1 /* 2 * Copyright (c) 1999, 2013, Oracle and/or its affiliates. All rights reserved. 3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. 4 * 5 * This code is free software; you can redistribute it and/or modify it 6 * under the terms of the GNU General Public License version 2 only, as 7 * published by the Free Software Foundation. Oracle designates this 8 * particular file as subject to the "Classpath" exception as provided 9 * by Oracle in the LICENSE file that accompanied this code. 10 * 11 * This code is distributed in the hope that it will be useful, but WITHOUT 12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 14 * version 2 for more details (a copy is included in the LICENSE file that 15 * accompanied this code). 16 * 17 * You should have received a copy of the GNU General Public License version 18 * 2 along with this work; if not, write to the Free Software Foundation, 19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. 20 * 21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA 22 * or visit www.oracle.com if you need additional information or have any 23 * questions. 24 */ 25 26 package java.lang; 27 import java.util.Random; 28 import sun.misc.FpUtils; 29 import sun.misc.DoubleConsts; 30 31 /** 32 * The class {@code StrictMath} contains methods for performing basic 33 * numeric operations such as the elementary exponential, logarithm, 34 * square root, and trigonometric functions. 35 * 36 * <p>To help ensure portability of Java programs, the definitions of 37 * some of the numeric functions in this package require that they 38 * produce the same results as certain published algorithms. These 39 * algorithms are available from the well-known network library 40 * {@code netlib} as the package "Freely Distributable Math 41 * Library," <a 42 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These 43 * algorithms, which are written in the C programming language, are 44 * then to be understood as executed with all floating-point 45 * operations following the rules of Java floating-point arithmetic. 46 * 47 * <p>The Java math library is defined with respect to 48 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides 49 * more than one definition for a function (such as 50 * {@code acos}), use the "IEEE 754 core function" version 51 * (residing in a file whose name begins with the letter 52 * {@code e}). The methods which require {@code fdlibm} 53 * semantics are {@code sin}, {@code cos}, {@code tan}, 54 * {@code asin}, {@code acos}, {@code atan}, 55 * {@code exp}, {@code log}, {@code log10}, 56 * {@code cbrt}, {@code atan2}, {@code pow}, 57 * {@code sinh}, {@code cosh}, {@code tanh}, 58 * {@code hypot}, {@code expm1}, and {@code log1p}. 59 * 60 * @author unascribed 61 * @author Joseph D. Darcy 62 * @since 1.3 63 */ 64 65 public final class StrictMath { 66 67 /** 68 * Don't let anyone instantiate this class. 69 */ StrictMath()70 private StrictMath() {} 71 72 /** 73 * The {@code double} value that is closer than any other to 74 * <i>e</i>, the base of the natural logarithms. 75 */ 76 public static final double E = 2.7182818284590452354; 77 78 /** 79 * The {@code double} value that is closer than any other to 80 * <i>pi</i>, the ratio of the circumference of a circle to its 81 * diameter. 82 */ 83 public static final double PI = 3.14159265358979323846; 84 85 /** 86 * Returns the trigonometric sine of an angle. Special cases: 87 * <ul><li>If the argument is NaN or an infinity, then the 88 * result is NaN. 89 * <li>If the argument is zero, then the result is a zero with the 90 * same sign as the argument.</ul> 91 * 92 * @param a an angle, in radians. 93 * @return the sine of the argument. 94 */ sin(double a)95 public static native double sin(double a); 96 97 /** 98 * Returns the trigonometric cosine of an angle. Special cases: 99 * <ul><li>If the argument is NaN or an infinity, then the 100 * result is NaN.</ul> 101 * 102 * @param a an angle, in radians. 103 * @return the cosine of the argument. 104 */ cos(double a)105 public static native double cos(double a); 106 107 /** 108 * Returns the trigonometric tangent of an angle. Special cases: 109 * <ul><li>If the argument is NaN or an infinity, then the result 110 * 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 * @param a an angle, in radians. 115 * @return the tangent of the argument. 116 */ tan(double a)117 public static native double tan(double a); 118 119 /** 120 * Returns the arc sine of a value; the returned angle is in the 121 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: 122 * <ul><li>If the argument is NaN or its absolute value is greater 123 * than 1, then the result is NaN. 124 * <li>If the argument is zero, then the result is a zero with the 125 * same sign as the argument.</ul> 126 * 127 * @param a the value whose arc sine is to be returned. 128 * @return the arc sine of the argument. 129 */ asin(double a)130 public static native double asin(double a); 131 132 /** 133 * Returns the arc cosine of a value; the returned angle is in the 134 * range 0.0 through <i>pi</i>. Special case: 135 * <ul><li>If the argument is NaN or its absolute value is greater 136 * than 1, then the result is NaN.</ul> 137 * 138 * @param a the value whose arc cosine is to be returned. 139 * @return the arc cosine of the argument. 140 */ acos(double a)141 public static native double acos(double a); 142 143 /** 144 * Returns the arc tangent of a value; the returned angle is in the 145 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: 146 * <ul><li>If the argument is NaN, then the result is NaN. 147 * <li>If the argument is zero, then the result is a zero with the 148 * same sign as the argument.</ul> 149 * 150 * @param a the value whose arc tangent is to be returned. 151 * @return the arc tangent of the argument. 152 */ atan(double a)153 public static native double atan(double a); 154 155 /** 156 * Converts an angle measured in degrees to an approximately 157 * equivalent angle measured in radians. The conversion from 158 * degrees to radians is generally inexact. 159 * 160 * @param angdeg an angle, in degrees 161 * @return the measurement of the angle {@code angdeg} 162 * in radians. 163 */ toRadians(double angdeg)164 public static strictfp double toRadians(double angdeg) { 165 return angdeg / 180.0 * PI; 166 } 167 168 /** 169 * Converts an angle measured in radians to an approximately 170 * equivalent angle measured in degrees. The conversion from 171 * radians to degrees is generally inexact; users should 172 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly 173 * equal {@code 0.0}. 174 * 175 * @param angrad an angle, in radians 176 * @return the measurement of the angle {@code angrad} 177 * in degrees. 178 */ toDegrees(double angrad)179 public static strictfp double toDegrees(double angrad) { 180 return angrad * 180.0 / PI; 181 } 182 183 /** 184 * Returns Euler's number <i>e</i> raised to the power of a 185 * {@code double} value. Special cases: 186 * <ul><li>If the argument is NaN, the result is NaN. 187 * <li>If the argument is positive infinity, then the result is 188 * positive infinity. 189 * <li>If the argument is negative infinity, then the result is 190 * positive zero.</ul> 191 * 192 * @param a the exponent to raise <i>e</i> to. 193 * @return the value <i>e</i><sup>{@code a}</sup>, 194 * where <i>e</i> is the base of the natural logarithms. 195 */ exp(double a)196 public static native double exp(double a); 197 198 /** 199 * Returns the natural logarithm (base <i>e</i>) of a {@code double} 200 * value. Special cases: 201 * <ul><li>If the argument is NaN or less than zero, then the result 202 * is NaN. 203 * <li>If the argument is positive infinity, then the result is 204 * positive infinity. 205 * <li>If the argument is positive zero or negative zero, then the 206 * result is negative infinity.</ul> 207 * 208 * @param a a value 209 * @return the value ln {@code a}, the natural logarithm of 210 * {@code a}. 211 */ log(double a)212 public static native double log(double a); 213 214 215 /** 216 * Returns the base 10 logarithm of a {@code double} value. 217 * Special cases: 218 * 219 * <ul><li>If the argument is NaN or less than zero, then the result 220 * is NaN. 221 * <li>If the argument is positive infinity, then the result is 222 * positive infinity. 223 * <li>If the argument is positive zero or negative zero, then the 224 * result is negative infinity. 225 * <li> If the argument is equal to 10<sup><i>n</i></sup> for 226 * integer <i>n</i>, then the result is <i>n</i>. 227 * </ul> 228 * 229 * @param a a value 230 * @return the base 10 logarithm of {@code a}. 231 * @since 1.5 232 */ log10(double a)233 public static native double log10(double a); 234 235 /** 236 * Returns the correctly rounded positive square root of a 237 * {@code double} value. 238 * Special cases: 239 * <ul><li>If the argument is NaN or less than zero, then the result 240 * is NaN. 241 * <li>If the argument is positive infinity, then the result is positive 242 * infinity. 243 * <li>If the argument is positive zero or negative zero, then the 244 * result is the same as the argument.</ul> 245 * Otherwise, the result is the {@code double} value closest to 246 * the true mathematical square root of the argument value. 247 * 248 * @param a a value. 249 * @return the positive square root of {@code a}. 250 */ sqrt(double a)251 public static native double sqrt(double a); 252 253 /** 254 * Returns the cube root of a {@code double} value. For 255 * positive finite {@code x}, {@code cbrt(-x) == 256 * -cbrt(x)}; that is, the cube root of a negative value is 257 * the negative of the cube root of that value's magnitude. 258 * Special cases: 259 * 260 * <ul> 261 * 262 * <li>If the argument is NaN, then the result is NaN. 263 * 264 * <li>If the argument is infinite, then the result is an infinity 265 * with the same sign as the argument. 266 * 267 * <li>If the argument is zero, then the result is a zero with the 268 * same sign as the argument. 269 * 270 * </ul> 271 * 272 * @param a a value. 273 * @return the cube root of {@code a}. 274 * @since 1.5 275 */ cbrt(double a)276 public static native double cbrt(double a); 277 278 /** 279 * Computes the remainder operation on two arguments as prescribed 280 * by the IEEE 754 standard. 281 * The remainder value is mathematically equal to 282 * <code>f1 - f2</code> × <i>n</i>, 283 * where <i>n</i> is the mathematical integer closest to the exact 284 * mathematical value of the quotient {@code f1/f2}, and if two 285 * mathematical integers are equally close to {@code f1/f2}, 286 * then <i>n</i> is the integer that is even. If the remainder is 287 * zero, its sign is the same as the sign of the first argument. 288 * Special cases: 289 * <ul><li>If either argument is NaN, or the first argument is infinite, 290 * or the second argument is positive zero or negative zero, then the 291 * result is NaN. 292 * <li>If the first argument is finite and the second argument is 293 * infinite, then the result is the same as the first argument.</ul> 294 * 295 * @param f1 the dividend. 296 * @param f2 the divisor. 297 * @return the remainder when {@code f1} is divided by 298 * {@code f2}. 299 */ IEEEremainder(double f1, double f2)300 public static native double IEEEremainder(double f1, double f2); 301 302 /** 303 * Returns the smallest (closest to negative infinity) 304 * {@code double} value that is greater than or equal to the 305 * argument and is equal to a mathematical integer. Special cases: 306 * <ul><li>If the argument value is already equal to a 307 * mathematical integer, then the result is the same as the 308 * argument. <li>If the argument is NaN or an infinity or 309 * positive zero or negative zero, then the result is the same as 310 * the argument. <li>If the argument value is less than zero but 311 * greater than -1.0, then the result is negative zero.</ul> Note 312 * that the value of {@code StrictMath.ceil(x)} is exactly the 313 * value of {@code -StrictMath.floor(-x)}. 314 * 315 * @param a a value. 316 * @return the smallest (closest to negative infinity) 317 * floating-point value that is greater than or equal to 318 * the argument and is equal to a mathematical integer. 319 */ ceil(double a)320 public static double ceil(double a) { 321 return floorOrCeil(a, -0.0, 1.0, 1.0); 322 } 323 324 /** 325 * Returns the largest (closest to positive infinity) 326 * {@code double} value that is less than or equal to the 327 * argument and is equal to a mathematical integer. Special cases: 328 * <ul><li>If the argument value is already equal to a 329 * mathematical integer, then the result is the same as the 330 * argument. <li>If the argument is NaN or an infinity or 331 * positive zero or negative zero, then the result is the same as 332 * the argument.</ul> 333 * 334 * @param a a value. 335 * @return the largest (closest to positive infinity) 336 * floating-point value that less than or equal to the argument 337 * and is equal to a mathematical integer. 338 */ floor(double a)339 public static double floor(double a) { 340 return floorOrCeil(a, -1.0, 0.0, -1.0); 341 } 342 343 /** 344 * Internal method to share logic between floor and ceil. 345 * 346 * @param a the value to be floored or ceiled 347 * @param negativeBoundary result for values in (-1, 0) 348 * @param positiveBoundary result for values in (0, 1) 349 * @param increment value to add when the argument is non-integral 350 */ floorOrCeil(double a, double negativeBoundary, double positiveBoundary, double sign)351 private static double floorOrCeil(double a, 352 double negativeBoundary, 353 double positiveBoundary, 354 double sign) { 355 int exponent = Math.getExponent(a); 356 357 if (exponent < 0) { 358 /* 359 * Absolute value of argument is less than 1. 360 * floorOrceil(-0.0) => -0.0 361 * floorOrceil(+0.0) => +0.0 362 */ 363 return ((a == 0.0) ? a : 364 ( (a < 0.0) ? negativeBoundary : positiveBoundary) ); 365 } else if (exponent >= 52) { 366 /* 367 * Infinity, NaN, or a value so large it must be integral. 368 */ 369 return a; 370 } 371 // Else the argument is either an integral value already XOR it 372 // has to be rounded to one. 373 assert exponent >= 0 && exponent <= 51; 374 375 long doppel = Double.doubleToRawLongBits(a); 376 long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent; 377 378 if ( (mask & doppel) == 0L ) 379 return a; // integral value 380 else { 381 double result = Double.longBitsToDouble(doppel & (~mask)); 382 if (sign*a > 0.0) 383 result = result + sign; 384 return result; 385 } 386 } 387 388 /** 389 * Returns the {@code double} value that is closest in value 390 * to the argument and is equal to a mathematical integer. If two 391 * {@code double} values that are mathematical integers are 392 * equally close to the value of the argument, the result is the 393 * integer value that is even. Special cases: 394 * <ul><li>If the argument value is already equal to a mathematical 395 * integer, then the result is the same as the argument. 396 * <li>If the argument is NaN or an infinity or positive zero or negative 397 * zero, then the result is the same as the argument.</ul> 398 * 399 * @param a a value. 400 * @return the closest floating-point value to {@code a} that is 401 * equal to a mathematical integer. 402 * @author Joseph D. Darcy 403 */ rint(double a)404 public static double rint(double a) { 405 /* 406 * If the absolute value of a is not less than 2^52, it 407 * is either a finite integer (the double format does not have 408 * enough significand bits for a number that large to have any 409 * fractional portion), an infinity, or a NaN. In any of 410 * these cases, rint of the argument is the argument. 411 * 412 * Otherwise, the sum (twoToThe52 + a ) will properly round 413 * away any fractional portion of a since ulp(twoToThe52) == 414 * 1.0; subtracting out twoToThe52 from this sum will then be 415 * exact and leave the rounded integer portion of a. 416 * 417 * This method does *not* need to be declared strictfp to get 418 * fully reproducible results. Whether or not a method is 419 * declared strictfp can only make a difference in the 420 * returned result if some operation would overflow or 421 * underflow with strictfp semantics. The operation 422 * (twoToThe52 + a ) cannot overflow since large values of a 423 * are screened out; the add cannot underflow since twoToThe52 424 * is too large. The subtraction ((twoToThe52 + a ) - 425 * twoToThe52) will be exact as discussed above and thus 426 * cannot overflow or meaningfully underflow. Finally, the 427 * last multiply in the return statement is by plus or minus 428 * 1.0, which is exact too. 429 */ 430 double twoToThe52 = (double)(1L << 52); // 2^52 431 double sign = FpUtils.rawCopySign(1.0, a); // preserve sign info 432 a = Math.abs(a); 433 434 if (a < twoToThe52) { // E_min <= ilogb(a) <= 51 435 a = ((twoToThe52 + a ) - twoToThe52); 436 } 437 438 return sign * a; // restore original sign 439 } 440 441 /** 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 447 * cases: 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 452 * zero. 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> 482 * 483 * @param y the ordinate coordinate 484 * @param x the abscissa coordinate 485 * @return the <i>theta</i> component of the point 486 * (<i>r</i>, <i>theta</i>) 487 * in polar coordinates that corresponds to the point 488 * (<i>x</i>, <i>y</i>) in Cartesian coordinates. 489 */ atan2(double y, double x)490 public static native double atan2(double y, double x); 491 492 493 /** 494 * Returns the value of the first argument raised to the power of the 495 * second argument. Special cases: 496 * 497 * <ul><li>If the second argument is positive or negative zero, then the 498 * result is 1.0. 499 * <li>If the second argument is 1.0, then the result is the same as the 500 * first argument. 501 * <li>If the second argument is NaN, then the result is NaN. 502 * <li>If the first argument is NaN and the second argument is nonzero, 503 * then the result is NaN. 504 * 505 * <li>If 506 * <ul> 507 * <li>the absolute value of the first argument is greater than 1 508 * and the second argument is positive infinity, or 509 * <li>the absolute value of the first argument is less than 1 and 510 * the second argument is negative infinity, 511 * </ul> 512 * then the result is positive infinity. 513 * 514 * <li>If 515 * <ul> 516 * <li>the absolute value of the first argument is greater than 1 and 517 * the second argument is negative infinity, or 518 * <li>the absolute value of the 519 * first argument is less than 1 and the second argument is positive 520 * infinity, 521 * </ul> 522 * then the result is positive zero. 523 * 524 * <li>If the absolute value of the first argument equals 1 and the 525 * second argument is infinite, then the result is NaN. 526 * 527 * <li>If 528 * <ul> 529 * <li>the first argument is positive zero and the second argument 530 * is greater than zero, or 531 * <li>the first argument is positive infinity and the second 532 * argument is less than zero, 533 * </ul> 534 * then the result is positive zero. 535 * 536 * <li>If 537 * <ul> 538 * <li>the first argument is positive zero and the second argument 539 * is less than zero, or 540 * <li>the first argument is positive infinity and the second 541 * argument is greater than zero, 542 * </ul> 543 * then the result is positive infinity. 544 * 545 * <li>If 546 * <ul> 547 * <li>the first argument is negative zero and the second argument 548 * is greater than zero but not a finite odd integer, or 549 * <li>the first argument is negative infinity and the second 550 * argument is less than zero but not a finite odd integer, 551 * </ul> 552 * then the result is positive zero. 553 * 554 * <li>If 555 * <ul> 556 * <li>the first argument is negative zero and the second argument 557 * is a positive finite odd integer, or 558 * <li>the first argument is negative infinity and the second 559 * argument is a negative finite odd integer, 560 * </ul> 561 * then the result is negative zero. 562 * 563 * <li>If 564 * <ul> 565 * <li>the first argument is negative zero and the second argument 566 * is less than zero but not a finite odd integer, or 567 * <li>the first argument is negative infinity and the second 568 * argument is greater than zero but not a finite odd integer, 569 * </ul> 570 * then the result is positive infinity. 571 * 572 * <li>If 573 * <ul> 574 * <li>the first argument is negative zero and the second argument 575 * is a negative finite odd integer, or 576 * <li>the first argument is negative infinity and the second 577 * argument is a positive finite odd integer, 578 * </ul> 579 * then the result is negative infinity. 580 * 581 * <li>If the first argument is finite and less than zero 582 * <ul> 583 * <li> if the second argument is a finite even integer, the 584 * result is equal to the result of raising the absolute value of 585 * the first argument to the power of the second argument 586 * 587 * <li>if the second argument is a finite odd integer, the result 588 * is equal to the negative of the result of raising the absolute 589 * value of the first argument to the power of the second 590 * argument 591 * 592 * <li>if the second argument is finite and not an integer, then 593 * the result is NaN. 594 * </ul> 595 * 596 * <li>If both arguments are integers, then the result is exactly equal 597 * to the mathematical result of raising the first argument to the power 598 * of the second argument if that result can in fact be represented 599 * exactly as a {@code double} value.</ul> 600 * 601 * <p>(In the foregoing descriptions, a floating-point value is 602 * considered to be an integer if and only if it is finite and a 603 * fixed point of the method {@link #ceil ceil} or, 604 * equivalently, a fixed point of the method {@link #floor 605 * floor}. A value is a fixed point of a one-argument 606 * method if and only if the result of applying the method to the 607 * value is equal to the value.) 608 * 609 * @param a base. 610 * @param b the exponent. 611 * @return the value {@code a}<sup>{@code b}</sup>. 612 */ pow(double a, double b)613 public static native double pow(double a, double b); 614 615 /** 616 * Returns the closest {@code int} to the argument, with ties 617 * rounding to positive infinity. 618 * 619 * <p>Special cases: 620 * <ul><li>If the argument is NaN, the result is 0. 621 * <li>If the argument is negative infinity or any value less than or 622 * equal to the value of {@code Integer.MIN_VALUE}, the result is 623 * equal to the value of {@code Integer.MIN_VALUE}. 624 * <li>If the argument is positive infinity or any value greater than or 625 * equal to the value of {@code Integer.MAX_VALUE}, the result is 626 * equal to the value of {@code Integer.MAX_VALUE}.</ul> 627 * 628 * @param a a floating-point value to be rounded to an integer. 629 * @return the value of the argument rounded to the nearest 630 * {@code int} value. 631 * @see java.lang.Integer#MAX_VALUE 632 * @see java.lang.Integer#MIN_VALUE 633 */ round(float a)634 public static int round(float a) { 635 return Math.round(a); 636 } 637 638 /** 639 * Returns the closest {@code long} to the argument, with ties 640 * rounding to positive infinity. 641 * 642 * <p>Special cases: 643 * <ul><li>If the argument is NaN, the result is 0. 644 * <li>If the argument is negative infinity or any value less than or 645 * equal to the value of {@code Long.MIN_VALUE}, the result is 646 * equal to the value of {@code Long.MIN_VALUE}. 647 * <li>If the argument is positive infinity or any value greater than or 648 * equal to the value of {@code Long.MAX_VALUE}, the result is 649 * equal to the value of {@code Long.MAX_VALUE}.</ul> 650 * 651 * @param a a floating-point value to be rounded to a 652 * {@code long}. 653 * @return the value of the argument rounded to the nearest 654 * {@code long} value. 655 * @see java.lang.Long#MAX_VALUE 656 * @see java.lang.Long#MIN_VALUE 657 */ round(double a)658 public static long round(double a) { 659 return Math.round(a); 660 } 661 662 private static Random randomNumberGenerator; 663 initRNG()664 private static synchronized Random initRNG() { 665 Random rnd = randomNumberGenerator; 666 return (rnd == null) ? (randomNumberGenerator = new Random()) : rnd; 667 } 668 669 /** 670 * Returns a {@code double} value with a positive sign, greater 671 * than or equal to {@code 0.0} and less than {@code 1.0}. 672 * Returned values are chosen pseudorandomly with (approximately) 673 * uniform distribution from that range. 674 * 675 * <p>When this method is first called, it creates a single new 676 * pseudorandom-number generator, exactly as if by the expression 677 * 678 * <blockquote>{@code new java.util.Random()}</blockquote> 679 * 680 * This new pseudorandom-number generator is used thereafter for 681 * all calls to this method and is used nowhere else. 682 * 683 * <p>This method is properly synchronized to allow correct use by 684 * more than one thread. However, if many threads need to generate 685 * pseudorandom numbers at a great rate, it may reduce contention 686 * for each thread to have its own pseudorandom number generator. 687 * 688 * @return a pseudorandom {@code double} greater than or equal 689 * to {@code 0.0} and less than {@code 1.0}. 690 * @see Random#nextDouble() 691 */ random()692 public static double random() { 693 Random rnd = randomNumberGenerator; 694 if (rnd == null) rnd = initRNG(); 695 return rnd.nextDouble(); 696 } 697 698 /** 699 * Returns the sum of its arguments, 700 * throwing an exception if the result overflows an {@code int}. 701 * 702 * @param x the first value 703 * @param y the second value 704 * @return the result 705 * @throws ArithmeticException if the result overflows an int 706 * @see Math#addExact(int,int) 707 * @since 1.8 708 */ addExact(int x, int y)709 public static int addExact(int x, int y) { 710 return Math.addExact(x, y); 711 } 712 713 /** 714 * Returns the sum of its arguments, 715 * throwing an exception if the result overflows a {@code long}. 716 * 717 * @param x the first value 718 * @param y the second value 719 * @return the result 720 * @throws ArithmeticException if the result overflows a long 721 * @see Math#addExact(long,long) 722 * @since 1.8 723 */ addExact(long x, long y)724 public static long addExact(long x, long y) { 725 return Math.addExact(x, y); 726 } 727 728 /** 729 * Returns the difference of the arguments, 730 * throwing an exception if the result overflows an {@code int}. 731 * 732 * @param x the first value 733 * @param y the second value to subtract from the first 734 * @return the result 735 * @throws ArithmeticException if the result overflows an int 736 * @see Math#subtractExact(int,int) 737 * @since 1.8 738 */ subtractExact(int x, int y)739 public static int subtractExact(int x, int y) { 740 return Math.subtractExact(x, y); 741 } 742 743 /** 744 * Returns the difference of the arguments, 745 * throwing an exception if the result overflows a {@code long}. 746 * 747 * @param x the first value 748 * @param y the second value to subtract from the first 749 * @return the result 750 * @throws ArithmeticException if the result overflows a long 751 * @see Math#subtractExact(long,long) 752 * @since 1.8 753 */ subtractExact(long x, long y)754 public static long subtractExact(long x, long y) { 755 return Math.subtractExact(x, y); 756 } 757 758 /** 759 * Returns the product of the arguments, 760 * throwing an exception if the result overflows an {@code int}. 761 * 762 * @param x the first value 763 * @param y the second value 764 * @return the result 765 * @throws ArithmeticException if the result overflows an int 766 * @see Math#multiplyExact(int,int) 767 * @since 1.8 768 */ multiplyExact(int x, int y)769 public static int multiplyExact(int x, int y) { 770 return Math.multiplyExact(x, y); 771 } 772 773 /** 774 * Returns the product of the arguments, 775 * throwing an exception if the result overflows a {@code long}. 776 * 777 * @param x the first value 778 * @param y the second value 779 * @return the result 780 * @throws ArithmeticException if the result overflows a long 781 * @see Math#multiplyExact(long,long) 782 * @since 1.8 783 */ multiplyExact(long x, long y)784 public static long multiplyExact(long x, long y) { 785 return Math.multiplyExact(x, y); 786 } 787 788 /** 789 * Returns the value of the {@code long} argument; 790 * throwing an exception if the value overflows an {@code int}. 791 * 792 * @param value the long value 793 * @return the argument as an int 794 * @throws ArithmeticException if the {@code argument} overflows an int 795 * @see Math#toIntExact(long) 796 * @since 1.8 797 */ toIntExact(long value)798 public static int toIntExact(long value) { 799 return Math.toIntExact(value); 800 } 801 802 /** 803 * Returns the largest (closest to positive infinity) 804 * {@code int} value that is less than or equal to the algebraic quotient. 805 * There is one special case, if the dividend is the 806 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1}, 807 * then integer overflow occurs and 808 * the result is equal to the {@code Integer.MIN_VALUE}. 809 * <p> 810 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and 811 * a comparison to the integer division {@code /} operator. 812 * 813 * @param x the dividend 814 * @param y the divisor 815 * @return the largest (closest to positive infinity) 816 * {@code int} value that is less than or equal to the algebraic quotient. 817 * @throws ArithmeticException if the divisor {@code y} is zero 818 * @see Math#floorDiv(int, int) 819 * @see Math#floor(double) 820 * @since 1.8 821 */ floorDiv(int x, int y)822 public static int floorDiv(int x, int y) { 823 return Math.floorDiv(x, y); 824 } 825 826 /** 827 * Returns the largest (closest to positive infinity) 828 * {@code long} value that is less than or equal to the algebraic quotient. 829 * There is one special case, if the dividend is the 830 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, 831 * then integer overflow occurs and 832 * the result is equal to the {@code Long.MIN_VALUE}. 833 * <p> 834 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and 835 * a comparison to the integer division {@code /} operator. 836 * 837 * @param x the dividend 838 * @param y the divisor 839 * @return the largest (closest to positive infinity) 840 * {@code long} value that is less than or equal to the algebraic quotient. 841 * @throws ArithmeticException if the divisor {@code y} is zero 842 * @see Math#floorDiv(long, long) 843 * @see Math#floor(double) 844 * @since 1.8 845 */ floorDiv(long x, long y)846 public static long floorDiv(long x, long y) { 847 return Math.floorDiv(x, y); 848 } 849 850 /** 851 * Returns the floor modulus of the {@code int} arguments. 852 * <p> 853 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, 854 * has the same sign as the divisor {@code y}, and 855 * is in the range of {@code -abs(y) < r < +abs(y)}. 856 * <p> 857 * The relationship between {@code floorDiv} and {@code floorMod} is such that: 858 * <ul> 859 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} 860 * </ul> 861 * <p> 862 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and 863 * a comparison to the {@code %} operator. 864 * 865 * @param x the dividend 866 * @param y the divisor 867 * @return the floor modulus {@code x - (floorDiv(x, y) * y)} 868 * @throws ArithmeticException if the divisor {@code y} is zero 869 * @see Math#floorMod(int, int) 870 * @see StrictMath#floorDiv(int, int) 871 * @since 1.8 872 */ floorMod(int x, int y)873 public static int floorMod(int x, int y) { 874 return Math.floorMod(x , y); 875 } 876 /** 877 * Returns the floor modulus of the {@code long} arguments. 878 * <p> 879 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, 880 * has the same sign as the divisor {@code y}, and 881 * is in the range of {@code -abs(y) < r < +abs(y)}. 882 * <p> 883 * The relationship between {@code floorDiv} and {@code floorMod} is such that: 884 * <ul> 885 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} 886 * </ul> 887 * <p> 888 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and 889 * a comparison to the {@code %} operator. 890 * 891 * @param x the dividend 892 * @param y the divisor 893 * @return the floor modulus {@code x - (floorDiv(x, y) * y)} 894 * @throws ArithmeticException if the divisor {@code y} is zero 895 * @see Math#floorMod(long, long) 896 * @see StrictMath#floorDiv(long, long) 897 * @since 1.8 898 */ floorMod(long x, long y)899 public static long floorMod(long x, long y) { 900 return Math.floorMod(x, y); 901 } 902 903 /** 904 * Returns the absolute value of an {@code int} value.. 905 * If the argument is not negative, the argument is returned. 906 * If the argument is negative, the negation of the argument is returned. 907 * 908 * <p>Note that if the argument is equal to the value of 909 * {@link Integer#MIN_VALUE}, the most negative representable 910 * {@code int} value, the result is that same value, which is 911 * negative. 912 * 913 * @param a the argument whose absolute value is to be determined. 914 * @return the absolute value of the argument. 915 */ abs(int a)916 public static int abs(int a) { 917 return (a < 0) ? -a : a; 918 } 919 920 /** 921 * Returns the absolute value of a {@code long} value. 922 * If the argument is not negative, the argument is returned. 923 * If the argument is negative, the negation of the argument is returned. 924 * 925 * <p>Note that if the argument is equal to the value of 926 * {@link Long#MIN_VALUE}, the most negative representable 927 * {@code long} value, the result is that same value, which 928 * is negative. 929 * 930 * @param a the argument whose absolute value is to be determined. 931 * @return the absolute value of the argument. 932 */ abs(long a)933 public static long abs(long a) { 934 return (a < 0) ? -a : a; 935 } 936 937 /** 938 * Returns the absolute value of a {@code float} value. 939 * If the argument is not negative, the argument is returned. 940 * If the argument is negative, the negation of the argument is returned. 941 * Special cases: 942 * <ul><li>If the argument is positive zero or negative zero, the 943 * result is positive zero. 944 * <li>If the argument is infinite, the result is positive infinity. 945 * <li>If the argument is NaN, the result is NaN.</ul> 946 * In other words, the result is the same as the value of the expression: 947 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} 948 * 949 * @param a the argument whose absolute value is to be determined 950 * @return the absolute value of the argument. 951 */ abs(float a)952 public static float abs(float a) { 953 return (a <= 0.0F) ? 0.0F - a : a; 954 } 955 956 /** 957 * Returns the absolute value of a {@code double} value. 958 * If the argument is not negative, the argument is returned. 959 * If the argument is negative, the negation of the argument is returned. 960 * Special cases: 961 * <ul><li>If the argument is positive zero or negative zero, the result 962 * is positive zero. 963 * <li>If the argument is infinite, the result is positive infinity. 964 * <li>If the argument is NaN, the result is NaN.</ul> 965 * In other words, the result is the same as the value of the expression: 966 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} 967 * 968 * @param a the argument whose absolute value is to be determined 969 * @return the absolute value of the argument. 970 */ abs(double a)971 public static double abs(double a) { 972 return (a <= 0.0D) ? 0.0D - a : a; 973 } 974 975 /** 976 * Returns the greater of two {@code int} values. That is, the 977 * result is the argument closer to the value of 978 * {@link Integer#MAX_VALUE}. If the arguments have the same value, 979 * the result is that same value. 980 * 981 * @param a an argument. 982 * @param b another argument. 983 * @return the larger of {@code a} and {@code b}. 984 */ max(int a, int b)985 public static int max(int a, int b) { 986 return (a >= b) ? a : b; 987 } 988 989 /** 990 * Returns the greater of two {@code long} values. That is, the 991 * result is the argument closer to the value of 992 * {@link Long#MAX_VALUE}. If the arguments have the same value, 993 * the result is that same value. 994 * 995 * @param a an argument. 996 * @param b another argument. 997 * @return the larger of {@code a} and {@code b}. 998 */ max(long a, long b)999 public static long max(long a, long b) { 1000 return (a >= b) ? a : b; 1001 } 1002 1003 // Use raw bit-wise conversions on guaranteed non-NaN arguments. 1004 private static long negativeZeroFloatBits = Float.floatToRawIntBits(-0.0f); 1005 private static long negativeZeroDoubleBits = Double.doubleToRawLongBits(-0.0d); 1006 1007 /** 1008 * Returns the greater of two {@code float} values. That is, 1009 * the result is the argument closer to positive infinity. If the 1010 * arguments have the same value, the result is that same 1011 * value. If either value is NaN, then the result is NaN. Unlike 1012 * the numerical comparison operators, this method considers 1013 * negative zero to be strictly smaller than positive zero. If one 1014 * argument is positive zero and the other negative zero, the 1015 * result is positive zero. 1016 * 1017 * @param a an argument. 1018 * @param b another argument. 1019 * @return the larger of {@code a} and {@code b}. 1020 */ max(float a, float b)1021 public static float max(float a, float b) { 1022 if (a != a) 1023 return a; // a is NaN 1024 if ((a == 0.0f) && 1025 (b == 0.0f) && 1026 (Float.floatToRawIntBits(a) == negativeZeroFloatBits)) { 1027 // Raw conversion ok since NaN can't map to -0.0. 1028 return b; 1029 } 1030 return (a >= b) ? a : b; 1031 } 1032 1033 /** 1034 * Returns the greater of two {@code double} values. That 1035 * is, the result is the argument closer to positive infinity. If 1036 * the arguments have the same value, the result is that same 1037 * value. If either value is NaN, then the result is NaN. Unlike 1038 * the numerical comparison operators, this method considers 1039 * negative zero to be strictly smaller than positive zero. If one 1040 * argument is positive zero and the other negative zero, the 1041 * result is positive zero. 1042 * 1043 * @param a an argument. 1044 * @param b another argument. 1045 * @return the larger of {@code a} and {@code b}. 1046 */ max(double a, double b)1047 public static double max(double a, double b) { 1048 if (a != a) 1049 return a; // a is NaN 1050 if ((a == 0.0d) && 1051 (b == 0.0d) && 1052 (Double.doubleToRawLongBits(a) == negativeZeroDoubleBits)) { 1053 // Raw conversion ok since NaN can't map to -0.0. 1054 return b; 1055 } 1056 return (a >= b) ? a : b; 1057 } 1058 1059 /** 1060 * Returns the smaller of two {@code int} values. That is, 1061 * the result the argument closer to the value of 1062 * {@link Integer#MIN_VALUE}. If the arguments have the same 1063 * value, the result is that same value. 1064 * 1065 * @param a an argument. 1066 * @param b another argument. 1067 * @return the smaller of {@code a} and {@code b}. 1068 */ min(int a, int b)1069 public static int min(int a, int b) { 1070 return (a <= b) ? a : b; 1071 } 1072 1073 /** 1074 * Returns the smaller of two {@code long} values. That is, 1075 * the result is the argument closer to the value of 1076 * {@link Long#MIN_VALUE}. If the arguments have the same 1077 * value, the result is that same value. 1078 * 1079 * @param a an argument. 1080 * @param b another argument. 1081 * @return the smaller of {@code a} and {@code b}. 1082 */ min(long a, long b)1083 public static long min(long a, long b) { 1084 return (a <= b) ? a : b; 1085 } 1086 1087 /** 1088 * Returns the smaller of two {@code float} values. That is, 1089 * the result is the value closer to negative infinity. If the 1090 * arguments have the same value, the result is that same 1091 * value. If either value is NaN, then the result is NaN. Unlike 1092 * the numerical comparison operators, this method considers 1093 * negative zero to be strictly smaller than positive zero. If 1094 * one argument is positive zero and the other is negative zero, 1095 * the result is negative zero. 1096 * 1097 * @param a an argument. 1098 * @param b another argument. 1099 * @return the smaller of {@code a} and {@code b.} 1100 */ min(float a, float b)1101 public static float min(float a, float b) { 1102 if (a != a) 1103 return a; // a is NaN 1104 if ((a == 0.0f) && 1105 (b == 0.0f) && 1106 (Float.floatToRawIntBits(b) == negativeZeroFloatBits)) { 1107 // Raw conversion ok since NaN can't map to -0.0. 1108 return b; 1109 } 1110 return (a <= b) ? a : b; 1111 } 1112 1113 /** 1114 * Returns the smaller of two {@code double} values. That 1115 * is, the result is the value closer to negative infinity. If the 1116 * arguments have the same value, the result is that same 1117 * value. If either value is NaN, then the result is NaN. Unlike 1118 * the numerical comparison operators, this method considers 1119 * negative zero to be strictly smaller than positive zero. If one 1120 * argument is positive zero and the other is negative zero, the 1121 * result is negative zero. 1122 * 1123 * @param a an argument. 1124 * @param b another argument. 1125 * @return the smaller of {@code a} and {@code b}. 1126 */ min(double a, double b)1127 public static double min(double a, double b) { 1128 if (a != a) 1129 return a; // a is NaN 1130 if ((a == 0.0d) && 1131 (b == 0.0d) && 1132 (Double.doubleToRawLongBits(b) == negativeZeroDoubleBits)) { 1133 // Raw conversion ok since NaN can't map to -0.0. 1134 return b; 1135 } 1136 return (a <= b) ? a : b; 1137 } 1138 1139 /** 1140 * Returns the size of an ulp of the argument. An ulp of a 1141 * {@code double} value is the positive distance between this 1142 * floating-point value and the {@code double} value next 1143 * larger in magnitude. Note that for non-NaN <i>x</i>, 1144 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. 1145 * 1146 * <p>Special Cases: 1147 * <ul> 1148 * <li> If the argument is NaN, then the result is NaN. 1149 * <li> If the argument is positive or negative infinity, then the 1150 * result is positive infinity. 1151 * <li> If the argument is positive or negative zero, then the result is 1152 * {@code Double.MIN_VALUE}. 1153 * <li> If the argument is ±{@code Double.MAX_VALUE}, then 1154 * the result is equal to 2<sup>971</sup>. 1155 * </ul> 1156 * 1157 * @param d the floating-point value whose ulp is to be returned 1158 * @return the size of an ulp of the argument 1159 * @author Joseph D. Darcy 1160 * @since 1.5 1161 */ ulp(double d)1162 public static double ulp(double d) { 1163 return sun.misc.FpUtils.ulp(d); 1164 } 1165 1166 /** 1167 * Returns the size of an ulp of the argument. An ulp of a 1168 * {@code float} value is the positive distance between this 1169 * floating-point value and the {@code float} value next 1170 * larger in magnitude. Note that for non-NaN <i>x</i>, 1171 * <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. 1172 * 1173 * <p>Special Cases: 1174 * <ul> 1175 * <li> If the argument is NaN, then the result is NaN. 1176 * <li> If the argument is positive or negative infinity, then the 1177 * result is positive infinity. 1178 * <li> If the argument is positive or negative zero, then the result is 1179 * {@code Float.MIN_VALUE}. 1180 * <li> If the argument is ±{@code Float.MAX_VALUE}, then 1181 * the result is equal to 2<sup>104</sup>. 1182 * </ul> 1183 * 1184 * @param f the floating-point value whose ulp is to be returned 1185 * @return the size of an ulp of the argument 1186 * @author Joseph D. Darcy 1187 * @since 1.5 1188 */ ulp(float f)1189 public static float ulp(float f) { 1190 return sun.misc.FpUtils.ulp(f); 1191 } 1192 1193 /** 1194 * Returns the signum function of the argument; zero if the argument 1195 * is zero, 1.0 if the argument is greater than zero, -1.0 if the 1196 * argument is less than zero. 1197 * 1198 * <p>Special Cases: 1199 * <ul> 1200 * <li> If the argument is NaN, then the result is NaN. 1201 * <li> If the argument is positive zero or negative zero, then the 1202 * result is the same as the argument. 1203 * </ul> 1204 * 1205 * @param d the floating-point value whose signum is to be returned 1206 * @return the signum function of the argument 1207 * @author Joseph D. Darcy 1208 * @since 1.5 1209 */ signum(double d)1210 public static double signum(double d) { 1211 return sun.misc.FpUtils.signum(d); 1212 } 1213 1214 /** 1215 * Returns the signum function of the argument; zero if the argument 1216 * is zero, 1.0f if the argument is greater than zero, -1.0f if the 1217 * argument is less than zero. 1218 * 1219 * <p>Special Cases: 1220 * <ul> 1221 * <li> If the argument is NaN, then the result is NaN. 1222 * <li> If the argument is positive zero or negative zero, then the 1223 * result is the same as the argument. 1224 * </ul> 1225 * 1226 * @param f the floating-point value whose signum is to be returned 1227 * @return the signum function of the argument 1228 * @author Joseph D. Darcy 1229 * @since 1.5 1230 */ signum(float f)1231 public static float signum(float f) { 1232 return sun.misc.FpUtils.signum(f); 1233 } 1234 1235 /** 1236 * Returns the hyperbolic sine of a {@code double} value. 1237 * The hyperbolic sine of <i>x</i> is defined to be 1238 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 1239 * where <i>e</i> is {@linkplain Math#E Euler's number}. 1240 * 1241 * <p>Special cases: 1242 * <ul> 1243 * 1244 * <li>If the argument is NaN, then the result is NaN. 1245 * 1246 * <li>If the argument is infinite, then the result is an infinity 1247 * with the same sign as the argument. 1248 * 1249 * <li>If the argument is zero, then the result is a zero with the 1250 * same sign as the argument. 1251 * 1252 * </ul> 1253 * 1254 * @param x The number whose hyperbolic sine is to be returned. 1255 * @return The hyperbolic sine of {@code x}. 1256 * @since 1.5 1257 */ sinh(double x)1258 public static native double sinh(double x); 1259 1260 /** 1261 * Returns the hyperbolic cosine of a {@code double} value. 1262 * The hyperbolic cosine of <i>x</i> is defined to be 1263 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 1264 * where <i>e</i> is {@linkplain Math#E Euler's number}. 1265 * 1266 * <p>Special cases: 1267 * <ul> 1268 * 1269 * <li>If the argument is NaN, then the result is NaN. 1270 * 1271 * <li>If the argument is infinite, then the result is positive 1272 * infinity. 1273 * 1274 * <li>If the argument is zero, then the result is {@code 1.0}. 1275 * 1276 * </ul> 1277 * 1278 * @param x The number whose hyperbolic cosine is to be returned. 1279 * @return The hyperbolic cosine of {@code x}. 1280 * @since 1.5 1281 */ cosh(double x)1282 public static native double cosh(double x); 1283 1284 /** 1285 * Returns the hyperbolic tangent of a {@code double} value. 1286 * The hyperbolic tangent of <i>x</i> is defined to be 1287 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), 1288 * in other words, {@linkplain Math#sinh 1289 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note 1290 * that the absolute value of the exact tanh is always less than 1291 * 1. 1292 * 1293 * <p>Special cases: 1294 * <ul> 1295 * 1296 * <li>If the argument is NaN, then the result is NaN. 1297 * 1298 * <li>If the argument is zero, then the result is a zero with the 1299 * same sign as the argument. 1300 * 1301 * <li>If the argument is positive infinity, then the result is 1302 * {@code +1.0}. 1303 * 1304 * <li>If the argument is negative infinity, then the result is 1305 * {@code -1.0}. 1306 * 1307 * </ul> 1308 * 1309 * @param x The number whose hyperbolic tangent is to be returned. 1310 * @return The hyperbolic tangent of {@code x}. 1311 * @since 1.5 1312 */ tanh(double x)1313 public static native double tanh(double x); 1314 1315 /** 1316 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) 1317 * without intermediate overflow or underflow. 1318 * 1319 * <p>Special cases: 1320 * <ul> 1321 * 1322 * <li> If either argument is infinite, then the result 1323 * is positive infinity. 1324 * 1325 * <li> If either argument is NaN and neither argument is infinite, 1326 * then the result is NaN. 1327 * 1328 * </ul> 1329 * 1330 * @param x a value 1331 * @param y a value 1332 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) 1333 * without intermediate overflow or underflow 1334 * @since 1.5 1335 */ hypot(double x, double y)1336 public static native double hypot(double x, double y); 1337 1338 /** 1339 * Returns <i>e</i><sup>x</sup> -1. Note that for values of 1340 * <i>x</i> near 0, the exact sum of 1341 * {@code expm1(x)} + 1 is much closer to the true 1342 * result of <i>e</i><sup>x</sup> than {@code exp(x)}. 1343 * 1344 * <p>Special cases: 1345 * <ul> 1346 * <li>If the argument is NaN, the result is NaN. 1347 * 1348 * <li>If the argument is positive infinity, then the result is 1349 * positive infinity. 1350 * 1351 * <li>If the argument is negative infinity, then the result is 1352 * -1.0. 1353 * 1354 * <li>If the argument is zero, then the result is a zero with the 1355 * same sign as the argument. 1356 * 1357 * </ul> 1358 * 1359 * @param x the exponent to raise <i>e</i> to in the computation of 1360 * <i>e</i><sup>{@code x}</sup> -1. 1361 * @return the value <i>e</i><sup>{@code x}</sup> - 1. 1362 * @since 1.5 1363 */ expm1(double x)1364 public static native double expm1(double x); 1365 1366 /** 1367 * Returns the natural logarithm of the sum of the argument and 1. 1368 * Note that for small values {@code x}, the result of 1369 * {@code log1p(x)} is much closer to the true result of ln(1 1370 * + {@code x}) than the floating-point evaluation of 1371 * {@code log(1.0+x)}. 1372 * 1373 * <p>Special cases: 1374 * <ul> 1375 * 1376 * <li>If the argument is NaN or less than -1, then the result is 1377 * NaN. 1378 * 1379 * <li>If the argument is positive infinity, then the result is 1380 * positive infinity. 1381 * 1382 * <li>If the argument is negative one, then the result is 1383 * negative infinity. 1384 * 1385 * <li>If the argument is zero, then the result is a zero with the 1386 * same sign as the argument. 1387 * 1388 * </ul> 1389 * 1390 * @param x a value 1391 * @return the value ln({@code x} + 1), the natural 1392 * log of {@code x} + 1 1393 * @since 1.5 1394 */ log1p(double x)1395 public static native double log1p(double x); 1396 1397 /** 1398 * Returns the first floating-point argument with the sign of the 1399 * second floating-point argument. For this method, a NaN 1400 * {@code sign} argument is always treated as if it were 1401 * positive. 1402 * 1403 * @param magnitude the parameter providing the magnitude of the result 1404 * @param sign the parameter providing the sign of the result 1405 * @return a value with the magnitude of {@code magnitude} 1406 * and the sign of {@code sign}. 1407 * @since 1.6 1408 */ copySign(double magnitude, double sign)1409 public static double copySign(double magnitude, double sign) { 1410 return sun.misc.FpUtils.copySign(magnitude, sign); 1411 } 1412 1413 /** 1414 * Returns the first floating-point argument with the sign of the 1415 * second floating-point argument. For this method, a NaN 1416 * {@code sign} argument is always treated as if it were 1417 * positive. 1418 * 1419 * @param magnitude the parameter providing the magnitude of the result 1420 * @param sign the parameter providing the sign of the result 1421 * @return a value with the magnitude of {@code magnitude} 1422 * and the sign of {@code sign}. 1423 * @since 1.6 1424 */ copySign(float magnitude, float sign)1425 public static float copySign(float magnitude, float sign) { 1426 return sun.misc.FpUtils.copySign(magnitude, sign); 1427 } 1428 /** 1429 * Returns the unbiased exponent used in the representation of a 1430 * {@code float}. Special cases: 1431 * 1432 * <ul> 1433 * <li>If the argument is NaN or infinite, then the result is 1434 * {@link Float#MAX_EXPONENT} + 1. 1435 * <li>If the argument is zero or subnormal, then the result is 1436 * {@link Float#MIN_EXPONENT} -1. 1437 * </ul> 1438 * @param f a {@code float} value 1439 * @since 1.6 1440 */ getExponent(float f)1441 public static int getExponent(float f) { 1442 return sun.misc.FpUtils.getExponent(f); 1443 } 1444 1445 /** 1446 * Returns the unbiased exponent used in the representation of a 1447 * {@code double}. Special cases: 1448 * 1449 * <ul> 1450 * <li>If the argument is NaN or infinite, then the result is 1451 * {@link Double#MAX_EXPONENT} + 1. 1452 * <li>If the argument is zero or subnormal, then the result is 1453 * {@link Double#MIN_EXPONENT} -1. 1454 * </ul> 1455 * @param d a {@code double} value 1456 * @since 1.6 1457 */ getExponent(double d)1458 public static int getExponent(double d) { 1459 return sun.misc.FpUtils.getExponent(d); 1460 } 1461 1462 /** 1463 * Returns the floating-point number adjacent to the first 1464 * argument in the direction of the second argument. If both 1465 * arguments compare as equal the second argument is returned. 1466 * 1467 * <p>Special cases: 1468 * <ul> 1469 * <li> If either argument is a NaN, then NaN is returned. 1470 * 1471 * <li> If both arguments are signed zeros, {@code direction} 1472 * is returned unchanged (as implied by the requirement of 1473 * returning the second argument if the arguments compare as 1474 * equal). 1475 * 1476 * <li> If {@code start} is 1477 * ±{@link Double#MIN_VALUE} and {@code direction} 1478 * has a value such that the result should have a smaller 1479 * magnitude, then a zero with the same sign as {@code start} 1480 * is returned. 1481 * 1482 * <li> If {@code start} is infinite and 1483 * {@code direction} has a value such that the result should 1484 * have a smaller magnitude, {@link Double#MAX_VALUE} with the 1485 * same sign as {@code start} is returned. 1486 * 1487 * <li> If {@code start} is equal to ± 1488 * {@link Double#MAX_VALUE} and {@code direction} has a 1489 * value such that the result should have a larger magnitude, an 1490 * infinity with same sign as {@code start} is returned. 1491 * </ul> 1492 * 1493 * @param start starting floating-point value 1494 * @param direction value indicating which of 1495 * {@code start}'s neighbors or {@code start} should 1496 * be returned 1497 * @return The floating-point number adjacent to {@code start} in the 1498 * direction of {@code direction}. 1499 * @since 1.6 1500 */ nextAfter(double start, double direction)1501 public static double nextAfter(double start, double direction) { 1502 return sun.misc.FpUtils.nextAfter(start, direction); 1503 } 1504 1505 /** 1506 * Returns the floating-point number adjacent to the first 1507 * argument in the direction of the second argument. If both 1508 * arguments compare as equal a value equivalent to the second argument 1509 * is returned. 1510 * 1511 * <p>Special cases: 1512 * <ul> 1513 * <li> If either argument is a NaN, then NaN is returned. 1514 * 1515 * <li> If both arguments are signed zeros, a value equivalent 1516 * to {@code direction} is returned. 1517 * 1518 * <li> If {@code start} is 1519 * ±{@link Float#MIN_VALUE} and {@code direction} 1520 * has a value such that the result should have a smaller 1521 * magnitude, then a zero with the same sign as {@code start} 1522 * is returned. 1523 * 1524 * <li> If {@code start} is infinite and 1525 * {@code direction} has a value such that the result should 1526 * have a smaller magnitude, {@link Float#MAX_VALUE} with the 1527 * same sign as {@code start} is returned. 1528 * 1529 * <li> If {@code start} is equal to ± 1530 * {@link Float#MAX_VALUE} and {@code direction} has a 1531 * value such that the result should have a larger magnitude, an 1532 * infinity with same sign as {@code start} is returned. 1533 * </ul> 1534 * 1535 * @param start starting floating-point value 1536 * @param direction value indicating which of 1537 * {@code start}'s neighbors or {@code start} should 1538 * be returned 1539 * @return The floating-point number adjacent to {@code start} in the 1540 * direction of {@code direction}. 1541 * @since 1.6 1542 */ nextAfter(float start, double direction)1543 public static float nextAfter(float start, double direction) { 1544 return sun.misc.FpUtils.nextAfter(start, direction); 1545 } 1546 1547 /** 1548 * Returns the floating-point value adjacent to {@code d} in 1549 * the direction of positive infinity. This method is 1550 * semantically equivalent to {@code nextAfter(d, 1551 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} 1552 * implementation may run faster than its equivalent 1553 * {@code nextAfter} call. 1554 * 1555 * <p>Special Cases: 1556 * <ul> 1557 * <li> If the argument is NaN, the result is NaN. 1558 * 1559 * <li> If the argument is positive infinity, the result is 1560 * positive infinity. 1561 * 1562 * <li> If the argument is zero, the result is 1563 * {@link Double#MIN_VALUE} 1564 * 1565 * </ul> 1566 * 1567 * @param d starting floating-point value 1568 * @return The adjacent floating-point value closer to positive 1569 * infinity. 1570 * @since 1.6 1571 */ nextUp(double d)1572 public static double nextUp(double d) { 1573 return sun.misc.FpUtils.nextUp(d); 1574 } 1575 1576 /** 1577 * Returns the floating-point value adjacent to {@code f} in 1578 * the direction of positive infinity. This method is 1579 * semantically equivalent to {@code nextAfter(f, 1580 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} 1581 * implementation may run faster than its equivalent 1582 * {@code nextAfter} call. 1583 * 1584 * <p>Special Cases: 1585 * <ul> 1586 * <li> If the argument is NaN, the result is NaN. 1587 * 1588 * <li> If the argument is positive infinity, the result is 1589 * positive infinity. 1590 * 1591 * <li> If the argument is zero, the result is 1592 * {@link Float#MIN_VALUE} 1593 * 1594 * </ul> 1595 * 1596 * @param f starting floating-point value 1597 * @return The adjacent floating-point value closer to positive 1598 * infinity. 1599 * @since 1.6 1600 */ nextUp(float f)1601 public static float nextUp(float f) { 1602 return sun.misc.FpUtils.nextUp(f); 1603 } 1604 1605 /** 1606 * Returns the floating-point value adjacent to {@code d} in 1607 * the direction of negative infinity. This method is 1608 * semantically equivalent to {@code nextAfter(d, 1609 * Double.NEGATIVE_INFINITY)}; however, a 1610 * {@code nextDown} implementation may run faster than its 1611 * equivalent {@code nextAfter} call. 1612 * 1613 * <p>Special Cases: 1614 * <ul> 1615 * <li> If the argument is NaN, the result is NaN. 1616 * 1617 * <li> If the argument is negative infinity, the result is 1618 * negative infinity. 1619 * 1620 * <li> If the argument is zero, the result is 1621 * {@code -Double.MIN_VALUE} 1622 * 1623 * </ul> 1624 * 1625 * @param d starting floating-point value 1626 * @return The adjacent floating-point value closer to negative 1627 * infinity. 1628 * @since 1.8 1629 */ nextDown(double d)1630 public static double nextDown(double d) { 1631 return Math.nextDown(d); 1632 } 1633 1634 /** 1635 * Returns the floating-point value adjacent to {@code f} in 1636 * the direction of negative infinity. This method is 1637 * semantically equivalent to {@code nextAfter(f, 1638 * Float.NEGATIVE_INFINITY)}; however, a 1639 * {@code nextDown} implementation may run faster than its 1640 * equivalent {@code nextAfter} call. 1641 * 1642 * <p>Special Cases: 1643 * <ul> 1644 * <li> If the argument is NaN, the result is NaN. 1645 * 1646 * <li> If the argument is negative infinity, the result is 1647 * negative infinity. 1648 * 1649 * <li> If the argument is zero, the result is 1650 * {@code -Float.MIN_VALUE} 1651 * 1652 * </ul> 1653 * 1654 * @param f starting floating-point value 1655 * @return The adjacent floating-point value closer to negative 1656 * infinity. 1657 * @since 1.8 1658 */ nextDown(float f)1659 public static float nextDown(float f) { 1660 return Math.nextDown(f); 1661 } 1662 1663 /** 1664 * Return {@code d} × 1665 * 2<sup>{@code scaleFactor}</sup> rounded as if performed 1666 * by a single correctly rounded floating-point multiply to a 1667 * member of the double value set. See the Java 1668 * Language Specification for a discussion of floating-point 1669 * value sets. If the exponent of the result is between {@link 1670 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the 1671 * answer is calculated exactly. If the exponent of the result 1672 * would be larger than {@code Double.MAX_EXPONENT}, an 1673 * infinity is returned. Note that if the result is subnormal, 1674 * precision may be lost; that is, when {@code scalb(x, n)} 1675 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal 1676 * <i>x</i>. When the result is non-NaN, the result has the same 1677 * sign as {@code d}. 1678 * 1679 * <p>Special cases: 1680 * <ul> 1681 * <li> If the first argument is NaN, NaN is returned. 1682 * <li> If the first argument is infinite, then an infinity of the 1683 * same sign is returned. 1684 * <li> If the first argument is zero, then a zero of the same 1685 * sign is returned. 1686 * </ul> 1687 * 1688 * @param d number to be scaled by a power of two. 1689 * @param scaleFactor power of 2 used to scale {@code d} 1690 * @return {@code d} × 2<sup>{@code scaleFactor}</sup> 1691 * @since 1.6 1692 */ scalb(double d, int scaleFactor)1693 public static double scalb(double d, int scaleFactor) { 1694 return sun.misc.FpUtils.scalb(d, scaleFactor); 1695 } 1696 1697 /** 1698 * Return {@code f} × 1699 * 2<sup>{@code scaleFactor}</sup> rounded as if performed 1700 * by a single correctly rounded floating-point multiply to a 1701 * member of the float value set. See the Java 1702 * Language Specification for a discussion of floating-point 1703 * value sets. If the exponent of the result is between {@link 1704 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the 1705 * answer is calculated exactly. If the exponent of the result 1706 * would be larger than {@code Float.MAX_EXPONENT}, an 1707 * infinity is returned. Note that if the result is subnormal, 1708 * precision may be lost; that is, when {@code scalb(x, n)} 1709 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal 1710 * <i>x</i>. When the result is non-NaN, the result has the same 1711 * sign as {@code f}. 1712 * 1713 * <p>Special cases: 1714 * <ul> 1715 * <li> If the first argument is NaN, NaN is returned. 1716 * <li> If the first argument is infinite, then an infinity of the 1717 * same sign is returned. 1718 * <li> If the first argument is zero, then a zero of the same 1719 * sign is returned. 1720 * </ul> 1721 * 1722 * @param f number to be scaled by a power of two. 1723 * @param scaleFactor power of 2 used to scale {@code f} 1724 * @return {@code f} × 2<sup>{@code scaleFactor}</sup> 1725 * @since 1.6 1726 */ scalb(float f, int scaleFactor)1727 public static float scalb(float f, int scaleFactor) { 1728 return sun.misc.FpUtils.scalb(f, scaleFactor); 1729 } 1730 } 1731