'use strict';
let Long = require('./long');
var PARSE_STRING_REGEXP = /^(\+|-)?(\d+|(\d*\.\d*))?(E|e)?([-+])?(\d+)?$/;
var PARSE_INF_REGEXP = /^(\+|-)?(Infinity|inf)$/i;
var PARSE_NAN_REGEXP = /^(\+|-)?NaN$/i;
var EXPONENT_MAX = 6111;
var EXPONENT_MIN = -6176;
var EXPONENT_BIAS = 6176;
var MAX_DIGITS = 34;
// Nan value bits as 32 bit values (due to lack of longs)
var NAN_BUFFER = [
0x7c,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00
].reverse();
// Infinity value bits 32 bit values (due to lack of longs)
var INF_NEGATIVE_BUFFER = [
0xf8,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00
].reverse();
var INF_POSITIVE_BUFFER = [
0x78,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00,
0x00
].reverse();
var EXPONENT_REGEX = /^([-+])?(\d+)?$/;
// Detect if the value is a digit
var isDigit = function(value) {
return !isNaN(parseInt(value, 10));
};
// Divide two uint128 values
var divideu128 = function(value) {
var DIVISOR = Long.fromNumber(1000 * 1000 * 1000);
var _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
var multiply64x2 = function(left, right) {
if (!left && !right) {
return { high: Long.fromNumber(0), low: Long.fromNumber(0) };
}
var leftHigh = left.shiftRightUnsigned(32);
var leftLow = new Long(left.getLowBits(), 0);
var rightHigh = right.shiftRightUnsigned(32);
var rightLow = new Long(right.getLowBits(), 0);
var productHigh = leftHigh.multiply(rightHigh);
var productMid = leftHigh.multiply(rightLow);
var productMid2 = leftLow.multiply(rightHigh);
var 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 };
};
var lessThan = function(left, right) {
// Make values unsigned
var uhleft = left.high_ >>> 0;
var uhright = right.high_ >>> 0;
// Compare high bits first
if (uhleft < uhright) {
return true;
} else if (uhleft === uhright) {
var ulleft = left.low_ >>> 0;
var ulright = right.low_ >>> 0;
if (ulleft < ulright) return true;
}
return false;
};
var invalidErr = function(string, message) {
throw new TypeError('"${string}" not a valid Decimal128 string - ' + message);
};
/**
* A class representation of the BSON Decimal128 type.
*
* @class
* @param {Buffer} bytes a buffer containing the raw Decimal128 bytes.
* @return {Double}
*/
function Decimal128(bytes) {
this._bsontype = 'Decimal128';
this.bytes = bytes;
}
/**
* Create a Decimal128 instance from a string representation
*
* @method
* @param {string} string a numeric string representation.
* @return {Decimal128} returns a Decimal128 instance.
*/
Decimal128.fromString = function(string) {
// Parse state tracking
var isNegative = false;
var sawRadix = false;
var foundNonZero = false;
// Total number of significant digits (no leading or trailing zero)
var significantDigits = 0;
// Total number of significand digits read
var nDigitsRead = 0;
// Total number of digits (no leading zeros)
var nDigits = 0;
// The number of the digits after radix
var radixPosition = 0;
// The index of the first non-zero in *str*
var firstNonZero = 0;
// Digits Array
var digits = [0];
// The number of digits in digits
var nDigitsStored = 0;
// Insertion pointer for digits
var digitsInsert = 0;
// The index of the first non-zero digit
var firstDigit = 0;
// The index of the last digit
var lastDigit = 0;
// Exponent
var exponent = 0;
// loop index over array
var i = 0;
// The high 17 digits of the significand
var significandHigh = [0, 0];
// The low 17 digits of the significand
var significandLow = [0, 0];
// The biased exponent
var biasedExponent = 0;
// Read index
var index = 0;
// Naively prevent against REDOS attacks.
// TODO: implementing a custom parsing for this, or refactoring the regex would yield
// further gains.
if (string.length >= 7000) {
throw new TypeError('' + string + ' not a valid Decimal128 string');
}
// Results
var stringMatch = string.match(PARSE_STRING_REGEXP);
var infMatch = string.match(PARSE_INF_REGEXP);
var nanMatch = string.match(PARSE_NAN_REGEXP);
// Validate the string
if ((!stringMatch && !infMatch && !nanMatch) || string.length === 0) {
throw new TypeError('' + string + ' not a valid Decimal128 string');
}
if (stringMatch) {
// full_match = stringMatch[0]
// sign = stringMatch[1]
var 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")
var e = stringMatch[4];
var expSign = stringMatch[5];
var expNumber = stringMatch[6];
// they provided e, but didn't give an exponent number. for ex "1e"
if (e && expNumber === undefined) invalidErr(string, 'missing exponent power');
// they provided e, but didn't give a number before it. for ex "e1"
if (e && unsignedNumber === undefined) invalidErr(string, 'missing exponent base');
if (e === undefined && (expSign || expNumber)) {
invalidErr(string, 'missing e before exponent');
}
}
// Get the negative or positive sign
if (string[index] === '+' || string[index] === '-') {
isNegative = string[index++] === '-';
}
// Check if user passed Infinity or NaN
if (!isDigit(string[index]) && string[index] !== '.') {
if (string[index] === 'i' || string[index] === 'I') {
return new Decimal128(new Buffer(isNegative ? INF_NEGATIVE_BUFFER : INF_POSITIVE_BUFFER));
} else if (string[index] === 'N') {
return new Decimal128(new Buffer(NAN_BUFFER));
}
}
// Read all the digits
while (isDigit(string[index]) || string[index] === '.') {
if (string[index] === '.') {
if (sawRadix) invalidErr(string, 'contains multiple periods');
sawRadix = true;
index = index + 1;
continue;
}
if (nDigitsStored < 34) {
if (string[index] !== '0' || foundNonZero) {
if (!foundNonZero) {
firstNonZero = nDigitsRead;
}
foundNonZero = true;
// Only store 34 digits
digits[digitsInsert++] = parseInt(string[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 TypeError('' + string + ' not a valid Decimal128 string');
// Read exponent if exists
if (string[index] === 'e' || string[index] === 'E') {
// Read exponent digits
var match = string.substr(++index).match(EXPONENT_REGEX);
// No digits read
if (!match || !match[2]) return new Decimal128(new Buffer(NAN_BUFFER));
// Get exponent
exponent = parseInt(match[0], 10);
// Adjust the index
index = index + match[0].length;
}
// Return not a number
if (string[index]) return new Decimal128(new Buffer(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 (string[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
var digitsString = digits.join('');
if (digitsString.match(/^0+$/)) {
exponent = EXPONENT_MAX;
break;
}
invalidErr(string, '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
digitsString = digits.join('');
if (digitsString.match(/^0+$/)) {
exponent = EXPONENT_MAX;
break;
}
invalidErr(string, 'overflow');
}
}
// Round
// We've normalized the exponent, but might still need to round.
if (lastDigit - firstDigit + 1 < significantDigits) {
var 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;
}
var roundDigit = parseInt(string[firstNonZero + lastDigit + 1], 10);
var roundBit = 0;
if (roundDigit >= 5) {
roundBit = 1;
if (roundDigit === 5) {
roundBit = digits[lastDigit] % 2 === 1;
for (i = firstNonZero + lastDigit + 2; i < endOfString; i++) {
if (parseInt(string[i], 10)) {
roundBit = 1;
break;
}
}
}
}
if (roundBit) {
var 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(
new Buffer(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) {
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 {
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]));
}
}
var 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;
var 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)
) {
// 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
var buffer = new Buffer(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);
};
// Extract least significant 5 bits
var COMBINATION_MASK = 0x1f;
// Extract least significant 14 bits
var EXPONENT_MASK = 0x3fff;
// Value of combination field for Inf
var COMBINATION_INFINITY = 30;
// Value of combination field for NaN
var COMBINATION_NAN = 31;
// Value of combination field for NaN
// var COMBINATION_SNAN = 32;
// decimal128 exponent bias
EXPONENT_BIAS = 6176;
/**
* Create a string representation of the raw Decimal128 value
*
* @method
* @return {string} returns a Decimal128 string representation.
*/
Decimal128.prototype.toString = function() {
// Note: bits in this routine are referred to starting at 0,
// from the sign bit, towards the coefficient.
// bits 0 - 31
var high;
// bits 32 - 63
var midh;
// bits 64 - 95
var midl;
// bits 96 - 127
var low;
// bits 1 - 5
var combination;
// decoded biased exponent (14 bits)
var biased_exponent;
// the number of significand digits
var significand_digits = 0;
// the base-10 digits in the significand
var significand = new Array(36);
for (var i = 0; i < significand.length; i++) significand[i] = 0;
// read pointer into significand
var index = 0;
// unbiased exponent
var exponent;
// the exponent if scientific notation is used
var scientific_exponent;
// true if the number is zero
var is_zero = false;
// the most signifcant significand bits (50-46)
var significand_msb;
// temporary storage for significand decoding
var significand128 = { parts: new Array(4) };
// indexing variables
var j, k;
// Output string
var string = [];
// Unpack index
index = 0;
// Buffer reference
var buffer = this.bytes;
// Unpack the low 64bits into a long
low =
buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
midl =
buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
// Unpack the high 64bits into a long
midh =
buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
high =
buffer[index++] | (buffer[index++] << 8) | (buffer[index++] << 16) | (buffer[index++] << 24);
// Unpack index
index = 0;
// Create the state of the decimal
var dec = {
low: new Long(low, midl),
high: new Long(midh, high)
};
if (dec.high.lessThan(Long.ZERO)) {
string.push('-');
}
// Decode combination field and exponent
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;
}
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--) {
var least_digits = 0;
// Peform the divide
var 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;
i = 0;
while (!significand[index]) {
i++;
significand_digits = significand_digits - 1;
index = index + 1;
}
}
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 (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 (i = 0; i < significand_digits; i++) {
string.push(significand[index++]);
}
} else {
var radix_position = significand_digits + exponent;
// non-zero digits before radix
if (radix_position > 0) {
for (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 (i = 0; i < significand_digits - Math.max(radix_position - 1, 0); i++) {
string.push(significand[index++]);
}
}
}
return string.join('');
};
Decimal128.prototype.toJSON = function() {
return { $numberDecimal: this.toString() };
};
module.exports = Decimal128;
module.exports.Decimal128 = Decimal128;