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(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' });