flow like the river

BACK_BACK/node_modules/bson/src/decimal128.ts

@@ -0,0 +1,858 @@
+import { BSONValue } from './bson_value';
+import { BSONError } from './error';
+import { Long } from './long';
+import { isUint8Array } from './parser/utils';
+import { ByteUtils } from './utils/byte_utils';
+
+const PARSE_STRING_REGEXP = /^(\+|-)?(\d+|(\d*\.\d*))?(E|e)?([-+])?(\d+)?$/;
+const PARSE_INF_REGEXP = /^(\+|-)?(Infinity|inf)$/i;
+const PARSE_NAN_REGEXP = /^(\+|-)?NaN$/i;
+
+const EXPONENT_MAX = 6111;
+const EXPONENT_MIN = -6176;
+const EXPONENT_BIAS = 6176;
+const MAX_DIGITS = 34;
+
+// Nan value bits as 32 bit values (due to lack of longs)
+const NAN_BUFFER = ByteUtils.fromNumberArray(
+  [
+    0x7c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+  ].reverse()
+);
+// Infinity value bits 32 bit values (due to lack of longs)
+const INF_NEGATIVE_BUFFER = ByteUtils.fromNumberArray(
+  [
+    0xf8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+  ].reverse()
+);
+const INF_POSITIVE_BUFFER = ByteUtils.fromNumberArray(
+  [
+    0x78, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
+  ].reverse()
+);
+
+const EXPONENT_REGEX = /^([-+])?(\d+)?$/;
+
+// 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 BSONError(`"${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 extends BSONValue {
+  get _bsontype(): 'Decimal128' {
+    return 'Decimal128';
+  }
+
+  readonly bytes!: Uint8Array;
+
+  /**
+   * @param bytes - a buffer containing the raw Decimal128 bytes in little endian order,
+   *                or a string representation as returned by .toString()
+   */
+  constructor(bytes: Uint8Array | string) {
+    super();
+    if (typeof bytes === 'string') {
+      this.bytes = Decimal128.fromString(bytes).bytes;
+    } else if (isUint8Array(bytes)) {
+      if (bytes.byteLength !== 16) {
+        throw new BSONError('Decimal128 must take a Buffer of 16 bytes');
+      }
+      this.bytes = bytes;
+    } else {
+      throw new BSONError('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 {
+    return Decimal128._fromString(representation, { allowRounding: false });
+  }
+
+  /**
+   * Create a Decimal128 instance from a string representation, allowing for rounding to 34
+   * significant digits
+   *
+   * @example Example of a number that will be rounded
+   * ```ts
+   * > let d = Decimal128.fromString('37.499999999999999196428571428571375')
+   * Uncaught:
+   * BSONError: "37.499999999999999196428571428571375" is not a valid Decimal128 string - inexact rounding
+   * at invalidErr (/home/wajames/js-bson/lib/bson.cjs:1402:11)
+   * at Decimal128.fromStringInternal (/home/wajames/js-bson/lib/bson.cjs:1633:25)
+   * at Decimal128.fromString (/home/wajames/js-bson/lib/bson.cjs:1424:27)
+   *
+   * > d = Decimal128.fromStringWithRounding('37.499999999999999196428571428571375')
+   * new Decimal128("37.49999999999999919642857142857138")
+   * ```
+   * @param representation - a numeric string representation.
+   */
+  static fromStringWithRounding(representation: string): Decimal128 {
+    return Decimal128._fromString(representation, { allowRounding: true });
+  }
+
+  private static _fromString(representation: string, options: { allowRounding: boolean }) {
+    // Parse state tracking
+    let isNegative = false;
+    let sawSign = 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 last digit
+    let lastDigit = 0;
+
+    // Exponent
+    let exponent = 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 BSONError('' + 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 BSONError('' + 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] === '-') {
+      sawSign = true;
+      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(isNegative ? INF_NEGATIVE_BUFFER : INF_POSITIVE_BUFFER);
+      } else if (representation[index] === 'N') {
+        return new Decimal128(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 < MAX_DIGITS) {
+        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 BSONError('' + 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(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(NAN_BUFFER);
+
+    // Done reading input
+    // Find first non-zero digit in digits
+    if (!nDigitsStored) {
+      digits[0] = 0;
+      nDigits = 1;
+      nDigitsStored = 1;
+      significantDigits = 0;
+    } else {
+      lastDigit = nDigitsStored - 1;
+      significantDigits = nDigits;
+      if (significantDigits !== 1) {
+        while (
+          representation[
+            firstNonZero + significantDigits - 1 + Number(sawSign) + Number(sawRadix)
+          ] === '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 >= MAX_DIGITS) {
+        // Check if we have a zero then just hard clamp, otherwise fail
+        if (significantDigits === 0) {
+          exponent = EXPONENT_MAX;
+          break;
+        }
+
+        invalidErr(representation, 'overflow');
+      }
+      exponent = exponent - 1;
+    }
+
+    if (options.allowRounding) {
+      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 + 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 (sawSign) {
+          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 (let 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(isNegative ? INF_NEGATIVE_BUFFER : INF_POSITIVE_BUFFER);
+                }
+              }
+            } else {
+              break;
+            }
+          }
+        }
+      }
+    } else {
+      while (exponent < EXPONENT_MIN || nDigitsStored < nDigits) {
+        // Shift last digit. can only do this if < significant digits than # stored.
+        if (lastDigit === 0) {
+          if (significantDigits === 0) {
+            exponent = EXPONENT_MIN;
+            break;
+          }
+
+          invalidErr(representation, 'exponent underflow');
+        }
+
+        if (nDigitsStored < nDigits) {
+          if (
+            representation[nDigits - 1 + Number(sawSign) + Number(sawRadix)] !== '0' &&
+            significantDigits !== 0
+          ) {
+            invalidErr(representation, 'inexact rounding');
+          }
+          // adjust to match digits not stored
+          nDigits = nDigits - 1;
+        } else {
+          if (digits[lastDigit] !== 0) {
+            invalidErr(representation, 'inexact rounding');
+          }
+          // adjust to round
+          lastDigit = lastDigit - 1;
+        }
+
+        if (exponent < EXPONENT_MAX) {
+          exponent = exponent + 1;
+        } else {
+          invalidErr(representation, 'overflow');
+        }
+      }
+
+      // Round
+      // We've normalized the exponent, but might still need to round.
+      if (lastDigit + 1 < significantDigits) {
+        // 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;
+        }
+        // if saw sign, we need to increment again to account for - or + sign at start.
+        if (sawSign) {
+          firstNonZero = firstNonZero + 1;
+        }
+
+        const roundDigit = parseInt(representation[firstNonZero + lastDigit + 1], 10);
+
+        if (roundDigit !== 0) {
+          invalidErr(representation, 'inexact rounding');
+        }
+      }
+    }
+
+    // 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 < 17) {
+      let dIdx = 0;
+      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 = 0;
+      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 = ByteUtils.allocate(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()}")`;
+  }
+}