ − 457 * zero.
+ − 458 * <li>If the first argument is negative zero and the second argument
+ − 459 * is positive, or the first argument is negative and finite and the
+ − 460 * second argument is positive infinity, then the result is negative zero.
+ − 461 * <li>If the first argument is positive zero and the second argument
+ − 462 * is negative, or the first argument is positive and finite and the
+ − 463 * second argument is negative infinity, then the result is the
+ − 464 * {@code double} value closest to <i>pi</i>.
+ − 465 * <li>If the first argument is negative zero and the second argument
+ − 466 * is negative, or the first argument is negative and finite and the
+ − 467 * second argument is negative infinity, then the result is the
+ − 468 * {@code double} value closest to -<i>pi</i>.
+ − 469 * <li>If the first argument is positive and the second argument is
+ − 470 * positive zero or negative zero, or the first argument is positive
+ − 471 * infinity and the second argument is finite, then the result is the
+ − 472 * {@code double} value closest to <i>pi</i>/2.
+ − 473 * <li>If the first argument is negative and the second argument is
+ − 474 * positive zero or negative zero, or the first argument is negative
+ − 475 * infinity and the second argument is finite, then the result is the
+ − 476 * {@code double} value closest to -<i>pi</i>/2.
+ − 477 * <li>If both arguments are positive infinity, then the result is the
+ − 478 * {@code double} value closest to <i>pi</i>/4.
+ − 479 * <li>If the first argument is positive infinity and the second argument
+ − 480 * is negative infinity, then the result is the {@code double}
+ − 481 * value closest to 3*<i>pi</i>/4.
+ − 482 * <li>If the first argument is negative infinity and the second argument
+ − 483 * is positive infinity, then the result is the {@code double} value
+ − 484 * closest to -<i>pi</i>/4.
+ − 485 * <li>If both arguments are negative infinity, then the result is the
+ − 486 * {@code double} value closest to -3*<i>pi</i>/4.</ul>
+ − 487 *
+ − 488 * <p>The computed result must be within 2 ulps of the exact result.
+ − 489 * Results must be semi-monotonic.
+ − 490 *
+ − 491 * @param y the ordinate coordinate
+ − 492 * @param x the abscissa coordinate
+ − 493 * @return the <i>theta</i> component of the point
+ − 494 * (<i>r</i>, <i>theta</i>)
+ − 495 * in polar coordinates that corresponds to the point
+ − 496 * (<i>x</i>, <i>y</i>) in Cartesian coordinates.
+ − 497 */
+ − 498 public static double atan2(double y, double x) {
+ − 499 return StrictMath.atan2(y, x); // default impl. delegates to StrictMath
+ − 500 }
+ − 501
+ − 502 /**
+ − 503 * Returns the value of the first argument raised to the power of the
+ − 504 * second argument. Special cases:
+ − 505 *
+ − 506 * <ul><li>If the second argument is positive or negative zero, then the
+ − 507 * result is 1.0.
+ − 508 * <li>If the second argument is 1.0, then the result is the same as the
+ − 509 * first argument.
+ − 510 * <li>If the second argument is NaN, then the result is NaN.
+ − 511 * <li>If the first argument is NaN and the second argument is nonzero,
+ − 512 * then the result is NaN.
+ − 513 *
+ − 514 * <li>If
+ − 515 * <ul>
+ − 516 * <li>the absolute value of the first argument is greater than 1
+ − 517 * and the second argument is positive infinity, or
+ − 518 * <li>the absolute value of the first argument is less than 1 and
+ − 519 * the second argument is negative infinity,
+ − 520 * </ul>
+ − 521 * then the result is positive infinity.
+ − 522 *
+ − 523 * <li>If
+ − 524 * <ul>
+ − 525 * <li>the absolute value of the first argument is greater than 1 and
+ − 526 * the second argument is negative infinity, or
+ − 527 * <li>the absolute value of the
+ − 528 * first argument is less than 1 and the second argument is positive
+ − 529 * infinity,
+ − 530 * </ul>
+ − 531 * then the result is positive zero.
+ − 532 *
+ − 533 * <li>If the absolute value of the first argument equals 1 and the
+ − 534 * second argument is infinite, then the result is NaN.
+ − 535 *
+ − 536 * <li>If
+ − 537 * <ul>
+ − 538 * <li>the first argument is positive zero and the second argument
+ − 539 * is greater than zero, or
+ − 540 * <li>the first argument is positive infinity and the second
+ − 541 * argument is less than zero,
+ − 542 * </ul>
+ − 543 * then the result is positive zero.
+ − 544 *
+ − 545 * <li>If
+ − 546 * <ul>
+ − 547 * <li>the first argument is positive zero and the second argument
+ − 548 * is less than zero, or
+ − 549 * <li>the first argument is positive infinity and the second
+ − 550 * argument is greater than zero,
+ − 551 * </ul>
+ − 552 * then the result is positive infinity.
+ − 553 *
+ − 554 * <li>If
+ − 555 * <ul>
+ − 556 * <li>the first argument is negative zero and the second argument
+ − 557 * is greater than zero but not a finite odd integer, or
+ − 558 * <li>the first argument is negative infinity and the second
+ − 559 * argument is less than zero but not a finite odd integer,
+ − 560 * </ul>
+ − 561 * then the result is positive zero.
+ − 562 *
+ − 563 * <li>If
+ − 564 * <ul>
+ − 565 * <li>the first argument is negative zero and the second argument
+ − 566 * is a positive finite odd integer, or
+ − 567 * <li>the first argument is negative infinity and the second
+ − 568 * argument is a negative finite odd integer,
+ − 569 * </ul>
+ − 570 * then the result is negative zero.
+ − 571 *
+ − 572 * <li>If
+ − 573 * <ul>
+ − 574 * <li>the first argument is negative zero and the second argument
+ − 575 * is less than zero but not a finite odd integer, or
+ − 576 * <li>the first argument is negative infinity and the second
+ − 577 * argument is greater than zero but not a finite odd integer,
+ − 578 * </ul>
+ − 579 * then the result is positive infinity.
+ − 580 *
+ − 581 * <li>If
+ − 582 * <ul>
+ − 583 * <li>the first argument is negative zero and the second argument
+ − 584 * is a negative finite odd integer, or
+ − 585 * <li>the first argument is negative infinity and the second
+ − 586 * argument is a positive finite odd integer,
+ − 587 * </ul>
+ − 588 * then the result is negative infinity.
+ − 589 *
+ − 590 * <li>If the first argument is finite and less than zero
+ − 591 * <ul>
+ − 592 * <li> if the second argument is a finite even integer, the
+ − 593 * result is equal to the result of raising the absolute value of
+ − 594 * the first argument to the power of the second argument
+ − 595 *
+ − 596 * <li>if the second argument is a finite odd integer, the result
+ − 597 * is equal to the negative of the result of raising the absolute
+ − 598 * value of the first argument to the power of the second
+ − 599 * argument
+ − 600 *
+ − 601 * <li>if the second argument is finite and not an integer, then
+ − 602 * the result is NaN.
+ − 603 * </ul>
+ − 604 *
+ − 605 * <li>If both arguments are integers, then the result is exactly equal
+ − 606 * to the mathematical result of raising the first argument to the power
+ − 607 * of the second argument if that result can in fact be represented
+ − 608 * exactly as a {@code double} value.</ul>
+ − 609 *
+ − 610 * <p>(In the foregoing descriptions, a floating-point value is
+ − 611 * considered to be an integer if and only if it is finite and a
+ − 612 * fixed point of the method {@link #ceil ceil} or,
+ − 613 * equivalently, a fixed point of the method {@link #floor
+ − 614 * floor}. A value is a fixed point of a one-argument
+ − 615 * method if and only if the result of applying the method to the
+ − 616 * value is equal to the value.)
+ − 617 *
+ − 618 * <p>The computed result must be within 1 ulp of the exact result.
+ − 619 * Results must be semi-monotonic.
+ − 620 *
+ − 621 * @param a the base.
+ − 622 * @param b the exponent.
+ − 623 * @return the value {@code a}<sup>{@code b}</sup>.
+ − 624 */
+ − 625 public static double pow(double a, double b) {
+ − 626 return StrictMath.pow(a, b); // default impl. delegates to StrictMath
+ − 627 }
+ − 628
+ − 629 /**
+ − 630 * Returns the closest {@code int} to the argument. The
+ − 631 * result is rounded to an integer by adding 1/2, taking the
+ − 632 * floor of the result, and casting the result to type {@code int}.
+ − 633 * In other words, the result is equal to the value of the expression:
+ − 634 * <p>{@code (int)Math.floor(a + 0.5f)}
+ − 635 * <p>
+ − 636 * Special cases:
+ − 637 * <ul><li>If the argument is NaN, the result is 0.
+ − 638 * <li>If the argument is negative infinity or any value less than or
+ − 639 * equal to the value of {@code Integer.MIN_VALUE}, the result is
+ − 640 * equal to the value of {@code Integer.MIN_VALUE}.
+ − 641 * <li>If the argument is positive infinity or any value greater than or
+ − 642 * equal to the value of {@code Integer.MAX_VALUE}, the result is
+ − 643 * equal to the value of {@code Integer.MAX_VALUE}.</ul>
+ − 644 *
+ − 645 * @param a a floating-point value to be rounded to an integer.
+ − 646 * @return the value of the argument rounded to the nearest
+ − 647 * {@code int} value.
+ − 648 * @see java.lang.Integer#MAX_VALUE
+ − 649 * @see java.lang.Integer#MIN_VALUE
+ − 650 */
+ − 651 public static int round(float a) {
+ − 652 return (int)floor(a + 0.5f);
+ − 653 }
+ − 654
+ − 655 /**
+ − 656 * Returns the closest {@code long} to the argument. The result
+ − 657 * is rounded to an integer by adding 1/2, taking the floor of the
+ − 658 * result, and casting the result to type {@code long}. In other
+ − 659 * words, the result is equal to the value of the expression:
+ − 660 * <p>{@code (long)Math.floor(a + 0.5d)}
+ − 661 * <p>
+ − 662 * Special cases:
+ − 663 * <ul><li>If the argument is NaN, the result is 0.
+ − 664 * <li>If the argument is negative infinity or any value less than or
+ − 665 * equal to the value of {@code Long.MIN_VALUE}, the result is
+ − 666 * equal to the value of {@code Long.MIN_VALUE}.
+ − 667 * <li>If the argument is positive infinity or any value greater than or
+ − 668 * equal to the value of {@code Long.MAX_VALUE}, the result is
+ − 669 * equal to the value of {@code Long.MAX_VALUE}.</ul>
+ − 670 *
+ − 671 * @param a a floating-point value to be rounded to a
+ − 672 * {@code long}.
+ − 673 * @return the value of the argument rounded to the nearest
+ − 674 * {@code long} value.
+ − 675 * @see java.lang.Long#MAX_VALUE
+ − 676 * @see java.lang.Long#MIN_VALUE
+ − 677 */
+ − 678 public static long round(double a) {
+ − 679 return (long)floor(a + 0.5d);
+ − 680 }
+ − 681
+ − 682 private static Random randomNumberGenerator;
+ − 683
+ − 684 private static synchronized void initRNG() {
+ − 685 if (randomNumberGenerator == null)
+ − 686 randomNumberGenerator = new Random();
+ − 687 }
+ − 688
+ − 689 /**
+ − 690 * Returns a {@code double} value with a positive sign, greater
+ − 691 * than or equal to {@code 0.0} and less than {@code 1.0}.
+ − 692 * Returned values are chosen pseudorandomly with (approximately)
+ − 693 * uniform distribution from that range.
+ − 694 *
+ − 695 * <p>When this method is first called, it creates a single new
+ − 696 * pseudorandom-number generator, exactly as if by the expression
+ − 697 * <blockquote>{@code new java.util.Random}</blockquote> This
+ − 698 * new pseudorandom-number generator is used thereafter for all
+ − 699 * calls to this method and is used nowhere else.
+ − 700 *
+ − 701 * <p>This method is properly synchronized to allow correct use by
+ − 702 * more than one thread. However, if many threads need to generate
+ − 703 * pseudorandom numbers at a great rate, it may reduce contention
+ − 704 * for each thread to have its own pseudorandom-number generator.
+ − 705 *
+ − 706 * @return a pseudorandom {@code double} greater than or equal
+ − 707 * to {@code 0.0} and less than {@code 1.0}.
+ − 708 * @see java.util.Random#nextDouble()
+ − 709 */
+ − 710 public static double random() {
+ − 711 if (randomNumberGenerator == null) initRNG();
+ − 712 return randomNumberGenerator.nextDouble();
+ − 713 }
+ − 714
+ − 715 /**
+ − 716 * Returns the absolute value of an {@code int} value.
+ − 717 * If the argument is not negative, the argument is returned.
+ − 718 * If the argument is negative, the negation of the argument is returned.
+ − 719 *
+ − 720 * <p>Note that if the argument is equal to the value of
+ − 721 * {@link Integer#MIN_VALUE}, the most negative representable
+ − 722 * {@code int} value, the result is that same value, which is
+ − 723 * negative.
+ − 724 *
+ − 725 * @param a the argument whose absolute value is to be determined
+ − 726 * @return the absolute value of the argument.
+ − 727 */
+ − 728 public static int abs(int a) {
+ − 729 return (a < 0) ? -a : a;
+ − 730 }
+ − 731
+ − 732 /**
+ − 733 * Returns the absolute value of a {@code long} value.
+ − 734 * If the argument is not negative, the argument is returned.
+ − 735 * If the argument is negative, the negation of the argument is returned.
+ − 736 *
+ − 737 * <p>Note that if the argument is equal to the value of
+ − 738 * {@link Long#MIN_VALUE}, the most negative representable
+ − 739 * {@code long} value, the result is that same value, which
+ − 740 * is negative.
+ − 741 *
+ − 742 * @param a the argument whose absolute value is to be determined
+ − 743 * @return the absolute value of the argument.
+ − 744 */
+ − 745 public static long abs(long a) {
+ − 746 return (a < 0) ? -a : a;
+ − 747 }
+ − 748
+ − 749 /**
+ − 750 * Returns the absolute value of a {@code float} value.
+ − 751 * If the argument is not negative, the argument is returned.
+ − 752 * If the argument is negative, the negation of the argument is returned.
+ − 753 * Special cases:
+ − 754 * <ul><li>If the argument is positive zero or negative zero, the
+ − 755 * result is positive zero.
+ − 756 * <li>If the argument is infinite, the result is positive infinity.
+ − 757 * <li>If the argument is NaN, the result is NaN.</ul>
+ − 758 * In other words, the result is the same as the value of the expression:
+ − 759 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))}
+ − 760 *
+ − 761 * @param a the argument whose absolute value is to be determined
+ − 762 * @return the absolute value of the argument.
+ − 763 */
+ − 764 public static float abs(float a) {
+ − 765 return (a <= 0.0F) ? 0.0F - a : a;
+ − 766 }
+ − 767
+ − 768 /**
+ − 769 * Returns the absolute value of a {@code double} value.
+ − 770 * If the argument is not negative, the argument is returned.
+ − 771 * If the argument is negative, the negation of the argument is returned.
+ − 772 * Special cases:
+ − 773 * <ul><li>If the argument is positive zero or negative zero, the result
+ − 774 * is positive zero.
+ − 775 * <li>If the argument is infinite, the result is positive infinity.
+ − 776 * <li>If the argument is NaN, the result is NaN.</ul>
+ − 777 * In other words, the result is the same as the value of the expression:
+ − 778 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)}
+ − 779 *
+ − 780 * @param a the argument whose absolute value is to be determined
+ − 781 * @return the absolute value of the argument.
+ − 782 */
+ − 783 public static double abs(double a) {
+ − 784 return (a <= 0.0D) ? 0.0D - a : a;
+ − 785 }
+ − 786
+ − 787 /**
+ − 788 * Returns the greater of two {@code int} values. That is, the
+ − 789 * result is the argument closer to the value of
+ − 790 * {@link Integer#MAX_VALUE}. If the arguments have the same value,
+ − 791 * the result is that same value.
+ − 792 *
+ − 793 * @param a an argument.
+ − 794 * @param b another argument.
+ − 795 * @return the larger of {@code a} and {@code b}.
+ − 796 */
+ − 797 public static int max(int a, int b) {
+ − 798 return (a >= b) ? a : b;
+ − 799 }
+ − 800
+ − 801 /**
+ − 802 * Returns the greater of two {@code long} values. That is, the
+ − 803 * result is the argument closer to the value of
+ − 804 * {@link Long#MAX_VALUE}. If the arguments have the same value,
+ − 805 * the result is that same value.
+ − 806 *
+ − 807 * @param a an argument.
+ − 808 * @param b another argument.
+ − 809 * @return the larger of {@code a} and {@code b}.
+ − 810 */
+ − 811 public static long max(long a, long b) {
+ − 812 return (a >= b) ? a : b;
+ − 813 }
+ − 814
+ − 815 private static long negativeZeroFloatBits = Float.floatToIntBits(-0.0f);
+ − 816 private static long negativeZeroDoubleBits = Double.doubleToLongBits(-0.0d);
+ − 817
+ − 818 /**
+ − 819 * Returns the greater of two {@code float} values. That is,
+ − 820 * the result is the argument closer to positive infinity. If the
+ − 821 * arguments have the same value, the result is that same
+ − 822 * value. If either value is NaN, then the result is NaN. Unlike
+ − 823 * the numerical comparison operators, this method considers
+ − 824 * negative zero to be strictly smaller than positive zero. If one
+ − 825 * argument is positive zero and the other negative zero, the
+ − 826 * result is positive zero.
+ − 827 *
+ − 828 * @param a an argument.
+ − 829 * @param b another argument.
+ − 830 * @return the larger of {@code a} and {@code b}.
+ − 831 */
+ − 832 public static float max(float a, float b) {
+ − 833 if (a != a) return a; // a is NaN
+ − 834 if ((a == 0.0f) && (b == 0.0f)
+ − 835 && (Float.floatToIntBits(a) == negativeZeroFloatBits)) {
+ − 836 return b;
+ − 837 }
+ − 838 return (a >= b) ? a : b;
+ − 839 }
+ − 840
+ − 841 /**
+ − 842 * Returns the greater of two {@code double} values. That
+ − 843 * is, the result is the argument closer to positive infinity. If
+ − 844 * the arguments have the same value, the result is that same
+ − 845 * value. If either value is NaN, then the result is NaN. Unlike
+ − 846 * the numerical comparison operators, this method considers
+ − 847 * negative zero to be strictly smaller than positive zero. If one
+ − 848 * argument is positive zero and the other negative zero, the
+ − 849 * result is positive zero.
+ − 850 *
+ − 851 * @param a an argument.
+ − 852 * @param b another argument.
+ − 853 * @return the larger of {@code a} and {@code b}.
+ − 854 */
+ − 855 public static double max(double a, double b) {
+ − 856 if (a != a) return a; // a is NaN
+ − 857 if ((a == 0.0d) && (b == 0.0d)
+ − 858 && (Double.doubleToLongBits(a) == negativeZeroDoubleBits)) {
+ − 859 return b;
+ − 860 }
+ − 861 return (a >= b) ? a : b;
+ − 862 }
+ − 863
+ − 864 /**
+ − 865 * Returns the smaller of two {@code int} values. That is,
+ − 866 * the result the argument closer to the value of
+ − 867 * {@link Integer#MIN_VALUE}. If the arguments have the same
+ − 868 * value, the result is that same value.
+ − 869 *
+ − 870 * @param a an argument.
+ − 871 * @param b another argument.
+ − 872 * @return the smaller of {@code a} and {@code b}.
+ − 873 */
+ − 874 public static int min(int a, int b) {
+ − 875 return (a <= b) ? a : b;
+ − 876 }
+ − 877
+ − 878 /**
+ − 879 * Returns the smaller of two {@code long} values. That is,
+ − 880 * the result is the argument closer to the value of
+ − 881 * {@link Long#MIN_VALUE}. If the arguments have the same
+ − 882 * value, the result is that same value.
+ − 883 *
+ − 884 * @param a an argument.
+ − 885 * @param b another argument.
+ − 886 * @return the smaller of {@code a} and {@code b}.
+ − 887 */
+ − 888 public static long min(long a, long b) {
+ − 889 return (a <= b) ? a : b;
+ − 890 }
+ − 891
+ − 892 /**
+ − 893 * Returns the smaller of two {@code float} values. That is,
+ − 894 * the result is the value closer to negative infinity. If the
+ − 895 * arguments have the same value, the result is that same
+ − 896 * value. If either value is NaN, then the result is NaN. Unlike
+ − 897 * the numerical comparison operators, this method considers
+ − 898 * negative zero to be strictly smaller than positive zero. If
+ − 899 * one argument is positive zero and the other is negative zero,
+ − 900 * the result is negative zero.
+ − 901 *
+ − 902 * @param a an argument.
+ − 903 * @param b another argument.
+ − 904 * @return the smaller of {@code a} and {@code b}.
+ − 905 */
+ − 906 public static float min(float a, float b) {
+ − 907 if (a != a) return a; // a is NaN
+ − 908 if ((a == 0.0f) && (b == 0.0f)
+ − 909 && (Float.floatToIntBits(b) == negativeZeroFloatBits)) {
+ − 910 return b;
+ − 911 }
+ − 912 return (a <= b) ? a : b;
+ − 913 }
+ − 914
+ − 915 /**
+ − 916 * Returns the smaller of two {@code double} values. That
+ − 917 * is, the result is the value closer to negative infinity. If the
+ − 918 * arguments have the same value, the result is that same
+ − 919 * value. If either value is NaN, then the result is NaN. Unlike
+ − 920 * the numerical comparison operators, this method considers
+ − 921 * negative zero to be strictly smaller than positive zero. If one
+ − 922 * argument is positive zero and the other is negative zero, the
+ − 923 * result is negative zero.
+ − 924 *
+ − 925 * @param a an argument.
+ − 926 * @param b another argument.
+ − 927 * @return the smaller of {@code a} and {@code b}.
+ − 928 */
+ − 929 public static double min(double a, double b) {
+ − 930 if (a != a) return a; // a is NaN
+ − 931 if ((a == 0.0d) && (b == 0.0d)
+ − 932 && (Double.doubleToLongBits(b) == negativeZeroDoubleBits)) {
+ − 933 return b;
+ − 934 }
+ − 935 return (a <= b) ? a : b;
+ − 936 }
+ − 937
+ − 938 /**
+ − 939 * Returns the size of an ulp of the argument. An ulp of a
+ − 940 * {@code double} value is the positive distance between this
+ − 941 * floating-point value and the {@code double} value next
+ − 942 * larger in magnitude. Note that for non-NaN <i>x</i>,
+ − 943 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
+ − 944 *
+ − 945 * <p>Special Cases:
+ − 946 * <ul>
+ − 947 * <li> If the argument is NaN, then the result is NaN.
+ − 948 * <li> If the argument is positive or negative infinity, then the
+ − 949 * result is positive infinity.
+ − 950 * <li> If the argument is positive or negative zero, then the result is
+ − 951 * {@code Double.MIN_VALUE}.
+ − 952 * <li> If the argument is ±{@code Double.MAX_VALUE}, then
+ − 953 * the result is equal to 2<sup>971</sup>.
+ − 954 * </ul>
+ − 955 *
+ − 956 * @param d the floating-point value whose ulp is to be returned
+ − 957 * @return the size of an ulp of the argument
+ − 958 * @author Joseph D. Darcy
+ − 959 * @since 1.5
+ − 960 */
+ − 961 public static double ulp(double d) {
+ − 962 return sun.misc.FpUtils.ulp(d);
+ − 963 }
+ − 964
+ − 965 /**
+ − 966 * Returns the size of an ulp of the argument. An ulp of a
+ − 967 * {@code float} value is the positive distance between this
+ − 968 * floating-point value and the {@code float} value next
+ − 969 * larger in magnitude. Note that for non-NaN <i>x</i>,
+ − 970 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>.
+ − 971 *
+ − 972 * <p>Special Cases:
+ − 973 * <ul>
+ − 974 * <li> If the argument is NaN, then the result is NaN.
+ − 975 * <li> If the argument is positive or negative infinity, then the
+ − 976 * result is positive infinity.
+ − 977 * <li> If the argument is positive or negative zero, then the result is
+ − 978 * {@code Float.MIN_VALUE}.
+ − 979 * <li> If the argument is ±{@code Float.MAX_VALUE}, then
+ − 980 * the result is equal to 2<sup>104</sup>.
+ − 981 * </ul>
+ − 982 *
+ − 983 * @param f the floating-point value whose ulp is to be returned
+ − 984 * @return the size of an ulp of the argument
+ − 985 * @author Joseph D. Darcy
+ − 986 * @since 1.5
+ − 987 */
+ − 988 public static float ulp(float f) {
+ − 989 return sun.misc.FpUtils.ulp(f);
+ − 990 }
+ − 991
+ − 992 /**
+ − 993 * Returns the signum function of the argument; zero if the argument
+ − 994 * is zero, 1.0 if the argument is greater than zero, -1.0 if the
+ − 995 * argument is less than zero.
+ − 996 *
+ − 997 * <p>Special Cases:
+ − 998 * <ul>
+ − 999 * <li> If the argument is NaN, then the result is NaN.
+ − 1000 * <li> If the argument is positive zero or negative zero, then the
+ − 1001 * result is the same as the argument.
+ − 1002 * </ul>
+ − 1003 *
+ − 1004 * @param d the floating-point value whose signum is to be returned
+ − 1005 * @return the signum function of the argument
+ − 1006 * @author Joseph D. Darcy
+ − 1007 * @since 1.5
+ − 1008 */
+ − 1009 public static double signum(double d) {
+ − 1010 return sun.misc.FpUtils.signum(d);
+ − 1011 }
+ − 1012
+ − 1013 /**
+ − 1014 * Returns the signum function of the argument; zero if the argument
+ − 1015 * is zero, 1.0f if the argument is greater than zero, -1.0f if the
+ − 1016 * argument is less than zero.
+ − 1017 *
+ − 1018 * <p>Special Cases:
+ − 1019 * <ul>
+ − 1020 * <li> If the argument is NaN, then the result is NaN.
+ − 1021 * <li> If the argument is positive zero or negative zero, then the
+ − 1022 * result is the same as the argument.
+ − 1023 * </ul>
+ − 1024 *
+ − 1025 * @param f the floating-point value whose signum is to be returned
+ − 1026 * @return the signum function of the argument
+ − 1027 * @author Joseph D. Darcy
+ − 1028 * @since 1.5
+ − 1029 */
+ − 1030 public static float signum(float f) {
+ − 1031 return sun.misc.FpUtils.signum(f);
+ − 1032 }
+ − 1033
+ − 1034 /**
+ − 1035 * Returns the hyperbolic sine of a {@code double} value.
+ − 1036 * The hyperbolic sine of <i>x</i> is defined to be
+ − 1037 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2
+ − 1038 * where <i>e</i> is {@linkplain Math#E Euler's number}.
+ − 1039 *
+ − 1040 * <p>Special cases:
+ − 1041 * <ul>
+ − 1042 *
+ − 1043 * <li>If the argument is NaN, then the result is NaN.
+ − 1044 *
+ − 1045 * <li>If the argument is infinite, then the result is an infinity
+ − 1046 * with the same sign as the argument.
+ − 1047 *
+ − 1048 * <li>If the argument is zero, then the result is a zero with the
+ − 1049 * same sign as the argument.
+ − 1050 *
+ − 1051 * </ul>
+ − 1052 *
+ − 1053 * <p>The computed result must be within 2.5 ulps of the exact result.
+ − 1054 *
+ − 1055 * @param x The number whose hyperbolic sine is to be returned.
+ − 1056 * @return The hyperbolic sine of {@code x}.
+ − 1057 * @since 1.5
+ − 1058 */
+ − 1059 public static double sinh(double x) {
+ − 1060 return StrictMath.sinh(x);
+ − 1061 }
+ − 1062
+ − 1063 /**
+ − 1064 * Returns the hyperbolic cosine of a {@code double} value.
+ − 1065 * The hyperbolic cosine of <i>x</i> is defined to be
+ − 1066 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2
+ − 1067 * where <i>e</i> is {@linkplain Math#E Euler's number}.
+ − 1068 *
+ − 1069 * <p>Special cases:
+ − 1070 * <ul>
+ − 1071 *
+ − 1072 * <li>If the argument is NaN, then the result is NaN.
+ − 1073 *
+ − 1074 * <li>If the argument is infinite, then the result is positive
+ − 1075 * infinity.
+ − 1076 *
+ − 1077 * <li>If the argument is zero, then the result is {@code 1.0}.
+ − 1078 *
+ − 1079 * </ul>
+ − 1080 *
+ − 1081 * <p>The computed result must be within 2.5 ulps of the exact result.
+ − 1082 *
+ − 1083 * @param x The number whose hyperbolic cosine is to be returned.
+ − 1084 * @return The hyperbolic cosine of {@code x}.
+ − 1085 * @since 1.5
+ − 1086 */
+ − 1087 public static double cosh(double x) {
+ − 1088 return StrictMath.cosh(x);
+ − 1089 }
+ − 1090
+ − 1091 /**
+ − 1092 * Returns the hyperbolic tangent of a {@code double} value.
+ − 1093 * The hyperbolic tangent of <i>x</i> is defined to be
+ − 1094 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>),
+ − 1095 * in other words, {@linkplain Math#sinh
+ − 1096 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note
+ − 1097 * that the absolute value of the exact tanh is always less than
+ − 1098 * 1.
+ − 1099 *
+ − 1100 * <p>Special cases:
+ − 1101 * <ul>
+ − 1102 *
+ − 1103 * <li>If the argument is NaN, then the result is NaN.
+ − 1104 *
+ − 1105 * <li>If the argument is zero, then the result is a zero with the
+ − 1106 * same sign as the argument.
+ − 1107 *
+ − 1108 * <li>If the argument is positive infinity, then the result is
+ − 1109 * {@code +1.0}.
+ − 1110 *
+ − 1111 * <li>If the argument is negative infinity, then the result is
+ − 1112 * {@code -1.0}.
+ − 1113 *
+ − 1114 * </ul>
+ − 1115 *
+ − 1116 * <p>The computed result must be within 2.5 ulps of the exact result.
+ − 1117 * The result of {@code tanh} for any finite input must have
+ − 1118 * an absolute value less than or equal to 1. Note that once the
+ − 1119 * exact result of tanh is within 1/2 of an ulp of the limit value
+ − 1120 * of ±1, correctly signed ±{@code 1.0} should
+ − 1121 * be returned.
+ − 1122 *
+ − 1123 * @param x The number whose hyperbolic tangent is to be returned.
+ − 1124 * @return The hyperbolic tangent of {@code x}.
+ − 1125 * @since 1.5
+ − 1126 */
+ − 1127 public static double tanh(double x) {
+ − 1128 return StrictMath.tanh(x);
+ − 1129 }
+ − 1130
+ − 1131 /**
+ − 1132 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ − 1133 * without intermediate overflow or underflow.
+ − 1134 *
+ − 1135 * <p>Special cases:
+ − 1136 * <ul>
+ − 1137 *
+ − 1138 * <li> If either argument is infinite, then the result
+ − 1139 * is positive infinity.
+ − 1140 *
+ − 1141 * <li> If either argument is NaN and neither argument is infinite,
+ − 1142 * then the result is NaN.
+ − 1143 *
+ − 1144 * </ul>
+ − 1145 *
+ − 1146 * <p>The computed result must be within 1 ulp of the exact
+ − 1147 * result. If one parameter is held constant, the results must be
+ − 1148 * semi-monotonic in the other parameter.
+ − 1149 *
+ − 1150 * @param x a value
+ − 1151 * @param y a value
+ − 1152 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ − 1153 * without intermediate overflow or underflow
+ − 1154 * @since 1.5
+ − 1155 */
+ − 1156 public static double hypot(double x, double y) {
+ − 1157 return StrictMath.hypot(x, y);
+ − 1158 }
+ − 1159
+ − 1160 /**
+ − 1161 * Returns <i>e</i><sup>x</sup> -1. Note that for values of
+ − 1162 * <i>x</i> near 0, the exact sum of
+ − 1163 * {@code expm1(x)} + 1 is much closer to the true
+ − 1164 * result of <i>e</i><sup>x</sup> than {@code exp(x)}.
+ − 1165 *
+ − 1166 * <p>Special cases:
+ − 1167 * <ul>
+ − 1168 * <li>If the argument is NaN, the result is NaN.
+ − 1169 *
+ − 1170 * <li>If the argument is positive infinity, then the result is
+ − 1171 * positive infinity.
+ − 1172 *
+ − 1173 * <li>If the argument is negative infinity, then the result is
+ − 1174 * -1.0.
+ − 1175 *
+ − 1176 * <li>If the argument is zero, then the result is a zero with the
+ − 1177 * same sign as the argument.
+ − 1178 *
+ − 1179 * </ul>
+ − 1180 *
+ − 1181 * <p>The computed result must be within 1 ulp of the exact result.
+ − 1182 * Results must be semi-monotonic. The result of
+ − 1183 * {@code expm1} for any finite input must be greater than or
+ − 1184 * equal to {@code -1.0}. Note that once the exact result of
+ − 1185 * <i>e</i><sup>{@code x}</sup> - 1 is within 1/2
+ − 1186 * ulp of the limit value -1, {@code -1.0} should be
+ − 1187 * returned.
+ − 1188 *
+ − 1189 * @param x the exponent to raise <i>e</i> to in the computation of
+ − 1190 * <i>e</i><sup>{@code x}</sup> -1.
+ − 1191 * @return the value <i>e</i><sup>{@code x}</sup> - 1.
+ − 1192 * @since 1.5
+ − 1193 */
+ − 1194 public static double expm1(double x) {
+ − 1195 return StrictMath.expm1(x);
+ − 1196 }
+ − 1197
+ − 1198 /**
+ − 1199 * Returns the natural logarithm of the sum of the argument and 1.
+ − 1200 * Note that for small values {@code x}, the result of
+ − 1201 * {@code log1p(x)} is much closer to the true result of ln(1
+ − 1202 * + {@code x}) than the floating-point evaluation of
+ − 1203 * {@code log(1.0+x)}.
+ − 1204 *
+ − 1205 * <p>Special cases:
+ − 1206 *
+ − 1207 * <ul>
+ − 1208 *
+ − 1209 * <li>If the argument is NaN or less than -1, then the result is
+ − 1210 * NaN.
+ − 1211 *
+ − 1212 * <li>If the argument is positive infinity, then the result is
+ − 1213 * positive infinity.
+ − 1214 *
+ − 1215 * <li>If the argument is negative one, then the result is
+ − 1216 * negative infinity.
+ − 1217 *
+ − 1218 * <li>If the argument is zero, then the result is a zero with the
+ − 1219 * same sign as the argument.
+ − 1220 *
+ − 1221 * </ul>
+ − 1222 *
+ − 1223 * <p>The computed result must be within 1 ulp of the exact result.
+ − 1224 * Results must be semi-monotonic.
+ − 1225 *
+ − 1226 * @param x a value
+ − 1227 * @return the value ln({@code x} + 1), the natural
+ − 1228 * log of {@code x} + 1
+ − 1229 * @since 1.5
+ − 1230 */
+ − 1231 public static double log1p(double x) {
+ − 1232 return StrictMath.log1p(x);
+ − 1233 }
+ − 1234
+ − 1235 /**
+ − 1236 * Returns the first floating-point argument with the sign of the
+ − 1237 * second floating-point argument. Note that unlike the {@link
+ − 1238 * StrictMath#copySign(double, double) StrictMath.copySign}
+ − 1239 * method, this method does not require NaN {@code sign}
+ − 1240 * arguments to be treated as positive values; implementations are
+ − 1241 * permitted to treat some NaN arguments as positive and other NaN
+ − 1242 * arguments as negative to allow greater performance.
+ − 1243 *
+ − 1244 * @param magnitude the parameter providing the magnitude of the result
+ − 1245 * @param sign the parameter providing the sign of the result
+ − 1246 * @return a value with the magnitude of {@code magnitude}
+ − 1247 * and the sign of {@code sign}.
+ − 1248 * @since 1.6
+ − 1249 */
+ − 1250 public static double copySign(double magnitude, double sign) {
+ − 1251 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
+ − 1252 }
+ − 1253
+ − 1254 /**
+ − 1255 * Returns the first floating-point argument with the sign of the
+ − 1256 * second floating-point argument. Note that unlike the {@link
+ − 1257 * StrictMath#copySign(float, float) StrictMath.copySign}
+ − 1258 * method, this method does not require NaN {@code sign}
+ − 1259 * arguments to be treated as positive values; implementations are
+ − 1260 * permitted to treat some NaN arguments as positive and other NaN
+ − 1261 * arguments as negative to allow greater performance.
+ − 1262 *
+ − 1263 * @param magnitude the parameter providing the magnitude of the result
+ − 1264 * @param sign the parameter providing the sign of the result
+ − 1265 * @return a value with the magnitude of {@code magnitude}
+ − 1266 * and the sign of {@code sign}.
+ − 1267 * @since 1.6
+ − 1268 */
+ − 1269 public static float copySign(float magnitude, float sign) {
+ − 1270 return sun.misc.FpUtils.rawCopySign(magnitude, sign);
+ − 1271 }
+ − 1272
+ − 1273 /**
+ − 1274 * Returns the unbiased exponent used in the representation of a
+ − 1275 * {@code float}. Special cases:
+ − 1276 *
+ − 1277 * <ul>
+ − 1278 * <li>If the argument is NaN or infinite, then the result is
+ − 1279 * {@link Float#MAX_EXPONENT} + 1.
+ − 1280 * <li>If the argument is zero or subnormal, then the result is
+ − 1281 * {@link Float#MIN_EXPONENT} -1.
+ − 1282 * </ul>
+ − 1283 * @param f a {@code float} value
+ − 1284 * @return the unbiased exponent of the argument
+ − 1285 * @since 1.6
+ − 1286 */
+ − 1287 public static int getExponent(float f) {
+ − 1288 return sun.misc.FpUtils.getExponent(f);
+ − 1289 }
+ − 1290
+ − 1291 /**
+ − 1292 * Returns the unbiased exponent used in the representation of a
+ − 1293 * {@code double}. Special cases:
+ − 1294 *
+ − 1295 * <ul>
+ − 1296 * <li>If the argument is NaN or infinite, then the result is
+ − 1297 * {@link Double#MAX_EXPONENT} + 1.
+ − 1298 * <li>If the argument is zero or subnormal, then the result is
+ − 1299 * {@link Double#MIN_EXPONENT} -1.
+ − 1300 * </ul>
+ − 1301 * @param d a {@code double} value
+ − 1302 * @return the unbiased exponent of the argument
+ − 1303 * @since 1.6
+ − 1304 */
+ − 1305 public static int getExponent(double d) {
+ − 1306 return sun.misc.FpUtils.getExponent(d);
+ − 1307 }
+ − 1308
+ − 1309 /**
+ − 1310 * Returns the floating-point number adjacent to the first
+ − 1311 * argument in the direction of the second argument. If both
+ − 1312 * arguments compare as equal the second argument is returned.
+ − 1313 *
+ − 1314 * <p>
+ − 1315 * Special cases:
+ − 1316 * <ul>
+ − 1317 * <li> If either argument is a NaN, then NaN is returned.
+ − 1318 *
+ − 1319 * <li> If both arguments are signed zeros, {@code direction}
+ − 1320 * is returned unchanged (as implied by the requirement of
+ − 1321 * returning the second argument if the arguments compare as
+ − 1322 * equal).
+ − 1323 *
+ − 1324 * <li> If {@code start} is
+ − 1325 * ±{@link Double#MIN_VALUE} and {@code direction}
+ − 1326 * has a value such that the result should have a smaller
+ − 1327 * magnitude, then a zero with the same sign as {@code start}
+ − 1328 * is returned.
+ − 1329 *
+ − 1330 * <li> If {@code start} is infinite and
+ − 1331 * {@code direction} has a value such that the result should
+ − 1332 * have a smaller magnitude, {@link Double#MAX_VALUE} with the
+ − 1333 * same sign as {@code start} is returned.
+ − 1334 *
+ − 1335 * <li> If {@code start} is equal to ±
+ − 1336 * {@link Double#MAX_VALUE} and {@code direction} has a
+ − 1337 * value such that the result should have a larger magnitude, an
+ − 1338 * infinity with same sign as {@code start} is returned.
+ − 1339 * </ul>
+ − 1340 *
+ − 1341 * @param start starting floating-point value
+ − 1342 * @param direction value indicating which of
+ − 1343 * {@code start}'s neighbors or {@code start} should
+ − 1344 * be returned
+ − 1345 * @return The floating-point number adjacent to {@code start} in the
+ − 1346 * direction of {@code direction}.
+ − 1347 * @since 1.6
+ − 1348 */
+ − 1349 public static double nextAfter(double start, double direction) {
+ − 1350 return sun.misc.FpUtils.nextAfter(start, direction);
+ − 1351 }
+ − 1352
+ − 1353 /**
+ − 1354 * Returns the floating-point number adjacent to the first
+ − 1355 * argument in the direction of the second argument. If both
+ − 1356 * arguments compare as equal a value equivalent to the second argument
+ − 1357 * is returned.
+ − 1358 *
+ − 1359 * <p>
+ − 1360 * Special cases:
+ − 1361 * <ul>
+ − 1362 * <li> If either argument is a NaN, then NaN is returned.
+ − 1363 *
+ − 1364 * <li> If both arguments are signed zeros, a value equivalent
+ − 1365 * to {@code direction} is returned.
+ − 1366 *
+ − 1367 * <li> If {@code start} is
+ − 1368 * ±{@link Float#MIN_VALUE} and {@code direction}
+ − 1369 * has a value such that the result should have a smaller
+ − 1370 * magnitude, then a zero with the same sign as {@code start}
+ − 1371 * is returned.
+ − 1372 *
+ − 1373 * <li> If {@code start} is infinite and
+ − 1374 * {@code direction} has a value such that the result should
+ − 1375 * have a smaller magnitude, {@link Float#MAX_VALUE} with the
+ − 1376 * same sign as {@code start} is returned.
+ − 1377 *
+ − 1378 * <li> If {@code start} is equal to ±
+ − 1379 * {@link Float#MAX_VALUE} and {@code direction} has a
+ − 1380 * value such that the result should have a larger magnitude, an
+ − 1381 * infinity with same sign as {@code start} is returned.
+ − 1382 * </ul>
+ − 1383 *
+ − 1384 * @param start starting floating-point value
+ − 1385 * @param direction value indicating which of
+ − 1386 * {@code start}'s neighbors or {@code start} should
+ − 1387 * be returned
+ − 1388 * @return The floating-point number adjacent to {@code start} in the
+ − 1389 * direction of {@code direction}.
+ − 1390 * @since 1.6
+ − 1391 */
+ − 1392 public static float nextAfter(float start, double direction) {
+ − 1393 return sun.misc.FpUtils.nextAfter(start, direction);
+ − 1394 }
+ − 1395
+ − 1396 /**
+ − 1397 * Returns the floating-point value adjacent to {@code d} in
+ − 1398 * the direction of positive infinity. This method is
+ − 1399 * semantically equivalent to {@code nextAfter(d,
+ − 1400 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp}
+ − 1401 * implementation may run faster than its equivalent
+ − 1402 * {@code nextAfter} call.
+ − 1403 *
+ − 1404 * <p>Special Cases:
+ − 1405 * <ul>
+ − 1406 * <li> If the argument is NaN, the result is NaN.
+ − 1407 *
+ − 1408 * <li> If the argument is positive infinity, the result is
+ − 1409 * positive infinity.
+ − 1410 *
+ − 1411 * <li> If the argument is zero, the result is
+ − 1412 * {@link Double#MIN_VALUE}
+ − 1413 *
+ − 1414 * </ul>
+ − 1415 *
+ − 1416 * @param d starting floating-point value
+ − 1417 * @return The adjacent floating-point value closer to positive
+ − 1418 * infinity.
+ − 1419 * @since 1.6
+ − 1420 */
+ − 1421 public static double nextUp(double d) {
+ − 1422 return sun.misc.FpUtils.nextUp(d);
+ − 1423 }
+ − 1424
+ − 1425 /**
+ − 1426 * Returns the floating-point value adjacent to {@code f} in
+ − 1427 * the direction of positive infinity. This method is
+ − 1428 * semantically equivalent to {@code nextAfter(f,
+ − 1429 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp}
+ − 1430 * implementation may run faster than its equivalent
+ − 1431 * {@code nextAfter} call.
+ − 1432 *
+ − 1433 * <p>Special Cases:
+ − 1434 * <ul>
+ − 1435 * <li> If the argument is NaN, the result is NaN.
+ − 1436 *
+ − 1437 * <li> If the argument is positive infinity, the result is
+ − 1438 * positive infinity.
+ − 1439 *
+ − 1440 * <li> If the argument is zero, the result is
+ − 1441 * {@link Float#MIN_VALUE}
+ − 1442 *
+ − 1443 * </ul>
+ − 1444 *
+ − 1445 * @param f starting floating-point value
+ − 1446 * @return The adjacent floating-point value closer to positive
+ − 1447 * infinity.
+ − 1448 * @since 1.6
+ − 1449 */
+ − 1450 public static float nextUp(float f) {
+ − 1451 return sun.misc.FpUtils.nextUp(f);
+ − 1452 }
+ − 1453
+ − 1454
+ − 1455 /**
+ − 1456 * Return {@code d} ×
+ − 1457 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
+ − 1458 * by a single correctly rounded floating-point multiply to a
+ − 1459 * member of the double value set. See the Java
+ − 1460 * Language Specification for a discussion of floating-point
+ − 1461 * value sets. If the exponent of the result is between {@link
+ − 1462 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the
+ − 1463 * answer is calculated exactly. If the exponent of the result
+ − 1464 * would be larger than {@code Double.MAX_EXPONENT}, an
+ − 1465 * infinity is returned. Note that if the result is subnormal,
+ − 1466 * precision may be lost; that is, when {@code scalb(x, n)}
+ − 1467 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
+ − 1468 * <i>x</i>. When the result is non-NaN, the result has the same
+ − 1469 * sign as {@code d}.
+ − 1470 *
+ − 1471 * <p>Special cases:
+ − 1472 * <ul>
+ − 1473 * <li> If the first argument is NaN, NaN is returned.
+ − 1474 * <li> If the first argument is infinite, then an infinity of the
+ − 1475 * same sign is returned.
+ − 1476 * <li> If the first argument is zero, then a zero of the same
+ − 1477 * sign is returned.
+ − 1478 * </ul>
+ − 1479 *
+ − 1480 * @param d number to be scaled by a power of two.
+ − 1481 * @param scaleFactor power of 2 used to scale {@code d}
+ − 1482 * @return {@code d} × 2<sup>{@code scaleFactor}</sup>
+ − 1483 * @since 1.6
+ − 1484 */
+ − 1485 public static double scalb(double d, int scaleFactor) {
+ − 1486 return sun.misc.FpUtils.scalb(d, scaleFactor);
+ − 1487 }
+ − 1488
+ − 1489 /**
+ − 1490 * Return {@code f} ×
+ − 1491 * 2<sup>{@code scaleFactor}</sup> rounded as if performed
+ − 1492 * by a single correctly rounded floating-point multiply to a
+ − 1493 * member of the float value set. See the Java
+ − 1494 * Language Specification for a discussion of floating-point
+ − 1495 * value sets. If the exponent of the result is between {@link
+ − 1496 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the
+ − 1497 * answer is calculated exactly. If the exponent of the result
+ − 1498 * would be larger than {@code Float.MAX_EXPONENT}, an
+ − 1499 * infinity is returned. Note that if the result is subnormal,
+ − 1500 * precision may be lost; that is, when {@code scalb(x, n)}
+ − 1501 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal
+ − 1502 * <i>x</i>. When the result is non-NaN, the result has the same
+ − 1503 * sign as {@code f}.
+ − 1504 *
+ − 1505 * <p>Special cases:
+ − 1506 * <ul>
+ − 1507 * <li> If the first argument is NaN, NaN is returned.
+ − 1508 * <li> If the first argument is infinite, then an infinity of the
+ − 1509 * same sign is returned.
+ − 1510 * <li> If the first argument is zero, then a zero of the same
+ − 1511 * sign is returned.
+ − 1512 * </ul>
+ − 1513 *
+ − 1514 * @param f number to be scaled by a power of two.
+ − 1515 * @param scaleFactor power of 2 used to scale {@code f}
+ − 1516 * @return {@code f} × 2<sup>{@code scaleFactor}</sup>
+ − 1517 * @since 1.6
+ − 1518 */
+ − 1519 public static float scalb(float f, int scaleFactor) {
+ − 1520 return sun.misc.FpUtils.scalb(f, scaleFactor);
+ − 1521 }
+ − 1522 }