The goal of this library is to produce all the utility routines necessary to work with arbitrarily large numbers.
1 // 2 // LargeNumber library 3 // 4 // authors: Isaac Traxler & students 5 // 6 // This is a project started back in 2000 that was not finished 7 // and forgotten. It has now been resurrected. 8 // 9 // The goal of this project is to produce a usable c source library 10 // for large number arithmetic. 11 // 12 // Students in my Psychology of Programming class in 2000 contributed. 13 // Since I have largely restructured it, individual names have been 14 // removed from the individual routines. So here are the names of the 15 // original contributing students: 16 // - Paul Miller 17 // - Wojciech Stryjewski 18 // - Phil Bordelon 19 // - John Walker 20 // - Erin Valentine 21 // - Jay Ponville 22 // - Jamie Ahmad 23 // - Helen 24 // 25 // Contributed to revamped version: 26 // - Josh Abadie 27 // 28 #include <ctype.h> 29 // 30 // Make sure that LN_MAX_DIGITS is large enough to handle worst case. 31 // Be aware that as many as 5 LN instances might exist in a routine. 32 // Be aware that excessively large values will result in CPU consumption 33 // in certain situations (like division of repeating decimals). 34 // 35 #define LN_MAX_DIGITS 1000 36 37 typedef struct LARGE_NUMBER_STRUCT 38 { 39 unsigned short int array[LN_MAX_DIGITS]; // might consider unsigned char here 40 // to reduce storage by 50% 41 signed short int sign; 42 signed long int exponent; 43 signed short int digitCount; 44 } 45 LARGE_NUMBER_STRUCT; 46 // 47 // ASSUMPTIONS: 48 // 1) That no value sent to the library will exceed bounds 49 // a) Exponent will fit into a signed long at ALL times 50 // b) Significant digit count will not exceed LN_MAX_DIGITS 51 // 52 // 2) LN instances are ALWAYS normalized when passed into a routine 53 // 54 // 3) Adding or subtracting two 501 digit numbers can exceed 1000 digits 55 // 56 // 4) No bounds checking is done against LN_MAX_DIGITS 57 // 58 // 5) Normalization does the following: 59 // a) Adjusts exponent, adjusts digitCount, and removes leading zeroes 60 // b) Adjusts digitCount and removes trailing zeroes 61 // c) Leaves number so that a decimal point is implied before the first digit 62 // 63 // 64 // ******************************************************************************** 65 // rules: 66 // - all routines return 0 if everything is okay, a different positive number 67 // for each different error 68 // - Any result passed back (except from LNshift) is normalized 69 // - LNadd adds any two numbers with same sign (calls subtract if signs differ) 70 // - LNsubtract subtracts any two numbers with same sign (calls add if signs differ) 71 // 72 // a = 1 73 // b = -1 74 // add(a,b,c) ==> subtract(a,(-b),c) 75 // subtract(a,b,c) ==> add(a,(-b),c) 76 // 77 // - 0 ALWAYS has a + sign and an exponent of 0 78 // 79 // 80 81 void LNprint(LARGE_NUMBER_STRUCT *n) 82 // simple routine to print large number 83 { // BEGIN function LNprint -- (200302) 84 char str[LN_MAX_DIGITS+25]; 85 86 LNarr2strExp(n, str); 87 printf("[%s]\n", str); 88 } // END function LNprint -- (200302) 89 90 int LNnegate(LARGE_NUMBER_STRUCT *ln1) 91 // changes sign of ln1 92 { // BEGIN function LNnegate -- (200302) 93 if (0 != ln1->digitCount) 94 ln1->sign *= -1; 95 return 0; 96 } // END function LNnegate -- (200302) 97 98 int LNcompare(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2) 99 // compares to see if a<b (-1), a=b (0), a>b (1); assumes both numbers 100 // are normalized (have first digit non-zero and no trailing zeros) 101 { // BEGIN function LNcompare -- (200303) 102 int toReturn = 0; 103 104 // XOR the two, if same 0 (false) results, if different -2 (true) 105 if (ln1->sign ^ ln2->sign) // signs are same, result is 0 106 { // have different signs 107 toReturn = (0 > ln1->sign) ? -1 : 1; 108 } // have different signs 109 else 110 { // have same sign 111 if (ln1->exponent != ln2->exponent) 112 { // exponents not equal, return 1 (1st one) or -1 (2nd one) to show larger 113 toReturn = (ln1->exponent > ln2->exponent) ? 1 : -1; 114 } // exponents not equal, return 1 (1st one) or -1 (2nd one) to show larger 115 else 116 { // numbers have same exponent 117 int i, t; 118 119 t = (ln1->digitCount > ln2->digitCount) ? ln2->digitCount : ln1->digitCount; 120 for (i=0; (i<t) && (0 == toReturn) ; i++) 121 { // for - compare each digit 122 if (ln1->array[i] != ln2->array[i]) 123 toReturn = (ln1->array[i] > ln2->array[i]) ? ln1->sign : - ln2->sign; 124 } // for - compare each digit 125 // digits identical, but one number has extra digits, so number with extra digits 126 // is bigger if positive, smaller if negative. 127 if ((0 == toReturn) && (ln1->digitCount != ln2->digitCount)) 128 toReturn = (ln1->digitCount > ln2->digitCount) ? ln1->sign : - ln2->sign; 129 } // numbers have same exponent 130 } // have same sign 131 return toReturn; 132 } // END function LNcompare -- (200303) 133 134 int LNstr2arr(char str[], LARGE_NUMBER_STRUCT *ln) 135 // convert from string into LN data structure 136 // assume no invalid characters in string (but skip over leading and trailing blanks) 137 // 138 // State diagram: 139 // 140 // state | val | whitespace | - | + | . | digit | Ee | end of string` 141 // ------+-----+------------+------+------+------+-------+------+-------------- 142 // start | 1 | start | num1 | num1 | dec1 | num2 | err | 0 143 // num1 | 2 | err | err | err | dec1 | num2 | err | err 144 // num2 | 3 | normalize | err | err | dec2 | num2 | exp1 | normalize 145 // dec1 | 4 | err | err | err | err | dec2 | err | err 146 // dec2 | 5 | normalize | err | err | err | dec2 | exp1 | normalize 147 // exp1 | 6 | err | exp2 | exp2 | err | exp3 | err | err 148 // exp2 | 7 | err | err | err | err | exp3 | err | err 149 // exp3 | 8 | normalize | err | err | err | exp3 | err | normalize 150 { // BEGIN function LNstr2arr -- (200302) 151 #define START 1 152 #define NUM1 2 153 #define NUM2 3 154 #define DEC1 4 155 #define DEC2 5 156 #define EXP1 6 157 #define EXP2 7 158 #define EXP3 8 159 // 160 // status - (succes/failure) flag (init to SUCCESS) 161 // done - are we done yet? (init to NO) 162 // dpflag - decimal point flag - Have we encountered one yet? (init to NO) 163 // numflag - number flag - Have we encountered any NON-ZERO digits yet? (init to NO) 164 // n - counter/subscript for large number (init to start) 165 // ch - point to main string 166 // These next two need not be used if their values are stored directly into large number. 167 // sign 168 // exp 169 // 170 int state = START, done = 0, n = 0; 171 signed short int dpflag = 0, numflag = 0, sign = 1; 172 signed long int exp; 173 char *ch = str; 174 175 // skip leading blanks and leading zeroes (start < > start) 176 while ( (isspace(*ch)) || ('0' == *ch) ) ch++; 177 178 if (0 != *ch) // is it end of string? 179 { // not empty string 180 // do we have a sign (must be first char) 181 if ('-' == *ch) 182 { // negative - state is NUM1 183 sign = -1; 184 ch++; 185 } // negative - state is NUM1 186 else 187 // Check for plus sign: Not really necessary...(these 4 lines may 188 // be omitted) if numbers are not going to have unary pluses 189 if (*ch == '+') 190 { // positive (the default) - state is NUM1 191 ch++; 192 } // positive (the default) - state is NUM1 193 194 // now get digits until the decimal point or exponent 195 while (isdigit(*ch)) 196 { // process digits -- into state NUM2 197 state = NUM2; 198 ln->array[n++] = *ch - '0'; 199 ch++; // move to next char in string 200 } // process digits -- into state NUM2 201 exp = n; 202 203 if ('.' == *ch) 204 { // decimal point 205 // set state to DEC1 if no digits, DEC2 if digits already 206 state = (NUM2 != state) ? DEC1 : DEC2; 207 ch++; 208 209 // now get digits after the decimal point 210 if (isdigit(*ch)) state = DEC2; 211 while (isdigit(*ch)) 212 { // process digits -- into state NUM2 213 ln->array[n++] = *ch - '0'; 214 ch++; // move to next char in string 215 } // process digits -- into state NUM2 216 } // decimal point 217 218 // only things left are Ee (exponent), whitespace and end of string 219 if (('E' == *ch) || ('e' == *ch)) 220 { // okay we have an exponent 221 signed long int texp; 222 223 state = EXP2; 224 ch++; 225 sscanf(ch, "%d", &texp); 226 exp += texp; 227 } // okay we have an exponent 228 } // not empty string 229 230 if ((EXP2 == state) || (DEC2 == state) || (NUM2 == state)) 231 { // normalize number 232 ln->sign = sign; 233 ln->exponent = exp; 234 ln->digitCount = n; 235 state = 0; 236 } // normalize number 237 return state; 238 } // END function LNstr2arr -- (200302) 239 240 int LNicnvrt(long int number, LARGE_NUMBER_STRUCT *n) 241 // convert a long int to Large Number 242 { // BEGIN function LNicnvrt -- (200302) 243 int idx, digit, j; 244 245 // do sign 246 n->sign = (number < 0) ? -1 : 1; 247 248 // set mantissa and exponent 249 n->exponent = 0; 250 idx = LN_MAX_DIGITS; 251 while (number > 0) 252 { // while 253 digit = number % 10; 254 n->array[--idx] = digit; 255 number /= 10; 256 } // while 257 n->exponent = LN_MAX_DIGITS - idx; 258 n->digitCount = n->exponent; 259 for (j=0; LN_MAX_DIGITS > (j + idx); j++) 260 { // for 261 n->array[j] = n->array[idx+j]; 262 } // for 263 return 0; 264 } // END function LNicnvrt -- (200302) 265 266 int LNarr2strExp(LARGE_NUMBER_STRUCT *ln, char str[]) 267 // convert the ln struct to a string in scientific notation 268 { // BEGIN function LNarr2strExp -- (200302) 269 int i, cnt = 0; 270 271 if (0 == ln->digitCount) 272 { // handle zero 273 strncpy("+0E0", str); 274 } // handle zero 275 else 276 { // handle non-zero 277 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 278 str[cnt++] = '0' + ln->array[0]; 279 str[cnt++] = '.'; 280 for (i = 1; i < ln->digitCount; i++) 281 str[cnt++] = '0' + ln->array[i]; 282 str[cnt++] = 'E'; 283 sprintf(&(str[cnt]), "%+ld", (ln->exponent-1)); 284 } // handle non-zero 285 return 0; 286 } // END function LNarr2strExp -- (200302) 287 288 int LNarr2strInt(LARGE_NUMBER_STRUCT *ln, char str[]) 289 // convert the ln struct to a string n integer format with truncate 290 { // BEGIN function LNarr2strInt -- (200302) 291 int i, cnt = 0; 292 293 if ((0 > ln->exponent) || (0 >= ln->digitCount)) 294 { // abs(number) less than 0 or number is zero 295 strncpy("+0", str); 296 } // abs(number) less than 0 or number is zero 297 else 298 { // something to convert 299 int x; 300 301 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 302 x = (ln->exponent > ln->digitCount) ? ln->digitCount : ln->exponent; 303 for (i = 0; i < x; i++) 304 str[cnt++] = '0' + ln->array[i]; 305 x = ln->exponent - ln->digitCount; 306 for (i=0; i < x; i++) 307 str[cnt++] = '0'; 308 str[cnt] = 0; 309 } // something to convert 310 return 0; 311 } // END function LNstrInt -- (200302) 312 313 int LNln2strFloat(LARGE_NUMBER_STRUCT *ln, char str[]) 314 // convert the ln struct to a string in float format 315 { // BEGIN function LNln2strFloat -- (200302) 316 int i, cnt = 0; 317 318 if (0 == ln->digitCount) 319 { // hadle 0 320 strncpy("+0.0", str); 321 } // hadle 0 322 else 323 { // not zero 324 int x1, x2; 325 326 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 327 x1 = (ln->exponent > ln->digitCount) ? ln->digitCount : ln->exponent; 328 for (i = 0; i < x1; i++) 329 str[cnt++] = '0' + ln->array[i]; 330 x2 = ln->exponent - ln->digitCount; 331 if (0 > x2) 332 { // digitCount larger 333 str[cnt++] = '.'; 334 for (i = x1; i < ln->digitCount; i++) 335 str[cnt++] = '0' + ln->array[i]; 336 } // digitCount larger 337 else 338 { // exponent larger 339 for (i=0; i < x2; i++) 340 str[cnt++] = '0'; 341 str[cnt++] = '.'; 342 str[cnt++] = '0'; 343 } // exponent larger 344 str[cnt++] = 0; 345 } // not zero 346 return 0; 347 } // END function LNstrFloat -- (200302) 348 349 int LNshift(LARGE_NUMBER_STRUCT *ln, int cnt) 350 // shift the implied decimal point 351 { // BEGIN function LiNshift -- (200302) 352 // errorLevel - Errorlevel to return. 353 // i - Loop variable. 354 int i, errorLevel = 0; 355 356 if (0 < ln->digitCount) 357 if (0 < cnt) 358 { // non-negative - do the shift 359 for ((i = ln->digitCount - 1); i >= 0 ; i --) 360 ln->array[i + cnt] = ln->array[i]; 361 for (i = 0; i < cnt; i ++) 362 ln->array[i] = 0; 363 ln->exponent += cnt; 364 ln->digitCount += cnt; 365 } // non-negative - do the shift 366 else 367 if (0 != cnt) 368 { // can't do it 369 fprintf (stderr, "Error: Cannot shift negative bits.\n"); 370 errorLevel = 1; 371 } // can't do it 372 return errorLevel; 373 } // END function LNshift -- (200302) 374 375 int LNnormalize(LARGE_NUMBER_STRUCT *ln) 376 // fix LN so that arr[0] <> 0 (if possible) 377 { // BEGIN function LNnormalize -- (200302) 378 // errorLevel - Errorlevel to return. 379 // zeroCount - How many zeroes? 380 // i - Loop variable 381 int i, errorLevel = 0, zeroCount = 0; 382 383 if (0 < ln->digitCount) 384 { // digits to process 385 while ((ln->array[zeroCount] == 0) && (zeroCount < ln->digitCount)) 386 { // count leading zeroes 387 zeroCount ++; 388 } // count leading zeroes 389 if (0 < zeroCount) 390 { // found leading zeroes 391 if (zeroCount == ln->digitCount) 392 { // entire number is zero 393 ln->exponent = 0; 394 ln->digitCount = 0; 395 ln->sign = 1; 396 } // entire number is zero 397 else 398 { // digits to shift 399 ln->digitCount -= zeroCount; 400 ln->exponent -= zeroCount; 401 for (i = 0; i < ln->digitCount; i++) 402 { // shift them 403 ln->array[i] = ln->array[i + zeroCount]; 404 } // shift them 405 } // digits to shift 406 } // found leading zeroes 407 // handle railing zeroes 408 i = ln->digitCount - 1; 409 while ((i >= 0) && (0 == ln->array[i])) 410 { // while 411 ln->digitCount--; 412 i--; 413 } // while 414 if (0 == ln->digitCount) 415 { // entire number is zero 416 ln->exponent = 0; 417 ln->sign = 1; 418 } // entire number is zero 419 } // digits to process 420 return (errorLevel); 421 } // END function LNnormalize -- (200302) 422 423 int LNadd(LARGE_NUMBER_STRUCT *lna, LARGE_NUMBER_STRUCT *lnb, 424 LARGE_NUMBER_STRUCT *ln3) 425 // ln3=ln1+ln2 426 { // BEGIN function LNadd -- (200302) 427 int i, cnt, state = 0, carry = 0; 428 LARGE_NUMBER_STRUCT ln1, ln2; 429 430 if (0 == lna->digitCount) 431 *ln3 = *lnb; 432 else 433 if (0 == lnb->digitCount) 434 *ln3 = *lna; 435 else 436 { // add non-zero numbers 437 ln1 = *lna; 438 ln2 = *lnb; 439 if (ln1.sign != ln2.sign) 440 { // signs different 441 LNnegate(&ln2); 442 state = LNsubtract(&ln1, &ln2, ln3); 443 } // signs different 444 else 445 { // signs are same -- continue adding 446 if (ln1.exponent > ln2.exponent) 447 { // ln1 is biger 448 LNshift(&ln1, 1); 449 LNshift(&ln2, (ln1.exponent - ln2.exponent)); 450 } // ln1 is biger 451 else 452 { // ln2 is biger 453 LNshift(&ln2, 1); 454 LNshift(&ln1, (ln2.exponent - ln1.exponent)); 455 } // ln2 is biger 456 457 if (ln1.digitCount > ln2.digitCount) 458 { // 1 has more digits 459 for (i = ln1.digitCount - 1; i >= ln2.digitCount; i--) 460 ln3->array[i] = ln1.array[i]; 461 cnt = ln2.digitCount; 462 ln3->digitCount = ln1.digitCount; 463 } // 1 has more digits 464 else 465 { // 2 has more digits 466 for (i = ln2.digitCount - 1; i >= ln1.digitCount; i--) 467 ln3->array[i] = ln2.array[i]; 468 cnt = ln1.digitCount; 469 ln3->digitCount = ln2.digitCount; 470 } // 2 has more digits 471 // now actually add 472 ln3->exponent = ln1.exponent; 473 for (i = cnt - 1; i >= 0; i--) 474 { // for 475 ln3->array[i] = ln1.array[i] + ln2.array[i] + carry; 476 if (ln3->array[i] > 9) 477 { // set carry 478 carry = 1; 479 ln3->array[i] -= 10; 480 } // set carry 481 else 482 { // reset carry 483 carry = 0; 484 } // reset carry 485 } // for 486 LNnormalize(ln3); 487 } // signs are same -- continue adding 488 } // add non-zero numbers 489 return state; 490 } // END function LNadd -- (200302) 491 492 int LNsubtract(LARGE_NUMBER_STRUCT *lna, LARGE_NUMBER_STRUCT *lnb, 493 LARGE_NUMBER_STRUCT *ln3) 494 // ln3=ln1-ln2 495 { // BEGIN function LNsubtract -- (200303) 496 int toReturn = 0; 497 LARGE_NUMBER_STRUCT ln1, ln2; 498 499 ln1 = *lna; 500 ln2 = *lnb; 501 502 if (0 == lna->digitCount) 503 { // first number is zero 504 *ln3 = *lnb; 505 LNnegate(ln3); 506 } // first number is zero 507 else 508 if (0 == lnb->digitCount) 509 *ln3 = *lna; 510 else 511 { // subtract non-zero numbers 512 if (ln1.sign != ln2.sign) 513 { // signs different 514 LNnegate(&ln2); 515 toReturn = LNadd(&ln1, &ln2, ln3); 516 } // signs different 517 else 518 { // signs are same - so subtract 519 int t, i, tmp, borrow = 0; 520 521 t = LNcompare(&ln1, &ln2); 522 if (0 == t) 523 { // same number - return 9 524 ln3->sign = 1; 525 ln3->exponent = 0; 526 ln3->digitCount = 0; 527 } // same number - return 9 528 else 529 if (0 > t) 530 { // first number smaller 531 toReturn = LNsubtract(&ln2, &ln1, ln3); 532 ln3->sign = -1 * ln3->sign; 533 } // first number smaller 534 else 535 { // everything okay - actually subtract 536 ln3->sign = ln1.sign; 537 ln3->exponent = ln1.exponent; 538 LNshift(&ln2, (ln1.exponent - ln2.exponent)); 539 if (ln1.digitCount != ln2.digitCount) 540 if (ln1.digitCount > ln2.digitCount) 541 { // add zeroes to ln2 542 for (i=ln2.digitCount; i < ln1.digitCount; i++) 543 ln2.array[i] = 0; 544 ln2.digitCount = ln1.digitCount; 545 } // add zeroes to ln2 546 else 547 { // add zeroes to ln1 548 for (i=ln1.digitCount; i < ln2.digitCount; i++) 549 ln1.array[i] = 0; 550 ln1.digitCount = ln2.digitCount; 551 } // add zeroes to ln1 552 553 for (i = ln1.digitCount - 1; i >= 0; i--) 554 { // loop through each digit 555 tmp = borrow + ln2.array[i]; 556 if (ln1.array[i] > tmp) 557 { // no borrow 558 ln3->array[i] = ln1.array[i] - tmp; 559 borrow = 0; 560 } // no borrow 561 else 562 { // have to borrow 563 ln3->array[i] = (10 + ln1.array[i]) - tmp; 564 borrow = 1; 565 } // have to borrow 566 } // loop through each digit 567 LNnormalize(ln3); 568 } // everything okay - actually subtract 569 } // signs are same - so subtract 570 } // subtract non-zero numbers 571 return toReturn; 572 } // END function LNsubtract -- (200303) 573 574 int LNmultiply(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2, 575 LARGE_NUMBER_STRUCT *ln3) 576 // ln3=ln1*ln2 577 { // BEGIN function LNmultiply -- (200303) 578 if ((0 == ln1->digitCount) || (0 == ln2->digitCount)) 579 { // multiply by 0 and get 0 580 ln3->digitCount = 0; 581 ln3->sign = 0; 582 ln3->exponent = 0; 583 ln3->array[0] = 0; 584 } // multiply by 0 and get 0 585 else 586 { // guess we have to multiply 587 int i1, i2, i3, dig, tmp, carry; 588 589 ln3->sign = ln1->sign * ln2->sign; 590 ln3->exponent = ln1->exponent + ln2->exponent; 591 ln3->digitCount = ln1->digitCount + ln2->digitCount; 592 dig = ln3->digitCount - 1; 593 // zero out ln3 so that it can be summed into 594 for (i3=0; i3 <= dig; i3++) 595 ln3->array[i3] = 0; 596 for (i2=ln2->digitCount - 1; i2 >= 0; i2--) 597 { // loop through the second numbers digits 598 carry = 0; 599 i3 = dig--; 600 for (i1=ln1->digitCount - 1; i1 >= 0; i1--) 601 { // process first number 602 tmp = (ln1->array[i1] * ln2->array[i2]) + carry + ln3->array[i3]; 603 if (tmp > 9) 604 { // deal with overflow 605 carry = tmp / 10; 606 ln3->array[i3] = (tmp % 10); 607 } // deal with overflow 608 else 609 { // no overflow 610 carry = 0; 611 ln3->array[i3] = tmp; 612 } // no overflow 613 i3--; 614 } // process first number 615 ln3->array[i3] = ln3->array[i3] + carry; 616 } // loop through the second numbers digits 617 LNnormalize(ln3); 618 } // guess we have to multiply 619 return 0; 620 } // END function LNmultiply -- (200303) 621 622 int LNdivide(LARGE_NUMBER_STRUCT *ln1, long int i2, LARGE_NUMBER_STRUCT *ln3) 623 // ln3=ln1/i2 624 { // BEGIN function LNdivide -- (200303) 625 int i, tot = 0; 626 627 ln3->exponent = ln1->exponent; 628 ln3->sign = ln1->sign * ((0 < i2) ? 1 : -1); 629 for (i=0; i < ln1->digitCount; i++) 630 { // for each digit 631 tot += ln1->array[i]; 632 if (tot >= i2) 633 { // we can divide 634 ln3->array[i] = tot / i2; 635 tot = (tot % i2) * 10; 636 } // we can divide 637 else 638 { // can't divide yet, so add a zero 639 ln3->array[i] = 0; 640 tot *= 10; 641 } // can't divide yet, so add a zero 642 } // for each digit 643 644 ln3->digitCount = i; 645 while ((LN_MAX_DIGITS > ln3->digitCount) && (0 < tot)) 646 { // add zeroes on right 647 if (tot >= i2) 648 { // we can divide 649 ln3->array[ln3->digitCount] = tot / i2; 650 tot = (tot % i2) * 10; 651 } // we can divide 652 else 653 { // can't divide yet, so add a zero 654 ln3->array[ln3->digitCount] = 0; 655 tot *= 10; 656 } // can't divide yet, so add a zero 657 ln3->digitCount++; 658 } // add zeroes on right 659 LNnormalize(ln3); 660 return 0; 661 } // END function LNdivide -- (200303) 662 663 int LNdcnvrt(double d, LARGE_NUMBER_STRUCT *n) 664 // convert a double to Large Number 665 { // BEGIN function LNdcnvrt -- (200303) 666 char str[LN_MAX_DIGITS]; 667 668 sprintf(str, "%ld:", d); 669 return LNstr2arr(str, n); 670 } // END function LNdcnvrt -- (200303) 671 672 int LNcopy(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2) 673 // copy from ln1 to ln2 674 { // BEGIN function LNcopy -- (200302) 675 int i; 676 677 ln2->sign = ln1->sign; 678 ln2->exponent = ln1->exponent; 679 ln2->digitCount = ln1->digitCount; 680 for (i=0; i < ln1->digitCount; i++) 681 ln2->array[i] = ln1->array[i]; 682 return 0; 683 } // END function LNcopy -- (200302)
1 #include <stdio.h> 2 #define DEBUG1 (1 != 1) 3 4 #include "LargeNumber.c" 5 6 int main () 7 { /* begin FUNCTION main */ 8 int i; 9 LARGE_NUMBER_STRUCT a; 10 LARGE_NUMBER_STRUCT b; 11 LARGE_NUMBER_STRUCT c; 12 int res; 13 long int ii; 14 char num[1000]; 15 char tmp[1000]; 16 17 ii = 123456789; 18 if (DEBUG1) printf ("A\n"); 19 res = LNicnvrt(ii, &a); 20 printf("------- Display Test ----------\n"); 21 LNarr2strExp(&a, num); 22 printf("LNarr2strExp(a)=%s\n",num); 23 LNarr2strInt(&a, num); 24 printf("LNarr2strInt(a)=%s\n",num); 25 LNln2strFloat(&a, num); 26 printf("LNln2strFloat(a)=%s\n",num); 27 LNprint(&a); 28 printf("-------------------------------\n"); 29 30 printf("------- Multiply Test ---------\n"); 31 LNicnvrt(123, &a); 32 LNicnvrt(12, &b); 33 LNmultiply(&a, &b, &c); 34 LNarr2strInt(&a, num); 35 printf("a(%s) * ", num); 36 LNarr2strInt(&b, num); 37 printf("b(%s) ", num); 38 LNarr2strInt(&c, num); 39 printf(" = c(%s)\n", num); 40 printf("\n"); 41 42 printf("-------------------------------\n"); 43 44 printf("------- Divide Test ---------\n"); 45 LNicnvrt(1224, &a); 46 LNdivide(&a, 12, &c); 47 LNarr2strInt(&a, num); 48 printf("a(%s) / 12 ", num); 49 LNarr2strExp(&c, num); 50 printf(" = c(%s)\n", num); 51 printf("\n"); 52 53 LNicnvrt(12, &a); 54 LNdivide(&a, 12, &c); 55 LNarr2strInt(&a, num); 56 printf("a(%s) / 12 ", num); 57 LNarr2strExp(&c, num); 58 printf(" = c(%s)\n", num); 59 printf("\n"); 60 61 LNicnvrt(1, &a); 62 LNdivide(&a, 1, &c); 63 LNarr2strInt(&a, num); 64 printf("a(%s) / 1 ", num); 65 LNarr2strExp(&c, num); 66 printf(" = c(%s)\n", num); 67 printf("\n"); 68 69 LNicnvrt(1, &a); 70 LNdivide(&a, 12, &c); 71 LNarr2strInt(&a, num); 72 printf("a(%s) / 12 ", num); 73 LNarr2strExp(&c, num); 74 printf(" = c(%s)\n", num); 75 printf("\n"); 76 77 LNicnvrt(1, &a); 78 LNdivide(&a, 125, &c); 79 LNarr2strInt(&a, num); 80 printf("a(%s) / 125 ", num); 81 LNarr2strExp(&c, num); 82 printf(" = c(%s)\n", num); 83 84 for (i=100000; i > 0; i = i / 10) { 85 LNstr2arr("1111.111111111", &a); 86 LNdivide(&a, i, &c); 87 LNarr2strInt(&a, num); 88 printf("a(%s) / %d ", num, i); 89 LNarr2strExp(&c, num); 90 printf(" = c(%s)\n", num); } 91 92 tmp = "0.000000000000000000000000000000000000000000000"; 93 strcat(tmp, "0000000000000000000000000001111111111111"); 94 LNstr2arr(tmp, &a); 95 LNdivide(&a, 10, &c); 96 LNarr2strInt(&a, num); 97 printf("a(%s) / 10 ", num); 98 LNarr2strExp(&c, num); 99 printf(" = c(%s)\n", num); 100 101 tmp ="30765988567369.34938637363858653405834085348673"; 102 strcat(tmp, "4086334739573957397534757357345973497375"); 103 strcat(tmp, "734573453957"); 104 LNstr2arr(tmp, &a); 105 LNdivide(&a, 123456789, &c); 106 LNarr2strInt(&a, num); 107 printf("a(%s) / 123456789 ", num); 108 LNarr2strExp(&c, num); 109 printf(" = c(%s)\n", num); 110 111 printf("\n"); 112 113 printf("-------------------------------\n"); 114 LNicnvrt(123, &a); 115 if (DEBUG1) printf ("B\n"); 116 printf("\n"); 117 118 printf("-------------------------------\n"); 119 LNicnvrt(123, &a); 120 if (DEBUG1) printf ("B\n"); 121 res = LNcopy(&a,&b); 122 b.array[b.exponent] = 3; 123 if (DEBUG1) printf ("C\n"); 124 LNprint(&a); 125 printf("%d - %d\n",a.exponent,a.digitCount); 126 LNprint(&b); 127 printf("%d - %d\n",b.exponent,b.digitCount); 128 if (DEBUG1) printf ("D\n"); 129 a.array[0] = 2; 130 LNarr2strExp(&a, num); 131 printf("arr2str: [%s]\n", num); 132 133 a.array[0] = 3; 134 LNarr2strExp(&a, num); 135 printf("ln2strExp: [%s]\n", num); 136 137 a.array[0] = 4; 138 LNarr2strInt(&a, num); 139 printf("ln2strInt: [%s]\n", num); 140 141 a.array[0] = 5; 142 a.exponent = 3; 143 LNarr2strInt(&a, num); 144 printf("ln2strInt: [%s]\n", num); 145 146 a.array[0] = 6; 147 a.exponent = 15; 148 LNarr2strInt(&a, num); 149 printf("ln2strInt: [%s]\n", num); 150 151 a.array[0] = 7; 152 a.exponent = 7; 153 LNln2strFloat(&a, num); 154 printf("ln2strFloat: [%s]\n", num); 155 156 LNadd(&a, &b, &c); 157 LNarr2strExp(&a, num); 158 printf("[%s] + ", num); 159 LNarr2strExp(&b, num); 160 printf("[%s] = ", num); 161 LNarr2strExp(&c, num); 162 printf("[%s]\n", num); 163 164 LNsubtract(&a, &b, &c); 165 LNarr2strExp(&a, num); 166 printf("[%s] - ", num); 167 LNarr2strExp(&b, num); 168 printf("[%s] = ", num); 169 LNarr2strExp(&c, num); 170 printf("[%s]\n", num); 171 172 LNsubtract(&b, &a, &c); 173 LNarr2strExp(&b, num); 174 printf("[%s] - ", num); 175 LNarr2strExp(&a, num); 176 printf("[%s] = ", num); 177 LNarr2strExp(&c, num); 178 printf("[%s]\n", num); 179 180 } /* end FUNCTION main */
1 #include <ctype.h> 2 #define LN_MAX_DIGITS 1000 3 4 typedef struct LARGE_NUMBER_STRUCT 5 { 6 unsigned short int array[LN_MAX_DIGITS]; 7 signed short int sign; 8 signed long int exponent; 9 signed short int digitCount; 10 } 11 LARGE_NUMBER_STRUCT; 12 13 void LNprint(LARGE_NUMBER_STRUCT *n) 14 { 15 char str[LN_MAX_DIGITS+25]; 16 17 LNarr2strExp(n, str); 18 printf("[%s]\n", str); 19 } 20 21 int LNnegate(LARGE_NUMBER_STRUCT *ln1) 22 { 23 if (0 != ln1->digitCount) 24 ln1->sign *= -1; 25 return 0; 26 } 27 28 int LNcompare(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2) 29 { 30 int toReturn = 0; 31 32 if (ln1->sign ^ ln2->sign) 33 { 34 toReturn = (0 > ln1->sign) ? -1 : 1; 35 } 36 else 37 { 38 if (ln1->exponent != ln2->exponent) 39 { 40 toReturn = (ln1->exponent > ln2->exponent) ? 1 : -1; 41 } 42 else 43 { 44 int i, t; 45 46 t = (ln1->digitCount > ln2->digitCount) ? ln2->digitCount : ln1->digitCount; 47 for (i=0; (i<t) && (0 == toReturn) ; i++) 48 { 49 if (ln1->array[i] != ln2->array[i]) 50 toReturn = (ln1->array[i] > ln2->array[i]) ? ln1->sign : - ln2->sign; 51 } 52 if ((0 == toReturn) && (ln1->digitCount != ln2->digitCount)) 53 toReturn = (ln1->digitCount > ln2->digitCount) ? ln1->sign : - ln2->sign; 54 } 55 } 56 return toReturn; 57 } 58 59 int LNstr2arr(char str[], LARGE_NUMBER_STRUCT *ln) 60 { 61 #define START 1 62 #define NUM1 2 63 #define NUM2 3 64 #define DEC1 4 65 #define DEC2 5 66 #define EXP1 6 67 #define EXP2 7 68 #define EXP3 8 69 int state = START, done = 0, n = 0; 70 signed short int dpflag = 0, numflag = 0, sign = 1; 71 signed long int exp; 72 char *ch = str; 73 74 while ( (isspace(*ch)) || ('0' == *ch) ) ch++; 75 76 if (0 != *ch) 77 { 78 if ('-' == *ch) 79 { 80 sign = -1; 81 ch++; 82 } 83 else 84 if (*ch == '+') 85 { 86 ch++; 87 } 88 89 while (isdigit(*ch)) 90 { 91 state = NUM2; 92 ln->array[n++] = *ch - '0'; 93 ch++; 94 } 95 exp = n; 96 97 if ('.' == *ch) 98 { 99 state = (NUM2 != state) ? DEC1 : DEC2; 100 ch++; 101 102 if (isdigit(*ch)) state = DEC2; 103 while (isdigit(*ch)) 104 { 105 ln->array[n++] = *ch - '0'; 106 ch++; 107 } 108 } 109 110 if (('E' == *ch) || ('e' == *ch)) 111 { 112 signed long int texp; 113 114 state = EXP2; 115 ch++; 116 sscanf(ch, "%d", &texp); 117 exp += texp; 118 } 119 } 120 121 if ((EXP2 == state) || (DEC2 == state) || (NUM2 == state)) 122 { 123 ln->sign = sign; 124 ln->exponent = exp; 125 ln->digitCount = n; 126 state = 0; 127 } 128 return state; 129 } 130 131 int LNicnvrt(long int number, LARGE_NUMBER_STRUCT *n) 132 { 133 int idx, digit, j; 134 135 n->sign = (number < 0) ? -1 : 1; 136 137 n->exponent = 0; 138 idx = LN_MAX_DIGITS; 139 while (number > 0) 140 { 141 digit = number % 10; 142 n->array[--idx] = digit; 143 number /= 10; 144 } 145 n->exponent = LN_MAX_DIGITS - idx; 146 n->digitCount = n->exponent; 147 for (j=0; LN_MAX_DIGITS > (j + idx); j++) 148 { 149 n->array[j] = n->array[idx+j]; 150 } 151 return 0; 152 } 153 154 int LNarr2strExp(LARGE_NUMBER_STRUCT *ln, char str[]) 155 { 156 int i, cnt = 0; 157 158 if (0 == ln->digitCount) 159 { 160 strncpy("+0E0", str); 161 } 162 else 163 { 164 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 165 str[cnt++] = '0' + ln->array[0]; 166 str[cnt++] = '.'; 167 for (i = 1; i < ln->digitCount; i++) 168 str[cnt++] = '0' + ln->array[i]; 169 str[cnt++] = 'E'; 170 sprintf(&(str[cnt]), "%+ld", (ln->exponent-1)); 171 } 172 return 0; 173 } 174 175 int LNarr2strInt(LARGE_NUMBER_STRUCT *ln, char str[]) 176 { 177 int i, cnt = 0; 178 179 if ((0 > ln->exponent) || (0 >= ln->digitCount)) 180 { 181 strncpy("+0", str); 182 } 183 else 184 { 185 int x; 186 187 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 188 x = (ln->exponent > ln->digitCount) ? ln->digitCount : ln->exponent; 189 for (i = 0; i < x; i++) 190 str[cnt++] = '0' + ln->array[i]; 191 x = ln->exponent - ln->digitCount; 192 for (i=0; i < x; i++) 193 str[cnt++] = '0'; 194 str[cnt] = 0; 195 } 196 return 0; 197 } 198 199 int LNln2strFloat(LARGE_NUMBER_STRUCT *ln, char str[]) 200 { 201 int i, cnt = 0; 202 203 if (0 == ln->digitCount) 204 { 205 strncpy("+0.0", str); 206 } 207 else 208 { 209 int x1, x2; 210 211 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 212 x1 = (ln->exponent > ln->digitCount) ? ln->digitCount : ln->exponent; 213 for (i = 0; i < x1; i++) 214 str[cnt++] = '0' + ln->array[i]; 215 x2 = ln->exponent - ln->digitCount; 216 if (0 > x2) 217 { 218 str[cnt++] = '.'; 219 for (i = x1; i < ln->digitCount; i++) 220 str[cnt++] = '0' + ln->array[i]; 221 } 222 else 223 { 224 for (i=0; i < x2; i++) 225 str[cnt++] = '0'; 226 str[cnt++] = '.'; 227 str[cnt++] = '0'; 228 } 229 str[cnt++] = 0; 230 } 231 return 0; 232 } 233 234 int LNshift(LARGE_NUMBER_STRUCT *ln, int cnt) 235 { 236 int i, errorLevel = 0; 237 238 if (0 < ln->digitCount) 239 if (0 < cnt) 240 { 241 for ((i = ln->digitCount - 1); i >= 0 ; i --) 242 ln->array[i + cnt] = ln->array[i]; 243 for (i = 0; i < cnt; i ++) 244 ln->array[i] = 0; 245 ln->exponent += cnt; 246 ln->digitCount += cnt; 247 } 248 else 249 if (0 != cnt) 250 { 251 fprintf (stderr, "Error: Cannot shift negative bits.\n"); 252 errorLevel = 1; 253 } 254 return errorLevel; 255 } 256 257 int LNnormalize(LARGE_NUMBER_STRUCT *ln) 258 { 259 int i, errorLevel = 0, zeroCount = 0; 260 261 if (0 < ln->digitCount) 262 { 263 while ((ln->array[zeroCount] == 0) && (zeroCount < ln->digitCount)) 264 { 265 zeroCount ++; 266 } 267 if (0 < zeroCount) 268 { 269 if (zeroCount == ln->digitCount) 270 { 271 ln->exponent = 0; 272 ln->digitCount = 0; 273 ln->sign = 1; 274 } 275 else 276 { 277 ln->digitCount -= zeroCount; 278 ln->exponent -= zeroCount; 279 for (i = 0; i < ln->digitCount; i++) 280 { 281 ln->array[i] = ln->array[i + zeroCount]; 282 } 283 } 284 } 285 i = ln->digitCount - 1; 286 while ((i >= 0) && (0 == ln->array[i])) 287 { 288 ln->digitCount--; 289 i--; 290 } 291 if (0 == ln->digitCount) 292 { 293 ln->exponent = 0; 294 ln->sign = 1; 295 } 296 } 297 return (errorLevel); 298 } 299 300 int LNadd(LARGE_NUMBER_STRUCT *lna, LARGE_NUMBER_STRUCT *lnb, 301 LARGE_NUMBER_STRUCT *ln3) 302 { 303 int i, cnt, state = 0, carry = 0; 304 LARGE_NUMBER_STRUCT ln1, ln2; 305 306 if (0 == lna->digitCount) 307 *ln3 = *lnb; 308 else 309 if (0 == lnb->digitCount) 310 *ln3 = *lna; 311 else 312 { 313 ln1 = *lna; 314 ln2 = *lnb; 315 if (ln1.sign != ln2.sign) 316 { 317 LNnegate(&ln2); 318 state = LNsubtract(&ln1, &ln2, ln3); 319 } 320 else 321 { 322 if (ln1.exponent > ln2.exponent) 323 { 324 LNshift(&ln1, 1); 325 LNshift(&ln2, (ln1.exponent - ln2.exponent)); 326 } 327 else 328 { 329 LNshift(&ln2, 1); 330 LNshift(&ln1, (ln2.exponent - ln1.exponent)); 331 } 332 333 if (ln1.digitCount > ln2.digitCount) 334 { 335 for (i = ln1.digitCount - 1; i >= ln2.digitCount; i--) 336 ln3->array[i] = ln1.array[i]; 337 cnt = ln2.digitCount; 338 ln3->digitCount = ln1.digitCount; 339 } 340 else 341 { 342 for (i = ln2.digitCount - 1; i >= ln1.digitCount; i--) 343 ln3->array[i] = ln2.array[i]; 344 cnt = ln1.digitCount; 345 ln3->digitCount = ln2.digitCount; 346 } 347 ln3->exponent = ln1.exponent; 348 for (i = cnt - 1; i >= 0; i--) 349 { 350 ln3->array[i] = ln1.array[i] + ln2.array[i] + carry; 351 if (ln3->array[i] > 9) 352 { 353 carry = 1; 354 ln3->array[i] -= 10; 355 } 356 else 357 { 358 carry = 0; 359 } 360 } 361 LNnormalize(ln3); 362 } 363 } 364 return state; 365 } 366 367 int LNsubtract(LARGE_NUMBER_STRUCT *lna, LARGE_NUMBER_STRUCT *lnb, 368 LARGE_NUMBER_STRUCT *ln3) 369 { 370 int toReturn = 0; 371 LARGE_NUMBER_STRUCT ln1, ln2; 372 373 ln1 = *lna; 374 ln2 = *lnb; 375 376 if (0 == lna->digitCount) 377 { 378 *ln3 = *lnb; 379 LNnegate(ln3); 380 } 381 else 382 if (0 == lnb->digitCount) 383 *ln3 = *lna; 384 else 385 { 386 if (ln1.sign != ln2.sign) 387 { 388 LNnegate(&ln2); 389 toReturn = LNadd(&ln1, &ln2, ln3); 390 } 391 else 392 { 393 int t, i, tmp, borrow = 0; 394 395 t = LNcompare(&ln1, &ln2); 396 if (0 == t) 397 { 398 ln3->sign = 1; 399 ln3->exponent = 0; 400 ln3->digitCount = 0; 401 } 402 else 403 if (0 > t) 404 { 405 toReturn = LNsubtract(&ln2, &ln1, ln3); 406 ln3->sign = -1 * ln3->sign; 407 } 408 else 409 { 410 ln3->sign = ln1.sign; 411 ln3->exponent = ln1.exponent; 412 LNshift(&ln2, (ln1.exponent - ln2.exponent)); 413 if (ln1.digitCount != ln2.digitCount) 414 if (ln1.digitCount > ln2.digitCount) 415 { 416 for (i=ln2.digitCount; i < ln1.digitCount; i++) 417 ln2.array[i] = 0; 418 ln2.digitCount = ln1.digitCount; 419 } 420 else 421 { 422 for (i=ln1.digitCount; i < ln2.digitCount; i++) 423 ln1.array[i] = 0; 424 ln1.digitCount = ln2.digitCount; 425 } 426 427 for (i = ln1.digitCount - 1; i >= 0; i--) 428 { 429 tmp = borrow + ln2.array[i]; 430 if (ln1.array[i] > tmp) 431 { 432 ln3->array[i] = ln1.array[i] - tmp; 433 borrow = 0; 434 } 435 else 436 { 437 ln3->array[i] = (10 + ln1.array[i]) - tmp; 438 borrow = 1; 439 } 440 } 441 LNnormalize(ln3); 442 } 443 } 444 } 445 return toReturn; 446 } 447 448 int LNmultiply(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2, 449 LARGE_NUMBER_STRUCT *ln3) 450 { 451 if ((0 == ln1->digitCount) || (0 == ln2->digitCount)) 452 { 453 ln3->digitCount = 0; 454 ln3->sign = 0; 455 ln3->exponent = 0; 456 ln3->array[0] = 0; 457 } 458 else 459 { 460 int i1, i2, i3, dig, tmp, carry; 461 462 ln3->sign = ln1->sign * ln2->sign; 463 ln3->exponent = ln1->exponent + ln2->exponent; 464 ln3->digitCount = ln1->digitCount + ln2->digitCount; 465 dig = ln3->digitCount - 1; 466 for (i3=0; i3 <= dig; i3++) 467 ln3->array[i3] = 0; 468 for (i2=ln2->digitCount - 1; i2 >= 0; i2--) 469 { 470 carry = 0; 471 i3 = dig--; 472 for (i1=ln1->digitCount - 1; i1 >= 0; i1--) 473 { 474 tmp = (ln1->array[i1] * ln2->array[i2]) + carry + ln3->array[i3]; 475 if (tmp > 9) 476 { 477 carry = tmp / 10; 478 ln3->array[i3] = (tmp % 10); 479 } 480 else 481 { 482 carry = 0; 483 ln3->array[i3] = tmp; 484 } 485 i3--; 486 } 487 ln3->array[i3] = ln3->array[i3] + carry; 488 } 489 LNnormalize(ln3); 490 } 491 return 0; 492 } 493 494 int LNdivide(LARGE_NUMBER_STRUCT *ln1, long int i2, LARGE_NUMBER_STRUCT *ln3) 495 { 496 int i, tot = 0; 497 498 ln3->exponent = ln1->exponent; 499 ln3->sign = ln1->sign * ((0 < i2) ? 1 : -1); 500 for (i=0; i < ln1->digitCount; i++) 501 { 502 tot += ln1->array[i]; 503 if (tot >= i2) 504 { 505 ln3->array[i] = tot / i2; 506 tot = (tot % i2) * 10; 507 } 508 else 509 { 510 ln3->array[i] = 0; 511 tot *= 10; 512 } 513 } 514 515 ln3->digitCount = i; 516 while ((LN_MAX_DIGITS > ln3->digitCount) && (0 < tot)) 517 { 518 if (tot >= i2) 519 { 520 ln3->array[ln3->digitCount] = tot / i2; 521 tot = (tot % i2) * 10; 522 } 523 else 524 { 525 ln3->array[ln3->digitCount] = 0; 526 tot *= 10; 527 } 528 ln3->digitCount++; 529 } 530 LNnormalize(ln3); 531 return 0; 532 } 533 534 int LNdcnvrt(double d, LARGE_NUMBER_STRUCT *n) 535 { 536 char str[LN_MAX_DIGITS]; 537 538 sprintf(str, "%ld:", d); 539 return LNstr2arr(str, n); 540 } 541 542 int LNcopy(LARGE_NUMBER_STRUCT *ln1, LARGE_NUMBER_STRUCT *ln2) 543 { 544 int i; 545 546 ln2->sign = ln1->sign; 547 ln2->exponent = ln1->exponent; 548 ln2->digitCount = ln1->digitCount; 549 for (i=0; i < ln1->digitCount; i++) 550 ln2->array[i] = ln1->array[i]; 551 return 0; 552 }
1 #include <ctype.h> 2 #define LMD 1000 3 4 typedef struct LNS 5 { 6 unsigned short int a[LMD]; 7 signed short int sign; 8 signed long int exp; 9 signed short int dc; 10 } 11 LNS; 12 13 void LNprint(LNS *n) 14 { 15 char str[LMD+25]; 16 17 LNarr2strExp(n, str); 18 printf("[%s]\n", str); 19 } 20 21 int LNnegate(LNS *ln1) 22 { 23 if (0 != ln1->dc) 24 ln1->sign *= -1; 25 return 0; 26 } 27 28 int LNcompare(LNS *ln1, LNS *ln2) 29 { 30 int ret = 0; 31 32 if (ln1->sign ^ ln2->sign) 33 { 34 ret = (0 > ln1->sign) ? -1 : 1; 35 } 36 else 37 { 38 if (ln1->exp != ln2->exp) 39 { 40 ret = (ln1->exp > ln2->exp) ? 1 : -1; 41 } 42 else 43 { 44 int i, t; 45 46 t = (ln1->dc > ln2->dc) ? ln2->dc : ln1->dc; 47 for (i=0; (i<t) && (0 == ret) ; i++) 48 { 49 if (ln1->a[i] != ln2->a[i]) 50 ret = (ln1->a[i] > ln2->a[i]) ? ln1->sign : - ln2->sign; 51 } 52 if ((0 == ret) && (ln1->dc != ln2->dc)) 53 ret = (ln1->dc > ln2->dc) ? ln1->sign : - ln2->sign; 54 } 55 } 56 return ret; 57 } 58 59 int LNstr2arr(char str[], LNS *ln) 60 { 61 #define START 1 62 #define NUM1 2 63 #define NUM2 3 64 #define DEC1 4 65 #define DEC2 5 66 #define EXP1 6 67 #define EXP2 7 68 #define EXP3 8 69 int state = START, done = 0, n = 0; 70 signed short int dpflag = 0, numflag = 0, sign = 1; 71 signed long int exp; 72 char *ch = str; 73 74 while ( (isspace(*ch)) || ('0' == *ch) ) ch++; 75 76 if (0 != *ch) 77 { 78 if ('-' == *ch) 79 { 80 sign = -1; 81 ch++; 82 } 83 else 84 if (*ch == '+') 85 { 86 ch++; 87 } 88 89 while (isdigit(*ch)) 90 { 91 state = NUM2; 92 ln->a[n++] = *ch - '0'; 93 ch++; 94 } 95 exp = n; 96 97 if ('.' == *ch) 98 { 99 state = (NUM2 != state) ? DEC1 : DEC2; 100 ch++; 101 102 if (isdigit(*ch)) state = DEC2; 103 while (isdigit(*ch)) 104 { 105 ln->a[n++] = *ch - '0'; 106 ch++; 107 } 108 } 109 110 if (('E' == *ch) || ('e' == *ch)) 111 { 112 signed long int texp; 113 114 state = EXP2; 115 ch++; 116 sscanf(ch, "%d", &texp); 117 exp += texp; 118 } 119 } 120 121 if ((EXP2 == state) || (DEC2 == state) || (NUM2 == state)) 122 { 123 ln->sign = sign; 124 ln->exp = exp; 125 ln->dc = n; 126 state = 0; 127 } 128 return state; 129 } 130 131 int LNicnvrt(long int number, LNS *n) 132 { 133 int idx, digit, j; 134 135 n->sign = (number < 0) ? -1 : 1; 136 137 n->exp = 0; 138 idx = LMD; 139 while (number > 0) 140 { 141 digit = number % 10; 142 n->a[--idx] = digit; 143 number /= 10; 144 } 145 n->exp = LMD - idx; 146 n->dc = n->exp; 147 for (j=0; LMD > (j + idx); j++) 148 { 149 n->a[j] = n->a[idx+j]; 150 } 151 return 0; 152 } 153 154 int LNarr2strExp(LNS *ln, char str[]) 155 { 156 int i, cnt = 0; 157 158 if (0 == ln->dc) 159 { 160 strncpy("+0E0", str); 161 } 162 else 163 { 164 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 165 str[cnt++] = '0' + ln->a[0]; 166 str[cnt++] = '.'; 167 for (i = 1; i < ln->dc; i++) 168 str[cnt++] = '0' + ln->a[i]; 169 str[cnt++] = 'E'; 170 sprintf(&(str[cnt]), "%+ld", (ln->exp-1)); 171 } 172 return 0; 173 } 174 175 int LNarr2strInt(LNS *ln, char str[]) 176 { 177 int i, cnt = 0; 178 179 if ((0 > ln->exp) || (0 >= ln->dc)) 180 { 181 strncpy("+0", str); 182 } 183 else 184 { 185 int x; 186 187 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 188 x = (ln->exp > ln->dc) ? ln->dc : ln->exp; 189 for (i = 0; i < x; i++) 190 str[cnt++] = '0' + ln->a[i]; 191 x = ln->exp - ln->dc; 192 for (i=0; i < x; i++) 193 str[cnt++] = '0'; 194 str[cnt] = 0; 195 } 196 return 0; 197 } 198 199 int LNln2strFloat(LNS *ln, char str[]) 200 { 201 int i, cnt = 0; 202 203 if (0 == ln->dc) 204 { 205 strncpy("+0.0", str); 206 } 207 else 208 { 209 int x1, x2; 210 211 str[cnt++] = (0 > ln->sign) ? '-' : '+'; 212 x1 = (ln->exp > ln->dc) ? ln->dc : ln->exp; 213 for (i = 0; i < x1; i++) 214 str[cnt++] = '0' + ln->a[i]; 215 x2 = ln->exp - ln->dc; 216 if (0 > x2) 217 { 218 str[cnt++] = '.'; 219 for (i = x1; i < ln->dc; i++) 220 str[cnt++] = '0' + ln->a[i]; 221 } 222 else 223 { 224 for (i=0; i < x2; i++) 225 str[cnt++] = '0'; 226 str[cnt++] = '.'; 227 str[cnt++] = '0'; 228 } 229 str[cnt++] = 0; 230 } 231 return 0; 232 } 233 234 int LNshift(LNS *ln, int cnt) 235 { 236 int i, errorLevel = 0; 237 238 if (0 < ln->dc) 239 if (0 < cnt) 240 { 241 for ((i = ln->dc - 1); i >= 0 ; i --) 242 ln->a[i + cnt] = ln->a[i]; 243 for (i = 0; i < cnt; i ++) 244 ln->a[i] = 0; 245 ln->exp += cnt; 246 ln->dc += cnt; 247 } 248 else 249 if (0 != cnt) 250 { 251 fprintf (stderr, "Error: Cannot shift negative bits.\n"); 252 errorLevel = 1; 253 } 254 return errorLevel; 255 } 256 257 int LNnormalize(LNS *ln) 258 { 259 int i, errorLevel = 0, zeroCount = 0; 260 261 if (0 < ln->dc) 262 { 263 while ((ln->a[zeroCount] == 0) && (zeroCount < ln->dc)) 264 { 265 zeroCount ++; 266 } 267 if (0 < zeroCount) 268 { 269 if (zeroCount == ln->dc) 270 { 271 ln->exp = 0; 272 ln->dc = 0; 273 ln->sign = 1; 274 } 275 else 276 { 277 ln->dc -= zeroCount; 278 ln->exp -= zeroCount; 279 for (i = 0; i < ln->dc; i++) 280 { 281 ln->a[i] = ln->a[i + zeroCount]; 282 } 283 } 284 } 285 i = ln->dc - 1; 286 while ((i >= 0) && (0 == ln->a[i])) 287 { 288 ln->dc--; 289 i--; 290 } 291 if (0 == ln->dc) 292 { 293 ln->exp = 0; 294 ln->sign = 1; 295 } 296 } 297 return (errorLevel); 298 } 299 300 int LNadd(LNS *lna, LNS *lnb, 301 LNS *ln3) 302 { 303 int i, cnt, state = 0, carry = 0; 304 LNS ln1, ln2; 305 306 if (0 == lna->dc) 307 *ln3 = *lnb; 308 else 309 if (0 == lnb->dc) 310 *ln3 = *lna; 311 else 312 { 313 ln1 = *lna; 314 ln2 = *lnb; 315 if (ln1.sign != ln2.sign) 316 { 317 LNnegate(&ln2); 318 state = LNsubtract(&ln1, &ln2, ln3); 319 } 320 else 321 { 322 if (ln1.exp > ln2.exp) 323 { 324 LNshift(&ln1, 1); 325 LNshift(&ln2, (ln1.exp - ln2.exp)); 326 } 327 else 328 { 329 LNshift(&ln2, 1); 330 LNshift(&ln1, (ln2.exp - ln1.exp)); 331 } 332 333 if (ln1.dc > ln2.dc) 334 { 335 for (i = ln1.dc - 1; i >= ln2.dc; i--) 336 ln3->a[i] = ln1.a[i]; 337 cnt = ln2.dc; 338 ln3->dc = ln1.dc; 339 } 340 else 341 { 342 for (i = ln2.dc - 1; i >= ln1.dc; i--) 343 ln3->a[i] = ln2.a[i]; 344 cnt = ln1.dc; 345 ln3->dc = ln2.dc; 346 } 347 ln3->exp = ln1.exp; 348 for (i = cnt - 1; i >= 0; i--) 349 { 350 ln3->a[i] = ln1.a[i] + ln2.a[i] + carry; 351 if (ln3->a[i] > 9) 352 { 353 carry = 1; 354 ln3->a[i] -= 10; 355 } 356 else 357 { 358 carry = 0; 359 } 360 } 361 LNnormalize(ln3); 362 } 363 } 364 return state; 365 } 366 367 int LNsubtract(LNS *lna, LNS *lnb, 368 LNS *ln3) 369 { 370 int ret = 0; 371 LNS ln1, ln2; 372 373 ln1 = *lna; 374 ln2 = *lnb; 375 376 if (0 == lna->dc) 377 { 378 *ln3 = *lnb; 379 LNnegate(ln3); 380 } 381 else 382 if (0 == lnb->dc) 383 *ln3 = *lna; 384 else 385 { 386 if (ln1.sign != ln2.sign) 387 { 388 LNnegate(&ln2); 389 ret = LNadd(&ln1, &ln2, ln3); 390 } 391 else 392 { 393 int t, i, tmp, borrow = 0; 394 395 t = LNcompare(&ln1, &ln2); 396 if (0 == t) 397 { 398 ln3->sign = 1; 399 ln3->exp = 0; 400 ln3->dc = 0; 401 } 402 else 403 if (0 > t) 404 { 405 ret = LNsubtract(&ln2, &ln1, ln3); 406 ln3->sign = -1 * ln3->sign; 407 } 408 else 409 { 410 ln3->sign = ln1.sign; 411 ln3->exp = ln1.exp; 412 LNshift(&ln2, (ln1.exp - ln2.exp)); 413 if (ln1.dc != ln2.dc) 414 if (ln1.dc > ln2.dc) 415 { 416 for (i=ln2.dc; i < ln1.dc; i++) 417 ln2.a[i] = 0; 418 ln2.dc = ln1.dc; 419 } 420 else 421 { 422 for (i=ln1.dc; i < ln2.dc; i++) 423 ln1.a[i] = 0; 424 ln1.dc = ln2.dc; 425 } 426 427 for (i = ln1.dc - 1; i >= 0; i--) 428 { 429 tmp = borrow + ln2.a[i]; 430 if (ln1.a[i] > tmp) 431 { 432 ln3->a[i] = ln1.a[i] - tmp; 433 borrow = 0; 434 } 435 else 436 { 437 ln3->a[i] = (10 + ln1.a[i]) - tmp; 438 borrow = 1; 439 } 440 } 441 LNnormalize(ln3); 442 } 443 } 444 } 445 return ret; 446 } 447 448 int LNmultiply(LNS *ln1, LNS *ln2, 449 LNS *ln3) 450 { 451 if ((0 == ln1->dc) || (0 == ln2->dc)) 452 { 453 ln3->dc = 0; 454 ln3->sign = 0; 455 ln3->exp = 0; 456 ln3->a[0] = 0; 457 } 458 else 459 { 460 int i1, i2, i3, dig, tmp, carry; 461 462 ln3->sign = ln1->sign * ln2->sign; 463 ln3->exp = ln1->exp + ln2->exp; 464 ln3->dc = ln1->dc + ln2->dc; 465 dig = ln3->dc - 1; 466 for (i3=0; i3 <= dig; i3++) 467 ln3->a[i3] = 0; 468 for (i2=ln2->dc - 1; i2 >= 0; i2--) 469 { 470 carry = 0; 471 i3 = dig--; 472 for (i1=ln1->dc - 1; i1 >= 0; i1--) 473 { 474 tmp = (ln1->a[i1] * ln2->a[i2]) + carry + ln3->a[i3]; 475 if (tmp > 9) 476 { 477 carry = tmp / 10; 478 ln3->a[i3] = (tmp % 10); 479 } 480 else 481 { 482 carry = 0; 483 ln3->a[i3] = tmp; 484 } 485 i3--; 486 } 487 ln3->a[i3] = ln3->a[i3] + carry; 488 } 489 LNnormalize(ln3); 490 } 491 return 0; 492 } 493 494 int LNdivide(LNS *ln1, long int i2, LNS *ln3) 495 { 496 int i, tot = 0; 497 498 ln3->exp = ln1->exp; 499 ln3->sign = ln1->sign * ((0 < i2) ? 1 : -1); 500 for (i=0; i < ln1->dc; i++) 501 { 502 tot += ln1->a[i]; 503 if (tot >= i2) 504 { 505 ln3->a[i] = tot / i2; 506 tot = (tot % i2) * 10; 507 } 508 else 509 { 510 ln3->a[i] = 0; 511 tot *= 10; 512 } 513 } 514 515 ln3->dc = i; 516 while ((LMD > ln3->dc) && (0 < tot)) 517 { 518 if (tot >= i2) 519 { 520 ln3->a[ln3->dc] = tot / i2; 521 tot = (tot % i2) * 10; 522 } 523 else 524 { 525 ln3->a[ln3->dc] = 0; 526 tot *= 10; 527 } 528 ln3->dc++; 529 } 530 LNnormalize(ln3); 531 return 0; 532 } 533 534 int LNdcnvrt(double d, LNS *n) 535 { 536 char str[LMD]; 537 538 sprintf(str, "%ld:", d); 539 return LNstr2arr(str, n); 540 } 541 542 int LNcopy(LNS *ln1, LNS *ln2) 543 { 544 int i; 545 546 ln2->sign = ln1->sign; 547 ln2->exp = ln1->exp; 548 ln2->dc = ln1->dc; 549 for (i=0; i < ln1->dc; i++) 550 ln2->a[i] = ln1->a[i]; 551 return 0; 552 }
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© 1999, 2000, 2001, 2002, 2003 Isaac Traxler