1 /* 2 * Copyright (c) 1996, 2020, 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 /* 27 * Portions Copyright IBM Corporation, 2001. All Rights Reserved. 28 */ 29 30 package java.math; 31 32 import static java.math.BigInteger.LONG_MASK; 33 import java.util.Arrays; 34 import java.util.Objects; 35 36 /** 37 * Immutable, arbitrary-precision signed decimal numbers. A 38 * {@code BigDecimal} consists of an arbitrary precision integer 39 * <i>unscaled value</i> and a 32-bit integer <i>scale</i>. If zero 40 * or positive, the scale is the number of digits to the right of the 41 * decimal point. If negative, the unscaled value of the number is 42 * multiplied by ten to the power of the negation of the scale. The 43 * value of the number represented by the {@code BigDecimal} is 44 * therefore <code>(unscaledValue × 10<sup>-scale</sup>)</code>. 45 * 46 * <p>The {@code BigDecimal} class provides operations for 47 * arithmetic, scale manipulation, rounding, comparison, hashing, and 48 * format conversion. The {@link #toString} method provides a 49 * canonical representation of a {@code BigDecimal}. 50 * 51 * <p>The {@code BigDecimal} class gives its user complete control 52 * over rounding behavior. If no rounding mode is specified and the 53 * exact result cannot be represented, an exception is thrown; 54 * otherwise, calculations can be carried out to a chosen precision 55 * and rounding mode by supplying an appropriate {@link MathContext} 56 * object to the operation. In either case, eight <em>rounding 57 * modes</em> are provided for the control of rounding. Using the 58 * integer fields in this class (such as {@link #ROUND_HALF_UP}) to 59 * represent rounding mode is deprecated; the enumeration values 60 * of the {@code RoundingMode} {@code enum}, (such as {@link 61 * RoundingMode#HALF_UP}) should be used instead. 62 * 63 * <p>When a {@code MathContext} object is supplied with a precision 64 * setting of 0 (for example, {@link MathContext#UNLIMITED}), 65 * arithmetic operations are exact, as are the arithmetic methods 66 * which take no {@code MathContext} object. (This is the only 67 * behavior that was supported in releases prior to 5.) As a 68 * corollary of computing the exact result, the rounding mode setting 69 * of a {@code MathContext} object with a precision setting of 0 is 70 * not used and thus irrelevant. In the case of divide, the exact 71 * quotient could have an infinitely long decimal expansion; for 72 * example, 1 divided by 3. If the quotient has a nonterminating 73 * decimal expansion and the operation is specified to return an exact 74 * result, an {@code ArithmeticException} is thrown. Otherwise, the 75 * exact result of the division is returned, as done for other 76 * operations. 77 * 78 * <p>When the precision setting is not 0, the rules of 79 * {@code BigDecimal} arithmetic are broadly compatible with selected 80 * modes of operation of the arithmetic defined in ANSI X3.274-1996 81 * and ANSI X3.274-1996/AM 1-2000 (section 7.4). Unlike those 82 * standards, {@code BigDecimal} includes many rounding modes, which 83 * were mandatory for division in {@code BigDecimal} releases prior 84 * to 5. Any conflicts between these ANSI standards and the 85 * {@code BigDecimal} specification are resolved in favor of 86 * {@code BigDecimal}. 87 * 88 * <p>Since the same numerical value can have different 89 * representations (with different scales), the rules of arithmetic 90 * and rounding must specify both the numerical result and the scale 91 * used in the result's representation. 92 * 93 * 94 * <p>In general the rounding modes and precision setting determine 95 * how operations return results with a limited number of digits when 96 * the exact result has more digits (perhaps infinitely many in the 97 * case of division and square root) than the number of digits returned. 98 * 99 * First, the 100 * total number of digits to return is specified by the 101 * {@code MathContext}'s {@code precision} setting; this determines 102 * the result's <i>precision</i>. The digit count starts from the 103 * leftmost nonzero digit of the exact result. The rounding mode 104 * determines how any discarded trailing digits affect the returned 105 * result. 106 * 107 * <p>For all arithmetic operators, the operation is carried out as 108 * though an exact intermediate result were first calculated and then 109 * rounded to the number of digits specified by the precision setting 110 * (if necessary), using the selected rounding mode. If the exact 111 * result is not returned, some digit positions of the exact result 112 * are discarded. When rounding increases the magnitude of the 113 * returned result, it is possible for a new digit position to be 114 * created by a carry propagating to a leading {@literal "9"} digit. 115 * For example, rounding the value 999.9 to three digits rounding up 116 * would be numerically equal to one thousand, represented as 117 * 100×10<sup>1</sup>. In such cases, the new {@literal "1"} is 118 * the leading digit position of the returned result. 119 * 120 * <p>Besides a logical exact result, each arithmetic operation has a 121 * preferred scale for representing a result. The preferred 122 * scale for each operation is listed in the table below. 123 * 124 * <table class="striped" style="text-align:left"> 125 * <caption>Preferred Scales for Results of Arithmetic Operations 126 * </caption> 127 * <thead> 128 * <tr><th scope="col">Operation</th><th scope="col">Preferred Scale of Result</th></tr> 129 * </thead> 130 * <tbody> 131 * <tr><th scope="row">Add</th><td>max(addend.scale(), augend.scale())</td> 132 * <tr><th scope="row">Subtract</th><td>max(minuend.scale(), subtrahend.scale())</td> 133 * <tr><th scope="row">Multiply</th><td>multiplier.scale() + multiplicand.scale()</td> 134 * <tr><th scope="row">Divide</th><td>dividend.scale() - divisor.scale()</td> 135 * <tr><th scope="row">Square root</th><td>radicand.scale()/2</td> 136 * </tbody> 137 * </table> 138 * 139 * These scales are the ones used by the methods which return exact 140 * arithmetic results; except that an exact divide may have to use a 141 * larger scale since the exact result may have more digits. For 142 * example, {@code 1/32} is {@code 0.03125}. 143 * 144 * <p>Before rounding, the scale of the logical exact intermediate 145 * result is the preferred scale for that operation. If the exact 146 * numerical result cannot be represented in {@code precision} 147 * digits, rounding selects the set of digits to return and the scale 148 * of the result is reduced from the scale of the intermediate result 149 * to the least scale which can represent the {@code precision} 150 * digits actually returned. If the exact result can be represented 151 * with at most {@code precision} digits, the representation 152 * of the result with the scale closest to the preferred scale is 153 * returned. In particular, an exactly representable quotient may be 154 * represented in fewer than {@code precision} digits by removing 155 * trailing zeros and decreasing the scale. For example, rounding to 156 * three digits using the {@linkplain RoundingMode#FLOOR floor} 157 * rounding mode, <br> 158 * 159 * {@code 19/100 = 0.19 // integer=19, scale=2} <br> 160 * 161 * but<br> 162 * 163 * {@code 21/110 = 0.190 // integer=190, scale=3} <br> 164 * 165 * <p>Note that for add, subtract, and multiply, the reduction in 166 * scale will equal the number of digit positions of the exact result 167 * which are discarded. If the rounding causes a carry propagation to 168 * create a new high-order digit position, an additional digit of the 169 * result is discarded than when no new digit position is created. 170 * 171 * <p>Other methods may have slightly different rounding semantics. 172 * For example, the result of the {@code pow} method using the 173 * {@linkplain #pow(int, MathContext) specified algorithm} can 174 * occasionally differ from the rounded mathematical result by more 175 * than one unit in the last place, one <i>{@linkplain #ulp() ulp}</i>. 176 * 177 * <p>Two types of operations are provided for manipulating the scale 178 * of a {@code BigDecimal}: scaling/rounding operations and decimal 179 * point motion operations. Scaling/rounding operations ({@link 180 * #setScale setScale} and {@link #round round}) return a 181 * {@code BigDecimal} whose value is approximately (or exactly) equal 182 * to that of the operand, but whose scale or precision is the 183 * specified value; that is, they increase or decrease the precision 184 * of the stored number with minimal effect on its value. Decimal 185 * point motion operations ({@link #movePointLeft movePointLeft} and 186 * {@link #movePointRight movePointRight}) return a 187 * {@code BigDecimal} created from the operand by moving the decimal 188 * point a specified distance in the specified direction. 189 * 190 * <p>For the sake of brevity and clarity, pseudo-code is used 191 * throughout the descriptions of {@code BigDecimal} methods. The 192 * pseudo-code expression {@code (i + j)} is shorthand for "a 193 * {@code BigDecimal} whose value is that of the {@code BigDecimal} 194 * {@code i} added to that of the {@code BigDecimal} 195 * {@code j}." The pseudo-code expression {@code (i == j)} is 196 * shorthand for "{@code true} if and only if the 197 * {@code BigDecimal} {@code i} represents the same value as the 198 * {@code BigDecimal} {@code j}." Other pseudo-code expressions 199 * are interpreted similarly. Square brackets are used to represent 200 * the particular {@code BigInteger} and scale pair defining a 201 * {@code BigDecimal} value; for example [19, 2] is the 202 * {@code BigDecimal} numerically equal to 0.19 having a scale of 2. 203 * 204 * 205 * <p>All methods and constructors for this class throw 206 * {@code NullPointerException} when passed a {@code null} object 207 * reference for any input parameter. 208 * 209 * @apiNote Care should be exercised if {@code BigDecimal} objects 210 * are used as keys in a {@link java.util.SortedMap SortedMap} or 211 * elements in a {@link java.util.SortedSet SortedSet} since 212 * {@code BigDecimal}'s <i>natural ordering</i> is <em>inconsistent 213 * with equals</em>. See {@link Comparable}, {@link 214 * java.util.SortedMap} or {@link java.util.SortedSet} for more 215 * information. 216 * 217 * @see BigInteger 218 * @see MathContext 219 * @see RoundingMode 220 * @see java.util.SortedMap 221 * @see java.util.SortedSet 222 * @author Josh Bloch 223 * @author Mike Cowlishaw 224 * @author Joseph D. Darcy 225 * @author Sergey V. Kuksenko 226 * @since 1.1 227 */ 228 public class BigDecimal extends Number implements Comparable<BigDecimal> { 229 /** 230 * The unscaled value of this BigDecimal, as returned by {@link 231 * #unscaledValue}. 232 * 233 * @serial 234 * @see #unscaledValue 235 */ 236 private final BigInteger intVal; 237 238 /** 239 * The scale of this BigDecimal, as returned by {@link #scale}. 240 * 241 * @serial 242 * @see #scale 243 */ 244 private final int scale; // Note: this may have any value, so 245 // calculations must be done in longs 246 247 /** 248 * The number of decimal digits in this BigDecimal, or 0 if the 249 * number of digits are not known (lookaside information). If 250 * nonzero, the value is guaranteed correct. Use the precision() 251 * method to obtain and set the value if it might be 0. This 252 * field is mutable until set nonzero. 253 * 254 * @since 1.5 255 */ 256 private transient int precision; 257 258 /** 259 * Used to store the canonical string representation, if computed. 260 */ 261 private transient String stringCache; 262 263 /** 264 * Sentinel value for {@link #intCompact} indicating the 265 * significand information is only available from {@code intVal}. 266 */ 267 static final long INFLATED = Long.MIN_VALUE; 268 269 private static final BigInteger INFLATED_BIGINT = BigInteger.valueOf(INFLATED); 270 271 /** 272 * If the absolute value of the significand of this BigDecimal is 273 * less than or equal to {@code Long.MAX_VALUE}, the value can be 274 * compactly stored in this field and used in computations. 275 */ 276 private final transient long intCompact; 277 278 // All 18-digit base ten strings fit into a long; not all 19-digit 279 // strings will 280 private static final int MAX_COMPACT_DIGITS = 18; 281 282 /* Appease the serialization gods */ 283 @java.io.Serial 284 private static final long serialVersionUID = 6108874887143696463L; 285 286 private static final ThreadLocal<StringBuilderHelper> 287 threadLocalStringBuilderHelper = new ThreadLocal<StringBuilderHelper>() { 288 @Override 289 protected StringBuilderHelper initialValue() { 290 return new StringBuilderHelper(); 291 } 292 }; 293 294 // Cache of common small BigDecimal values. 295 private static final BigDecimal ZERO_THROUGH_TEN[] = { 296 new BigDecimal(BigInteger.ZERO, 0, 0, 1), 297 new BigDecimal(BigInteger.ONE, 1, 0, 1), 298 new BigDecimal(BigInteger.TWO, 2, 0, 1), 299 new BigDecimal(BigInteger.valueOf(3), 3, 0, 1), 300 new BigDecimal(BigInteger.valueOf(4), 4, 0, 1), 301 new BigDecimal(BigInteger.valueOf(5), 5, 0, 1), 302 new BigDecimal(BigInteger.valueOf(6), 6, 0, 1), 303 new BigDecimal(BigInteger.valueOf(7), 7, 0, 1), 304 new BigDecimal(BigInteger.valueOf(8), 8, 0, 1), 305 new BigDecimal(BigInteger.valueOf(9), 9, 0, 1), 306 new BigDecimal(BigInteger.TEN, 10, 0, 2), 307 }; 308 309 // Cache of zero scaled by 0 - 15 310 private static final BigDecimal[] ZERO_SCALED_BY = { 311 ZERO_THROUGH_TEN[0], 312 new BigDecimal(BigInteger.ZERO, 0, 1, 1), 313 new BigDecimal(BigInteger.ZERO, 0, 2, 1), 314 new BigDecimal(BigInteger.ZERO, 0, 3, 1), 315 new BigDecimal(BigInteger.ZERO, 0, 4, 1), 316 new BigDecimal(BigInteger.ZERO, 0, 5, 1), 317 new BigDecimal(BigInteger.ZERO, 0, 6, 1), 318 new BigDecimal(BigInteger.ZERO, 0, 7, 1), 319 new BigDecimal(BigInteger.ZERO, 0, 8, 1), 320 new BigDecimal(BigInteger.ZERO, 0, 9, 1), 321 new BigDecimal(BigInteger.ZERO, 0, 10, 1), 322 new BigDecimal(BigInteger.ZERO, 0, 11, 1), 323 new BigDecimal(BigInteger.ZERO, 0, 12, 1), 324 new BigDecimal(BigInteger.ZERO, 0, 13, 1), 325 new BigDecimal(BigInteger.ZERO, 0, 14, 1), 326 new BigDecimal(BigInteger.ZERO, 0, 15, 1), 327 }; 328 329 // Half of Long.MIN_VALUE & Long.MAX_VALUE. 330 private static final long HALF_LONG_MAX_VALUE = Long.MAX_VALUE / 2; 331 private static final long HALF_LONG_MIN_VALUE = Long.MIN_VALUE / 2; 332 333 // Constants 334 /** 335 * The value 0, with a scale of 0. 336 * 337 * @since 1.5 338 */ 339 public static final BigDecimal ZERO = 340 ZERO_THROUGH_TEN[0]; 341 342 /** 343 * The value 1, with a scale of 0. 344 * 345 * @since 1.5 346 */ 347 public static final BigDecimal ONE = 348 ZERO_THROUGH_TEN[1]; 349 350 /** 351 * The value 10, with a scale of 0. 352 * 353 * @since 1.5 354 */ 355 public static final BigDecimal TEN = 356 ZERO_THROUGH_TEN[10]; 357 358 /** 359 * The value 0.1, with a scale of 1. 360 */ 361 private static final BigDecimal ONE_TENTH = valueOf(1L, 1); 362 363 /** 364 * The value 0.5, with a scale of 1. 365 */ 366 private static final BigDecimal ONE_HALF = valueOf(5L, 1); 367 368 // Constructors 369 370 /** 371 * Trusted package private constructor. 372 * Trusted simply means if val is INFLATED, intVal could not be null and 373 * if intVal is null, val could not be INFLATED. 374 */ 375 BigDecimal(BigInteger intVal, long val, int scale, int prec) { 376 this.scale = scale; 377 this.precision = prec; 378 this.intCompact = val; 379 this.intVal = intVal; 380 } 381 382 /** 383 * Translates a character array representation of a 384 * {@code BigDecimal} into a {@code BigDecimal}, accepting the 385 * same sequence of characters as the {@link #BigDecimal(String)} 386 * constructor, while allowing a sub-array to be specified. 387 * 388 * @implNote If the sequence of characters is already available 389 * within a character array, using this constructor is faster than 390 * converting the {@code char} array to string and using the 391 * {@code BigDecimal(String)} constructor. 392 * 393 * @param in {@code char} array that is the source of characters. 394 * @param offset first character in the array to inspect. 395 * @param len number of characters to consider. 396 * @throws NumberFormatException if {@code in} is not a valid 397 * representation of a {@code BigDecimal} or the defined subarray 398 * is not wholly within {@code in}. 399 * @since 1.5 400 */ 401 public BigDecimal(char[] in, int offset, int len) { 402 this(in,offset,len,MathContext.UNLIMITED); 403 } 404 405 /** 406 * Translates a character array representation of a 407 * {@code BigDecimal} into a {@code BigDecimal}, accepting the 408 * same sequence of characters as the {@link #BigDecimal(String)} 409 * constructor, while allowing a sub-array to be specified and 410 * with rounding according to the context settings. 411 * 412 * @implNote If the sequence of characters is already available 413 * within a character array, using this constructor is faster than 414 * converting the {@code char} array to string and using the 415 * {@code BigDecimal(String)} constructor. 416 * 417 * @param in {@code char} array that is the source of characters. 418 * @param offset first character in the array to inspect. 419 * @param len number of characters to consider. 420 * @param mc the context to use. 421 * @throws ArithmeticException if the result is inexact but the 422 * rounding mode is {@code UNNECESSARY}. 423 * @throws NumberFormatException if {@code in} is not a valid 424 * representation of a {@code BigDecimal} or the defined subarray 425 * is not wholly within {@code in}. 426 * @since 1.5 427 */ 428 public BigDecimal(char[] in, int offset, int len, MathContext mc) { 429 // protect against huge length, negative values, and integer overflow 430 try { 431 Objects.checkFromIndexSize(offset, len, in.length); 432 } catch (IndexOutOfBoundsException e) { 433 throw new NumberFormatException 434 ("Bad offset or len arguments for char[] input."); 435 } 436 437 // This is the primary string to BigDecimal constructor; all 438 // incoming strings end up here; it uses explicit (inline) 439 // parsing for speed and generates at most one intermediate 440 // (temporary) object (a char[] array) for non-compact case. 441 442 // Use locals for all fields values until completion 443 int prec = 0; // record precision value 444 int scl = 0; // record scale value 445 long rs = 0; // the compact value in long 446 BigInteger rb = null; // the inflated value in BigInteger 447 // use array bounds checking to handle too-long, len == 0, 448 // bad offset, etc. 449 try { 450 // handle the sign 451 boolean isneg = false; // assume positive 452 if (in[offset] == '-') { 453 isneg = true; // leading minus means negative 454 offset++; 455 len--; 456 } else if (in[offset] == '+') { // leading + allowed 457 offset++; 458 len--; 459 } 460 461 // should now be at numeric part of the significand 462 boolean dot = false; // true when there is a '.' 463 long exp = 0; // exponent 464 char c; // current character 465 boolean isCompact = (len <= MAX_COMPACT_DIGITS); 466 // integer significand array & idx is the index to it. The array 467 // is ONLY used when we can't use a compact representation. 468 int idx = 0; 469 if (isCompact) { 470 // First compact case, we need not to preserve the character 471 // and we can just compute the value in place. 472 for (; len > 0; offset++, len--) { 473 c = in[offset]; 474 if ((c == '0')) { // have zero 475 if (prec == 0) 476 prec = 1; 477 else if (rs != 0) { 478 rs *= 10; 479 ++prec; 480 } // else digit is a redundant leading zero 481 if (dot) 482 ++scl; 483 } else if ((c >= '1' && c <= '9')) { // have digit 484 int digit = c - '0'; 485 if (prec != 1 || rs != 0) 486 ++prec; // prec unchanged if preceded by 0s 487 rs = rs * 10 + digit; 488 if (dot) 489 ++scl; 490 } else if (c == '.') { // have dot 491 // have dot 492 if (dot) // two dots 493 throw new NumberFormatException("Character array" 494 + " contains more than one decimal point."); 495 dot = true; 496 } else if (Character.isDigit(c)) { // slow path 497 int digit = Character.digit(c, 10); 498 if (digit == 0) { 499 if (prec == 0) 500 prec = 1; 501 else if (rs != 0) { 502 rs *= 10; 503 ++prec; 504 } // else digit is a redundant leading zero 505 } else { 506 if (prec != 1 || rs != 0) 507 ++prec; // prec unchanged if preceded by 0s 508 rs = rs * 10 + digit; 509 } 510 if (dot) 511 ++scl; 512 } else if ((c == 'e') || (c == 'E')) { 513 exp = parseExp(in, offset, len); 514 // Next test is required for backwards compatibility 515 if ((int) exp != exp) // overflow 516 throw new NumberFormatException("Exponent overflow."); 517 break; // [saves a test] 518 } else { 519 throw new NumberFormatException("Character " + c 520 + " is neither a decimal digit number, decimal point, nor" 521 + " \"e\" notation exponential mark."); 522 } 523 } 524 if (prec == 0) // no digits found 525 throw new NumberFormatException("No digits found."); 526 // Adjust scale if exp is not zero. 527 if (exp != 0) { // had significant exponent 528 scl = adjustScale(scl, exp); 529 } 530 rs = isneg ? -rs : rs; 531 int mcp = mc.precision; 532 int drop = prec - mcp; // prec has range [1, MAX_INT], mcp has range [0, MAX_INT]; 533 // therefore, this subtract cannot overflow 534 if (mcp > 0 && drop > 0) { // do rounding 535 while (drop > 0) { 536 scl = checkScaleNonZero((long) scl - drop); 537 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 538 prec = longDigitLength(rs); 539 drop = prec - mcp; 540 } 541 } 542 } else { 543 char coeff[] = new char[len]; 544 for (; len > 0; offset++, len--) { 545 c = in[offset]; 546 // have digit 547 if ((c >= '0' && c <= '9') || Character.isDigit(c)) { 548 // First compact case, we need not to preserve the character 549 // and we can just compute the value in place. 550 if (c == '0' || Character.digit(c, 10) == 0) { 551 if (prec == 0) { 552 coeff[idx] = c; 553 prec = 1; 554 } else if (idx != 0) { 555 coeff[idx++] = c; 556 ++prec; 557 } // else c must be a redundant leading zero 558 } else { 559 if (prec != 1 || idx != 0) 560 ++prec; // prec unchanged if preceded by 0s 561 coeff[idx++] = c; 562 } 563 if (dot) 564 ++scl; 565 continue; 566 } 567 // have dot 568 if (c == '.') { 569 // have dot 570 if (dot) // two dots 571 throw new NumberFormatException("Character array" 572 + " contains more than one decimal point."); 573 dot = true; 574 continue; 575 } 576 // exponent expected 577 if ((c != 'e') && (c != 'E')) 578 throw new NumberFormatException("Character array" 579 + " is missing \"e\" notation exponential mark."); 580 exp = parseExp(in, offset, len); 581 // Next test is required for backwards compatibility 582 if ((int) exp != exp) // overflow 583 throw new NumberFormatException("Exponent overflow."); 584 break; // [saves a test] 585 } 586 // here when no characters left 587 if (prec == 0) // no digits found 588 throw new NumberFormatException("No digits found."); 589 // Adjust scale if exp is not zero. 590 if (exp != 0) { // had significant exponent 591 scl = adjustScale(scl, exp); 592 } 593 // Remove leading zeros from precision (digits count) 594 rb = new BigInteger(coeff, isneg ? -1 : 1, prec); 595 rs = compactValFor(rb); 596 int mcp = mc.precision; 597 if (mcp > 0 && (prec > mcp)) { 598 if (rs == INFLATED) { 599 int drop = prec - mcp; 600 while (drop > 0) { 601 scl = checkScaleNonZero((long) scl - drop); 602 rb = divideAndRoundByTenPow(rb, drop, mc.roundingMode.oldMode); 603 rs = compactValFor(rb); 604 if (rs != INFLATED) { 605 prec = longDigitLength(rs); 606 break; 607 } 608 prec = bigDigitLength(rb); 609 drop = prec - mcp; 610 } 611 } 612 if (rs != INFLATED) { 613 int drop = prec - mcp; 614 while (drop > 0) { 615 scl = checkScaleNonZero((long) scl - drop); 616 rs = divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 617 prec = longDigitLength(rs); 618 drop = prec - mcp; 619 } 620 rb = null; 621 } 622 } 623 } 624 } catch (ArrayIndexOutOfBoundsException | NegativeArraySizeException e) { 625 NumberFormatException nfe = new NumberFormatException(); 626 nfe.initCause(e); 627 throw nfe; 628 } 629 this.scale = scl; 630 this.precision = prec; 631 this.intCompact = rs; 632 this.intVal = rb; 633 } 634 635 private int adjustScale(int scl, long exp) { 636 long adjustedScale = scl - exp; 637 if (adjustedScale > Integer.MAX_VALUE || adjustedScale < Integer.MIN_VALUE) 638 throw new NumberFormatException("Scale out of range."); 639 scl = (int) adjustedScale; 640 return scl; 641 } 642 643 /* 644 * parse exponent 645 */ 646 private static long parseExp(char[] in, int offset, int len){ 647 long exp = 0; 648 offset++; 649 char c = in[offset]; 650 len--; 651 boolean negexp = (c == '-'); 652 // optional sign 653 if (negexp || c == '+') { 654 offset++; 655 c = in[offset]; 656 len--; 657 } 658 if (len <= 0) // no exponent digits 659 throw new NumberFormatException("No exponent digits."); 660 // skip leading zeros in the exponent 661 while (len > 10 && (c=='0' || (Character.digit(c, 10) == 0))) { 662 offset++; 663 c = in[offset]; 664 len--; 665 } 666 if (len > 10) // too many nonzero exponent digits 667 throw new NumberFormatException("Too many nonzero exponent digits."); 668 // c now holds first digit of exponent 669 for (;; len--) { 670 int v; 671 if (c >= '0' && c <= '9') { 672 v = c - '0'; 673 } else { 674 v = Character.digit(c, 10); 675 if (v < 0) // not a digit 676 throw new NumberFormatException("Not a digit."); 677 } 678 exp = exp * 10 + v; 679 if (len == 1) 680 break; // that was final character 681 offset++; 682 c = in[offset]; 683 } 684 if (negexp) // apply sign 685 exp = -exp; 686 return exp; 687 } 688 689 /** 690 * Translates a character array representation of a 691 * {@code BigDecimal} into a {@code BigDecimal}, accepting the 692 * same sequence of characters as the {@link #BigDecimal(String)} 693 * constructor. 694 * 695 * @implNote If the sequence of characters is already available 696 * as a character array, using this constructor is faster than 697 * converting the {@code char} array to string and using the 698 * {@code BigDecimal(String)} constructor. 699 * 700 * @param in {@code char} array that is the source of characters. 701 * @throws NumberFormatException if {@code in} is not a valid 702 * representation of a {@code BigDecimal}. 703 * @since 1.5 704 */ 705 public BigDecimal(char[] in) { 706 this(in, 0, in.length); 707 } 708 709 /** 710 * Translates a character array representation of a 711 * {@code BigDecimal} into a {@code BigDecimal}, accepting the 712 * same sequence of characters as the {@link #BigDecimal(String)} 713 * constructor and with rounding according to the context 714 * settings. 715 * 716 * @implNote If the sequence of characters is already available 717 * as a character array, using this constructor is faster than 718 * converting the {@code char} array to string and using the 719 * {@code BigDecimal(String)} constructor. 720 * 721 * @param in {@code char} array that is the source of characters. 722 * @param mc the context to use. 723 * @throws ArithmeticException if the result is inexact but the 724 * rounding mode is {@code UNNECESSARY}. 725 * @throws NumberFormatException if {@code in} is not a valid 726 * representation of a {@code BigDecimal}. 727 * @since 1.5 728 */ 729 public BigDecimal(char[] in, MathContext mc) { 730 this(in, 0, in.length, mc); 731 } 732 733 /** 734 * Translates the string representation of a {@code BigDecimal} 735 * into a {@code BigDecimal}. The string representation consists 736 * of an optional sign, {@code '+'} (<code> '\u002B'</code>) or 737 * {@code '-'} (<code>'\u002D'</code>), followed by a sequence of 738 * zero or more decimal digits ("the integer"), optionally 739 * followed by a fraction, optionally followed by an exponent. 740 * 741 * <p>The fraction consists of a decimal point followed by zero 742 * or more decimal digits. The string must contain at least one 743 * digit in either the integer or the fraction. The number formed 744 * by the sign, the integer and the fraction is referred to as the 745 * <i>significand</i>. 746 * 747 * <p>The exponent consists of the character {@code 'e'} 748 * (<code>'\u0065'</code>) or {@code 'E'} (<code>'\u0045'</code>) 749 * followed by one or more decimal digits. The value of the 750 * exponent must lie between -{@link Integer#MAX_VALUE} ({@link 751 * Integer#MIN_VALUE}+1) and {@link Integer#MAX_VALUE}, inclusive. 752 * 753 * <p>More formally, the strings this constructor accepts are 754 * described by the following grammar: 755 * <blockquote> 756 * <dl> 757 * <dt><i>BigDecimalString:</i> 758 * <dd><i>Sign<sub>opt</sub> Significand Exponent<sub>opt</sub></i> 759 * <dt><i>Sign:</i> 760 * <dd>{@code +} 761 * <dd>{@code -} 762 * <dt><i>Significand:</i> 763 * <dd><i>IntegerPart</i> {@code .} <i>FractionPart<sub>opt</sub></i> 764 * <dd>{@code .} <i>FractionPart</i> 765 * <dd><i>IntegerPart</i> 766 * <dt><i>IntegerPart:</i> 767 * <dd><i>Digits</i> 768 * <dt><i>FractionPart:</i> 769 * <dd><i>Digits</i> 770 * <dt><i>Exponent:</i> 771 * <dd><i>ExponentIndicator SignedInteger</i> 772 * <dt><i>ExponentIndicator:</i> 773 * <dd>{@code e} 774 * <dd>{@code E} 775 * <dt><i>SignedInteger:</i> 776 * <dd><i>Sign<sub>opt</sub> Digits</i> 777 * <dt><i>Digits:</i> 778 * <dd><i>Digit</i> 779 * <dd><i>Digits Digit</i> 780 * <dt><i>Digit:</i> 781 * <dd>any character for which {@link Character#isDigit} 782 * returns {@code true}, including 0, 1, 2 ... 783 * </dl> 784 * </blockquote> 785 * 786 * <p>The scale of the returned {@code BigDecimal} will be the 787 * number of digits in the fraction, or zero if the string 788 * contains no decimal point, subject to adjustment for any 789 * exponent; if the string contains an exponent, the exponent is 790 * subtracted from the scale. The value of the resulting scale 791 * must lie between {@code Integer.MIN_VALUE} and 792 * {@code Integer.MAX_VALUE}, inclusive. 793 * 794 * <p>The character-to-digit mapping is provided by {@link 795 * java.lang.Character#digit} set to convert to radix 10. The 796 * String may not contain any extraneous characters (whitespace, 797 * for example). 798 * 799 * <p><b>Examples:</b><br> 800 * The value of the returned {@code BigDecimal} is equal to 801 * <i>significand</i> × 10<sup> <i>exponent</i></sup>. 802 * For each string on the left, the resulting representation 803 * [{@code BigInteger}, {@code scale}] is shown on the right. 804 * <pre> 805 * "0" [0,0] 806 * "0.00" [0,2] 807 * "123" [123,0] 808 * "-123" [-123,0] 809 * "1.23E3" [123,-1] 810 * "1.23E+3" [123,-1] 811 * "12.3E+7" [123,-6] 812 * "12.0" [120,1] 813 * "12.3" [123,1] 814 * "0.00123" [123,5] 815 * "-1.23E-12" [-123,14] 816 * "1234.5E-4" [12345,5] 817 * "0E+7" [0,-7] 818 * "-0" [0,0] 819 * </pre> 820 * 821 * @apiNote For values other than {@code float} and 822 * {@code double} NaN and ±Infinity, this constructor is 823 * compatible with the values returned by {@link Float#toString} 824 * and {@link Double#toString}. This is generally the preferred 825 * way to convert a {@code float} or {@code double} into a 826 * BigDecimal, as it doesn't suffer from the unpredictability of 827 * the {@link #BigDecimal(double)} constructor. 828 * 829 * @param val String representation of {@code BigDecimal}. 830 * 831 * @throws NumberFormatException if {@code val} is not a valid 832 * representation of a {@code BigDecimal}. 833 */ 834 public BigDecimal(String val) { 835 this(val.toCharArray(), 0, val.length()); 836 } 837 838 /** 839 * Translates the string representation of a {@code BigDecimal} 840 * into a {@code BigDecimal}, accepting the same strings as the 841 * {@link #BigDecimal(String)} constructor, with rounding 842 * according to the context settings. 843 * 844 * @param val string representation of a {@code BigDecimal}. 845 * @param mc the context to use. 846 * @throws ArithmeticException if the result is inexact but the 847 * rounding mode is {@code UNNECESSARY}. 848 * @throws NumberFormatException if {@code val} is not a valid 849 * representation of a BigDecimal. 850 * @since 1.5 851 */ 852 public BigDecimal(String val, MathContext mc) { 853 this(val.toCharArray(), 0, val.length(), mc); 854 } 855 856 /** 857 * Translates a {@code double} into a {@code BigDecimal} which 858 * is the exact decimal representation of the {@code double}'s 859 * binary floating-point value. The scale of the returned 860 * {@code BigDecimal} is the smallest value such that 861 * <code>(10<sup>scale</sup> × val)</code> is an integer. 862 * <p> 863 * <b>Notes:</b> 864 * <ol> 865 * <li> 866 * The results of this constructor can be somewhat unpredictable. 867 * One might assume that writing {@code new BigDecimal(0.1)} in 868 * Java creates a {@code BigDecimal} which is exactly equal to 869 * 0.1 (an unscaled value of 1, with a scale of 1), but it is 870 * actually equal to 871 * 0.1000000000000000055511151231257827021181583404541015625. 872 * This is because 0.1 cannot be represented exactly as a 873 * {@code double} (or, for that matter, as a binary fraction of 874 * any finite length). Thus, the value that is being passed 875 * <em>in</em> to the constructor is not exactly equal to 0.1, 876 * appearances notwithstanding. 877 * 878 * <li> 879 * The {@code String} constructor, on the other hand, is 880 * perfectly predictable: writing {@code new BigDecimal("0.1")} 881 * creates a {@code BigDecimal} which is <em>exactly</em> equal to 882 * 0.1, as one would expect. Therefore, it is generally 883 * recommended that the {@linkplain #BigDecimal(String) 884 * String constructor} be used in preference to this one. 885 * 886 * <li> 887 * When a {@code double} must be used as a source for a 888 * {@code BigDecimal}, note that this constructor provides an 889 * exact conversion; it does not give the same result as 890 * converting the {@code double} to a {@code String} using the 891 * {@link Double#toString(double)} method and then using the 892 * {@link #BigDecimal(String)} constructor. To get that result, 893 * use the {@code static} {@link #valueOf(double)} method. 894 * </ol> 895 * 896 * @param val {@code double} value to be converted to 897 * {@code BigDecimal}. 898 * @throws NumberFormatException if {@code val} is infinite or NaN. 899 */ 900 public BigDecimal(double val) { 901 this(val,MathContext.UNLIMITED); 902 } 903 904 /** 905 * Translates a {@code double} into a {@code BigDecimal}, with 906 * rounding according to the context settings. The scale of the 907 * {@code BigDecimal} is the smallest value such that 908 * <code>(10<sup>scale</sup> × val)</code> is an integer. 909 * 910 * <p>The results of this constructor can be somewhat unpredictable 911 * and its use is generally not recommended; see the notes under 912 * the {@link #BigDecimal(double)} constructor. 913 * 914 * @param val {@code double} value to be converted to 915 * {@code BigDecimal}. 916 * @param mc the context to use. 917 * @throws ArithmeticException if the result is inexact but the 918 * RoundingMode is UNNECESSARY. 919 * @throws NumberFormatException if {@code val} is infinite or NaN. 920 * @since 1.5 921 */ 922 public BigDecimal(double val, MathContext mc) { 923 if (Double.isInfinite(val) || Double.isNaN(val)) 924 throw new NumberFormatException("Infinite or NaN"); 925 // Translate the double into sign, exponent and significand, according 926 // to the formulae in JLS, Section 20.10.22. 927 long valBits = Double.doubleToLongBits(val); 928 int sign = ((valBits >> 63) == 0 ? 1 : -1); 929 int exponent = (int) ((valBits >> 52) & 0x7ffL); 930 long significand = (exponent == 0 931 ? (valBits & ((1L << 52) - 1)) << 1 932 : (valBits & ((1L << 52) - 1)) | (1L << 52)); 933 exponent -= 1075; 934 // At this point, val == sign * significand * 2**exponent. 935 936 /* 937 * Special case zero to suppress nonterminating normalization and bogus 938 * scale calculation. 939 */ 940 if (significand == 0) { 941 this.intVal = BigInteger.ZERO; 942 this.scale = 0; 943 this.intCompact = 0; 944 this.precision = 1; 945 return; 946 } 947 // Normalize 948 while ((significand & 1) == 0) { // i.e., significand is even 949 significand >>= 1; 950 exponent++; 951 } 952 int scl = 0; 953 // Calculate intVal and scale 954 BigInteger rb; 955 long compactVal = sign * significand; 956 if (exponent == 0) { 957 rb = (compactVal == INFLATED) ? INFLATED_BIGINT : null; 958 } else { 959 if (exponent < 0) { 960 rb = BigInteger.valueOf(5).pow(-exponent).multiply(compactVal); 961 scl = -exponent; 962 } else { // (exponent > 0) 963 rb = BigInteger.TWO.pow(exponent).multiply(compactVal); 964 } 965 compactVal = compactValFor(rb); 966 } 967 int prec = 0; 968 int mcp = mc.precision; 969 if (mcp > 0) { // do rounding 970 int mode = mc.roundingMode.oldMode; 971 int drop; 972 if (compactVal == INFLATED) { 973 prec = bigDigitLength(rb); 974 drop = prec - mcp; 975 while (drop > 0) { 976 scl = checkScaleNonZero((long) scl - drop); 977 rb = divideAndRoundByTenPow(rb, drop, mode); 978 compactVal = compactValFor(rb); 979 if (compactVal != INFLATED) { 980 break; 981 } 982 prec = bigDigitLength(rb); 983 drop = prec - mcp; 984 } 985 } 986 if (compactVal != INFLATED) { 987 prec = longDigitLength(compactVal); 988 drop = prec - mcp; 989 while (drop > 0) { 990 scl = checkScaleNonZero((long) scl - drop); 991 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 992 prec = longDigitLength(compactVal); 993 drop = prec - mcp; 994 } 995 rb = null; 996 } 997 } 998 this.intVal = rb; 999 this.intCompact = compactVal; 1000 this.scale = scl; 1001 this.precision = prec; 1002 } 1003 1004 /** 1005 * Translates a {@code BigInteger} into a {@code BigDecimal}. 1006 * The scale of the {@code BigDecimal} is zero. 1007 * 1008 * @param val {@code BigInteger} value to be converted to 1009 * {@code BigDecimal}. 1010 */ 1011 public BigDecimal(BigInteger val) { 1012 scale = 0; 1013 intVal = val; 1014 intCompact = compactValFor(val); 1015 } 1016 1017 /** 1018 * Translates a {@code BigInteger} into a {@code BigDecimal} 1019 * rounding according to the context settings. The scale of the 1020 * {@code BigDecimal} is zero. 1021 * 1022 * @param val {@code BigInteger} value to be converted to 1023 * {@code BigDecimal}. 1024 * @param mc the context to use. 1025 * @throws ArithmeticException if the result is inexact but the 1026 * rounding mode is {@code UNNECESSARY}. 1027 * @since 1.5 1028 */ 1029 public BigDecimal(BigInteger val, MathContext mc) { 1030 this(val,0,mc); 1031 } 1032 1033 /** 1034 * Translates a {@code BigInteger} unscaled value and an 1035 * {@code int} scale into a {@code BigDecimal}. The value of 1036 * the {@code BigDecimal} is 1037 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>. 1038 * 1039 * @param unscaledVal unscaled value of the {@code BigDecimal}. 1040 * @param scale scale of the {@code BigDecimal}. 1041 */ 1042 public BigDecimal(BigInteger unscaledVal, int scale) { 1043 // Negative scales are now allowed 1044 this.intVal = unscaledVal; 1045 this.intCompact = compactValFor(unscaledVal); 1046 this.scale = scale; 1047 } 1048 1049 /** 1050 * Translates a {@code BigInteger} unscaled value and an 1051 * {@code int} scale into a {@code BigDecimal}, with rounding 1052 * according to the context settings. The value of the 1053 * {@code BigDecimal} is <code>(unscaledVal × 1054 * 10<sup>-scale</sup>)</code>, rounded according to the 1055 * {@code precision} and rounding mode settings. 1056 * 1057 * @param unscaledVal unscaled value of the {@code BigDecimal}. 1058 * @param scale scale of the {@code BigDecimal}. 1059 * @param mc the context to use. 1060 * @throws ArithmeticException if the result is inexact but the 1061 * rounding mode is {@code UNNECESSARY}. 1062 * @since 1.5 1063 */ 1064 public BigDecimal(BigInteger unscaledVal, int scale, MathContext mc) { 1065 long compactVal = compactValFor(unscaledVal); 1066 int mcp = mc.precision; 1067 int prec = 0; 1068 if (mcp > 0) { // do rounding 1069 int mode = mc.roundingMode.oldMode; 1070 if (compactVal == INFLATED) { 1071 prec = bigDigitLength(unscaledVal); 1072 int drop = prec - mcp; 1073 while (drop > 0) { 1074 scale = checkScaleNonZero((long) scale - drop); 1075 unscaledVal = divideAndRoundByTenPow(unscaledVal, drop, mode); 1076 compactVal = compactValFor(unscaledVal); 1077 if (compactVal != INFLATED) { 1078 break; 1079 } 1080 prec = bigDigitLength(unscaledVal); 1081 drop = prec - mcp; 1082 } 1083 } 1084 if (compactVal != INFLATED) { 1085 prec = longDigitLength(compactVal); 1086 int drop = prec - mcp; // drop can't be more than 18 1087 while (drop > 0) { 1088 scale = checkScaleNonZero((long) scale - drop); 1089 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mode); 1090 prec = longDigitLength(compactVal); 1091 drop = prec - mcp; 1092 } 1093 unscaledVal = null; 1094 } 1095 } 1096 this.intVal = unscaledVal; 1097 this.intCompact = compactVal; 1098 this.scale = scale; 1099 this.precision = prec; 1100 } 1101 1102 /** 1103 * Translates an {@code int} into a {@code BigDecimal}. The 1104 * scale of the {@code BigDecimal} is zero. 1105 * 1106 * @param val {@code int} value to be converted to 1107 * {@code BigDecimal}. 1108 * @since 1.5 1109 */ 1110 public BigDecimal(int val) { 1111 this.intCompact = val; 1112 this.scale = 0; 1113 this.intVal = null; 1114 } 1115 1116 /** 1117 * Translates an {@code int} into a {@code BigDecimal}, with 1118 * rounding according to the context settings. The scale of the 1119 * {@code BigDecimal}, before any rounding, is zero. 1120 * 1121 * @param val {@code int} value to be converted to {@code BigDecimal}. 1122 * @param mc the context to use. 1123 * @throws ArithmeticException if the result is inexact but the 1124 * rounding mode is {@code UNNECESSARY}. 1125 * @since 1.5 1126 */ 1127 public BigDecimal(int val, MathContext mc) { 1128 int mcp = mc.precision; 1129 long compactVal = val; 1130 int scl = 0; 1131 int prec = 0; 1132 if (mcp > 0) { // do rounding 1133 prec = longDigitLength(compactVal); 1134 int drop = prec - mcp; // drop can't be more than 18 1135 while (drop > 0) { 1136 scl = checkScaleNonZero((long) scl - drop); 1137 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 1138 prec = longDigitLength(compactVal); 1139 drop = prec - mcp; 1140 } 1141 } 1142 this.intVal = null; 1143 this.intCompact = compactVal; 1144 this.scale = scl; 1145 this.precision = prec; 1146 } 1147 1148 /** 1149 * Translates a {@code long} into a {@code BigDecimal}. The 1150 * scale of the {@code BigDecimal} is zero. 1151 * 1152 * @param val {@code long} value to be converted to {@code BigDecimal}. 1153 * @since 1.5 1154 */ 1155 public BigDecimal(long val) { 1156 this.intCompact = val; 1157 this.intVal = (val == INFLATED) ? INFLATED_BIGINT : null; 1158 this.scale = 0; 1159 } 1160 1161 /** 1162 * Translates a {@code long} into a {@code BigDecimal}, with 1163 * rounding according to the context settings. The scale of the 1164 * {@code BigDecimal}, before any rounding, is zero. 1165 * 1166 * @param val {@code long} value to be converted to {@code BigDecimal}. 1167 * @param mc the context to use. 1168 * @throws ArithmeticException if the result is inexact but the 1169 * rounding mode is {@code UNNECESSARY}. 1170 * @since 1.5 1171 */ 1172 public BigDecimal(long val, MathContext mc) { 1173 int mcp = mc.precision; 1174 int mode = mc.roundingMode.oldMode; 1175 int prec = 0; 1176 int scl = 0; 1177 BigInteger rb = (val == INFLATED) ? INFLATED_BIGINT : null; 1178 if (mcp > 0) { // do rounding 1179 if (val == INFLATED) { 1180 prec = 19; 1181 int drop = prec - mcp; 1182 while (drop > 0) { 1183 scl = checkScaleNonZero((long) scl - drop); 1184 rb = divideAndRoundByTenPow(rb, drop, mode); 1185 val = compactValFor(rb); 1186 if (val != INFLATED) { 1187 break; 1188 } 1189 prec = bigDigitLength(rb); 1190 drop = prec - mcp; 1191 } 1192 } 1193 if (val != INFLATED) { 1194 prec = longDigitLength(val); 1195 int drop = prec - mcp; 1196 while (drop > 0) { 1197 scl = checkScaleNonZero((long) scl - drop); 1198 val = divideAndRound(val, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 1199 prec = longDigitLength(val); 1200 drop = prec - mcp; 1201 } 1202 rb = null; 1203 } 1204 } 1205 this.intVal = rb; 1206 this.intCompact = val; 1207 this.scale = scl; 1208 this.precision = prec; 1209 } 1210 1211 // Static Factory Methods 1212 1213 /** 1214 * Translates a {@code long} unscaled value and an 1215 * {@code int} scale into a {@code BigDecimal}. 1216 * 1217 * @apiNote This static factory method is provided in preference 1218 * to a ({@code long}, {@code int}) constructor because it allows 1219 * for reuse of frequently used {@code BigDecimal} values. 1220 * 1221 * @param unscaledVal unscaled value of the {@code BigDecimal}. 1222 * @param scale scale of the {@code BigDecimal}. 1223 * @return a {@code BigDecimal} whose value is 1224 * <code>(unscaledVal × 10<sup>-scale</sup>)</code>. 1225 */ 1226 public static BigDecimal valueOf(long unscaledVal, int scale) { 1227 if (scale == 0) 1228 return valueOf(unscaledVal); 1229 else if (unscaledVal == 0) { 1230 return zeroValueOf(scale); 1231 } 1232 return new BigDecimal(unscaledVal == INFLATED ? 1233 INFLATED_BIGINT : null, 1234 unscaledVal, scale, 0); 1235 } 1236 1237 /** 1238 * Translates a {@code long} value into a {@code BigDecimal} 1239 * with a scale of zero. 1240 * 1241 * @apiNote This static factory method is provided in preference 1242 * to a ({@code long}) constructor because it allows for reuse of 1243 * frequently used {@code BigDecimal} values. 1244 * 1245 * @param val value of the {@code BigDecimal}. 1246 * @return a {@code BigDecimal} whose value is {@code val}. 1247 */ 1248 public static BigDecimal valueOf(long val) { 1249 if (val >= 0 && val < ZERO_THROUGH_TEN.length) 1250 return ZERO_THROUGH_TEN[(int)val]; 1251 else if (val != INFLATED) 1252 return new BigDecimal(null, val, 0, 0); 1253 return new BigDecimal(INFLATED_BIGINT, val, 0, 0); 1254 } 1255 1256 static BigDecimal valueOf(long unscaledVal, int scale, int prec) { 1257 if (scale == 0 && unscaledVal >= 0 && unscaledVal < ZERO_THROUGH_TEN.length) { 1258 return ZERO_THROUGH_TEN[(int) unscaledVal]; 1259 } else if (unscaledVal == 0) { 1260 return zeroValueOf(scale); 1261 } 1262 return new BigDecimal(unscaledVal == INFLATED ? INFLATED_BIGINT : null, 1263 unscaledVal, scale, prec); 1264 } 1265 1266 static BigDecimal valueOf(BigInteger intVal, int scale, int prec) { 1267 long val = compactValFor(intVal); 1268 if (val == 0) { 1269 return zeroValueOf(scale); 1270 } else if (scale == 0 && val >= 0 && val < ZERO_THROUGH_TEN.length) { 1271 return ZERO_THROUGH_TEN[(int) val]; 1272 } 1273 return new BigDecimal(intVal, val, scale, prec); 1274 } 1275 1276 static BigDecimal zeroValueOf(int scale) { 1277 if (scale >= 0 && scale < ZERO_SCALED_BY.length) 1278 return ZERO_SCALED_BY[scale]; 1279 else 1280 return new BigDecimal(BigInteger.ZERO, 0, scale, 1); 1281 } 1282 1283 /** 1284 * Translates a {@code double} into a {@code BigDecimal}, using 1285 * the {@code double}'s canonical string representation provided 1286 * by the {@link Double#toString(double)} method. 1287 * 1288 * @apiNote This is generally the preferred way to convert a 1289 * {@code double} (or {@code float}) into a {@code BigDecimal}, as 1290 * the value returned is equal to that resulting from constructing 1291 * a {@code BigDecimal} from the result of using {@link 1292 * Double#toString(double)}. 1293 * 1294 * @param val {@code double} to convert to a {@code BigDecimal}. 1295 * @return a {@code BigDecimal} whose value is equal to or approximately 1296 * equal to the value of {@code val}. 1297 * @throws NumberFormatException if {@code val} is infinite or NaN. 1298 * @since 1.5 1299 */ 1300 public static BigDecimal valueOf(double val) { 1301 // Reminder: a zero double returns '0.0', so we cannot fastpath 1302 // to use the constant ZERO. This might be important enough to 1303 // justify a factory approach, a cache, or a few private 1304 // constants, later. 1305 return new BigDecimal(Double.toString(val)); 1306 } 1307 1308 // Arithmetic Operations 1309 /** 1310 * Returns a {@code BigDecimal} whose value is {@code (this + 1311 * augend)}, and whose scale is {@code max(this.scale(), 1312 * augend.scale())}. 1313 * 1314 * @param augend value to be added to this {@code BigDecimal}. 1315 * @return {@code this + augend} 1316 */ 1317 public BigDecimal add(BigDecimal augend) { 1318 if (this.intCompact != INFLATED) { 1319 if ((augend.intCompact != INFLATED)) { 1320 return add(this.intCompact, this.scale, augend.intCompact, augend.scale); 1321 } else { 1322 return add(this.intCompact, this.scale, augend.intVal, augend.scale); 1323 } 1324 } else { 1325 if ((augend.intCompact != INFLATED)) { 1326 return add(augend.intCompact, augend.scale, this.intVal, this.scale); 1327 } else { 1328 return add(this.intVal, this.scale, augend.intVal, augend.scale); 1329 } 1330 } 1331 } 1332 1333 /** 1334 * Returns a {@code BigDecimal} whose value is {@code (this + augend)}, 1335 * with rounding according to the context settings. 1336 * 1337 * If either number is zero and the precision setting is nonzero then 1338 * the other number, rounded if necessary, is used as the result. 1339 * 1340 * @param augend value to be added to this {@code BigDecimal}. 1341 * @param mc the context to use. 1342 * @return {@code this + augend}, rounded as necessary. 1343 * @throws ArithmeticException if the result is inexact but the 1344 * rounding mode is {@code UNNECESSARY}. 1345 * @since 1.5 1346 */ 1347 public BigDecimal add(BigDecimal augend, MathContext mc) { 1348 if (mc.precision == 0) 1349 return add(augend); 1350 BigDecimal lhs = this; 1351 1352 // If either number is zero then the other number, rounded and 1353 // scaled if necessary, is used as the result. 1354 { 1355 boolean lhsIsZero = lhs.signum() == 0; 1356 boolean augendIsZero = augend.signum() == 0; 1357 1358 if (lhsIsZero || augendIsZero) { 1359 int preferredScale = Math.max(lhs.scale(), augend.scale()); 1360 BigDecimal result; 1361 1362 if (lhsIsZero && augendIsZero) 1363 return zeroValueOf(preferredScale); 1364 result = lhsIsZero ? doRound(augend, mc) : doRound(lhs, mc); 1365 1366 if (result.scale() == preferredScale) 1367 return result; 1368 else if (result.scale() > preferredScale) { 1369 return stripZerosToMatchScale(result.intVal, result.intCompact, result.scale, preferredScale); 1370 } else { // result.scale < preferredScale 1371 int precisionDiff = mc.precision - result.precision(); 1372 int scaleDiff = preferredScale - result.scale(); 1373 1374 if (precisionDiff >= scaleDiff) 1375 return result.setScale(preferredScale); // can achieve target scale 1376 else 1377 return result.setScale(result.scale() + precisionDiff); 1378 } 1379 } 1380 } 1381 1382 long padding = (long) lhs.scale - augend.scale; 1383 if (padding != 0) { // scales differ; alignment needed 1384 BigDecimal arg[] = preAlign(lhs, augend, padding, mc); 1385 matchScale(arg); 1386 lhs = arg[0]; 1387 augend = arg[1]; 1388 } 1389 return doRound(lhs.inflated().add(augend.inflated()), lhs.scale, mc); 1390 } 1391 1392 /** 1393 * Returns an array of length two, the sum of whose entries is 1394 * equal to the rounded sum of the {@code BigDecimal} arguments. 1395 * 1396 * <p>If the digit positions of the arguments have a sufficient 1397 * gap between them, the value smaller in magnitude can be 1398 * condensed into a {@literal "sticky bit"} and the end result will 1399 * round the same way <em>if</em> the precision of the final 1400 * result does not include the high order digit of the small 1401 * magnitude operand. 1402 * 1403 * <p>Note that while strictly speaking this is an optimization, 1404 * it makes a much wider range of additions practical. 1405 * 1406 * <p>This corresponds to a pre-shift operation in a fixed 1407 * precision floating-point adder; this method is complicated by 1408 * variable precision of the result as determined by the 1409 * MathContext. A more nuanced operation could implement a 1410 * {@literal "right shift"} on the smaller magnitude operand so 1411 * that the number of digits of the smaller operand could be 1412 * reduced even though the significands partially overlapped. 1413 */ 1414 private BigDecimal[] preAlign(BigDecimal lhs, BigDecimal augend, long padding, MathContext mc) { 1415 assert padding != 0; 1416 BigDecimal big; 1417 BigDecimal small; 1418 1419 if (padding < 0) { // lhs is big; augend is small 1420 big = lhs; 1421 small = augend; 1422 } else { // lhs is small; augend is big 1423 big = augend; 1424 small = lhs; 1425 } 1426 1427 /* 1428 * This is the estimated scale of an ulp of the result; it assumes that 1429 * the result doesn't have a carry-out on a true add (e.g. 999 + 1 => 1430 * 1000) or any subtractive cancellation on borrowing (e.g. 100 - 1.2 => 1431 * 98.8) 1432 */ 1433 long estResultUlpScale = (long) big.scale - big.precision() + mc.precision; 1434 1435 /* 1436 * The low-order digit position of big is big.scale(). This 1437 * is true regardless of whether big has a positive or 1438 * negative scale. The high-order digit position of small is 1439 * small.scale - (small.precision() - 1). To do the full 1440 * condensation, the digit positions of big and small must be 1441 * disjoint *and* the digit positions of small should not be 1442 * directly visible in the result. 1443 */ 1444 long smallHighDigitPos = (long) small.scale - small.precision() + 1; 1445 if (smallHighDigitPos > big.scale + 2 && // big and small disjoint 1446 smallHighDigitPos > estResultUlpScale + 2) { // small digits not visible 1447 small = BigDecimal.valueOf(small.signum(), this.checkScale(Math.max(big.scale, estResultUlpScale) + 3)); 1448 } 1449 1450 // Since addition is symmetric, preserving input order in 1451 // returned operands doesn't matter 1452 BigDecimal[] result = {big, small}; 1453 return result; 1454 } 1455 1456 /** 1457 * Returns a {@code BigDecimal} whose value is {@code (this - 1458 * subtrahend)}, and whose scale is {@code max(this.scale(), 1459 * subtrahend.scale())}. 1460 * 1461 * @param subtrahend value to be subtracted from this {@code BigDecimal}. 1462 * @return {@code this - subtrahend} 1463 */ 1464 public BigDecimal subtract(BigDecimal subtrahend) { 1465 if (this.intCompact != INFLATED) { 1466 if ((subtrahend.intCompact != INFLATED)) { 1467 return add(this.intCompact, this.scale, -subtrahend.intCompact, subtrahend.scale); 1468 } else { 1469 return add(this.intCompact, this.scale, subtrahend.intVal.negate(), subtrahend.scale); 1470 } 1471 } else { 1472 if ((subtrahend.intCompact != INFLATED)) { 1473 // Pair of subtrahend values given before pair of 1474 // values from this BigDecimal to avoid need for 1475 // method overloading on the specialized add method 1476 return add(-subtrahend.intCompact, subtrahend.scale, this.intVal, this.scale); 1477 } else { 1478 return add(this.intVal, this.scale, subtrahend.intVal.negate(), subtrahend.scale); 1479 } 1480 } 1481 } 1482 1483 /** 1484 * Returns a {@code BigDecimal} whose value is {@code (this - subtrahend)}, 1485 * with rounding according to the context settings. 1486 * 1487 * If {@code subtrahend} is zero then this, rounded if necessary, is used as the 1488 * result. If this is zero then the result is {@code subtrahend.negate(mc)}. 1489 * 1490 * @param subtrahend value to be subtracted from this {@code BigDecimal}. 1491 * @param mc the context to use. 1492 * @return {@code this - subtrahend}, rounded as necessary. 1493 * @throws ArithmeticException if the result is inexact but the 1494 * rounding mode is {@code UNNECESSARY}. 1495 * @since 1.5 1496 */ 1497 public BigDecimal subtract(BigDecimal subtrahend, MathContext mc) { 1498 if (mc.precision == 0) 1499 return subtract(subtrahend); 1500 // share the special rounding code in add() 1501 return add(subtrahend.negate(), mc); 1502 } 1503 1504 /** 1505 * Returns a {@code BigDecimal} whose value is <code>(this × 1506 * multiplicand)</code>, and whose scale is {@code (this.scale() + 1507 * multiplicand.scale())}. 1508 * 1509 * @param multiplicand value to be multiplied by this {@code BigDecimal}. 1510 * @return {@code this * multiplicand} 1511 */ 1512 public BigDecimal multiply(BigDecimal multiplicand) { 1513 int productScale = checkScale((long) scale + multiplicand.scale); 1514 if (this.intCompact != INFLATED) { 1515 if ((multiplicand.intCompact != INFLATED)) { 1516 return multiply(this.intCompact, multiplicand.intCompact, productScale); 1517 } else { 1518 return multiply(this.intCompact, multiplicand.intVal, productScale); 1519 } 1520 } else { 1521 if ((multiplicand.intCompact != INFLATED)) { 1522 return multiply(multiplicand.intCompact, this.intVal, productScale); 1523 } else { 1524 return multiply(this.intVal, multiplicand.intVal, productScale); 1525 } 1526 } 1527 } 1528 1529 /** 1530 * Returns a {@code BigDecimal} whose value is <code>(this × 1531 * multiplicand)</code>, with rounding according to the context settings. 1532 * 1533 * @param multiplicand value to be multiplied by this {@code BigDecimal}. 1534 * @param mc the context to use. 1535 * @return {@code this * multiplicand}, rounded as necessary. 1536 * @throws ArithmeticException if the result is inexact but the 1537 * rounding mode is {@code UNNECESSARY}. 1538 * @since 1.5 1539 */ 1540 public BigDecimal multiply(BigDecimal multiplicand, MathContext mc) { 1541 if (mc.precision == 0) 1542 return multiply(multiplicand); 1543 int productScale = checkScale((long) scale + multiplicand.scale); 1544 if (this.intCompact != INFLATED) { 1545 if ((multiplicand.intCompact != INFLATED)) { 1546 return multiplyAndRound(this.intCompact, multiplicand.intCompact, productScale, mc); 1547 } else { 1548 return multiplyAndRound(this.intCompact, multiplicand.intVal, productScale, mc); 1549 } 1550 } else { 1551 if ((multiplicand.intCompact != INFLATED)) { 1552 return multiplyAndRound(multiplicand.intCompact, this.intVal, productScale, mc); 1553 } else { 1554 return multiplyAndRound(this.intVal, multiplicand.intVal, productScale, mc); 1555 } 1556 } 1557 } 1558 1559 /** 1560 * Returns a {@code BigDecimal} whose value is {@code (this / 1561 * divisor)}, and whose scale is as specified. If rounding must 1562 * be performed to generate a result with the specified scale, the 1563 * specified rounding mode is applied. 1564 * 1565 * @deprecated The method {@link #divide(BigDecimal, int, RoundingMode)} 1566 * should be used in preference to this legacy method. 1567 * 1568 * @param divisor value by which this {@code BigDecimal} is to be divided. 1569 * @param scale scale of the {@code BigDecimal} quotient to be returned. 1570 * @param roundingMode rounding mode to apply. 1571 * @return {@code this / divisor} 1572 * @throws ArithmeticException if {@code divisor} is zero, 1573 * {@code roundingMode==ROUND_UNNECESSARY} and 1574 * the specified scale is insufficient to represent the result 1575 * of the division exactly. 1576 * @throws IllegalArgumentException if {@code roundingMode} does not 1577 * represent a valid rounding mode. 1578 * @see #ROUND_UP 1579 * @see #ROUND_DOWN 1580 * @see #ROUND_CEILING 1581 * @see #ROUND_FLOOR 1582 * @see #ROUND_HALF_UP 1583 * @see #ROUND_HALF_DOWN 1584 * @see #ROUND_HALF_EVEN 1585 * @see #ROUND_UNNECESSARY 1586 */ 1587 @Deprecated(since="9") 1588 public BigDecimal divide(BigDecimal divisor, int scale, int roundingMode) { 1589 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY) 1590 throw new IllegalArgumentException("Invalid rounding mode"); 1591 if (this.intCompact != INFLATED) { 1592 if ((divisor.intCompact != INFLATED)) { 1593 return divide(this.intCompact, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode); 1594 } else { 1595 return divide(this.intCompact, this.scale, divisor.intVal, divisor.scale, scale, roundingMode); 1596 } 1597 } else { 1598 if ((divisor.intCompact != INFLATED)) { 1599 return divide(this.intVal, this.scale, divisor.intCompact, divisor.scale, scale, roundingMode); 1600 } else { 1601 return divide(this.intVal, this.scale, divisor.intVal, divisor.scale, scale, roundingMode); 1602 } 1603 } 1604 } 1605 1606 /** 1607 * Returns a {@code BigDecimal} whose value is {@code (this / 1608 * divisor)}, and whose scale is as specified. If rounding must 1609 * be performed to generate a result with the specified scale, the 1610 * specified rounding mode is applied. 1611 * 1612 * @param divisor value by which this {@code BigDecimal} is to be divided. 1613 * @param scale scale of the {@code BigDecimal} quotient to be returned. 1614 * @param roundingMode rounding mode to apply. 1615 * @return {@code this / divisor} 1616 * @throws ArithmeticException if {@code divisor} is zero, 1617 * {@code roundingMode==RoundingMode.UNNECESSARY} and 1618 * the specified scale is insufficient to represent the result 1619 * of the division exactly. 1620 * @since 1.5 1621 */ 1622 public BigDecimal divide(BigDecimal divisor, int scale, RoundingMode roundingMode) { 1623 return divide(divisor, scale, roundingMode.oldMode); 1624 } 1625 1626 /** 1627 * Returns a {@code BigDecimal} whose value is {@code (this / 1628 * divisor)}, and whose scale is {@code this.scale()}. If 1629 * rounding must be performed to generate a result with the given 1630 * scale, the specified rounding mode is applied. 1631 * 1632 * @deprecated The method {@link #divide(BigDecimal, RoundingMode)} 1633 * should be used in preference to this legacy method. 1634 * 1635 * @param divisor value by which this {@code BigDecimal} is to be divided. 1636 * @param roundingMode rounding mode to apply. 1637 * @return {@code this / divisor} 1638 * @throws ArithmeticException if {@code divisor==0}, or 1639 * {@code roundingMode==ROUND_UNNECESSARY} and 1640 * {@code this.scale()} is insufficient to represent the result 1641 * of the division exactly. 1642 * @throws IllegalArgumentException if {@code roundingMode} does not 1643 * represent a valid rounding mode. 1644 * @see #ROUND_UP 1645 * @see #ROUND_DOWN 1646 * @see #ROUND_CEILING 1647 * @see #ROUND_FLOOR 1648 * @see #ROUND_HALF_UP 1649 * @see #ROUND_HALF_DOWN 1650 * @see #ROUND_HALF_EVEN 1651 * @see #ROUND_UNNECESSARY 1652 */ 1653 @Deprecated(since="9") 1654 public BigDecimal divide(BigDecimal divisor, int roundingMode) { 1655 return this.divide(divisor, scale, roundingMode); 1656 } 1657 1658 /** 1659 * Returns a {@code BigDecimal} whose value is {@code (this / 1660 * divisor)}, and whose scale is {@code this.scale()}. If 1661 * rounding must be performed to generate a result with the given 1662 * scale, the specified rounding mode is applied. 1663 * 1664 * @param divisor value by which this {@code BigDecimal} is to be divided. 1665 * @param roundingMode rounding mode to apply. 1666 * @return {@code this / divisor} 1667 * @throws ArithmeticException if {@code divisor==0}, or 1668 * {@code roundingMode==RoundingMode.UNNECESSARY} and 1669 * {@code this.scale()} is insufficient to represent the result 1670 * of the division exactly. 1671 * @since 1.5 1672 */ 1673 public BigDecimal divide(BigDecimal divisor, RoundingMode roundingMode) { 1674 return this.divide(divisor, scale, roundingMode.oldMode); 1675 } 1676 1677 /** 1678 * Returns a {@code BigDecimal} whose value is {@code (this / 1679 * divisor)}, and whose preferred scale is {@code (this.scale() - 1680 * divisor.scale())}; if the exact quotient cannot be 1681 * represented (because it has a non-terminating decimal 1682 * expansion) an {@code ArithmeticException} is thrown. 1683 * 1684 * @param divisor value by which this {@code BigDecimal} is to be divided. 1685 * @throws ArithmeticException if the exact quotient does not have a 1686 * terminating decimal expansion 1687 * @return {@code this / divisor} 1688 * @since 1.5 1689 * @author Joseph D. Darcy 1690 */ 1691 public BigDecimal divide(BigDecimal divisor) { 1692 /* 1693 * Handle zero cases first. 1694 */ 1695 if (divisor.signum() == 0) { // x/0 1696 if (this.signum() == 0) // 0/0 1697 throw new ArithmeticException("Division undefined"); // NaN 1698 throw new ArithmeticException("Division by zero"); 1699 } 1700 1701 // Calculate preferred scale 1702 int preferredScale = saturateLong((long) this.scale - divisor.scale); 1703 1704 if (this.signum() == 0) // 0/y 1705 return zeroValueOf(preferredScale); 1706 else { 1707 /* 1708 * If the quotient this/divisor has a terminating decimal 1709 * expansion, the expansion can have no more than 1710 * (a.precision() + ceil(10*b.precision)/3) digits. 1711 * Therefore, create a MathContext object with this 1712 * precision and do a divide with the UNNECESSARY rounding 1713 * mode. 1714 */ 1715 MathContext mc = new MathContext( (int)Math.min(this.precision() + 1716 (long)Math.ceil(10.0*divisor.precision()/3.0), 1717 Integer.MAX_VALUE), 1718 RoundingMode.UNNECESSARY); 1719 BigDecimal quotient; 1720 try { 1721 quotient = this.divide(divisor, mc); 1722 } catch (ArithmeticException e) { 1723 throw new ArithmeticException("Non-terminating decimal expansion; " + 1724 "no exact representable decimal result."); 1725 } 1726 1727 int quotientScale = quotient.scale(); 1728 1729 // divide(BigDecimal, mc) tries to adjust the quotient to 1730 // the desired one by removing trailing zeros; since the 1731 // exact divide method does not have an explicit digit 1732 // limit, we can add zeros too. 1733 if (preferredScale > quotientScale) 1734 return quotient.setScale(preferredScale, ROUND_UNNECESSARY); 1735 1736 return quotient; 1737 } 1738 } 1739 1740 /** 1741 * Returns a {@code BigDecimal} whose value is {@code (this / 1742 * divisor)}, with rounding according to the context settings. 1743 * 1744 * @param divisor value by which this {@code BigDecimal} is to be divided. 1745 * @param mc the context to use. 1746 * @return {@code this / divisor}, rounded as necessary. 1747 * @throws ArithmeticException if the result is inexact but the 1748 * rounding mode is {@code UNNECESSARY} or 1749 * {@code mc.precision == 0} and the quotient has a 1750 * non-terminating decimal expansion. 1751 * @since 1.5 1752 */ 1753 public BigDecimal divide(BigDecimal divisor, MathContext mc) { 1754 int mcp = mc.precision; 1755 if (mcp == 0) 1756 return divide(divisor); 1757 1758 BigDecimal dividend = this; 1759 long preferredScale = (long)dividend.scale - divisor.scale; 1760 // Now calculate the answer. We use the existing 1761 // divide-and-round method, but as this rounds to scale we have 1762 // to normalize the values here to achieve the desired result. 1763 // For x/y we first handle y=0 and x=0, and then normalize x and 1764 // y to give x' and y' with the following constraints: 1765 // (a) 0.1 <= x' < 1 1766 // (b) x' <= y' < 10*x' 1767 // Dividing x'/y' with the required scale set to mc.precision then 1768 // will give a result in the range 0.1 to 1 rounded to exactly 1769 // the right number of digits (except in the case of a result of 1770 // 1.000... which can arise when x=y, or when rounding overflows 1771 // The 1.000... case will reduce properly to 1. 1772 if (divisor.signum() == 0) { // x/0 1773 if (dividend.signum() == 0) // 0/0 1774 throw new ArithmeticException("Division undefined"); // NaN 1775 throw new ArithmeticException("Division by zero"); 1776 } 1777 if (dividend.signum() == 0) // 0/y 1778 return zeroValueOf(saturateLong(preferredScale)); 1779 int xscale = dividend.precision(); 1780 int yscale = divisor.precision(); 1781 if(dividend.intCompact!=INFLATED) { 1782 if(divisor.intCompact!=INFLATED) { 1783 return divide(dividend.intCompact, xscale, divisor.intCompact, yscale, preferredScale, mc); 1784 } else { 1785 return divide(dividend.intCompact, xscale, divisor.intVal, yscale, preferredScale, mc); 1786 } 1787 } else { 1788 if(divisor.intCompact!=INFLATED) { 1789 return divide(dividend.intVal, xscale, divisor.intCompact, yscale, preferredScale, mc); 1790 } else { 1791 return divide(dividend.intVal, xscale, divisor.intVal, yscale, preferredScale, mc); 1792 } 1793 } 1794 } 1795 1796 /** 1797 * Returns a {@code BigDecimal} whose value is the integer part 1798 * of the quotient {@code (this / divisor)} rounded down. The 1799 * preferred scale of the result is {@code (this.scale() - 1800 * divisor.scale())}. 1801 * 1802 * @param divisor value by which this {@code BigDecimal} is to be divided. 1803 * @return The integer part of {@code this / divisor}. 1804 * @throws ArithmeticException if {@code divisor==0} 1805 * @since 1.5 1806 */ 1807 public BigDecimal divideToIntegralValue(BigDecimal divisor) { 1808 // Calculate preferred scale 1809 int preferredScale = saturateLong((long) this.scale - divisor.scale); 1810 if (this.compareMagnitude(divisor) < 0) { 1811 // much faster when this << divisor 1812 return zeroValueOf(preferredScale); 1813 } 1814 1815 if (this.signum() == 0 && divisor.signum() != 0) 1816 return this.setScale(preferredScale, ROUND_UNNECESSARY); 1817 1818 // Perform a divide with enough digits to round to a correct 1819 // integer value; then remove any fractional digits 1820 1821 int maxDigits = (int)Math.min(this.precision() + 1822 (long)Math.ceil(10.0*divisor.precision()/3.0) + 1823 Math.abs((long)this.scale() - divisor.scale()) + 2, 1824 Integer.MAX_VALUE); 1825 BigDecimal quotient = this.divide(divisor, new MathContext(maxDigits, 1826 RoundingMode.DOWN)); 1827 if (quotient.scale > 0) { 1828 quotient = quotient.setScale(0, RoundingMode.DOWN); 1829 quotient = stripZerosToMatchScale(quotient.intVal, quotient.intCompact, quotient.scale, preferredScale); 1830 } 1831 1832 if (quotient.scale < preferredScale) { 1833 // pad with zeros if necessary 1834 quotient = quotient.setScale(preferredScale, ROUND_UNNECESSARY); 1835 } 1836 1837 return quotient; 1838 } 1839 1840 /** 1841 * Returns a {@code BigDecimal} whose value is the integer part 1842 * of {@code (this / divisor)}. Since the integer part of the 1843 * exact quotient does not depend on the rounding mode, the 1844 * rounding mode does not affect the values returned by this 1845 * method. The preferred scale of the result is 1846 * {@code (this.scale() - divisor.scale())}. An 1847 * {@code ArithmeticException} is thrown if the integer part of 1848 * the exact quotient needs more than {@code mc.precision} 1849 * digits. 1850 * 1851 * @param divisor value by which this {@code BigDecimal} is to be divided. 1852 * @param mc the context to use. 1853 * @return The integer part of {@code this / divisor}. 1854 * @throws ArithmeticException if {@code divisor==0} 1855 * @throws ArithmeticException if {@code mc.precision} {@literal >} 0 and the result 1856 * requires a precision of more than {@code mc.precision} digits. 1857 * @since 1.5 1858 * @author Joseph D. Darcy 1859 */ 1860 public BigDecimal divideToIntegralValue(BigDecimal divisor, MathContext mc) { 1861 if (mc.precision == 0 || // exact result 1862 (this.compareMagnitude(divisor) < 0)) // zero result 1863 return divideToIntegralValue(divisor); 1864 1865 // Calculate preferred scale 1866 int preferredScale = saturateLong((long)this.scale - divisor.scale); 1867 1868 /* 1869 * Perform a normal divide to mc.precision digits. If the 1870 * remainder has absolute value less than the divisor, the 1871 * integer portion of the quotient fits into mc.precision 1872 * digits. Next, remove any fractional digits from the 1873 * quotient and adjust the scale to the preferred value. 1874 */ 1875 BigDecimal result = this.divide(divisor, new MathContext(mc.precision, RoundingMode.DOWN)); 1876 1877 if (result.scale() < 0) { 1878 /* 1879 * Result is an integer. See if quotient represents the 1880 * full integer portion of the exact quotient; if it does, 1881 * the computed remainder will be less than the divisor. 1882 */ 1883 BigDecimal product = result.multiply(divisor); 1884 // If the quotient is the full integer value, 1885 // |dividend-product| < |divisor|. 1886 if (this.subtract(product).compareMagnitude(divisor) >= 0) { 1887 throw new ArithmeticException("Division impossible"); 1888 } 1889 } else if (result.scale() > 0) { 1890 /* 1891 * Integer portion of quotient will fit into precision 1892 * digits; recompute quotient to scale 0 to avoid double 1893 * rounding and then try to adjust, if necessary. 1894 */ 1895 result = result.setScale(0, RoundingMode.DOWN); 1896 } 1897 // else result.scale() == 0; 1898 1899 int precisionDiff; 1900 if ((preferredScale > result.scale()) && 1901 (precisionDiff = mc.precision - result.precision()) > 0) { 1902 return result.setScale(result.scale() + 1903 Math.min(precisionDiff, preferredScale - result.scale) ); 1904 } else { 1905 return stripZerosToMatchScale(result.intVal,result.intCompact,result.scale,preferredScale); 1906 } 1907 } 1908 1909 /** 1910 * Returns a {@code BigDecimal} whose value is {@code (this % divisor)}. 1911 * 1912 * <p>The remainder is given by 1913 * {@code this.subtract(this.divideToIntegralValue(divisor).multiply(divisor))}. 1914 * Note that this is <em>not</em> the modulo operation (the result can be 1915 * negative). 1916 * 1917 * @param divisor value by which this {@code BigDecimal} is to be divided. 1918 * @return {@code this % divisor}. 1919 * @throws ArithmeticException if {@code divisor==0} 1920 * @since 1.5 1921 */ 1922 public BigDecimal remainder(BigDecimal divisor) { 1923 BigDecimal divrem[] = this.divideAndRemainder(divisor); 1924 return divrem[1]; 1925 } 1926 1927 1928 /** 1929 * Returns a {@code BigDecimal} whose value is {@code (this % 1930 * divisor)}, with rounding according to the context settings. 1931 * The {@code MathContext} settings affect the implicit divide 1932 * used to compute the remainder. The remainder computation 1933 * itself is by definition exact. Therefore, the remainder may 1934 * contain more than {@code mc.getPrecision()} digits. 1935 * 1936 * <p>The remainder is given by 1937 * {@code this.subtract(this.divideToIntegralValue(divisor, 1938 * mc).multiply(divisor))}. Note that this is not the modulo 1939 * operation (the result can be negative). 1940 * 1941 * @param divisor value by which this {@code BigDecimal} is to be divided. 1942 * @param mc the context to use. 1943 * @return {@code this % divisor}, rounded as necessary. 1944 * @throws ArithmeticException if {@code divisor==0} 1945 * @throws ArithmeticException if the result is inexact but the 1946 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision} 1947 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would 1948 * require a precision of more than {@code mc.precision} digits. 1949 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) 1950 * @since 1.5 1951 */ 1952 public BigDecimal remainder(BigDecimal divisor, MathContext mc) { 1953 BigDecimal divrem[] = this.divideAndRemainder(divisor, mc); 1954 return divrem[1]; 1955 } 1956 1957 /** 1958 * Returns a two-element {@code BigDecimal} array containing the 1959 * result of {@code divideToIntegralValue} followed by the result of 1960 * {@code remainder} on the two operands. 1961 * 1962 * <p>Note that if both the integer quotient and remainder are 1963 * needed, this method is faster than using the 1964 * {@code divideToIntegralValue} and {@code remainder} methods 1965 * separately because the division need only be carried out once. 1966 * 1967 * @param divisor value by which this {@code BigDecimal} is to be divided, 1968 * and the remainder computed. 1969 * @return a two element {@code BigDecimal} array: the quotient 1970 * (the result of {@code divideToIntegralValue}) is the initial element 1971 * and the remainder is the final element. 1972 * @throws ArithmeticException if {@code divisor==0} 1973 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) 1974 * @see #remainder(java.math.BigDecimal, java.math.MathContext) 1975 * @since 1.5 1976 */ 1977 public BigDecimal[] divideAndRemainder(BigDecimal divisor) { 1978 // we use the identity x = i * y + r to determine r 1979 BigDecimal[] result = new BigDecimal[2]; 1980 1981 result[0] = this.divideToIntegralValue(divisor); 1982 result[1] = this.subtract(result[0].multiply(divisor)); 1983 return result; 1984 } 1985 1986 /** 1987 * Returns a two-element {@code BigDecimal} array containing the 1988 * result of {@code divideToIntegralValue} followed by the result of 1989 * {@code remainder} on the two operands calculated with rounding 1990 * according to the context settings. 1991 * 1992 * <p>Note that if both the integer quotient and remainder are 1993 * needed, this method is faster than using the 1994 * {@code divideToIntegralValue} and {@code remainder} methods 1995 * separately because the division need only be carried out once. 1996 * 1997 * @param divisor value by which this {@code BigDecimal} is to be divided, 1998 * and the remainder computed. 1999 * @param mc the context to use. 2000 * @return a two element {@code BigDecimal} array: the quotient 2001 * (the result of {@code divideToIntegralValue}) is the 2002 * initial element and the remainder is the final element. 2003 * @throws ArithmeticException if {@code divisor==0} 2004 * @throws ArithmeticException if the result is inexact but the 2005 * rounding mode is {@code UNNECESSARY}, or {@code mc.precision} 2006 * {@literal >} 0 and the result of {@code this.divideToIntgralValue(divisor)} would 2007 * require a precision of more than {@code mc.precision} digits. 2008 * @see #divideToIntegralValue(java.math.BigDecimal, java.math.MathContext) 2009 * @see #remainder(java.math.BigDecimal, java.math.MathContext) 2010 * @since 1.5 2011 */ 2012 public BigDecimal[] divideAndRemainder(BigDecimal divisor, MathContext mc) { 2013 if (mc.precision == 0) 2014 return divideAndRemainder(divisor); 2015 2016 BigDecimal[] result = new BigDecimal[2]; 2017 BigDecimal lhs = this; 2018 2019 result[0] = lhs.divideToIntegralValue(divisor, mc); 2020 result[1] = lhs.subtract(result[0].multiply(divisor)); 2021 return result; 2022 } 2023 2024 /** 2025 * Returns an approximation to the square root of {@code this} 2026 * with rounding according to the context settings. 2027 * 2028 * <p>The preferred scale of the returned result is equal to 2029 * {@code this.scale()/2}. The value of the returned result is 2030 * always within one ulp of the exact decimal value for the 2031 * precision in question. If the rounding mode is {@link 2032 * RoundingMode#HALF_UP HALF_UP}, {@link RoundingMode#HALF_DOWN 2033 * HALF_DOWN}, or {@link RoundingMode#HALF_EVEN HALF_EVEN}, the 2034 * result is within one half an ulp of the exact decimal value. 2035 * 2036 * <p>Special case: 2037 * <ul> 2038 * <li> The square root of a number numerically equal to {@code 2039 * ZERO} is numerically equal to {@code ZERO} with a preferred 2040 * scale according to the general rule above. In particular, for 2041 * {@code ZERO}, {@code ZERO.sqrt(mc).equals(ZERO)} is true with 2042 * any {@code MathContext} as an argument. 2043 * </ul> 2044 * 2045 * @param mc the context to use. 2046 * @return the square root of {@code this}. 2047 * @throws ArithmeticException if {@code this} is less than zero. 2048 * @throws ArithmeticException if an exact result is requested 2049 * ({@code mc.getPrecision()==0}) and there is no finite decimal 2050 * expansion of the exact result 2051 * @throws ArithmeticException if 2052 * {@code (mc.getRoundingMode()==RoundingMode.UNNECESSARY}) and 2053 * the exact result cannot fit in {@code mc.getPrecision()} 2054 * digits. 2055 * @see BigInteger#sqrt() 2056 * @since 9 2057 */ 2058 public BigDecimal sqrt(MathContext mc) { 2059 int signum = signum(); 2060 if (signum == 1) { 2061 /* 2062 * The following code draws on the algorithm presented in 2063 * "Properly Rounded Variable Precision Square Root," Hull and 2064 * Abrham, ACM Transactions on Mathematical Software, Vol 11, 2065 * No. 3, September 1985, Pages 229-237. 2066 * 2067 * The BigDecimal computational model differs from the one 2068 * presented in the paper in several ways: first BigDecimal 2069 * numbers aren't necessarily normalized, second many more 2070 * rounding modes are supported, including UNNECESSARY, and 2071 * exact results can be requested. 2072 * 2073 * The main steps of the algorithm below are as follows, 2074 * first argument reduce the value to the numerical range 2075 * [1, 10) using the following relations: 2076 * 2077 * x = y * 10 ^ exp 2078 * sqrt(x) = sqrt(y) * 10^(exp / 2) if exp is even 2079 * sqrt(x) = sqrt(y/10) * 10 ^((exp+1)/2) is exp is odd 2080 * 2081 * Then use Newton's iteration on the reduced value to compute 2082 * the numerical digits of the desired result. 2083 * 2084 * Finally, scale back to the desired exponent range and 2085 * perform any adjustment to get the preferred scale in the 2086 * representation. 2087 */ 2088 2089 // The code below favors relative simplicity over checking 2090 // for special cases that could run faster. 2091 2092 int preferredScale = this.scale()/2; 2093 BigDecimal zeroWithFinalPreferredScale = valueOf(0L, preferredScale); 2094 2095 // First phase of numerical normalization, strip trailing 2096 // zeros and check for even powers of 10. 2097 BigDecimal stripped = this.stripTrailingZeros(); 2098 int strippedScale = stripped.scale(); 2099 2100 // Numerically sqrt(10^2N) = 10^N 2101 if (stripped.isPowerOfTen() && 2102 strippedScale % 2 == 0) { 2103 BigDecimal result = valueOf(1L, strippedScale/2); 2104 if (result.scale() != preferredScale) { 2105 // Adjust to requested precision and preferred 2106 // scale as appropriate. 2107 result = result.add(zeroWithFinalPreferredScale, mc); 2108 } 2109 return result; 2110 } 2111 2112 // After stripTrailingZeros, the representation is normalized as 2113 // 2114 // unscaledValue * 10^(-scale) 2115 // 2116 // where unscaledValue is an integer with the mimimum 2117 // precision for the cohort of the numerical value. To 2118 // allow binary floating-point hardware to be used to get 2119 // approximately a 15 digit approximation to the square 2120 // root, it is helpful to instead normalize this so that 2121 // the significand portion is to right of the decimal 2122 // point by roughly (scale() - precision() + 1). 2123 2124 // Now the precision / scale adjustment 2125 int scaleAdjust = 0; 2126 int scale = stripped.scale() - stripped.precision() + 1; 2127 if (scale % 2 == 0) { 2128 scaleAdjust = scale; 2129 } else { 2130 scaleAdjust = scale - 1; 2131 } 2132 2133 BigDecimal working = stripped.scaleByPowerOfTen(scaleAdjust); 2134 2135 assert // Verify 0.1 <= working < 10 2136 ONE_TENTH.compareTo(working) <= 0 && working.compareTo(TEN) < 0; 2137 2138 // Use good ole' Math.sqrt to get the initial guess for 2139 // the Newton iteration, good to at least 15 decimal 2140 // digits. This approach does incur the cost of a 2141 // 2142 // BigDecimal -> double -> BigDecimal 2143 // 2144 // conversion cycle, but it avoids the need for several 2145 // Newton iterations in BigDecimal arithmetic to get the 2146 // working answer to 15 digits of precision. If many fewer 2147 // than 15 digits were needed, it might be faster to do 2148 // the loop entirely in BigDecimal arithmetic. 2149 // 2150 // (A double value might have as many as 17 decimal 2151 // digits of precision; it depends on the relative density 2152 // of binary and decimal numbers at different regions of 2153 // the number line.) 2154 // 2155 // (It would be possible to check for certain special 2156 // cases to avoid doing any Newton iterations. For 2157 // example, if the BigDecimal -> double conversion was 2158 // known to be exact and the rounding mode had a 2159 // low-enough precision, the post-Newton rounding logic 2160 // could be applied directly.) 2161 2162 BigDecimal guess = new BigDecimal(Math.sqrt(working.doubleValue())); 2163 int guessPrecision = 15; 2164 int originalPrecision = mc.getPrecision(); 2165 int targetPrecision; 2166 2167 // If an exact value is requested, it must only need about 2168 // half of the input digits to represent since multiplying 2169 // an N digit number by itself yield a 2N-1 digit or 2N 2170 // digit result. 2171 if (originalPrecision == 0) { 2172 targetPrecision = stripped.precision()/2 + 1; 2173 } else { 2174 /* 2175 * To avoid the need for post-Newton fix-up logic, in 2176 * the case of half-way rounding modes, double the 2177 * target precision so that the "2p + 2" property can 2178 * be relied on to accomplish the final rounding. 2179 */ 2180 switch (mc.getRoundingMode()) { 2181 case HALF_UP: 2182 case HALF_DOWN: 2183 case HALF_EVEN: 2184 targetPrecision = 2 * originalPrecision; 2185 if (targetPrecision < 0) // Overflow 2186 targetPrecision = Integer.MAX_VALUE - 2; 2187 break; 2188 2189 default: 2190 targetPrecision = originalPrecision; 2191 break; 2192 } 2193 } 2194 2195 // When setting the precision to use inside the Newton 2196 // iteration loop, take care to avoid the case where the 2197 // precision of the input exceeds the requested precision 2198 // and rounding the input value too soon. 2199 BigDecimal approx = guess; 2200 int workingPrecision = working.precision(); 2201 do { 2202 int tmpPrecision = Math.max(Math.max(guessPrecision, targetPrecision + 2), 2203 workingPrecision); 2204 MathContext mcTmp = new MathContext(tmpPrecision, RoundingMode.HALF_EVEN); 2205 // approx = 0.5 * (approx + fraction / approx) 2206 approx = ONE_HALF.multiply(approx.add(working.divide(approx, mcTmp), mcTmp)); 2207 guessPrecision *= 2; 2208 } while (guessPrecision < targetPrecision + 2); 2209 2210 BigDecimal result; 2211 RoundingMode targetRm = mc.getRoundingMode(); 2212 if (targetRm == RoundingMode.UNNECESSARY || originalPrecision == 0) { 2213 RoundingMode tmpRm = 2214 (targetRm == RoundingMode.UNNECESSARY) ? RoundingMode.DOWN : targetRm; 2215 MathContext mcTmp = new MathContext(targetPrecision, tmpRm); 2216 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mcTmp); 2217 2218 // If result*result != this numerically, the square 2219 // root isn't exact 2220 if (this.subtract(result.square()).compareTo(ZERO) != 0) { 2221 throw new ArithmeticException("Computed square root not exact."); 2222 } 2223 } else { 2224 result = approx.scaleByPowerOfTen(-scaleAdjust/2).round(mc); 2225 2226 switch (targetRm) { 2227 case DOWN: 2228 case FLOOR: 2229 // Check if too big 2230 if (result.square().compareTo(this) > 0) { 2231 BigDecimal ulp = result.ulp(); 2232 // Adjust increment down in case of 1.0 = 10^0 2233 // since the next smaller number is only 1/10 2234 // as far way as the next larger at exponent 2235 // boundaries. Test approx and *not* result to 2236 // avoid having to detect an arbitrary power 2237 // of ten. 2238 if (approx.compareTo(ONE) == 0) { 2239 ulp = ulp.multiply(ONE_TENTH); 2240 } 2241 result = result.subtract(ulp); 2242 } 2243 break; 2244 2245 case UP: 2246 case CEILING: 2247 // Check if too small 2248 if (result.square().compareTo(this) < 0) { 2249 result = result.add(result.ulp()); 2250 } 2251 break; 2252 2253 default: 2254 // No additional work, rely on "2p + 2" property 2255 // for correct rounding. Alternatively, could 2256 // instead run the Newton iteration to around p 2257 // digits and then do tests and fix-ups on the 2258 // rounded value. One possible set of tests and 2259 // fix-ups is given in the Hull and Abrham paper; 2260 // however, additional half-way cases can occur 2261 // for BigDecimal given the more varied 2262 // combinations of input and output precisions 2263 // supported. 2264 break; 2265 } 2266 2267 } 2268 2269 // Test numerical properties at full precision before any 2270 // scale adjustments. 2271 assert squareRootResultAssertions(result, mc); 2272 if (result.scale() != preferredScale) { 2273 // The preferred scale of an add is 2274 // max(addend.scale(), augend.scale()). Therefore, if 2275 // the scale of the result is first minimized using 2276 // stripTrailingZeros(), adding a zero of the 2277 // preferred scale rounding to the correct precision 2278 // will perform the proper scale vs precision 2279 // tradeoffs. 2280 result = result.stripTrailingZeros(). 2281 add(zeroWithFinalPreferredScale, 2282 new MathContext(originalPrecision, RoundingMode.UNNECESSARY)); 2283 } 2284 return result; 2285 } else { 2286 BigDecimal result = null; 2287 switch (signum) { 2288 case -1: 2289 throw new ArithmeticException("Attempted square root " + 2290 "of negative BigDecimal"); 2291 case 0: 2292 result = valueOf(0L, scale()/2); 2293 assert squareRootResultAssertions(result, mc); 2294 return result; 2295 2296 default: 2297 throw new AssertionError("Bad value from signum"); 2298 } 2299 } 2300 } 2301 2302 private BigDecimal square() { 2303 return this.multiply(this); 2304 } 2305 2306 private boolean isPowerOfTen() { 2307 return BigInteger.ONE.equals(this.unscaledValue()); 2308 } 2309 2310 /** 2311 * For nonzero values, check numerical correctness properties of 2312 * the computed result for the chosen rounding mode. 2313 * 2314 * For the directed rounding modes: 2315 * 2316 * <ul> 2317 * 2318 * <li> For DOWN and FLOOR, result^2 must be {@code <=} the input 2319 * and (result+ulp)^2 must be {@code >} the input. 2320 * 2321 * <li>Conversely, for UP and CEIL, result^2 must be {@code >=} 2322 * the input and (result-ulp)^2 must be {@code <} the input. 2323 * </ul> 2324 */ 2325 private boolean squareRootResultAssertions(BigDecimal result, MathContext mc) { 2326 if (result.signum() == 0) { 2327 return squareRootZeroResultAssertions(result, mc); 2328 } else { 2329 RoundingMode rm = mc.getRoundingMode(); 2330 BigDecimal ulp = result.ulp(); 2331 BigDecimal neighborUp = result.add(ulp); 2332 // Make neighbor down accurate even for powers of ten 2333 if (result.isPowerOfTen()) { 2334 ulp = ulp.divide(TEN); 2335 } 2336 BigDecimal neighborDown = result.subtract(ulp); 2337 2338 // Both the starting value and result should be nonzero and positive. 2339 assert (result.signum() == 1 && 2340 this.signum() == 1) : 2341 "Bad signum of this and/or its sqrt."; 2342 2343 switch (rm) { 2344 case DOWN: 2345 case FLOOR: 2346 assert 2347 result.square().compareTo(this) <= 0 && 2348 neighborUp.square().compareTo(this) > 0: 2349 "Square of result out for bounds rounding " + rm; 2350 return true; 2351 2352 case UP: 2353 case CEILING: 2354 assert 2355 result.square().compareTo(this) >= 0 && 2356 neighborDown.square().compareTo(this) < 0: 2357 "Square of result out for bounds rounding " + rm; 2358 return true; 2359 2360 2361 case HALF_DOWN: 2362 case HALF_EVEN: 2363 case HALF_UP: 2364 BigDecimal err = result.square().subtract(this).abs(); 2365 BigDecimal errUp = neighborUp.square().subtract(this); 2366 BigDecimal errDown = this.subtract(neighborDown.square()); 2367 // All error values should be positive so don't need to 2368 // compare absolute values. 2369 2370 int err_comp_errUp = err.compareTo(errUp); 2371 int err_comp_errDown = err.compareTo(errDown); 2372 2373 assert 2374 errUp.signum() == 1 && 2375 errDown.signum() == 1 : 2376 "Errors of neighbors squared don't have correct signs"; 2377 2378 // For breaking a half-way tie, the return value may 2379 // have a larger error than one of the neighbors. For 2380 // example, the square root of 2.25 to a precision of 2381 // 1 digit is either 1 or 2 depending on how the exact 2382 // value of 1.5 is rounded. If 2 is returned, it will 2383 // have a larger rounding error than its neighbor 1. 2384 assert 2385 err_comp_errUp <= 0 || 2386 err_comp_errDown <= 0 : 2387 "Computed square root has larger error than neighbors for " + rm; 2388 2389 assert 2390 ((err_comp_errUp == 0 ) ? err_comp_errDown < 0 : true) && 2391 ((err_comp_errDown == 0 ) ? err_comp_errUp < 0 : true) : 2392 "Incorrect error relationships"; 2393 // && could check for digit conditions for ties too 2394 return true; 2395 2396 default: // Definition of UNNECESSARY already verified. 2397 return true; 2398 } 2399 } 2400 } 2401 2402 private boolean squareRootZeroResultAssertions(BigDecimal result, MathContext mc) { 2403 return this.compareTo(ZERO) == 0; 2404 } 2405 2406 /** 2407 * Returns a {@code BigDecimal} whose value is 2408 * <code>(this<sup>n</sup>)</code>, The power is computed exactly, to 2409 * unlimited precision. 2410 * 2411 * <p>The parameter {@code n} must be in the range 0 through 2412 * 999999999, inclusive. {@code ZERO.pow(0)} returns {@link 2413 * #ONE}. 2414 * 2415 * Note that future releases may expand the allowable exponent 2416 * range of this method. 2417 * 2418 * @param n power to raise this {@code BigDecimal} to. 2419 * @return <code>this<sup>n</sup></code> 2420 * @throws ArithmeticException if {@code n} is out of range. 2421 * @since 1.5 2422 */ 2423 public BigDecimal pow(int n) { 2424 if (n < 0 || n > 999999999) 2425 throw new ArithmeticException("Invalid operation"); 2426 // No need to calculate pow(n) if result will over/underflow. 2427 // Don't attempt to support "supernormal" numbers. 2428 int newScale = checkScale((long)scale * n); 2429 return new BigDecimal(this.inflated().pow(n), newScale); 2430 } 2431 2432 2433 /** 2434 * Returns a {@code BigDecimal} whose value is 2435 * <code>(this<sup>n</sup>)</code>. The current implementation uses 2436 * the core algorithm defined in ANSI standard X3.274-1996 with 2437 * rounding according to the context settings. In general, the 2438 * returned numerical value is within two ulps of the exact 2439 * numerical value for the chosen precision. Note that future 2440 * releases may use a different algorithm with a decreased 2441 * allowable error bound and increased allowable exponent range. 2442 * 2443 * <p>The X3.274-1996 algorithm is: 2444 * 2445 * <ul> 2446 * <li> An {@code ArithmeticException} exception is thrown if 2447 * <ul> 2448 * <li>{@code abs(n) > 999999999} 2449 * <li>{@code mc.precision == 0} and {@code n < 0} 2450 * <li>{@code mc.precision > 0} and {@code n} has more than 2451 * {@code mc.precision} decimal digits 2452 * </ul> 2453 * 2454 * <li> if {@code n} is zero, {@link #ONE} is returned even if 2455 * {@code this} is zero, otherwise 2456 * <ul> 2457 * <li> if {@code n} is positive, the result is calculated via 2458 * the repeated squaring technique into a single accumulator. 2459 * The individual multiplications with the accumulator use the 2460 * same math context settings as in {@code mc} except for a 2461 * precision increased to {@code mc.precision + elength + 1} 2462 * where {@code elength} is the number of decimal digits in 2463 * {@code n}. 2464 * 2465 * <li> if {@code n} is negative, the result is calculated as if 2466 * {@code n} were positive; this value is then divided into one 2467 * using the working precision specified above. 2468 * 2469 * <li> The final value from either the positive or negative case 2470 * is then rounded to the destination precision. 2471 * </ul> 2472 * </ul> 2473 * 2474 * @param n power to raise this {@code BigDecimal} to. 2475 * @param mc the context to use. 2476 * @return <code>this<sup>n</sup></code> using the ANSI standard X3.274-1996 2477 * algorithm 2478 * @throws ArithmeticException if the result is inexact but the 2479 * rounding mode is {@code UNNECESSARY}, or {@code n} is out 2480 * of range. 2481 * @since 1.5 2482 */ 2483 public BigDecimal pow(int n, MathContext mc) { 2484 if (mc.precision == 0) 2485 return pow(n); 2486 if (n < -999999999 || n > 999999999) 2487 throw new ArithmeticException("Invalid operation"); 2488 if (n == 0) 2489 return ONE; // x**0 == 1 in X3.274 2490 BigDecimal lhs = this; 2491 MathContext workmc = mc; // working settings 2492 int mag = Math.abs(n); // magnitude of n 2493 if (mc.precision > 0) { 2494 int elength = longDigitLength(mag); // length of n in digits 2495 if (elength > mc.precision) // X3.274 rule 2496 throw new ArithmeticException("Invalid operation"); 2497 workmc = new MathContext(mc.precision + elength + 1, 2498 mc.roundingMode); 2499 } 2500 // ready to carry out power calculation... 2501 BigDecimal acc = ONE; // accumulator 2502 boolean seenbit = false; // set once we've seen a 1-bit 2503 for (int i=1;;i++) { // for each bit [top bit ignored] 2504 mag += mag; // shift left 1 bit 2505 if (mag < 0) { // top bit is set 2506 seenbit = true; // OK, we're off 2507 acc = acc.multiply(lhs, workmc); // acc=acc*x 2508 } 2509 if (i == 31) 2510 break; // that was the last bit 2511 if (seenbit) 2512 acc=acc.multiply(acc, workmc); // acc=acc*acc [square] 2513 // else (!seenbit) no point in squaring ONE 2514 } 2515 // if negative n, calculate the reciprocal using working precision 2516 if (n < 0) // [hence mc.precision>0] 2517 acc=ONE.divide(acc, workmc); 2518 // round to final precision and strip zeros 2519 return doRound(acc, mc); 2520 } 2521 2522 /** 2523 * Returns a {@code BigDecimal} whose value is the absolute value 2524 * of this {@code BigDecimal}, and whose scale is 2525 * {@code this.scale()}. 2526 * 2527 * @return {@code abs(this)} 2528 */ 2529 public BigDecimal abs() { 2530 return (signum() < 0 ? negate() : this); 2531 } 2532 2533 /** 2534 * Returns a {@code BigDecimal} whose value is the absolute value 2535 * of this {@code BigDecimal}, with rounding according to the 2536 * context settings. 2537 * 2538 * @param mc the context to use. 2539 * @return {@code abs(this)}, rounded as necessary. 2540 * @throws ArithmeticException if the result is inexact but the 2541 * rounding mode is {@code UNNECESSARY}. 2542 * @since 1.5 2543 */ 2544 public BigDecimal abs(MathContext mc) { 2545 return (signum() < 0 ? negate(mc) : plus(mc)); 2546 } 2547 2548 /** 2549 * Returns a {@code BigDecimal} whose value is {@code (-this)}, 2550 * and whose scale is {@code this.scale()}. 2551 * 2552 * @return {@code -this}. 2553 */ 2554 public BigDecimal negate() { 2555 if (intCompact == INFLATED) { 2556 return new BigDecimal(intVal.negate(), INFLATED, scale, precision); 2557 } else { 2558 return valueOf(-intCompact, scale, precision); 2559 } 2560 } 2561 2562 /** 2563 * Returns a {@code BigDecimal} whose value is {@code (-this)}, 2564 * with rounding according to the context settings. 2565 * 2566 * @param mc the context to use. 2567 * @return {@code -this}, rounded as necessary. 2568 * @throws ArithmeticException if the result is inexact but the 2569 * rounding mode is {@code UNNECESSARY}. 2570 * @since 1.5 2571 */ 2572 public BigDecimal negate(MathContext mc) { 2573 return negate().plus(mc); 2574 } 2575 2576 /** 2577 * Returns a {@code BigDecimal} whose value is {@code (+this)}, and whose 2578 * scale is {@code this.scale()}. 2579 * 2580 * <p>This method, which simply returns this {@code BigDecimal} 2581 * is included for symmetry with the unary minus method {@link 2582 * #negate()}. 2583 * 2584 * @return {@code this}. 2585 * @see #negate() 2586 * @since 1.5 2587 */ 2588 public BigDecimal plus() { 2589 return this; 2590 } 2591 2592 /** 2593 * Returns a {@code BigDecimal} whose value is {@code (+this)}, 2594 * with rounding according to the context settings. 2595 * 2596 * <p>The effect of this method is identical to that of the {@link 2597 * #round(MathContext)} method. 2598 * 2599 * @param mc the context to use. 2600 * @return {@code this}, rounded as necessary. A zero result will 2601 * have a scale of 0. 2602 * @throws ArithmeticException if the result is inexact but the 2603 * rounding mode is {@code UNNECESSARY}. 2604 * @see #round(MathContext) 2605 * @since 1.5 2606 */ 2607 public BigDecimal plus(MathContext mc) { 2608 if (mc.precision == 0) // no rounding please 2609 return this; 2610 return doRound(this, mc); 2611 } 2612 2613 /** 2614 * Returns the signum function of this {@code BigDecimal}. 2615 * 2616 * @return -1, 0, or 1 as the value of this {@code BigDecimal} 2617 * is negative, zero, or positive. 2618 */ 2619 public int signum() { 2620 return (intCompact != INFLATED)? 2621 Long.signum(intCompact): 2622 intVal.signum(); 2623 } 2624 2625 /** 2626 * Returns the <i>scale</i> of this {@code BigDecimal}. If zero 2627 * or positive, the scale is the number of digits to the right of 2628 * the decimal point. If negative, the unscaled value of the 2629 * number is multiplied by ten to the power of the negation of the 2630 * scale. For example, a scale of {@code -3} means the unscaled 2631 * value is multiplied by 1000. 2632 * 2633 * @return the scale of this {@code BigDecimal}. 2634 */ 2635 public int scale() { 2636 return scale; 2637 } 2638 2639 /** 2640 * Returns the <i>precision</i> of this {@code BigDecimal}. (The 2641 * precision is the number of digits in the unscaled value.) 2642 * 2643 * <p>The precision of a zero value is 1. 2644 * 2645 * @return the precision of this {@code BigDecimal}. 2646 * @since 1.5 2647 */ 2648 public int precision() { 2649 int result = precision; 2650 if (result == 0) { 2651 long s = intCompact; 2652 if (s != INFLATED) 2653 result = longDigitLength(s); 2654 else 2655 result = bigDigitLength(intVal); 2656 precision = result; 2657 } 2658 return result; 2659 } 2660 2661 2662 /** 2663 * Returns a {@code BigInteger} whose value is the <i>unscaled 2664 * value</i> of this {@code BigDecimal}. (Computes <code>(this * 2665 * 10<sup>this.scale()</sup>)</code>.) 2666 * 2667 * @return the unscaled value of this {@code BigDecimal}. 2668 * @since 1.2 2669 */ 2670 public BigInteger unscaledValue() { 2671 return this.inflated(); 2672 } 2673 2674 // Rounding Modes 2675 2676 /** 2677 * Rounding mode to round away from zero. Always increments the 2678 * digit prior to a nonzero discarded fraction. Note that this rounding 2679 * mode never decreases the magnitude of the calculated value. 2680 * 2681 * @deprecated Use {@link RoundingMode#UP} instead. 2682 */ 2683 @Deprecated(since="9") 2684 public static final int ROUND_UP = 0; 2685 2686 /** 2687 * Rounding mode to round towards zero. Never increments the digit 2688 * prior to a discarded fraction (i.e., truncates). Note that this 2689 * rounding mode never increases the magnitude of the calculated value. 2690 * 2691 * @deprecated Use {@link RoundingMode#DOWN} instead. 2692 */ 2693 @Deprecated(since="9") 2694 public static final int ROUND_DOWN = 1; 2695 2696 /** 2697 * Rounding mode to round towards positive infinity. If the 2698 * {@code BigDecimal} is positive, behaves as for 2699 * {@code ROUND_UP}; if negative, behaves as for 2700 * {@code ROUND_DOWN}. Note that this rounding mode never 2701 * decreases the calculated value. 2702 * 2703 * @deprecated Use {@link RoundingMode#CEILING} instead. 2704 */ 2705 @Deprecated(since="9") 2706 public static final int ROUND_CEILING = 2; 2707 2708 /** 2709 * Rounding mode to round towards negative infinity. If the 2710 * {@code BigDecimal} is positive, behave as for 2711 * {@code ROUND_DOWN}; if negative, behave as for 2712 * {@code ROUND_UP}. Note that this rounding mode never 2713 * increases the calculated value. 2714 * 2715 * @deprecated Use {@link RoundingMode#FLOOR} instead. 2716 */ 2717 @Deprecated(since="9") 2718 public static final int ROUND_FLOOR = 3; 2719 2720 /** 2721 * Rounding mode to round towards {@literal "nearest neighbor"} 2722 * unless both neighbors are equidistant, in which case round up. 2723 * Behaves as for {@code ROUND_UP} if the discarded fraction is 2724 * ≥ 0.5; otherwise, behaves as for {@code ROUND_DOWN}. Note 2725 * that this is the rounding mode that most of us were taught in 2726 * grade school. 2727 * 2728 * @deprecated Use {@link RoundingMode#HALF_UP} instead. 2729 */ 2730 @Deprecated(since="9") 2731 public static final int ROUND_HALF_UP = 4; 2732 2733 /** 2734 * Rounding mode to round towards {@literal "nearest neighbor"} 2735 * unless both neighbors are equidistant, in which case round 2736 * down. Behaves as for {@code ROUND_UP} if the discarded 2737 * fraction is {@literal >} 0.5; otherwise, behaves as for 2738 * {@code ROUND_DOWN}. 2739 * 2740 * @deprecated Use {@link RoundingMode#HALF_DOWN} instead. 2741 */ 2742 @Deprecated(since="9") 2743 public static final int ROUND_HALF_DOWN = 5; 2744 2745 /** 2746 * Rounding mode to round towards the {@literal "nearest neighbor"} 2747 * unless both neighbors are equidistant, in which case, round 2748 * towards the even neighbor. Behaves as for 2749 * {@code ROUND_HALF_UP} if the digit to the left of the 2750 * discarded fraction is odd; behaves as for 2751 * {@code ROUND_HALF_DOWN} if it's even. Note that this is the 2752 * rounding mode that minimizes cumulative error when applied 2753 * repeatedly over a sequence of calculations. 2754 * 2755 * @deprecated Use {@link RoundingMode#HALF_EVEN} instead. 2756 */ 2757 @Deprecated(since="9") 2758 public static final int ROUND_HALF_EVEN = 6; 2759 2760 /** 2761 * Rounding mode to assert that the requested operation has an exact 2762 * result, hence no rounding is necessary. If this rounding mode is 2763 * specified on an operation that yields an inexact result, an 2764 * {@code ArithmeticException} is thrown. 2765 * 2766 * @deprecated Use {@link RoundingMode#UNNECESSARY} instead. 2767 */ 2768 @Deprecated(since="9") 2769 public static final int ROUND_UNNECESSARY = 7; 2770 2771 2772 // Scaling/Rounding Operations 2773 2774 /** 2775 * Returns a {@code BigDecimal} rounded according to the 2776 * {@code MathContext} settings. If the precision setting is 0 then 2777 * no rounding takes place. 2778 * 2779 * <p>The effect of this method is identical to that of the 2780 * {@link #plus(MathContext)} method. 2781 * 2782 * @param mc the context to use. 2783 * @return a {@code BigDecimal} rounded according to the 2784 * {@code MathContext} settings. 2785 * @throws ArithmeticException if the rounding mode is 2786 * {@code UNNECESSARY} and the 2787 * {@code BigDecimal} operation would require rounding. 2788 * @see #plus(MathContext) 2789 * @since 1.5 2790 */ 2791 public BigDecimal round(MathContext mc) { 2792 return plus(mc); 2793 } 2794 2795 /** 2796 * Returns a {@code BigDecimal} whose scale is the specified 2797 * value, and whose unscaled value is determined by multiplying or 2798 * dividing this {@code BigDecimal}'s unscaled value by the 2799 * appropriate power of ten to maintain its overall value. If the 2800 * scale is reduced by the operation, the unscaled value must be 2801 * divided (rather than multiplied), and the value may be changed; 2802 * in this case, the specified rounding mode is applied to the 2803 * division. 2804 * 2805 * @apiNote Since BigDecimal objects are immutable, calls of 2806 * this method do <em>not</em> result in the original object being 2807 * modified, contrary to the usual convention of having methods 2808 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>. 2809 * Instead, {@code setScale} returns an object with the proper 2810 * scale; the returned object may or may not be newly allocated. 2811 * 2812 * @param newScale scale of the {@code BigDecimal} value to be returned. 2813 * @param roundingMode The rounding mode to apply. 2814 * @return a {@code BigDecimal} whose scale is the specified value, 2815 * and whose unscaled value is determined by multiplying or 2816 * dividing this {@code BigDecimal}'s unscaled value by the 2817 * appropriate power of ten to maintain its overall value. 2818 * @throws ArithmeticException if {@code roundingMode==UNNECESSARY} 2819 * and the specified scaling operation would require 2820 * rounding. 2821 * @see RoundingMode 2822 * @since 1.5 2823 */ 2824 public BigDecimal setScale(int newScale, RoundingMode roundingMode) { 2825 return setScale(newScale, roundingMode.oldMode); 2826 } 2827 2828 /** 2829 * Returns a {@code BigDecimal} whose scale is the specified 2830 * value, and whose unscaled value is determined by multiplying or 2831 * dividing this {@code BigDecimal}'s unscaled value by the 2832 * appropriate power of ten to maintain its overall value. If the 2833 * scale is reduced by the operation, the unscaled value must be 2834 * divided (rather than multiplied), and the value may be changed; 2835 * in this case, the specified rounding mode is applied to the 2836 * division. 2837 * 2838 * @apiNote Since BigDecimal objects are immutable, calls of 2839 * this method do <em>not</em> result in the original object being 2840 * modified, contrary to the usual convention of having methods 2841 * named <code>set<i>X</i></code> mutate field <i>{@code X}</i>. 2842 * Instead, {@code setScale} returns an object with the proper 2843 * scale; the returned object may or may not be newly allocated. 2844 * 2845 * @deprecated The method {@link #setScale(int, RoundingMode)} should 2846 * be used in preference to this legacy method. 2847 * 2848 * @param newScale scale of the {@code BigDecimal} value to be returned. 2849 * @param roundingMode The rounding mode to apply. 2850 * @return a {@code BigDecimal} whose scale is the specified value, 2851 * and whose unscaled value is determined by multiplying or 2852 * dividing this {@code BigDecimal}'s unscaled value by the 2853 * appropriate power of ten to maintain its overall value. 2854 * @throws ArithmeticException if {@code roundingMode==ROUND_UNNECESSARY} 2855 * and the specified scaling operation would require 2856 * rounding. 2857 * @throws IllegalArgumentException if {@code roundingMode} does not 2858 * represent a valid rounding mode. 2859 * @see #ROUND_UP 2860 * @see #ROUND_DOWN 2861 * @see #ROUND_CEILING 2862 * @see #ROUND_FLOOR 2863 * @see #ROUND_HALF_UP 2864 * @see #ROUND_HALF_DOWN 2865 * @see #ROUND_HALF_EVEN 2866 * @see #ROUND_UNNECESSARY 2867 */ 2868 @Deprecated(since="9") 2869 public BigDecimal setScale(int newScale, int roundingMode) { 2870 if (roundingMode < ROUND_UP || roundingMode > ROUND_UNNECESSARY) 2871 throw new IllegalArgumentException("Invalid rounding mode"); 2872 2873 int oldScale = this.scale; 2874 if (newScale == oldScale) // easy case 2875 return this; 2876 if (this.signum() == 0) // zero can have any scale 2877 return zeroValueOf(newScale); 2878 if(this.intCompact!=INFLATED) { 2879 long rs = this.intCompact; 2880 if (newScale > oldScale) { 2881 int raise = checkScale((long) newScale - oldScale); 2882 if ((rs = longMultiplyPowerTen(rs, raise)) != INFLATED) { 2883 return valueOf(rs,newScale); 2884 } 2885 BigInteger rb = bigMultiplyPowerTen(raise); 2886 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0); 2887 } else { 2888 // newScale < oldScale -- drop some digits 2889 // Can't predict the precision due to the effect of rounding. 2890 int drop = checkScale((long) oldScale - newScale); 2891 if (drop < LONG_TEN_POWERS_TABLE.length) { 2892 return divideAndRound(rs, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, newScale); 2893 } else { 2894 return divideAndRound(this.inflated(), bigTenToThe(drop), newScale, roundingMode, newScale); 2895 } 2896 } 2897 } else { 2898 if (newScale > oldScale) { 2899 int raise = checkScale((long) newScale - oldScale); 2900 BigInteger rb = bigMultiplyPowerTen(this.intVal,raise); 2901 return new BigDecimal(rb, INFLATED, newScale, (precision > 0) ? precision + raise : 0); 2902 } else { 2903 // newScale < oldScale -- drop some digits 2904 // Can't predict the precision due to the effect of rounding. 2905 int drop = checkScale((long) oldScale - newScale); 2906 if (drop < LONG_TEN_POWERS_TABLE.length) 2907 return divideAndRound(this.intVal, LONG_TEN_POWERS_TABLE[drop], newScale, roundingMode, 2908 newScale); 2909 else 2910 return divideAndRound(this.intVal, bigTenToThe(drop), newScale, roundingMode, newScale); 2911 } 2912 } 2913 } 2914 2915 /** 2916 * Returns a {@code BigDecimal} whose scale is the specified 2917 * value, and whose value is numerically equal to this 2918 * {@code BigDecimal}'s. Throws an {@code ArithmeticException} 2919 * if this is not possible. 2920 * 2921 * <p>This call is typically used to increase the scale, in which 2922 * case it is guaranteed that there exists a {@code BigDecimal} 2923 * of the specified scale and the correct value. The call can 2924 * also be used to reduce the scale if the caller knows that the 2925 * {@code BigDecimal} has sufficiently many zeros at the end of 2926 * its fractional part (i.e., factors of ten in its integer value) 2927 * to allow for the rescaling without changing its value. 2928 * 2929 * <p>This method returns the same result as the two-argument 2930 * versions of {@code setScale}, but saves the caller the trouble 2931 * of specifying a rounding mode in cases where it is irrelevant. 2932 * 2933 * @apiNote Since {@code BigDecimal} objects are immutable, 2934 * calls of this method do <em>not</em> result in the original 2935 * object being modified, contrary to the usual convention of 2936 * having methods named <code>set<i>X</i></code> mutate field 2937 * <i>{@code X}</i>. Instead, {@code setScale} returns an 2938 * object with the proper scale; the returned object may or may 2939 * not be newly allocated. 2940 * 2941 * @param newScale scale of the {@code BigDecimal} value to be returned. 2942 * @return a {@code BigDecimal} whose scale is the specified value, and 2943 * whose unscaled value is determined by multiplying or dividing 2944 * this {@code BigDecimal}'s unscaled value by the appropriate 2945 * power of ten to maintain its overall value. 2946 * @throws ArithmeticException if the specified scaling operation would 2947 * require rounding. 2948 * @see #setScale(int, int) 2949 * @see #setScale(int, RoundingMode) 2950 */ 2951 public BigDecimal setScale(int newScale) { 2952 return setScale(newScale, ROUND_UNNECESSARY); 2953 } 2954 2955 // Decimal Point Motion Operations 2956 2957 /** 2958 * Returns a {@code BigDecimal} which is equivalent to this one 2959 * with the decimal point moved {@code n} places to the left. If 2960 * {@code n} is non-negative, the call merely adds {@code n} to 2961 * the scale. If {@code n} is negative, the call is equivalent 2962 * to {@code movePointRight(-n)}. The {@code BigDecimal} 2963 * returned by this call has value <code>(this × 2964 * 10<sup>-n</sup>)</code> and scale {@code max(this.scale()+n, 2965 * 0)}. 2966 * 2967 * @param n number of places to move the decimal point to the left. 2968 * @return a {@code BigDecimal} which is equivalent to this one with the 2969 * decimal point moved {@code n} places to the left. 2970 * @throws ArithmeticException if scale overflows. 2971 */ 2972 public BigDecimal movePointLeft(int n) { 2973 if (n == 0) return this; 2974 2975 // Cannot use movePointRight(-n) in case of n==Integer.MIN_VALUE 2976 int newScale = checkScale((long)scale + n); 2977 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0); 2978 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num; 2979 } 2980 2981 /** 2982 * Returns a {@code BigDecimal} which is equivalent to this one 2983 * with the decimal point moved {@code n} places to the right. 2984 * If {@code n} is non-negative, the call merely subtracts 2985 * {@code n} from the scale. If {@code n} is negative, the call 2986 * is equivalent to {@code movePointLeft(-n)}. The 2987 * {@code BigDecimal} returned by this call has value <code>(this 2988 * × 10<sup>n</sup>)</code> and scale {@code max(this.scale()-n, 2989 * 0)}. 2990 * 2991 * @param n number of places to move the decimal point to the right. 2992 * @return a {@code BigDecimal} which is equivalent to this one 2993 * with the decimal point moved {@code n} places to the right. 2994 * @throws ArithmeticException if scale overflows. 2995 */ 2996 public BigDecimal movePointRight(int n) { 2997 if (n == 0) return this; 2998 2999 // Cannot use movePointLeft(-n) in case of n==Integer.MIN_VALUE 3000 int newScale = checkScale((long)scale - n); 3001 BigDecimal num = new BigDecimal(intVal, intCompact, newScale, 0); 3002 return num.scale < 0 ? num.setScale(0, ROUND_UNNECESSARY) : num; 3003 } 3004 3005 /** 3006 * Returns a BigDecimal whose numerical value is equal to 3007 * ({@code this} * 10<sup>n</sup>). The scale of 3008 * the result is {@code (this.scale() - n)}. 3009 * 3010 * @param n the exponent power of ten to scale by 3011 * @return a BigDecimal whose numerical value is equal to 3012 * ({@code this} * 10<sup>n</sup>) 3013 * @throws ArithmeticException if the scale would be 3014 * outside the range of a 32-bit integer. 3015 * 3016 * @since 1.5 3017 */ 3018 public BigDecimal scaleByPowerOfTen(int n) { 3019 return new BigDecimal(intVal, intCompact, 3020 checkScale((long)scale - n), precision); 3021 } 3022 3023 /** 3024 * Returns a {@code BigDecimal} which is numerically equal to 3025 * this one but with any trailing zeros removed from the 3026 * representation. For example, stripping the trailing zeros from 3027 * the {@code BigDecimal} value {@code 600.0}, which has 3028 * [{@code BigInteger}, {@code scale}] components equal to 3029 * [6000, 1], yields {@code 6E2} with [{@code BigInteger}, 3030 * {@code scale}] components equal to [6, -2]. If 3031 * this BigDecimal is numerically equal to zero, then 3032 * {@code BigDecimal.ZERO} is returned. 3033 * 3034 * @return a numerically equal {@code BigDecimal} with any 3035 * trailing zeros removed. 3036 * @since 1.5 3037 */ 3038 public BigDecimal stripTrailingZeros() { 3039 if (intCompact == 0 || (intVal != null && intVal.signum() == 0)) { 3040 return BigDecimal.ZERO; 3041 } else if (intCompact != INFLATED) { 3042 return createAndStripZerosToMatchScale(intCompact, scale, Long.MIN_VALUE); 3043 } else { 3044 return createAndStripZerosToMatchScale(intVal, scale, Long.MIN_VALUE); 3045 } 3046 } 3047 3048 // Comparison Operations 3049 3050 /** 3051 * Compares this {@code BigDecimal} with the specified 3052 * {@code BigDecimal}. Two {@code BigDecimal} objects that are 3053 * equal in value but have a different scale (like 2.0 and 2.00) 3054 * are considered equal by this method. This method is provided 3055 * in preference to individual methods for each of the six boolean 3056 * comparison operators ({@literal <}, ==, 3057 * {@literal >}, {@literal >=}, !=, {@literal <=}). The 3058 * suggested idiom for performing these comparisons is: 3059 * {@code (x.compareTo(y)} <<i>op</i>> {@code 0)}, where 3060 * <<i>op</i>> is one of the six comparison operators. 3061 * 3062 * @param val {@code BigDecimal} to which this {@code BigDecimal} is 3063 * to be compared. 3064 * @return -1, 0, or 1 as this {@code BigDecimal} is numerically 3065 * less than, equal to, or greater than {@code val}. 3066 */ 3067 @Override 3068 public int compareTo(BigDecimal val) { 3069 // Quick path for equal scale and non-inflated case. 3070 if (scale == val.scale) { 3071 long xs = intCompact; 3072 long ys = val.intCompact; 3073 if (xs != INFLATED && ys != INFLATED) 3074 return xs != ys ? ((xs > ys) ? 1 : -1) : 0; 3075 } 3076 int xsign = this.signum(); 3077 int ysign = val.signum(); 3078 if (xsign != ysign) 3079 return (xsign > ysign) ? 1 : -1; 3080 if (xsign == 0) 3081 return 0; 3082 int cmp = compareMagnitude(val); 3083 return (xsign > 0) ? cmp : -cmp; 3084 } 3085 3086 /** 3087 * Version of compareTo that ignores sign. 3088 */ 3089 private int compareMagnitude(BigDecimal val) { 3090 // Match scales, avoid unnecessary inflation 3091 long ys = val.intCompact; 3092 long xs = this.intCompact; 3093 if (xs == 0) 3094 return (ys == 0) ? 0 : -1; 3095 if (ys == 0) 3096 return 1; 3097 3098 long sdiff = (long)this.scale - val.scale; 3099 if (sdiff != 0) { 3100 // Avoid matching scales if the (adjusted) exponents differ 3101 long xae = (long)this.precision() - this.scale; // [-1] 3102 long yae = (long)val.precision() - val.scale; // [-1] 3103 if (xae < yae) 3104 return -1; 3105 if (xae > yae) 3106 return 1; 3107 if (sdiff < 0) { 3108 // The cases sdiff <= Integer.MIN_VALUE intentionally fall through. 3109 if ( sdiff > Integer.MIN_VALUE && 3110 (xs == INFLATED || 3111 (xs = longMultiplyPowerTen(xs, (int)-sdiff)) == INFLATED) && 3112 ys == INFLATED) { 3113 BigInteger rb = bigMultiplyPowerTen((int)-sdiff); 3114 return rb.compareMagnitude(val.intVal); 3115 } 3116 } else { // sdiff > 0 3117 // The cases sdiff > Integer.MAX_VALUE intentionally fall through. 3118 if ( sdiff <= Integer.MAX_VALUE && 3119 (ys == INFLATED || 3120 (ys = longMultiplyPowerTen(ys, (int)sdiff)) == INFLATED) && 3121 xs == INFLATED) { 3122 BigInteger rb = val.bigMultiplyPowerTen((int)sdiff); 3123 return this.intVal.compareMagnitude(rb); 3124 } 3125 } 3126 } 3127 if (xs != INFLATED) 3128 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1; 3129 else if (ys != INFLATED) 3130 return 1; 3131 else 3132 return this.intVal.compareMagnitude(val.intVal); 3133 } 3134 3135 /** 3136 * Compares this {@code BigDecimal} with the specified 3137 * {@code Object} for equality. Unlike {@link 3138 * #compareTo(BigDecimal) compareTo}, this method considers two 3139 * {@code BigDecimal} objects equal only if they are equal in 3140 * value and scale (thus 2.0 is not equal to 2.00 when compared by 3141 * this method). 3142 * 3143 * @param x {@code Object} to which this {@code BigDecimal} is 3144 * to be compared. 3145 * @return {@code true} if and only if the specified {@code Object} is a 3146 * {@code BigDecimal} whose value and scale are equal to this 3147 * {@code BigDecimal}'s. 3148 * @see #compareTo(java.math.BigDecimal) 3149 * @see #hashCode 3150 */ 3151 @Override 3152 public boolean equals(Object x) { 3153 if (!(x instanceof BigDecimal)) 3154 return false; 3155 BigDecimal xDec = (BigDecimal) x; 3156 if (x == this) 3157 return true; 3158 if (scale != xDec.scale) 3159 return false; 3160 long s = this.intCompact; 3161 long xs = xDec.intCompact; 3162 if (s != INFLATED) { 3163 if (xs == INFLATED) 3164 xs = compactValFor(xDec.intVal); 3165 return xs == s; 3166 } else if (xs != INFLATED) 3167 return xs == compactValFor(this.intVal); 3168 3169 return this.inflated().equals(xDec.inflated()); 3170 } 3171 3172 /** 3173 * Returns the minimum of this {@code BigDecimal} and 3174 * {@code val}. 3175 * 3176 * @param val value with which the minimum is to be computed. 3177 * @return the {@code BigDecimal} whose value is the lesser of this 3178 * {@code BigDecimal} and {@code val}. If they are equal, 3179 * as defined by the {@link #compareTo(BigDecimal) compareTo} 3180 * method, {@code this} is returned. 3181 * @see #compareTo(java.math.BigDecimal) 3182 */ 3183 public BigDecimal min(BigDecimal val) { 3184 return (compareTo(val) <= 0 ? this : val); 3185 } 3186 3187 /** 3188 * Returns the maximum of this {@code BigDecimal} and {@code val}. 3189 * 3190 * @param val value with which the maximum is to be computed. 3191 * @return the {@code BigDecimal} whose value is the greater of this 3192 * {@code BigDecimal} and {@code val}. If they are equal, 3193 * as defined by the {@link #compareTo(BigDecimal) compareTo} 3194 * method, {@code this} is returned. 3195 * @see #compareTo(java.math.BigDecimal) 3196 */ 3197 public BigDecimal max(BigDecimal val) { 3198 return (compareTo(val) >= 0 ? this : val); 3199 } 3200 3201 // Hash Function 3202 3203 /** 3204 * Returns the hash code for this {@code BigDecimal}. Note that 3205 * two {@code BigDecimal} objects that are numerically equal but 3206 * differ in scale (like 2.0 and 2.00) will generally <em>not</em> 3207 * have the same hash code. 3208 * 3209 * @return hash code for this {@code BigDecimal}. 3210 * @see #equals(Object) 3211 */ 3212 @Override 3213 public int hashCode() { 3214 if (intCompact != INFLATED) { 3215 long val2 = (intCompact < 0)? -intCompact : intCompact; 3216 int temp = (int)( ((int)(val2 >>> 32)) * 31 + 3217 (val2 & LONG_MASK)); 3218 return 31*((intCompact < 0) ?-temp:temp) + scale; 3219 } else 3220 return 31*intVal.hashCode() + scale; 3221 } 3222 3223 // Format Converters 3224 3225 /** 3226 * Returns the string representation of this {@code BigDecimal}, 3227 * using scientific notation if an exponent is needed. 3228 * 3229 * <p>A standard canonical string form of the {@code BigDecimal} 3230 * is created as though by the following steps: first, the 3231 * absolute value of the unscaled value of the {@code BigDecimal} 3232 * is converted to a string in base ten using the characters 3233 * {@code '0'} through {@code '9'} with no leading zeros (except 3234 * if its value is zero, in which case a single {@code '0'} 3235 * character is used). 3236 * 3237 * <p>Next, an <i>adjusted exponent</i> is calculated; this is the 3238 * negated scale, plus the number of characters in the converted 3239 * unscaled value, less one. That is, 3240 * {@code -scale+(ulength-1)}, where {@code ulength} is the 3241 * length of the absolute value of the unscaled value in decimal 3242 * digits (its <i>precision</i>). 3243 * 3244 * <p>If the scale is greater than or equal to zero and the 3245 * adjusted exponent is greater than or equal to {@code -6}, the 3246 * number will be converted to a character form without using 3247 * exponential notation. In this case, if the scale is zero then 3248 * no decimal point is added and if the scale is positive a 3249 * decimal point will be inserted with the scale specifying the 3250 * number of characters to the right of the decimal point. 3251 * {@code '0'} characters are added to the left of the converted 3252 * unscaled value as necessary. If no character precedes the 3253 * decimal point after this insertion then a conventional 3254 * {@code '0'} character is prefixed. 3255 * 3256 * <p>Otherwise (that is, if the scale is negative, or the 3257 * adjusted exponent is less than {@code -6}), the number will be 3258 * converted to a character form using exponential notation. In 3259 * this case, if the converted {@code BigInteger} has more than 3260 * one digit a decimal point is inserted after the first digit. 3261 * An exponent in character form is then suffixed to the converted 3262 * unscaled value (perhaps with inserted decimal point); this 3263 * comprises the letter {@code 'E'} followed immediately by the 3264 * adjusted exponent converted to a character form. The latter is 3265 * in base ten, using the characters {@code '0'} through 3266 * {@code '9'} with no leading zeros, and is always prefixed by a 3267 * sign character {@code '-'} (<code>'\u002D'</code>) if the 3268 * adjusted exponent is negative, {@code '+'} 3269 * (<code>'\u002B'</code>) otherwise). 3270 * 3271 * <p>Finally, the entire string is prefixed by a minus sign 3272 * character {@code '-'} (<code>'\u002D'</code>) if the unscaled 3273 * value is less than zero. No sign character is prefixed if the 3274 * unscaled value is zero or positive. 3275 * 3276 * <p><b>Examples:</b> 3277 * <p>For each representation [<i>unscaled value</i>, <i>scale</i>] 3278 * on the left, the resulting string is shown on the right. 3279 * <pre> 3280 * [123,0] "123" 3281 * [-123,0] "-123" 3282 * [123,-1] "1.23E+3" 3283 * [123,-3] "1.23E+5" 3284 * [123,1] "12.3" 3285 * [123,5] "0.00123" 3286 * [123,10] "1.23E-8" 3287 * [-123,12] "-1.23E-10" 3288 * </pre> 3289 * 3290 * <b>Notes:</b> 3291 * <ol> 3292 * 3293 * <li>There is a one-to-one mapping between the distinguishable 3294 * {@code BigDecimal} values and the result of this conversion. 3295 * That is, every distinguishable {@code BigDecimal} value 3296 * (unscaled value and scale) has a unique string representation 3297 * as a result of using {@code toString}. If that string 3298 * representation is converted back to a {@code BigDecimal} using 3299 * the {@link #BigDecimal(String)} constructor, then the original 3300 * value will be recovered. 3301 * 3302 * <li>The string produced for a given number is always the same; 3303 * it is not affected by locale. This means that it can be used 3304 * as a canonical string representation for exchanging decimal 3305 * data, or as a key for a Hashtable, etc. Locale-sensitive 3306 * number formatting and parsing is handled by the {@link 3307 * java.text.NumberFormat} class and its subclasses. 3308 * 3309 * <li>The {@link #toEngineeringString} method may be used for 3310 * presenting numbers with exponents in engineering notation, and the 3311 * {@link #setScale(int,RoundingMode) setScale} method may be used for 3312 * rounding a {@code BigDecimal} so it has a known number of digits after 3313 * the decimal point. 3314 * 3315 * <li>The digit-to-character mapping provided by 3316 * {@code Character.forDigit} is used. 3317 * 3318 * </ol> 3319 * 3320 * @return string representation of this {@code BigDecimal}. 3321 * @see Character#forDigit 3322 * @see #BigDecimal(java.lang.String) 3323 */ 3324 @Override 3325 public String toString() { 3326 String sc = stringCache; 3327 if (sc == null) { 3328 stringCache = sc = layoutChars(true); 3329 } 3330 return sc; 3331 } 3332 3333 /** 3334 * Returns a string representation of this {@code BigDecimal}, 3335 * using engineering notation if an exponent is needed. 3336 * 3337 * <p>Returns a string that represents the {@code BigDecimal} as 3338 * described in the {@link #toString()} method, except that if 3339 * exponential notation is used, the power of ten is adjusted to 3340 * be a multiple of three (engineering notation) such that the 3341 * integer part of nonzero values will be in the range 1 through 3342 * 999. If exponential notation is used for zero values, a 3343 * decimal point and one or two fractional zero digits are used so 3344 * that the scale of the zero value is preserved. Note that 3345 * unlike the output of {@link #toString()}, the output of this 3346 * method is <em>not</em> guaranteed to recover the same [integer, 3347 * scale] pair of this {@code BigDecimal} if the output string is 3348 * converting back to a {@code BigDecimal} using the {@linkplain 3349 * #BigDecimal(String) string constructor}. The result of this method meets 3350 * the weaker constraint of always producing a numerically equal 3351 * result from applying the string constructor to the method's output. 3352 * 3353 * @return string representation of this {@code BigDecimal}, using 3354 * engineering notation if an exponent is needed. 3355 * @since 1.5 3356 */ 3357 public String toEngineeringString() { 3358 return layoutChars(false); 3359 } 3360 3361 /** 3362 * Returns a string representation of this {@code BigDecimal} 3363 * without an exponent field. For values with a positive scale, 3364 * the number of digits to the right of the decimal point is used 3365 * to indicate scale. For values with a zero or negative scale, 3366 * the resulting string is generated as if the value were 3367 * converted to a numerically equal value with zero scale and as 3368 * if all the trailing zeros of the zero scale value were present 3369 * in the result. 3370 * 3371 * The entire string is prefixed by a minus sign character '-' 3372 * (<code>'\u002D'</code>) if the unscaled value is less than 3373 * zero. No sign character is prefixed if the unscaled value is 3374 * zero or positive. 3375 * 3376 * Note that if the result of this method is passed to the 3377 * {@linkplain #BigDecimal(String) string constructor}, only the 3378 * numerical value of this {@code BigDecimal} will necessarily be 3379 * recovered; the representation of the new {@code BigDecimal} 3380 * may have a different scale. In particular, if this 3381 * {@code BigDecimal} has a negative scale, the string resulting 3382 * from this method will have a scale of zero when processed by 3383 * the string constructor. 3384 * 3385 * (This method behaves analogously to the {@code toString} 3386 * method in 1.4 and earlier releases.) 3387 * 3388 * @return a string representation of this {@code BigDecimal} 3389 * without an exponent field. 3390 * @since 1.5 3391 * @see #toString() 3392 * @see #toEngineeringString() 3393 */ 3394 public String toPlainString() { 3395 if(scale==0) { 3396 if(intCompact!=INFLATED) { 3397 return Long.toString(intCompact); 3398 } else { 3399 return intVal.toString(); 3400 } 3401 } 3402 if(this.scale<0) { // No decimal point 3403 if(signum()==0) { 3404 return "0"; 3405 } 3406 int trailingZeros = checkScaleNonZero((-(long)scale)); 3407 StringBuilder buf; 3408 if(intCompact!=INFLATED) { 3409 buf = new StringBuilder(20+trailingZeros); 3410 buf.append(intCompact); 3411 } else { 3412 String str = intVal.toString(); 3413 buf = new StringBuilder(str.length()+trailingZeros); 3414 buf.append(str); 3415 } 3416 for (int i = 0; i < trailingZeros; i++) { 3417 buf.append('0'); 3418 } 3419 return buf.toString(); 3420 } 3421 String str ; 3422 if(intCompact!=INFLATED) { 3423 str = Long.toString(Math.abs(intCompact)); 3424 } else { 3425 str = intVal.abs().toString(); 3426 } 3427 return getValueString(signum(), str, scale); 3428 } 3429 3430 /* Returns a digit.digit string */ 3431 private String getValueString(int signum, String intString, int scale) { 3432 /* Insert decimal point */ 3433 StringBuilder buf; 3434 int insertionPoint = intString.length() - scale; 3435 if (insertionPoint == 0) { /* Point goes right before intVal */ 3436 return (signum<0 ? "-0." : "0.") + intString; 3437 } else if (insertionPoint > 0) { /* Point goes inside intVal */ 3438 buf = new StringBuilder(intString); 3439 buf.insert(insertionPoint, '.'); 3440 if (signum < 0) 3441 buf.insert(0, '-'); 3442 } else { /* We must insert zeros between point and intVal */ 3443 buf = new StringBuilder(3-insertionPoint + intString.length()); 3444 buf.append(signum<0 ? "-0." : "0."); 3445 for (int i=0; i<-insertionPoint; i++) { 3446 buf.append('0'); 3447 } 3448 buf.append(intString); 3449 } 3450 return buf.toString(); 3451 } 3452 3453 /** 3454 * Converts this {@code BigDecimal} to a {@code BigInteger}. 3455 * This conversion is analogous to the 3456 * <i>narrowing primitive conversion</i> from {@code double} to 3457 * {@code long} as defined in 3458 * <cite>The Java™ Language Specification</cite>: 3459 * any fractional part of this 3460 * {@code BigDecimal} will be discarded. Note that this 3461 * conversion can lose information about the precision of the 3462 * {@code BigDecimal} value. 3463 * <p> 3464 * To have an exception thrown if the conversion is inexact (in 3465 * other words if a nonzero fractional part is discarded), use the 3466 * {@link #toBigIntegerExact()} method. 3467 * 3468 * @return this {@code BigDecimal} converted to a {@code BigInteger}. 3469 * @jls 5.1.3 Narrowing Primitive Conversion 3470 */ 3471 public BigInteger toBigInteger() { 3472 // force to an integer, quietly 3473 return this.setScale(0, ROUND_DOWN).inflated(); 3474 } 3475 3476 /** 3477 * Converts this {@code BigDecimal} to a {@code BigInteger}, 3478 * checking for lost information. An exception is thrown if this 3479 * {@code BigDecimal} has a nonzero fractional part. 3480 * 3481 * @return this {@code BigDecimal} converted to a {@code BigInteger}. 3482 * @throws ArithmeticException if {@code this} has a nonzero 3483 * fractional part. 3484 * @since 1.5 3485 */ 3486 public BigInteger toBigIntegerExact() { 3487 // round to an integer, with Exception if decimal part non-0 3488 return this.setScale(0, ROUND_UNNECESSARY).inflated(); 3489 } 3490 3491 /** 3492 * Converts this {@code BigDecimal} to a {@code long}. 3493 * This conversion is analogous to the 3494 * <i>narrowing primitive conversion</i> from {@code double} to 3495 * {@code short} as defined in 3496 * <cite>The Java™ Language Specification</cite>: 3497 * any fractional part of this 3498 * {@code BigDecimal} will be discarded, and if the resulting 3499 * "{@code BigInteger}" is too big to fit in a 3500 * {@code long}, only the low-order 64 bits are returned. 3501 * Note that this conversion can lose information about the 3502 * overall magnitude and precision of this {@code BigDecimal} value as well 3503 * as return a result with the opposite sign. 3504 * 3505 * @return this {@code BigDecimal} converted to a {@code long}. 3506 * @jls 5.1.3 Narrowing Primitive Conversion 3507 */ 3508 @Override 3509 public long longValue(){ 3510 if (intCompact != INFLATED && scale == 0) { 3511 return intCompact; 3512 } else { 3513 // Fastpath zero and small values 3514 if (this.signum() == 0 || fractionOnly() || 3515 // Fastpath very large-scale values that will result 3516 // in a truncated value of zero. If the scale is -64 3517 // or less, there are at least 64 powers of 10 in the 3518 // value of the numerical result. Since 10 = 2*5, in 3519 // that case there would also be 64 powers of 2 in the 3520 // result, meaning all 64 bits of a long will be zero. 3521 scale <= -64) { 3522 return 0; 3523 } else { 3524 return toBigInteger().longValue(); 3525 } 3526 } 3527 } 3528 3529 /** 3530 * Return true if a nonzero BigDecimal has an absolute value less 3531 * than one; i.e. only has fraction digits. 3532 */ 3533 private boolean fractionOnly() { 3534 assert this.signum() != 0; 3535 return (this.precision() - this.scale) <= 0; 3536 } 3537 3538 /** 3539 * Converts this {@code BigDecimal} to a {@code long}, checking 3540 * for lost information. If this {@code BigDecimal} has a 3541 * nonzero fractional part or is out of the possible range for a 3542 * {@code long} result then an {@code ArithmeticException} is 3543 * thrown. 3544 * 3545 * @return this {@code BigDecimal} converted to a {@code long}. 3546 * @throws ArithmeticException if {@code this} has a nonzero 3547 * fractional part, or will not fit in a {@code long}. 3548 * @since 1.5 3549 */ 3550 public long longValueExact() { 3551 if (intCompact != INFLATED && scale == 0) 3552 return intCompact; 3553 3554 // Fastpath zero 3555 if (this.signum() == 0) 3556 return 0; 3557 3558 // Fastpath numbers less than 1.0 (the latter can be very slow 3559 // to round if very small) 3560 if (fractionOnly()) 3561 throw new ArithmeticException("Rounding necessary"); 3562 3563 // If more than 19 digits in integer part it cannot possibly fit 3564 if ((precision() - scale) > 19) // [OK for negative scale too] 3565 throw new java.lang.ArithmeticException("Overflow"); 3566 3567 // round to an integer, with Exception if decimal part non-0 3568 BigDecimal num = this.setScale(0, ROUND_UNNECESSARY); 3569 if (num.precision() >= 19) // need to check carefully 3570 LongOverflow.check(num); 3571 return num.inflated().longValue(); 3572 } 3573 3574 private static class LongOverflow { 3575 /** BigInteger equal to Long.MIN_VALUE. */ 3576 private static final BigInteger LONGMIN = BigInteger.valueOf(Long.MIN_VALUE); 3577 3578 /** BigInteger equal to Long.MAX_VALUE. */ 3579 private static final BigInteger LONGMAX = BigInteger.valueOf(Long.MAX_VALUE); 3580 3581 public static void check(BigDecimal num) { 3582 BigInteger intVal = num.inflated(); 3583 if (intVal.compareTo(LONGMIN) < 0 || 3584 intVal.compareTo(LONGMAX) > 0) 3585 throw new java.lang.ArithmeticException("Overflow"); 3586 } 3587 } 3588 3589 /** 3590 * Converts this {@code BigDecimal} to an {@code int}. 3591 * This conversion is analogous to the 3592 * <i>narrowing primitive conversion</i> from {@code double} to 3593 * {@code short} as defined in 3594 * <cite>The Java™ Language Specification</cite>: 3595 * any fractional part of this 3596 * {@code BigDecimal} will be discarded, and if the resulting 3597 * "{@code BigInteger}" is too big to fit in an 3598 * {@code int}, only the low-order 32 bits are returned. 3599 * Note that this conversion can lose information about the 3600 * overall magnitude and precision of this {@code BigDecimal} 3601 * value as well as return a result with the opposite sign. 3602 * 3603 * @return this {@code BigDecimal} converted to an {@code int}. 3604 * @jls 5.1.3 Narrowing Primitive Conversion 3605 */ 3606 @Override 3607 public int intValue() { 3608 return (intCompact != INFLATED && scale == 0) ? 3609 (int)intCompact : 3610 (int)longValue(); 3611 } 3612 3613 /** 3614 * Converts this {@code BigDecimal} to an {@code int}, checking 3615 * for lost information. If this {@code BigDecimal} has a 3616 * nonzero fractional part or is out of the possible range for an 3617 * {@code int} result then an {@code ArithmeticException} is 3618 * thrown. 3619 * 3620 * @return this {@code BigDecimal} converted to an {@code int}. 3621 * @throws ArithmeticException if {@code this} has a nonzero 3622 * fractional part, or will not fit in an {@code int}. 3623 * @since 1.5 3624 */ 3625 public int intValueExact() { 3626 long num; 3627 num = this.longValueExact(); // will check decimal part 3628 if ((int)num != num) 3629 throw new java.lang.ArithmeticException("Overflow"); 3630 return (int)num; 3631 } 3632 3633 /** 3634 * Converts this {@code BigDecimal} to a {@code short}, checking 3635 * for lost information. If this {@code BigDecimal} has a 3636 * nonzero fractional part or is out of the possible range for a 3637 * {@code short} result then an {@code ArithmeticException} is 3638 * thrown. 3639 * 3640 * @return this {@code BigDecimal} converted to a {@code short}. 3641 * @throws ArithmeticException if {@code this} has a nonzero 3642 * fractional part, or will not fit in a {@code short}. 3643 * @since 1.5 3644 */ 3645 public short shortValueExact() { 3646 long num; 3647 num = this.longValueExact(); // will check decimal part 3648 if ((short)num != num) 3649 throw new java.lang.ArithmeticException("Overflow"); 3650 return (short)num; 3651 } 3652 3653 /** 3654 * Converts this {@code BigDecimal} to a {@code byte}, checking 3655 * for lost information. If this {@code BigDecimal} has a 3656 * nonzero fractional part or is out of the possible range for a 3657 * {@code byte} result then an {@code ArithmeticException} is 3658 * thrown. 3659 * 3660 * @return this {@code BigDecimal} converted to a {@code byte}. 3661 * @throws ArithmeticException if {@code this} has a nonzero 3662 * fractional part, or will not fit in a {@code byte}. 3663 * @since 1.5 3664 */ 3665 public byte byteValueExact() { 3666 long num; 3667 num = this.longValueExact(); // will check decimal part 3668 if ((byte)num != num) 3669 throw new java.lang.ArithmeticException("Overflow"); 3670 return (byte)num; 3671 } 3672 3673 /** 3674 * Converts this {@code BigDecimal} to a {@code float}. 3675 * This conversion is similar to the 3676 * <i>narrowing primitive conversion</i> from {@code double} to 3677 * {@code float} as defined in 3678 * <cite>The Java™ Language Specification</cite>: 3679 * if this {@code BigDecimal} has too great a 3680 * magnitude to represent as a {@code float}, it will be 3681 * converted to {@link Float#NEGATIVE_INFINITY} or {@link 3682 * Float#POSITIVE_INFINITY} as appropriate. Note that even when 3683 * the return value is finite, this conversion can lose 3684 * information about the precision of the {@code BigDecimal} 3685 * value. 3686 * 3687 * @return this {@code BigDecimal} converted to a {@code float}. 3688 * @jls 5.1.3 Narrowing Primitive Conversion 3689 */ 3690 @Override 3691 public float floatValue(){ 3692 if(intCompact != INFLATED) { 3693 if (scale == 0) { 3694 return (float)intCompact; 3695 } else { 3696 /* 3697 * If both intCompact and the scale can be exactly 3698 * represented as float values, perform a single float 3699 * multiply or divide to compute the (properly 3700 * rounded) result. 3701 */ 3702 if (Math.abs(intCompact) < 1L<<22 ) { 3703 // Don't have too guard against 3704 // Math.abs(MIN_VALUE) because of outer check 3705 // against INFLATED. 3706 if (scale > 0 && scale < FLOAT_10_POW.length) { 3707 return (float)intCompact / FLOAT_10_POW[scale]; 3708 } else if (scale < 0 && scale > -FLOAT_10_POW.length) { 3709 return (float)intCompact * FLOAT_10_POW[-scale]; 3710 } 3711 } 3712 } 3713 } 3714 // Somewhat inefficient, but guaranteed to work. 3715 return Float.parseFloat(this.toString()); 3716 } 3717 3718 /** 3719 * Converts this {@code BigDecimal} to a {@code double}. 3720 * This conversion is similar to the 3721 * <i>narrowing primitive conversion</i> from {@code double} to 3722 * {@code float} as defined in 3723 * <cite>The Java™ Language Specification</cite>: 3724 * if this {@code BigDecimal} has too great a 3725 * magnitude represent as a {@code double}, it will be 3726 * converted to {@link Double#NEGATIVE_INFINITY} or {@link 3727 * Double#POSITIVE_INFINITY} as appropriate. Note that even when 3728 * the return value is finite, this conversion can lose 3729 * information about the precision of the {@code BigDecimal} 3730 * value. 3731 * 3732 * @return this {@code BigDecimal} converted to a {@code double}. 3733 * @jls 5.1.3 Narrowing Primitive Conversion 3734 */ 3735 @Override 3736 public double doubleValue(){ 3737 if(intCompact != INFLATED) { 3738 if (scale == 0) { 3739 return (double)intCompact; 3740 } else { 3741 /* 3742 * If both intCompact and the scale can be exactly 3743 * represented as double values, perform a single 3744 * double multiply or divide to compute the (properly 3745 * rounded) result. 3746 */ 3747 if (Math.abs(intCompact) < 1L<<52 ) { 3748 // Don't have too guard against 3749 // Math.abs(MIN_VALUE) because of outer check 3750 // against INFLATED. 3751 if (scale > 0 && scale < DOUBLE_10_POW.length) { 3752 return (double)intCompact / DOUBLE_10_POW[scale]; 3753 } else if (scale < 0 && scale > -DOUBLE_10_POW.length) { 3754 return (double)intCompact * DOUBLE_10_POW[-scale]; 3755 } 3756 } 3757 } 3758 } 3759 // Somewhat inefficient, but guaranteed to work. 3760 return Double.parseDouble(this.toString()); 3761 } 3762 3763 /** 3764 * Powers of 10 which can be represented exactly in {@code 3765 * double}. 3766 */ 3767 private static final double DOUBLE_10_POW[] = { 3768 1.0e0, 1.0e1, 1.0e2, 1.0e3, 1.0e4, 1.0e5, 3769 1.0e6, 1.0e7, 1.0e8, 1.0e9, 1.0e10, 1.0e11, 3770 1.0e12, 1.0e13, 1.0e14, 1.0e15, 1.0e16, 1.0e17, 3771 1.0e18, 1.0e19, 1.0e20, 1.0e21, 1.0e22 3772 }; 3773 3774 /** 3775 * Powers of 10 which can be represented exactly in {@code 3776 * float}. 3777 */ 3778 private static final float FLOAT_10_POW[] = { 3779 1.0e0f, 1.0e1f, 1.0e2f, 1.0e3f, 1.0e4f, 1.0e5f, 3780 1.0e6f, 1.0e7f, 1.0e8f, 1.0e9f, 1.0e10f 3781 }; 3782 3783 /** 3784 * Returns the size of an ulp, a unit in the last place, of this 3785 * {@code BigDecimal}. An ulp of a nonzero {@code BigDecimal} 3786 * value is the positive distance between this value and the 3787 * {@code BigDecimal} value next larger in magnitude with the 3788 * same number of digits. An ulp of a zero value is numerically 3789 * equal to 1 with the scale of {@code this}. The result is 3790 * stored with the same scale as {@code this} so the result 3791 * for zero and nonzero values is equal to {@code [1, 3792 * this.scale()]}. 3793 * 3794 * @return the size of an ulp of {@code this} 3795 * @since 1.5 3796 */ 3797 public BigDecimal ulp() { 3798 return BigDecimal.valueOf(1, this.scale(), 1); 3799 } 3800 3801 // Private class to build a string representation for BigDecimal object. 3802 // "StringBuilderHelper" is constructed as a thread local variable so it is 3803 // thread safe. The StringBuilder field acts as a buffer to hold the temporary 3804 // representation of BigDecimal. The cmpCharArray holds all the characters for 3805 // the compact representation of BigDecimal (except for '-' sign' if it is 3806 // negative) if its intCompact field is not INFLATED. It is shared by all 3807 // calls to toString() and its variants in that particular thread. 3808 static class StringBuilderHelper { 3809 final StringBuilder sb; // Placeholder for BigDecimal string 3810 final char[] cmpCharArray; // character array to place the intCompact 3811 3812 StringBuilderHelper() { 3813 sb = new StringBuilder(); 3814 // All non negative longs can be made to fit into 19 character array. 3815 cmpCharArray = new char[19]; 3816 } 3817 3818 // Accessors. 3819 StringBuilder getStringBuilder() { 3820 sb.setLength(0); 3821 return sb; 3822 } 3823 3824 char[] getCompactCharArray() { 3825 return cmpCharArray; 3826 } 3827 3828 /** 3829 * Places characters representing the intCompact in {@code long} into 3830 * cmpCharArray and returns the offset to the array where the 3831 * representation starts. 3832 * 3833 * @param intCompact the number to put into the cmpCharArray. 3834 * @return offset to the array where the representation starts. 3835 * Note: intCompact must be greater or equal to zero. 3836 */ 3837 int putIntCompact(long intCompact) { 3838 assert intCompact >= 0; 3839 3840 long q; 3841 int r; 3842 // since we start from the least significant digit, charPos points to 3843 // the last character in cmpCharArray. 3844 int charPos = cmpCharArray.length; 3845 3846 // Get 2 digits/iteration using longs until quotient fits into an int 3847 while (intCompact > Integer.MAX_VALUE) { 3848 q = intCompact / 100; 3849 r = (int)(intCompact - q * 100); 3850 intCompact = q; 3851 cmpCharArray[--charPos] = DIGIT_ONES[r]; 3852 cmpCharArray[--charPos] = DIGIT_TENS[r]; 3853 } 3854 3855 // Get 2 digits/iteration using ints when i2 >= 100 3856 int q2; 3857 int i2 = (int)intCompact; 3858 while (i2 >= 100) { 3859 q2 = i2 / 100; 3860 r = i2 - q2 * 100; 3861 i2 = q2; 3862 cmpCharArray[--charPos] = DIGIT_ONES[r]; 3863 cmpCharArray[--charPos] = DIGIT_TENS[r]; 3864 } 3865 3866 cmpCharArray[--charPos] = DIGIT_ONES[i2]; 3867 if (i2 >= 10) 3868 cmpCharArray[--charPos] = DIGIT_TENS[i2]; 3869 3870 return charPos; 3871 } 3872 3873 static final char[] DIGIT_TENS = { 3874 '0', '0', '0', '0', '0', '0', '0', '0', '0', '0', 3875 '1', '1', '1', '1', '1', '1', '1', '1', '1', '1', 3876 '2', '2', '2', '2', '2', '2', '2', '2', '2', '2', 3877 '3', '3', '3', '3', '3', '3', '3', '3', '3', '3', 3878 '4', '4', '4', '4', '4', '4', '4', '4', '4', '4', 3879 '5', '5', '5', '5', '5', '5', '5', '5', '5', '5', 3880 '6', '6', '6', '6', '6', '6', '6', '6', '6', '6', 3881 '7', '7', '7', '7', '7', '7', '7', '7', '7', '7', 3882 '8', '8', '8', '8', '8', '8', '8', '8', '8', '8', 3883 '9', '9', '9', '9', '9', '9', '9', '9', '9', '9', 3884 }; 3885 3886 static final char[] DIGIT_ONES = { 3887 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3888 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3889 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3890 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3891 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3892 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3893 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3894 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3895 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3896 '0', '1', '2', '3', '4', '5', '6', '7', '8', '9', 3897 }; 3898 } 3899 3900 /** 3901 * Lay out this {@code BigDecimal} into a {@code char[]} array. 3902 * The Java 1.2 equivalent to this was called {@code getValueString}. 3903 * 3904 * @param sci {@code true} for Scientific exponential notation; 3905 * {@code false} for Engineering 3906 * @return string with canonical string representation of this 3907 * {@code BigDecimal} 3908 */ 3909 private String layoutChars(boolean sci) { 3910 if (scale == 0) // zero scale is trivial 3911 return (intCompact != INFLATED) ? 3912 Long.toString(intCompact): 3913 intVal.toString(); 3914 if (scale == 2 && 3915 intCompact >= 0 && intCompact < Integer.MAX_VALUE) { 3916 // currency fast path 3917 int lowInt = (int)intCompact % 100; 3918 int highInt = (int)intCompact / 100; 3919 return (Integer.toString(highInt) + '.' + 3920 StringBuilderHelper.DIGIT_TENS[lowInt] + 3921 StringBuilderHelper.DIGIT_ONES[lowInt]) ; 3922 } 3923 3924 StringBuilderHelper sbHelper = threadLocalStringBuilderHelper.get(); 3925 char[] coeff; 3926 int offset; // offset is the starting index for coeff array 3927 // Get the significand as an absolute value 3928 if (intCompact != INFLATED) { 3929 offset = sbHelper.putIntCompact(Math.abs(intCompact)); 3930 coeff = sbHelper.getCompactCharArray(); 3931 } else { 3932 offset = 0; 3933 coeff = intVal.abs().toString().toCharArray(); 3934 } 3935 3936 // Construct a buffer, with sufficient capacity for all cases. 3937 // If E-notation is needed, length will be: +1 if negative, +1 3938 // if '.' needed, +2 for "E+", + up to 10 for adjusted exponent. 3939 // Otherwise it could have +1 if negative, plus leading "0.00000" 3940 StringBuilder buf = sbHelper.getStringBuilder(); 3941 if (signum() < 0) // prefix '-' if negative 3942 buf.append('-'); 3943 int coeffLen = coeff.length - offset; 3944 long adjusted = -(long)scale + (coeffLen -1); 3945 if ((scale >= 0) && (adjusted >= -6)) { // plain number 3946 int pad = scale - coeffLen; // count of padding zeros 3947 if (pad >= 0) { // 0.xxx form 3948 buf.append('0'); 3949 buf.append('.'); 3950 for (; pad>0; pad--) { 3951 buf.append('0'); 3952 } 3953 buf.append(coeff, offset, coeffLen); 3954 } else { // xx.xx form 3955 buf.append(coeff, offset, -pad); 3956 buf.append('.'); 3957 buf.append(coeff, -pad + offset, scale); 3958 } 3959 } else { // E-notation is needed 3960 if (sci) { // Scientific notation 3961 buf.append(coeff[offset]); // first character 3962 if (coeffLen > 1) { // more to come 3963 buf.append('.'); 3964 buf.append(coeff, offset + 1, coeffLen - 1); 3965 } 3966 } else { // Engineering notation 3967 int sig = (int)(adjusted % 3); 3968 if (sig < 0) 3969 sig += 3; // [adjusted was negative] 3970 adjusted -= sig; // now a multiple of 3 3971 sig++; 3972 if (signum() == 0) { 3973 switch (sig) { 3974 case 1: 3975 buf.append('0'); // exponent is a multiple of three 3976 break; 3977 case 2: 3978 buf.append("0.00"); 3979 adjusted += 3; 3980 break; 3981 case 3: 3982 buf.append("0.0"); 3983 adjusted += 3; 3984 break; 3985 default: 3986 throw new AssertionError("Unexpected sig value " + sig); 3987 } 3988 } else if (sig >= coeffLen) { // significand all in integer 3989 buf.append(coeff, offset, coeffLen); 3990 // may need some zeros, too 3991 for (int i = sig - coeffLen; i > 0; i--) { 3992 buf.append('0'); 3993 } 3994 } else { // xx.xxE form 3995 buf.append(coeff, offset, sig); 3996 buf.append('.'); 3997 buf.append(coeff, offset + sig, coeffLen - sig); 3998 } 3999 } 4000 if (adjusted != 0) { // [!sci could have made 0] 4001 buf.append('E'); 4002 if (adjusted > 0) // force sign for positive 4003 buf.append('+'); 4004 buf.append(adjusted); 4005 } 4006 } 4007 return buf.toString(); 4008 } 4009 4010 /** 4011 * Return 10 to the power n, as a {@code BigInteger}. 4012 * 4013 * @param n the power of ten to be returned (>=0) 4014 * @return a {@code BigInteger} with the value (10<sup>n</sup>) 4015 */ 4016 private static BigInteger bigTenToThe(int n) { 4017 if (n < 0) 4018 return BigInteger.ZERO; 4019 4020 if (n < BIG_TEN_POWERS_TABLE_MAX) { 4021 BigInteger[] pows = BIG_TEN_POWERS_TABLE; 4022 if (n < pows.length) 4023 return pows[n]; 4024 else 4025 return expandBigIntegerTenPowers(n); 4026 } 4027 4028 return BigInteger.TEN.pow(n); 4029 } 4030 4031 /** 4032 * Expand the BIG_TEN_POWERS_TABLE array to contain at least 10**n. 4033 * 4034 * @param n the power of ten to be returned (>=0) 4035 * @return a {@code BigDecimal} with the value (10<sup>n</sup>) and 4036 * in the meantime, the BIG_TEN_POWERS_TABLE array gets 4037 * expanded to the size greater than n. 4038 */ 4039 private static BigInteger expandBigIntegerTenPowers(int n) { 4040 synchronized(BigDecimal.class) { 4041 BigInteger[] pows = BIG_TEN_POWERS_TABLE; 4042 int curLen = pows.length; 4043 // The following comparison and the above synchronized statement is 4044 // to prevent multiple threads from expanding the same array. 4045 if (curLen <= n) { 4046 int newLen = curLen << 1; 4047 while (newLen <= n) { 4048 newLen <<= 1; 4049 } 4050 pows = Arrays.copyOf(pows, newLen); 4051 for (int i = curLen; i < newLen; i++) { 4052 pows[i] = pows[i - 1].multiply(BigInteger.TEN); 4053 } 4054 // Based on the following facts: 4055 // 1. pows is a private local variable; 4056 // 2. the following store is a volatile store. 4057 // the newly created array elements can be safely published. 4058 BIG_TEN_POWERS_TABLE = pows; 4059 } 4060 return pows[n]; 4061 } 4062 } 4063 4064 private static final long[] LONG_TEN_POWERS_TABLE = { 4065 1, // 0 / 10^0 4066 10, // 1 / 10^1 4067 100, // 2 / 10^2 4068 1000, // 3 / 10^3 4069 10000, // 4 / 10^4 4070 100000, // 5 / 10^5 4071 1000000, // 6 / 10^6 4072 10000000, // 7 / 10^7 4073 100000000, // 8 / 10^8 4074 1000000000, // 9 / 10^9 4075 10000000000L, // 10 / 10^10 4076 100000000000L, // 11 / 10^11 4077 1000000000000L, // 12 / 10^12 4078 10000000000000L, // 13 / 10^13 4079 100000000000000L, // 14 / 10^14 4080 1000000000000000L, // 15 / 10^15 4081 10000000000000000L, // 16 / 10^16 4082 100000000000000000L, // 17 / 10^17 4083 1000000000000000000L // 18 / 10^18 4084 }; 4085 4086 private static volatile BigInteger BIG_TEN_POWERS_TABLE[] = { 4087 BigInteger.ONE, 4088 BigInteger.valueOf(10), 4089 BigInteger.valueOf(100), 4090 BigInteger.valueOf(1000), 4091 BigInteger.valueOf(10000), 4092 BigInteger.valueOf(100000), 4093 BigInteger.valueOf(1000000), 4094 BigInteger.valueOf(10000000), 4095 BigInteger.valueOf(100000000), 4096 BigInteger.valueOf(1000000000), 4097 BigInteger.valueOf(10000000000L), 4098 BigInteger.valueOf(100000000000L), 4099 BigInteger.valueOf(1000000000000L), 4100 BigInteger.valueOf(10000000000000L), 4101 BigInteger.valueOf(100000000000000L), 4102 BigInteger.valueOf(1000000000000000L), 4103 BigInteger.valueOf(10000000000000000L), 4104 BigInteger.valueOf(100000000000000000L), 4105 BigInteger.valueOf(1000000000000000000L) 4106 }; 4107 4108 private static final int BIG_TEN_POWERS_TABLE_INITLEN = 4109 BIG_TEN_POWERS_TABLE.length; 4110 private static final int BIG_TEN_POWERS_TABLE_MAX = 4111 16 * BIG_TEN_POWERS_TABLE_INITLEN; 4112 4113 private static final long THRESHOLDS_TABLE[] = { 4114 Long.MAX_VALUE, // 0 4115 Long.MAX_VALUE/10L, // 1 4116 Long.MAX_VALUE/100L, // 2 4117 Long.MAX_VALUE/1000L, // 3 4118 Long.MAX_VALUE/10000L, // 4 4119 Long.MAX_VALUE/100000L, // 5 4120 Long.MAX_VALUE/1000000L, // 6 4121 Long.MAX_VALUE/10000000L, // 7 4122 Long.MAX_VALUE/100000000L, // 8 4123 Long.MAX_VALUE/1000000000L, // 9 4124 Long.MAX_VALUE/10000000000L, // 10 4125 Long.MAX_VALUE/100000000000L, // 11 4126 Long.MAX_VALUE/1000000000000L, // 12 4127 Long.MAX_VALUE/10000000000000L, // 13 4128 Long.MAX_VALUE/100000000000000L, // 14 4129 Long.MAX_VALUE/1000000000000000L, // 15 4130 Long.MAX_VALUE/10000000000000000L, // 16 4131 Long.MAX_VALUE/100000000000000000L, // 17 4132 Long.MAX_VALUE/1000000000000000000L // 18 4133 }; 4134 4135 /** 4136 * Compute val * 10 ^ n; return this product if it is 4137 * representable as a long, INFLATED otherwise. 4138 */ 4139 private static long longMultiplyPowerTen(long val, int n) { 4140 if (val == 0 || n <= 0) 4141 return val; 4142 long[] tab = LONG_TEN_POWERS_TABLE; 4143 long[] bounds = THRESHOLDS_TABLE; 4144 if (n < tab.length && n < bounds.length) { 4145 long tenpower = tab[n]; 4146 if (val == 1) 4147 return tenpower; 4148 if (Math.abs(val) <= bounds[n]) 4149 return val * tenpower; 4150 } 4151 return INFLATED; 4152 } 4153 4154 /** 4155 * Compute this * 10 ^ n. 4156 * Needed mainly to allow special casing to trap zero value 4157 */ 4158 private BigInteger bigMultiplyPowerTen(int n) { 4159 if (n <= 0) 4160 return this.inflated(); 4161 4162 if (intCompact != INFLATED) 4163 return bigTenToThe(n).multiply(intCompact); 4164 else 4165 return intVal.multiply(bigTenToThe(n)); 4166 } 4167 4168 /** 4169 * Returns appropriate BigInteger from intVal field if intVal is 4170 * null, i.e. the compact representation is in use. 4171 */ 4172 private BigInteger inflated() { 4173 if (intVal == null) { 4174 return BigInteger.valueOf(intCompact); 4175 } 4176 return intVal; 4177 } 4178 4179 /** 4180 * Match the scales of two {@code BigDecimal}s to align their 4181 * least significant digits. 4182 * 4183 * <p>If the scales of val[0] and val[1] differ, rescale 4184 * (non-destructively) the lower-scaled {@code BigDecimal} so 4185 * they match. That is, the lower-scaled reference will be 4186 * replaced by a reference to a new object with the same scale as 4187 * the other {@code BigDecimal}. 4188 * 4189 * @param val array of two elements referring to the two 4190 * {@code BigDecimal}s to be aligned. 4191 */ 4192 private static void matchScale(BigDecimal[] val) { 4193 if (val[0].scale < val[1].scale) { 4194 val[0] = val[0].setScale(val[1].scale, ROUND_UNNECESSARY); 4195 } else if (val[1].scale < val[0].scale) { 4196 val[1] = val[1].setScale(val[0].scale, ROUND_UNNECESSARY); 4197 } 4198 } 4199 4200 private static class UnsafeHolder { 4201 private static final jdk.internal.misc.Unsafe unsafe 4202 = jdk.internal.misc.Unsafe.getUnsafe(); 4203 private static final long intCompactOffset 4204 = unsafe.objectFieldOffset(BigDecimal.class, "intCompact"); 4205 private static final long intValOffset 4206 = unsafe.objectFieldOffset(BigDecimal.class, "intVal"); 4207 4208 static void setIntCompact(BigDecimal bd, long val) { 4209 unsafe.putLong(bd, intCompactOffset, val); 4210 } 4211 4212 static void setIntValVolatile(BigDecimal bd, BigInteger val) { 4213 unsafe.putReferenceVolatile(bd, intValOffset, val); 4214 } 4215 } 4216 4217 /** 4218 * Reconstitute the {@code BigDecimal} instance from a stream (that is, 4219 * deserialize it). 4220 * 4221 * @param s the stream being read. 4222 */ 4223 @java.io.Serial 4224 private void readObject(java.io.ObjectInputStream s) 4225 throws java.io.IOException, ClassNotFoundException { 4226 // Read in all fields 4227 s.defaultReadObject(); 4228 // validate possibly bad fields 4229 if (intVal == null) { 4230 String message = "BigDecimal: null intVal in stream"; 4231 throw new java.io.StreamCorruptedException(message); 4232 // [all values of scale are now allowed] 4233 } 4234 UnsafeHolder.setIntCompact(this, compactValFor(intVal)); 4235 } 4236 4237 /** 4238 * Serialize this {@code BigDecimal} to the stream in question 4239 * 4240 * @param s the stream to serialize to. 4241 */ 4242 @java.io.Serial 4243 private void writeObject(java.io.ObjectOutputStream s) 4244 throws java.io.IOException { 4245 // Must inflate to maintain compatible serial form. 4246 if (this.intVal == null) 4247 UnsafeHolder.setIntValVolatile(this, BigInteger.valueOf(this.intCompact)); 4248 // Could reset intVal back to null if it has to be set. 4249 s.defaultWriteObject(); 4250 } 4251 4252 /** 4253 * Returns the length of the absolute value of a {@code long}, in decimal 4254 * digits. 4255 * 4256 * @param x the {@code long} 4257 * @return the length of the unscaled value, in deciaml digits. 4258 */ 4259 static int longDigitLength(long x) { 4260 /* 4261 * As described in "Bit Twiddling Hacks" by Sean Anderson, 4262 * (http://graphics.stanford.edu/~seander/bithacks.html) 4263 * integer log 10 of x is within 1 of (1233/4096)* (1 + 4264 * integer log 2 of x). The fraction 1233/4096 approximates 4265 * log10(2). So we first do a version of log2 (a variant of 4266 * Long class with pre-checks and opposite directionality) and 4267 * then scale and check against powers table. This is a little 4268 * simpler in present context than the version in Hacker's 4269 * Delight sec 11-4. Adding one to bit length allows comparing 4270 * downward from the LONG_TEN_POWERS_TABLE that we need 4271 * anyway. 4272 */ 4273 assert x != BigDecimal.INFLATED; 4274 if (x < 0) 4275 x = -x; 4276 if (x < 10) // must screen for 0, might as well 10 4277 return 1; 4278 int r = ((64 - Long.numberOfLeadingZeros(x) + 1) * 1233) >>> 12; 4279 long[] tab = LONG_TEN_POWERS_TABLE; 4280 // if r >= length, must have max possible digits for long 4281 return (r >= tab.length || x < tab[r]) ? r : r + 1; 4282 } 4283 4284 /** 4285 * Returns the length of the absolute value of a BigInteger, in 4286 * decimal digits. 4287 * 4288 * @param b the BigInteger 4289 * @return the length of the unscaled value, in decimal digits 4290 */ 4291 private static int bigDigitLength(BigInteger b) { 4292 /* 4293 * Same idea as the long version, but we need a better 4294 * approximation of log10(2). Using 646456993/2^31 4295 * is accurate up to max possible reported bitLength. 4296 */ 4297 if (b.signum == 0) 4298 return 1; 4299 int r = (int)((((long)b.bitLength() + 1) * 646456993) >>> 31); 4300 return b.compareMagnitude(bigTenToThe(r)) < 0? r : r+1; 4301 } 4302 4303 /** 4304 * Check a scale for Underflow or Overflow. If this BigDecimal is 4305 * nonzero, throw an exception if the scale is outof range. If this 4306 * is zero, saturate the scale to the extreme value of the right 4307 * sign if the scale is out of range. 4308 * 4309 * @param val The new scale. 4310 * @throws ArithmeticException (overflow or underflow) if the new 4311 * scale is out of range. 4312 * @return validated scale as an int. 4313 */ 4314 private int checkScale(long val) { 4315 int asInt = (int)val; 4316 if (asInt != val) { 4317 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; 4318 BigInteger b; 4319 if (intCompact != 0 && 4320 ((b = intVal) == null || b.signum() != 0)) 4321 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); 4322 } 4323 return asInt; 4324 } 4325 4326 /** 4327 * Returns the compact value for given {@code BigInteger}, or 4328 * INFLATED if too big. Relies on internal representation of 4329 * {@code BigInteger}. 4330 */ 4331 private static long compactValFor(BigInteger b) { 4332 int[] m = b.mag; 4333 int len = m.length; 4334 if (len == 0) 4335 return 0; 4336 int d = m[0]; 4337 if (len > 2 || (len == 2 && d < 0)) 4338 return INFLATED; 4339 4340 long u = (len == 2)? 4341 (((long) m[1] & LONG_MASK) + (((long)d) << 32)) : 4342 (((long)d) & LONG_MASK); 4343 return (b.signum < 0)? -u : u; 4344 } 4345 4346 private static int longCompareMagnitude(long x, long y) { 4347 if (x < 0) 4348 x = -x; 4349 if (y < 0) 4350 y = -y; 4351 return (x < y) ? -1 : ((x == y) ? 0 : 1); 4352 } 4353 4354 private static int saturateLong(long s) { 4355 int i = (int)s; 4356 return (s == i) ? i : (s < 0 ? Integer.MIN_VALUE : Integer.MAX_VALUE); 4357 } 4358 4359 /* 4360 * Internal printing routine 4361 */ 4362 private static void print(String name, BigDecimal bd) { 4363 System.err.format("%s:\tintCompact %d\tintVal %d\tscale %d\tprecision %d%n", 4364 name, 4365 bd.intCompact, 4366 bd.intVal, 4367 bd.scale, 4368 bd.precision); 4369 } 4370 4371 /** 4372 * Check internal invariants of this BigDecimal. These invariants 4373 * include: 4374 * 4375 * <ul> 4376 * 4377 * <li>The object must be initialized; either intCompact must not be 4378 * INFLATED or intVal is non-null. Both of these conditions may 4379 * be true. 4380 * 4381 * <li>If both intCompact and intVal and set, their values must be 4382 * consistent. 4383 * 4384 * <li>If precision is nonzero, it must have the right value. 4385 * </ul> 4386 * 4387 * Note: Since this is an audit method, we are not supposed to change the 4388 * state of this BigDecimal object. 4389 */ 4390 private BigDecimal audit() { 4391 if (intCompact == INFLATED) { 4392 if (intVal == null) { 4393 print("audit", this); 4394 throw new AssertionError("null intVal"); 4395 } 4396 // Check precision 4397 if (precision > 0 && precision != bigDigitLength(intVal)) { 4398 print("audit", this); 4399 throw new AssertionError("precision mismatch"); 4400 } 4401 } else { 4402 if (intVal != null) { 4403 long val = intVal.longValue(); 4404 if (val != intCompact) { 4405 print("audit", this); 4406 throw new AssertionError("Inconsistent state, intCompact=" + 4407 intCompact + "\t intVal=" + val); 4408 } 4409 } 4410 // Check precision 4411 if (precision > 0 && precision != longDigitLength(intCompact)) { 4412 print("audit", this); 4413 throw new AssertionError("precision mismatch"); 4414 } 4415 } 4416 return this; 4417 } 4418 4419 /* the same as checkScale where value!=0 */ 4420 private static int checkScaleNonZero(long val) { 4421 int asInt = (int)val; 4422 if (asInt != val) { 4423 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); 4424 } 4425 return asInt; 4426 } 4427 4428 private static int checkScale(long intCompact, long val) { 4429 int asInt = (int)val; 4430 if (asInt != val) { 4431 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; 4432 if (intCompact != 0) 4433 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); 4434 } 4435 return asInt; 4436 } 4437 4438 private static int checkScale(BigInteger intVal, long val) { 4439 int asInt = (int)val; 4440 if (asInt != val) { 4441 asInt = val>Integer.MAX_VALUE ? Integer.MAX_VALUE : Integer.MIN_VALUE; 4442 if (intVal.signum() != 0) 4443 throw new ArithmeticException(asInt>0 ? "Underflow":"Overflow"); 4444 } 4445 return asInt; 4446 } 4447 4448 /** 4449 * Returns a {@code BigDecimal} rounded according to the MathContext 4450 * settings; 4451 * If rounding is needed a new {@code BigDecimal} is created and returned. 4452 * 4453 * @param val the value to be rounded 4454 * @param mc the context to use. 4455 * @return a {@code BigDecimal} rounded according to the MathContext 4456 * settings. May return {@code value}, if no rounding needed. 4457 * @throws ArithmeticException if the rounding mode is 4458 * {@code RoundingMode.UNNECESSARY} and the 4459 * result is inexact. 4460 */ 4461 private static BigDecimal doRound(BigDecimal val, MathContext mc) { 4462 int mcp = mc.precision; 4463 boolean wasDivided = false; 4464 if (mcp > 0) { 4465 BigInteger intVal = val.intVal; 4466 long compactVal = val.intCompact; 4467 int scale = val.scale; 4468 int prec = val.precision(); 4469 int mode = mc.roundingMode.oldMode; 4470 int drop; 4471 if (compactVal == INFLATED) { 4472 drop = prec - mcp; 4473 while (drop > 0) { 4474 scale = checkScaleNonZero((long) scale - drop); 4475 intVal = divideAndRoundByTenPow(intVal, drop, mode); 4476 wasDivided = true; 4477 compactVal = compactValFor(intVal); 4478 if (compactVal != INFLATED) { 4479 prec = longDigitLength(compactVal); 4480 break; 4481 } 4482 prec = bigDigitLength(intVal); 4483 drop = prec - mcp; 4484 } 4485 } 4486 if (compactVal != INFLATED) { 4487 drop = prec - mcp; // drop can't be more than 18 4488 while (drop > 0) { 4489 scale = checkScaleNonZero((long) scale - drop); 4490 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 4491 wasDivided = true; 4492 prec = longDigitLength(compactVal); 4493 drop = prec - mcp; 4494 intVal = null; 4495 } 4496 } 4497 return wasDivided ? new BigDecimal(intVal,compactVal,scale,prec) : val; 4498 } 4499 return val; 4500 } 4501 4502 /* 4503 * Returns a {@code BigDecimal} created from {@code long} value with 4504 * given scale rounded according to the MathContext settings 4505 */ 4506 private static BigDecimal doRound(long compactVal, int scale, MathContext mc) { 4507 int mcp = mc.precision; 4508 if (mcp > 0 && mcp < 19) { 4509 int prec = longDigitLength(compactVal); 4510 int drop = prec - mcp; // drop can't be more than 18 4511 while (drop > 0) { 4512 scale = checkScaleNonZero((long) scale - drop); 4513 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 4514 prec = longDigitLength(compactVal); 4515 drop = prec - mcp; 4516 } 4517 return valueOf(compactVal, scale, prec); 4518 } 4519 return valueOf(compactVal, scale); 4520 } 4521 4522 /* 4523 * Returns a {@code BigDecimal} created from {@code BigInteger} value with 4524 * given scale rounded according to the MathContext settings 4525 */ 4526 private static BigDecimal doRound(BigInteger intVal, int scale, MathContext mc) { 4527 int mcp = mc.precision; 4528 int prec = 0; 4529 if (mcp > 0) { 4530 long compactVal = compactValFor(intVal); 4531 int mode = mc.roundingMode.oldMode; 4532 int drop; 4533 if (compactVal == INFLATED) { 4534 prec = bigDigitLength(intVal); 4535 drop = prec - mcp; 4536 while (drop > 0) { 4537 scale = checkScaleNonZero((long) scale - drop); 4538 intVal = divideAndRoundByTenPow(intVal, drop, mode); 4539 compactVal = compactValFor(intVal); 4540 if (compactVal != INFLATED) { 4541 break; 4542 } 4543 prec = bigDigitLength(intVal); 4544 drop = prec - mcp; 4545 } 4546 } 4547 if (compactVal != INFLATED) { 4548 prec = longDigitLength(compactVal); 4549 drop = prec - mcp; // drop can't be more than 18 4550 while (drop > 0) { 4551 scale = checkScaleNonZero((long) scale - drop); 4552 compactVal = divideAndRound(compactVal, LONG_TEN_POWERS_TABLE[drop], mc.roundingMode.oldMode); 4553 prec = longDigitLength(compactVal); 4554 drop = prec - mcp; 4555 } 4556 return valueOf(compactVal,scale,prec); 4557 } 4558 } 4559 return new BigDecimal(intVal,INFLATED,scale,prec); 4560 } 4561 4562 /* 4563 * Divides {@code BigInteger} value by ten power. 4564 */ 4565 private static BigInteger divideAndRoundByTenPow(BigInteger intVal, int tenPow, int roundingMode) { 4566 if (tenPow < LONG_TEN_POWERS_TABLE.length) 4567 intVal = divideAndRound(intVal, LONG_TEN_POWERS_TABLE[tenPow], roundingMode); 4568 else 4569 intVal = divideAndRound(intVal, bigTenToThe(tenPow), roundingMode); 4570 return intVal; 4571 } 4572 4573 /** 4574 * Internally used for division operation for division {@code long} by 4575 * {@code long}. 4576 * The returned {@code BigDecimal} object is the quotient whose scale is set 4577 * to the passed in scale. If the remainder is not zero, it will be rounded 4578 * based on the passed in roundingMode. Also, if the remainder is zero and 4579 * the last parameter, i.e. preferredScale is NOT equal to scale, the 4580 * trailing zeros of the result is stripped to match the preferredScale. 4581 */ 4582 private static BigDecimal divideAndRound(long ldividend, long ldivisor, int scale, int roundingMode, 4583 int preferredScale) { 4584 4585 int qsign; // quotient sign 4586 long q = ldividend / ldivisor; // store quotient in long 4587 if (roundingMode == ROUND_DOWN && scale == preferredScale) 4588 return valueOf(q, scale); 4589 long r = ldividend % ldivisor; // store remainder in long 4590 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1; 4591 if (r != 0) { 4592 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r); 4593 return valueOf((increment ? q + qsign : q), scale); 4594 } else { 4595 if (preferredScale != scale) 4596 return createAndStripZerosToMatchScale(q, scale, preferredScale); 4597 else 4598 return valueOf(q, scale); 4599 } 4600 } 4601 4602 /** 4603 * Divides {@code long} by {@code long} and do rounding based on the 4604 * passed in roundingMode. 4605 */ 4606 private static long divideAndRound(long ldividend, long ldivisor, int roundingMode) { 4607 int qsign; // quotient sign 4608 long q = ldividend / ldivisor; // store quotient in long 4609 if (roundingMode == ROUND_DOWN) 4610 return q; 4611 long r = ldividend % ldivisor; // store remainder in long 4612 qsign = ((ldividend < 0) == (ldivisor < 0)) ? 1 : -1; 4613 if (r != 0) { 4614 boolean increment = needIncrement(ldivisor, roundingMode, qsign, q, r); 4615 return increment ? q + qsign : q; 4616 } else { 4617 return q; 4618 } 4619 } 4620 4621 /** 4622 * Shared logic of need increment computation. 4623 */ 4624 private static boolean commonNeedIncrement(int roundingMode, int qsign, 4625 int cmpFracHalf, boolean oddQuot) { 4626 switch(roundingMode) { 4627 case ROUND_UNNECESSARY: 4628 throw new ArithmeticException("Rounding necessary"); 4629 4630 case ROUND_UP: // Away from zero 4631 return true; 4632 4633 case ROUND_DOWN: // Towards zero 4634 return false; 4635 4636 case ROUND_CEILING: // Towards +infinity 4637 return qsign > 0; 4638 4639 case ROUND_FLOOR: // Towards -infinity 4640 return qsign < 0; 4641 4642 default: // Some kind of half-way rounding 4643 assert roundingMode >= ROUND_HALF_UP && 4644 roundingMode <= ROUND_HALF_EVEN: "Unexpected rounding mode" + RoundingMode.valueOf(roundingMode); 4645 4646 if (cmpFracHalf < 0 ) // We're closer to higher digit 4647 return false; 4648 else if (cmpFracHalf > 0 ) // We're closer to lower digit 4649 return true; 4650 else { // half-way 4651 assert cmpFracHalf == 0; 4652 4653 switch(roundingMode) { 4654 case ROUND_HALF_DOWN: 4655 return false; 4656 4657 case ROUND_HALF_UP: 4658 return true; 4659 4660 case ROUND_HALF_EVEN: 4661 return oddQuot; 4662 4663 default: 4664 throw new AssertionError("Unexpected rounding mode" + roundingMode); 4665 } 4666 } 4667 } 4668 } 4669 4670 /** 4671 * Tests if quotient has to be incremented according the roundingMode 4672 */ 4673 private static boolean needIncrement(long ldivisor, int roundingMode, 4674 int qsign, long q, long r) { 4675 assert r != 0L; 4676 4677 int cmpFracHalf; 4678 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) { 4679 cmpFracHalf = 1; // 2 * r can't fit into long 4680 } else { 4681 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor); 4682 } 4683 4684 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, (q & 1L) != 0L); 4685 } 4686 4687 /** 4688 * Divides {@code BigInteger} value by {@code long} value and 4689 * do rounding based on the passed in roundingMode. 4690 */ 4691 private static BigInteger divideAndRound(BigInteger bdividend, long ldivisor, int roundingMode) { 4692 // Descend into mutables for faster remainder checks 4693 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); 4694 // store quotient 4695 MutableBigInteger mq = new MutableBigInteger(); 4696 // store quotient & remainder in long 4697 long r = mdividend.divide(ldivisor, mq); 4698 // record remainder is zero or not 4699 boolean isRemainderZero = (r == 0); 4700 // quotient sign 4701 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum; 4702 if (!isRemainderZero) { 4703 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) { 4704 mq.add(MutableBigInteger.ONE); 4705 } 4706 } 4707 return mq.toBigInteger(qsign); 4708 } 4709 4710 /** 4711 * Internally used for division operation for division {@code BigInteger} 4712 * by {@code long}. 4713 * The returned {@code BigDecimal} object is the quotient whose scale is set 4714 * to the passed in scale. If the remainder is not zero, it will be rounded 4715 * based on the passed in roundingMode. Also, if the remainder is zero and 4716 * the last parameter, i.e. preferredScale is NOT equal to scale, the 4717 * trailing zeros of the result is stripped to match the preferredScale. 4718 */ 4719 private static BigDecimal divideAndRound(BigInteger bdividend, 4720 long ldivisor, int scale, int roundingMode, int preferredScale) { 4721 // Descend into mutables for faster remainder checks 4722 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); 4723 // store quotient 4724 MutableBigInteger mq = new MutableBigInteger(); 4725 // store quotient & remainder in long 4726 long r = mdividend.divide(ldivisor, mq); 4727 // record remainder is zero or not 4728 boolean isRemainderZero = (r == 0); 4729 // quotient sign 4730 int qsign = (ldivisor < 0) ? -bdividend.signum : bdividend.signum; 4731 if (!isRemainderZero) { 4732 if(needIncrement(ldivisor, roundingMode, qsign, mq, r)) { 4733 mq.add(MutableBigInteger.ONE); 4734 } 4735 return mq.toBigDecimal(qsign, scale); 4736 } else { 4737 if (preferredScale != scale) { 4738 long compactVal = mq.toCompactValue(qsign); 4739 if(compactVal!=INFLATED) { 4740 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale); 4741 } 4742 BigInteger intVal = mq.toBigInteger(qsign); 4743 return createAndStripZerosToMatchScale(intVal,scale, preferredScale); 4744 } else { 4745 return mq.toBigDecimal(qsign, scale); 4746 } 4747 } 4748 } 4749 4750 /** 4751 * Tests if quotient has to be incremented according the roundingMode 4752 */ 4753 private static boolean needIncrement(long ldivisor, int roundingMode, 4754 int qsign, MutableBigInteger mq, long r) { 4755 assert r != 0L; 4756 4757 int cmpFracHalf; 4758 if (r <= HALF_LONG_MIN_VALUE || r > HALF_LONG_MAX_VALUE) { 4759 cmpFracHalf = 1; // 2 * r can't fit into long 4760 } else { 4761 cmpFracHalf = longCompareMagnitude(2 * r, ldivisor); 4762 } 4763 4764 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd()); 4765 } 4766 4767 /** 4768 * Divides {@code BigInteger} value by {@code BigInteger} value and 4769 * do rounding based on the passed in roundingMode. 4770 */ 4771 private static BigInteger divideAndRound(BigInteger bdividend, BigInteger bdivisor, int roundingMode) { 4772 boolean isRemainderZero; // record remainder is zero or not 4773 int qsign; // quotient sign 4774 // Descend into mutables for faster remainder checks 4775 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); 4776 MutableBigInteger mq = new MutableBigInteger(); 4777 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag); 4778 MutableBigInteger mr = mdividend.divide(mdivisor, mq); 4779 isRemainderZero = mr.isZero(); 4780 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1; 4781 if (!isRemainderZero) { 4782 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) { 4783 mq.add(MutableBigInteger.ONE); 4784 } 4785 } 4786 return mq.toBigInteger(qsign); 4787 } 4788 4789 /** 4790 * Internally used for division operation for division {@code BigInteger} 4791 * by {@code BigInteger}. 4792 * The returned {@code BigDecimal} object is the quotient whose scale is set 4793 * to the passed in scale. If the remainder is not zero, it will be rounded 4794 * based on the passed in roundingMode. Also, if the remainder is zero and 4795 * the last parameter, i.e. preferredScale is NOT equal to scale, the 4796 * trailing zeros of the result is stripped to match the preferredScale. 4797 */ 4798 private static BigDecimal divideAndRound(BigInteger bdividend, BigInteger bdivisor, int scale, int roundingMode, 4799 int preferredScale) { 4800 boolean isRemainderZero; // record remainder is zero or not 4801 int qsign; // quotient sign 4802 // Descend into mutables for faster remainder checks 4803 MutableBigInteger mdividend = new MutableBigInteger(bdividend.mag); 4804 MutableBigInteger mq = new MutableBigInteger(); 4805 MutableBigInteger mdivisor = new MutableBigInteger(bdivisor.mag); 4806 MutableBigInteger mr = mdividend.divide(mdivisor, mq); 4807 isRemainderZero = mr.isZero(); 4808 qsign = (bdividend.signum != bdivisor.signum) ? -1 : 1; 4809 if (!isRemainderZero) { 4810 if (needIncrement(mdivisor, roundingMode, qsign, mq, mr)) { 4811 mq.add(MutableBigInteger.ONE); 4812 } 4813 return mq.toBigDecimal(qsign, scale); 4814 } else { 4815 if (preferredScale != scale) { 4816 long compactVal = mq.toCompactValue(qsign); 4817 if (compactVal != INFLATED) { 4818 return createAndStripZerosToMatchScale(compactVal, scale, preferredScale); 4819 } 4820 BigInteger intVal = mq.toBigInteger(qsign); 4821 return createAndStripZerosToMatchScale(intVal, scale, preferredScale); 4822 } else { 4823 return mq.toBigDecimal(qsign, scale); 4824 } 4825 } 4826 } 4827 4828 /** 4829 * Tests if quotient has to be incremented according the roundingMode 4830 */ 4831 private static boolean needIncrement(MutableBigInteger mdivisor, int roundingMode, 4832 int qsign, MutableBigInteger mq, MutableBigInteger mr) { 4833 assert !mr.isZero(); 4834 int cmpFracHalf = mr.compareHalf(mdivisor); 4835 return commonNeedIncrement(roundingMode, qsign, cmpFracHalf, mq.isOdd()); 4836 } 4837 4838 /** 4839 * Remove insignificant trailing zeros from this 4840 * {@code BigInteger} value until the preferred scale is reached or no 4841 * more zeros can be removed. If the preferred scale is less than 4842 * Integer.MIN_VALUE, all the trailing zeros will be removed. 4843 * 4844 * @return new {@code BigDecimal} with a scale possibly reduced 4845 * to be closed to the preferred scale. 4846 */ 4847 private static BigDecimal createAndStripZerosToMatchScale(BigInteger intVal, int scale, long preferredScale) { 4848 BigInteger qr[]; // quotient-remainder pair 4849 while (intVal.compareMagnitude(BigInteger.TEN) >= 0 4850 && scale > preferredScale) { 4851 if (intVal.testBit(0)) 4852 break; // odd number cannot end in 0 4853 qr = intVal.divideAndRemainder(BigInteger.TEN); 4854 if (qr[1].signum() != 0) 4855 break; // non-0 remainder 4856 intVal = qr[0]; 4857 scale = checkScale(intVal,(long) scale - 1); // could Overflow 4858 } 4859 return valueOf(intVal, scale, 0); 4860 } 4861 4862 /** 4863 * Remove insignificant trailing zeros from this 4864 * {@code long} value until the preferred scale is reached or no 4865 * more zeros can be removed. If the preferred scale is less than 4866 * Integer.MIN_VALUE, all the trailing zeros will be removed. 4867 * 4868 * @return new {@code BigDecimal} with a scale possibly reduced 4869 * to be closed to the preferred scale. 4870 */ 4871 private static BigDecimal createAndStripZerosToMatchScale(long compactVal, int scale, long preferredScale) { 4872 while (Math.abs(compactVal) >= 10L && scale > preferredScale) { 4873 if ((compactVal & 1L) != 0L) 4874 break; // odd number cannot end in 0 4875 long r = compactVal % 10L; 4876 if (r != 0L) 4877 break; // non-0 remainder 4878 compactVal /= 10; 4879 scale = checkScale(compactVal, (long) scale - 1); // could Overflow 4880 } 4881 return valueOf(compactVal, scale); 4882 } 4883 4884 private static BigDecimal stripZerosToMatchScale(BigInteger intVal, long intCompact, int scale, int preferredScale) { 4885 if(intCompact!=INFLATED) { 4886 return createAndStripZerosToMatchScale(intCompact, scale, preferredScale); 4887 } else { 4888 return createAndStripZerosToMatchScale(intVal==null ? INFLATED_BIGINT : intVal, 4889 scale, preferredScale); 4890 } 4891 } 4892 4893 /* 4894 * returns INFLATED if oveflow 4895 */ 4896 private static long add(long xs, long ys){ 4897 long sum = xs + ys; 4898 // See "Hacker's Delight" section 2-12 for explanation of 4899 // the overflow test. 4900 if ( (((sum ^ xs) & (sum ^ ys))) >= 0L) { // not overflowed 4901 return sum; 4902 } 4903 return INFLATED; 4904 } 4905 4906 private static BigDecimal add(long xs, long ys, int scale){ 4907 long sum = add(xs, ys); 4908 if (sum!=INFLATED) 4909 return BigDecimal.valueOf(sum, scale); 4910 return new BigDecimal(BigInteger.valueOf(xs).add(ys), scale); 4911 } 4912 4913 private static BigDecimal add(final long xs, int scale1, final long ys, int scale2) { 4914 long sdiff = (long) scale1 - scale2; 4915 if (sdiff == 0) { 4916 return add(xs, ys, scale1); 4917 } else if (sdiff < 0) { 4918 int raise = checkScale(xs,-sdiff); 4919 long scaledX = longMultiplyPowerTen(xs, raise); 4920 if (scaledX != INFLATED) { 4921 return add(scaledX, ys, scale2); 4922 } else { 4923 BigInteger bigsum = bigMultiplyPowerTen(xs,raise).add(ys); 4924 return ((xs^ys)>=0) ? // same sign test 4925 new BigDecimal(bigsum, INFLATED, scale2, 0) 4926 : valueOf(bigsum, scale2, 0); 4927 } 4928 } else { 4929 int raise = checkScale(ys,sdiff); 4930 long scaledY = longMultiplyPowerTen(ys, raise); 4931 if (scaledY != INFLATED) { 4932 return add(xs, scaledY, scale1); 4933 } else { 4934 BigInteger bigsum = bigMultiplyPowerTen(ys,raise).add(xs); 4935 return ((xs^ys)>=0) ? 4936 new BigDecimal(bigsum, INFLATED, scale1, 0) 4937 : valueOf(bigsum, scale1, 0); 4938 } 4939 } 4940 } 4941 4942 private static BigDecimal add(final long xs, int scale1, BigInteger snd, int scale2) { 4943 int rscale = scale1; 4944 long sdiff = (long)rscale - scale2; 4945 boolean sameSigns = (Long.signum(xs) == snd.signum); 4946 BigInteger sum; 4947 if (sdiff < 0) { 4948 int raise = checkScale(xs,-sdiff); 4949 rscale = scale2; 4950 long scaledX = longMultiplyPowerTen(xs, raise); 4951 if (scaledX == INFLATED) { 4952 sum = snd.add(bigMultiplyPowerTen(xs,raise)); 4953 } else { 4954 sum = snd.add(scaledX); 4955 } 4956 } else { //if (sdiff > 0) { 4957 int raise = checkScale(snd,sdiff); 4958 snd = bigMultiplyPowerTen(snd,raise); 4959 sum = snd.add(xs); 4960 } 4961 return (sameSigns) ? 4962 new BigDecimal(sum, INFLATED, rscale, 0) : 4963 valueOf(sum, rscale, 0); 4964 } 4965 4966 private static BigDecimal add(BigInteger fst, int scale1, BigInteger snd, int scale2) { 4967 int rscale = scale1; 4968 long sdiff = (long)rscale - scale2; 4969 if (sdiff != 0) { 4970 if (sdiff < 0) { 4971 int raise = checkScale(fst,-sdiff); 4972 rscale = scale2; 4973 fst = bigMultiplyPowerTen(fst,raise); 4974 } else { 4975 int raise = checkScale(snd,sdiff); 4976 snd = bigMultiplyPowerTen(snd,raise); 4977 } 4978 } 4979 BigInteger sum = fst.add(snd); 4980 return (fst.signum == snd.signum) ? 4981 new BigDecimal(sum, INFLATED, rscale, 0) : 4982 valueOf(sum, rscale, 0); 4983 } 4984 4985 private static BigInteger bigMultiplyPowerTen(long value, int n) { 4986 if (n <= 0) 4987 return BigInteger.valueOf(value); 4988 return bigTenToThe(n).multiply(value); 4989 } 4990 4991 private static BigInteger bigMultiplyPowerTen(BigInteger value, int n) { 4992 if (n <= 0) 4993 return value; 4994 if(n<LONG_TEN_POWERS_TABLE.length) { 4995 return value.multiply(LONG_TEN_POWERS_TABLE[n]); 4996 } 4997 return value.multiply(bigTenToThe(n)); 4998 } 4999 5000 /** 5001 * Returns a {@code BigDecimal} whose value is {@code (xs / 5002 * ys)}, with rounding according to the context settings. 5003 * 5004 * Fast path - used only when (xscale <= yscale && yscale < 18 5005 * && mc.presision<18) { 5006 */ 5007 private static BigDecimal divideSmallFastPath(final long xs, int xscale, 5008 final long ys, int yscale, 5009 long preferredScale, MathContext mc) { 5010 int mcp = mc.precision; 5011 int roundingMode = mc.roundingMode.oldMode; 5012 5013 assert (xscale <= yscale) && (yscale < 18) && (mcp < 18); 5014 int xraise = yscale - xscale; // xraise >=0 5015 long scaledX = (xraise==0) ? xs : 5016 longMultiplyPowerTen(xs, xraise); // can't overflow here! 5017 BigDecimal quotient; 5018 5019 int cmp = longCompareMagnitude(scaledX, ys); 5020 if(cmp > 0) { // satisfy constraint (b) 5021 yscale -= 1; // [that is, divisor *= 10] 5022 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5023 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { 5024 // assert newScale >= xscale 5025 int raise = checkScaleNonZero((long) mcp + yscale - xscale); 5026 long scaledXs; 5027 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) { 5028 quotient = null; 5029 if((mcp-1) >=0 && (mcp-1)<LONG_TEN_POWERS_TABLE.length) { 5030 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp-1], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5031 } 5032 if(quotient==null) { 5033 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp-1); 5034 quotient = divideAndRound(rb, ys, 5035 scl, roundingMode, checkScaleNonZero(preferredScale)); 5036 } 5037 } else { 5038 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5039 } 5040 } else { 5041 int newScale = checkScaleNonZero((long) xscale - mcp); 5042 // assert newScale >= yscale 5043 if (newScale == yscale) { // easy case 5044 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); 5045 } else { 5046 int raise = checkScaleNonZero((long) newScale - yscale); 5047 long scaledYs; 5048 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { 5049 BigInteger rb = bigMultiplyPowerTen(ys,raise); 5050 quotient = divideAndRound(BigInteger.valueOf(xs), 5051 rb, scl, roundingMode,checkScaleNonZero(preferredScale)); 5052 } else { 5053 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); 5054 } 5055 } 5056 } 5057 } else { 5058 // abs(scaledX) <= abs(ys) 5059 // result is "scaledX * 10^msp / ys" 5060 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5061 if(cmp==0) { 5062 // abs(scaleX)== abs(ys) => result will be scaled 10^mcp + correct sign 5063 quotient = roundedTenPower(((scaledX < 0) == (ys < 0)) ? 1 : -1, mcp, scl, checkScaleNonZero(preferredScale)); 5064 } else { 5065 // abs(scaledX) < abs(ys) 5066 long scaledXs; 5067 if ((scaledXs = longMultiplyPowerTen(scaledX, mcp)) == INFLATED) { 5068 quotient = null; 5069 if(mcp<LONG_TEN_POWERS_TABLE.length) { 5070 quotient = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[mcp], scaledX, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5071 } 5072 if(quotient==null) { 5073 BigInteger rb = bigMultiplyPowerTen(scaledX,mcp); 5074 quotient = divideAndRound(rb, ys, 5075 scl, roundingMode, checkScaleNonZero(preferredScale)); 5076 } 5077 } else { 5078 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5079 } 5080 } 5081 } 5082 // doRound, here, only affects 1000000000 case. 5083 return doRound(quotient,mc); 5084 } 5085 5086 /** 5087 * Returns a {@code BigDecimal} whose value is {@code (xs / 5088 * ys)}, with rounding according to the context settings. 5089 */ 5090 private static BigDecimal divide(final long xs, int xscale, final long ys, int yscale, long preferredScale, MathContext mc) { 5091 int mcp = mc.precision; 5092 if(xscale <= yscale && yscale < 18 && mcp<18) { 5093 return divideSmallFastPath(xs, xscale, ys, yscale, preferredScale, mc); 5094 } 5095 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) 5096 yscale -= 1; // [that is, divisor *= 10] 5097 } 5098 int roundingMode = mc.roundingMode.oldMode; 5099 // In order to find out whether the divide generates the exact result, 5100 // we avoid calling the above divide method. 'quotient' holds the 5101 // return BigDecimal object whose scale will be set to 'scl'. 5102 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5103 BigDecimal quotient; 5104 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { 5105 int raise = checkScaleNonZero((long) mcp + yscale - xscale); 5106 long scaledXs; 5107 if ((scaledXs = longMultiplyPowerTen(xs, raise)) == INFLATED) { 5108 BigInteger rb = bigMultiplyPowerTen(xs,raise); 5109 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5110 } else { 5111 quotient = divideAndRound(scaledXs, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5112 } 5113 } else { 5114 int newScale = checkScaleNonZero((long) xscale - mcp); 5115 // assert newScale >= yscale 5116 if (newScale == yscale) { // easy case 5117 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); 5118 } else { 5119 int raise = checkScaleNonZero((long) newScale - yscale); 5120 long scaledYs; 5121 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { 5122 BigInteger rb = bigMultiplyPowerTen(ys,raise); 5123 quotient = divideAndRound(BigInteger.valueOf(xs), 5124 rb, scl, roundingMode,checkScaleNonZero(preferredScale)); 5125 } else { 5126 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); 5127 } 5128 } 5129 } 5130 // doRound, here, only affects 1000000000 case. 5131 return doRound(quotient,mc); 5132 } 5133 5134 /** 5135 * Returns a {@code BigDecimal} whose value is {@code (xs / 5136 * ys)}, with rounding according to the context settings. 5137 */ 5138 private static BigDecimal divide(BigInteger xs, int xscale, long ys, int yscale, long preferredScale, MathContext mc) { 5139 // Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5140 if ((-compareMagnitudeNormalized(ys, yscale, xs, xscale)) > 0) {// satisfy constraint (b) 5141 yscale -= 1; // [that is, divisor *= 10] 5142 } 5143 int mcp = mc.precision; 5144 int roundingMode = mc.roundingMode.oldMode; 5145 5146 // In order to find out whether the divide generates the exact result, 5147 // we avoid calling the above divide method. 'quotient' holds the 5148 // return BigDecimal object whose scale will be set to 'scl'. 5149 BigDecimal quotient; 5150 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5151 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { 5152 int raise = checkScaleNonZero((long) mcp + yscale - xscale); 5153 BigInteger rb = bigMultiplyPowerTen(xs,raise); 5154 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5155 } else { 5156 int newScale = checkScaleNonZero((long) xscale - mcp); 5157 // assert newScale >= yscale 5158 if (newScale == yscale) { // easy case 5159 quotient = divideAndRound(xs, ys, scl, roundingMode,checkScaleNonZero(preferredScale)); 5160 } else { 5161 int raise = checkScaleNonZero((long) newScale - yscale); 5162 long scaledYs; 5163 if ((scaledYs = longMultiplyPowerTen(ys, raise)) == INFLATED) { 5164 BigInteger rb = bigMultiplyPowerTen(ys,raise); 5165 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale)); 5166 } else { 5167 quotient = divideAndRound(xs, scaledYs, scl, roundingMode,checkScaleNonZero(preferredScale)); 5168 } 5169 } 5170 } 5171 // doRound, here, only affects 1000000000 case. 5172 return doRound(quotient, mc); 5173 } 5174 5175 /** 5176 * Returns a {@code BigDecimal} whose value is {@code (xs / 5177 * ys)}, with rounding according to the context settings. 5178 */ 5179 private static BigDecimal divide(long xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) { 5180 // Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5181 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) 5182 yscale -= 1; // [that is, divisor *= 10] 5183 } 5184 int mcp = mc.precision; 5185 int roundingMode = mc.roundingMode.oldMode; 5186 5187 // In order to find out whether the divide generates the exact result, 5188 // we avoid calling the above divide method. 'quotient' holds the 5189 // return BigDecimal object whose scale will be set to 'scl'. 5190 BigDecimal quotient; 5191 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5192 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { 5193 int raise = checkScaleNonZero((long) mcp + yscale - xscale); 5194 BigInteger rb = bigMultiplyPowerTen(xs,raise); 5195 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5196 } else { 5197 int newScale = checkScaleNonZero((long) xscale - mcp); 5198 int raise = checkScaleNonZero((long) newScale - yscale); 5199 BigInteger rb = bigMultiplyPowerTen(ys,raise); 5200 quotient = divideAndRound(BigInteger.valueOf(xs), rb, scl, roundingMode,checkScaleNonZero(preferredScale)); 5201 } 5202 // doRound, here, only affects 1000000000 case. 5203 return doRound(quotient, mc); 5204 } 5205 5206 /** 5207 * Returns a {@code BigDecimal} whose value is {@code (xs / 5208 * ys)}, with rounding according to the context settings. 5209 */ 5210 private static BigDecimal divide(BigInteger xs, int xscale, BigInteger ys, int yscale, long preferredScale, MathContext mc) { 5211 // Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5212 if (compareMagnitudeNormalized(xs, xscale, ys, yscale) > 0) {// satisfy constraint (b) 5213 yscale -= 1; // [that is, divisor *= 10] 5214 } 5215 int mcp = mc.precision; 5216 int roundingMode = mc.roundingMode.oldMode; 5217 5218 // In order to find out whether the divide generates the exact result, 5219 // we avoid calling the above divide method. 'quotient' holds the 5220 // return BigDecimal object whose scale will be set to 'scl'. 5221 BigDecimal quotient; 5222 int scl = checkScaleNonZero(preferredScale + yscale - xscale + mcp); 5223 if (checkScaleNonZero((long) mcp + yscale - xscale) > 0) { 5224 int raise = checkScaleNonZero((long) mcp + yscale - xscale); 5225 BigInteger rb = bigMultiplyPowerTen(xs,raise); 5226 quotient = divideAndRound(rb, ys, scl, roundingMode, checkScaleNonZero(preferredScale)); 5227 } else { 5228 int newScale = checkScaleNonZero((long) xscale - mcp); 5229 int raise = checkScaleNonZero((long) newScale - yscale); 5230 BigInteger rb = bigMultiplyPowerTen(ys,raise); 5231 quotient = divideAndRound(xs, rb, scl, roundingMode,checkScaleNonZero(preferredScale)); 5232 } 5233 // doRound, here, only affects 1000000000 case. 5234 return doRound(quotient, mc); 5235 } 5236 5237 /* 5238 * performs divideAndRound for (dividend0*dividend1, divisor) 5239 * returns null if quotient can't fit into long value; 5240 */ 5241 private static BigDecimal multiplyDivideAndRound(long dividend0, long dividend1, long divisor, int scale, int roundingMode, 5242 int preferredScale) { 5243 int qsign = Long.signum(dividend0)*Long.signum(dividend1)*Long.signum(divisor); 5244 dividend0 = Math.abs(dividend0); 5245 dividend1 = Math.abs(dividend1); 5246 divisor = Math.abs(divisor); 5247 // multiply dividend0 * dividend1 5248 long d0_hi = dividend0 >>> 32; 5249 long d0_lo = dividend0 & LONG_MASK; 5250 long d1_hi = dividend1 >>> 32; 5251 long d1_lo = dividend1 & LONG_MASK; 5252 long product = d0_lo * d1_lo; 5253 long d0 = product & LONG_MASK; 5254 long d1 = product >>> 32; 5255 product = d0_hi * d1_lo + d1; 5256 d1 = product & LONG_MASK; 5257 long d2 = product >>> 32; 5258 product = d0_lo * d1_hi + d1; 5259 d1 = product & LONG_MASK; 5260 d2 += product >>> 32; 5261 long d3 = d2>>>32; 5262 d2 &= LONG_MASK; 5263 product = d0_hi*d1_hi + d2; 5264 d2 = product & LONG_MASK; 5265 d3 = ((product>>>32) + d3) & LONG_MASK; 5266 final long dividendHi = make64(d3,d2); 5267 final long dividendLo = make64(d1,d0); 5268 // divide 5269 return divideAndRound128(dividendHi, dividendLo, divisor, qsign, scale, roundingMode, preferredScale); 5270 } 5271 5272 private static final long DIV_NUM_BASE = (1L<<32); // Number base (32 bits). 5273 5274 /* 5275 * divideAndRound 128-bit value by long divisor. 5276 * returns null if quotient can't fit into long value; 5277 * Specialized version of Knuth's division 5278 */ 5279 private static BigDecimal divideAndRound128(final long dividendHi, final long dividendLo, long divisor, int sign, 5280 int scale, int roundingMode, int preferredScale) { 5281 if (dividendHi >= divisor) { 5282 return null; 5283 } 5284 5285 final int shift = Long.numberOfLeadingZeros(divisor); 5286 divisor <<= shift; 5287 5288 final long v1 = divisor >>> 32; 5289 final long v0 = divisor & LONG_MASK; 5290 5291 long tmp = dividendLo << shift; 5292 long u1 = tmp >>> 32; 5293 long u0 = tmp & LONG_MASK; 5294 5295 tmp = (dividendHi << shift) | (dividendLo >>> 64 - shift); 5296 long u2 = tmp & LONG_MASK; 5297 long q1, r_tmp; 5298 if (v1 == 1) { 5299 q1 = tmp; 5300 r_tmp = 0; 5301 } else if (tmp >= 0) { 5302 q1 = tmp / v1; 5303 r_tmp = tmp - q1 * v1; 5304 } else { 5305 long[] rq = divRemNegativeLong(tmp, v1); 5306 q1 = rq[1]; 5307 r_tmp = rq[0]; 5308 } 5309 5310 while(q1 >= DIV_NUM_BASE || unsignedLongCompare(q1*v0, make64(r_tmp, u1))) { 5311 q1--; 5312 r_tmp += v1; 5313 if (r_tmp >= DIV_NUM_BASE) 5314 break; 5315 } 5316 5317 tmp = mulsub(u2,u1,v1,v0,q1); 5318 u1 = tmp & LONG_MASK; 5319 long q0; 5320 if (v1 == 1) { 5321 q0 = tmp; 5322 r_tmp = 0; 5323 } else if (tmp >= 0) { 5324 q0 = tmp / v1; 5325 r_tmp = tmp - q0 * v1; 5326 } else { 5327 long[] rq = divRemNegativeLong(tmp, v1); 5328 q0 = rq[1]; 5329 r_tmp = rq[0]; 5330 } 5331 5332 while(q0 >= DIV_NUM_BASE || unsignedLongCompare(q0*v0,make64(r_tmp,u0))) { 5333 q0--; 5334 r_tmp += v1; 5335 if (r_tmp >= DIV_NUM_BASE) 5336 break; 5337 } 5338 5339 if((int)q1 < 0) { 5340 // result (which is positive and unsigned here) 5341 // can't fit into long due to sign bit is used for value 5342 MutableBigInteger mq = new MutableBigInteger(new int[]{(int)q1, (int)q0}); 5343 if (roundingMode == ROUND_DOWN && scale == preferredScale) { 5344 return mq.toBigDecimal(sign, scale); 5345 } 5346 long r = mulsub(u1, u0, v1, v0, q0) >>> shift; 5347 if (r != 0) { 5348 if(needIncrement(divisor >>> shift, roundingMode, sign, mq, r)){ 5349 mq.add(MutableBigInteger.ONE); 5350 } 5351 return mq.toBigDecimal(sign, scale); 5352 } else { 5353 if (preferredScale != scale) { 5354 BigInteger intVal = mq.toBigInteger(sign); 5355 return createAndStripZerosToMatchScale(intVal,scale, preferredScale); 5356 } else { 5357 return mq.toBigDecimal(sign, scale); 5358 } 5359 } 5360 } 5361 5362 long q = make64(q1,q0); 5363 q*=sign; 5364 5365 if (roundingMode == ROUND_DOWN && scale == preferredScale) 5366 return valueOf(q, scale); 5367 5368 long r = mulsub(u1, u0, v1, v0, q0) >>> shift; 5369 if (r != 0) { 5370 boolean increment = needIncrement(divisor >>> shift, roundingMode, sign, q, r); 5371 return valueOf((increment ? q + sign : q), scale); 5372 } else { 5373 if (preferredScale != scale) { 5374 return createAndStripZerosToMatchScale(q, scale, preferredScale); 5375 } else { 5376 return valueOf(q, scale); 5377 } 5378 } 5379 } 5380 5381 /* 5382 * calculate divideAndRound for ldividend*10^raise / divisor 5383 * when abs(dividend)==abs(divisor); 5384 */ 5385 private static BigDecimal roundedTenPower(int qsign, int raise, int scale, int preferredScale) { 5386 if (scale > preferredScale) { 5387 int diff = scale - preferredScale; 5388 if(diff < raise) { 5389 return scaledTenPow(raise - diff, qsign, preferredScale); 5390 } else { 5391 return valueOf(qsign,scale-raise); 5392 } 5393 } else { 5394 return scaledTenPow(raise, qsign, scale); 5395 } 5396 } 5397 5398 static BigDecimal scaledTenPow(int n, int sign, int scale) { 5399 if (n < LONG_TEN_POWERS_TABLE.length) 5400 return valueOf(sign*LONG_TEN_POWERS_TABLE[n],scale); 5401 else { 5402 BigInteger unscaledVal = bigTenToThe(n); 5403 if(sign==-1) { 5404 unscaledVal = unscaledVal.negate(); 5405 } 5406 return new BigDecimal(unscaledVal, INFLATED, scale, n+1); 5407 } 5408 } 5409 5410 /** 5411 * Calculate the quotient and remainder of dividing a negative long by 5412 * another long. 5413 * 5414 * @param n the numerator; must be negative 5415 * @param d the denominator; must not be unity 5416 * @return a two-element {@long} array with the remainder and quotient in 5417 * the initial and final elements, respectively 5418 */ 5419 private static long[] divRemNegativeLong(long n, long d) { 5420 assert n < 0 : "Non-negative numerator " + n; 5421 assert d != 1 : "Unity denominator"; 5422 5423 // Approximate the quotient and remainder 5424 long q = (n >>> 1) / (d >>> 1); 5425 long r = n - q * d; 5426 5427 // Correct the approximation 5428 while (r < 0) { 5429 r += d; 5430 q--; 5431 } 5432 while (r >= d) { 5433 r -= d; 5434 q++; 5435 } 5436 5437 // n - q*d == r && 0 <= r < d, hence we're done. 5438 return new long[] {r, q}; 5439 } 5440 5441 private static long make64(long hi, long lo) { 5442 return hi<<32 | lo; 5443 } 5444 5445 private static long mulsub(long u1, long u0, final long v1, final long v0, long q0) { 5446 long tmp = u0 - q0*v0; 5447 return make64(u1 + (tmp>>>32) - q0*v1,tmp & LONG_MASK); 5448 } 5449 5450 private static boolean unsignedLongCompare(long one, long two) { 5451 return (one+Long.MIN_VALUE) > (two+Long.MIN_VALUE); 5452 } 5453 5454 private static boolean unsignedLongCompareEq(long one, long two) { 5455 return (one+Long.MIN_VALUE) >= (two+Long.MIN_VALUE); 5456 } 5457 5458 5459 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5460 private static int compareMagnitudeNormalized(long xs, int xscale, long ys, int yscale) { 5461 // assert xs!=0 && ys!=0 5462 int sdiff = xscale - yscale; 5463 if (sdiff != 0) { 5464 if (sdiff < 0) { 5465 xs = longMultiplyPowerTen(xs, -sdiff); 5466 } else { // sdiff > 0 5467 ys = longMultiplyPowerTen(ys, sdiff); 5468 } 5469 } 5470 if (xs != INFLATED) 5471 return (ys != INFLATED) ? longCompareMagnitude(xs, ys) : -1; 5472 else 5473 return 1; 5474 } 5475 5476 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5477 private static int compareMagnitudeNormalized(long xs, int xscale, BigInteger ys, int yscale) { 5478 // assert "ys can't be represented as long" 5479 if (xs == 0) 5480 return -1; 5481 int sdiff = xscale - yscale; 5482 if (sdiff < 0) { 5483 if (longMultiplyPowerTen(xs, -sdiff) == INFLATED ) { 5484 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys); 5485 } 5486 } 5487 return -1; 5488 } 5489 5490 // Compare Normalize dividend & divisor so that both fall into [0.1, 0.999...] 5491 private static int compareMagnitudeNormalized(BigInteger xs, int xscale, BigInteger ys, int yscale) { 5492 int sdiff = xscale - yscale; 5493 if (sdiff < 0) { 5494 return bigMultiplyPowerTen(xs, -sdiff).compareMagnitude(ys); 5495 } else { // sdiff >= 0 5496 return xs.compareMagnitude(bigMultiplyPowerTen(ys, sdiff)); 5497 } 5498 } 5499 5500 private static long multiply(long x, long y){ 5501 long product = x * y; 5502 long ax = Math.abs(x); 5503 long ay = Math.abs(y); 5504 if (((ax | ay) >>> 31 == 0) || (y == 0) || (product / y == x)){ 5505 return product; 5506 } 5507 return INFLATED; 5508 } 5509 5510 private static BigDecimal multiply(long x, long y, int scale) { 5511 long product = multiply(x, y); 5512 if(product!=INFLATED) { 5513 return valueOf(product,scale); 5514 } 5515 return new BigDecimal(BigInteger.valueOf(x).multiply(y),INFLATED,scale,0); 5516 } 5517 5518 private static BigDecimal multiply(long x, BigInteger y, int scale) { 5519 if(x==0) { 5520 return zeroValueOf(scale); 5521 } 5522 return new BigDecimal(y.multiply(x),INFLATED,scale,0); 5523 } 5524 5525 private static BigDecimal multiply(BigInteger x, BigInteger y, int scale) { 5526 return new BigDecimal(x.multiply(y),INFLATED,scale,0); 5527 } 5528 5529 /** 5530 * Multiplies two long values and rounds according {@code MathContext} 5531 */ 5532 private static BigDecimal multiplyAndRound(long x, long y, int scale, MathContext mc) { 5533 long product = multiply(x, y); 5534 if(product!=INFLATED) { 5535 return doRound(product, scale, mc); 5536 } 5537 // attempt to do it in 128 bits 5538 int rsign = 1; 5539 if(x < 0) { 5540 x = -x; 5541 rsign = -1; 5542 } 5543 if(y < 0) { 5544 y = -y; 5545 rsign *= -1; 5546 } 5547 // multiply dividend0 * dividend1 5548 long m0_hi = x >>> 32; 5549 long m0_lo = x & LONG_MASK; 5550 long m1_hi = y >>> 32; 5551 long m1_lo = y & LONG_MASK; 5552 product = m0_lo * m1_lo; 5553 long m0 = product & LONG_MASK; 5554 long m1 = product >>> 32; 5555 product = m0_hi * m1_lo + m1; 5556 m1 = product & LONG_MASK; 5557 long m2 = product >>> 32; 5558 product = m0_lo * m1_hi + m1; 5559 m1 = product & LONG_MASK; 5560 m2 += product >>> 32; 5561 long m3 = m2>>>32; 5562 m2 &= LONG_MASK; 5563 product = m0_hi*m1_hi + m2; 5564 m2 = product & LONG_MASK; 5565 m3 = ((product>>>32) + m3) & LONG_MASK; 5566 final long mHi = make64(m3,m2); 5567 final long mLo = make64(m1,m0); 5568 BigDecimal res = doRound128(mHi, mLo, rsign, scale, mc); 5569 if(res!=null) { 5570 return res; 5571 } 5572 res = new BigDecimal(BigInteger.valueOf(x).multiply(y*rsign), INFLATED, scale, 0); 5573 return doRound(res,mc); 5574 } 5575 5576 private static BigDecimal multiplyAndRound(long x, BigInteger y, int scale, MathContext mc) { 5577 if(x==0) { 5578 return zeroValueOf(scale); 5579 } 5580 return doRound(y.multiply(x), scale, mc); 5581 } 5582 5583 private static BigDecimal multiplyAndRound(BigInteger x, BigInteger y, int scale, MathContext mc) { 5584 return doRound(x.multiply(y), scale, mc); 5585 } 5586 5587 /** 5588 * rounds 128-bit value according {@code MathContext} 5589 * returns null if result can't be repsented as compact BigDecimal. 5590 */ 5591 private static BigDecimal doRound128(long hi, long lo, int sign, int scale, MathContext mc) { 5592 int mcp = mc.precision; 5593 int drop; 5594 BigDecimal res = null; 5595 if(((drop = precision(hi, lo) - mcp) > 0)&&(drop<LONG_TEN_POWERS_TABLE.length)) { 5596 scale = checkScaleNonZero((long)scale - drop); 5597 res = divideAndRound128(hi, lo, LONG_TEN_POWERS_TABLE[drop], sign, scale, mc.roundingMode.oldMode, scale); 5598 } 5599 if(res!=null) { 5600 return doRound(res,mc); 5601 } 5602 return null; 5603 } 5604 5605 private static final long[][] LONGLONG_TEN_POWERS_TABLE = { 5606 { 0L, 0x8AC7230489E80000L }, //10^19 5607 { 0x5L, 0x6bc75e2d63100000L }, //10^20 5608 { 0x36L, 0x35c9adc5dea00000L }, //10^21 5609 { 0x21eL, 0x19e0c9bab2400000L }, //10^22 5610 { 0x152dL, 0x02c7e14af6800000L }, //10^23 5611 { 0xd3c2L, 0x1bcecceda1000000L }, //10^24 5612 { 0x84595L, 0x161401484a000000L }, //10^25 5613 { 0x52b7d2L, 0xdcc80cd2e4000000L }, //10^26 5614 { 0x33b2e3cL, 0x9fd0803ce8000000L }, //10^27 5615 { 0x204fce5eL, 0x3e25026110000000L }, //10^28 5616 { 0x1431e0faeL, 0x6d7217caa0000000L }, //10^29 5617 { 0xc9f2c9cd0L, 0x4674edea40000000L }, //10^30 5618 { 0x7e37be2022L, 0xc0914b2680000000L }, //10^31 5619 { 0x4ee2d6d415bL, 0x85acef8100000000L }, //10^32 5620 { 0x314dc6448d93L, 0x38c15b0a00000000L }, //10^33 5621 { 0x1ed09bead87c0L, 0x378d8e6400000000L }, //10^34 5622 { 0x13426172c74d82L, 0x2b878fe800000000L }, //10^35 5623 { 0xc097ce7bc90715L, 0xb34b9f1000000000L }, //10^36 5624 { 0x785ee10d5da46d9L, 0x00f436a000000000L }, //10^37 5625 { 0x4b3b4ca85a86c47aL, 0x098a224000000000L }, //10^38 5626 }; 5627 5628 /* 5629 * returns precision of 128-bit value 5630 */ 5631 private static int precision(long hi, long lo){ 5632 if(hi==0) { 5633 if(lo>=0) { 5634 return longDigitLength(lo); 5635 } 5636 return (unsignedLongCompareEq(lo, LONGLONG_TEN_POWERS_TABLE[0][1])) ? 20 : 19; 5637 // 0x8AC7230489E80000L = unsigned 2^19 5638 } 5639 int r = ((128 - Long.numberOfLeadingZeros(hi) + 1) * 1233) >>> 12; 5640 int idx = r-19; 5641 return (idx >= LONGLONG_TEN_POWERS_TABLE.length || longLongCompareMagnitude(hi, lo, 5642 LONGLONG_TEN_POWERS_TABLE[idx][0], LONGLONG_TEN_POWERS_TABLE[idx][1])) ? r : r + 1; 5643 } 5644 5645 /* 5646 * returns true if 128 bit number <hi0,lo0> is less than <hi1,lo1> 5647 * hi0 & hi1 should be non-negative 5648 */ 5649 private static boolean longLongCompareMagnitude(long hi0, long lo0, long hi1, long lo1) { 5650 if(hi0!=hi1) { 5651 return hi0<hi1; 5652 } 5653 return (lo0+Long.MIN_VALUE) <(lo1+Long.MIN_VALUE); 5654 } 5655 5656 private static BigDecimal divide(long dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) { 5657 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { 5658 int newScale = scale + divisorScale; 5659 int raise = newScale - dividendScale; 5660 if(raise<LONG_TEN_POWERS_TABLE.length) { 5661 long xs = dividend; 5662 if ((xs = longMultiplyPowerTen(xs, raise)) != INFLATED) { 5663 return divideAndRound(xs, divisor, scale, roundingMode, scale); 5664 } 5665 BigDecimal q = multiplyDivideAndRound(LONG_TEN_POWERS_TABLE[raise], dividend, divisor, scale, roundingMode, scale); 5666 if(q!=null) { 5667 return q; 5668 } 5669 } 5670 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); 5671 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); 5672 } else { 5673 int newScale = checkScale(divisor,(long)dividendScale - scale); 5674 int raise = newScale - divisorScale; 5675 if(raise<LONG_TEN_POWERS_TABLE.length) { 5676 long ys = divisor; 5677 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) { 5678 return divideAndRound(dividend, ys, scale, roundingMode, scale); 5679 } 5680 } 5681 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); 5682 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale); 5683 } 5684 } 5685 5686 private static BigDecimal divide(BigInteger dividend, int dividendScale, long divisor, int divisorScale, int scale, int roundingMode) { 5687 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { 5688 int newScale = scale + divisorScale; 5689 int raise = newScale - dividendScale; 5690 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); 5691 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); 5692 } else { 5693 int newScale = checkScale(divisor,(long)dividendScale - scale); 5694 int raise = newScale - divisorScale; 5695 if(raise<LONG_TEN_POWERS_TABLE.length) { 5696 long ys = divisor; 5697 if ((ys = longMultiplyPowerTen(ys, raise)) != INFLATED) { 5698 return divideAndRound(dividend, ys, scale, roundingMode, scale); 5699 } 5700 } 5701 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); 5702 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale); 5703 } 5704 } 5705 5706 private static BigDecimal divide(long dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) { 5707 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { 5708 int newScale = scale + divisorScale; 5709 int raise = newScale - dividendScale; 5710 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); 5711 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); 5712 } else { 5713 int newScale = checkScale(divisor,(long)dividendScale - scale); 5714 int raise = newScale - divisorScale; 5715 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); 5716 return divideAndRound(BigInteger.valueOf(dividend), scaledDivisor, scale, roundingMode, scale); 5717 } 5718 } 5719 5720 private static BigDecimal divide(BigInteger dividend, int dividendScale, BigInteger divisor, int divisorScale, int scale, int roundingMode) { 5721 if (checkScale(dividend,(long)scale + divisorScale) > dividendScale) { 5722 int newScale = scale + divisorScale; 5723 int raise = newScale - dividendScale; 5724 BigInteger scaledDividend = bigMultiplyPowerTen(dividend, raise); 5725 return divideAndRound(scaledDividend, divisor, scale, roundingMode, scale); 5726 } else { 5727 int newScale = checkScale(divisor,(long)dividendScale - scale); 5728 int raise = newScale - divisorScale; 5729 BigInteger scaledDivisor = bigMultiplyPowerTen(divisor, raise); 5730 return divideAndRound(dividend, scaledDivisor, scale, roundingMode, scale); 5731 } 5732 } 5733 5734 }