| 1 | /* (C) Copyright 2001 William Rossi |
| 2 | */ |
| 3 | |
| 4 | package rossi.dfp; |
| 5 | |
| 6 | /**<pre> |
| 7 | * Decimal floating point library for Java |
| 8 | * |
| 9 | * Another floating point class. This one is built using radix 10000 |
| 10 | * which is 10^4, so its almost decimal. |
| 11 | * |
| 12 | * The design goals here are - |
| 13 | * 1.) decimal math, or close to it. |
| 14 | * 2.) Compile-time settable precision |
| 15 | * 3.) Portability. Code should be keep as portable as possible. |
| 16 | * 4.) Performance |
| 17 | * 5.) Accuracy - Results should always be +/- 1 ULP for basic |
| 18 | * algebraic operation |
| 19 | * 6.) Comply with IEEE 854-1987 as much as possible. |
| 20 | * (See IEEE 854-1987 notes below) |
| 21 | * |
| 22 | * The trade offs - |
| 23 | * 1.) Memory foot print. I'm using more memory than necessary to |
| 24 | * represent numbers to get better performance. |
| 25 | * 2.) Digits are bigger, so rounding is a greater loss. So, if you |
| 26 | * really need 12 decimal digits, better use 4 base 10000 digits |
| 27 | * there can be one partially filled. |
| 28 | * |
| 29 | * Numbers are represented in the following form: |
| 30 | * |
| 31 | * n = sign * mant * (radix) ^ exp; |
| 32 | * |
| 33 | * where sign is +/- 1, mantissa represents a fractional number between |
| 34 | * zero and one. mant[0] is the least significant digit. |
| 35 | * exp is in the range of -32767 to 32768 |
| 36 | * |
| 37 | * dfp objects are immuatable via their public interface. |
| 38 | * |
| 39 | * IEEE 854-1987 Notes and differences |
| 40 | * |
| 41 | * IEEE 854 requires the radix to be either 2 or 10. The radix here is |
| 42 | * 10000, so that requirement is not met, but it is possible that a |
| 43 | * subclassed can be made to make it behave as a radix 10 |
| 44 | * number. It is my opinion that if it looks and behaves as a radix |
| 45 | * 10 number then it is one and that requirement would be met. |
| 46 | * |
| 47 | * The radix of 10000 was chosen because it should be faster to operate |
| 48 | * on 4 decimal digits at once intead of one at a time. Radix 10 behaviour |
| 49 | * can be realized by add an additional rounding step to ensure that |
| 50 | * the number of decimal digits represented is constant. |
| 51 | * |
| 52 | * The IEEE standard specifically leaves out internal data encoding, |
| 53 | * so it is reasonable to conclude that such a subclass of this radix |
| 54 | * 10000 system is merely an encoding of a radix 10 system. |
| 55 | * |
| 56 | * IEEE 854 also specifies the existance of "sub-normal" numbers. This |
| 57 | * class does not contain any such entities. The most significant radix |
| 58 | * 10000 digit is always non-zero. Instead, we support "gradual underflow" |
| 59 | * by raising the underflow flag for numbers less with exponent less than |
| 60 | * expMin, but dont flush to zero until the exponent reaches expMin-DIGITS. |
| 61 | * Thus the smallest number we can represent would be: |
| 62 | * 1E(-(minExp-DIGITS-1)*4), eg, for DIGITS=5, minExp=-32767, that would |
| 63 | * be 1e-131092. |
| 64 | * |
| 65 | * IEEE 854 defines that the implied radix point lies just to the right |
| 66 | * of the most significant digit and to the left of the remaining digits. |
| 67 | * This implementation puts the implied radix point to the left of all |
| 68 | * digits including the most significant one. The most significant digit |
| 69 | * here is the one just to the right of the radix point. This is a fine |
| 70 | * detail and is really only a matter of definition. Any side effects of |
| 71 | * this can be rendered invisible by a subclass. |
| 72 | * </pre> |
| 73 | */ |
| 74 | |
| 75 | public class dfp |
| 76 | { |
| 77 | protected int[] mant; // the mantissa |
| 78 | protected byte sign; // the sign bit. 1 for positive, -1 for negative |
| 79 | protected int exp; // the exponent. |
| 80 | protected byte nans; // Indicates non-finite / non-number values |
| 81 | |
| 82 | protected static int rMode = 4; // Current rounding mode |
| 83 | protected static int ieeeFlags = 0; // IEEE 854-1987 signals |
| 84 | |
| 85 | /** The number of digits. note these are radix 10000 digits, so each |
| 86 | * one is equivilent to 4 decimal digits */ |
| 87 | public final static int DIGITS = 5; // each digit yeilds 4 decimal digits |
| 88 | |
| 89 | /** The radix, or base of this system. Set to 10000 */ |
| 90 | public final static int radix = 10000; |
| 91 | |
| 92 | /** The minium exponent before underflow is signaled. Flush to zero |
| 93 | * occurs at minExp-DIGITS */ |
| 94 | public final static int minExp = -32767; |
| 95 | |
| 96 | /** The maximum exponent before overflow is signaled and results flushed |
| 97 | * to infinity */ |
| 98 | public final static int maxExp = 32768; |
| 99 | |
| 100 | /** The amount under/overflows are scaled by before going to trap handler */ |
| 101 | public final static int errScale = 32760; |
| 102 | |
| 103 | /**** Rounding modes *****/ |
| 104 | |
| 105 | /** Rounds toward zero. I.E. truncation */ |
| 106 | public final static int ROUND_DOWN = 0; |
| 107 | |
| 108 | /** Rounds away from zero if discarded digit is non-zero */ |
| 109 | public final static int ROUND_UP = 1; |
| 110 | |
| 111 | /** Rounds towards nearest unless both are equidistant in which case |
| 112 | * it rounds away from zero */ |
| 113 | public final static int ROUND_HALF_UP = 2; |
| 114 | |
| 115 | /** Rounds towards nearest unless both are equidistant in which case |
| 116 | * it rounds toward zero */ |
| 117 | public final static int ROUND_HALF_DOWN = 3; |
| 118 | |
| 119 | /** Rounds towards nearest unless both are equidistant in which case |
| 120 | * it rounds toward the even neighbor. This is the default as |
| 121 | * specified by IEEE 854-1987 */ |
| 122 | public final static int ROUND_HALF_EVEN = 4; |
| 123 | |
| 124 | /** Rounds towards nearest unless both are equidistant in which case |
| 125 | * it rounds toward the odd neighbor. */ |
| 126 | public final static int ROUND_HALF_ODD = 5; |
| 127 | |
| 128 | /** Rounds towards positive infinity */ |
| 129 | public final static int ROUND_CEIL = 6; |
| 130 | |
| 131 | /** Rounds towards negative infinity */ |
| 132 | public final static int ROUND_FLOOR = 7; |
| 133 | |
| 134 | /* non-numbers per IEEE 854-1987 */ |
| 135 | public final static byte FINITE = 0; // Normal finite numbers |
| 136 | public final static byte INFINITE = 1; // Infinity |
| 137 | public final static byte SNAN = 2; // Signaling NaN |
| 138 | public final static byte QNAN = 3; // Quiet NaN |
| 139 | |
| 140 | /* Flags */ |
| 141 | public final static int FLAG_INVALID = 1; // Invalid operation |
| 142 | public final static int FLAG_DIV_ZERO = 2; // Division by zero |
| 143 | public final static int FLAG_OVERFLOW = 4; // Overflow |
| 144 | public final static int FLAG_UNDERFLOW = 8; // Underflow |
| 145 | public final static int FLAG_INEXACT = 16; // Inexact |
| 146 | |
| 147 | /* Handy constants */ |
| 148 | public final static dfp zero = new dfp(); |
| 149 | public final static dfp one = new dfp("1"); |
| 150 | public final static dfp two = new dfp("2"); |
| 151 | |
| 152 | /** Default constructor. Makes a dfp with a value of zero */ |
| 153 | public dfp() |
| 154 | { |
| 155 | mant = new int[DIGITS]; |
| 156 | for (int i=DIGITS-1; i>=0; i--) |
| 157 | mant[i] = 0; |
| 158 | sign = 1; |
| 159 | exp = 0; |
| 160 | nans = FINITE; |
| 161 | } |
| 162 | |
| 163 | /** Copy constructor. Creates a copy of the supplied dfp */ |
| 164 | public dfp(dfp d) |
| 165 | { |
| 166 | mant = new int[DIGITS]; |
| 167 | |
| 168 | for (int i=DIGITS-1; i>=0; i--) |
| 169 | mant[i] = d.mant[i]; |
| 170 | sign = d.sign; |
| 171 | exp = d.exp; |
| 172 | nans = d.nans; |
| 173 | } |
| 174 | |
| 175 | /** Create a dfp given a String representation */ |
| 176 | public dfp(String s) |
| 177 | { |
| 178 | dfp r = string2dfp(s); |
| 179 | this.mant = r.mant; |
| 180 | this.exp = r.exp; |
| 181 | this.sign = r.sign; |
| 182 | this.nans = r.nans; |
| 183 | } |
| 184 | |
| 185 | /** Create a dfp. Use this internally in preferenct to constructors to facilitate |
| 186 | subclasses. */ |
| 187 | public dfp newInstance(dfp d) |
| 188 | { |
| 189 | return new dfp(d); |
| 190 | } |
| 191 | |
| 192 | /** Create a dfp. Use this internally in preferenct to constructors to facilitate |
| 193 | subclasses. */ |
| 194 | public dfp newInstance(String s) |
| 195 | { |
| 196 | return new dfp(s); |
| 197 | } |
| 198 | |
| 199 | /** Shift the mantissa left, and adjust the exponent to compensate */ |
| 200 | protected void shiftLeft() |
| 201 | { |
| 202 | for (int i=DIGITS-1; i>0; i--) |
| 203 | mant[i] = mant[i-1]; |
| 204 | mant[0] = 0; |
| 205 | exp--; |
| 206 | } |
| 207 | |
| 208 | /* Note that shiftRight() does not call round() as that round() itself |
| 209 | uses shiftRight() */ |
| 210 | /** Shift the mantissa right, and adjust the exponent to compensate */ |
| 211 | protected void shiftRight() |
| 212 | { |
| 213 | for (int i=0; i<DIGITS-1; i++) |
| 214 | mant[i] = mant[i+1]; |
| 215 | mant[DIGITS-1] = 0; |
| 216 | exp++; |
| 217 | } |
| 218 | |
| 219 | /** Make our exp equal to the supplied one. This may cause rounding. |
| 220 | * Also causes de-normalized numbers. These numbers are generally |
| 221 | * dangerous because most routines assume normalized numbers. |
| 222 | * Align doesn't round, so it will return the last digit destroyed |
| 223 | * by shifting right. |
| 224 | */ |
| 225 | protected int align(int e) |
| 226 | { |
| 227 | int diff; |
| 228 | int adiff; |
| 229 | int lostdigit = 0; |
| 230 | boolean inexact = false; |
| 231 | |
| 232 | diff = exp - e; |
| 233 | |
| 234 | adiff = diff; |
| 235 | if (adiff < 0) |
| 236 | adiff = -adiff; |
| 237 | |
| 238 | if (diff == 0) |
| 239 | return 0; |
| 240 | |
| 241 | if (adiff > (DIGITS+1)) // Special case |
| 242 | { |
| 243 | for (int i=DIGITS-1; i>=0; i--) |
| 244 | mant[i] = 0; |
| 245 | exp = e; |
| 246 | |
| 247 | ieeeFlags |= FLAG_INEXACT; |
| 248 | dotrap(FLAG_INEXACT, "align", this, this); |
| 249 | |
| 250 | return 0; |
| 251 | } |
| 252 | |
| 253 | for (int i=0; i<adiff; i++) |
| 254 | { |
| 255 | if (diff < 0) |
| 256 | { |
| 257 | /* Keep track of loss -- only signal inexact after losing 2 digits. |
| 258 | * the first lost digit is returned to add() and may be incorporated |
| 259 | * into the result. |
| 260 | */ |
| 261 | if (lostdigit != 0) |
| 262 | inexact = true; |
| 263 | |
| 264 | lostdigit = mant[0]; |
| 265 | |
| 266 | shiftRight(); |
| 267 | } |
| 268 | else |
| 269 | shiftLeft(); |
| 270 | } |
| 271 | |
| 272 | if (inexact) |
| 273 | { |
| 274 | ieeeFlags |= FLAG_INEXACT; |
| 275 | dotrap(FLAG_INEXACT, "align", this, this); |
| 276 | } |
| 277 | |
| 278 | return lostdigit; |
| 279 | } |
| 280 | |
| 281 | /** returns true if this is less than x. |
| 282 | * returns false if this or x is NaN */ |
| 283 | public boolean lessThan(dfp x) |
| 284 | { |
| 285 | /* if a nan is involved, signal invalid and return false */ |
| 286 | if (nans == SNAN || nans == QNAN || x.nans == SNAN || x.nans == QNAN) |
| 287 | { |
| 288 | ieeeFlags |= FLAG_INVALID; |
| 289 | dotrap(FLAG_INVALID, "lessThan", x, newInstance(zero)); |
| 290 | return false; |
| 291 | } |
| 292 | |
| 293 | return (compare(this, x) < 0); |
| 294 | } |
| 295 | |
| 296 | /** returns true if this is greater than x. |
| 297 | * returns false if this or x is NaN */ |
| 298 | public boolean greaterThan(dfp x) |
| 299 | { |
| 300 | /* if a nan is involved, signal invalid and return false */ |
| 301 | if (nans == SNAN || nans == QNAN || x.nans == SNAN || x.nans == QNAN) |
| 302 | { |
| 303 | ieeeFlags |= FLAG_INVALID; |
| 304 | dotrap(FLAG_INVALID, "lessThan", x, newInstance(zero)); |
| 305 | return false; |
| 306 | } |
| 307 | |
| 308 | return (compare(this, x) > 0); |
| 309 | } |
| 310 | |
| 311 | /** returns true if this is equal to x. |
| 312 | * returns false if this or x is NaN */ |
| 313 | public boolean equal(dfp x) |
| 314 | { |
| 315 | if (nans == SNAN || nans == QNAN || x.nans == SNAN || x.nans == QNAN) |
| 316 | return false; |
| 317 | |
| 318 | return (compare(this, x) == 0); |
| 319 | } |
| 320 | |
| 321 | /** returns true if this is not equal to x. |
| 322 | * different from !equal(x) in the way NaNs are handled. |
| 323 | */ |
| 324 | public boolean unequal(dfp x) |
| 325 | { |
| 326 | if (nans == SNAN || nans == QNAN || x.nans == SNAN || x.nans == QNAN) |
| 327 | return false; |
| 328 | |
| 329 | return (greaterThan(x) || lessThan(x)); |
| 330 | } |
| 331 | |
| 332 | /** compare a and b. return -1 if a<b, 1 if a>b and 0 if a==b |
| 333 | * Note this method does not properly handle NaNs. */ |
| 334 | protected static int compare(dfp a, dfp b) |
| 335 | { |
| 336 | /* Ignore the sign of zero */ |
| 337 | if (a.mant[DIGITS-1] == 0 && b.mant[DIGITS-1] == 0 && a.nans == FINITE && b.nans == FINITE) |
| 338 | return 0; |
| 339 | |
| 340 | if (a.sign != b.sign) |
| 341 | { |
| 342 | if (a.sign == -1) |
| 343 | return -1; |
| 344 | else |
| 345 | return 1; |
| 346 | } |
| 347 | |
| 348 | /* deal with the infinities */ |
| 349 | if (a.nans == INFINITE && b.nans == FINITE) |
| 350 | return a.sign; |
| 351 | |
| 352 | if (a.nans == FINITE && b.nans == INFINITE) |
| 353 | return -b.sign; |
| 354 | |
| 355 | if (a.nans == INFINITE && b.nans == INFINITE) |
| 356 | return 0; |
| 357 | |
| 358 | /* Handle special case when a or b is zero, by ignoring the exponents */ |
| 359 | if (b.mant[DIGITS-1] != 0 && a.mant[DIGITS-1] != 0) |
| 360 | { |
| 361 | if (a.exp < b.exp) |
| 362 | return -a.sign; |
| 363 | |
| 364 | if (a.exp > b.exp) |
| 365 | return a.sign; |
| 366 | } |
| 367 | |
| 368 | /* compare the mantissas */ |
| 369 | for (int i=DIGITS-1; i>=0; i--) |
| 370 | { |
| 371 | if (a.mant[i] > b.mant[i]) |
| 372 | return a.sign; |
| 373 | |
| 374 | if (a.mant[i] < b.mant[i]) |
| 375 | return -a.sign; |
| 376 | } |
| 377 | |
| 378 | return 0; |
| 379 | } |
| 380 | |
| 381 | /** Round to nearest integer using the round-half-even method. |
| 382 | * That is round to nearest integer unless both are equidistant. |
| 383 | * In which case round to the even one. |
| 384 | */ |
| 385 | public dfp rint() |
| 386 | { |
| 387 | return trunc(ROUND_HALF_EVEN); |
| 388 | } |
| 389 | |
| 390 | /** Round to an integer using the round floor mode. That is, |
| 391 | * round toward -Infinity */ |
| 392 | public dfp floor() |
| 393 | { |
| 394 | return trunc(ROUND_FLOOR); |
| 395 | } |
| 396 | |
| 397 | /** Round to an integer using the ceil floor mode. That is, |
| 398 | * round toward +Infinity */ |
| 399 | public dfp ceil() |
| 400 | { |
| 401 | return trunc(ROUND_CEIL); |
| 402 | } |
| 403 | |
| 404 | /** Returns the IEEE remainder. That is the result of this less |
| 405 | * n times d, where n is the integer closest to this/d. |
| 406 | */ |
| 407 | public dfp remainder(dfp d) |
| 408 | { |
| 409 | dfp q = this.divide(d); |
| 410 | dfp result; |
| 411 | |
| 412 | result = this.subtract(this.divide(d).rint().multiply(d)); |
| 413 | |
| 414 | /* IEEE 854-1987 says that if the result is zero, then it |
| 415 | carries the sign of this */ |
| 416 | |
| 417 | if (result.mant[DIGITS-1] == 0) |
| 418 | result.sign = sign; |
| 419 | |
| 420 | return result; |
| 421 | } |
| 422 | |
| 423 | /** Does the integer conversions with the spec rounding. */ |
| 424 | protected dfp trunc(int rmode) |
| 425 | { |
| 426 | dfp result, a, half; |
| 427 | boolean changed = false; |
| 428 | |
| 429 | if (nans == SNAN || nans == QNAN) |
| 430 | return newInstance(this); |
| 431 | |
| 432 | if (nans == INFINITE) |
| 433 | return newInstance(this); |
| 434 | |
| 435 | if (mant[DIGITS-1] == 0) // a is zero |
| 436 | return newInstance(this); |
| 437 | |
| 438 | /* If the exponent is less than zero then we can certainly |
| 439 | * return zero */ |
| 440 | if (exp < 0) |
| 441 | { |
| 442 | ieeeFlags |= FLAG_INEXACT; |
| 443 | result = newInstance(zero); |
| 444 | result = dotrap(FLAG_INEXACT, "trunc", this, result); |
| 445 | return result; |
| 446 | } |
| 447 | |
| 448 | /* If the exponent is greater than or equal to digits, then it |
| 449 | * must already be an integer since there is no precision left |
| 450 | * for any fractional part */ |
| 451 | |
| 452 | if (exp >= DIGITS) |
| 453 | return newInstance(this); |
| 454 | |
| 455 | /* General case: create another dfp, result, that contains the |
| 456 | * a with the fractional part lopped off. */ |
| 457 | |
| 458 | result = newInstance(this); |
| 459 | for (int i=0; i<(DIGITS-result.exp); i++) |
| 460 | { |
| 461 | changed |= (result.mant[i] != 0); |
| 462 | result.mant[i] = 0; |
| 463 | } |
| 464 | |
| 465 | if (changed) |
| 466 | { |
| 467 | switch (rmode) |
| 468 | { |
| 469 | case ROUND_FLOOR: |
| 470 | if (result.sign == -1) // then we must increment the mantissa by one |
| 471 | result = result.add(newInstance("-1")); |
| 472 | break; |
| 473 | |
| 474 | case ROUND_CEIL: |
| 475 | if (result.sign == 1) // then we must increment the mantissa by one |
| 476 | result = result.add(one); |
| 477 | break; |
| 478 | |
| 479 | case ROUND_HALF_EVEN: |
| 480 | default: |
| 481 | half = newInstance("0.5"); |
| 482 | a = subtract(result); // difference between this and result |
| 483 | a.sign = 1; // force positive (take abs) |
| 484 | if (a.greaterThan(half)) |
| 485 | { |
| 486 | a = newInstance(one); |
| 487 | a.sign = sign; |
| 488 | result = result.add(a); |
| 489 | } |
| 490 | |
| 491 | /** If exactly equal to 1/2 and odd then increment */ |
| 492 | if (a.equal(half) && result.exp > 0 && (result.mant[DIGITS-result.exp]&1) != 0) |
| 493 | { |
| 494 | a = newInstance(one); |
| 495 | a.sign = sign; |
| 496 | result = result.add(a); |
| 497 | } |
| 498 | break; |
| 499 | } |
| 500 | |
| 501 | ieeeFlags |= FLAG_INEXACT; // signal inexact |
| 502 | result = dotrap(FLAG_INEXACT, "trunc", this, result); |
| 503 | return result; |
| 504 | } |
| 505 | |
| 506 | return result; |
| 507 | } |
| 508 | |
| 509 | /** Convert this to an integer. If greater than 2147483647, it returns |
| 510 | * 2147483647. If less than -2147483648 it returns -2147483648. |
| 511 | */ |
| 512 | public int intValue() |
| 513 | { |
| 514 | dfp rounded; |
| 515 | int result = 0; |
| 516 | |
| 517 | rounded = rint(); |
| 518 | |
| 519 | if (rounded.greaterThan(newInstance("2147483647"))) |
| 520 | return 2147483647; |
| 521 | |
| 522 | if (rounded.lessThan(newInstance("-2147483648"))) |
| 523 | return -2147483648; |
| 524 | |
| 525 | for (int i=DIGITS-1; i>=DIGITS-rounded.exp; i--) |
| 526 | result = result*radix+rounded.mant[i]; |
| 527 | |
| 528 | if (rounded.sign == -1) |
| 529 | result = -result; |
| 530 | |
| 531 | return result; |
| 532 | } |
| 533 | |
| 534 | /** Returns the exponent of the greatest power of 10000 that is |
| 535 | * less than or equal to the absolute value of this. I.E. if |
| 536 | * this is 10e6 then log10K would return 1. |
| 537 | */ |
| 538 | public int log10K() |
| 539 | { |
| 540 | return exp-1; |
| 541 | } |
| 542 | |
| 543 | /** Return the specified power of 10000 */ |
| 544 | public dfp power10K(int e) |
| 545 | { |
| 546 | dfp d = newInstance(one); |
| 547 | d.exp = e + 1; |
| 548 | return d; |
| 549 | } |
| 550 | |
| 551 | /** |
| 552 | * Return the exponent of the greatest power of 10 that is less than |
| 553 | * or equal to than abs(this). |
| 554 | */ |
| 555 | public int log10() |
| 556 | { |
| 557 | if (mant[DIGITS-1] > 1000) return exp * 4 - 1; |
| 558 | if (mant[DIGITS-1] > 100) return exp * 4 - 2; |
| 559 | if (mant[DIGITS-1] > 10) return exp * 4 - 3; |
| 560 | return exp * 4 - 4; |
| 561 | } |
| 562 | |
| 563 | /** Return the specified power of 10 */ |
| 564 | public dfp power10(int e) |
| 565 | { |
| 566 | dfp d = newInstance(one); |
| 567 | |
| 568 | if (e >= 0) |
| 569 | d.exp = e/4 + 1; |
| 570 | else |
| 571 | d.exp = (e+1)/4; |
| 572 | |
| 573 | switch ((e%4+4)%4) |
| 574 | { |
| 575 | case 0: break; |
| 576 | case 1: d = d.multiply(10); break; |
| 577 | case 2: d = d.multiply(100); break; |
| 578 | case 3: d = d.multiply(1000); break; |
| 579 | } |
| 580 | |
| 581 | return d; |
| 582 | } |
| 583 | |
| 584 | /** Negate the mantissa of this by computing the complement. |
| 585 | * Leaves the sign bit unchanged, used internally by add. |
| 586 | * Denormalized numbers are handled properly here. */ |
| 587 | protected int complement(int extra) |
| 588 | { |
| 589 | int r, rl, rh; |
| 590 | |
| 591 | extra = radix-extra; |
| 592 | for (int i=0; i<DIGITS; i++) |
| 593 | mant[i] = radix-mant[i]-1; |
| 594 | |
| 595 | rh = extra / radix; |
| 596 | extra = extra % radix; |
| 597 | for (int i=0; i<DIGITS; i++) |
| 598 | { |
| 599 | r = mant[i]+rh; |
| 600 | rl = r % radix; |
| 601 | rh = r / radix; |
| 602 | mant[i] = rl; |
| 603 | } |
| 604 | |
| 605 | return extra; |
| 606 | } |
| 607 | |
| 608 | /** Add x to this and return the result */ |
| 609 | public dfp add(dfp x) |
| 610 | { |
| 611 | int r, rh, rl; |
| 612 | dfp a, b, result; |
| 613 | byte asign, bsign, rsign; |
| 614 | int aextradigit = 0, bextradigit = 0; |
| 615 | |
| 616 | /* handle special cases */ |
| 617 | if (nans != FINITE || x.nans != FINITE) |
| 618 | { |
| 619 | if (nans == QNAN || nans == SNAN) |
| 620 | return this; |
| 621 | |
| 622 | if (x.nans == QNAN || x.nans == SNAN) |
| 623 | return x; |
| 624 | |
| 625 | if (nans == INFINITE && x.nans == FINITE) |
| 626 | return this; |
| 627 | |
| 628 | if (x.nans == INFINITE && nans == FINITE) |
| 629 | return x; |
| 630 | |
| 631 | if (x.nans == INFINITE && nans == INFINITE && sign == x.sign) |
| 632 | return x; |
| 633 | |
| 634 | if (x.nans == INFINITE && nans == INFINITE && sign != x.sign) |
| 635 | { |
| 636 | ieeeFlags |= FLAG_INVALID; |
| 637 | result = newInstance(zero); |
| 638 | result.nans = QNAN; |
| 639 | result = dotrap(FLAG_INVALID, "add", x, result); |
| 640 | return result; |
| 641 | } |
| 642 | } |
| 643 | |
| 644 | /* copy this and the arg */ |
| 645 | a = newInstance(this); |
| 646 | b = newInstance(x); |
| 647 | |
| 648 | /* initialize the result object */ |
| 649 | result = newInstance(zero); |
| 650 | |
| 651 | /* Make all numbers positive, but remember their sign */ |
| 652 | asign = a.sign; |
| 653 | bsign = b.sign; |
| 654 | |
| 655 | a.sign = 1; |
| 656 | b.sign = 1; |
| 657 | |
| 658 | /* The result will be signed like the arg with greatest magnitude */ |
| 659 | rsign = bsign; |
| 660 | if (compare(a, b) > 0) |
| 661 | rsign = asign; |
| 662 | |
| 663 | /* Handle special case when a or b is zero, by setting the exponent |
| 664 | of the zero number equal to the other one. This avoids an alignment |
| 665 | which would cause catastropic loss of precision */ |
| 666 | if (b.mant[DIGITS-1] == 0) |
| 667 | b.exp = a.exp; |
| 668 | |
| 669 | if (a.mant[DIGITS-1] == 0) |
| 670 | a.exp = b.exp; |
| 671 | |
| 672 | /* align number with the smaller exponent */ |
| 673 | if (a.exp < b.exp) |
| 674 | aextradigit = a.align(b.exp); |
| 675 | else |
| 676 | bextradigit = b.align(a.exp); |
| 677 | |
| 678 | /* complement the smaller of the two if the signs are different */ |
| 679 | if (asign != bsign) |
| 680 | { |
| 681 | if (asign == rsign) |
| 682 | bextradigit = b.complement(bextradigit); |
| 683 | else |
| 684 | aextradigit = a.complement(aextradigit); |
| 685 | } |
| 686 | |
| 687 | /* add the mantissas */ |
| 688 | rh = 0; /* acts as a carry */ |
| 689 | for (int i=0; i<DIGITS; i++) |
| 690 | { |
| 691 | r = a.mant[i]+b.mant[i]+rh; |
| 692 | rl = r % radix; |
| 693 | rh = r / radix; |
| 694 | result.mant[i] = rl; |
| 695 | } |
| 696 | result.exp = a.exp; |
| 697 | result.sign = rsign; |
| 698 | |
| 699 | //System.out.println("a = "+a.mant[2]+" "+a.mant[1]+" "+a.mant[0]); |
| 700 | //System.out.println("b = "+b.mant[2]+" "+b.mant[1]+" "+b.mant[0]); |
| 701 | //System.out.println("result = "+result.mant[2]+" "+result.mant[1]+" "+result.mant[0]); |
| 702 | |
| 703 | /* handle overflow -- note, when asign!=bsign an overflow is |
| 704 | * normal and should be ignored. */ |
| 705 | |
| 706 | if (rh != 0 && (asign == bsign)) |
| 707 | { |
| 708 | int lostdigit = result.mant[0]; |
| 709 | result.shiftRight(); |
| 710 | result.mant[DIGITS-1] = rh; |
| 711 | int excp = result.round(lostdigit); |
| 712 | if (excp != 0) |
| 713 | result = dotrap(excp, "add", x, result); |
| 714 | } |
| 715 | |
| 716 | /* normalize the result */ |
| 717 | for (int i=0; i<DIGITS; i++) |
| 718 | { |
| 719 | if (result.mant[DIGITS-1] != 0) |
| 720 | break; |
| 721 | result.shiftLeft(); |
| 722 | if (i == 0) |
| 723 | { |
| 724 | result.mant[0] = aextradigit+bextradigit; |
| 725 | aextradigit = 0; |
| 726 | bextradigit = 0; |
| 727 | } |
| 728 | } |
| 729 | |
| 730 | /* result is zero if after normalization the most sig. digit is zero */ |
| 731 | if (result.mant[DIGITS-1] == 0) |
| 732 | { |
| 733 | result.exp = 0; |
| 734 | |
| 735 | if (asign != bsign) // Unless adding 2 negative zeros, sign is positive |
| 736 | result.sign = 1; // Per IEEE 854-1987 Section 6.3 |
| 737 | } |
| 738 | |
| 739 | /* Call round to test for over/under flows */ |
| 740 | int excp = result.round((aextradigit+bextradigit)); |
| 741 | if (excp != 0) |
| 742 | result = dotrap(excp, "add", x, result); |
| 743 | |
| 744 | return result; |
| 745 | } |
| 746 | |
| 747 | /** Returns a number that is this number with the sign bit reversed */ |
| 748 | public dfp negate() |
| 749 | { |
| 750 | dfp result = newInstance(this); |
| 751 | result.sign = (byte) -result.sign; |
| 752 | return result; |
| 753 | } |
| 754 | |
| 755 | /** Subtract a from this */ |
| 756 | public dfp subtract(dfp a) |
| 757 | { |
| 758 | return add(a.negate()); |
| 759 | } |
| 760 | |
| 761 | /** round this given the next digit n using the current rounding mode |
| 762 | * returns a flag if an exception occured |
| 763 | */ |
| 764 | protected int round(int n) |
| 765 | { |
| 766 | int r, rh, rl; |
| 767 | boolean inc=false; |
| 768 | |
| 769 | switch (rMode) |
| 770 | { |
| 771 | case ROUND_DOWN: |
| 772 | inc = false; |
| 773 | break; |
| 774 | |
| 775 | case ROUND_UP: |
| 776 | inc = (n!=0); // round up if n!=0 |
| 777 | break; |
| 778 | |
| 779 | case ROUND_HALF_UP: |
| 780 | inc = (n >= 5000); // round half up |
| 781 | break; |
| 782 | |
| 783 | case ROUND_HALF_DOWN: |
| 784 | inc = (n > 5000); // round half down |
| 785 | break; |
| 786 | |
| 787 | case ROUND_HALF_EVEN: |
| 788 | inc = (n > 5000 || (n == 5000 && (mant[0]&1)==1)); // round half-even |
| 789 | break; |
| 790 | |
| 791 | case ROUND_HALF_ODD: |
| 792 | inc = (n > 5000 || (n == 5000 && (mant[0]&1)==0)); // round half-odd |
| 793 | break; |
| 794 | |
| 795 | case ROUND_CEIL: |
| 796 | inc = (sign == 1 && n != 0); // round ceil |
| 797 | break; |
| 798 | |
| 799 | case ROUND_FLOOR: |
| 800 | inc = (sign == -1 && n != 0); // round floor |
| 801 | break; |
| 802 | } |
| 803 | |
| 804 | if (inc) // increment if necessary |
| 805 | { |
| 806 | rh = 1; |
| 807 | for (int i=0; i<DIGITS; i++) |
| 808 | { |
| 809 | r = mant[i] + rh; |
| 810 | rh = r / radix; |
| 811 | rl = r % radix; |
| 812 | mant[i] = rl; |
| 813 | } |
| 814 | |
| 815 | if (rh != 0) |
| 816 | { |
| 817 | shiftRight(); |
| 818 | mant[DIGITS-1]=rh; |
| 819 | } |
| 820 | } |
| 821 | |
| 822 | /* Check for exceptional cases and raise signals if necessary */ |
| 823 | if (exp < minExp) // Gradual Underflow |
| 824 | { |
| 825 | ieeeFlags |= FLAG_UNDERFLOW; |
| 826 | return FLAG_UNDERFLOW; |
| 827 | } |
| 828 | |
| 829 | if (exp > maxExp) // Overflow |
| 830 | { |
| 831 | ieeeFlags |= FLAG_OVERFLOW; |
| 832 | return FLAG_OVERFLOW; |
| 833 | } |
| 834 | |
| 835 | if (n != 0) // Inexact |
| 836 | { |
| 837 | ieeeFlags |= FLAG_INEXACT; |
| 838 | return FLAG_INEXACT; |
| 839 | } |
| 840 | return 0; |
| 841 | } |
| 842 | |
| 843 | /** Multiply this by x */ |
| 844 | public dfp multiply(dfp x) |
| 845 | { |
| 846 | int product[]; // product array |
| 847 | int r, rh, rl; // working registers |
| 848 | int md=0; // most sig digit in result |
| 849 | int excp; // exception code if any |
| 850 | dfp result = newInstance(zero); |
| 851 | |
| 852 | /* handle special cases */ |
| 853 | if (nans != FINITE || x.nans != FINITE) |
| 854 | { |
| 855 | if (nans == QNAN || nans == SNAN) |
| 856 | return this; |
| 857 | |
| 858 | if (x.nans == QNAN || x.nans == SNAN) |
| 859 | return x; |
| 860 | |
| 861 | if (nans == INFINITE && x.nans == FINITE && x.mant[DIGITS-1] != 0) |
| 862 | { |
| 863 | result = newInstance(this); |
| 864 | result.sign = (byte) (sign * x.sign); |
| 865 | return result; |
| 866 | } |
| 867 | |
| 868 | if (x.nans == INFINITE && nans == FINITE && mant[DIGITS-1] != 0) |
| 869 | { |
| 870 | result = newInstance(x); |
| 871 | result.sign = (byte) (sign * x.sign); |
| 872 | return result; |
| 873 | } |
| 874 | |
| 875 | if (x.nans == INFINITE && nans == INFINITE) |
| 876 | { |
| 877 | result = newInstance(this); |
| 878 | result.sign = (byte) (sign * x.sign); |
| 879 | return result; |
| 880 | } |
| 881 | |
| 882 | if ( (x.nans == INFINITE && nans == FINITE && mant[DIGITS-1] == 0) || |
| 883 | (nans == INFINITE && x.nans == FINITE && x.mant[DIGITS-1] == 0) ) |
| 884 | { |
| 885 | ieeeFlags |= FLAG_INVALID; |
| 886 | result = newInstance(zero); |
| 887 | result.nans = QNAN; |
| 888 | result = dotrap(FLAG_INVALID, "multiply", x, result); |
| 889 | return result; |
| 890 | } |
| 891 | } |
| 892 | |
| 893 | product = new int[DIGITS*2]; // Big enough to hold even the largest result |
| 894 | |
| 895 | for (int i=0; i<DIGITS*2; i++) |
| 896 | product[i] = 0; |
| 897 | |
| 898 | for (int i=0; i<DIGITS; i++) |
| 899 | { |
| 900 | rh = 0; // acts as a carry |
| 901 | for (int j=0; j<DIGITS; j++) |
| 902 | { |
| 903 | r = mant[i] * x.mant[j]; // multiply the 2 digits |
| 904 | r = r + product[i+j] + rh; // add to the product digit with carry in |
| 905 | rl = r % radix; |
| 906 | rh = r / radix; |
| 907 | product[i+j] = rl; |
| 908 | } |
| 909 | product[i+DIGITS] = rh; |
| 910 | } |
| 911 | |
| 912 | /* Find the most sig digit */ |
| 913 | md = DIGITS*2-1; // default, in case result is zero |
| 914 | for (int i=DIGITS*2-1; i>=0; i--) |
| 915 | { |
| 916 | if (product[i] != 0) |
| 917 | { |
| 918 | md = i; |
| 919 | break; |
| 920 | } |
| 921 | } |
| 922 | |
| 923 | /* Copy the digits into the result */ |
| 924 | for (int i=0; i<DIGITS; i++) |
| 925 | result.mant[DIGITS-i-1] = product[md-i]; |
| 926 | |
| 927 | /* Fixup the exponent. */ |
| 928 | result.exp = (exp + x.exp + md - 2*DIGITS + 1); |
| 929 | result.sign = (byte)((sign == x.sign)?1:-1); |
| 930 | |
| 931 | if (result.mant[DIGITS-1] == 0) // if result is zero, set exp to zero |
| 932 | result.exp = 0; |
| 933 | |
| 934 | if (md > (DIGITS-1)) |
| 935 | excp = result.round(product[md-DIGITS]); |
| 936 | else |
| 937 | excp = result.round(0); // has no effect except to check status |
| 938 | |
| 939 | if (excp != 0) |
| 940 | result = dotrap(excp, "multiply", x, result); |
| 941 | |
| 942 | return result; |
| 943 | } |
| 944 | |
| 945 | /** Multiply this by a single digit 0<=x<radix. There are speed |
| 946 | * advantages in this special case */ |
| 947 | public dfp multiply(int x) |
| 948 | { |
| 949 | int product[]; // product array |
| 950 | int r, rh, rl; // working registers |
| 951 | int excp; // exception code if any |
| 952 | int lostdigit; // rounded off digit |
| 953 | dfp result = newInstance(this); |
| 954 | |
| 955 | /* handle special cases */ |
| 956 | if (nans != FINITE) |
| 957 | { |
| 958 | if (nans == QNAN || nans == SNAN) |
| 959 | return this; |
| 960 | |
| 961 | if (nans == INFINITE && x != 0) |
| 962 | { |
| 963 | result = newInstance(this); |
| 964 | return result; |
| 965 | } |
| 966 | |
| 967 | if (nans == INFINITE && x == 0) |
| 968 | { |
| 969 | ieeeFlags |= FLAG_INVALID; |
| 970 | result = newInstance(zero); |
| 971 | result.nans = QNAN; |
| 972 | result = dotrap(FLAG_INVALID, "multiply", newInstance(zero), result); |
| 973 | return result; |
| 974 | } |
| 975 | } |
| 976 | |
| 977 | /* range check x */ |
| 978 | if (x < 0 || x >= radix) |
| 979 | { |
| 980 | ieeeFlags |= FLAG_INVALID; |
| 981 | result = newInstance(zero); |
| 982 | result.nans = QNAN; |
| 983 | result = dotrap(FLAG_INVALID, "multiply", result, result); |
| 984 | return result; |
| 985 | } |
| 986 | |
| 987 | rh = 0; |
| 988 | for (int i=0; i<DIGITS; i++) |
| 989 | { |
| 990 | r = mant[i] * x + rh; |
| 991 | rl = r % radix; |
| 992 | rh = r / radix; |
| 993 | result.mant[i] = rl; |
| 994 | } |
| 995 | |
| 996 | lostdigit = 0; |
| 997 | if (rh != 0) |
| 998 | { |
| 999 | lostdigit = result.mant[0]; |
| 1000 | result.shiftRight(); |
| 1001 | result.mant[DIGITS-1] = rh; |
| 1002 | } |
| 1003 | |
| 1004 | if (result.mant[DIGITS-1] == 0) // if result is zero, set exp to zero |
| 1005 | result.exp = 0; |
| 1006 | |
| 1007 | excp = result.round(lostdigit); |
| 1008 | |
| 1009 | if (excp != 0) |
| 1010 | result = dotrap(excp, "multiply", result, result); |
| 1011 | |
| 1012 | return result; |
| 1013 | } |
| 1014 | |
| 1015 | /** Divide this by divisor */ |
| 1016 | public dfp divide(dfp divisor) |
| 1017 | { |
| 1018 | int dividend[]; // current status of the dividend |
| 1019 | int quotient[]; // quotient |
| 1020 | int remainder[];// remainder |
| 1021 | int qd; // current quotient digit we're working with |
| 1022 | int nsqd; // number of significant quotient digits we have |
| 1023 | int trial=0; // trial quotient digit |
| 1024 | int min, max; // quotient digit limits |
| 1025 | int minadj; // minimum adjustment |
| 1026 | boolean trialgood; // Flag to indicate a good trail digit |
| 1027 | int r, rh, rl; // working registers |
| 1028 | int md=0; // most sig digit in result |
| 1029 | int excp; // exceptions |
| 1030 | dfp result = newInstance(zero); |
| 1031 | |
| 1032 | /* handle special cases */ |
| 1033 | if (nans != FINITE || divisor.nans != FINITE) |
| 1034 | { |
| 1035 | if (nans == QNAN || nans == SNAN) |
| 1036 | return this; |
| 1037 | |
| 1038 | if (divisor.nans == QNAN || divisor.nans == SNAN) |
| 1039 | return divisor; |
| 1040 | |
| 1041 | if (nans == INFINITE && divisor.nans == FINITE) |
| 1042 | { |
| 1043 | result = newInstance(this); |
| 1044 | result.sign = (byte) (sign * divisor.sign); |
| 1045 | return result; |
| 1046 | } |
| 1047 | |
| 1048 | if (divisor.nans == INFINITE && nans == FINITE) |
| 1049 | { |
| 1050 | result = newInstance(zero); |
| 1051 | result.sign = (byte) (sign * divisor.sign); |
| 1052 | return result; |
| 1053 | } |
| 1054 | |
| 1055 | if (divisor.nans == INFINITE && nans == INFINITE) |
| 1056 | { |
| 1057 | ieeeFlags |= FLAG_INVALID; |
| 1058 | result = newInstance(zero); |
| 1059 | result.nans = QNAN; |
| 1060 | result = dotrap(FLAG_INVALID, "divide", divisor, result); |
| 1061 | return result; |
| 1062 | } |
| 1063 | } |
| 1064 | |
| 1065 | /* Test for divide by zero */ |
| 1066 | if (divisor.mant[DIGITS-1] == 0) |
| 1067 | { |
| 1068 | ieeeFlags |= FLAG_DIV_ZERO; |
| 1069 | result = newInstance(zero); |
| 1070 | result.sign = (byte) (sign * divisor.sign); |
| 1071 | result.nans = INFINITE; |
| 1072 | result = dotrap(FLAG_DIV_ZERO, "divide", divisor, result); |
| 1073 | return result; |
| 1074 | } |
| 1075 | |
| 1076 | dividend = new int[DIGITS+1]; // one extra digit needed |
| 1077 | quotient = new int[DIGITS+2]; // two extra digits needed 1 for overflow, 1 for rounding |
| 1078 | remainder = new int[DIGITS+1]; // one extra digit needed |
| 1079 | |
| 1080 | /* Initialize our most significat digits to zero */ |
| 1081 | |
| 1082 | dividend[DIGITS] = 0; |
| 1083 | quotient[DIGITS] = 0; |
| 1084 | quotient[DIGITS+1] = 0; |
| 1085 | remainder[DIGITS] = 0; |
| 1086 | |
| 1087 | /* copy our mantissa into the dividend, initialize the |
| 1088 | quotient while we are at it */ |
| 1089 | |
| 1090 | for (int i=0; i<DIGITS; i++) |
| 1091 | { |
| 1092 | dividend[i] = mant[i]; |
| 1093 | quotient[i] = 0; |
| 1094 | remainder[i] = 0; |
| 1095 | } |
| 1096 | |
| 1097 | /* outer loop. Once per quotient digit */ |
| 1098 | nsqd = 0; |
| 1099 | for (qd = DIGITS+1; qd >= 0; qd--) |
| 1100 | { |
| 1101 | /* Determine outer limits of our quotient digit */ |
| 1102 | |
| 1103 | // r = most sig 2 digits of dividend |
| 1104 | r = dividend[DIGITS]*radix+dividend[DIGITS-1]; |
| 1105 | min = r / (divisor.mant[DIGITS-1]+1); |
| 1106 | max = (r+1) / divisor.mant[DIGITS-1]; |
| 1107 | |
| 1108 | trialgood = false; |
| 1109 | |
| 1110 | while (!trialgood) |
| 1111 | { |
| 1112 | // try the mean |
| 1113 | trial = (min+max)/2; |
| 1114 | |
| 1115 | //System.out.println("dividend = "+dividend[2]+" "+dividend[1]+" "+dividend[0]); |
| 1116 | //System.out.println("divisor = "+divisor.mant[1]+" "+divisor.mant[0]); |
| 1117 | //System.out.println("min = "+min+" max = "+max+" trial = "+trial); |
| 1118 | |
| 1119 | /* Multiply by divisor and store as remainder */ |
| 1120 | rh = 0; |
| 1121 | for (int i=0; i<(DIGITS+1); i++) |
| 1122 | { |
| 1123 | int dm = (i<DIGITS)?divisor.mant[i]:0; |
| 1124 | r = (dm * trial) + rh; |
| 1125 | |
| 1126 | rh = r / radix; |
| 1127 | rl = r % radix; |
| 1128 | remainder[i] = rl; |
| 1129 | } |
| 1130 | |
| 1131 | //System.out.println(" *remainder = "+remainder[1]+" "+remainder[0]); |
| 1132 | |
| 1133 | /* subtract the remainder from the dividend */ |
| 1134 | rh = 1; // carry in to aid the subtraction |
| 1135 | for (int i=0; i<(DIGITS+1); i++) |
| 1136 | { |
| 1137 | r = ((radix-1) - remainder[i]) + dividend[i] + rh; |
| 1138 | rh = r / radix; |
| 1139 | rl = r % radix; |
| 1140 | remainder[i] = rl; |
| 1141 | } |
| 1142 | //System.out.println(" +remainder = "+remainder[1]+" "+remainder[0]); |
| 1143 | |
| 1144 | /* Lets analyse what we have here */ |
| 1145 | if (rh == 0) // trial is too big -- negative remainder |
| 1146 | { |
| 1147 | max = trial-1; |
| 1148 | //System.out.println("neg remainder"); |
| 1149 | //System.out.println(" remainder = "+remainder[1]+" "+remainder[0]); |
| 1150 | //System.out.println(" rh = "+rh); |
| 1151 | continue; |
| 1152 | } |
| 1153 | |
| 1154 | /* find out how far off the remainder is telling us we are */ |
| 1155 | minadj = (remainder[DIGITS] * radix)+remainder[DIGITS-1]; |
| 1156 | minadj = minadj / (divisor.mant[DIGITS-1]+1); |
| 1157 | |
| 1158 | //System.out.println("minadj = "+minadj); |
| 1159 | |
| 1160 | if (minadj >= 2) |
| 1161 | { |
| 1162 | min = trial+minadj; // update the minium |
| 1163 | continue; |
| 1164 | } |
| 1165 | |
| 1166 | /* May have a good one here, check more thoughly. Basically |
| 1167 | its a good one if it is less than the divisor */ |
| 1168 | trialgood = false; // assume false |
| 1169 | for (int i=(DIGITS-1); i >=0; i--) |
| 1170 | { |
| 1171 | if (divisor.mant[i] > remainder[i]) |
| 1172 | trialgood = true; |
| 1173 | if (divisor.mant[i] < remainder[i]) |
| 1174 | break; |
| 1175 | } |
| 1176 | |
| 1177 | //System.out.println("remainder = "+remainder[1]+" "+remainder[0]); |
| 1178 | if (remainder[DIGITS] != 0) |
| 1179 | trialgood = false; |
| 1180 | |
| 1181 | if (trialgood == false) |
| 1182 | min = trial+1; |
| 1183 | } |
| 1184 | |
| 1185 | /* Great we have a digit! */ |
| 1186 | quotient[qd] = trial; |
| 1187 | if (trial != 0 || nsqd != 0) |
| 1188 | nsqd++; |
| 1189 | |
| 1190 | if (rMode == ROUND_DOWN && nsqd == DIGITS) // We have enough for this mode |
| 1191 | break; |
| 1192 | |
| 1193 | if (nsqd > DIGITS) // We have enough digits |
| 1194 | break; |
| 1195 | |
| 1196 | /* move the remainder into the dividend while left shifting */ |
| 1197 | dividend[0] = 0; |
| 1198 | for (int i=0; i<DIGITS; i++) |
| 1199 | dividend[i+1] = remainder[i]; |
| 1200 | } |
| 1201 | |
| 1202 | /* Find the most sig digit */ |
| 1203 | md = DIGITS; // default |
| 1204 | for (int i=DIGITS+1; i>=0; i--) |
| 1205 | { |
| 1206 | if (quotient[i] != 0) |
| 1207 | { |
| 1208 | md = i; |
| 1209 | break; |
| 1210 | } |
| 1211 | } |
| 1212 | |
| 1213 | //System.out.println("quotient = "+quotient[2]+" "+quotient[1]+" "+quotient[0]); |
| 1214 | |
| 1215 | /* Copy the digits into the result */ |
| 1216 | for (int i=0; i<DIGITS; i++) |
| 1217 | result.mant[DIGITS-i-1] = quotient[md-i]; |
| 1218 | |
| 1219 | /* Fixup the exponent. */ |
| 1220 | result.exp = (exp - divisor.exp + md - DIGITS + 1 - 1); |
| 1221 | result.sign = (byte)((sign == divisor.sign)?1:-1); |
| 1222 | |
| 1223 | if (result.mant[DIGITS-1] == 0) // if result is zero, set exp to zero |
| 1224 | result.exp = 0; |
| 1225 | |
| 1226 | if (md > (DIGITS-1)) |
| 1227 | excp = result.round(quotient[md-DIGITS]); |
| 1228 | else |
| 1229 | excp = result.round(0); |
| 1230 | |
| 1231 | if (excp != 0) |
| 1232 | result = dotrap(excp, "divide", divisor, result); |
| 1233 | |
| 1234 | return result; |
| 1235 | } |
| 1236 | |
| 1237 | /** Divide by a single digit less than radix. |
| 1238 | * Special case, so there are speed advantages. |
| 1239 | * 0 <= divisor < radix */ |
| 1240 | public dfp divide(int divisor) |
| 1241 | { |
| 1242 | dfp result; |
| 1243 | int r, rh, rl; |
| 1244 | int excp; |
| 1245 | |
| 1246 | /* handle special cases */ |
| 1247 | if (nans != FINITE) |
| 1248 | { |
| 1249 | if (nans == QNAN || nans == SNAN) |
| 1250 | return this; |
| 1251 | |
| 1252 | if (nans == INFINITE) |
| 1253 | { |
| 1254 | result = newInstance(this); |
| 1255 | return result; |
| 1256 | } |
| 1257 | } |
| 1258 | |
| 1259 | /* Test for divide by zero */ |
| 1260 | if (divisor == 0) |
| 1261 | { |
| 1262 | ieeeFlags |= FLAG_DIV_ZERO; |
| 1263 | result = newInstance(zero); |
| 1264 | result.sign = sign; |
| 1265 | result.nans = INFINITE; |
| 1266 | result = dotrap(FLAG_DIV_ZERO, "divide", zero, result); |
| 1267 | return result; |
| 1268 | } |
| 1269 | |
| 1270 | /* range check divisor */ |
| 1271 | if (divisor < 0 || divisor >= radix) |
| 1272 | { |
| 1273 | ieeeFlags |= FLAG_INVALID; |
| 1274 | result = newInstance(zero); |
| 1275 | result.nans = QNAN; |
| 1276 | result = dotrap(FLAG_INVALID, "divide", result, result); |
| 1277 | return result; |
| 1278 | } |
| 1279 | |
| 1280 | result = newInstance(this); |
| 1281 | |
| 1282 | rl = 0; |
| 1283 | for (int i=DIGITS-1; i>=0; i--) |
| 1284 | { |
| 1285 | r = rl*radix + result.mant[i]; |
| 1286 | rh = r / divisor; |
| 1287 | rl = r % divisor; |
| 1288 | result.mant[i] = rh; |
| 1289 | } |
| 1290 | |
| 1291 | if (result.mant[DIGITS-1] == 0) // normalize |
| 1292 | { |
| 1293 | result.shiftLeft(); |
| 1294 | r = rl*radix; // compute the next digit and put it in |
| 1295 | rh = r / divisor; |
| 1296 | rl = r % divisor; |
| 1297 | result.mant[0] = rh; |
| 1298 | } |
| 1299 | |
| 1300 | excp = result.round(rl*radix/divisor); // do the rounding |
| 1301 | |
| 1302 | if (excp != 0) |
| 1303 | result = dotrap(excp, "divide", result, result); |
| 1304 | |
| 1305 | return result; |
| 1306 | } |
| 1307 | |
| 1308 | public dfp sqrt() /* returns the square root of this */ |
| 1309 | { |
| 1310 | dfp x, dx, px; |
| 1311 | |
| 1312 | /* check for unusual cases */ |
| 1313 | if (nans == FINITE && mant[DIGITS-1] == 0) // if zero |
| 1314 | return newInstance(this); |
| 1315 | |
| 1316 | if (nans != FINITE) |
| 1317 | { |
| 1318 | if (nans == INFINITE && sign == 1) // if positive infinity |
| 1319 | return newInstance(this); |
| 1320 | |
| 1321 | if (nans == QNAN) |
| 1322 | return newInstance(this); |
| 1323 | |
| 1324 | if (nans == SNAN) |
| 1325 | { |
| 1326 | dfp result; |
| 1327 | |
| 1328 | ieeeFlags |= FLAG_INVALID; |
| 1329 | result = newInstance(this); |
| 1330 | result = dotrap(FLAG_INVALID, "sqrt", null, result); |
| 1331 | return result; |
| 1332 | } |
| 1333 | } |
| 1334 | |
| 1335 | if (sign == -1) // if negative |
| 1336 | { |
| 1337 | dfp result; |
| 1338 | |
| 1339 | ieeeFlags |= FLAG_INVALID; |
| 1340 | result = newInstance(this); |
| 1341 | result.nans = QNAN; |
| 1342 | result = dotrap(FLAG_INVALID, "sqrt", null, result); |
| 1343 | return result; |
| 1344 | } |
| 1345 | |
| 1346 | x = newInstance(this); |
| 1347 | |
| 1348 | /* Lets make a reasonable guess as to the size of the square root */ |
| 1349 | if (x.exp < -1 || x.exp > 1) |
| 1350 | x.exp = (this.exp/2); |
| 1351 | |
| 1352 | /* Coarsely estimate the mantissa */ |
| 1353 | switch (x.mant[DIGITS-1] / 2000) |
| 1354 | { |
| 1355 | case 0: x.mant[DIGITS-1] = x.mant[DIGITS-1]/2+1; break; |
| 1356 | case 2: x.mant[DIGITS-1] = 1500; break; |
| 1357 | case 3: x.mant[DIGITS-1] = 2200; break; |
| 1358 | case 4: x.mant[DIGITS-1] = 3000; break; |
| 1359 | } |
| 1360 | |
| 1361 | dx = newInstance(x); |
| 1362 | |
| 1363 | /* Now that we have the first pass estimiate, compute the rest |
| 1364 | by the formula dx = (y - x*x) / (2x); */ |
| 1365 | |
| 1366 | px = zero; |
| 1367 | while (x.unequal(px)) |
| 1368 | { |
| 1369 | dx = newInstance(x); |
| 1370 | dx.sign = -1; |
| 1371 | dx = dx.add(this.divide(x)); |
| 1372 | dx = dx.divide(2); |
| 1373 | px = x; |
| 1374 | x = x.add(dx); |
| 1375 | |
| 1376 | // if dx is zero, break. Note testing the most sig digit |
| 1377 | // is a sufficient test since dx is normalized |
| 1378 | if (dx.mant[DIGITS-1] == 0) |
| 1379 | break; |
| 1380 | } |
| 1381 | |
| 1382 | return x; |
| 1383 | } |
| 1384 | |
| 1385 | public String toString() |
| 1386 | { |
| 1387 | if (nans != FINITE) // if non-finite exceptional cases |
| 1388 | { |
| 1389 | switch (sign*nans) |
| 1390 | { |
| 1391 | case INFINITE: return "Infinity"; |
| 1392 | case -INFINITE: return "-Infinity"; |
| 1393 | case QNAN: return "NaN"; |
| 1394 | case -QNAN: return "NaN"; |
| 1395 | case SNAN: return "NaN"; |
| 1396 | case -SNAN: return "NaN"; |
| 1397 | } |
| 1398 | } |
| 1399 | |
| 1400 | if (exp > DIGITS || exp < -1) |
| 1401 | return dfp2sci(this); |
| 1402 | |
| 1403 | return dfp2string(this); |
| 1404 | } |
| 1405 | |
| 1406 | /* Convert a dfp to a string using scientific notation */ |
| 1407 | protected String dfp2sci(dfp a) |
| 1408 | { |
| 1409 | char rawdigits[] = new char[DIGITS*4]; |
| 1410 | char outputbuffer[] = new char[DIGITS*4 + 20]; |
| 1411 | int p; |
| 1412 | int q; |
| 1413 | int e; |
| 1414 | int ae; |
| 1415 | int shf; |
| 1416 | |
| 1417 | |
| 1418 | /* Get all the digits */ |
| 1419 | p = 0; |
| 1420 | for (int i=DIGITS-1; i>=0; i--) |
| 1421 | { |
| 1422 | rawdigits[p++] = (char) ((a.mant[i]/1000) + '0'); |
| 1423 | rawdigits[p++] = (char) (((a.mant[i]/100)%10) + '0'); |
| 1424 | rawdigits[p++] = (char) (((a.mant[i]/10)%10) + '0'); |
| 1425 | rawdigits[p++] = (char) (((a.mant[i])%10) + '0'); |
| 1426 | } |
| 1427 | |
| 1428 | /* find the first non-zero one */ |
| 1429 | for (p=0; p<rawdigits.length; p++) |
| 1430 | if (rawdigits[p] != '0') |
| 1431 | break; |
| 1432 | shf = p; |
| 1433 | |
| 1434 | /* Now do the conversion */ |
| 1435 | q = 0; |
| 1436 | if (a.sign == -1) |
| 1437 | outputbuffer[q++] = '-'; |
| 1438 | |
| 1439 | if (p != rawdigits.length) // there are non zero digits... |
| 1440 | { |
| 1441 | outputbuffer[q++] = rawdigits[p++]; |
| 1442 | outputbuffer[q++] = '.'; |
| 1443 | |
| 1444 | while (p<rawdigits.length) |
| 1445 | outputbuffer[q++] = rawdigits[p++]; |
| 1446 | } |
| 1447 | else |
| 1448 | { |
| 1449 | outputbuffer[q++] = '0'; |
| 1450 | outputbuffer[q++] = '.'; |
| 1451 | outputbuffer[q++] = '0'; |
| 1452 | outputbuffer[q++] = 'e'; |
| 1453 | outputbuffer[q++] = '0'; |
| 1454 | return new String(outputbuffer, 0, 5); |
| 1455 | } |
| 1456 | |
| 1457 | outputbuffer[q++] = 'e'; |
| 1458 | |
| 1459 | /* find the msd of the exponent */ |
| 1460 | |
| 1461 | e = a.exp * 4 - shf - 1; |
| 1462 | ae = e; |
| 1463 | if (e < 0) |
| 1464 | ae = -e; |
| 1465 | |
| 1466 | /* Find the largest p such that p < e */ |
| 1467 | for (p=1000000000; p>ae; p /= 10); |
| 1468 | |
| 1469 | if (e < 0) |
| 1470 | outputbuffer[q++] = '-'; |
| 1471 | |
| 1472 | while (p > 0) |
| 1473 | { |
| 1474 | outputbuffer[q++] = (char)(ae/p + '0'); |
| 1475 | ae = ae % p; |
| 1476 | p = p / 10; |
| 1477 | } |
| 1478 | |
| 1479 | return new String(outputbuffer, 0, q); |
| 1480 | } |
| 1481 | |
| 1482 | /* converts a dfp to a string handling the normal case */ |
| 1483 | protected String dfp2string(dfp a) |
| 1484 | { |
| 1485 | char buffer[] = new char[DIGITS*4 + 20]; |
| 1486 | int p = 1; |
| 1487 | int q; |
| 1488 | int e = a.exp; |
| 1489 | boolean pointInserted = false; |
| 1490 | |
| 1491 | buffer[0] = ' '; |
| 1492 | |
| 1493 | if (e <= 0) |
| 1494 | { |
| 1495 | buffer[p++] = '0'; |
| 1496 | buffer[p++] = '.'; |
| 1497 | pointInserted = true; |
| 1498 | } |
| 1499 | |
| 1500 | while (e < 0) |
| 1501 | { |
| 1502 | buffer[p++] = '0'; |
| 1503 | buffer[p++] = '0'; |
| 1504 | buffer[p++] = '0'; |
| 1505 | buffer[p++] = '0'; |
| 1506 | e++; |
| 1507 | } |
| 1508 | |
| 1509 | for (int i=DIGITS-1; i>=0; i--) |
| 1510 | { |
| 1511 | buffer[p++] = (char) ((a.mant[i]/1000) + '0'); |
| 1512 | buffer[p++] = (char) (((a.mant[i]/100)%10) + '0'); |
| 1513 | buffer[p++] = (char) (((a.mant[i]/10)%10) + '0'); |
| 1514 | buffer[p++] = (char) (((a.mant[i])%10) + '0'); |
| 1515 | if (--e == 0) |
| 1516 | { |
| 1517 | buffer[p++] = '.'; |
| 1518 | pointInserted = true; |
| 1519 | } |
| 1520 | } |
| 1521 | |
| 1522 | while (e > 0) |
| 1523 | { |
| 1524 | buffer[p++] = '0'; |
| 1525 | buffer[p++] = '0'; |
| 1526 | buffer[p++] = '0'; |
| 1527 | buffer[p++] = '0'; |
| 1528 | e--; |
| 1529 | } |
| 1530 | |
| 1531 | if (!pointInserted) /* Ensure we have a radix point! */ |
| 1532 | buffer[p++] = '.'; |
| 1533 | |
| 1534 | /* Supress leading zeros */ |
| 1535 | q = 1; |
| 1536 | while (buffer[q] == '0') |
| 1537 | q++; |
| 1538 | if (buffer[q] == '.') |
| 1539 | q--; |
| 1540 | |
| 1541 | /* Suppress trailing zeros */ |
| 1542 | while (buffer[p-1] == '0') |
| 1543 | p--; |
| 1544 | |
| 1545 | /* Insert sign */ |
| 1546 | if (a.sign < 0) |
| 1547 | buffer[--q] = '-'; |
| 1548 | |
| 1549 | return new String(buffer, q, p-q); |
| 1550 | } |
| 1551 | |
| 1552 | protected dfp string2dfp(String fpin) |
| 1553 | { |
| 1554 | String fpdecimal; |
| 1555 | int trailing_zeros; |
| 1556 | int significant_digits; |
| 1557 | int decimal; |
| 1558 | int p, q; |
| 1559 | char Striped[]; |
| 1560 | dfp result; |
| 1561 | boolean decimalFound = false; |
| 1562 | int decimalPos = 0; // position of the decimal. |
| 1563 | final int rsize = 4; // size of radix in decimal digits |
| 1564 | final int offset = 4; // Starting offset into Striped |
| 1565 | int sciexp = 0; |
| 1566 | int i; |
| 1567 | |
| 1568 | Striped = new char[DIGITS*rsize+offset*2]; |
| 1569 | |
| 1570 | /* Check some special cases */ |
| 1571 | if (fpin.equals("Infinite")) |
| 1572 | return create((byte) 1, (byte) INFINITE); |
| 1573 | |
| 1574 | if (fpin.equals("-Infinite")) |
| 1575 | return create((byte) -1, (byte) INFINITE); |
| 1576 | |
| 1577 | if (fpin.equals("NaN")) |
| 1578 | return create((byte) 1, (byte) QNAN); |
| 1579 | |
| 1580 | result = newInstance(zero); |
| 1581 | |
| 1582 | /* Check for scientific notation */ |
| 1583 | p = fpin.indexOf("e"); |
| 1584 | if (p == -1) // try upper case? |
| 1585 | p = fpin.indexOf("E"); |
| 1586 | |
| 1587 | if (p != -1) // scientific notation |
| 1588 | { |
| 1589 | fpdecimal = fpin.substring(0, p); |
| 1590 | String fpexp = fpin.substring(p+1); |
| 1591 | boolean negative = false; |
| 1592 | |
| 1593 | sciexp = 0; |
| 1594 | for (i=0; i<fpexp.length(); i++) |
| 1595 | { |
| 1596 | if (fpexp.charAt(i) == '-') |
| 1597 | { |
| 1598 | negative = true; |
| 1599 | continue; |
| 1600 | } |
| 1601 | if (fpexp.charAt(i) >= '0' && fpexp.charAt(i) <= '9') |
| 1602 | sciexp = sciexp * 10 + fpexp.charAt(i) - '0'; |
| 1603 | } |
| 1604 | |
| 1605 | if (negative) |
| 1606 | sciexp = -sciexp; |
| 1607 | } |
| 1608 | else // normal case |
| 1609 | { |
| 1610 | fpdecimal = fpin; |
| 1611 | } |
| 1612 | |
| 1613 | /* If there is a minus sign in the number then it is negative */ |
| 1614 | |
| 1615 | if (fpdecimal.indexOf("-") != -1) |
| 1616 | result.sign = -1; |
| 1617 | |
| 1618 | /* First off, find all of the leading zeros, trailing zeros, and |
| 1619 | siginificant digits */ |
| 1620 | |
| 1621 | p = 0; |
| 1622 | |
| 1623 | /* Move p to first significant digit */ |
| 1624 | |
| 1625 | for(;;) |
| 1626 | { |
| 1627 | if (fpdecimal.charAt(p) >= '1' && fpdecimal.charAt(p) <= '9') |
| 1628 | break; |
| 1629 | |
| 1630 | if (decimalFound && fpdecimal.charAt(p) == '0') |
| 1631 | decimalPos--; |
| 1632 | |
| 1633 | if (fpdecimal.charAt(p) == '.') |
| 1634 | decimalFound = true; |
| 1635 | |
| 1636 | p++; |
| 1637 | |
| 1638 | if (p == fpdecimal.length()) |
| 1639 | break; |
| 1640 | } |
| 1641 | |
| 1642 | /* Copy the string onto Stripped */ |
| 1643 | |
| 1644 | q = offset; |
| 1645 | Striped[0] = '0'; |
| 1646 | Striped[1] = '0'; |
| 1647 | Striped[2] = '0'; |
| 1648 | Striped[3] = '0'; |
| 1649 | significant_digits=0; |
| 1650 | for(;;) |
| 1651 | { |
| 1652 | if (p == (fpdecimal.length())) |
| 1653 | break; |
| 1654 | |
| 1655 | // Dont want to run pass the end of the array |
| 1656 | if (q == DIGITS*rsize+offset+1) |
| 1657 | break; |
| 1658 | |
| 1659 | if (fpdecimal.charAt(p) == '.') |
| 1660 | { |
| 1661 | decimalFound = true; |
| 1662 | decimalPos = significant_digits; |
| 1663 | p++; |
| 1664 | continue; |
| 1665 | } |
| 1666 | |
| 1667 | if (fpdecimal.charAt(p) < '0' || fpdecimal.charAt(p) > '9') |
| 1668 | { |
| 1669 | p++; |
| 1670 | continue; |
| 1671 | } |
| 1672 | |
| 1673 | Striped[q] = fpdecimal.charAt(p); |
| 1674 | q++; |
| 1675 | p++; |
| 1676 | significant_digits++; |
| 1677 | } |
| 1678 | |
| 1679 | |
| 1680 | // If the decimal point has been found then get rid of trailing zeros. |
| 1681 | if (decimalFound && q != offset) |
| 1682 | { |
| 1683 | for (;;) |
| 1684 | { |
| 1685 | q--; |
| 1686 | if (q == offset) |
| 1687 | break; |
| 1688 | if (Striped[q] == '0') |
| 1689 | { |
| 1690 | significant_digits--; |
| 1691 | } |
| 1692 | else |
| 1693 | { |
| 1694 | break; |
| 1695 | } |
| 1696 | } |
| 1697 | } |
| 1698 | |
| 1699 | // special case of numbers like "0.00000" |
| 1700 | if (decimalFound && significant_digits == 0) |
| 1701 | decimalPos = 0; |
| 1702 | |
| 1703 | // Implicit decimal point at end of number if not present |
| 1704 | if (!decimalFound) |
| 1705 | decimalPos = q-offset; |
| 1706 | |
| 1707 | /* Find the number of significant trailing zeros */ |
| 1708 | |
| 1709 | q = offset; // set q to point to first sig digit |
| 1710 | p = significant_digits-1+offset; |
| 1711 | |
| 1712 | trailing_zeros = 0; |
| 1713 | while (p>q) |
| 1714 | { |
| 1715 | if (Striped[p] != '0') |
| 1716 | break; |
| 1717 | trailing_zeros++; |
| 1718 | p--; |
| 1719 | } |
| 1720 | |
| 1721 | /* Make sure the decimal is on a mod 10000 boundary */ |
| 1722 | i = (((rsize*100) - decimalPos - sciexp%rsize) % rsize); |
| 1723 | q -= i; |
| 1724 | decimalPos += i; |
| 1725 | |
| 1726 | /* Make the mantissa length right by adding zeros at the end if |
| 1727 | necessary */ |
| 1728 | |
| 1729 | while ( (p-q) < (DIGITS*rsize) ) |
| 1730 | { |
| 1731 | for (i=0; i<rsize; i++) |
| 1732 | Striped[++p] = '0'; |
| 1733 | } |
| 1734 | |
| 1735 | /* Ok, now we know how many trailing zeros there are, and |
| 1736 | where the least significant digit is. */ |
| 1737 | |
| 1738 | for (i=(DIGITS-1); i>=0; i--) |
| 1739 | { |
| 1740 | result.mant[i] = (Striped[q] - '0')*1000 + |
| 1741 | (Striped[q+1] - '0')*100 + |
| 1742 | (Striped[q+2] - '0')*10 + |
| 1743 | (Striped[q+3] - '0'); |
| 1744 | q += 4; |
| 1745 | } |
| 1746 | |
| 1747 | |
| 1748 | result.exp = ((decimalPos+sciexp) / rsize); |
| 1749 | |
| 1750 | if (q < Striped.length) // Is there possible another digit? |
| 1751 | result.round((Striped[q] - '0')*1000); |
| 1752 | |
| 1753 | return result; |
| 1754 | } |
| 1755 | |
| 1756 | /** Set the rounding mode to be one of the following values: |
| 1757 | * ROUND_UP, ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_DOWN, |
| 1758 | * ROUND_HALF_EVEN, ROUND_HALF_ODD, ROUND_CEIL, ROUND_FLOOR. |
| 1759 | * |
| 1760 | * Default is ROUND_HALF_EVEN |
| 1761 | * |
| 1762 | * Note that the rounding mode is common to all instances |
| 1763 | * in the system and will effect all future calculations. |
| 1764 | */ |
| 1765 | public static void setRoundingMode(int mode) |
| 1766 | { |
| 1767 | rMode = mode; |
| 1768 | } |
| 1769 | |
| 1770 | /** Returns the current rounding mode */ |
| 1771 | public static int getRoundingMode() |
| 1772 | { |
| 1773 | return rMode; |
| 1774 | } |
| 1775 | |
| 1776 | /** Raises a trap. This does not set the corresponding flag however. |
| 1777 | * @param type the trap type |
| 1778 | * @param what - name of routine trap occured in |
| 1779 | * @param oper - input operator to function |
| 1780 | * @param result - the result computed prior to the trap |
| 1781 | * @return The suggested return value from the trap handler |
| 1782 | */ |
| 1783 | public dfp dotrap(int type, String what, dfp oper, dfp result) |
| 1784 | { |
| 1785 | dfp def = result; |
| 1786 | |
| 1787 | switch (type) |
| 1788 | { |
| 1789 | case FLAG_INVALID: |
| 1790 | def = newInstance(zero); |
| 1791 | def.sign = result.sign; |
| 1792 | def.nans = QNAN; |
| 1793 | break; |
| 1794 | |
| 1795 | case FLAG_DIV_ZERO: |
| 1796 | if (nans == FINITE && mant[DIGITS-1] != 0) // normal case, we are finite, non-zero |
| 1797 | { |
| 1798 | def = newInstance(zero); |
| 1799 | def.sign = (byte)(sign*oper.sign); |
| 1800 | def.nans = INFINITE; |
| 1801 | } |
| 1802 | |
| 1803 | if (nans == FINITE && mant[DIGITS-1] == 0) // 0/0 |
| 1804 | { |
| 1805 | def = newInstance(zero); |
| 1806 | def.nans = QNAN; |
| 1807 | } |
| 1808 | |
| 1809 | if (nans == INFINITE || nans == QNAN) |
| 1810 | { |
| 1811 | def = newInstance(zero); |
| 1812 | def.nans = QNAN; |
| 1813 | } |
| 1814 | |
| 1815 | if (nans == INFINITE || nans == SNAN) |
| 1816 | { |
| 1817 | def = newInstance(zero); |
| 1818 | def.nans = QNAN; |
| 1819 | } |
| 1820 | break; |
| 1821 | |
| 1822 | case FLAG_UNDERFLOW: |
| 1823 | if ( (result.exp+DIGITS) < minExp) |
| 1824 | { |
| 1825 | def = newInstance(zero); |
| 1826 | def.sign = result.sign; |
| 1827 | } |
| 1828 | else |
| 1829 | { |
| 1830 | def = newInstance(result); // gradual underflow |
| 1831 | } |
| 1832 | result.exp = result.exp + errScale; |
| 1833 | break; |
| 1834 | |
| 1835 | case FLAG_OVERFLOW: |
| 1836 | result.exp = result.exp - errScale; |
| 1837 | def = newInstance(zero); |
| 1838 | def.sign = result.sign; |
| 1839 | def.nans = INFINITE; |
| 1840 | break; |
| 1841 | |
| 1842 | default: def = result; break; |
| 1843 | } |
| 1844 | |
| 1845 | return trap(type, what, oper, def, result); |
| 1846 | } |
| 1847 | |
| 1848 | /** Trap handler. Subclasses may override this to provide trap |
| 1849 | * functionality per IEEE 854-1987. |
| 1850 | * |
| 1851 | * @param type The exception type - e.g. FLAG_OVERFLOW |
| 1852 | * @param what The name of the routine we were in e.g. divide() |
| 1853 | * @param oper An operand to this function if any |
| 1854 | * @param def The default return value if trap not enabled |
| 1855 | * @param result The result that is spcefied to be delivered per |
| 1856 | * IEEE 854, if any |
| 1857 | */ |
| 1858 | protected dfp trap(int type, String what, dfp oper, |
| 1859 | dfp def, dfp result) |
| 1860 | { |
| 1861 | return def; |
| 1862 | } |
| 1863 | |
| 1864 | /** Returns the IEEE 854 status flags */ |
| 1865 | public static int getIEEEFlags() |
| 1866 | { |
| 1867 | return ieeeFlags; |
| 1868 | } |
| 1869 | |
| 1870 | /** Clears the IEEE 854 status flags */ |
| 1871 | public static void clearIEEEFlags() |
| 1872 | { |
| 1873 | ieeeFlags = 0; |
| 1874 | } |
| 1875 | |
| 1876 | /** Sets the IEEE 854 status flags */ |
| 1877 | public static void setIEEEFlags(int flags) |
| 1878 | { |
| 1879 | ieeeFlags = flags; |
| 1880 | } |
| 1881 | |
| 1882 | /** Returns the type - one of FINITE, INFINITE, SNAN, QNAN */ |
| 1883 | public int classify() |
| 1884 | { |
| 1885 | return nans; |
| 1886 | } |
| 1887 | |
| 1888 | /** Creates a dfp with a non-finite value */ |
| 1889 | public static dfp create(byte sign, byte nans) |
| 1890 | { |
| 1891 | dfp result = new dfp(); |
| 1892 | result.sign = sign; |
| 1893 | result.nans = nans; |
| 1894 | |
| 1895 | return result; |
| 1896 | } |
| 1897 | |
| 1898 | /** Creates a dfp that is the same as x except that it has |
| 1899 | * the sign of y. abs(x) = dfp.copysign(x, dfp.one) */ |
| 1900 | public static dfp copysign(dfp x, dfp y) |
| 1901 | { |
| 1902 | dfp result = x.newInstance(x); |
| 1903 | result.sign = y.sign; |
| 1904 | return result; |
| 1905 | } |
| 1906 | |
| 1907 | /** Returns the next number greater than this one in the direction |
| 1908 | * of x. If this==x then simply returns this. */ |
| 1909 | |
| 1910 | public dfp nextAfter(dfp x) |
| 1911 | { |
| 1912 | boolean up = false; |
| 1913 | dfp result, inc; |
| 1914 | |
| 1915 | // if this is greater than x |
| 1916 | if (this.lessThan(x)) |
| 1917 | up = true; |
| 1918 | |
| 1919 | if (compare(this, x) == 0) |
| 1920 | return newInstance(x); |
| 1921 | |
| 1922 | if (lessThan(zero)) |
| 1923 | up = !up; |
| 1924 | |
| 1925 | if (up) |
| 1926 | { |
| 1927 | inc = newInstance(one); |
| 1928 | inc.exp = this.exp-DIGITS+1; |
| 1929 | inc.sign = this.sign; |
| 1930 | |
| 1931 | if (this.equal(zero)) |
| 1932 | inc.exp = minExp-DIGITS; |
| 1933 | |
| 1934 | result = add(inc); |
| 1935 | } |
| 1936 | else |
| 1937 | { |
| 1938 | inc = newInstance(one); |
| 1939 | inc.exp = this.exp; |
| 1940 | inc.sign = this.sign; |
| 1941 | |
| 1942 | if (this.equal(inc)) |
| 1943 | inc.exp = this.exp-DIGITS; |
| 1944 | else |
| 1945 | inc.exp = this.exp-DIGITS+1; |
| 1946 | |
| 1947 | if (this.equal(zero)) |
| 1948 | inc.exp = minExp-DIGITS; |
| 1949 | |
| 1950 | result = this.subtract(inc); |
| 1951 | } |
| 1952 | |
| 1953 | if (result.classify() == INFINITE && this.classify() != INFINITE) |
| 1954 | { |
| 1955 | ieeeFlags |= FLAG_INEXACT; |
| 1956 | result = dotrap(FLAG_INEXACT, "nextAfter", x, result); |
| 1957 | } |
| 1958 | |
| 1959 | if (result.equal(zero) && this.equal(zero) == false) |
| 1960 | { |
| 1961 | ieeeFlags |= FLAG_INEXACT; |
| 1962 | result = dotrap(FLAG_INEXACT, "nextAfter", x, result); |
| 1963 | } |
| 1964 | |
| 1965 | return result; |
| 1966 | } |
| 1967 | } |