decimal128.ts 24 KB
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773
import { Buffer } from 'buffer';
import { BSONTypeError } from './error';
import { Long } from './long';
import { isUint8Array } from './parser/utils';

const PARSE_STRING_REGEXP = /^(\+|-)?(\d+|(\d*\.\d*))?(E|e)?([-+])?(\d+)?$/;
const PARSE_INF_REGEXP = /^(\+|-)?(Infinity|inf)$/i;
const PARSE_NAN_REGEXP = /^(\+|-)?NaN$/i;

const EXPONENT_MAX = 6111;
const EXPONENT_MIN = -6176;
const EXPONENT_BIAS = 6176;
const MAX_DIGITS = 34;

// Nan value bits as 32 bit values (due to lack of longs)
const NAN_BUFFER = [
  0x7c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
].reverse();
// Infinity value bits 32 bit values (due to lack of longs)
const INF_NEGATIVE_BUFFER = [
  0xf8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
].reverse();
const INF_POSITIVE_BUFFER = [
  0x78, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
].reverse();

const EXPONENT_REGEX = /^([-+])?(\d+)?$/;

// Extract least significant 5 bits
const COMBINATION_MASK = 0x1f;
// Extract least significant 14 bits
const EXPONENT_MASK = 0x3fff;
// Value of combination field for Inf
const COMBINATION_INFINITY = 30;
// Value of combination field for NaN
const COMBINATION_NAN = 31;

// Detect if the value is a digit
function isDigit(value: string): boolean {
  return !isNaN(parseInt(value, 10));
}

// Divide two uint128 values
function divideu128(value: { parts: [number, number, number, number] }) {
  const DIVISOR = Long.fromNumber(1000 * 1000 * 1000);
  let _rem = Long.fromNumber(0);

  if (!value.parts[0] && !value.parts[1] && !value.parts[2] && !value.parts[3]) {
    return { quotient: value, rem: _rem };
  }

  for (let i = 0; i <= 3; i++) {
    // Adjust remainder to match value of next dividend
    _rem = _rem.shiftLeft(32);
    // Add the divided to _rem
    _rem = _rem.add(new Long(value.parts[i], 0));
    value.parts[i] = _rem.div(DIVISOR).low;
    _rem = _rem.modulo(DIVISOR);
  }

  return { quotient: value, rem: _rem };
}

// Multiply two Long values and return the 128 bit value
function multiply64x2(left: Long, right: Long): { high: Long; low: Long } {
  if (!left && !right) {
    return { high: Long.fromNumber(0), low: Long.fromNumber(0) };
  }

  const leftHigh = left.shiftRightUnsigned(32);
  const leftLow = new Long(left.getLowBits(), 0);
  const rightHigh = right.shiftRightUnsigned(32);
  const rightLow = new Long(right.getLowBits(), 0);

  let productHigh = leftHigh.multiply(rightHigh);
  let productMid = leftHigh.multiply(rightLow);
  const productMid2 = leftLow.multiply(rightHigh);
  let productLow = leftLow.multiply(rightLow);

  productHigh = productHigh.add(productMid.shiftRightUnsigned(32));
  productMid = new Long(productMid.getLowBits(), 0)
    .add(productMid2)
    .add(productLow.shiftRightUnsigned(32));

  productHigh = productHigh.add(productMid.shiftRightUnsigned(32));
  productLow = productMid.shiftLeft(32).add(new Long(productLow.getLowBits(), 0));

  // Return the 128 bit result
  return { high: productHigh, low: productLow };
}

function lessThan(left: Long, right: Long): boolean {
  // Make values unsigned
  const uhleft = left.high >>> 0;
  const uhright = right.high >>> 0;

  // Compare high bits first
  if (uhleft < uhright) {
    return true;
  } else if (uhleft === uhright) {
    const ulleft = left.low >>> 0;
    const ulright = right.low >>> 0;
    if (ulleft < ulright) return true;
  }

  return false;
}

function invalidErr(string: string, message: string) {
  throw new BSONTypeError(`"${string}" is not a valid Decimal128 string - ${message}`);
}

/** @public */
export interface Decimal128Extended {
  $numberDecimal: string;
}

/**
 * A class representation of the BSON Decimal128 type.
 * @public
 * @category BSONType
 */
export class Decimal128 {
  _bsontype!: 'Decimal128';

  readonly bytes!: Buffer;

  /**
   * @param bytes - a buffer containing the raw Decimal128 bytes in little endian order,
   *                or a string representation as returned by .toString()
   */
  constructor(bytes: Buffer | string) {
    if (!(this instanceof Decimal128)) return new Decimal128(bytes);

    if (typeof bytes === 'string') {
      this.bytes = Decimal128.fromString(bytes).bytes;
    } else if (isUint8Array(bytes)) {
      if (bytes.byteLength !== 16) {
        throw new BSONTypeError('Decimal128 must take a Buffer of 16 bytes');
      }
      this.bytes = bytes;
    } else {
      throw new BSONTypeError('Decimal128 must take a Buffer or string');
    }
  }

  /**
   * Create a Decimal128 instance from a string representation
   *
   * @param representation - a numeric string representation.
   */
  static fromString(representation: string): Decimal128 {
    // Parse state tracking
    let isNegative = false;
    let sawRadix = false;
    let foundNonZero = false;

    // Total number of significant digits (no leading or trailing zero)
    let significantDigits = 0;
    // Total number of significand digits read
    let nDigitsRead = 0;
    // Total number of digits (no leading zeros)
    let nDigits = 0;
    // The number of the digits after radix
    let radixPosition = 0;
    // The index of the first non-zero in *str*
    let firstNonZero = 0;

    // Digits Array
    const digits = [0];
    // The number of digits in digits
    let nDigitsStored = 0;
    // Insertion pointer for digits
    let digitsInsert = 0;
    // The index of the first non-zero digit
    let firstDigit = 0;
    // The index of the last digit
    let lastDigit = 0;

    // Exponent
    let exponent = 0;
    // loop index over array
    let i = 0;
    // The high 17 digits of the significand
    let significandHigh = new Long(0, 0);
    // The low 17 digits of the significand
    let significandLow = new Long(0, 0);
    // The biased exponent
    let biasedExponent = 0;

    // Read index
    let index = 0;

    // Naively prevent against REDOS attacks.
    // TODO: implementing a custom parsing for this, or refactoring the regex would yield
    //       further gains.
    if (representation.length >= 7000) {
      throw new BSONTypeError('' + representation + ' not a valid Decimal128 string');
    }

    // Results
    const stringMatch = representation.match(PARSE_STRING_REGEXP);
    const infMatch = representation.match(PARSE_INF_REGEXP);
    const nanMatch = representation.match(PARSE_NAN_REGEXP);

    // Validate the string
    if ((!stringMatch && !infMatch && !nanMatch) || representation.length === 0) {
      throw new BSONTypeError('' + representation + ' not a valid Decimal128 string');
    }

    if (stringMatch) {
      // full_match = stringMatch[0]
      // sign = stringMatch[1]

      const unsignedNumber = stringMatch[2];
      // stringMatch[3] is undefined if a whole number (ex "1", 12")
      // but defined if a number w/ decimal in it (ex "1.0, 12.2")

      const e = stringMatch[4];
      const expSign = stringMatch[5];
      const expNumber = stringMatch[6];

      // they provided e, but didn't give an exponent number. for ex "1e"
      if (e && expNumber === undefined) invalidErr(representation, 'missing exponent power');

      // they provided e, but didn't give a number before it. for ex "e1"
      if (e && unsignedNumber === undefined) invalidErr(representation, 'missing exponent base');

      if (e === undefined && (expSign || expNumber)) {
        invalidErr(representation, 'missing e before exponent');
      }
    }

    // Get the negative or positive sign
    if (representation[index] === '+' || representation[index] === '-') {
      isNegative = representation[index++] === '-';
    }

    // Check if user passed Infinity or NaN
    if (!isDigit(representation[index]) && representation[index] !== '.') {
      if (representation[index] === 'i' || representation[index] === 'I') {
        return new Decimal128(Buffer.from(isNegative ? INF_NEGATIVE_BUFFER : INF_POSITIVE_BUFFER));
      } else if (representation[index] === 'N') {
        return new Decimal128(Buffer.from(NAN_BUFFER));
      }
    }

    // Read all the digits
    while (isDigit(representation[index]) || representation[index] === '.') {
      if (representation[index] === '.') {
        if (sawRadix) invalidErr(representation, 'contains multiple periods');

        sawRadix = true;
        index = index + 1;
        continue;
      }

      if (nDigitsStored < 34) {
        if (representation[index] !== '0' || foundNonZero) {
          if (!foundNonZero) {
            firstNonZero = nDigitsRead;
          }

          foundNonZero = true;

          // Only store 34 digits
          digits[digitsInsert++] = parseInt(representation[index], 10);
          nDigitsStored = nDigitsStored + 1;
        }
      }

      if (foundNonZero) nDigits = nDigits + 1;
      if (sawRadix) radixPosition = radixPosition + 1;

      nDigitsRead = nDigitsRead + 1;
      index = index + 1;
    }

    if (sawRadix && !nDigitsRead)
      throw new BSONTypeError('' + representation + ' not a valid Decimal128 string');

    // Read exponent if exists
    if (representation[index] === 'e' || representation[index] === 'E') {
      // Read exponent digits
      const match = representation.substr(++index).match(EXPONENT_REGEX);

      // No digits read
      if (!match || !match[2]) return new Decimal128(Buffer.from(NAN_BUFFER));

      // Get exponent
      exponent = parseInt(match[0], 10);

      // Adjust the index
      index = index + match[0].length;
    }

    // Return not a number
    if (representation[index]) return new Decimal128(Buffer.from(NAN_BUFFER));

    // Done reading input
    // Find first non-zero digit in digits
    firstDigit = 0;

    if (!nDigitsStored) {
      firstDigit = 0;
      lastDigit = 0;
      digits[0] = 0;
      nDigits = 1;
      nDigitsStored = 1;
      significantDigits = 0;
    } else {
      lastDigit = nDigitsStored - 1;
      significantDigits = nDigits;
      if (significantDigits !== 1) {
        while (digits[firstNonZero + significantDigits - 1] === 0) {
          significantDigits = significantDigits - 1;
        }
      }
    }

    // Normalization of exponent
    // Correct exponent based on radix position, and shift significand as needed
    // to represent user input

    // Overflow prevention
    if (exponent <= radixPosition && radixPosition - exponent > 1 << 14) {
      exponent = EXPONENT_MIN;
    } else {
      exponent = exponent - radixPosition;
    }

    // Attempt to normalize the exponent
    while (exponent > EXPONENT_MAX) {
      // Shift exponent to significand and decrease
      lastDigit = lastDigit + 1;

      if (lastDigit - firstDigit > MAX_DIGITS) {
        // Check if we have a zero then just hard clamp, otherwise fail
        const digitsString = digits.join('');
        if (digitsString.match(/^0+$/)) {
          exponent = EXPONENT_MAX;
          break;
        }

        invalidErr(representation, 'overflow');
      }
      exponent = exponent - 1;
    }

    while (exponent < EXPONENT_MIN || nDigitsStored < nDigits) {
      // Shift last digit. can only do this if < significant digits than # stored.
      if (lastDigit === 0 && significantDigits < nDigitsStored) {
        exponent = EXPONENT_MIN;
        significantDigits = 0;
        break;
      }

      if (nDigitsStored < nDigits) {
        // adjust to match digits not stored
        nDigits = nDigits - 1;
      } else {
        // adjust to round
        lastDigit = lastDigit - 1;
      }

      if (exponent < EXPONENT_MAX) {
        exponent = exponent + 1;
      } else {
        // Check if we have a zero then just hard clamp, otherwise fail
        const digitsString = digits.join('');
        if (digitsString.match(/^0+$/)) {
          exponent = EXPONENT_MAX;
          break;
        }
        invalidErr(representation, 'overflow');
      }
    }

    // Round
    // We've normalized the exponent, but might still need to round.
    if (lastDigit - firstDigit + 1 < significantDigits) {
      let endOfString = nDigitsRead;

      // If we have seen a radix point, 'string' is 1 longer than we have
      // documented with ndigits_read, so inc the position of the first nonzero
      // digit and the position that digits are read to.
      if (sawRadix) {
        firstNonZero = firstNonZero + 1;
        endOfString = endOfString + 1;
      }
      // if negative, we need to increment again to account for - sign at start.
      if (isNegative) {
        firstNonZero = firstNonZero + 1;
        endOfString = endOfString + 1;
      }

      const roundDigit = parseInt(representation[firstNonZero + lastDigit + 1], 10);
      let roundBit = 0;

      if (roundDigit >= 5) {
        roundBit = 1;
        if (roundDigit === 5) {
          roundBit = digits[lastDigit] % 2 === 1 ? 1 : 0;
          for (i = firstNonZero + lastDigit + 2; i < endOfString; i++) {
            if (parseInt(representation[i], 10)) {
              roundBit = 1;
              break;
            }
          }
        }
      }

      if (roundBit) {
        let dIdx = lastDigit;

        for (; dIdx >= 0; dIdx--) {
          if (++digits[dIdx] > 9) {
            digits[dIdx] = 0;

            // overflowed most significant digit
            if (dIdx === 0) {
              if (exponent < EXPONENT_MAX) {
                exponent = exponent + 1;
                digits[dIdx] = 1;
              } else {
                return new Decimal128(
                  Buffer.from(isNegative ? INF_NEGATIVE_BUFFER : INF_POSITIVE_BUFFER)
                );
              }
            }
          }
        }
      }
    }

    // Encode significand
    // The high 17 digits of the significand
    significandHigh = Long.fromNumber(0);
    // The low 17 digits of the significand
    significandLow = Long.fromNumber(0);

    // read a zero
    if (significantDigits === 0) {
      significandHigh = Long.fromNumber(0);
      significandLow = Long.fromNumber(0);
    } else if (lastDigit - firstDigit < 17) {
      let dIdx = firstDigit;
      significandLow = Long.fromNumber(digits[dIdx++]);
      significandHigh = new Long(0, 0);

      for (; dIdx <= lastDigit; dIdx++) {
        significandLow = significandLow.multiply(Long.fromNumber(10));
        significandLow = significandLow.add(Long.fromNumber(digits[dIdx]));
      }
    } else {
      let dIdx = firstDigit;
      significandHigh = Long.fromNumber(digits[dIdx++]);

      for (; dIdx <= lastDigit - 17; dIdx++) {
        significandHigh = significandHigh.multiply(Long.fromNumber(10));
        significandHigh = significandHigh.add(Long.fromNumber(digits[dIdx]));
      }

      significandLow = Long.fromNumber(digits[dIdx++]);

      for (; dIdx <= lastDigit; dIdx++) {
        significandLow = significandLow.multiply(Long.fromNumber(10));
        significandLow = significandLow.add(Long.fromNumber(digits[dIdx]));
      }
    }

    const significand = multiply64x2(significandHigh, Long.fromString('100000000000000000'));
    significand.low = significand.low.add(significandLow);

    if (lessThan(significand.low, significandLow)) {
      significand.high = significand.high.add(Long.fromNumber(1));
    }

    // Biased exponent
    biasedExponent = exponent + EXPONENT_BIAS;
    const dec = { low: Long.fromNumber(0), high: Long.fromNumber(0) };

    // Encode combination, exponent, and significand.
    if (
      significand.high.shiftRightUnsigned(49).and(Long.fromNumber(1)).equals(Long.fromNumber(1))
    ) {
      // Encode '11' into bits 1 to 3
      dec.high = dec.high.or(Long.fromNumber(0x3).shiftLeft(61));
      dec.high = dec.high.or(
        Long.fromNumber(biasedExponent).and(Long.fromNumber(0x3fff).shiftLeft(47))
      );
      dec.high = dec.high.or(significand.high.and(Long.fromNumber(0x7fffffffffff)));
    } else {
      dec.high = dec.high.or(Long.fromNumber(biasedExponent & 0x3fff).shiftLeft(49));
      dec.high = dec.high.or(significand.high.and(Long.fromNumber(0x1ffffffffffff)));
    }

    dec.low = significand.low;

    // Encode sign
    if (isNegative) {
      dec.high = dec.high.or(Long.fromString('9223372036854775808'));
    }

    // Encode into a buffer
    const buffer = Buffer.alloc(16);
    index = 0;

    // Encode the low 64 bits of the decimal
    // Encode low bits
    buffer[index++] = dec.low.low & 0xff;
    buffer[index++] = (dec.low.low >> 8) & 0xff;
    buffer[index++] = (dec.low.low >> 16) & 0xff;
    buffer[index++] = (dec.low.low >> 24) & 0xff;
    // Encode high bits
    buffer[index++] = dec.low.high & 0xff;
    buffer[index++] = (dec.low.high >> 8) & 0xff;
    buffer[index++] = (dec.low.high >> 16) & 0xff;
    buffer[index++] = (dec.low.high >> 24) & 0xff;

    // Encode the high 64 bits of the decimal
    // Encode low bits
    buffer[index++] = dec.high.low & 0xff;
    buffer[index++] = (dec.high.low >> 8) & 0xff;
    buffer[index++] = (dec.high.low >> 16) & 0xff;
    buffer[index++] = (dec.high.low >> 24) & 0xff;
    // Encode high bits
    buffer[index++] = dec.high.high & 0xff;
    buffer[index++] = (dec.high.high >> 8) & 0xff;
    buffer[index++] = (dec.high.high >> 16) & 0xff;
    buffer[index++] = (dec.high.high >> 24) & 0xff;

    // Return the new Decimal128
    return new Decimal128(buffer);
  }

  /** Create a string representation of the raw Decimal128 value */
  toString(): string {
    // Note: bits in this routine are referred to starting at 0,
    // from the sign bit, towards the coefficient.

    // decoded biased exponent (14 bits)
    let biased_exponent;
    // the number of significand digits
    let significand_digits = 0;
    // the base-10 digits in the significand
    const significand = new Array<number>(36);
    for (let i = 0; i < significand.length; i++) significand[i] = 0;
    // read pointer into significand
    let index = 0;

    // true if the number is zero
    let is_zero = false;

    // the most significant significand bits (50-46)
    let significand_msb;
    // temporary storage for significand decoding
    let significand128: { parts: [number, number, number, number] } = { parts: [0, 0, 0, 0] };
    // indexing variables
    let j, k;

    // Output string
    const string: string[] = [];

    // Unpack index
    index = 0;

    // Buffer reference
    const buffer = this.bytes;

    // Unpack the low 64bits into a long
    // bits 96 - 127
    const low =
      buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
    // bits 64 - 95
    const midl =
      buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);

    // Unpack the high 64bits into a long
    // bits 32 - 63
    const midh =
      buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
    // bits 0 - 31
    const high =
      buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);

    // Unpack index
    index = 0;

    // Create the state of the decimal
    const dec = {
      low: new Long(low, midl),
      high: new Long(midh, high)
    };

    if (dec.high.lessThan(Long.ZERO)) {
      string.push('-');
    }

    // Decode combination field and exponent
    // bits 1 - 5
    const combination = (high >> 26) & COMBINATION_MASK;

    if (combination >> 3 === 3) {
      // Check for 'special' values
      if (combination === COMBINATION_INFINITY) {
        return string.join('') + 'Infinity';
      } else if (combination === COMBINATION_NAN) {
        return 'NaN';
      } else {
        biased_exponent = (high >> 15) & EXPONENT_MASK;
        significand_msb = 0x08 + ((high >> 14) & 0x01);
      }
    } else {
      significand_msb = (high >> 14) & 0x07;
      biased_exponent = (high >> 17) & EXPONENT_MASK;
    }

    // unbiased exponent
    const exponent = biased_exponent - EXPONENT_BIAS;

    // Create string of significand digits

    // Convert the 114-bit binary number represented by
    // (significand_high, significand_low) to at most 34 decimal
    // digits through modulo and division.
    significand128.parts[0] = (high & 0x3fff) + ((significand_msb & 0xf) << 14);
    significand128.parts[1] = midh;
    significand128.parts[2] = midl;
    significand128.parts[3] = low;

    if (
      significand128.parts[0] === 0 &&
      significand128.parts[1] === 0 &&
      significand128.parts[2] === 0 &&
      significand128.parts[3] === 0
    ) {
      is_zero = true;
    } else {
      for (k = 3; k >= 0; k--) {
        let least_digits = 0;
        // Perform the divide
        const result = divideu128(significand128);
        significand128 = result.quotient;
        least_digits = result.rem.low;

        // We now have the 9 least significant digits (in base 2).
        // Convert and output to string.
        if (!least_digits) continue;

        for (j = 8; j >= 0; j--) {
          // significand[k * 9 + j] = Math.round(least_digits % 10);
          significand[k * 9 + j] = least_digits % 10;
          // least_digits = Math.round(least_digits / 10);
          least_digits = Math.floor(least_digits / 10);
        }
      }
    }

    // Output format options:
    // Scientific - [-]d.dddE(+/-)dd or [-]dE(+/-)dd
    // Regular    - ddd.ddd

    if (is_zero) {
      significand_digits = 1;
      significand[index] = 0;
    } else {
      significand_digits = 36;
      while (!significand[index]) {
        significand_digits = significand_digits - 1;
        index = index + 1;
      }
    }

    // the exponent if scientific notation is used
    const scientific_exponent = significand_digits - 1 + exponent;

    // The scientific exponent checks are dictated by the string conversion
    // specification and are somewhat arbitrary cutoffs.
    //
    // We must check exponent > 0, because if this is the case, the number
    // has trailing zeros.  However, we *cannot* output these trailing zeros,
    // because doing so would change the precision of the value, and would
    // change stored data if the string converted number is round tripped.
    if (scientific_exponent >= 34 || scientific_exponent <= -7 || exponent > 0) {
      // Scientific format

      // if there are too many significant digits, we should just be treating numbers
      // as + or - 0 and using the non-scientific exponent (this is for the "invalid
      // representation should be treated as 0/-0" spec cases in decimal128-1.json)
      if (significand_digits > 34) {
        string.push(`${0}`);
        if (exponent > 0) string.push('E+' + exponent);
        else if (exponent < 0) string.push('E' + exponent);
        return string.join('');
      }

      string.push(`${significand[index++]}`);
      significand_digits = significand_digits - 1;

      if (significand_digits) {
        string.push('.');
      }

      for (let i = 0; i < significand_digits; i++) {
        string.push(`${significand[index++]}`);
      }

      // Exponent
      string.push('E');
      if (scientific_exponent > 0) {
        string.push('+' + scientific_exponent);
      } else {
        string.push(`${scientific_exponent}`);
      }
    } else {
      // Regular format with no decimal place
      if (exponent >= 0) {
        for (let i = 0; i < significand_digits; i++) {
          string.push(`${significand[index++]}`);
        }
      } else {
        let radix_position = significand_digits + exponent;

        // non-zero digits before radix
        if (radix_position > 0) {
          for (let i = 0; i < radix_position; i++) {
            string.push(`${significand[index++]}`);
          }
        } else {
          string.push('0');
        }

        string.push('.');
        // add leading zeros after radix
        while (radix_position++ < 0) {
          string.push('0');
        }

        for (let i = 0; i < significand_digits - Math.max(radix_position - 1, 0); i++) {
          string.push(`${significand[index++]}`);
        }
      }
    }

    return string.join('');
  }

  toJSON(): Decimal128Extended {
    return { $numberDecimal: this.toString() };
  }

  /** @internal */
  toExtendedJSON(): Decimal128Extended {
    return { $numberDecimal: this.toString() };
  }

  /** @internal */
  static fromExtendedJSON(doc: Decimal128Extended): Decimal128 {
    return Decimal128.fromString(doc.$numberDecimal);
  }

  /** @internal */
  [Symbol.for('nodejs.util.inspect.custom')](): string {
    return this.inspect();
  }

  inspect(): string {
    return `new Decimal128("${this.toString()}")`;
  }
}

Object.defineProperty(Decimal128.prototype, '_bsontype', { value: 'Decimal128' });