Raymond | dee0849 | 2015-04-02 10:43:13 -0700 | [diff] [blame] | 1 | /* |
| 2 | * Licensed to the Apache Software Foundation (ASF) under one or more |
| 3 | * contributor license agreements. See the NOTICE file distributed with |
| 4 | * this work for additional information regarding copyright ownership. |
| 5 | * The ASF licenses this file to You under the Apache License, Version 2.0 |
| 6 | * (the "License"); you may not use this file except in compliance with |
| 7 | * the License. You may obtain a copy of the License at |
| 8 | * |
| 9 | * http://www.apache.org/licenses/LICENSE-2.0 |
| 10 | * |
| 11 | * Unless required by applicable law or agreed to in writing, software |
| 12 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 13 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 14 | * See the License for the specific language governing permissions and |
| 15 | * limitations under the License. |
| 16 | */ |
| 17 | |
| 18 | package org.apache.commons.math.dfp; |
| 19 | |
| 20 | import java.util.Arrays; |
| 21 | |
| 22 | import org.apache.commons.math.FieldElement; |
| 23 | |
| 24 | /** |
| 25 | * Decimal floating point library for Java |
| 26 | * |
| 27 | * <p>Another floating point class. This one is built using radix 10000 |
| 28 | * which is 10<sup>4</sup>, so its almost decimal.</p> |
| 29 | * |
| 30 | * <p>The design goals here are: |
| 31 | * <ol> |
| 32 | * <li>Decimal math, or close to it</li> |
| 33 | * <li>Settable precision (but no mix between numbers using different settings)</li> |
| 34 | * <li>Portability. Code should be keep as portable as possible.</li> |
| 35 | * <li>Performance</li> |
| 36 | * <li>Accuracy - Results should always be +/- 1 ULP for basic |
| 37 | * algebraic operation</li> |
| 38 | * <li>Comply with IEEE 854-1987 as much as possible. |
| 39 | * (See IEEE 854-1987 notes below)</li> |
| 40 | * </ol></p> |
| 41 | * |
| 42 | * <p>Trade offs: |
| 43 | * <ol> |
| 44 | * <li>Memory foot print. I'm using more memory than necessary to |
| 45 | * represent numbers to get better performance.</li> |
| 46 | * <li>Digits are bigger, so rounding is a greater loss. So, if you |
| 47 | * really need 12 decimal digits, better use 4 base 10000 digits |
| 48 | * there can be one partially filled.</li> |
| 49 | * </ol></p> |
| 50 | * |
| 51 | * <p>Numbers are represented in the following form: |
| 52 | * <pre> |
| 53 | * n = sign × mant × (radix)<sup>exp</sup>;</p> |
| 54 | * </pre> |
| 55 | * where sign is ±1, mantissa represents a fractional number between |
| 56 | * zero and one. mant[0] is the least significant digit. |
| 57 | * exp is in the range of -32767 to 32768</p> |
| 58 | * |
| 59 | * <p>IEEE 854-1987 Notes and differences</p> |
| 60 | * |
| 61 | * <p>IEEE 854 requires the radix to be either 2 or 10. The radix here is |
| 62 | * 10000, so that requirement is not met, but it is possible that a |
| 63 | * subclassed can be made to make it behave as a radix 10 |
| 64 | * number. It is my opinion that if it looks and behaves as a radix |
| 65 | * 10 number then it is one and that requirement would be met.</p> |
| 66 | * |
| 67 | * <p>The radix of 10000 was chosen because it should be faster to operate |
| 68 | * on 4 decimal digits at once instead of one at a time. Radix 10 behavior |
| 69 | * can be realized by add an additional rounding step to ensure that |
| 70 | * the number of decimal digits represented is constant.</p> |
| 71 | * |
| 72 | * <p>The IEEE standard specifically leaves out internal data encoding, |
| 73 | * so it is reasonable to conclude that such a subclass of this radix |
| 74 | * 10000 system is merely an encoding of a radix 10 system.</p> |
| 75 | * |
| 76 | * <p>IEEE 854 also specifies the existence of "sub-normal" numbers. This |
| 77 | * class does not contain any such entities. The most significant radix |
| 78 | * 10000 digit is always non-zero. Instead, we support "gradual underflow" |
| 79 | * by raising the underflow flag for numbers less with exponent less than |
| 80 | * expMin, but don't flush to zero until the exponent reaches MIN_EXP-digits. |
| 81 | * Thus the smallest number we can represent would be: |
| 82 | * 1E(-(MIN_EXP-digits-1)*4), eg, for digits=5, MIN_EXP=-32767, that would |
| 83 | * be 1e-131092.</p> |
| 84 | * |
| 85 | * <p>IEEE 854 defines that the implied radix point lies just to the right |
| 86 | * of the most significant digit and to the left of the remaining digits. |
| 87 | * This implementation puts the implied radix point to the left of all |
| 88 | * digits including the most significant one. The most significant digit |
| 89 | * here is the one just to the right of the radix point. This is a fine |
| 90 | * detail and is really only a matter of definition. Any side effects of |
| 91 | * this can be rendered invisible by a subclass.</p> |
| 92 | * @see DfpField |
| 93 | * @version $Revision: 1003889 $ $Date: 2010-10-02 23:11:55 +0200 (sam. 02 oct. 2010) $ |
| 94 | * @since 2.2 |
| 95 | */ |
| 96 | public class Dfp implements FieldElement<Dfp> { |
| 97 | |
| 98 | /** The radix, or base of this system. Set to 10000 */ |
| 99 | public static final int RADIX = 10000; |
| 100 | |
| 101 | /** The minimum exponent before underflow is signaled. Flush to zero |
| 102 | * occurs at minExp-DIGITS */ |
| 103 | public static final int MIN_EXP = -32767; |
| 104 | |
| 105 | /** The maximum exponent before overflow is signaled and results flushed |
| 106 | * to infinity */ |
| 107 | public static final int MAX_EXP = 32768; |
| 108 | |
| 109 | /** The amount under/overflows are scaled by before going to trap handler */ |
| 110 | public static final int ERR_SCALE = 32760; |
| 111 | |
| 112 | /** Indicator value for normal finite numbers. */ |
| 113 | public static final byte FINITE = 0; |
| 114 | |
| 115 | /** Indicator value for Infinity. */ |
| 116 | public static final byte INFINITE = 1; |
| 117 | |
| 118 | /** Indicator value for signaling NaN. */ |
| 119 | public static final byte SNAN = 2; |
| 120 | |
| 121 | /** Indicator value for quiet NaN. */ |
| 122 | public static final byte QNAN = 3; |
| 123 | |
| 124 | /** String for NaN representation. */ |
| 125 | private static final String NAN_STRING = "NaN"; |
| 126 | |
| 127 | /** String for positive infinity representation. */ |
| 128 | private static final String POS_INFINITY_STRING = "Infinity"; |
| 129 | |
| 130 | /** String for negative infinity representation. */ |
| 131 | private static final String NEG_INFINITY_STRING = "-Infinity"; |
| 132 | |
| 133 | /** Name for traps triggered by addition. */ |
| 134 | private static final String ADD_TRAP = "add"; |
| 135 | |
| 136 | /** Name for traps triggered by multiplication. */ |
| 137 | private static final String MULTIPLY_TRAP = "multiply"; |
| 138 | |
| 139 | /** Name for traps triggered by division. */ |
| 140 | private static final String DIVIDE_TRAP = "divide"; |
| 141 | |
| 142 | /** Name for traps triggered by square root. */ |
| 143 | private static final String SQRT_TRAP = "sqrt"; |
| 144 | |
| 145 | /** Name for traps triggered by alignment. */ |
| 146 | private static final String ALIGN_TRAP = "align"; |
| 147 | |
| 148 | /** Name for traps triggered by truncation. */ |
| 149 | private static final String TRUNC_TRAP = "trunc"; |
| 150 | |
| 151 | /** Name for traps triggered by nextAfter. */ |
| 152 | private static final String NEXT_AFTER_TRAP = "nextAfter"; |
| 153 | |
| 154 | /** Name for traps triggered by lessThan. */ |
| 155 | private static final String LESS_THAN_TRAP = "lessThan"; |
| 156 | |
| 157 | /** Name for traps triggered by greaterThan. */ |
| 158 | private static final String GREATER_THAN_TRAP = "greaterThan"; |
| 159 | |
| 160 | /** Name for traps triggered by newInstance. */ |
| 161 | private static final String NEW_INSTANCE_TRAP = "newInstance"; |
| 162 | |
| 163 | /** Mantissa. */ |
| 164 | protected int[] mant; |
| 165 | |
| 166 | /** Sign bit: & for positive, -1 for negative. */ |
| 167 | protected byte sign; |
| 168 | |
| 169 | /** Exponent. */ |
| 170 | protected int exp; |
| 171 | |
| 172 | /** Indicator for non-finite / non-number values. */ |
| 173 | protected byte nans; |
| 174 | |
| 175 | /** Factory building similar Dfp's. */ |
| 176 | private final DfpField field; |
| 177 | |
| 178 | /** Makes an instance with a value of zero. |
| 179 | * @param field field to which this instance belongs |
| 180 | */ |
| 181 | protected Dfp(final DfpField field) { |
| 182 | mant = new int[field.getRadixDigits()]; |
| 183 | sign = 1; |
| 184 | exp = 0; |
| 185 | nans = FINITE; |
| 186 | this.field = field; |
| 187 | } |
| 188 | |
| 189 | /** Create an instance from a byte value. |
| 190 | * @param field field to which this instance belongs |
| 191 | * @param x value to convert to an instance |
| 192 | */ |
| 193 | protected Dfp(final DfpField field, byte x) { |
| 194 | this(field, (long) x); |
| 195 | } |
| 196 | |
| 197 | /** Create an instance from an int value. |
| 198 | * @param field field to which this instance belongs |
| 199 | * @param x value to convert to an instance |
| 200 | */ |
| 201 | protected Dfp(final DfpField field, int x) { |
| 202 | this(field, (long) x); |
| 203 | } |
| 204 | |
| 205 | /** Create an instance from a long value. |
| 206 | * @param field field to which this instance belongs |
| 207 | * @param x value to convert to an instance |
| 208 | */ |
| 209 | protected Dfp(final DfpField field, long x) { |
| 210 | |
| 211 | // initialize as if 0 |
| 212 | mant = new int[field.getRadixDigits()]; |
| 213 | nans = FINITE; |
| 214 | this.field = field; |
| 215 | |
| 216 | boolean isLongMin = false; |
| 217 | if (x == Long.MIN_VALUE) { |
| 218 | // special case for Long.MIN_VALUE (-9223372036854775808) |
| 219 | // we must shift it before taking its absolute value |
| 220 | isLongMin = true; |
| 221 | ++x; |
| 222 | } |
| 223 | |
| 224 | // set the sign |
| 225 | if (x < 0) { |
| 226 | sign = -1; |
| 227 | x = -x; |
| 228 | } else { |
| 229 | sign = 1; |
| 230 | } |
| 231 | |
| 232 | exp = 0; |
| 233 | while (x != 0) { |
| 234 | System.arraycopy(mant, mant.length - exp, mant, mant.length - 1 - exp, exp); |
| 235 | mant[mant.length - 1] = (int) (x % RADIX); |
| 236 | x /= RADIX; |
| 237 | exp++; |
| 238 | } |
| 239 | |
| 240 | if (isLongMin) { |
| 241 | // remove the shift added for Long.MIN_VALUE |
| 242 | // we know in this case that fixing the last digit is sufficient |
| 243 | for (int i = 0; i < mant.length - 1; i++) { |
| 244 | if (mant[i] != 0) { |
| 245 | mant[i]++; |
| 246 | break; |
| 247 | } |
| 248 | } |
| 249 | } |
| 250 | } |
| 251 | |
| 252 | /** Create an instance from a double value. |
| 253 | * @param field field to which this instance belongs |
| 254 | * @param x value to convert to an instance |
| 255 | */ |
| 256 | protected Dfp(final DfpField field, double x) { |
| 257 | |
| 258 | // initialize as if 0 |
| 259 | mant = new int[field.getRadixDigits()]; |
| 260 | sign = 1; |
| 261 | exp = 0; |
| 262 | nans = FINITE; |
| 263 | this.field = field; |
| 264 | |
| 265 | long bits = Double.doubleToLongBits(x); |
| 266 | long mantissa = bits & 0x000fffffffffffffL; |
| 267 | int exponent = (int) ((bits & 0x7ff0000000000000L) >> 52) - 1023; |
| 268 | |
| 269 | if (exponent == -1023) { |
| 270 | // Zero or sub-normal |
| 271 | if (x == 0) { |
| 272 | return; |
| 273 | } |
| 274 | |
| 275 | exponent++; |
| 276 | |
| 277 | // Normalize the subnormal number |
| 278 | while ( (mantissa & 0x0010000000000000L) == 0) { |
| 279 | exponent--; |
| 280 | mantissa <<= 1; |
| 281 | } |
| 282 | mantissa &= 0x000fffffffffffffL; |
| 283 | } |
| 284 | |
| 285 | if (exponent == 1024) { |
| 286 | // infinity or NAN |
| 287 | if (x != x) { |
| 288 | sign = (byte) 1; |
| 289 | nans = QNAN; |
| 290 | } else if (x < 0) { |
| 291 | sign = (byte) -1; |
| 292 | nans = INFINITE; |
| 293 | } else { |
| 294 | sign = (byte) 1; |
| 295 | nans = INFINITE; |
| 296 | } |
| 297 | return; |
| 298 | } |
| 299 | |
| 300 | Dfp xdfp = new Dfp(field, mantissa); |
| 301 | xdfp = xdfp.divide(new Dfp(field, 4503599627370496l)).add(field.getOne()); // Divide by 2^52, then add one |
| 302 | xdfp = xdfp.multiply(DfpMath.pow(field.getTwo(), exponent)); |
| 303 | |
| 304 | if ((bits & 0x8000000000000000L) != 0) { |
| 305 | xdfp = xdfp.negate(); |
| 306 | } |
| 307 | |
| 308 | System.arraycopy(xdfp.mant, 0, mant, 0, mant.length); |
| 309 | sign = xdfp.sign; |
| 310 | exp = xdfp.exp; |
| 311 | nans = xdfp.nans; |
| 312 | |
| 313 | } |
| 314 | |
| 315 | /** Copy constructor. |
| 316 | * @param d instance to copy |
| 317 | */ |
| 318 | public Dfp(final Dfp d) { |
| 319 | mant = d.mant.clone(); |
| 320 | sign = d.sign; |
| 321 | exp = d.exp; |
| 322 | nans = d.nans; |
| 323 | field = d.field; |
| 324 | } |
| 325 | |
| 326 | /** Create an instance from a String representation. |
| 327 | * @param field field to which this instance belongs |
| 328 | * @param s string representation of the instance |
| 329 | */ |
| 330 | protected Dfp(final DfpField field, final String s) { |
| 331 | |
| 332 | // initialize as if 0 |
| 333 | mant = new int[field.getRadixDigits()]; |
| 334 | sign = 1; |
| 335 | exp = 0; |
| 336 | nans = FINITE; |
| 337 | this.field = field; |
| 338 | |
| 339 | boolean decimalFound = false; |
| 340 | final int rsize = 4; // size of radix in decimal digits |
| 341 | final int offset = 4; // Starting offset into Striped |
| 342 | final char[] striped = new char[getRadixDigits() * rsize + offset * 2]; |
| 343 | |
| 344 | // Check some special cases |
| 345 | if (s.equals(POS_INFINITY_STRING)) { |
| 346 | sign = (byte) 1; |
| 347 | nans = INFINITE; |
| 348 | return; |
| 349 | } |
| 350 | |
| 351 | if (s.equals(NEG_INFINITY_STRING)) { |
| 352 | sign = (byte) -1; |
| 353 | nans = INFINITE; |
| 354 | return; |
| 355 | } |
| 356 | |
| 357 | if (s.equals(NAN_STRING)) { |
| 358 | sign = (byte) 1; |
| 359 | nans = QNAN; |
| 360 | return; |
| 361 | } |
| 362 | |
| 363 | // Check for scientific notation |
| 364 | int p = s.indexOf("e"); |
| 365 | if (p == -1) { // try upper case? |
| 366 | p = s.indexOf("E"); |
| 367 | } |
| 368 | |
| 369 | final String fpdecimal; |
| 370 | int sciexp = 0; |
| 371 | if (p != -1) { |
| 372 | // scientific notation |
| 373 | fpdecimal = s.substring(0, p); |
| 374 | String fpexp = s.substring(p+1); |
| 375 | boolean negative = false; |
| 376 | |
| 377 | for (int i=0; i<fpexp.length(); i++) |
| 378 | { |
| 379 | if (fpexp.charAt(i) == '-') |
| 380 | { |
| 381 | negative = true; |
| 382 | continue; |
| 383 | } |
| 384 | if (fpexp.charAt(i) >= '0' && fpexp.charAt(i) <= '9') |
| 385 | sciexp = sciexp * 10 + fpexp.charAt(i) - '0'; |
| 386 | } |
| 387 | |
| 388 | if (negative) { |
| 389 | sciexp = -sciexp; |
| 390 | } |
| 391 | } else { |
| 392 | // normal case |
| 393 | fpdecimal = s; |
| 394 | } |
| 395 | |
| 396 | // If there is a minus sign in the number then it is negative |
| 397 | if (fpdecimal.indexOf("-") != -1) { |
| 398 | sign = -1; |
| 399 | } |
| 400 | |
| 401 | // First off, find all of the leading zeros, trailing zeros, and significant digits |
| 402 | p = 0; |
| 403 | |
| 404 | // Move p to first significant digit |
| 405 | int decimalPos = 0; |
| 406 | for (;;) { |
| 407 | if (fpdecimal.charAt(p) >= '1' && fpdecimal.charAt(p) <= '9') { |
| 408 | break; |
| 409 | } |
| 410 | |
| 411 | if (decimalFound && fpdecimal.charAt(p) == '0') { |
| 412 | decimalPos--; |
| 413 | } |
| 414 | |
| 415 | if (fpdecimal.charAt(p) == '.') { |
| 416 | decimalFound = true; |
| 417 | } |
| 418 | |
| 419 | p++; |
| 420 | |
| 421 | if (p == fpdecimal.length()) { |
| 422 | break; |
| 423 | } |
| 424 | } |
| 425 | |
| 426 | // Copy the string onto Stripped |
| 427 | int q = offset; |
| 428 | striped[0] = '0'; |
| 429 | striped[1] = '0'; |
| 430 | striped[2] = '0'; |
| 431 | striped[3] = '0'; |
| 432 | int significantDigits=0; |
| 433 | for(;;) { |
| 434 | if (p == (fpdecimal.length())) { |
| 435 | break; |
| 436 | } |
| 437 | |
| 438 | // Don't want to run pass the end of the array |
| 439 | if (q == mant.length*rsize+offset+1) { |
| 440 | break; |
| 441 | } |
| 442 | |
| 443 | if (fpdecimal.charAt(p) == '.') { |
| 444 | decimalFound = true; |
| 445 | decimalPos = significantDigits; |
| 446 | p++; |
| 447 | continue; |
| 448 | } |
| 449 | |
| 450 | if (fpdecimal.charAt(p) < '0' || fpdecimal.charAt(p) > '9') { |
| 451 | p++; |
| 452 | continue; |
| 453 | } |
| 454 | |
| 455 | striped[q] = fpdecimal.charAt(p); |
| 456 | q++; |
| 457 | p++; |
| 458 | significantDigits++; |
| 459 | } |
| 460 | |
| 461 | |
| 462 | // If the decimal point has been found then get rid of trailing zeros. |
| 463 | if (decimalFound && q != offset) { |
| 464 | for (;;) { |
| 465 | q--; |
| 466 | if (q == offset) { |
| 467 | break; |
| 468 | } |
| 469 | if (striped[q] == '0') { |
| 470 | significantDigits--; |
| 471 | } else { |
| 472 | break; |
| 473 | } |
| 474 | } |
| 475 | } |
| 476 | |
| 477 | // special case of numbers like "0.00000" |
| 478 | if (decimalFound && significantDigits == 0) { |
| 479 | decimalPos = 0; |
| 480 | } |
| 481 | |
| 482 | // Implicit decimal point at end of number if not present |
| 483 | if (!decimalFound) { |
| 484 | decimalPos = q-offset; |
| 485 | } |
| 486 | |
| 487 | // Find the number of significant trailing zeros |
| 488 | q = offset; // set q to point to first sig digit |
| 489 | p = significantDigits-1+offset; |
| 490 | |
| 491 | int trailingZeros = 0; |
| 492 | while (p > q) { |
| 493 | if (striped[p] != '0') { |
| 494 | break; |
| 495 | } |
| 496 | trailingZeros++; |
| 497 | p--; |
| 498 | } |
| 499 | |
| 500 | // Make sure the decimal is on a mod 10000 boundary |
| 501 | int i = ((rsize * 100) - decimalPos - sciexp % rsize) % rsize; |
| 502 | q -= i; |
| 503 | decimalPos += i; |
| 504 | |
| 505 | // Make the mantissa length right by adding zeros at the end if necessary |
| 506 | while ((p - q) < (mant.length * rsize)) { |
| 507 | for (i = 0; i < rsize; i++) { |
| 508 | striped[++p] = '0'; |
| 509 | } |
| 510 | } |
| 511 | |
| 512 | // Ok, now we know how many trailing zeros there are, |
| 513 | // and where the least significant digit is |
| 514 | for (i = mant.length - 1; i >= 0; i--) { |
| 515 | mant[i] = (striped[q] - '0') * 1000 + |
| 516 | (striped[q+1] - '0') * 100 + |
| 517 | (striped[q+2] - '0') * 10 + |
| 518 | (striped[q+3] - '0'); |
| 519 | q += 4; |
| 520 | } |
| 521 | |
| 522 | |
| 523 | exp = (decimalPos+sciexp) / rsize; |
| 524 | |
| 525 | if (q < striped.length) { |
| 526 | // Is there possible another digit? |
| 527 | round((striped[q] - '0')*1000); |
| 528 | } |
| 529 | |
| 530 | } |
| 531 | |
| 532 | /** Creates an instance with a non-finite value. |
| 533 | * @param field field to which this instance belongs |
| 534 | * @param sign sign of the Dfp to create |
| 535 | * @param nans code of the value, must be one of {@link #INFINITE}, |
| 536 | * {@link #SNAN}, {@link #QNAN} |
| 537 | */ |
| 538 | protected Dfp(final DfpField field, final byte sign, final byte nans) { |
| 539 | this.field = field; |
| 540 | this.mant = new int[field.getRadixDigits()]; |
| 541 | this.sign = sign; |
| 542 | this.exp = 0; |
| 543 | this.nans = nans; |
| 544 | } |
| 545 | |
| 546 | /** Create an instance with a value of 0. |
| 547 | * Use this internally in preference to constructors to facilitate subclasses |
| 548 | * @return a new instance with a value of 0 |
| 549 | */ |
| 550 | public Dfp newInstance() { |
| 551 | return new Dfp(getField()); |
| 552 | } |
| 553 | |
| 554 | /** Create an instance from a byte value. |
| 555 | * @param x value to convert to an instance |
| 556 | * @return a new instance with value x |
| 557 | */ |
| 558 | public Dfp newInstance(final byte x) { |
| 559 | return new Dfp(getField(), x); |
| 560 | } |
| 561 | |
| 562 | /** Create an instance from an int value. |
| 563 | * @param x value to convert to an instance |
| 564 | * @return a new instance with value x |
| 565 | */ |
| 566 | public Dfp newInstance(final int x) { |
| 567 | return new Dfp(getField(), x); |
| 568 | } |
| 569 | |
| 570 | /** Create an instance from a long value. |
| 571 | * @param x value to convert to an instance |
| 572 | * @return a new instance with value x |
| 573 | */ |
| 574 | public Dfp newInstance(final long x) { |
| 575 | return new Dfp(getField(), x); |
| 576 | } |
| 577 | |
| 578 | /** Create an instance from a double value. |
| 579 | * @param x value to convert to an instance |
| 580 | * @return a new instance with value x |
| 581 | */ |
| 582 | public Dfp newInstance(final double x) { |
| 583 | return new Dfp(getField(), x); |
| 584 | } |
| 585 | |
| 586 | /** Create an instance by copying an existing one. |
| 587 | * Use this internally in preference to constructors to facilitate subclasses. |
| 588 | * @param d instance to copy |
| 589 | * @return a new instance with the same value as d |
| 590 | */ |
| 591 | public Dfp newInstance(final Dfp d) { |
| 592 | |
| 593 | // make sure we don't mix number with different precision |
| 594 | if (field.getRadixDigits() != d.field.getRadixDigits()) { |
| 595 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 596 | final Dfp result = newInstance(getZero()); |
| 597 | result.nans = QNAN; |
| 598 | return dotrap(DfpField.FLAG_INVALID, NEW_INSTANCE_TRAP, d, result); |
| 599 | } |
| 600 | |
| 601 | return new Dfp(d); |
| 602 | |
| 603 | } |
| 604 | |
| 605 | /** Create an instance from a String representation. |
| 606 | * Use this internally in preference to constructors to facilitate subclasses. |
| 607 | * @param s string representation of the instance |
| 608 | * @return a new instance parsed from specified string |
| 609 | */ |
| 610 | public Dfp newInstance(final String s) { |
| 611 | return new Dfp(field, s); |
| 612 | } |
| 613 | |
| 614 | /** Creates an instance with a non-finite value. |
| 615 | * @param sig sign of the Dfp to create |
| 616 | * @param code code of the value, must be one of {@link #INFINITE}, |
| 617 | * {@link #SNAN}, {@link #QNAN} |
| 618 | * @return a new instance with a non-finite value |
| 619 | */ |
| 620 | public Dfp newInstance(final byte sig, final byte code) { |
| 621 | return field.newDfp(sig, code); |
| 622 | } |
| 623 | |
| 624 | /** Get the {@link org.apache.commons.math.Field Field} (really a {@link DfpField}) to which the instance belongs. |
| 625 | * <p> |
| 626 | * The field is linked to the number of digits and acts as a factory |
| 627 | * for {@link Dfp} instances. |
| 628 | * </p> |
| 629 | * @return {@link org.apache.commons.math.Field Field} (really a {@link DfpField}) to which the instance belongs |
| 630 | */ |
| 631 | public DfpField getField() { |
| 632 | return field; |
| 633 | } |
| 634 | |
| 635 | /** Get the number of radix digits of the instance. |
| 636 | * @return number of radix digits |
| 637 | */ |
| 638 | public int getRadixDigits() { |
| 639 | return field.getRadixDigits(); |
| 640 | } |
| 641 | |
| 642 | /** Get the constant 0. |
| 643 | * @return a Dfp with value zero |
| 644 | */ |
| 645 | public Dfp getZero() { |
| 646 | return field.getZero(); |
| 647 | } |
| 648 | |
| 649 | /** Get the constant 1. |
| 650 | * @return a Dfp with value one |
| 651 | */ |
| 652 | public Dfp getOne() { |
| 653 | return field.getOne(); |
| 654 | } |
| 655 | |
| 656 | /** Get the constant 2. |
| 657 | * @return a Dfp with value two |
| 658 | */ |
| 659 | public Dfp getTwo() { |
| 660 | return field.getTwo(); |
| 661 | } |
| 662 | |
| 663 | /** Shift the mantissa left, and adjust the exponent to compensate. |
| 664 | */ |
| 665 | protected void shiftLeft() { |
| 666 | for (int i = mant.length - 1; i > 0; i--) { |
| 667 | mant[i] = mant[i-1]; |
| 668 | } |
| 669 | mant[0] = 0; |
| 670 | exp--; |
| 671 | } |
| 672 | |
| 673 | /* Note that shiftRight() does not call round() as that round() itself |
| 674 | uses shiftRight() */ |
| 675 | /** Shift the mantissa right, and adjust the exponent to compensate. |
| 676 | */ |
| 677 | protected void shiftRight() { |
| 678 | for (int i = 0; i < mant.length - 1; i++) { |
| 679 | mant[i] = mant[i+1]; |
| 680 | } |
| 681 | mant[mant.length - 1] = 0; |
| 682 | exp++; |
| 683 | } |
| 684 | |
| 685 | /** Make our exp equal to the supplied one, this may cause rounding. |
| 686 | * Also causes de-normalized numbers. These numbers are generally |
| 687 | * dangerous because most routines assume normalized numbers. |
| 688 | * Align doesn't round, so it will return the last digit destroyed |
| 689 | * by shifting right. |
| 690 | * @param e desired exponent |
| 691 | * @return last digit destroyed by shifting right |
| 692 | */ |
| 693 | protected int align(int e) { |
| 694 | int lostdigit = 0; |
| 695 | boolean inexact = false; |
| 696 | |
| 697 | int diff = exp - e; |
| 698 | |
| 699 | int adiff = diff; |
| 700 | if (adiff < 0) { |
| 701 | adiff = -adiff; |
| 702 | } |
| 703 | |
| 704 | if (diff == 0) { |
| 705 | return 0; |
| 706 | } |
| 707 | |
| 708 | if (adiff > (mant.length + 1)) { |
| 709 | // Special case |
| 710 | Arrays.fill(mant, 0); |
| 711 | exp = e; |
| 712 | |
| 713 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 714 | dotrap(DfpField.FLAG_INEXACT, ALIGN_TRAP, this, this); |
| 715 | |
| 716 | return 0; |
| 717 | } |
| 718 | |
| 719 | for (int i = 0; i < adiff; i++) { |
| 720 | if (diff < 0) { |
| 721 | /* Keep track of loss -- only signal inexact after losing 2 digits. |
| 722 | * the first lost digit is returned to add() and may be incorporated |
| 723 | * into the result. |
| 724 | */ |
| 725 | if (lostdigit != 0) { |
| 726 | inexact = true; |
| 727 | } |
| 728 | |
| 729 | lostdigit = mant[0]; |
| 730 | |
| 731 | shiftRight(); |
| 732 | } else { |
| 733 | shiftLeft(); |
| 734 | } |
| 735 | } |
| 736 | |
| 737 | if (inexact) { |
| 738 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 739 | dotrap(DfpField.FLAG_INEXACT, ALIGN_TRAP, this, this); |
| 740 | } |
| 741 | |
| 742 | return lostdigit; |
| 743 | |
| 744 | } |
| 745 | |
| 746 | /** Check if instance is less than x. |
| 747 | * @param x number to check instance against |
| 748 | * @return true if instance is less than x and neither are NaN, false otherwise |
| 749 | */ |
| 750 | public boolean lessThan(final Dfp x) { |
| 751 | |
| 752 | // make sure we don't mix number with different precision |
| 753 | if (field.getRadixDigits() != x.field.getRadixDigits()) { |
| 754 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 755 | final Dfp result = newInstance(getZero()); |
| 756 | result.nans = QNAN; |
| 757 | dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, x, result); |
| 758 | return false; |
| 759 | } |
| 760 | |
| 761 | /* if a nan is involved, signal invalid and return false */ |
| 762 | if (isNaN() || x.isNaN()) { |
| 763 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 764 | dotrap(DfpField.FLAG_INVALID, LESS_THAN_TRAP, x, newInstance(getZero())); |
| 765 | return false; |
| 766 | } |
| 767 | |
| 768 | return compare(this, x) < 0; |
| 769 | } |
| 770 | |
| 771 | /** Check if instance is greater than x. |
| 772 | * @param x number to check instance against |
| 773 | * @return true if instance is greater than x and neither are NaN, false otherwise |
| 774 | */ |
| 775 | public boolean greaterThan(final Dfp x) { |
| 776 | |
| 777 | // make sure we don't mix number with different precision |
| 778 | if (field.getRadixDigits() != x.field.getRadixDigits()) { |
| 779 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 780 | final Dfp result = newInstance(getZero()); |
| 781 | result.nans = QNAN; |
| 782 | dotrap(DfpField.FLAG_INVALID, GREATER_THAN_TRAP, x, result); |
| 783 | return false; |
| 784 | } |
| 785 | |
| 786 | /* if a nan is involved, signal invalid and return false */ |
| 787 | if (isNaN() || x.isNaN()) { |
| 788 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 789 | dotrap(DfpField.FLAG_INVALID, GREATER_THAN_TRAP, x, newInstance(getZero())); |
| 790 | return false; |
| 791 | } |
| 792 | |
| 793 | return compare(this, x) > 0; |
| 794 | } |
| 795 | |
| 796 | /** Check if instance is infinite. |
| 797 | * @return true if instance is infinite |
| 798 | */ |
| 799 | public boolean isInfinite() { |
| 800 | return nans == INFINITE; |
| 801 | } |
| 802 | |
| 803 | /** Check if instance is not a number. |
| 804 | * @return true if instance is not a number |
| 805 | */ |
| 806 | public boolean isNaN() { |
| 807 | return (nans == QNAN) || (nans == SNAN); |
| 808 | } |
| 809 | |
| 810 | /** Check if instance is equal to x. |
| 811 | * @param other object to check instance against |
| 812 | * @return true if instance is equal to x and neither are NaN, false otherwise |
| 813 | */ |
| 814 | @Override |
| 815 | public boolean equals(final Object other) { |
| 816 | |
| 817 | if (other instanceof Dfp) { |
| 818 | final Dfp x = (Dfp) other; |
| 819 | if (isNaN() || x.isNaN() || field.getRadixDigits() != x.field.getRadixDigits()) { |
| 820 | return false; |
| 821 | } |
| 822 | |
| 823 | return compare(this, x) == 0; |
| 824 | } |
| 825 | |
| 826 | return false; |
| 827 | |
| 828 | } |
| 829 | |
| 830 | /** |
| 831 | * Gets a hashCode for the instance. |
| 832 | * @return a hash code value for this object |
| 833 | */ |
| 834 | @Override |
| 835 | public int hashCode() { |
| 836 | return 17 + (sign << 8) + (nans << 16) + exp + Arrays.hashCode(mant); |
| 837 | } |
| 838 | |
| 839 | /** Check if instance is not equal to x. |
| 840 | * @param x number to check instance against |
| 841 | * @return true if instance is not equal to x and neither are NaN, false otherwise |
| 842 | */ |
| 843 | public boolean unequal(final Dfp x) { |
| 844 | if (isNaN() || x.isNaN() || field.getRadixDigits() != x.field.getRadixDigits()) { |
| 845 | return false; |
| 846 | } |
| 847 | |
| 848 | return greaterThan(x) || lessThan(x); |
| 849 | } |
| 850 | |
| 851 | /** Compare two instances. |
| 852 | * @param a first instance in comparison |
| 853 | * @param b second instance in comparison |
| 854 | * @return -1 if a<b, 1 if a>b and 0 if a==b |
| 855 | * Note this method does not properly handle NaNs or numbers with different precision. |
| 856 | */ |
| 857 | private static int compare(final Dfp a, final Dfp b) { |
| 858 | // Ignore the sign of zero |
| 859 | if (a.mant[a.mant.length - 1] == 0 && b.mant[b.mant.length - 1] == 0 && |
| 860 | a.nans == FINITE && b.nans == FINITE) { |
| 861 | return 0; |
| 862 | } |
| 863 | |
| 864 | if (a.sign != b.sign) { |
| 865 | if (a.sign == -1) { |
| 866 | return -1; |
| 867 | } else { |
| 868 | return 1; |
| 869 | } |
| 870 | } |
| 871 | |
| 872 | // deal with the infinities |
| 873 | if (a.nans == INFINITE && b.nans == FINITE) { |
| 874 | return a.sign; |
| 875 | } |
| 876 | |
| 877 | if (a.nans == FINITE && b.nans == INFINITE) { |
| 878 | return -b.sign; |
| 879 | } |
| 880 | |
| 881 | if (a.nans == INFINITE && b.nans == INFINITE) { |
| 882 | return 0; |
| 883 | } |
| 884 | |
| 885 | // Handle special case when a or b is zero, by ignoring the exponents |
| 886 | if (b.mant[b.mant.length-1] != 0 && a.mant[b.mant.length-1] != 0) { |
| 887 | if (a.exp < b.exp) { |
| 888 | return -a.sign; |
| 889 | } |
| 890 | |
| 891 | if (a.exp > b.exp) { |
| 892 | return a.sign; |
| 893 | } |
| 894 | } |
| 895 | |
| 896 | // compare the mantissas |
| 897 | for (int i = a.mant.length - 1; i >= 0; i--) { |
| 898 | if (a.mant[i] > b.mant[i]) { |
| 899 | return a.sign; |
| 900 | } |
| 901 | |
| 902 | if (a.mant[i] < b.mant[i]) { |
| 903 | return -a.sign; |
| 904 | } |
| 905 | } |
| 906 | |
| 907 | return 0; |
| 908 | |
| 909 | } |
| 910 | |
| 911 | /** Round to nearest integer using the round-half-even method. |
| 912 | * That is round to nearest integer unless both are equidistant. |
| 913 | * In which case round to the even one. |
| 914 | * @return rounded value |
| 915 | */ |
| 916 | public Dfp rint() { |
| 917 | return trunc(DfpField.RoundingMode.ROUND_HALF_EVEN); |
| 918 | } |
| 919 | |
| 920 | /** Round to an integer using the round floor mode. |
| 921 | * That is, round toward -Infinity |
| 922 | * @return rounded value |
| 923 | */ |
| 924 | public Dfp floor() { |
| 925 | return trunc(DfpField.RoundingMode.ROUND_FLOOR); |
| 926 | } |
| 927 | |
| 928 | /** Round to an integer using the round ceil mode. |
| 929 | * That is, round toward +Infinity |
| 930 | * @return rounded value |
| 931 | */ |
| 932 | public Dfp ceil() { |
| 933 | return trunc(DfpField.RoundingMode.ROUND_CEIL); |
| 934 | } |
| 935 | |
| 936 | /** Returns the IEEE remainder. |
| 937 | * @param d divisor |
| 938 | * @return this less n × d, where n is the integer closest to this/d |
| 939 | */ |
| 940 | public Dfp remainder(final Dfp d) { |
| 941 | |
| 942 | final Dfp result = this.subtract(this.divide(d).rint().multiply(d)); |
| 943 | |
| 944 | // IEEE 854-1987 says that if the result is zero, then it carries the sign of this |
| 945 | if (result.mant[mant.length-1] == 0) { |
| 946 | result.sign = sign; |
| 947 | } |
| 948 | |
| 949 | return result; |
| 950 | |
| 951 | } |
| 952 | |
| 953 | /** Does the integer conversions with the specified rounding. |
| 954 | * @param rmode rounding mode to use |
| 955 | * @return truncated value |
| 956 | */ |
| 957 | protected Dfp trunc(final DfpField.RoundingMode rmode) { |
| 958 | boolean changed = false; |
| 959 | |
| 960 | if (isNaN()) { |
| 961 | return newInstance(this); |
| 962 | } |
| 963 | |
| 964 | if (nans == INFINITE) { |
| 965 | return newInstance(this); |
| 966 | } |
| 967 | |
| 968 | if (mant[mant.length-1] == 0) { |
| 969 | // a is zero |
| 970 | return newInstance(this); |
| 971 | } |
| 972 | |
| 973 | /* If the exponent is less than zero then we can certainly |
| 974 | * return zero */ |
| 975 | if (exp < 0) { |
| 976 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 977 | Dfp result = newInstance(getZero()); |
| 978 | result = dotrap(DfpField.FLAG_INEXACT, TRUNC_TRAP, this, result); |
| 979 | return result; |
| 980 | } |
| 981 | |
| 982 | /* If the exponent is greater than or equal to digits, then it |
| 983 | * must already be an integer since there is no precision left |
| 984 | * for any fractional part */ |
| 985 | |
| 986 | if (exp >= mant.length) { |
| 987 | return newInstance(this); |
| 988 | } |
| 989 | |
| 990 | /* General case: create another dfp, result, that contains the |
| 991 | * a with the fractional part lopped off. */ |
| 992 | |
| 993 | Dfp result = newInstance(this); |
| 994 | for (int i = 0; i < mant.length-result.exp; i++) { |
| 995 | changed |= result.mant[i] != 0; |
| 996 | result.mant[i] = 0; |
| 997 | } |
| 998 | |
| 999 | if (changed) { |
| 1000 | switch (rmode) { |
| 1001 | case ROUND_FLOOR: |
| 1002 | if (result.sign == -1) { |
| 1003 | // then we must increment the mantissa by one |
| 1004 | result = result.add(newInstance(-1)); |
| 1005 | } |
| 1006 | break; |
| 1007 | |
| 1008 | case ROUND_CEIL: |
| 1009 | if (result.sign == 1) { |
| 1010 | // then we must increment the mantissa by one |
| 1011 | result = result.add(getOne()); |
| 1012 | } |
| 1013 | break; |
| 1014 | |
| 1015 | case ROUND_HALF_EVEN: |
| 1016 | default: |
| 1017 | final Dfp half = newInstance("0.5"); |
| 1018 | Dfp a = subtract(result); // difference between this and result |
| 1019 | a.sign = 1; // force positive (take abs) |
| 1020 | if (a.greaterThan(half)) { |
| 1021 | a = newInstance(getOne()); |
| 1022 | a.sign = sign; |
| 1023 | result = result.add(a); |
| 1024 | } |
| 1025 | |
| 1026 | /** If exactly equal to 1/2 and odd then increment */ |
| 1027 | if (a.equals(half) && result.exp > 0 && (result.mant[mant.length-result.exp]&1) != 0) { |
| 1028 | a = newInstance(getOne()); |
| 1029 | a.sign = sign; |
| 1030 | result = result.add(a); |
| 1031 | } |
| 1032 | break; |
| 1033 | } |
| 1034 | |
| 1035 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); // signal inexact |
| 1036 | result = dotrap(DfpField.FLAG_INEXACT, TRUNC_TRAP, this, result); |
| 1037 | return result; |
| 1038 | } |
| 1039 | |
| 1040 | return result; |
| 1041 | } |
| 1042 | |
| 1043 | /** Convert this to an integer. |
| 1044 | * If greater than 2147483647, it returns 2147483647. If less than -2147483648 it returns -2147483648. |
| 1045 | * @return converted number |
| 1046 | */ |
| 1047 | public int intValue() { |
| 1048 | Dfp rounded; |
| 1049 | int result = 0; |
| 1050 | |
| 1051 | rounded = rint(); |
| 1052 | |
| 1053 | if (rounded.greaterThan(newInstance(2147483647))) { |
| 1054 | return 2147483647; |
| 1055 | } |
| 1056 | |
| 1057 | if (rounded.lessThan(newInstance(-2147483648))) { |
| 1058 | return -2147483648; |
| 1059 | } |
| 1060 | |
| 1061 | for (int i = mant.length - 1; i >= mant.length - rounded.exp; i--) { |
| 1062 | result = result * RADIX + rounded.mant[i]; |
| 1063 | } |
| 1064 | |
| 1065 | if (rounded.sign == -1) { |
| 1066 | result = -result; |
| 1067 | } |
| 1068 | |
| 1069 | return result; |
| 1070 | } |
| 1071 | |
| 1072 | /** Get the exponent of the greatest power of 10000 that is |
| 1073 | * less than or equal to the absolute value of this. I.E. if |
| 1074 | * this is 10<sup>6</sup> then log10K would return 1. |
| 1075 | * @return integer base 10000 logarithm |
| 1076 | */ |
| 1077 | public int log10K() { |
| 1078 | return exp - 1; |
| 1079 | } |
| 1080 | |
| 1081 | /** Get the specified power of 10000. |
| 1082 | * @param e desired power |
| 1083 | * @return 10000<sup>e</sup> |
| 1084 | */ |
| 1085 | public Dfp power10K(final int e) { |
| 1086 | Dfp d = newInstance(getOne()); |
| 1087 | d.exp = e + 1; |
| 1088 | return d; |
| 1089 | } |
| 1090 | |
| 1091 | /** Get the exponent of the greatest power of 10 that is less than or equal to abs(this). |
| 1092 | * @return integer base 10 logarithm |
| 1093 | */ |
| 1094 | public int log10() { |
| 1095 | if (mant[mant.length-1] > 1000) { |
| 1096 | return exp * 4 - 1; |
| 1097 | } |
| 1098 | if (mant[mant.length-1] > 100) { |
| 1099 | return exp * 4 - 2; |
| 1100 | } |
| 1101 | if (mant[mant.length-1] > 10) { |
| 1102 | return exp * 4 - 3; |
| 1103 | } |
| 1104 | return exp * 4 - 4; |
| 1105 | } |
| 1106 | |
| 1107 | /** Return the specified power of 10. |
| 1108 | * @param e desired power |
| 1109 | * @return 10<sup>e</sup> |
| 1110 | */ |
| 1111 | public Dfp power10(final int e) { |
| 1112 | Dfp d = newInstance(getOne()); |
| 1113 | |
| 1114 | if (e >= 0) { |
| 1115 | d.exp = e / 4 + 1; |
| 1116 | } else { |
| 1117 | d.exp = (e + 1) / 4; |
| 1118 | } |
| 1119 | |
| 1120 | switch ((e % 4 + 4) % 4) { |
| 1121 | case 0: |
| 1122 | break; |
| 1123 | case 1: |
| 1124 | d = d.multiply(10); |
| 1125 | break; |
| 1126 | case 2: |
| 1127 | d = d.multiply(100); |
| 1128 | break; |
| 1129 | default: |
| 1130 | d = d.multiply(1000); |
| 1131 | } |
| 1132 | |
| 1133 | return d; |
| 1134 | } |
| 1135 | |
| 1136 | /** Negate the mantissa of this by computing the complement. |
| 1137 | * Leaves the sign bit unchanged, used internally by add. |
| 1138 | * Denormalized numbers are handled properly here. |
| 1139 | * @param extra ??? |
| 1140 | * @return ??? |
| 1141 | */ |
| 1142 | protected int complement(int extra) { |
| 1143 | |
| 1144 | extra = RADIX-extra; |
| 1145 | for (int i = 0; i < mant.length; i++) { |
| 1146 | mant[i] = RADIX-mant[i]-1; |
| 1147 | } |
| 1148 | |
| 1149 | int rh = extra / RADIX; |
| 1150 | extra = extra - rh * RADIX; |
| 1151 | for (int i = 0; i < mant.length; i++) { |
| 1152 | final int r = mant[i] + rh; |
| 1153 | rh = r / RADIX; |
| 1154 | mant[i] = r - rh * RADIX; |
| 1155 | } |
| 1156 | |
| 1157 | return extra; |
| 1158 | } |
| 1159 | |
| 1160 | /** Add x to this. |
| 1161 | * @param x number to add |
| 1162 | * @return sum of this and x |
| 1163 | */ |
| 1164 | public Dfp add(final Dfp x) { |
| 1165 | |
| 1166 | // make sure we don't mix number with different precision |
| 1167 | if (field.getRadixDigits() != x.field.getRadixDigits()) { |
| 1168 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1169 | final Dfp result = newInstance(getZero()); |
| 1170 | result.nans = QNAN; |
| 1171 | return dotrap(DfpField.FLAG_INVALID, ADD_TRAP, x, result); |
| 1172 | } |
| 1173 | |
| 1174 | /* handle special cases */ |
| 1175 | if (nans != FINITE || x.nans != FINITE) { |
| 1176 | if (isNaN()) { |
| 1177 | return this; |
| 1178 | } |
| 1179 | |
| 1180 | if (x.isNaN()) { |
| 1181 | return x; |
| 1182 | } |
| 1183 | |
| 1184 | if (nans == INFINITE && x.nans == FINITE) { |
| 1185 | return this; |
| 1186 | } |
| 1187 | |
| 1188 | if (x.nans == INFINITE && nans == FINITE) { |
| 1189 | return x; |
| 1190 | } |
| 1191 | |
| 1192 | if (x.nans == INFINITE && nans == INFINITE && sign == x.sign) { |
| 1193 | return x; |
| 1194 | } |
| 1195 | |
| 1196 | if (x.nans == INFINITE && nans == INFINITE && sign != x.sign) { |
| 1197 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1198 | Dfp result = newInstance(getZero()); |
| 1199 | result.nans = QNAN; |
| 1200 | result = dotrap(DfpField.FLAG_INVALID, ADD_TRAP, x, result); |
| 1201 | return result; |
| 1202 | } |
| 1203 | } |
| 1204 | |
| 1205 | /* copy this and the arg */ |
| 1206 | Dfp a = newInstance(this); |
| 1207 | Dfp b = newInstance(x); |
| 1208 | |
| 1209 | /* initialize the result object */ |
| 1210 | Dfp result = newInstance(getZero()); |
| 1211 | |
| 1212 | /* Make all numbers positive, but remember their sign */ |
| 1213 | final byte asign = a.sign; |
| 1214 | final byte bsign = b.sign; |
| 1215 | |
| 1216 | a.sign = 1; |
| 1217 | b.sign = 1; |
| 1218 | |
| 1219 | /* The result will be signed like the arg with greatest magnitude */ |
| 1220 | byte rsign = bsign; |
| 1221 | if (compare(a, b) > 0) { |
| 1222 | rsign = asign; |
| 1223 | } |
| 1224 | |
| 1225 | /* Handle special case when a or b is zero, by setting the exponent |
| 1226 | of the zero number equal to the other one. This avoids an alignment |
| 1227 | which would cause catastropic loss of precision */ |
| 1228 | if (b.mant[mant.length-1] == 0) { |
| 1229 | b.exp = a.exp; |
| 1230 | } |
| 1231 | |
| 1232 | if (a.mant[mant.length-1] == 0) { |
| 1233 | a.exp = b.exp; |
| 1234 | } |
| 1235 | |
| 1236 | /* align number with the smaller exponent */ |
| 1237 | int aextradigit = 0; |
| 1238 | int bextradigit = 0; |
| 1239 | if (a.exp < b.exp) { |
| 1240 | aextradigit = a.align(b.exp); |
| 1241 | } else { |
| 1242 | bextradigit = b.align(a.exp); |
| 1243 | } |
| 1244 | |
| 1245 | /* complement the smaller of the two if the signs are different */ |
| 1246 | if (asign != bsign) { |
| 1247 | if (asign == rsign) { |
| 1248 | bextradigit = b.complement(bextradigit); |
| 1249 | } else { |
| 1250 | aextradigit = a.complement(aextradigit); |
| 1251 | } |
| 1252 | } |
| 1253 | |
| 1254 | /* add the mantissas */ |
| 1255 | int rh = 0; /* acts as a carry */ |
| 1256 | for (int i = 0; i < mant.length; i++) { |
| 1257 | final int r = a.mant[i]+b.mant[i]+rh; |
| 1258 | rh = r / RADIX; |
| 1259 | result.mant[i] = r - rh * RADIX; |
| 1260 | } |
| 1261 | result.exp = a.exp; |
| 1262 | result.sign = rsign; |
| 1263 | |
| 1264 | /* handle overflow -- note, when asign!=bsign an overflow is |
| 1265 | * normal and should be ignored. */ |
| 1266 | |
| 1267 | if (rh != 0 && (asign == bsign)) { |
| 1268 | final int lostdigit = result.mant[0]; |
| 1269 | result.shiftRight(); |
| 1270 | result.mant[mant.length-1] = rh; |
| 1271 | final int excp = result.round(lostdigit); |
| 1272 | if (excp != 0) { |
| 1273 | result = dotrap(excp, ADD_TRAP, x, result); |
| 1274 | } |
| 1275 | } |
| 1276 | |
| 1277 | /* normalize the result */ |
| 1278 | for (int i = 0; i < mant.length; i++) { |
| 1279 | if (result.mant[mant.length-1] != 0) { |
| 1280 | break; |
| 1281 | } |
| 1282 | result.shiftLeft(); |
| 1283 | if (i == 0) { |
| 1284 | result.mant[0] = aextradigit+bextradigit; |
| 1285 | aextradigit = 0; |
| 1286 | bextradigit = 0; |
| 1287 | } |
| 1288 | } |
| 1289 | |
| 1290 | /* result is zero if after normalization the most sig. digit is zero */ |
| 1291 | if (result.mant[mant.length-1] == 0) { |
| 1292 | result.exp = 0; |
| 1293 | |
| 1294 | if (asign != bsign) { |
| 1295 | // Unless adding 2 negative zeros, sign is positive |
| 1296 | result.sign = 1; // Per IEEE 854-1987 Section 6.3 |
| 1297 | } |
| 1298 | } |
| 1299 | |
| 1300 | /* Call round to test for over/under flows */ |
| 1301 | final int excp = result.round(aextradigit + bextradigit); |
| 1302 | if (excp != 0) { |
| 1303 | result = dotrap(excp, ADD_TRAP, x, result); |
| 1304 | } |
| 1305 | |
| 1306 | return result; |
| 1307 | } |
| 1308 | |
| 1309 | /** Returns a number that is this number with the sign bit reversed. |
| 1310 | * @return the opposite of this |
| 1311 | */ |
| 1312 | public Dfp negate() { |
| 1313 | Dfp result = newInstance(this); |
| 1314 | result.sign = (byte) - result.sign; |
| 1315 | return result; |
| 1316 | } |
| 1317 | |
| 1318 | /** Subtract x from this. |
| 1319 | * @param x number to subtract |
| 1320 | * @return difference of this and a |
| 1321 | */ |
| 1322 | public Dfp subtract(final Dfp x) { |
| 1323 | return add(x.negate()); |
| 1324 | } |
| 1325 | |
| 1326 | /** Round this given the next digit n using the current rounding mode. |
| 1327 | * @param n ??? |
| 1328 | * @return the IEEE flag if an exception occurred |
| 1329 | */ |
| 1330 | protected int round(int n) { |
| 1331 | boolean inc = false; |
| 1332 | switch (field.getRoundingMode()) { |
| 1333 | case ROUND_DOWN: |
| 1334 | inc = false; |
| 1335 | break; |
| 1336 | |
| 1337 | case ROUND_UP: |
| 1338 | inc = n != 0; // round up if n!=0 |
| 1339 | break; |
| 1340 | |
| 1341 | case ROUND_HALF_UP: |
| 1342 | inc = n >= 5000; // round half up |
| 1343 | break; |
| 1344 | |
| 1345 | case ROUND_HALF_DOWN: |
| 1346 | inc = n > 5000; // round half down |
| 1347 | break; |
| 1348 | |
| 1349 | case ROUND_HALF_EVEN: |
| 1350 | inc = n > 5000 || (n == 5000 && (mant[0] & 1) == 1); // round half-even |
| 1351 | break; |
| 1352 | |
| 1353 | case ROUND_HALF_ODD: |
| 1354 | inc = n > 5000 || (n == 5000 && (mant[0] & 1) == 0); // round half-odd |
| 1355 | break; |
| 1356 | |
| 1357 | case ROUND_CEIL: |
| 1358 | inc = sign == 1 && n != 0; // round ceil |
| 1359 | break; |
| 1360 | |
| 1361 | case ROUND_FLOOR: |
| 1362 | default: |
| 1363 | inc = sign == -1 && n != 0; // round floor |
| 1364 | break; |
| 1365 | } |
| 1366 | |
| 1367 | if (inc) { |
| 1368 | // increment if necessary |
| 1369 | int rh = 1; |
| 1370 | for (int i = 0; i < mant.length; i++) { |
| 1371 | final int r = mant[i] + rh; |
| 1372 | rh = r / RADIX; |
| 1373 | mant[i] = r - rh * RADIX; |
| 1374 | } |
| 1375 | |
| 1376 | if (rh != 0) { |
| 1377 | shiftRight(); |
| 1378 | mant[mant.length-1] = rh; |
| 1379 | } |
| 1380 | } |
| 1381 | |
| 1382 | // check for exceptional cases and raise signals if necessary |
| 1383 | if (exp < MIN_EXP) { |
| 1384 | // Gradual Underflow |
| 1385 | field.setIEEEFlagsBits(DfpField.FLAG_UNDERFLOW); |
| 1386 | return DfpField.FLAG_UNDERFLOW; |
| 1387 | } |
| 1388 | |
| 1389 | if (exp > MAX_EXP) { |
| 1390 | // Overflow |
| 1391 | field.setIEEEFlagsBits(DfpField.FLAG_OVERFLOW); |
| 1392 | return DfpField.FLAG_OVERFLOW; |
| 1393 | } |
| 1394 | |
| 1395 | if (n != 0) { |
| 1396 | // Inexact |
| 1397 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 1398 | return DfpField.FLAG_INEXACT; |
| 1399 | } |
| 1400 | |
| 1401 | return 0; |
| 1402 | |
| 1403 | } |
| 1404 | |
| 1405 | /** Multiply this by x. |
| 1406 | * @param x multiplicand |
| 1407 | * @return product of this and x |
| 1408 | */ |
| 1409 | public Dfp multiply(final Dfp x) { |
| 1410 | |
| 1411 | // make sure we don't mix number with different precision |
| 1412 | if (field.getRadixDigits() != x.field.getRadixDigits()) { |
| 1413 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1414 | final Dfp result = newInstance(getZero()); |
| 1415 | result.nans = QNAN; |
| 1416 | return dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, x, result); |
| 1417 | } |
| 1418 | |
| 1419 | Dfp result = newInstance(getZero()); |
| 1420 | |
| 1421 | /* handle special cases */ |
| 1422 | if (nans != FINITE || x.nans != FINITE) { |
| 1423 | if (isNaN()) { |
| 1424 | return this; |
| 1425 | } |
| 1426 | |
| 1427 | if (x.isNaN()) { |
| 1428 | return x; |
| 1429 | } |
| 1430 | |
| 1431 | if (nans == INFINITE && x.nans == FINITE && x.mant[mant.length-1] != 0) { |
| 1432 | result = newInstance(this); |
| 1433 | result.sign = (byte) (sign * x.sign); |
| 1434 | return result; |
| 1435 | } |
| 1436 | |
| 1437 | if (x.nans == INFINITE && nans == FINITE && mant[mant.length-1] != 0) { |
| 1438 | result = newInstance(x); |
| 1439 | result.sign = (byte) (sign * x.sign); |
| 1440 | return result; |
| 1441 | } |
| 1442 | |
| 1443 | if (x.nans == INFINITE && nans == INFINITE) { |
| 1444 | result = newInstance(this); |
| 1445 | result.sign = (byte) (sign * x.sign); |
| 1446 | return result; |
| 1447 | } |
| 1448 | |
| 1449 | if ( (x.nans == INFINITE && nans == FINITE && mant[mant.length-1] == 0) || |
| 1450 | (nans == INFINITE && x.nans == FINITE && x.mant[mant.length-1] == 0) ) { |
| 1451 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1452 | result = newInstance(getZero()); |
| 1453 | result.nans = QNAN; |
| 1454 | result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, x, result); |
| 1455 | return result; |
| 1456 | } |
| 1457 | } |
| 1458 | |
| 1459 | int[] product = new int[mant.length*2]; // Big enough to hold even the largest result |
| 1460 | |
| 1461 | for (int i = 0; i < mant.length; i++) { |
| 1462 | int rh = 0; // acts as a carry |
| 1463 | for (int j=0; j<mant.length; j++) { |
| 1464 | int r = mant[i] * x.mant[j]; // multiply the 2 digits |
| 1465 | r = r + product[i+j] + rh; // add to the product digit with carry in |
| 1466 | |
| 1467 | rh = r / RADIX; |
| 1468 | product[i+j] = r - rh * RADIX; |
| 1469 | } |
| 1470 | product[i+mant.length] = rh; |
| 1471 | } |
| 1472 | |
| 1473 | // Find the most sig digit |
| 1474 | int md = mant.length * 2 - 1; // default, in case result is zero |
| 1475 | for (int i = mant.length * 2 - 1; i >= 0; i--) { |
| 1476 | if (product[i] != 0) { |
| 1477 | md = i; |
| 1478 | break; |
| 1479 | } |
| 1480 | } |
| 1481 | |
| 1482 | // Copy the digits into the result |
| 1483 | for (int i = 0; i < mant.length; i++) { |
| 1484 | result.mant[mant.length - i - 1] = product[md - i]; |
| 1485 | } |
| 1486 | |
| 1487 | // Fixup the exponent. |
| 1488 | result.exp = exp + x.exp + md - 2 * mant.length + 1; |
| 1489 | result.sign = (byte)((sign == x.sign)?1:-1); |
| 1490 | |
| 1491 | if (result.mant[mant.length-1] == 0) { |
| 1492 | // if result is zero, set exp to zero |
| 1493 | result.exp = 0; |
| 1494 | } |
| 1495 | |
| 1496 | final int excp; |
| 1497 | if (md > (mant.length-1)) { |
| 1498 | excp = result.round(product[md-mant.length]); |
| 1499 | } else { |
| 1500 | excp = result.round(0); // has no effect except to check status |
| 1501 | } |
| 1502 | |
| 1503 | if (excp != 0) { |
| 1504 | result = dotrap(excp, MULTIPLY_TRAP, x, result); |
| 1505 | } |
| 1506 | |
| 1507 | return result; |
| 1508 | |
| 1509 | } |
| 1510 | |
| 1511 | /** Multiply this by a single digit 0<=x<radix. |
| 1512 | * There are speed advantages in this special case |
| 1513 | * @param x multiplicand |
| 1514 | * @return product of this and x |
| 1515 | */ |
| 1516 | public Dfp multiply(final int x) { |
| 1517 | Dfp result = newInstance(this); |
| 1518 | |
| 1519 | /* handle special cases */ |
| 1520 | if (nans != FINITE) { |
| 1521 | if (isNaN()) { |
| 1522 | return this; |
| 1523 | } |
| 1524 | |
| 1525 | if (nans == INFINITE && x != 0) { |
| 1526 | result = newInstance(this); |
| 1527 | return result; |
| 1528 | } |
| 1529 | |
| 1530 | if (nans == INFINITE && x == 0) { |
| 1531 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1532 | result = newInstance(getZero()); |
| 1533 | result.nans = QNAN; |
| 1534 | result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, newInstance(getZero()), result); |
| 1535 | return result; |
| 1536 | } |
| 1537 | } |
| 1538 | |
| 1539 | /* range check x */ |
| 1540 | if (x < 0 || x >= RADIX) { |
| 1541 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1542 | result = newInstance(getZero()); |
| 1543 | result.nans = QNAN; |
| 1544 | result = dotrap(DfpField.FLAG_INVALID, MULTIPLY_TRAP, result, result); |
| 1545 | return result; |
| 1546 | } |
| 1547 | |
| 1548 | int rh = 0; |
| 1549 | for (int i = 0; i < mant.length; i++) { |
| 1550 | final int r = mant[i] * x + rh; |
| 1551 | rh = r / RADIX; |
| 1552 | result.mant[i] = r - rh * RADIX; |
| 1553 | } |
| 1554 | |
| 1555 | int lostdigit = 0; |
| 1556 | if (rh != 0) { |
| 1557 | lostdigit = result.mant[0]; |
| 1558 | result.shiftRight(); |
| 1559 | result.mant[mant.length-1] = rh; |
| 1560 | } |
| 1561 | |
| 1562 | if (result.mant[mant.length-1] == 0) { // if result is zero, set exp to zero |
| 1563 | result.exp = 0; |
| 1564 | } |
| 1565 | |
| 1566 | final int excp = result.round(lostdigit); |
| 1567 | if (excp != 0) { |
| 1568 | result = dotrap(excp, MULTIPLY_TRAP, result, result); |
| 1569 | } |
| 1570 | |
| 1571 | return result; |
| 1572 | } |
| 1573 | |
| 1574 | /** Divide this by divisor. |
| 1575 | * @param divisor divisor |
| 1576 | * @return quotient of this by divisor |
| 1577 | */ |
| 1578 | public Dfp divide(Dfp divisor) { |
| 1579 | int dividend[]; // current status of the dividend |
| 1580 | int quotient[]; // quotient |
| 1581 | int remainder[];// remainder |
| 1582 | int qd; // current quotient digit we're working with |
| 1583 | int nsqd; // number of significant quotient digits we have |
| 1584 | int trial=0; // trial quotient digit |
| 1585 | int minadj; // minimum adjustment |
| 1586 | boolean trialgood; // Flag to indicate a good trail digit |
| 1587 | int md=0; // most sig digit in result |
| 1588 | int excp; // exceptions |
| 1589 | |
| 1590 | // make sure we don't mix number with different precision |
| 1591 | if (field.getRadixDigits() != divisor.field.getRadixDigits()) { |
| 1592 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1593 | final Dfp result = newInstance(getZero()); |
| 1594 | result.nans = QNAN; |
| 1595 | return dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, divisor, result); |
| 1596 | } |
| 1597 | |
| 1598 | Dfp result = newInstance(getZero()); |
| 1599 | |
| 1600 | /* handle special cases */ |
| 1601 | if (nans != FINITE || divisor.nans != FINITE) { |
| 1602 | if (isNaN()) { |
| 1603 | return this; |
| 1604 | } |
| 1605 | |
| 1606 | if (divisor.isNaN()) { |
| 1607 | return divisor; |
| 1608 | } |
| 1609 | |
| 1610 | if (nans == INFINITE && divisor.nans == FINITE) { |
| 1611 | result = newInstance(this); |
| 1612 | result.sign = (byte) (sign * divisor.sign); |
| 1613 | return result; |
| 1614 | } |
| 1615 | |
| 1616 | if (divisor.nans == INFINITE && nans == FINITE) { |
| 1617 | result = newInstance(getZero()); |
| 1618 | result.sign = (byte) (sign * divisor.sign); |
| 1619 | return result; |
| 1620 | } |
| 1621 | |
| 1622 | if (divisor.nans == INFINITE && nans == INFINITE) { |
| 1623 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1624 | result = newInstance(getZero()); |
| 1625 | result.nans = QNAN; |
| 1626 | result = dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, divisor, result); |
| 1627 | return result; |
| 1628 | } |
| 1629 | } |
| 1630 | |
| 1631 | /* Test for divide by zero */ |
| 1632 | if (divisor.mant[mant.length-1] == 0) { |
| 1633 | field.setIEEEFlagsBits(DfpField.FLAG_DIV_ZERO); |
| 1634 | result = newInstance(getZero()); |
| 1635 | result.sign = (byte) (sign * divisor.sign); |
| 1636 | result.nans = INFINITE; |
| 1637 | result = dotrap(DfpField.FLAG_DIV_ZERO, DIVIDE_TRAP, divisor, result); |
| 1638 | return result; |
| 1639 | } |
| 1640 | |
| 1641 | dividend = new int[mant.length+1]; // one extra digit needed |
| 1642 | quotient = new int[mant.length+2]; // two extra digits needed 1 for overflow, 1 for rounding |
| 1643 | remainder = new int[mant.length+1]; // one extra digit needed |
| 1644 | |
| 1645 | /* Initialize our most significant digits to zero */ |
| 1646 | |
| 1647 | dividend[mant.length] = 0; |
| 1648 | quotient[mant.length] = 0; |
| 1649 | quotient[mant.length+1] = 0; |
| 1650 | remainder[mant.length] = 0; |
| 1651 | |
| 1652 | /* copy our mantissa into the dividend, initialize the |
| 1653 | quotient while we are at it */ |
| 1654 | |
| 1655 | for (int i = 0; i < mant.length; i++) { |
| 1656 | dividend[i] = mant[i]; |
| 1657 | quotient[i] = 0; |
| 1658 | remainder[i] = 0; |
| 1659 | } |
| 1660 | |
| 1661 | /* outer loop. Once per quotient digit */ |
| 1662 | nsqd = 0; |
| 1663 | for (qd = mant.length+1; qd >= 0; qd--) { |
| 1664 | /* Determine outer limits of our quotient digit */ |
| 1665 | |
| 1666 | // r = most sig 2 digits of dividend |
| 1667 | final int divMsb = dividend[mant.length]*RADIX+dividend[mant.length-1]; |
| 1668 | int min = divMsb / (divisor.mant[mant.length-1]+1); |
| 1669 | int max = (divMsb + 1) / divisor.mant[mant.length-1]; |
| 1670 | |
| 1671 | trialgood = false; |
| 1672 | while (!trialgood) { |
| 1673 | // try the mean |
| 1674 | trial = (min+max)/2; |
| 1675 | |
| 1676 | /* Multiply by divisor and store as remainder */ |
| 1677 | int rh = 0; |
| 1678 | for (int i = 0; i < mant.length + 1; i++) { |
| 1679 | int dm = (i<mant.length)?divisor.mant[i]:0; |
| 1680 | final int r = (dm * trial) + rh; |
| 1681 | rh = r / RADIX; |
| 1682 | remainder[i] = r - rh * RADIX; |
| 1683 | } |
| 1684 | |
| 1685 | /* subtract the remainder from the dividend */ |
| 1686 | rh = 1; // carry in to aid the subtraction |
| 1687 | for (int i = 0; i < mant.length + 1; i++) { |
| 1688 | final int r = ((RADIX-1) - remainder[i]) + dividend[i] + rh; |
| 1689 | rh = r / RADIX; |
| 1690 | remainder[i] = r - rh * RADIX; |
| 1691 | } |
| 1692 | |
| 1693 | /* Lets analyze what we have here */ |
| 1694 | if (rh == 0) { |
| 1695 | // trial is too big -- negative remainder |
| 1696 | max = trial-1; |
| 1697 | continue; |
| 1698 | } |
| 1699 | |
| 1700 | /* find out how far off the remainder is telling us we are */ |
| 1701 | minadj = (remainder[mant.length] * RADIX)+remainder[mant.length-1]; |
| 1702 | minadj = minadj / (divisor.mant[mant.length-1]+1); |
| 1703 | |
| 1704 | if (minadj >= 2) { |
| 1705 | min = trial+minadj; // update the minimum |
| 1706 | continue; |
| 1707 | } |
| 1708 | |
| 1709 | /* May have a good one here, check more thoroughly. Basically |
| 1710 | its a good one if it is less than the divisor */ |
| 1711 | trialgood = false; // assume false |
| 1712 | for (int i = mant.length - 1; i >= 0; i--) { |
| 1713 | if (divisor.mant[i] > remainder[i]) { |
| 1714 | trialgood = true; |
| 1715 | } |
| 1716 | if (divisor.mant[i] < remainder[i]) { |
| 1717 | break; |
| 1718 | } |
| 1719 | } |
| 1720 | |
| 1721 | if (remainder[mant.length] != 0) { |
| 1722 | trialgood = false; |
| 1723 | } |
| 1724 | |
| 1725 | if (trialgood == false) { |
| 1726 | min = trial+1; |
| 1727 | } |
| 1728 | } |
| 1729 | |
| 1730 | /* Great we have a digit! */ |
| 1731 | quotient[qd] = trial; |
| 1732 | if (trial != 0 || nsqd != 0) { |
| 1733 | nsqd++; |
| 1734 | } |
| 1735 | |
| 1736 | if (field.getRoundingMode() == DfpField.RoundingMode.ROUND_DOWN && nsqd == mant.length) { |
| 1737 | // We have enough for this mode |
| 1738 | break; |
| 1739 | } |
| 1740 | |
| 1741 | if (nsqd > mant.length) { |
| 1742 | // We have enough digits |
| 1743 | break; |
| 1744 | } |
| 1745 | |
| 1746 | /* move the remainder into the dividend while left shifting */ |
| 1747 | dividend[0] = 0; |
| 1748 | for (int i = 0; i < mant.length; i++) { |
| 1749 | dividend[i + 1] = remainder[i]; |
| 1750 | } |
| 1751 | } |
| 1752 | |
| 1753 | /* Find the most sig digit */ |
| 1754 | md = mant.length; // default |
| 1755 | for (int i = mant.length + 1; i >= 0; i--) { |
| 1756 | if (quotient[i] != 0) { |
| 1757 | md = i; |
| 1758 | break; |
| 1759 | } |
| 1760 | } |
| 1761 | |
| 1762 | /* Copy the digits into the result */ |
| 1763 | for (int i=0; i<mant.length; i++) { |
| 1764 | result.mant[mant.length-i-1] = quotient[md-i]; |
| 1765 | } |
| 1766 | |
| 1767 | /* Fixup the exponent. */ |
| 1768 | result.exp = exp - divisor.exp + md - mant.length; |
| 1769 | result.sign = (byte) ((sign == divisor.sign) ? 1 : -1); |
| 1770 | |
| 1771 | if (result.mant[mant.length-1] == 0) { // if result is zero, set exp to zero |
| 1772 | result.exp = 0; |
| 1773 | } |
| 1774 | |
| 1775 | if (md > (mant.length-1)) { |
| 1776 | excp = result.round(quotient[md-mant.length]); |
| 1777 | } else { |
| 1778 | excp = result.round(0); |
| 1779 | } |
| 1780 | |
| 1781 | if (excp != 0) { |
| 1782 | result = dotrap(excp, DIVIDE_TRAP, divisor, result); |
| 1783 | } |
| 1784 | |
| 1785 | return result; |
| 1786 | } |
| 1787 | |
| 1788 | /** Divide by a single digit less than radix. |
| 1789 | * Special case, so there are speed advantages. 0 <= divisor < radix |
| 1790 | * @param divisor divisor |
| 1791 | * @return quotient of this by divisor |
| 1792 | */ |
| 1793 | public Dfp divide(int divisor) { |
| 1794 | |
| 1795 | // Handle special cases |
| 1796 | if (nans != FINITE) { |
| 1797 | if (isNaN()) { |
| 1798 | return this; |
| 1799 | } |
| 1800 | |
| 1801 | if (nans == INFINITE) { |
| 1802 | return newInstance(this); |
| 1803 | } |
| 1804 | } |
| 1805 | |
| 1806 | // Test for divide by zero |
| 1807 | if (divisor == 0) { |
| 1808 | field.setIEEEFlagsBits(DfpField.FLAG_DIV_ZERO); |
| 1809 | Dfp result = newInstance(getZero()); |
| 1810 | result.sign = sign; |
| 1811 | result.nans = INFINITE; |
| 1812 | result = dotrap(DfpField.FLAG_DIV_ZERO, DIVIDE_TRAP, getZero(), result); |
| 1813 | return result; |
| 1814 | } |
| 1815 | |
| 1816 | // range check divisor |
| 1817 | if (divisor < 0 || divisor >= RADIX) { |
| 1818 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1819 | Dfp result = newInstance(getZero()); |
| 1820 | result.nans = QNAN; |
| 1821 | result = dotrap(DfpField.FLAG_INVALID, DIVIDE_TRAP, result, result); |
| 1822 | return result; |
| 1823 | } |
| 1824 | |
| 1825 | Dfp result = newInstance(this); |
| 1826 | |
| 1827 | int rl = 0; |
| 1828 | for (int i = mant.length-1; i >= 0; i--) { |
| 1829 | final int r = rl*RADIX + result.mant[i]; |
| 1830 | final int rh = r / divisor; |
| 1831 | rl = r - rh * divisor; |
| 1832 | result.mant[i] = rh; |
| 1833 | } |
| 1834 | |
| 1835 | if (result.mant[mant.length-1] == 0) { |
| 1836 | // normalize |
| 1837 | result.shiftLeft(); |
| 1838 | final int r = rl * RADIX; // compute the next digit and put it in |
| 1839 | final int rh = r / divisor; |
| 1840 | rl = r - rh * divisor; |
| 1841 | result.mant[0] = rh; |
| 1842 | } |
| 1843 | |
| 1844 | final int excp = result.round(rl * RADIX / divisor); // do the rounding |
| 1845 | if (excp != 0) { |
| 1846 | result = dotrap(excp, DIVIDE_TRAP, result, result); |
| 1847 | } |
| 1848 | |
| 1849 | return result; |
| 1850 | |
| 1851 | } |
| 1852 | |
| 1853 | /** Compute the square root. |
| 1854 | * @return square root of the instance |
| 1855 | */ |
| 1856 | public Dfp sqrt() { |
| 1857 | |
| 1858 | // check for unusual cases |
| 1859 | if (nans == FINITE && mant[mant.length-1] == 0) { |
| 1860 | // if zero |
| 1861 | return newInstance(this); |
| 1862 | } |
| 1863 | |
| 1864 | if (nans != FINITE) { |
| 1865 | if (nans == INFINITE && sign == 1) { |
| 1866 | // if positive infinity |
| 1867 | return newInstance(this); |
| 1868 | } |
| 1869 | |
| 1870 | if (nans == QNAN) { |
| 1871 | return newInstance(this); |
| 1872 | } |
| 1873 | |
| 1874 | if (nans == SNAN) { |
| 1875 | Dfp result; |
| 1876 | |
| 1877 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1878 | result = newInstance(this); |
| 1879 | result = dotrap(DfpField.FLAG_INVALID, SQRT_TRAP, null, result); |
| 1880 | return result; |
| 1881 | } |
| 1882 | } |
| 1883 | |
| 1884 | if (sign == -1) { |
| 1885 | // if negative |
| 1886 | Dfp result; |
| 1887 | |
| 1888 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 1889 | result = newInstance(this); |
| 1890 | result.nans = QNAN; |
| 1891 | result = dotrap(DfpField.FLAG_INVALID, SQRT_TRAP, null, result); |
| 1892 | return result; |
| 1893 | } |
| 1894 | |
| 1895 | Dfp x = newInstance(this); |
| 1896 | |
| 1897 | /* Lets make a reasonable guess as to the size of the square root */ |
| 1898 | if (x.exp < -1 || x.exp > 1) { |
| 1899 | x.exp = this.exp / 2; |
| 1900 | } |
| 1901 | |
| 1902 | /* Coarsely estimate the mantissa */ |
| 1903 | switch (x.mant[mant.length-1] / 2000) { |
| 1904 | case 0: |
| 1905 | x.mant[mant.length-1] = x.mant[mant.length-1]/2+1; |
| 1906 | break; |
| 1907 | case 2: |
| 1908 | x.mant[mant.length-1] = 1500; |
| 1909 | break; |
| 1910 | case 3: |
| 1911 | x.mant[mant.length-1] = 2200; |
| 1912 | break; |
| 1913 | default: |
| 1914 | x.mant[mant.length-1] = 3000; |
| 1915 | } |
| 1916 | |
| 1917 | Dfp dx = newInstance(x); |
| 1918 | |
| 1919 | /* Now that we have the first pass estimate, compute the rest |
| 1920 | by the formula dx = (y - x*x) / (2x); */ |
| 1921 | |
| 1922 | Dfp px = getZero(); |
| 1923 | Dfp ppx = getZero(); |
| 1924 | while (x.unequal(px)) { |
| 1925 | dx = newInstance(x); |
| 1926 | dx.sign = -1; |
| 1927 | dx = dx.add(this.divide(x)); |
| 1928 | dx = dx.divide(2); |
| 1929 | ppx = px; |
| 1930 | px = x; |
| 1931 | x = x.add(dx); |
| 1932 | |
| 1933 | if (x.equals(ppx)) { |
| 1934 | // alternating between two values |
| 1935 | break; |
| 1936 | } |
| 1937 | |
| 1938 | // if dx is zero, break. Note testing the most sig digit |
| 1939 | // is a sufficient test since dx is normalized |
| 1940 | if (dx.mant[mant.length-1] == 0) { |
| 1941 | break; |
| 1942 | } |
| 1943 | } |
| 1944 | |
| 1945 | return x; |
| 1946 | |
| 1947 | } |
| 1948 | |
| 1949 | /** Get a string representation of the instance. |
| 1950 | * @return string representation of the instance |
| 1951 | */ |
| 1952 | @Override |
| 1953 | public String toString() { |
| 1954 | if (nans != FINITE) { |
| 1955 | // if non-finite exceptional cases |
| 1956 | if (nans == INFINITE) { |
| 1957 | return (sign < 0) ? NEG_INFINITY_STRING : POS_INFINITY_STRING; |
| 1958 | } else { |
| 1959 | return NAN_STRING; |
| 1960 | } |
| 1961 | } |
| 1962 | |
| 1963 | if (exp > mant.length || exp < -1) { |
| 1964 | return dfp2sci(); |
| 1965 | } |
| 1966 | |
| 1967 | return dfp2string(); |
| 1968 | |
| 1969 | } |
| 1970 | |
| 1971 | /** Convert an instance to a string using scientific notation. |
| 1972 | * @return string representation of the instance in scientific notation |
| 1973 | */ |
| 1974 | protected String dfp2sci() { |
| 1975 | char rawdigits[] = new char[mant.length * 4]; |
| 1976 | char outputbuffer[] = new char[mant.length * 4 + 20]; |
| 1977 | int p; |
| 1978 | int q; |
| 1979 | int e; |
| 1980 | int ae; |
| 1981 | int shf; |
| 1982 | |
| 1983 | // Get all the digits |
| 1984 | p = 0; |
| 1985 | for (int i = mant.length - 1; i >= 0; i--) { |
| 1986 | rawdigits[p++] = (char) ((mant[i] / 1000) + '0'); |
| 1987 | rawdigits[p++] = (char) (((mant[i] / 100) %10) + '0'); |
| 1988 | rawdigits[p++] = (char) (((mant[i] / 10) % 10) + '0'); |
| 1989 | rawdigits[p++] = (char) (((mant[i]) % 10) + '0'); |
| 1990 | } |
| 1991 | |
| 1992 | // Find the first non-zero one |
| 1993 | for (p = 0; p < rawdigits.length; p++) { |
| 1994 | if (rawdigits[p] != '0') { |
| 1995 | break; |
| 1996 | } |
| 1997 | } |
| 1998 | shf = p; |
| 1999 | |
| 2000 | // Now do the conversion |
| 2001 | q = 0; |
| 2002 | if (sign == -1) { |
| 2003 | outputbuffer[q++] = '-'; |
| 2004 | } |
| 2005 | |
| 2006 | if (p != rawdigits.length) { |
| 2007 | // there are non zero digits... |
| 2008 | outputbuffer[q++] = rawdigits[p++]; |
| 2009 | outputbuffer[q++] = '.'; |
| 2010 | |
| 2011 | while (p<rawdigits.length) { |
| 2012 | outputbuffer[q++] = rawdigits[p++]; |
| 2013 | } |
| 2014 | } else { |
| 2015 | outputbuffer[q++] = '0'; |
| 2016 | outputbuffer[q++] = '.'; |
| 2017 | outputbuffer[q++] = '0'; |
| 2018 | outputbuffer[q++] = 'e'; |
| 2019 | outputbuffer[q++] = '0'; |
| 2020 | return new String(outputbuffer, 0, 5); |
| 2021 | } |
| 2022 | |
| 2023 | outputbuffer[q++] = 'e'; |
| 2024 | |
| 2025 | // Find the msd of the exponent |
| 2026 | |
| 2027 | e = exp * 4 - shf - 1; |
| 2028 | ae = e; |
| 2029 | if (e < 0) { |
| 2030 | ae = -e; |
| 2031 | } |
| 2032 | |
| 2033 | // Find the largest p such that p < e |
| 2034 | for (p = 1000000000; p > ae; p /= 10) { |
| 2035 | // nothing to do |
| 2036 | } |
| 2037 | |
| 2038 | if (e < 0) { |
| 2039 | outputbuffer[q++] = '-'; |
| 2040 | } |
| 2041 | |
| 2042 | while (p > 0) { |
| 2043 | outputbuffer[q++] = (char)(ae / p + '0'); |
| 2044 | ae = ae % p; |
| 2045 | p = p / 10; |
| 2046 | } |
| 2047 | |
| 2048 | return new String(outputbuffer, 0, q); |
| 2049 | |
| 2050 | } |
| 2051 | |
| 2052 | /** Convert an instance to a string using normal notation. |
| 2053 | * @return string representation of the instance in normal notation |
| 2054 | */ |
| 2055 | protected String dfp2string() { |
| 2056 | char buffer[] = new char[mant.length*4 + 20]; |
| 2057 | int p = 1; |
| 2058 | int q; |
| 2059 | int e = exp; |
| 2060 | boolean pointInserted = false; |
| 2061 | |
| 2062 | buffer[0] = ' '; |
| 2063 | |
| 2064 | if (e <= 0) { |
| 2065 | buffer[p++] = '0'; |
| 2066 | buffer[p++] = '.'; |
| 2067 | pointInserted = true; |
| 2068 | } |
| 2069 | |
| 2070 | while (e < 0) { |
| 2071 | buffer[p++] = '0'; |
| 2072 | buffer[p++] = '0'; |
| 2073 | buffer[p++] = '0'; |
| 2074 | buffer[p++] = '0'; |
| 2075 | e++; |
| 2076 | } |
| 2077 | |
| 2078 | for (int i = mant.length - 1; i >= 0; i--) { |
| 2079 | buffer[p++] = (char) ((mant[i] / 1000) + '0'); |
| 2080 | buffer[p++] = (char) (((mant[i] / 100) % 10) + '0'); |
| 2081 | buffer[p++] = (char) (((mant[i] / 10) % 10) + '0'); |
| 2082 | buffer[p++] = (char) (((mant[i]) % 10) + '0'); |
| 2083 | if (--e == 0) { |
| 2084 | buffer[p++] = '.'; |
| 2085 | pointInserted = true; |
| 2086 | } |
| 2087 | } |
| 2088 | |
| 2089 | while (e > 0) { |
| 2090 | buffer[p++] = '0'; |
| 2091 | buffer[p++] = '0'; |
| 2092 | buffer[p++] = '0'; |
| 2093 | buffer[p++] = '0'; |
| 2094 | e--; |
| 2095 | } |
| 2096 | |
| 2097 | if (!pointInserted) { |
| 2098 | // Ensure we have a radix point! |
| 2099 | buffer[p++] = '.'; |
| 2100 | } |
| 2101 | |
| 2102 | // Suppress leading zeros |
| 2103 | q = 1; |
| 2104 | while (buffer[q] == '0') { |
| 2105 | q++; |
| 2106 | } |
| 2107 | if (buffer[q] == '.') { |
| 2108 | q--; |
| 2109 | } |
| 2110 | |
| 2111 | // Suppress trailing zeros |
| 2112 | while (buffer[p-1] == '0') { |
| 2113 | p--; |
| 2114 | } |
| 2115 | |
| 2116 | // Insert sign |
| 2117 | if (sign < 0) { |
| 2118 | buffer[--q] = '-'; |
| 2119 | } |
| 2120 | |
| 2121 | return new String(buffer, q, p - q); |
| 2122 | |
| 2123 | } |
| 2124 | |
| 2125 | /** Raises a trap. This does not set the corresponding flag however. |
| 2126 | * @param type the trap type |
| 2127 | * @param what - name of routine trap occurred in |
| 2128 | * @param oper - input operator to function |
| 2129 | * @param result - the result computed prior to the trap |
| 2130 | * @return The suggested return value from the trap handler |
| 2131 | */ |
| 2132 | public Dfp dotrap(int type, String what, Dfp oper, Dfp result) { |
| 2133 | Dfp def = result; |
| 2134 | |
| 2135 | switch (type) { |
| 2136 | case DfpField.FLAG_INVALID: |
| 2137 | def = newInstance(getZero()); |
| 2138 | def.sign = result.sign; |
| 2139 | def.nans = QNAN; |
| 2140 | break; |
| 2141 | |
| 2142 | case DfpField.FLAG_DIV_ZERO: |
| 2143 | if (nans == FINITE && mant[mant.length-1] != 0) { |
| 2144 | // normal case, we are finite, non-zero |
| 2145 | def = newInstance(getZero()); |
| 2146 | def.sign = (byte)(sign*oper.sign); |
| 2147 | def.nans = INFINITE; |
| 2148 | } |
| 2149 | |
| 2150 | if (nans == FINITE && mant[mant.length-1] == 0) { |
| 2151 | // 0/0 |
| 2152 | def = newInstance(getZero()); |
| 2153 | def.nans = QNAN; |
| 2154 | } |
| 2155 | |
| 2156 | if (nans == INFINITE || nans == QNAN) { |
| 2157 | def = newInstance(getZero()); |
| 2158 | def.nans = QNAN; |
| 2159 | } |
| 2160 | |
| 2161 | if (nans == INFINITE || nans == SNAN) { |
| 2162 | def = newInstance(getZero()); |
| 2163 | def.nans = QNAN; |
| 2164 | } |
| 2165 | break; |
| 2166 | |
| 2167 | case DfpField.FLAG_UNDERFLOW: |
| 2168 | if ( (result.exp+mant.length) < MIN_EXP) { |
| 2169 | def = newInstance(getZero()); |
| 2170 | def.sign = result.sign; |
| 2171 | } else { |
| 2172 | def = newInstance(result); // gradual underflow |
| 2173 | } |
| 2174 | result.exp = result.exp + ERR_SCALE; |
| 2175 | break; |
| 2176 | |
| 2177 | case DfpField.FLAG_OVERFLOW: |
| 2178 | result.exp = result.exp - ERR_SCALE; |
| 2179 | def = newInstance(getZero()); |
| 2180 | def.sign = result.sign; |
| 2181 | def.nans = INFINITE; |
| 2182 | break; |
| 2183 | |
| 2184 | default: def = result; break; |
| 2185 | } |
| 2186 | |
| 2187 | return trap(type, what, oper, def, result); |
| 2188 | |
| 2189 | } |
| 2190 | |
| 2191 | /** Trap handler. Subclasses may override this to provide trap |
| 2192 | * functionality per IEEE 854-1987. |
| 2193 | * |
| 2194 | * @param type The exception type - e.g. FLAG_OVERFLOW |
| 2195 | * @param what The name of the routine we were in e.g. divide() |
| 2196 | * @param oper An operand to this function if any |
| 2197 | * @param def The default return value if trap not enabled |
| 2198 | * @param result The result that is specified to be delivered per |
| 2199 | * IEEE 854, if any |
| 2200 | * @return the value that should be return by the operation triggering the trap |
| 2201 | */ |
| 2202 | protected Dfp trap(int type, String what, Dfp oper, Dfp def, Dfp result) { |
| 2203 | return def; |
| 2204 | } |
| 2205 | |
| 2206 | /** Returns the type - one of FINITE, INFINITE, SNAN, QNAN. |
| 2207 | * @return type of the number |
| 2208 | */ |
| 2209 | public int classify() { |
| 2210 | return nans; |
| 2211 | } |
| 2212 | |
| 2213 | /** Creates an instance that is the same as x except that it has the sign of y. |
| 2214 | * abs(x) = dfp.copysign(x, dfp.one) |
| 2215 | * @param x number to get the value from |
| 2216 | * @param y number to get the sign from |
| 2217 | * @return a number with the value of x and the sign of y |
| 2218 | */ |
| 2219 | public static Dfp copysign(final Dfp x, final Dfp y) { |
| 2220 | Dfp result = x.newInstance(x); |
| 2221 | result.sign = y.sign; |
| 2222 | return result; |
| 2223 | } |
| 2224 | |
| 2225 | /** Returns the next number greater than this one in the direction of x. |
| 2226 | * If this==x then simply returns this. |
| 2227 | * @param x direction where to look at |
| 2228 | * @return closest number next to instance in the direction of x |
| 2229 | */ |
| 2230 | public Dfp nextAfter(final Dfp x) { |
| 2231 | |
| 2232 | // make sure we don't mix number with different precision |
| 2233 | if (field.getRadixDigits() != x.field.getRadixDigits()) { |
| 2234 | field.setIEEEFlagsBits(DfpField.FLAG_INVALID); |
| 2235 | final Dfp result = newInstance(getZero()); |
| 2236 | result.nans = QNAN; |
| 2237 | return dotrap(DfpField.FLAG_INVALID, NEXT_AFTER_TRAP, x, result); |
| 2238 | } |
| 2239 | |
| 2240 | // if this is greater than x |
| 2241 | boolean up = false; |
| 2242 | if (this.lessThan(x)) { |
| 2243 | up = true; |
| 2244 | } |
| 2245 | |
| 2246 | if (compare(this, x) == 0) { |
| 2247 | return newInstance(x); |
| 2248 | } |
| 2249 | |
| 2250 | if (lessThan(getZero())) { |
| 2251 | up = !up; |
| 2252 | } |
| 2253 | |
| 2254 | final Dfp inc; |
| 2255 | Dfp result; |
| 2256 | if (up) { |
| 2257 | inc = newInstance(getOne()); |
| 2258 | inc.exp = this.exp-mant.length+1; |
| 2259 | inc.sign = this.sign; |
| 2260 | |
| 2261 | if (this.equals(getZero())) { |
| 2262 | inc.exp = MIN_EXP-mant.length; |
| 2263 | } |
| 2264 | |
| 2265 | result = add(inc); |
| 2266 | } else { |
| 2267 | inc = newInstance(getOne()); |
| 2268 | inc.exp = this.exp; |
| 2269 | inc.sign = this.sign; |
| 2270 | |
| 2271 | if (this.equals(inc)) { |
| 2272 | inc.exp = this.exp-mant.length; |
| 2273 | } else { |
| 2274 | inc.exp = this.exp-mant.length+1; |
| 2275 | } |
| 2276 | |
| 2277 | if (this.equals(getZero())) { |
| 2278 | inc.exp = MIN_EXP-mant.length; |
| 2279 | } |
| 2280 | |
| 2281 | result = this.subtract(inc); |
| 2282 | } |
| 2283 | |
| 2284 | if (result.classify() == INFINITE && this.classify() != INFINITE) { |
| 2285 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 2286 | result = dotrap(DfpField.FLAG_INEXACT, NEXT_AFTER_TRAP, x, result); |
| 2287 | } |
| 2288 | |
| 2289 | if (result.equals(getZero()) && this.equals(getZero()) == false) { |
| 2290 | field.setIEEEFlagsBits(DfpField.FLAG_INEXACT); |
| 2291 | result = dotrap(DfpField.FLAG_INEXACT, NEXT_AFTER_TRAP, x, result); |
| 2292 | } |
| 2293 | |
| 2294 | return result; |
| 2295 | |
| 2296 | } |
| 2297 | |
| 2298 | /** Convert the instance into a double. |
| 2299 | * @return a double approximating the instance |
| 2300 | * @see #toSplitDouble() |
| 2301 | */ |
| 2302 | public double toDouble() { |
| 2303 | |
| 2304 | if (isInfinite()) { |
| 2305 | if (lessThan(getZero())) { |
| 2306 | return Double.NEGATIVE_INFINITY; |
| 2307 | } else { |
| 2308 | return Double.POSITIVE_INFINITY; |
| 2309 | } |
| 2310 | } |
| 2311 | |
| 2312 | if (isNaN()) { |
| 2313 | return Double.NaN; |
| 2314 | } |
| 2315 | |
| 2316 | Dfp y = this; |
| 2317 | boolean negate = false; |
| 2318 | if (lessThan(getZero())) { |
| 2319 | y = negate(); |
| 2320 | negate = true; |
| 2321 | } |
| 2322 | |
| 2323 | /* Find the exponent, first estimate by integer log10, then adjust. |
| 2324 | Should be faster than doing a natural logarithm. */ |
| 2325 | int exponent = (int)(y.log10() * 3.32); |
| 2326 | if (exponent < 0) { |
| 2327 | exponent--; |
| 2328 | } |
| 2329 | |
| 2330 | Dfp tempDfp = DfpMath.pow(getTwo(), exponent); |
| 2331 | while (tempDfp.lessThan(y) || tempDfp.equals(y)) { |
| 2332 | tempDfp = tempDfp.multiply(2); |
| 2333 | exponent++; |
| 2334 | } |
| 2335 | exponent--; |
| 2336 | |
| 2337 | /* We have the exponent, now work on the mantissa */ |
| 2338 | |
| 2339 | y = y.divide(DfpMath.pow(getTwo(), exponent)); |
| 2340 | if (exponent > -1023) { |
| 2341 | y = y.subtract(getOne()); |
| 2342 | } |
| 2343 | |
| 2344 | if (exponent < -1074) { |
| 2345 | return 0; |
| 2346 | } |
| 2347 | |
| 2348 | if (exponent > 1023) { |
| 2349 | return negate ? Double.NEGATIVE_INFINITY : Double.POSITIVE_INFINITY; |
| 2350 | } |
| 2351 | |
| 2352 | |
| 2353 | y = y.multiply(newInstance(4503599627370496l)).rint(); |
| 2354 | String str = y.toString(); |
| 2355 | str = str.substring(0, str.length()-1); |
| 2356 | long mantissa = Long.parseLong(str); |
| 2357 | |
| 2358 | if (mantissa == 4503599627370496L) { |
| 2359 | // Handle special case where we round up to next power of two |
| 2360 | mantissa = 0; |
| 2361 | exponent++; |
| 2362 | } |
| 2363 | |
| 2364 | /* Its going to be subnormal, so make adjustments */ |
| 2365 | if (exponent <= -1023) { |
| 2366 | exponent--; |
| 2367 | } |
| 2368 | |
| 2369 | while (exponent < -1023) { |
| 2370 | exponent++; |
| 2371 | mantissa >>>= 1; |
| 2372 | } |
| 2373 | |
| 2374 | long bits = mantissa | ((exponent + 1023L) << 52); |
| 2375 | double x = Double.longBitsToDouble(bits); |
| 2376 | |
| 2377 | if (negate) { |
| 2378 | x = -x; |
| 2379 | } |
| 2380 | |
| 2381 | return x; |
| 2382 | |
| 2383 | } |
| 2384 | |
| 2385 | /** Convert the instance into a split double. |
| 2386 | * @return an array of two doubles which sum represent the instance |
| 2387 | * @see #toDouble() |
| 2388 | */ |
| 2389 | public double[] toSplitDouble() { |
| 2390 | double split[] = new double[2]; |
| 2391 | long mask = 0xffffffffc0000000L; |
| 2392 | |
| 2393 | split[0] = Double.longBitsToDouble(Double.doubleToLongBits(toDouble()) & mask); |
| 2394 | split[1] = subtract(newInstance(split[0])).toDouble(); |
| 2395 | |
| 2396 | return split; |
| 2397 | } |
| 2398 | |
| 2399 | } |