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.DoubleConsts; 29 30 /** 31 * The class {@code StrictMath} contains methods for performing basic 32 * numeric operations such as the elementary exponential, logarithm, 33 * square root, and trigonometric functions. 34 * 35 * <p>To help ensure portability of Java programs, the definitions of 36 * some of the numeric functions in this package require that they 37 * produce the same results as certain published algorithms. These 38 * algorithms are available from the well-known network library 39 * {@code netlib} as the package "Freely Distributable Math 40 * Library," <a 41 * href="ftp://ftp.netlib.org/fdlibm.tar">{@code fdlibm}</a>. These 42 * algorithms, which are written in the C programming language, are 43 * then to be understood as executed with all floating-point 44 * operations following the rules of Java floating-point arithmetic. 45 * 46 * <p>The Java math library is defined with respect to 47 * {@code fdlibm} version 5.3. Where {@code fdlibm} provides 48 * more than one definition for a function (such as 49 * {@code acos}), use the "IEEE 754 core function" version 50 * (residing in a file whose name begins with the letter 51 * {@code e}). The methods which require {@code fdlibm} 52 * semantics are {@code sin}, {@code cos}, {@code tan}, 53 * {@code asin}, {@code acos}, {@code atan}, 54 * {@code exp}, {@code log}, {@code log10}, 55 * {@code cbrt}, {@code atan2}, {@code pow}, 56 * {@code sinh}, {@code cosh}, {@code tanh}, 57 * {@code hypot}, {@code expm1}, and {@code log1p}. 58 * 59 * <p> 60 * The platform uses signed two's complement integer arithmetic with 61 * int and long primitive types. The developer should choose 62 * the primitive type to ensure that arithmetic operations consistently 63 * produce correct results, which in some cases means the operations 64 * will not overflow the range of values of the computation. 65 * The best practice is to choose the primitive type and algorithm to avoid 66 * overflow. In cases where the size is {@code int} or {@code long} and 67 * overflow errors need to be detected, the methods {@code addExact}, 68 * {@code subtractExact}, {@code multiplyExact}, and {@code toIntExact} 69 * throw an {@code ArithmeticException} when the results overflow. 70 * For other arithmetic operations such as divide, absolute value, 71 * increment, decrement, and negation overflow occurs only with 72 * a specific minimum or maximum value and should be checked against 73 * the minimum or maximum as appropriate. 74 * 75 * @author unascribed 76 * @author Joseph D. Darcy 77 * @since 1.3 78 */ 79 80 public final class StrictMath { 81 82 /** 83 * Don't let anyone instantiate this class. 84 */ 85 private StrictMath() {} 86 87 /** 88 * The {@code double} value that is closer than any other to 89 * <i>e</i>, the base of the natural logarithms. 90 */ 91 public static final double E = 2.7182818284590452354; 92 93 /** 94 * The {@code double} value that is closer than any other to 95 * <i>pi</i>, the ratio of the circumference of a circle to its 96 * diameter. 97 */ 98 public static final double PI = 3.14159265358979323846; 99 100 /** 101 * Returns the trigonometric sine of an angle. Special cases: 102 * <ul><li>If the argument is NaN or an infinity, then the 103 * result is NaN. 104 * <li>If the argument is zero, then the result is a zero with the 105 * same sign as the argument.</ul> 106 * 107 * @param a an angle, in radians. 108 * @return the sine of the argument. 109 */ 110 public static native double sin(double a); 111 112 /** 113 * Returns the trigonometric cosine of an angle. Special cases: 114 * <ul><li>If the argument is NaN or an infinity, then the 115 * result is NaN.</ul> 116 * 117 * @param a an angle, in radians. 118 * @return the cosine of the argument. 119 */ 120 public static native double cos(double a); 121 122 /** 123 * Returns the trigonometric tangent of an angle. Special cases: 124 * <ul><li>If the argument is NaN or an infinity, then the result 125 * is NaN. 126 * <li>If the argument is zero, then the result is a zero with the 127 * same sign as the argument.</ul> 128 * 129 * @param a an angle, in radians. 130 * @return the tangent of the argument. 131 */ 132 public static native double tan(double a); 133 134 /** 135 * Returns the arc sine of a value; the returned angle is in the 136 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: 137 * <ul><li>If the argument is NaN or its absolute value is greater 138 * than 1, then the result is NaN. 139 * <li>If the argument is zero, then the result is a zero with the 140 * same sign as the argument.</ul> 141 * 142 * @param a the value whose arc sine is to be returned. 143 * @return the arc sine of the argument. 144 */ 145 public static native double asin(double a); 146 147 /** 148 * Returns the arc cosine of a value; the returned angle is in the 149 * range 0.0 through <i>pi</i>. Special case: 150 * <ul><li>If the argument is NaN or its absolute value is greater 151 * than 1, then the result is NaN.</ul> 152 * 153 * @param a the value whose arc cosine is to be returned. 154 * @return the arc cosine of the argument. 155 */ 156 public static native double acos(double a); 157 158 /** 159 * Returns the arc tangent of a value; the returned angle is in the 160 * range -<i>pi</i>/2 through <i>pi</i>/2. Special cases: 161 * <ul><li>If the argument is NaN, then the result is NaN. 162 * <li>If the argument is zero, then the result is a zero with the 163 * same sign as the argument.</ul> 164 * 165 * @param a the value whose arc tangent is to be returned. 166 * @return the arc tangent of the argument. 167 */ 168 public static native double atan(double a); 169 170 /** 171 * Converts an angle measured in degrees to an approximately 172 * equivalent angle measured in radians. The conversion from 173 * degrees to radians is generally inexact. 174 * 175 * @param angdeg an angle, in degrees 176 * @return the measurement of the angle {@code angdeg} 177 * in radians. 178 */ 179 public static strictfp double toRadians(double angdeg) { 180 // Do not delegate to Math.toRadians(angdeg) because 181 // this method has the strictfp modifier. 182 return angdeg / 180.0 * PI; 183 } 184 185 /** 186 * Converts an angle measured in radians to an approximately 187 * equivalent angle measured in degrees. The conversion from 188 * radians to degrees is generally inexact; users should 189 * <i>not</i> expect {@code cos(toRadians(90.0))} to exactly 190 * equal {@code 0.0}. 191 * 192 * @param angrad an angle, in radians 193 * @return the measurement of the angle {@code angrad} 194 * in degrees. 195 */ 196 public static strictfp double toDegrees(double angrad) { 197 // Do not delegate to Math.toDegrees(angrad) because 198 // this method has the strictfp modifier. 199 return angrad * 180.0 / PI; 200 } 201 202 /** 203 * Returns Euler's number <i>e</i> raised to the power of a 204 * {@code double} value. Special cases: 205 * <ul><li>If the argument is NaN, the result is NaN. 206 * <li>If the argument is positive infinity, then the result is 207 * positive infinity. 208 * <li>If the argument is negative infinity, then the result is 209 * positive zero.</ul> 210 * 211 * @param a the exponent to raise <i>e</i> to. 212 * @return the value <i>e</i><sup>{@code a}</sup>, 213 * where <i>e</i> is the base of the natural logarithms. 214 */ 215 public static native double exp(double a); 216 217 /** 218 * Returns the natural logarithm (base <i>e</i>) of a {@code double} 219 * value. Special cases: 220 * <ul><li>If the argument is NaN or less than zero, then the result 221 * is NaN. 222 * <li>If the argument is positive infinity, then the result is 223 * positive infinity. 224 * <li>If the argument is positive zero or negative zero, then the 225 * result is negative infinity.</ul> 226 * 227 * @param a a value 228 * @return the value ln {@code a}, the natural logarithm of 229 * {@code a}. 230 */ 231 public static native double log(double a); 232 233 234 /** 235 * Returns the base 10 logarithm of a {@code double} value. 236 * Special cases: 237 * 238 * <ul><li>If the argument is NaN or less than zero, then the result 239 * is NaN. 240 * <li>If the argument is positive infinity, then the result is 241 * positive infinity. 242 * <li>If the argument is positive zero or negative zero, then the 243 * result is negative infinity. 244 * <li> If the argument is equal to 10<sup><i>n</i></sup> for 245 * integer <i>n</i>, then the result is <i>n</i>. 246 * </ul> 247 * 248 * @param a a value 249 * @return the base 10 logarithm of {@code a}. 250 * @since 1.5 251 */ 252 public static native double log10(double a); 253 254 /** 255 * Returns the correctly rounded positive square root of a 256 * {@code double} value. 257 * Special cases: 258 * <ul><li>If the argument is NaN or less than zero, then the result 259 * is NaN. 260 * <li>If the argument is positive infinity, then the result is positive 261 * infinity. 262 * <li>If the argument is positive zero or negative zero, then the 263 * result is the same as the argument.</ul> 264 * Otherwise, the result is the {@code double} value closest to 265 * the true mathematical square root of the argument value. 266 * 267 * @param a a value. 268 * @return the positive square root of {@code a}. 269 */ 270 public static native double sqrt(double a); 271 272 /** 273 * Returns the cube root of a {@code double} value. For 274 * positive finite {@code x}, {@code cbrt(-x) == 275 * -cbrt(x)}; that is, the cube root of a negative value is 276 * the negative of the cube root of that value's magnitude. 277 * Special cases: 278 * 279 * <ul> 280 * 281 * <li>If the argument is NaN, then the result is NaN. 282 * 283 * <li>If the argument is infinite, then the result is an infinity 284 * with the same sign as the argument. 285 * 286 * <li>If the argument is zero, then the result is a zero with the 287 * same sign as the argument. 288 * 289 * </ul> 290 * 291 * @param a a value. 292 * @return the cube root of {@code a}. 293 * @since 1.5 294 */ 295 public static native double cbrt(double a); 296 297 /** 298 * Computes the remainder operation on two arguments as prescribed 299 * by the IEEE 754 standard. 300 * The remainder value is mathematically equal to 301 * <code>f1 - f2</code> × <i>n</i>, 302 * where <i>n</i> is the mathematical integer closest to the exact 303 * mathematical value of the quotient {@code f1/f2}, and if two 304 * mathematical integers are equally close to {@code f1/f2}, 305 * then <i>n</i> is the integer that is even. If the remainder is 306 * zero, its sign is the same as the sign of the first argument. 307 * Special cases: 308 * <ul><li>If either argument is NaN, or the first argument is infinite, 309 * or the second argument is positive zero or negative zero, then the 310 * result is NaN. 311 * <li>If the first argument is finite and the second argument is 312 * infinite, then the result is the same as the first argument.</ul> 313 * 314 * @param f1 the dividend. 315 * @param f2 the divisor. 316 * @return the remainder when {@code f1} is divided by 317 * {@code f2}. 318 */ 319 public static native double IEEEremainder(double f1, double f2); 320 321 /** 322 * Returns the smallest (closest to negative infinity) 323 * {@code double} value that is greater than or equal to the 324 * argument and is equal to a mathematical integer. Special cases: 325 * <ul><li>If the argument value is already equal to a 326 * mathematical integer, then the result is the same as the 327 * argument. <li>If the argument is NaN or an infinity or 328 * positive zero or negative zero, then the result is the same as 329 * the argument. <li>If the argument value is less than zero but 330 * greater than -1.0, then the result is negative zero.</ul> Note 331 * that the value of {@code StrictMath.ceil(x)} is exactly the 332 * value of {@code -StrictMath.floor(-x)}. 333 * 334 * @param a a value. 335 * @return the smallest (closest to negative infinity) 336 * floating-point value that is greater than or equal to 337 * the argument and is equal to a mathematical integer. 338 */ 339 public static double ceil(double a) { 340 return floorOrCeil(a, -0.0, 1.0, 1.0); 341 } 342 343 /** 344 * Returns the largest (closest to positive infinity) 345 * {@code double} value that is less than or equal to the 346 * argument and is equal to a mathematical integer. Special cases: 347 * <ul><li>If the argument value is already equal to a 348 * mathematical integer, then the result is the same as the 349 * argument. <li>If the argument is NaN or an infinity or 350 * positive zero or negative zero, then the result is the same as 351 * the argument.</ul> 352 * 353 * @param a a value. 354 * @return the largest (closest to positive infinity) 355 * floating-point value that less than or equal to the argument 356 * and is equal to a mathematical integer. 357 */ 358 public static double floor(double a) { 359 return floorOrCeil(a, -1.0, 0.0, -1.0); 360 } 361 362 /** 363 * Internal method to share logic between floor and ceil. 364 * 365 * @param a the value to be floored or ceiled 366 * @param negativeBoundary result for values in (-1, 0) 367 * @param positiveBoundary result for values in (0, 1) 368 * @param increment value to add when the argument is non-integral 369 */ 370 private static double floorOrCeil(double a, 371 double negativeBoundary, 372 double positiveBoundary, 373 double sign) { 374 int exponent = Math.getExponent(a); 375 376 if (exponent < 0) { 377 /* 378 * Absolute value of argument is less than 1. 379 * floorOrceil(-0.0) => -0.0 380 * floorOrceil(+0.0) => +0.0 381 */ 382 return ((a == 0.0) ? a : 383 ( (a < 0.0) ? negativeBoundary : positiveBoundary) ); 384 } else if (exponent >= 52) { 385 /* 386 * Infinity, NaN, or a value so large it must be integral. 387 */ 388 return a; 389 } 390 // Else the argument is either an integral value already XOR it 391 // has to be rounded to one. 392 assert exponent >= 0 && exponent <= 51; 393 394 long doppel = Double.doubleToRawLongBits(a); 395 long mask = DoubleConsts.SIGNIF_BIT_MASK >> exponent; 396 397 if ( (mask & doppel) == 0L ) 398 return a; // integral value 399 else { 400 double result = Double.longBitsToDouble(doppel & (~mask)); 401 if (sign*a > 0.0) 402 result = result + sign; 403 return result; 404 } 405 } 406 407 /** 408 * Returns the {@code double} value that is closest in value 409 * to the argument and is equal to a mathematical integer. If two 410 * {@code double} values that are mathematical integers are 411 * equally close to the value of the argument, the result is the 412 * integer value that is even. Special cases: 413 * <ul><li>If the argument value is already equal to a mathematical 414 * integer, then the result is the same as the argument. 415 * <li>If the argument is NaN or an infinity or positive zero or negative 416 * zero, then the result is the same as the argument.</ul> 417 * 418 * @param a a value. 419 * @return the closest floating-point value to {@code a} that is 420 * equal to a mathematical integer. 421 * @author Joseph D. Darcy 422 */ 423 public static double rint(double a) { 424 /* 425 * If the absolute value of a is not less than 2^52, it 426 * is either a finite integer (the double format does not have 427 * enough significand bits for a number that large to have any 428 * fractional portion), an infinity, or a NaN. In any of 429 * these cases, rint of the argument is the argument. 430 * 431 * Otherwise, the sum (twoToThe52 + a ) will properly round 432 * away any fractional portion of a since ulp(twoToThe52) == 433 * 1.0; subtracting out twoToThe52 from this sum will then be 434 * exact and leave the rounded integer portion of a. 435 * 436 * This method does *not* need to be declared strictfp to get 437 * fully reproducible results. Whether or not a method is 438 * declared strictfp can only make a difference in the 439 * returned result if some operation would overflow or 440 * underflow with strictfp semantics. The operation 441 * (twoToThe52 + a ) cannot overflow since large values of a 442 * are screened out; the add cannot underflow since twoToThe52 443 * is too large. The subtraction ((twoToThe52 + a ) - 444 * twoToThe52) will be exact as discussed above and thus 445 * cannot overflow or meaningfully underflow. Finally, the 446 * last multiply in the return statement is by plus or minus 447 * 1.0, which is exact too. 448 */ 449 double twoToThe52 = (double)(1L << 52); // 2^52 450 double sign = Math.copySign(1.0, a); // preserve sign info 451 a = Math.abs(a); 452 453 if (a < twoToThe52) { // E_min <= ilogb(a) <= 51 454 a = ((twoToThe52 + a ) - twoToThe52); 455 } 456 457 return sign * a; // restore original sign 458 } 459 460 /** 461 * Returns the angle <i>theta</i> from the conversion of rectangular 462 * coordinates ({@code x}, {@code y}) to polar 463 * coordinates (r, <i>theta</i>). 464 * This method computes the phase <i>theta</i> by computing an arc tangent 465 * of {@code y/x} in the range of -<i>pi</i> to <i>pi</i>. Special 466 * cases: 467 * <ul><li>If either argument is NaN, then the result is NaN. 468 * <li>If the first argument is positive zero and the second argument 469 * is positive, or the first argument is positive and finite and the 470 * second argument is positive infinity, then the result is positive 471 * zero. 472 * <li>If the first argument is negative zero and the second argument 473 * is positive, or the first argument is negative and finite and the 474 * second argument is positive infinity, then the result is negative zero. 475 * <li>If the first argument is positive zero and the second argument 476 * is negative, or the first argument is positive and finite and the 477 * second argument is negative infinity, then the result is the 478 * {@code double} value closest to <i>pi</i>. 479 * <li>If the first argument is negative zero and the second argument 480 * is negative, or the first argument is negative and finite and the 481 * second argument is negative infinity, then the result is the 482 * {@code double} value closest to -<i>pi</i>. 483 * <li>If the first argument is positive and the second argument is 484 * positive zero or negative zero, or the first argument is positive 485 * infinity and the second argument is finite, then the result is the 486 * {@code double} value closest to <i>pi</i>/2. 487 * <li>If the first argument is negative and the second argument is 488 * positive zero or negative zero, or the first argument is negative 489 * infinity and the second argument is finite, then the result is the 490 * {@code double} value closest to -<i>pi</i>/2. 491 * <li>If both arguments are positive infinity, then the result is the 492 * {@code double} value closest to <i>pi</i>/4. 493 * <li>If the first argument is positive infinity and the second argument 494 * is negative infinity, then the result is the {@code double} 495 * value closest to 3*<i>pi</i>/4. 496 * <li>If the first argument is negative infinity and the second argument 497 * is positive infinity, then the result is the {@code double} value 498 * closest to -<i>pi</i>/4. 499 * <li>If both arguments are negative infinity, then the result is the 500 * {@code double} value closest to -3*<i>pi</i>/4.</ul> 501 * 502 * @param y the ordinate coordinate 503 * @param x the abscissa coordinate 504 * @return the <i>theta</i> component of the point 505 * (<i>r</i>, <i>theta</i>) 506 * in polar coordinates that corresponds to the point 507 * (<i>x</i>, <i>y</i>) in Cartesian coordinates. 508 */ 509 public static native double atan2(double y, double x); 510 511 512 /** 513 * Returns the value of the first argument raised to the power of the 514 * second argument. Special cases: 515 * 516 * <ul><li>If the second argument is positive or negative zero, then the 517 * result is 1.0. 518 * <li>If the second argument is 1.0, then the result is the same as the 519 * first argument. 520 * <li>If the second argument is NaN, then the result is NaN. 521 * <li>If the first argument is NaN and the second argument is nonzero, 522 * then the result is NaN. 523 * 524 * <li>If 525 * <ul> 526 * <li>the absolute value of the first argument is greater than 1 527 * and the second argument is positive infinity, or 528 * <li>the absolute value of the first argument is less than 1 and 529 * the second argument is negative infinity, 530 * </ul> 531 * then the result is positive infinity. 532 * 533 * <li>If 534 * <ul> 535 * <li>the absolute value of the first argument is greater than 1 and 536 * the second argument is negative infinity, or 537 * <li>the absolute value of the 538 * first argument is less than 1 and the second argument is positive 539 * infinity, 540 * </ul> 541 * then the result is positive zero. 542 * 543 * <li>If the absolute value of the first argument equals 1 and the 544 * second argument is infinite, then the result is NaN. 545 * 546 * <li>If 547 * <ul> 548 * <li>the first argument is positive zero and the second argument 549 * is greater than zero, or 550 * <li>the first argument is positive infinity and the second 551 * argument is less than zero, 552 * </ul> 553 * then the result is positive zero. 554 * 555 * <li>If 556 * <ul> 557 * <li>the first argument is positive zero and the second argument 558 * is less than zero, or 559 * <li>the first argument is positive infinity and the second 560 * argument is greater than zero, 561 * </ul> 562 * then the result is positive infinity. 563 * 564 * <li>If 565 * <ul> 566 * <li>the first argument is negative zero and the second argument 567 * is greater than zero but not a finite odd integer, or 568 * <li>the first argument is negative infinity and the second 569 * argument is less than zero but not a finite odd integer, 570 * </ul> 571 * then the result is positive zero. 572 * 573 * <li>If 574 * <ul> 575 * <li>the first argument is negative zero and the second argument 576 * is a positive finite odd integer, or 577 * <li>the first argument is negative infinity and the second 578 * argument is a negative finite odd integer, 579 * </ul> 580 * then the result is negative zero. 581 * 582 * <li>If 583 * <ul> 584 * <li>the first argument is negative zero and the second argument 585 * is less than zero but not a finite odd integer, or 586 * <li>the first argument is negative infinity and the second 587 * argument is greater than zero but not a finite odd integer, 588 * </ul> 589 * then the result is positive infinity. 590 * 591 * <li>If 592 * <ul> 593 * <li>the first argument is negative zero and the second argument 594 * is a negative finite odd integer, or 595 * <li>the first argument is negative infinity and the second 596 * argument is a positive finite odd integer, 597 * </ul> 598 * then the result is negative infinity. 599 * 600 * <li>If the first argument is finite and less than zero 601 * <ul> 602 * <li> if the second argument is a finite even integer, the 603 * result is equal to the result of raising the absolute value of 604 * the first argument to the power of the second argument 605 * 606 * <li>if the second argument is a finite odd integer, the result 607 * is equal to the negative of the result of raising the absolute 608 * value of the first argument to the power of the second 609 * argument 610 * 611 * <li>if the second argument is finite and not an integer, then 612 * the result is NaN. 613 * </ul> 614 * 615 * <li>If both arguments are integers, then the result is exactly equal 616 * to the mathematical result of raising the first argument to the power 617 * of the second argument if that result can in fact be represented 618 * exactly as a {@code double} value.</ul> 619 * 620 * <p>(In the foregoing descriptions, a floating-point value is 621 * considered to be an integer if and only if it is finite and a 622 * fixed point of the method {@link #ceil ceil} or, 623 * equivalently, a fixed point of the method {@link #floor 624 * floor}. A value is a fixed point of a one-argument 625 * method if and only if the result of applying the method to the 626 * value is equal to the value.) 627 * 628 * @param a base. 629 * @param b the exponent. 630 * @return the value {@code a}<sup>{@code b}</sup>. 631 */ 632 public static native double pow(double a, double b); 633 634 /** 635 * Returns the closest {@code int} to the argument, with ties 636 * rounding to positive infinity. 637 * 638 * <p>Special cases: 639 * <ul><li>If the argument is NaN, the result is 0. 640 * <li>If the argument is negative infinity or any value less than or 641 * equal to the value of {@code Integer.MIN_VALUE}, the result is 642 * equal to the value of {@code Integer.MIN_VALUE}. 643 * <li>If the argument is positive infinity or any value greater than or 644 * equal to the value of {@code Integer.MAX_VALUE}, the result is 645 * equal to the value of {@code Integer.MAX_VALUE}.</ul> 646 * 647 * @param a a floating-point value to be rounded to an integer. 648 * @return the value of the argument rounded to the nearest 649 * {@code int} value. 650 * @see java.lang.Integer#MAX_VALUE 651 * @see java.lang.Integer#MIN_VALUE 652 */ 653 public static int round(float a) { 654 return Math.round(a); 655 } 656 657 /** 658 * Returns the closest {@code long} to the argument, with ties 659 * rounding to positive infinity. 660 * 661 * <p>Special cases: 662 * <ul><li>If the argument is NaN, the result is 0. 663 * <li>If the argument is negative infinity or any value less than or 664 * equal to the value of {@code Long.MIN_VALUE}, the result is 665 * equal to the value of {@code Long.MIN_VALUE}. 666 * <li>If the argument is positive infinity or any value greater than or 667 * equal to the value of {@code Long.MAX_VALUE}, the result is 668 * equal to the value of {@code Long.MAX_VALUE}.</ul> 669 * 670 * @param a a floating-point value to be rounded to a 671 * {@code long}. 672 * @return the value of the argument rounded to the nearest 673 * {@code long} value. 674 * @see java.lang.Long#MAX_VALUE 675 * @see java.lang.Long#MIN_VALUE 676 */ 677 public static long round(double a) { 678 return Math.round(a); 679 } 680 681 private static final class RandomNumberGeneratorHolder { 682 static final Random randomNumberGenerator = new Random(); 683 } 684 685 /** 686 * Returns a {@code double} value with a positive sign, greater 687 * than or equal to {@code 0.0} and less than {@code 1.0}. 688 * Returned values are chosen pseudorandomly with (approximately) 689 * uniform distribution from that range. 690 * 691 * <p>When this method is first called, it creates a single new 692 * pseudorandom-number generator, exactly as if by the expression 693 * 694 * <blockquote>{@code new java.util.Random()}</blockquote> 695 * 696 * This new pseudorandom-number generator is used thereafter for 697 * all calls to this method and is used nowhere else. 698 * 699 * <p>This method is properly synchronized to allow correct use by 700 * more than one thread. However, if many threads need to generate 701 * pseudorandom numbers at a great rate, it may reduce contention 702 * for each thread to have its own pseudorandom-number generator. 703 * 704 * @return a pseudorandom {@code double} greater than or equal 705 * to {@code 0.0} and less than {@code 1.0}. 706 * @see Random#nextDouble() 707 */ 708 public static double random() { 709 return RandomNumberGeneratorHolder.randomNumberGenerator.nextDouble(); 710 } 711 712 /** 713 * Returns the sum of its arguments, 714 * throwing an exception if the result overflows an {@code int}. 715 * 716 * @param x the first value 717 * @param y the second value 718 * @return the result 719 * @throws ArithmeticException if the result overflows an int 720 * @see Math#addExact(int,int) 721 * @since 1.8 722 */ 723 public static int addExact(int x, int y) { 724 return Math.addExact(x, y); 725 } 726 727 /** 728 * Returns the sum of its arguments, 729 * throwing an exception if the result overflows a {@code long}. 730 * 731 * @param x the first value 732 * @param y the second value 733 * @return the result 734 * @throws ArithmeticException if the result overflows a long 735 * @see Math#addExact(long,long) 736 * @since 1.8 737 */ 738 public static long addExact(long x, long y) { 739 return Math.addExact(x, y); 740 } 741 742 /** 743 * Returns the difference of the arguments, 744 * throwing an exception if the result overflows an {@code int}. 745 * 746 * @param x the first value 747 * @param y the second value to subtract from the first 748 * @return the result 749 * @throws ArithmeticException if the result overflows an int 750 * @see Math#subtractExact(int,int) 751 * @since 1.8 752 */ 753 public static int subtractExact(int x, int y) { 754 return Math.subtractExact(x, y); 755 } 756 757 /** 758 * Returns the difference of the arguments, 759 * throwing an exception if the result overflows a {@code long}. 760 * 761 * @param x the first value 762 * @param y the second value to subtract from the first 763 * @return the result 764 * @throws ArithmeticException if the result overflows a long 765 * @see Math#subtractExact(long,long) 766 * @since 1.8 767 */ 768 public static long subtractExact(long x, long y) { 769 return Math.subtractExact(x, y); 770 } 771 772 /** 773 * Returns the product of the arguments, 774 * throwing an exception if the result overflows an {@code int}. 775 * 776 * @param x the first value 777 * @param y the second value 778 * @return the result 779 * @throws ArithmeticException if the result overflows an int 780 * @see Math#multiplyExact(int,int) 781 * @since 1.8 782 */ 783 public static int multiplyExact(int x, int y) { 784 return Math.multiplyExact(x, y); 785 } 786 787 /** 788 * Returns the product of the arguments, 789 * throwing an exception if the result overflows a {@code long}. 790 * 791 * @param x the first value 792 * @param y the second value 793 * @return the result 794 * @throws ArithmeticException if the result overflows a long 795 * @see Math#multiplyExact(long,long) 796 * @since 1.8 797 */ 798 public static long multiplyExact(long x, long y) { 799 return Math.multiplyExact(x, y); 800 } 801 802 /** 803 * Returns the value of the {@code long} argument; 804 * throwing an exception if the value overflows an {@code int}. 805 * 806 * @param value the long value 807 * @return the argument as an int 808 * @throws ArithmeticException if the {@code argument} overflows an int 809 * @see Math#toIntExact(long) 810 * @since 1.8 811 */ 812 public static int toIntExact(long value) { 813 return Math.toIntExact(value); 814 } 815 816 /** 817 * Returns the largest (closest to positive infinity) 818 * {@code int} value that is less than or equal to the algebraic quotient. 819 * There is one special case, if the dividend is the 820 * {@linkplain Integer#MIN_VALUE Integer.MIN_VALUE} and the divisor is {@code -1}, 821 * then integer overflow occurs and 822 * the result is equal to the {@code Integer.MIN_VALUE}. 823 * <p> 824 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and 825 * a comparison to the integer division {@code /} operator. 826 * 827 * @param x the dividend 828 * @param y the divisor 829 * @return the largest (closest to positive infinity) 830 * {@code int} value that is less than or equal to the algebraic quotient. 831 * @throws ArithmeticException if the divisor {@code y} is zero 832 * @see Math#floorDiv(int, int) 833 * @see Math#floor(double) 834 * @since 1.8 835 */ 836 public static int floorDiv(int x, int y) { 837 return Math.floorDiv(x, y); 838 } 839 840 /** 841 * Returns the largest (closest to positive infinity) 842 * {@code long} value that is less than or equal to the algebraic quotient. 843 * There is one special case, if the dividend is the 844 * {@linkplain Long#MIN_VALUE Long.MIN_VALUE} and the divisor is {@code -1}, 845 * then integer overflow occurs and 846 * the result is equal to the {@code Long.MIN_VALUE}. 847 * <p> 848 * See {@link Math#floorDiv(int, int) Math.floorDiv} for examples and 849 * a comparison to the integer division {@code /} operator. 850 * 851 * @param x the dividend 852 * @param y the divisor 853 * @return the largest (closest to positive infinity) 854 * {@code long} value that is less than or equal to the algebraic quotient. 855 * @throws ArithmeticException if the divisor {@code y} is zero 856 * @see Math#floorDiv(long, long) 857 * @see Math#floor(double) 858 * @since 1.8 859 */ 860 public static long floorDiv(long x, long y) { 861 return Math.floorDiv(x, y); 862 } 863 864 /** 865 * Returns the floor modulus of the {@code int} arguments. 866 * <p> 867 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, 868 * has the same sign as the divisor {@code y}, and 869 * is in the range of {@code -abs(y) < r < +abs(y)}. 870 * <p> 871 * The relationship between {@code floorDiv} and {@code floorMod} is such that: 872 * <ul> 873 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} 874 * </ul> 875 * <p> 876 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and 877 * a comparison to the {@code %} operator. 878 * 879 * @param x the dividend 880 * @param y the divisor 881 * @return the floor modulus {@code x - (floorDiv(x, y) * y)} 882 * @throws ArithmeticException if the divisor {@code y} is zero 883 * @see Math#floorMod(int, int) 884 * @see StrictMath#floorDiv(int, int) 885 * @since 1.8 886 */ 887 public static int floorMod(int x, int y) { 888 return Math.floorMod(x , y); 889 } 890 /** 891 * Returns the floor modulus of the {@code long} arguments. 892 * <p> 893 * The floor modulus is {@code x - (floorDiv(x, y) * y)}, 894 * has the same sign as the divisor {@code y}, and 895 * is in the range of {@code -abs(y) < r < +abs(y)}. 896 * <p> 897 * The relationship between {@code floorDiv} and {@code floorMod} is such that: 898 * <ul> 899 * <li>{@code floorDiv(x, y) * y + floorMod(x, y) == x} 900 * </ul> 901 * <p> 902 * See {@link Math#floorMod(int, int) Math.floorMod} for examples and 903 * a comparison to the {@code %} operator. 904 * 905 * @param x the dividend 906 * @param y the divisor 907 * @return the floor modulus {@code x - (floorDiv(x, y) * y)} 908 * @throws ArithmeticException if the divisor {@code y} is zero 909 * @see Math#floorMod(long, long) 910 * @see StrictMath#floorDiv(long, long) 911 * @since 1.8 912 */ 913 public static long floorMod(long x, long y) { 914 return Math.floorMod(x, y); 915 } 916 917 /** 918 * Returns the absolute value of an {@code int} value. 919 * If the argument is not negative, the argument is returned. 920 * If the argument is negative, the negation of the argument is returned. 921 * 922 * <p>Note that if the argument is equal to the value of 923 * {@link Integer#MIN_VALUE}, the most negative representable 924 * {@code int} value, the result is that same value, which is 925 * negative. 926 * 927 * @param a the argument whose absolute value is to be determined. 928 * @return the absolute value of the argument. 929 */ 930 public static int abs(int a) { 931 return Math.abs(a); 932 } 933 934 /** 935 * Returns the absolute value of a {@code long} value. 936 * If the argument is not negative, the argument is returned. 937 * If the argument is negative, the negation of the argument is returned. 938 * 939 * <p>Note that if the argument is equal to the value of 940 * {@link Long#MIN_VALUE}, the most negative representable 941 * {@code long} value, the result is that same value, which 942 * is negative. 943 * 944 * @param a the argument whose absolute value is to be determined. 945 * @return the absolute value of the argument. 946 */ 947 public static long abs(long a) { 948 return Math.abs(a); 949 } 950 951 /** 952 * Returns the absolute value of a {@code float} value. 953 * If the argument is not negative, the argument is returned. 954 * If the argument is negative, the negation of the argument is returned. 955 * Special cases: 956 * <ul><li>If the argument is positive zero or negative zero, the 957 * result is positive zero. 958 * <li>If the argument is infinite, the result is positive infinity. 959 * <li>If the argument is NaN, the result is NaN.</ul> 960 * In other words, the result is the same as the value of the expression: 961 * <p>{@code Float.intBitsToFloat(0x7fffffff & Float.floatToIntBits(a))} 962 * 963 * @param a the argument whose absolute value is to be determined 964 * @return the absolute value of the argument. 965 */ 966 public static float abs(float a) { 967 return Math.abs(a); 968 } 969 970 /** 971 * Returns the absolute value of a {@code double} value. 972 * If the argument is not negative, the argument is returned. 973 * If the argument is negative, the negation of the argument is returned. 974 * Special cases: 975 * <ul><li>If the argument is positive zero or negative zero, the result 976 * is positive zero. 977 * <li>If the argument is infinite, the result is positive infinity. 978 * <li>If the argument is NaN, the result is NaN.</ul> 979 * In other words, the result is the same as the value of the expression: 980 * <p>{@code Double.longBitsToDouble((Double.doubleToLongBits(a)<<1)>>>1)} 981 * 982 * @param a the argument whose absolute value is to be determined 983 * @return the absolute value of the argument. 984 */ 985 public static double abs(double a) { 986 return Math.abs(a); 987 } 988 989 /** 990 * Returns the greater of two {@code int} values. That is, the 991 * result is the argument closer to the value of 992 * {@link Integer#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 */ 999 public static int max(int a, int b) { 1000 return Math.max(a, b); 1001 } 1002 1003 /** 1004 * Returns the greater of two {@code long} values. That is, the 1005 * result is the argument closer to the value of 1006 * {@link Long#MAX_VALUE}. If the arguments have the same value, 1007 * the result is that same value. 1008 * 1009 * @param a an argument. 1010 * @param b another argument. 1011 * @return the larger of {@code a} and {@code b}. 1012 */ 1013 public static long max(long a, long b) { 1014 return Math.max(a, b); 1015 } 1016 1017 /** 1018 * Returns the greater of two {@code float} values. That is, 1019 * the result is the argument closer to positive infinity. If the 1020 * arguments have the same value, the result is that same 1021 * value. If either value is NaN, then the result is NaN. Unlike 1022 * the numerical comparison operators, this method considers 1023 * negative zero to be strictly smaller than positive zero. If one 1024 * argument is positive zero and the other negative zero, the 1025 * result is positive zero. 1026 * 1027 * @param a an argument. 1028 * @param b another argument. 1029 * @return the larger of {@code a} and {@code b}. 1030 */ 1031 public static float max(float a, float b) { 1032 return Math.max(a, b); 1033 } 1034 1035 /** 1036 * Returns the greater of two {@code double} values. That 1037 * is, the result is the argument closer to positive infinity. If 1038 * the arguments have the same value, the result is that same 1039 * value. If either value is NaN, then the result is NaN. Unlike 1040 * the numerical comparison operators, this method considers 1041 * negative zero to be strictly smaller than positive zero. If one 1042 * argument is positive zero and the other negative zero, the 1043 * result is positive zero. 1044 * 1045 * @param a an argument. 1046 * @param b another argument. 1047 * @return the larger of {@code a} and {@code b}. 1048 */ 1049 public static double max(double a, double b) { 1050 return Math.max(a, b); 1051 } 1052 1053 /** 1054 * Returns the smaller of two {@code int} values. That is, 1055 * the result the argument closer to the value of 1056 * {@link Integer#MIN_VALUE}. If the arguments have the same 1057 * value, the result is that same value. 1058 * 1059 * @param a an argument. 1060 * @param b another argument. 1061 * @return the smaller of {@code a} and {@code b}. 1062 */ 1063 public static int min(int a, int b) { 1064 return Math.min(a, b); 1065 } 1066 1067 /** 1068 * Returns the smaller of two {@code long} values. That is, 1069 * the result is the argument closer to the value of 1070 * {@link Long#MIN_VALUE}. If the arguments have the same 1071 * value, the result is that same value. 1072 * 1073 * @param a an argument. 1074 * @param b another argument. 1075 * @return the smaller of {@code a} and {@code b}. 1076 */ 1077 public static long min(long a, long b) { 1078 return Math.min(a, b); 1079 } 1080 1081 /** 1082 * Returns the smaller of two {@code float} values. That is, 1083 * the result is the value closer to negative infinity. If the 1084 * arguments have the same value, the result is that same 1085 * value. If either value is NaN, then the result is NaN. Unlike 1086 * the numerical comparison operators, this method considers 1087 * negative zero to be strictly smaller than positive zero. If 1088 * one argument is positive zero and the other is negative zero, 1089 * the result is negative zero. 1090 * 1091 * @param a an argument. 1092 * @param b another argument. 1093 * @return the smaller of {@code a} and {@code b.} 1094 */ 1095 public static float min(float a, float b) { 1096 return Math.min(a, b); 1097 } 1098 1099 /** 1100 * Returns the smaller of two {@code double} values. That 1101 * is, the result is the value closer to negative infinity. If the 1102 * arguments have the same value, the result is that same 1103 * value. If either value is NaN, then the result is NaN. Unlike 1104 * the numerical comparison operators, this method considers 1105 * negative zero to be strictly smaller than positive zero. If one 1106 * argument is positive zero and the other is negative zero, the 1107 * result is negative zero. 1108 * 1109 * @param a an argument. 1110 * @param b another argument. 1111 * @return the smaller of {@code a} and {@code b}. 1112 */ 1113 public static double min(double a, double b) { 1114 return Math.min(a, b); 1115 } 1116 1117 /** 1118 * Returns the size of an ulp of the argument. An ulp, unit in 1119 * the last place, of a {@code double} value is the positive 1120 * distance between this floating-point value and the {@code 1121 * double} value next larger in magnitude. Note that for non-NaN 1122 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. 1123 * 1124 * <p>Special Cases: 1125 * <ul> 1126 * <li> If the argument is NaN, then the result is NaN. 1127 * <li> If the argument is positive or negative infinity, then the 1128 * result is positive infinity. 1129 * <li> If the argument is positive or negative zero, then the result is 1130 * {@code Double.MIN_VALUE}. 1131 * <li> If the argument is ±{@code Double.MAX_VALUE}, then 1132 * the result is equal to 2<sup>971</sup>. 1133 * </ul> 1134 * 1135 * @param d the floating-point value whose ulp is to be returned 1136 * @return the size of an ulp of the argument 1137 * @author Joseph D. Darcy 1138 * @since 1.5 1139 */ 1140 public static double ulp(double d) { 1141 return Math.ulp(d); 1142 } 1143 1144 /** 1145 * Returns the size of an ulp of the argument. An ulp, unit in 1146 * the last place, of a {@code float} value is the positive 1147 * distance between this floating-point value and the {@code 1148 * float} value next larger in magnitude. Note that for non-NaN 1149 * <i>x</i>, <code>ulp(-<i>x</i>) == ulp(<i>x</i>)</code>. 1150 * 1151 * <p>Special Cases: 1152 * <ul> 1153 * <li> If the argument is NaN, then the result is NaN. 1154 * <li> If the argument is positive or negative infinity, then the 1155 * result is positive infinity. 1156 * <li> If the argument is positive or negative zero, then the result is 1157 * {@code Float.MIN_VALUE}. 1158 * <li> If the argument is ±{@code Float.MAX_VALUE}, then 1159 * the result is equal to 2<sup>104</sup>. 1160 * </ul> 1161 * 1162 * @param f the floating-point value whose ulp is to be returned 1163 * @return the size of an ulp of the argument 1164 * @author Joseph D. Darcy 1165 * @since 1.5 1166 */ 1167 public static float ulp(float f) { 1168 return Math.ulp(f); 1169 } 1170 1171 /** 1172 * Returns the signum function of the argument; zero if the argument 1173 * is zero, 1.0 if the argument is greater than zero, -1.0 if the 1174 * argument is less than zero. 1175 * 1176 * <p>Special Cases: 1177 * <ul> 1178 * <li> If the argument is NaN, then the result is NaN. 1179 * <li> If the argument is positive zero or negative zero, then the 1180 * result is the same as the argument. 1181 * </ul> 1182 * 1183 * @param d the floating-point value whose signum is to be returned 1184 * @return the signum function of the argument 1185 * @author Joseph D. Darcy 1186 * @since 1.5 1187 */ 1188 public static double signum(double d) { 1189 return Math.signum(d); 1190 } 1191 1192 /** 1193 * Returns the signum function of the argument; zero if the argument 1194 * is zero, 1.0f if the argument is greater than zero, -1.0f if the 1195 * argument is less than zero. 1196 * 1197 * <p>Special Cases: 1198 * <ul> 1199 * <li> If the argument is NaN, then the result is NaN. 1200 * <li> If the argument is positive zero or negative zero, then the 1201 * result is the same as the argument. 1202 * </ul> 1203 * 1204 * @param f the floating-point value whose signum is to be returned 1205 * @return the signum function of the argument 1206 * @author Joseph D. Darcy 1207 * @since 1.5 1208 */ 1209 public static float signum(float f) { 1210 return Math.signum(f); 1211 } 1212 1213 /** 1214 * Returns the hyperbolic sine of a {@code double} value. 1215 * The hyperbolic sine of <i>x</i> is defined to be 1216 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/2 1217 * where <i>e</i> is {@linkplain Math#E Euler's number}. 1218 * 1219 * <p>Special cases: 1220 * <ul> 1221 * 1222 * <li>If the argument is NaN, then the result is NaN. 1223 * 1224 * <li>If the argument is infinite, then the result is an infinity 1225 * with the same sign as the argument. 1226 * 1227 * <li>If the argument is zero, then the result is a zero with the 1228 * same sign as the argument. 1229 * 1230 * </ul> 1231 * 1232 * @param x The number whose hyperbolic sine is to be returned. 1233 * @return The hyperbolic sine of {@code x}. 1234 * @since 1.5 1235 */ 1236 public static native double sinh(double x); 1237 1238 /** 1239 * Returns the hyperbolic cosine of a {@code double} value. 1240 * The hyperbolic cosine of <i>x</i> is defined to be 1241 * (<i>e<sup>x</sup> + e<sup>-x</sup></i>)/2 1242 * where <i>e</i> is {@linkplain Math#E Euler's number}. 1243 * 1244 * <p>Special cases: 1245 * <ul> 1246 * 1247 * <li>If the argument is NaN, then the result is NaN. 1248 * 1249 * <li>If the argument is infinite, then the result is positive 1250 * infinity. 1251 * 1252 * <li>If the argument is zero, then the result is {@code 1.0}. 1253 * 1254 * </ul> 1255 * 1256 * @param x The number whose hyperbolic cosine is to be returned. 1257 * @return The hyperbolic cosine of {@code x}. 1258 * @since 1.5 1259 */ 1260 public static native double cosh(double x); 1261 1262 /** 1263 * Returns the hyperbolic tangent of a {@code double} value. 1264 * The hyperbolic tangent of <i>x</i> is defined to be 1265 * (<i>e<sup>x</sup> - e<sup>-x</sup></i>)/(<i>e<sup>x</sup> + e<sup>-x</sup></i>), 1266 * in other words, {@linkplain Math#sinh 1267 * sinh(<i>x</i>)}/{@linkplain Math#cosh cosh(<i>x</i>)}. Note 1268 * that the absolute value of the exact tanh is always less than 1269 * 1. 1270 * 1271 * <p>Special cases: 1272 * <ul> 1273 * 1274 * <li>If the argument is NaN, then the result is NaN. 1275 * 1276 * <li>If the argument is zero, then the result is a zero with the 1277 * same sign as the argument. 1278 * 1279 * <li>If the argument is positive infinity, then the result is 1280 * {@code +1.0}. 1281 * 1282 * <li>If the argument is negative infinity, then the result is 1283 * {@code -1.0}. 1284 * 1285 * </ul> 1286 * 1287 * @param x The number whose hyperbolic tangent is to be returned. 1288 * @return The hyperbolic tangent of {@code x}. 1289 * @since 1.5 1290 */ 1291 public static native double tanh(double x); 1292 1293 /** 1294 * Returns sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) 1295 * without intermediate overflow or underflow. 1296 * 1297 * <p>Special cases: 1298 * <ul> 1299 * 1300 * <li> If either argument is infinite, then the result 1301 * is positive infinity. 1302 * 1303 * <li> If either argument is NaN and neither argument is infinite, 1304 * then the result is NaN. 1305 * 1306 * </ul> 1307 * 1308 * @param x a value 1309 * @param y a value 1310 * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>) 1311 * without intermediate overflow or underflow 1312 * @since 1.5 1313 */ 1314 public static native double hypot(double x, double y); 1315 1316 /** 1317 * Returns <i>e</i><sup>x</sup> -1. Note that for values of 1318 * <i>x</i> near 0, the exact sum of 1319 * {@code expm1(x)} + 1 is much closer to the true 1320 * result of <i>e</i><sup>x</sup> than {@code exp(x)}. 1321 * 1322 * <p>Special cases: 1323 * <ul> 1324 * <li>If the argument is NaN, the result is NaN. 1325 * 1326 * <li>If the argument is positive infinity, then the result is 1327 * positive infinity. 1328 * 1329 * <li>If the argument is negative infinity, then the result is 1330 * -1.0. 1331 * 1332 * <li>If the argument is zero, then the result is a zero with the 1333 * same sign as the argument. 1334 * 1335 * </ul> 1336 * 1337 * @param x the exponent to raise <i>e</i> to in the computation of 1338 * <i>e</i><sup>{@code x}</sup> -1. 1339 * @return the value <i>e</i><sup>{@code x}</sup> - 1. 1340 * @since 1.5 1341 */ 1342 public static native double expm1(double x); 1343 1344 /** 1345 * Returns the natural logarithm of the sum of the argument and 1. 1346 * Note that for small values {@code x}, the result of 1347 * {@code log1p(x)} is much closer to the true result of ln(1 1348 * + {@code x}) than the floating-point evaluation of 1349 * {@code log(1.0+x)}. 1350 * 1351 * <p>Special cases: 1352 * <ul> 1353 * 1354 * <li>If the argument is NaN or less than -1, then the result is 1355 * NaN. 1356 * 1357 * <li>If the argument is positive infinity, then the result is 1358 * positive infinity. 1359 * 1360 * <li>If the argument is negative one, then the result is 1361 * negative infinity. 1362 * 1363 * <li>If the argument is zero, then the result is a zero with the 1364 * same sign as the argument. 1365 * 1366 * </ul> 1367 * 1368 * @param x a value 1369 * @return the value ln({@code x} + 1), the natural 1370 * log of {@code x} + 1 1371 * @since 1.5 1372 */ 1373 public static native double log1p(double x); 1374 1375 /** 1376 * Returns the first floating-point argument with the sign of the 1377 * second floating-point argument. For this method, a NaN 1378 * {@code sign} argument is always treated as if it were 1379 * positive. 1380 * 1381 * @param magnitude the parameter providing the magnitude of the result 1382 * @param sign the parameter providing the sign of the result 1383 * @return a value with the magnitude of {@code magnitude} 1384 * and the sign of {@code sign}. 1385 * @since 1.6 1386 */ 1387 public static double copySign(double magnitude, double sign) { 1388 return Math.copySign(magnitude, (Double.isNaN(sign)?1.0d:sign)); 1389 } 1390 1391 /** 1392 * Returns the first floating-point argument with the sign of the 1393 * second floating-point argument. For this method, a NaN 1394 * {@code sign} argument is always treated as if it were 1395 * positive. 1396 * 1397 * @param magnitude the parameter providing the magnitude of the result 1398 * @param sign the parameter providing the sign of the result 1399 * @return a value with the magnitude of {@code magnitude} 1400 * and the sign of {@code sign}. 1401 * @since 1.6 1402 */ 1403 public static float copySign(float magnitude, float sign) { 1404 return Math.copySign(magnitude, (Float.isNaN(sign)?1.0f:sign)); 1405 } 1406 /** 1407 * Returns the unbiased exponent used in the representation of a 1408 * {@code float}. Special cases: 1409 * 1410 * <ul> 1411 * <li>If the argument is NaN or infinite, then the result is 1412 * {@link Float#MAX_EXPONENT} + 1. 1413 * <li>If the argument is zero or subnormal, then the result is 1414 * {@link Float#MIN_EXPONENT} -1. 1415 * </ul> 1416 * @param f a {@code float} value 1417 * @return the unbiased exponent of the argument 1418 * @since 1.6 1419 */ 1420 public static int getExponent(float f) { 1421 return Math.getExponent(f); 1422 } 1423 1424 /** 1425 * Returns the unbiased exponent used in the representation of a 1426 * {@code double}. Special cases: 1427 * 1428 * <ul> 1429 * <li>If the argument is NaN or infinite, then the result is 1430 * {@link Double#MAX_EXPONENT} + 1. 1431 * <li>If the argument is zero or subnormal, then the result is 1432 * {@link Double#MIN_EXPONENT} -1. 1433 * </ul> 1434 * @param d a {@code double} value 1435 * @return the unbiased exponent of the argument 1436 * @since 1.6 1437 */ 1438 public static int getExponent(double d) { 1439 return Math.getExponent(d); 1440 } 1441 1442 /** 1443 * Returns the floating-point number adjacent to the first 1444 * argument in the direction of the second argument. If both 1445 * arguments compare as equal the second argument is returned. 1446 * 1447 * <p>Special cases: 1448 * <ul> 1449 * <li> If either argument is a NaN, then NaN is returned. 1450 * 1451 * <li> If both arguments are signed zeros, {@code direction} 1452 * is returned unchanged (as implied by the requirement of 1453 * returning the second argument if the arguments compare as 1454 * equal). 1455 * 1456 * <li> If {@code start} is 1457 * ±{@link Double#MIN_VALUE} and {@code direction} 1458 * has a value such that the result should have a smaller 1459 * magnitude, then a zero with the same sign as {@code start} 1460 * is returned. 1461 * 1462 * <li> If {@code start} is infinite and 1463 * {@code direction} has a value such that the result should 1464 * have a smaller magnitude, {@link Double#MAX_VALUE} with the 1465 * same sign as {@code start} is returned. 1466 * 1467 * <li> If {@code start} is equal to ± 1468 * {@link Double#MAX_VALUE} and {@code direction} has a 1469 * value such that the result should have a larger magnitude, an 1470 * infinity with same sign as {@code start} is returned. 1471 * </ul> 1472 * 1473 * @param start starting floating-point value 1474 * @param direction value indicating which of 1475 * {@code start}'s neighbors or {@code start} should 1476 * be returned 1477 * @return The floating-point number adjacent to {@code start} in the 1478 * direction of {@code direction}. 1479 * @since 1.6 1480 */ 1481 public static double nextAfter(double start, double direction) { 1482 return Math.nextAfter(start, direction); 1483 } 1484 1485 /** 1486 * Returns the floating-point number adjacent to the first 1487 * argument in the direction of the second argument. If both 1488 * arguments compare as equal a value equivalent to the second argument 1489 * is returned. 1490 * 1491 * <p>Special cases: 1492 * <ul> 1493 * <li> If either argument is a NaN, then NaN is returned. 1494 * 1495 * <li> If both arguments are signed zeros, a value equivalent 1496 * to {@code direction} is returned. 1497 * 1498 * <li> If {@code start} is 1499 * ±{@link Float#MIN_VALUE} and {@code direction} 1500 * has a value such that the result should have a smaller 1501 * magnitude, then a zero with the same sign as {@code start} 1502 * is returned. 1503 * 1504 * <li> If {@code start} is infinite and 1505 * {@code direction} has a value such that the result should 1506 * have a smaller magnitude, {@link Float#MAX_VALUE} with the 1507 * same sign as {@code start} is returned. 1508 * 1509 * <li> If {@code start} is equal to ± 1510 * {@link Float#MAX_VALUE} and {@code direction} has a 1511 * value such that the result should have a larger magnitude, an 1512 * infinity with same sign as {@code start} is returned. 1513 * </ul> 1514 * 1515 * @param start starting floating-point value 1516 * @param direction value indicating which of 1517 * {@code start}'s neighbors or {@code start} should 1518 * be returned 1519 * @return The floating-point number adjacent to {@code start} in the 1520 * direction of {@code direction}. 1521 * @since 1.6 1522 */ 1523 public static float nextAfter(float start, double direction) { 1524 return Math.nextAfter(start, direction); 1525 } 1526 1527 /** 1528 * Returns the floating-point value adjacent to {@code d} in 1529 * the direction of positive infinity. This method is 1530 * semantically equivalent to {@code nextAfter(d, 1531 * Double.POSITIVE_INFINITY)}; however, a {@code nextUp} 1532 * implementation may run faster than its equivalent 1533 * {@code nextAfter} call. 1534 * 1535 * <p>Special Cases: 1536 * <ul> 1537 * <li> If the argument is NaN, the result is NaN. 1538 * 1539 * <li> If the argument is positive infinity, the result is 1540 * positive infinity. 1541 * 1542 * <li> If the argument is zero, the result is 1543 * {@link Double#MIN_VALUE} 1544 * 1545 * </ul> 1546 * 1547 * @param d starting floating-point value 1548 * @return The adjacent floating-point value closer to positive 1549 * infinity. 1550 * @since 1.6 1551 */ 1552 public static double nextUp(double d) { 1553 return Math.nextUp(d); 1554 } 1555 1556 /** 1557 * Returns the floating-point value adjacent to {@code f} in 1558 * the direction of positive infinity. This method is 1559 * semantically equivalent to {@code nextAfter(f, 1560 * Float.POSITIVE_INFINITY)}; however, a {@code nextUp} 1561 * implementation may run faster than its equivalent 1562 * {@code nextAfter} call. 1563 * 1564 * <p>Special Cases: 1565 * <ul> 1566 * <li> If the argument is NaN, the result is NaN. 1567 * 1568 * <li> If the argument is positive infinity, the result is 1569 * positive infinity. 1570 * 1571 * <li> If the argument is zero, the result is 1572 * {@link Float#MIN_VALUE} 1573 * 1574 * </ul> 1575 * 1576 * @param f starting floating-point value 1577 * @return The adjacent floating-point value closer to positive 1578 * infinity. 1579 * @since 1.6 1580 */ 1581 public static float nextUp(float f) { 1582 return Math.nextUp(f); 1583 } 1584 1585 /** 1586 * Returns the floating-point value adjacent to {@code d} in 1587 * the direction of negative infinity. This method is 1588 * semantically equivalent to {@code nextAfter(d, 1589 * Double.NEGATIVE_INFINITY)}; however, a 1590 * {@code nextDown} implementation may run faster than its 1591 * equivalent {@code nextAfter} call. 1592 * 1593 * <p>Special Cases: 1594 * <ul> 1595 * <li> If the argument is NaN, the result is NaN. 1596 * 1597 * <li> If the argument is negative infinity, the result is 1598 * negative infinity. 1599 * 1600 * <li> If the argument is zero, the result is 1601 * {@code -Double.MIN_VALUE} 1602 * 1603 * </ul> 1604 * 1605 * @param d starting floating-point value 1606 * @return The adjacent floating-point value closer to negative 1607 * infinity. 1608 * @since 1.8 1609 */ 1610 public static double nextDown(double d) { 1611 return Math.nextDown(d); 1612 } 1613 1614 /** 1615 * Returns the floating-point value adjacent to {@code f} in 1616 * the direction of negative infinity. This method is 1617 * semantically equivalent to {@code nextAfter(f, 1618 * Float.NEGATIVE_INFINITY)}; however, a 1619 * {@code nextDown} implementation may run faster than its 1620 * equivalent {@code nextAfter} call. 1621 * 1622 * <p>Special Cases: 1623 * <ul> 1624 * <li> If the argument is NaN, the result is NaN. 1625 * 1626 * <li> If the argument is negative infinity, the result is 1627 * negative infinity. 1628 * 1629 * <li> If the argument is zero, the result is 1630 * {@code -Float.MIN_VALUE} 1631 * 1632 * </ul> 1633 * 1634 * @param f starting floating-point value 1635 * @return The adjacent floating-point value closer to negative 1636 * infinity. 1637 * @since 1.8 1638 */ 1639 public static float nextDown(float f) { 1640 return Math.nextDown(f); 1641 } 1642 1643 /** 1644 * Returns {@code d} × 1645 * 2<sup>{@code scaleFactor}</sup> rounded as if performed 1646 * by a single correctly rounded floating-point multiply to a 1647 * member of the double value set. See the Java 1648 * Language Specification for a discussion of floating-point 1649 * value sets. If the exponent of the result is between {@link 1650 * Double#MIN_EXPONENT} and {@link Double#MAX_EXPONENT}, the 1651 * answer is calculated exactly. If the exponent of the result 1652 * would be larger than {@code Double.MAX_EXPONENT}, an 1653 * infinity is returned. Note that if the result is subnormal, 1654 * precision may be lost; that is, when {@code scalb(x, n)} 1655 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal 1656 * <i>x</i>. When the result is non-NaN, the result has the same 1657 * sign as {@code d}. 1658 * 1659 * <p>Special cases: 1660 * <ul> 1661 * <li> If the first argument is NaN, NaN is returned. 1662 * <li> If the first argument is infinite, then an infinity of the 1663 * same sign is returned. 1664 * <li> If the first argument is zero, then a zero of the same 1665 * sign is returned. 1666 * </ul> 1667 * 1668 * @param d number to be scaled by a power of two. 1669 * @param scaleFactor power of 2 used to scale {@code d} 1670 * @return {@code d} × 2<sup>{@code scaleFactor}</sup> 1671 * @since 1.6 1672 */ 1673 public static double scalb(double d, int scaleFactor) { 1674 return Math.scalb(d, scaleFactor); 1675 } 1676 1677 /** 1678 * Returns {@code f} × 1679 * 2<sup>{@code scaleFactor}</sup> rounded as if performed 1680 * by a single correctly rounded floating-point multiply to a 1681 * member of the float value set. See the Java 1682 * Language Specification for a discussion of floating-point 1683 * value sets. If the exponent of the result is between {@link 1684 * Float#MIN_EXPONENT} and {@link Float#MAX_EXPONENT}, the 1685 * answer is calculated exactly. If the exponent of the result 1686 * would be larger than {@code Float.MAX_EXPONENT}, an 1687 * infinity is returned. Note that if the result is subnormal, 1688 * precision may be lost; that is, when {@code scalb(x, n)} 1689 * is subnormal, {@code scalb(scalb(x, n), -n)} may not equal 1690 * <i>x</i>. When the result is non-NaN, the result has the same 1691 * sign as {@code f}. 1692 * 1693 * <p>Special cases: 1694 * <ul> 1695 * <li> If the first argument is NaN, NaN is returned. 1696 * <li> If the first argument is infinite, then an infinity of the 1697 * same sign is returned. 1698 * <li> If the first argument is zero, then a zero of the same 1699 * sign is returned. 1700 * </ul> 1701 * 1702 * @param f number to be scaled by a power of two. 1703 * @param scaleFactor power of 2 used to scale {@code f} 1704 * @return {@code f} × 2<sup>{@code scaleFactor}</sup> 1705 * @since 1.6 1706 */ 1707 public static float scalb(float f, int scaleFactor) { 1708 return Math.scalb(f, scaleFactor); 1709 } 1710 } 1711
