bitcoincashjs/lib/browser/Bignum.js

/* bignumber.js v1.3.0 https://github.com/MikeMcl/bignumber.js/LICENCE */

/*jslint bitwise: true, eqeq: true, plusplus: true, sub: true, white: true, maxerr: 500 */
/*global module */

/*
  bignumber.js v1.3.0
  A JavaScript library for arbitrary-precision arithmetic.
  https://github.com/MikeMcl/bignumber.js
  Copyright (c) 2012 Michael Mclaughlin <M8ch88l@gmail.com>
  MIT Expat Licence
*/

/*********************************** DEFAULTS ************************************/

/*
 * The default values below must be integers within the stated ranges (inclusive).
 * Most of these values can be changed during run-time using BigNumber.config().
 */

/*
 * The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP,
 * MAX_EXP, and the argument to toFixed, toPrecision and toExponential, beyond
 * which an exception is thrown (if ERRORS is true).
 */
var MAX = 1E9, // 0 to 1e+9

  // Limit of magnitude of exponent argument to toPower.
  MAX_POWER = 1E6, // 1 to 1e+6

  // The maximum number of decimal places for operations involving division.
  DECIMAL_PLACES = 20, // 0 to MAX

  /*
   * The rounding mode used when rounding to the above decimal places, and when
   * using toFixed, toPrecision and toExponential, and round (default value).
   * UP         0 Away from zero.
   * DOWN       1 Towards zero.
   * CEIL       2 Towards +Infinity.
   * FLOOR      3 Towards -Infinity.
   * HALF_UP    4 Towards nearest neighbour. If equidistant, up.
   * HALF_DOWN  5 Towards nearest neighbour. If equidistant, down.
   * HALF_EVEN  6 Towards nearest neighbour. If equidistant, towards even neighbour.
   * HALF_CEIL  7 Towards nearest neighbour. If equidistant, towards +Infinity.
   * HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
   */
  ROUNDING_MODE = 4, // 0 to 8

  // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]

  // The exponent value at and beneath which toString returns exponential notation.
  // Number type: -7
  TO_EXP_NEG = -7, // 0 to -MAX

  // The exponent value at and above which toString returns exponential notation.
  // Number type: 21
  TO_EXP_POS = 21, // 0 to MAX

  // RANGE : [MIN_EXP, MAX_EXP]

  // The minimum exponent value, beneath which underflow to zero occurs.
  // Number type: -324  (5e-324)
  MIN_EXP = -MAX, // -1 to -MAX

  // The maximum exponent value, above which overflow to Infinity occurs.
  // Number type:  308  (1.7976931348623157e+308)
  MAX_EXP = MAX, // 1 to MAX

  // Whether BigNumber Errors are ever thrown.
  // CHANGE parseInt to parseFloat if changing ERRORS to false.
  ERRORS = true, // true or false
  parse = parseInt, // parseInt or parseFloat

  /***********************************************************************************/

  P = BigNumber.prototype,
  DIGITS = '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_',
  outOfRange,
  id = 0,
  isValid = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i,
  trim = String.prototype.trim || function() {
    return this.replace(/^\s+|\s+$/g, '')
  },
  ONE = BigNumber(1);


// CONSTRUCTOR


/*
 * The exported function.
 * Create and return a new instance of a BigNumber object.
 *
 * n {number|string|BigNumber} A numeric value.
 * [b] {number} The base of n. Integer, 2 to 64 inclusive.
 */
function BigNumber(n, b) {
  var e, i, isNum, digits, valid, orig,
    x = this;

  // Enable constructor usage without new.
  if (!(x instanceof BigNumber)) {
    return new BigNumber(n, b)
  }

  // Duplicate.
  if (n instanceof BigNumber) {
    id = 0;

    // e is undefined.
    if (b !== e) {
      n += ''
    } else {
      x['s'] = n['s'];
      x['e'] = n['e'];
      x['c'] = (n = n['c']) ? n.slice() : n;
      return;
    }
  }

  // Accept empty string as zero
  if (n === '') n = 0;

  // If number, check if minus zero.
  if (typeof n != 'string') {
    n = (isNum = typeof n == 'number' ||
      Object.prototype.toString.call(n) == '[object Number]') &&
      n === 0 && 1 / n < 0 ? '-0' : n + '';
  }

  orig = n;

  if (b === e && isValid.test(n)) {

    // Determine sign.
    x['s'] = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1;

    // Either n is not a valid BigNumber or a base has been specified.
  } else {

    // Enable exponential notation to be used with base 10 argument.
    // Ensure return value is rounded to DECIMAL_PLACES as with other bases.
    if (b == 10) {

      return setMode(n, DECIMAL_PLACES, ROUNDING_MODE);
    }

    n = trim.call(n).replace(/^\+(?!-)/, '');

    x['s'] = n.charAt(0) == '-' ? (n = n.replace(/^-(?!-)/, ''), -1) : 1;

    if (b != null) {

      if ((b == (b | 0) || !ERRORS) &&
        !(outOfRange = !(b >= 2 && b < 65))) {

        digits = '[' + DIGITS.slice(0, b = b | 0) + ']+';

        // Before non-decimal number validity test and base conversion
        // remove the `.` from e.g. '1.', and replace e.g. '.1' with '0.1'.
        n = n.replace(/\.$/, '').replace(/^\./, '0.');

        // Any number in exponential form will fail due to the e+/-.
        if (valid = new RegExp(
          '^' + digits + '(?:\\.' + digits + ')?$', b < 37 ? 'i' : '').test(n)) {

          if (isNum) {

            if (n.replace(/^0\.0*|\./, '').length > 15) {

              // 'new BigNumber() number type has more than 15 significant digits: {n}'
              ifExceptionsThrow(orig, 0);
            }

            // Prevent later check for length on converted number.
            isNum = !isNum;
          }
          n = convert(n, 10, b, x['s']);

        } else if (n != 'Infinity' && n != 'NaN') {

          // 'new BigNumber() not a base {b} number: {n}'
          ifExceptionsThrow(orig, 1, b);
          n = 'NaN';
        }
      } else {

        // 'new BigNumber() base not an integer: {b}'
        // 'new BigNumber() base out of range: {b}'
        ifExceptionsThrow(b, 2);

        // Ignore base.
        valid = isValid.test(n);
      }
    } else {
      valid = isValid.test(n);
    }

    if (!valid) {

      // Infinity/NaN
      x['c'] = x['e'] = null;

      // NaN
      if (n != 'Infinity') {

        // No exception on NaN.
        if (n != 'NaN') {

          // 'new BigNumber() not a number: {n}'
          ifExceptionsThrow(orig, 3);
        }
        x['s'] = null;
      }
      id = 0;

      return;
    }
  }

  // Decimal point?
  if ((e = n.indexOf('.')) > -1) {
    n = n.replace('.', '');
  }

  // Exponential form?
  if ((i = n.search(/e/i)) > 0) {

    // Determine exponent.
    if (e < 0) {
      e = i;
    }
    e += +n.slice(i + 1);
    n = n.substring(0, i);

  } else if (e < 0) {

    // Integer.
    e = n.length;
  }

  // Determine leading zeros.
  for (i = 0; n.charAt(i) == '0'; i++) {}

  b = n.length;

  // Disallow numbers with over 15 significant digits if number type.
  if (isNum && b > 15 && n.slice(i).length > 15) {

    // 'new BigNumber() number type has more than 15 significant digits: {n}'
    ifExceptionsThrow(orig, 0);
  }
  id = 0;

  // Overflow?
  if ((e -= i + 1) > MAX_EXP) {

    // Infinity.
    x['c'] = x['e'] = null;

    // Zero or underflow?
  } else if (i == b || e < MIN_EXP) {

    // Zero.
    x['c'] = [x['e'] = 0];
  } else {

    // Determine trailing zeros.
    for (; n.charAt(--b) == '0';) {}

    x['e'] = e;
    x['c'] = [];

    // Convert string to array of digits (without leading and trailing zeros).
    for (e = 0; i <= b; x['c'][e++] = +n.charAt(i++)) {}
  }
}


// CONSTRUCTOR PROPERTIES/METHODS


BigNumber['ROUND_UP'] = 0;
BigNumber['ROUND_DOWN'] = 1;
BigNumber['ROUND_CEIL'] = 2;
BigNumber['ROUND_FLOOR'] = 3;
BigNumber['ROUND_HALF_UP'] = 4;
BigNumber['ROUND_HALF_DOWN'] = 5;
BigNumber['ROUND_HALF_EVEN'] = 6;
BigNumber['ROUND_HALF_CEIL'] = 7;
BigNumber['ROUND_HALF_FLOOR'] = 8;

/*
 * Create an instance from a Buffer
 */
BigNumber['fromBuffer'] = function(buf, opts) {

  if (!opts) opts = {};

  var endian = {
    1: 'big',
    '-1': 'little'
  }[opts.endian] || opts.endian || 'big';

  var size = opts.size === 'auto' ? Math.ceil(buf.length) : (opts.size || 1);

  if (buf.length % size !== 0) {
    throw new RangeError('Buffer length (' + buf.length + ')' + ' must be a multiple of size (' + size + ')');
  }

  var hex = [];
  for (var i = 0; i < buf.length; i += size) {
    var chunk = [];
    for (var j = 0; j < size; j++) {
      chunk.push(buf[
        i + (endian === 'big' ? j : (size - j - 1))
      ]);
    }

    hex.push(chunk
      .map(function(c) {
        return (c < 16 ? '0' : '') + c.toString(16);
      })
      .join('')
    );
  }

  return BigNumber(hex.join(''), 16);

};

/*
 * Configure infrequently-changing library-wide settings.
 *
 * Accept an object or an argument list, with one or many of the following
 * properties or parameters respectively:
 * [ DECIMAL_PLACES [, ROUNDING_MODE [, EXPONENTIAL_AT [, RANGE [, ERRORS ]]]]]
 *
 * E.g.
 * BigNumber.config(20, 4) is equivalent to
 * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
 * Ignore properties/parameters set to null or undefined.
 *
 * Return an object with the properties current values.
 */
BigNumber['config'] = function() {
  var v, p,
    i = 0,
    r = {},
    a = arguments,
    o = a[0],
    c = 'config',
    inRange = function(n, lo, hi) {
      return !((outOfRange = n < lo || n > hi) ||
        parse(n) != n && n !== 0);
    },
    has = o && typeof o == 'object' ? function() {
      if (o.hasOwnProperty(p)) return (v = o[p]) != null
    } : function() {
      if (a.length > i) return (v = a[i++]) != null
    };

  // [DECIMAL_PLACES] {number} Integer, 0 to MAX inclusive.
  if (has(p = 'DECIMAL_PLACES')) {

    if (inRange(v, 0, MAX)) {
      DECIMAL_PLACES = v | 0;
    } else {

      // 'config() DECIMAL_PLACES not an integer: {v}'
      // 'config() DECIMAL_PLACES out of range: {v}'
      ifExceptionsThrow(v, p, c);
    }
  }
  r[p] = DECIMAL_PLACES;

  // [ROUNDING_MODE] {number} Integer, 0 to 8 inclusive.
  if (has(p = 'ROUNDING_MODE')) {

    if (inRange(v, 0, 8)) {
      ROUNDING_MODE = v | 0;
    } else {

      // 'config() ROUNDING_MODE not an integer: {v}'
      // 'config() ROUNDING_MODE out of range: {v}'
      ifExceptionsThrow(v, p, c);
    }
  }
  r[p] = ROUNDING_MODE;

  /*
   * [EXPONENTIAL_AT] {number|number[]} Integer, -MAX to MAX inclusive or
   * [ integer -MAX to 0 inclusive, 0 to MAX inclusive ].
   */
  if (has(p = 'EXPONENTIAL_AT')) {

    if (inRange(v, -MAX, MAX)) {
      TO_EXP_NEG = -(TO_EXP_POS = ~~ (v < 0 ? -v : +v));
    } else if (!outOfRange && v && inRange(v[0], -MAX, 0) &&
      inRange(v[1], 0, MAX)) {
      TO_EXP_NEG = ~~v[0];
      TO_EXP_POS = ~~v[1];
    } else {

      // 'config() EXPONENTIAL_AT not an integer or not [integer, integer]: {v}'
      // 'config() EXPONENTIAL_AT out of range or not [negative, positive: {v}'
      ifExceptionsThrow(v, p, c, 1);
    }
  }
  r[p] = [TO_EXP_NEG, TO_EXP_POS];

  /*
   * [RANGE][ {number|number[]} Non-zero integer, -MAX to MAX inclusive or
   * [ integer -MAX to -1 inclusive, integer 1 to MAX inclusive ].
   */
  if (has(p = 'RANGE')) {

    if (inRange(v, -MAX, MAX) && ~~v) {
      MIN_EXP = -(MAX_EXP = ~~ (v < 0 ? -v : +v));
    } else if (!outOfRange && v && inRange(v[0], -MAX, -1) &&
      inRange(v[1], 1, MAX)) {
      MIN_EXP = ~~v[0], MAX_EXP = ~~v[1];
    } else {

      // 'config() RANGE not a non-zero integer or not [integer, integer]: {v}'
      // 'config() RANGE out of range or not [negative, positive: {v}'
      ifExceptionsThrow(v, p, c, 1, 1);
    }
  }
  r[p] = [MIN_EXP, MAX_EXP];

  // [ERRORS] {boolean|number} true, false, 1 or 0.
  if (has(p = 'ERRORS')) {

    if (v === !!v || v === 1 || v === 0) {
      parse = (outOfRange = id = 0, ERRORS = !!v) ? parseInt : parseFloat;
    } else {

      // 'config() ERRORS not a boolean or binary digit: {v}'
      ifExceptionsThrow(v, p, c, 0, 0, 1);
    }
  }
  r[p] = ERRORS;

  return r;
};


// PRIVATE FUNCTIONS


// Assemble error messages. Throw BigNumber Errors.
function ifExceptionsThrow(arg, i, j, isArray, isRange, isErrors) {

  if (ERRORS) {
    var error,
      method = ['new BigNumber', 'cmp', 'div', 'eq', 'gt', 'gte', 'lt',
        'lte', 'minus', 'mod', 'plus', 'times', 'toFr'
      ][id ? id < 0 ? -id : id : 1 / id < 0 ? 1 : 0] + '()',
      message = outOfRange ? ' out of range' : ' not a' +
      (isRange ? ' non-zero' : 'n') + ' integer';

    message = ([
        method + ' number type has more than 15 significant digits',
        method + ' not a base ' + j + ' number',
        method + ' base' + message,
        method + ' not a number'
      ][i] ||
      j + '() ' + i + (isErrors ? ' not a boolean or binary digit' : message + (isArray ? ' or not [' + (outOfRange ? ' negative, positive' : ' integer, integer') + ' ]' : ''))) + ': ' + arg;

    outOfRange = id = 0;
    error = new Error(message);
    error['name'] = 'BigNumber Error';

    throw error;
  }
}


/*
 * Convert a numeric string of baseIn to a numeric string of baseOut.
 */
function convert(nStr, baseOut, baseIn, sign) {
  var e, dvs, dvd, nArr, fracArr, fracBN;

  // Convert string of base bIn to an array of numbers of baseOut.
  // Eg. strToArr('255', 10) where baseOut is 16, returns [15, 15].
  // Eg. strToArr('ff', 16)  where baseOut is 10, returns [2, 5, 5].
  function strToArr(str, bIn) {
    var j,
      i = 0,
      strL = str.length,
      arrL,
      arr = [0];

    for (bIn = bIn || baseIn; i < strL; i++) {

      for (arrL = arr.length, j = 0; j < arrL; arr[j] *= bIn, j++) {}

      for (arr[0] += DIGITS.indexOf(str.charAt(i)), j = 0; j < arr.length; j++) {

        if (arr[j] > baseOut - 1) {

          if (arr[j + 1] == null) {
            arr[j + 1] = 0;
          }
          arr[j + 1] += arr[j] / baseOut ^ 0;
          arr[j] %= baseOut;
        }
      }
    }

    return arr.reverse();
  }

  // Convert array to string.
  // E.g. arrToStr( [9, 10, 11] ) becomes '9ab' (in bases above 11).
  function arrToStr(arr) {
    var i = 0,
      arrL = arr.length,
      str = '';

    for (; i < arrL; str += DIGITS.charAt(arr[i++])) {}

    return str;
  }

  if (baseIn < 37) {
    nStr = nStr.toLowerCase();
  }

  /*
   * If non-integer convert integer part and fraction part separately.
   * Convert the fraction part as if it is an integer than use division to
   * reduce it down again to a value less than one.
   */
  if ((e = nStr.indexOf('.')) > -1) {

    /*
     * Calculate the power to which to raise the base to get the number
     * to divide the fraction part by after it has been converted as an
     * integer to the required base.
     */
    e = nStr.length - e - 1;

    // Use toFixed to avoid possible exponential notation.
    dvs = strToArr(new BigNumber(baseIn)['pow'](e)['toF'](), 10);

    nArr = nStr.split('.');

    // Convert the base of the fraction part (as integer).
    dvd = strToArr(nArr[1]);

    // Convert the base of the integer part.
    nArr = strToArr(nArr[0]);

    // Result will be a BigNumber with a value less than 1.
    fracBN = divide(dvd, dvs, dvd.length - dvs.length, sign, baseOut,
      // Is least significant digit of integer part an odd number?
      nArr[nArr.length - 1] & 1);

    fracArr = fracBN['c'];

    // e can be <= 0  ( if e == 0, fracArr is [0] or [1] ).
    if (e = fracBN['e']) {

      // Append zeros according to the exponent of the result.
      for (; ++e; fracArr.unshift(0)) {}

      // Append the fraction part to the converted integer part.
      nStr = arrToStr(nArr) + '.' + arrToStr(fracArr);

      // fracArr is [1].
      // Fraction digits rounded up, so increment last digit of integer part.
    } else if (fracArr[0]) {

      if (nArr[e = nArr.length - 1] < baseOut - 1) {
        ++nArr[e];
        nStr = arrToStr(nArr);
      } else {
        nStr = new BigNumber(arrToStr(nArr),
          baseOut)['plus'](ONE)['toS'](baseOut);
      }

      // fracArr is [0]. No fraction digits.
    } else {
      nStr = arrToStr(nArr);
    }
  } else {

    // Simple integer. Convert base.
    nStr = arrToStr(strToArr(nStr));
  }

  return nStr;
}


// Perform division in the specified base. Called by div and convert.
function divide(dvd, dvs, exp, s, base, isOdd) {
  var dvsL, dvsT, next, cmp, remI,
    dvsZ = dvs.slice(),
    dvdI = dvsL = dvs.length,
    dvdL = dvd.length,
    rem = dvd.slice(0, dvsL),
    remL = rem.length,
    quo = new BigNumber(ONE),
    qc = quo['c'] = [],
    qi = 0,
    dig = DECIMAL_PLACES + (quo['e'] = exp) + 1;

  quo['s'] = s;
  s = dig < 0 ? 0 : dig;

  // Add zeros to make remainder as long as divisor.
  for (; remL++ < dvsL; rem.push(0)) {}

  // Create version of divisor with leading zero.
  dvsZ.unshift(0);

  do {

    // 'next' is how many times the divisor goes into the current remainder.
    for (next = 0; next < base; next++) {

      // Compare divisor and remainder.
      if (dvsL != (remL = rem.length)) {
        cmp = dvsL > remL ? 1 : -1;
      } else {
        for (remI = -1, cmp = 0; ++remI < dvsL;) {

          if (dvs[remI] != rem[remI]) {
            cmp = dvs[remI] > rem[remI] ? 1 : -1;
            break;
          }
        }
      }

      // Subtract divisor from remainder (if divisor < remainder).
      if (cmp < 0) {

        // Remainder cannot be more than one digit longer than divisor.
        // Equalise lengths using divisor with extra leading zero?
        for (dvsT = remL == dvsL ? dvs : dvsZ; remL;) {

          if (rem[--remL] < dvsT[remL]) {

            for (remI = remL; remI && !rem[--remI]; rem[remI] = base - 1) {}
            --rem[remI];
            rem[remL] += base;
          }
          rem[remL] -= dvsT[remL];
        }
        for (; !rem[0]; rem.shift()) {}
      } else {
        break;
      }
    }

    // Add the 'next' digit to the result array.
    qc[qi++] = cmp ? next : ++next;

    // Update the remainder.
    rem[0] && cmp ? (rem[remL] = dvd[dvdI] || 0) : (rem = [dvd[dvdI]]);

  } while ((dvdI++ < dvdL || rem[0] != null) && s--);

  // Leading zero? Do not remove if result is simply zero (qi == 1).
  if (!qc[0] && qi != 1) {

    // There can't be more than one zero.
    --quo['e'];
    qc.shift();
  }

  // Round?
  if (qi > dig) {
    rnd(quo, DECIMAL_PLACES, base, isOdd, rem[0] != null);
  }

  // Overflow?
  if (quo['e'] > MAX_EXP) {

    // Infinity.
    quo['c'] = quo['e'] = null;

    // Underflow?
  } else if (quo['e'] < MIN_EXP) {

    // Zero.
    quo['c'] = [quo['e'] = 0];
  }

  return quo;
}


/*
 * Return a string representing the value of BigNumber n in normal or
 * exponential notation rounded to the specified decimal places or
 * significant digits.
 * Called by toString, toExponential (exp 1), toFixed, and toPrecision (exp 2).
 * d is the index (with the value in normal notation) of the digit that may be
 * rounded up.
 */
function format(n, d, exp) {

  // Initially, i is the number of decimal places required.
  var i = d - (n = new BigNumber(n))['e'],
    c = n['c'];

  // +-Infinity or NaN?
  if (!c) {
    return n['toS']();
  }

  // Round?
  if (c.length > ++d) {
    rnd(n, i, 10);
  }

  // Recalculate d if toFixed as n['e'] may have changed if value rounded up.
  i = c[0] == 0 ? i + 1 : exp ? d : n['e'] + i + 1;

  // Append zeros?
  for (; c.length < i; c.push(0)) {}
  i = n['e'];

  /*
   * toPrecision returns exponential notation if the number of significant
   * digits specified is less than the number of digits necessary to
   * represent the integer part of the value in normal notation.
   */
  return exp == 1 || exp == 2 && (--d < i || i <= TO_EXP_NEG)

  // Exponential notation.
  ? (n['s'] < 0 && c[0] ? '-' : '') + (c.length > 1 ? (c.splice(1, 0, '.'), c.join('')) : c[0]) + (i < 0 ? 'e' : 'e+') + i

  // Normal notation.
  : n['toS']();
}


// Round if necessary.
// Called by divide, format, setMode and sqrt.
function rnd(x, dp, base, isOdd, r) {
  var xc = x['c'],
    isNeg = x['s'] < 0,
    half = base / 2,
    i = x['e'] + dp + 1,

    // 'next' is the digit after the digit that may be rounded up.
    next = xc[i],

    /*
     * 'more' is whether there are digits after 'next'.
     * E.g.
     * 0.005 (e = -3) to be rounded to 0 decimal places (dp = 0) gives i = -2
     * The 'next' digit is zero, and there ARE 'more' digits after it.
     * 0.5 (e = -1) dp = 0 gives i = 0
     * The 'next' digit is 5 and there are no 'more' digits after it.
     */
    more = r || i < 0 || xc[i + 1] != null;

  r = ROUNDING_MODE < 4 ? (next != null || more) &&
    (ROUNDING_MODE == 0 ||
    ROUNDING_MODE == 2 && !isNeg ||
    ROUNDING_MODE == 3 && isNeg) : next > half || next == half &&
    (ROUNDING_MODE == 4 || more ||

    /*
     * isOdd is used in base conversion and refers to the least significant
     * digit of the integer part of the value to be converted. The fraction
     * part is rounded by this method separately from the integer part.
     */
    ROUNDING_MODE == 6 && (xc[i - 1] & 1 || !dp && isOdd) ||
    ROUNDING_MODE == 7 && !isNeg ||
    ROUNDING_MODE == 8 && isNeg);

  if (i < 1 || !xc[0]) {
    xc.length = 0;
    xc.push(0);

    if (r) {

      // 1, 0.1, 0.01, 0.001, 0.0001 etc.
      xc[0] = 1;
      x['e'] = -dp;
    } else {

      // Zero.
      x['e'] = 0;
    }

    return x;
  }

  // Remove any digits after the required decimal places.
  xc.length = i--;

  // Round up?
  if (r) {

    // Rounding up may mean the previous digit has to be rounded up and so on.
    for (--base; ++xc[i] > base;) {
      xc[i] = 0;

      if (!i--) {
        ++x['e'];
        xc.unshift(1);
      }
    }
  }

  // Remove trailing zeros.
  for (i = xc.length; !xc[--i]; xc.pop()) {}

  return x;
}


// Round after setting the appropriate rounding mode.
// Handles ceil, floor and round.
function setMode(x, dp, rm) {
  var r = ROUNDING_MODE;

  ROUNDING_MODE = rm;
  x = new BigNumber(x);
  x['c'] && rnd(x, dp, 10);
  ROUNDING_MODE = r;

  return x;
}


// PROTOTYPE/INSTANCE METHODS


/*
 * Return a new BigNumber whose value is the absolute value of this BigNumber.
 */
P['abs'] = P['absoluteValue'] = function() {
  var x = new BigNumber(this);

  if (x['s'] < 0) {
    x['s'] = 1;
  }

  return x;
};

/*
 * Return the bit length of the number.
 */
P['bitLength'] = function() {
  return this.toString(2).length;
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a whole number in the direction of Infinity.
 */
P['ceil'] = function() {
  return setMode(this, 0, 2);
};


/*
 * Return
 * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
 * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
 * 0 if they have the same value,
 * or null if the value of either is NaN.
 */
P['comparedTo'] = P['cmp'] = function(y, b) {
  var a,
    x = this,
    xc = x['c'],
    yc = (id = -id, y = new BigNumber(y, b))['c'],
    i = x['s'],
    j = y['s'],
    k = x['e'],
    l = y['e'];

  // Either NaN?
  if (!i || !j) {
    return null;
  }

  a = xc && !xc[0], b = yc && !yc[0];

  // Either zero?
  if (a || b) {
    return a ? b ? 0 : -j : i;
  }

  // Signs differ?
  if (i != j) {
    return i;
  }

  // Either Infinity?
  if (a = i < 0, b = k == l, !xc || !yc) {
    return b ? 0 : !xc ^ a ? 1 : -1;
  }

  // Compare exponents.
  if (!b) {
    return k > l ^ a ? 1 : -1;
  }

  // Compare digit by digit.
  for (i = -1,
    j = (k = xc.length) < (l = yc.length) ? k : l;
    ++i < j;) {

    if (xc[i] != yc[i]) {
      return xc[i] > yc[i] ^ a ? 1 : -1;
    }
  }
  // Compare lengths.
  return k == l ? 0 : k > l ^ a ? 1 : -1;
};


/*
 *  n / 0 = I
 *  n / N = N
 *  n / I = 0
 *  0 / n = 0
 *  0 / 0 = N
 *  0 / N = N
 *  0 / I = 0
 *  N / n = N
 *  N / 0 = N
 *  N / N = N
 *  N / I = N
 *  I / n = I
 *  I / 0 = I
 *  I / N = N
 *  I / I = N
 *
 * Return a new BigNumber whose value is the value of this BigNumber
 * divided by the value of BigNumber(y, b), rounded according to
 * DECIMAL_PLACES and ROUNDING_MODE.
 */
P['dividedBy'] = P['div'] = function(y, b) {
  var xc = this['c'],
    xe = this['e'],
    xs = this['s'],
    yc = (id = 2, y = new BigNumber(y, b))['c'],
    ye = y['e'],
    ys = y['s'],
    s = xs == ys ? 1 : -1;

  // Either NaN/Infinity/0?
  return !xe && (!xc || !xc[0]) || !ye && (!yc || !yc[0])

  // Either NaN?
  ? new BigNumber(!xs || !ys ||

    // Both 0 or both Infinity?
    (xc ? yc && xc[0] == yc[0] : !yc)

    // Return NaN.
    ? NaN

    // x is 0 or y is Infinity?
    : xc && xc[0] == 0 || !yc

    // Return +-0.
    ? s * 0

    // y is 0. Return +-Infinity.
    : s / 0)

  : divide(xc, yc, xe - ye, s, 10);
};


/*
 * Return true if the value of this BigNumber is equal to the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['equals'] = P['eq'] = function(n, b) {
  id = 3;
  return this['cmp'](n, b) === 0;
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a whole number in the direction of -Infinity.
 */
P['floor'] = function() {
  return setMode(this, 0, 3);
};


/*
 * Return true if the value of this BigNumber is greater than the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['greaterThan'] = P['gt'] = function(n, b) {
  id = 4;
  return this['cmp'](n, b) > 0;
};


/*
 * Return true if the value of this BigNumber is greater than or equal to
 * the value of BigNumber(n, b), otherwise returns false.
 */
P['greaterThanOrEqualTo'] = P['gte'] = function(n, b) {
  id = 5;
  return (b = this['cmp'](n, b)) == 1 || b === 0;
};


/*
 * Return true if the value of this BigNumber is a finite number, otherwise
 * returns false.
 */
P['isFinite'] = P['isF'] = function() {
  return !!this['c'];
};


/*
 * Return true if the value of this BigNumber is NaN, otherwise returns
 * false.
 */
P['isNaN'] = function() {
  return !this['s'];
};


/*
 * Return true if the value of this BigNumber is negative, otherwise
 * returns false.
 */
P['isNegative'] = P['isNeg'] = function() {
  return this['s'] < 0;
};


/*
 * Return true if the value of this BigNumber is 0 or -0, otherwise returns
 * false.
 */
P['isZero'] = P['isZ'] = function() {
  return !!this['c'] && this['c'][0] == 0;
};


/*
 * Return true if the value of this BigNumber is less than the value of
 * BigNumber(n, b), otherwise returns false.
 */
P['lessThan'] = P['lt'] = function(n, b) {
  id = 6;
  return this['cmp'](n, b) < 0;
};


/*
 * Return true if the value of this BigNumber is less than or equal to the
 * value of BigNumber(n, b), otherwise returns false.
 */
P['lessThanOrEqualTo'] = P['lte'] = P['le'] = function(n, b) {
  id = 7;
  return (b = this['cmp'](n, b)) == -1 || b === 0;
};


/*
 *  n - 0 = n
 *  n - N = N
 *  n - I = -I
 *  0 - n = -n
 *  0 - 0 = 0
 *  0 - N = N
 *  0 - I = -I
 *  N - n = N
 *  N - 0 = N
 *  N - N = N
 *  N - I = N
 *  I - n = I
 *  I - 0 = I
 *  I - N = N
 *  I - I = N
 *
 * Return a new BigNumber whose value is the value of this BigNumber minus
 * the value of BigNumber(y, b).
 */
P['minus'] = P['sub'] = function(y, b) {
  var d, i, j, xLTy,
    x = this,
    a = x['s'];

  b = (id = 8, y = new BigNumber(y, b))['s'];

  // Either NaN?
  if (!a || !b) {
    return new BigNumber(NaN);
  }

  // Signs differ?
  if (a != b) {
    return y['s'] = -b, x['plus'](y);
  }

  var xc = x['c'],
    xe = x['e'],
    yc = y['c'],
    ye = y['e'];

  if (!xe || !ye) {

    // Either Infinity?
    if (!xc || !yc) {
      return xc ? (y['s'] = -b, y) : new BigNumber(yc ? x : NaN);
    }

    // Either zero?
    if (!xc[0] || !yc[0]) {

      // y is non-zero?
      return yc[0] ? (y['s'] = -b, y)

      // x is non-zero?
      : new BigNumber(xc[0] ? x

        // Both are zero.
        // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
        : ROUNDING_MODE == 3 ? -0 : 0);
    }
  }

  // Determine which is the bigger number.
  // Prepend zeros to equalise exponents.
  if (xc = xc.slice(), a = xe - ye) {
    d = (xLTy = a < 0) ? (a = -a, xc) : (ye = xe, yc);

    for (d.reverse(), b = a; b--; d.push(0)) {}
    d.reverse();
  } else {

    // Exponents equal. Check digit by digit.
    j = ((xLTy = xc.length < yc.length) ? xc : yc).length;

    for (a = b = 0; b < j; b++) {

      if (xc[b] != yc[b]) {
        xLTy = xc[b] < yc[b];
        break;
      }
    }
  }

  // x < y? Point xc to the array of the bigger number.
  if (xLTy) {
    d = xc, xc = yc, yc = d;
    y['s'] = -y['s'];
  }

  /*
   * Append zeros to xc if shorter. No need to add zeros to yc if shorter
   * as subtraction only needs to start at yc.length.
   */
  if ((b = -((j = xc.length) - yc.length)) > 0) {

    for (; b--; xc[j++] = 0) {}
  }

  // Subtract yc from xc.
  for (b = yc.length; b > a;) {

    if (xc[--b] < yc[b]) {

      for (i = b; i && !xc[--i]; xc[i] = 9) {}
      --xc[i];
      xc[b] += 10;
    }
    xc[b] -= yc[b];
  }

  // Remove trailing zeros.
  for (; xc[--j] == 0; xc.pop()) {}

  // Remove leading zeros and adjust exponent accordingly.
  for (; xc[0] == 0; xc.shift(), --ye) {}

  /*
   * No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
   * when neither x or y are Infinity.
   */

  // Underflow?
  if (ye < MIN_EXP || !xc[0]) {

    /*
     * Following IEEE 754 (2008) 6.3,
     * n - n = +0  but  n - n = -0 when rounding towards -Infinity.
     */
    if (!xc[0]) {
      y['s'] = ROUNDING_MODE == 3 ? -1 : 1;
    }

    // Result is zero.
    xc = [ye = 0];
  }

  return y['c'] = xc, y['e'] = ye, y;
};


/*
 *   n % 0 =  N
 *   n % N =  N
 *   0 % n =  0
 *  -0 % n = -0
 *   0 % 0 =  N
 *   0 % N =  N
 *   N % n =  N
 *   N % 0 =  N
 *   N % N =  N
 *
 * Return a new BigNumber whose value is the value of this BigNumber modulo
 * the value of BigNumber(y, b).
 */
P['modulo'] = P['mod'] = function(y, b) {
  var x = this,
    xc = x['c'],
    yc = (id = 9, y = new BigNumber(y, b))['c'],
    i = x['s'],
    j = y['s'];

  // Is x or y NaN, or y zero?
  b = !i || !j || yc && !yc[0];

  if (b || xc && !xc[0]) {
    return new BigNumber(b ? NaN : x);
  }

  x['s'] = y['s'] = 1;
  b = y['cmp'](x) == 1;
  x['s'] = i, y['s'] = j;

  return b ? new BigNumber(x) : (i = DECIMAL_PLACES, j = ROUNDING_MODE,
    DECIMAL_PLACES = 0, ROUNDING_MODE = 1,
    x = x['div'](y),
    DECIMAL_PLACES = i, ROUNDING_MODE = j,
    this['minus'](x['times'](y)));
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * negated, i.e. multiplied by -1.
 */
P['negated'] = P['neg'] = function() {
  var x = new BigNumber(this);

  return x['s'] = -x['s'] || null, x;
};


/*
 *  n + 0 = n
 *  n + N = N
 *  n + I = I
 *  0 + n = n
 *  0 + 0 = 0
 *  0 + N = N
 *  0 + I = I
 *  N + n = N
 *  N + 0 = N
 *  N + N = N
 *  N + I = N
 *  I + n = I
 *  I + 0 = I
 *  I + N = N
 *  I + I = I
 *
 * Return a new BigNumber whose value is the value of this BigNumber plus
 * the value of BigNumber(y, b).
 */
P['plus'] = P['add'] = function(y, b) {
  var d,
    x = this,
    a = x['s'];

  b = (id = 10, y = new BigNumber(y, b))['s'];

  // Either NaN?
  if (!a || !b) {
    return new BigNumber(NaN);
  }

  // Signs differ?
  if (a != b) {
    return y['s'] = -b, x['minus'](y);
  }

  var xe = x['e'],
    xc = x['c'],
    ye = y['e'],
    yc = y['c'];

  if (!xe || !ye) {

    // Either Infinity?
    if (!xc || !yc) {

      // Return +-Infinity.
      return new BigNumber(a / 0);
    }

    // Either zero?
    if (!xc[0] || !yc[0]) {

      // y is non-zero?
      return yc[0] ? y

      // x is non-zero?
      : new BigNumber(xc[0] ? x

        // Both are zero. Return zero.
        : a * 0);
    }
  }

  // Prepend zeros to equalise exponents.
  // Note: Faster to use reverse then do unshifts.
  if (xc = xc.slice(), a = xe - ye) {
    d = a > 0 ? (ye = xe, yc) : (a = -a, xc);

    for (d.reverse(); a--; d.push(0)) {}
    d.reverse();
  }

  // Point xc to the longer array.
  if (xc.length - yc.length < 0) {
    d = yc, yc = xc, xc = d;
  }

  /*
   * Only start adding at yc.length - 1 as the
   * further digits of xc can be left as they are.
   */
  for (a = yc.length, b = 0; a; b = (xc[--a] = xc[a] + yc[a] + b) / 10 ^ 0, xc[a] %= 10) {}

  // No need to check for zero, as +x + +y != 0 && -x + -y != 0

  if (b) {
    xc.unshift(b);

    // Overflow? (MAX_EXP + 1 possible)
    if (++ye > MAX_EXP) {

      // Infinity.
      xc = ye = null;
    }
  }

  // Remove trailing zeros.
  for (a = xc.length; xc[--a] == 0; xc.pop()) {}

  return y['c'] = xc, y['e'] = ye, y;
};


/*
 * Return a BigNumber whose value is the value of this BigNumber raised to
 * the power e. If e is negative round according to DECIMAL_PLACES and
 * ROUNDING_MODE.
 *
 * e {number} Integer, -MAX_POWER to MAX_POWER inclusive.
 */
P['toPower'] = P['pow'] = function(e) {

  // e to integer, avoiding NaN or Infinity becoming 0.
  var i = e * 0 == 0 ? e | 0 : e,
    x = new BigNumber(this),
    y = new BigNumber(ONE);

  // Use Math.pow?
  // Pass +-Infinity for out of range exponents.
  if ((((outOfRange = e < -MAX_POWER || e > MAX_POWER) &&
        (i = e * 1 / 0)) ||

      /*
       * Any exponent that fails the parse becomes NaN.
       *
       * Include 'e !== 0' because on Opera -0 == parseFloat(-0) is false,
       * despite -0 === parseFloat(-0) && -0 == parseFloat('-0') is true.
       */
      parse(e) != e && e !== 0 && !(i = NaN)) &&

    // 'pow() exponent not an integer: {e}'
    // 'pow() exponent out of range: {e}'
    !ifExceptionsThrow(e, 'exponent', 'pow') ||

    // Pass zero to Math.pow, as any value to the power zero is 1.
    !i) {

    // i is +-Infinity, NaN or 0.
    return new BigNumber(Math.pow(x['toS'](), i));
  }

  for (i = i < 0 ? -i : i;;) {

    if (i & 1) {
      y = y['times'](x);
    }
    i >>= 1;

    if (!i) {
      break;
    }
    x = x['times'](x);
  }

  return e < 0 ? ONE['div'](y) : y;
};


/*
 * Return a BigNumber whose value is the value of this BigNumber raised to
 * the power m modulo n.
 *
 * m {BigNumber} the value to take the power of
 * n {BigNumber} the value to modulo by
 */
P['powm'] = function(m, n) {
  return this.pow(m).mod(n);
};


/*
 * Return a new BigNumber whose value is the value of this BigNumber
 * rounded to a maximum of dp decimal places using rounding mode rm, or to
 * 0 and ROUNDING_MODE respectively if omitted.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 * [rm] {number} Integer, 0 to 8 inclusive.
 */
P['round'] = function(dp, rm) {

  dp = dp == null || (((outOfRange = dp < 0 || dp > MAX) ||
      parse(dp) != dp) &&

    // 'round() decimal places out of range: {dp}'
    // 'round() decimal places not an integer: {dp}'
    !ifExceptionsThrow(dp, 'decimal places', 'round')) ? 0 : dp | 0;

  rm = rm == null || (((outOfRange = rm < 0 || rm > 8) ||

      // Include '&& rm !== 0' because with Opera -0 == parseFloat(-0) is false.
      parse(rm) != rm && rm !== 0) &&

    // 'round() mode not an integer: {rm}'
    // 'round() mode out of range: {rm}'
    !ifExceptionsThrow(rm, 'mode', 'round')) ? ROUNDING_MODE : rm | 0;

  return setMode(this, dp, rm);
};


/*
 *  sqrt(-n) =  N
 *  sqrt( N) =  N
 *  sqrt(-I) =  N
 *  sqrt( I) =  I
 *  sqrt( 0) =  0
 *  sqrt(-0) = -0
 *
 * Return a new BigNumber whose value is the square root of the value of
 * this BigNumber, rounded according to DECIMAL_PLACES and ROUNDING_MODE.
 */
P['squareRoot'] = P['sqrt'] = function() {
  var n, r, re, t,
    x = this,
    c = x['c'],
    s = x['s'],
    e = x['e'],
    dp = DECIMAL_PLACES,
    rm = ROUNDING_MODE,
    half = new BigNumber('0.5');

  // Negative/NaN/Infinity/zero?
  if (s !== 1 || !c || !c[0]) {

    return new BigNumber(!s || s < 0 && (!c || c[0]) ? NaN : c ? x : 1 / 0);
  }

  // Initial estimate.
  s = Math.sqrt(x['toS']());
  ROUNDING_MODE = 1;

  /*
      Math.sqrt underflow/overflow?
      Pass x to Math.sqrt as integer, then adjust the exponent of the result.
     */
  if (s == 0 || s == 1 / 0) {
    n = c.join('');

    if (!(n.length + e & 1)) {
      n += '0';
    }
    r = new BigNumber(Math.sqrt(n) + '');

    // r may still not be finite.
    if (!r['c']) {
      r['c'] = [1];
    }
    r['e'] = (((e + 1) / 2) | 0) - (e < 0 || e & 1);
  } else {
    r = new BigNumber(n = s.toString());
  }
  re = r['e'];
  s = re + (DECIMAL_PLACES += 4);

  if (s < 3) {
    s = 0;
  }
  e = s;

  // Newton-Raphson iteration.
  for (;;) {
    t = r;
    r = half['times'](t['plus'](x['div'](t)));

    if (t['c'].slice(0, s).join('') === r['c'].slice(0, s).join('')) {
      c = r['c'];

      /*
              The exponent of r may here be one less than the final result
              exponent (re), e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust
              s so the rounding digits are indexed correctly.
             */
      s = s - (n && r['e'] < re);

      /*
              The 4th rounding digit may be in error by -1 so if the 4 rounding
              digits are 9999 or 4999 (i.e. approaching a rounding boundary)
              continue the iteration.
             */
      if (c[s] == 9 && c[s - 1] == 9 && c[s - 2] == 9 &&
        (c[s - 3] == 9 || n && c[s - 3] == 4)) {

        /*
                  If 9999 on first run through, check to see if rounding up
                  gives the exact result as the nines may infinitely repeat.
                 */
        if (n && c[s - 3] == 9) {
          t = r['round'](dp, 0);

          if (t['times'](t)['eq'](x)) {
            ROUNDING_MODE = rm;
            DECIMAL_PLACES = dp;

            return t;
          }
        }
        DECIMAL_PLACES += 4;
        s += 4;
        n = '';
      } else {

        /*
                  If the rounding digits are null, 0000 or 5000, check for an
                  exact result. If not, then there are further digits so
                  increment the 1st rounding digit to ensure correct rounding.
                 */
        if (!c[e] && !c[e - 1] && !c[e - 2] &&
          (!c[e - 3] || c[e - 3] == 5)) {

          // Truncate to the first rounding digit.
          if (c.length > e - 2) {
            c.length = e - 2;
          }

          if (!r['times'](r)['eq'](x)) {

            while (c.length < e - 3) {
              c.push(0);
            }
            c[e - 3]++;
          }
        }
        ROUNDING_MODE = rm;
        rnd(r, DECIMAL_PLACES = dp, 10);

        return r;
      }
    }
  }
};


/*
 *  n * 0 = 0
 *  n * N = N
 *  n * I = I
 *  0 * n = 0
 *  0 * 0 = 0
 *  0 * N = N
 *  0 * I = N
 *  N * n = N
 *  N * 0 = N
 *  N * N = N
 *  N * I = N
 *  I * n = I
 *  I * 0 = N
 *  I * N = N
 *  I * I = I
 *
 * Return a new BigNumber whose value is the value of this BigNumber times
 * the value of BigNumber(y, b).
 */
P['times'] = P['mul'] = function(y, b) {
  var c,
    x = this,
    xc = x['c'],
    yc = (id = 11, y = new BigNumber(y, b))['c'],
    i = x['e'],
    j = y['e'],
    a = x['s'];

  y['s'] = a == (b = y['s']) ? 1 : -1;

  // Either NaN/Infinity/0?
  if (!i && (!xc || !xc[0]) || !j && (!yc || !yc[0])) {

    // Either NaN?
    return new BigNumber(!a || !b ||

      // x is 0 and y is Infinity  or  y is 0 and x is Infinity?
      xc && !xc[0] && !yc || yc && !yc[0] && !xc

      // Return NaN.
      ? NaN

      // Either Infinity?
      : !xc || !yc

      // Return +-Infinity.
      ? y['s'] / 0

      // x or y is 0. Return +-0.
      : y['s'] * 0);
  }
  y['e'] = i + j;

  if ((a = xc.length) < (b = yc.length)) {
    c = xc, xc = yc, yc = c, j = a, a = b, b = j;
  }

  for (j = a + b, c = []; j--; c.push(0)) {}

  // Multiply!
  for (i = b - 1; i > -1; i--) {

    for (b = 0, j = a + i; j > i; b = c[j] + yc[i] * xc[j - i - 1] + b,
      c[j--] = b % 10 | 0,
      b = b / 10 | 0) {}

    if (b) {
      c[j] = (c[j] + b) % 10;
    }
  }

  b && ++y['e'];

  // Remove any leading zero.
  !c[0] && c.shift();

  // Remove trailing zeros.
  for (j = c.length; !c[--j]; c.pop()) {}

  // No zero check needed as only x * 0 == 0 etc.

  // Overflow?
  y['c'] = y['e'] > MAX_EXP

  // Infinity.
  ? (y['e'] = null)

  // Underflow?
  : y['e'] < MIN_EXP

  // Zero.
  ? [y['e'] = 0]

  // Neither.
  : c;

  return y;
};

/*
 * Return a buffer containing the
 */
P['toBuffer'] = function(opts) {

  if (typeof opts === 'string') {
    if (opts !== 'mpint') return 'Unsupported Buffer representation';

    var abs = this.abs();
    var buf = abs.toBuffer({
      size: 1,
      endian: 'big'
    });
    var len = buf.length === 1 && buf[0] === 0 ? 0 : buf.length;
    if (buf[0] & 0x80) len++;

    var ret = new Buffer(4 + len);
    if (len > 0) buf.copy(ret, 4 + (buf[0] & 0x80 ? 1 : 0));
    if (buf[0] & 0x80) ret[4] = 0;

    ret[0] = len & (0xff << 24);
    ret[1] = len & (0xff << 16);
    ret[2] = len & (0xff << 8);
    ret[3] = len & (0xff << 0);

    // two's compliment for negative integers:
    var isNeg = this.lt(0);
    if (isNeg) {
      for (var i = 4; i < ret.length; i++) {
        ret[i] = 0xff - ret[i];
      }
    }
    ret[4] = (ret[4] & 0x7f) | (isNeg ? 0x80 : 0);
    if (isNeg) ret[ret.length - 1]++;

    return ret;
  }

  if (!opts) opts = {};

  var endian = {
    1: 'big',
    '-1': 'little'
  }[opts.endian] || opts.endian || 'big';

  var hex = this.toString(16);
  if (hex.charAt(0) === '-') throw new Error(
    'converting negative numbers to Buffers not supported yet'
  );

  var size = opts.size === 'auto' ? Math.ceil(hex.length / 2) : (opts.size || 1);

  var len = Math.ceil(hex.length / (2 * size)) * size;
  var buf = new Buffer(len);

  // zero-pad the hex string so the chunks are all `size` long
  while (hex.length < 2 * len) hex = '0' + hex;

  var hx = hex
    .split(new RegExp('(.{' + (2 * size) + '})'))
    .filter(function(s) {
      return s.length > 0
    });

  hx.forEach(function(chunk, i) {
    for (var j = 0; j < size; j++) {
      var ix = i * size + (endian === 'big' ? j : size - j - 1);
      buf[ix] = parseInt(chunk.slice(j * 2, j * 2 + 2), 16);
    }
  });

  return buf;
};

/*
 * Return a string representing the value of this BigNumber in exponential
 * notation to dp fixed decimal places and rounded using ROUNDING_MODE if
 * necessary.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 */
P['toExponential'] = P['toE'] = function(dp) {

  return format(this, (dp == null || ((outOfRange = dp < 0 || dp > MAX) ||

      /*
       * Include '&& dp !== 0' because with Opera -0 == parseFloat(-0) is
       * false, despite -0 == parseFloat('-0') && 0 == -0 being true.
       */
      parse(dp) != dp && dp !== 0) &&

    // 'toE() decimal places not an integer: {dp}'
    // 'toE() decimal places out of range: {dp}'
    !ifExceptionsThrow(dp, 'decimal places', 'toE')) && this['c'] ? this['c'].length - 1 : dp | 0, 1);
};


/*
 * Return a string representing the value of this BigNumber in normal
 * notation to dp fixed decimal places and rounded using ROUNDING_MODE if
 * necessary.
 *
 * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
 * but e.g. (-0.00001).toFixed(0) is '-0'.
 *
 * [dp] {number} Integer, 0 to MAX inclusive.
 */
P['toFixed'] = P['toF'] = function(dp) {
  var n, str, d,
    x = this;

  if (!(dp == null || ((outOfRange = dp < 0 || dp > MAX) ||
      parse(dp) != dp && dp !== 0) &&

    // 'toF() decimal places not an integer: {dp}'
    // 'toF() decimal places out of range: {dp}'
    !ifExceptionsThrow(dp, 'decimal places', 'toF'))) {
    d = x['e'] + (dp | 0);
  }

  n = TO_EXP_NEG, dp = TO_EXP_POS;
  TO_EXP_NEG = -(TO_EXP_POS = 1 / 0);

  // Note: str is initially undefined.
  if (d == str) {
    str = x['toS']();
  } else {
    str = format(x, d);

    // (-0).toFixed() is '0', but (-0.1).toFixed() is '-0'.
    // (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'.
    if (x['s'] < 0 && x['c']) {

      // As e.g. -0 toFixed(3), will wrongly be returned as -0.000 from toString.
      if (!x['c'][0]) {
        str = str.replace(/^-/, '');

        // As e.g. -0.5 if rounded to -0 will cause toString to omit the minus sign.
      } else if (str.indexOf('-') < 0) {
        str = '-' + str;
      }
    }
  }
  TO_EXP_NEG = n, TO_EXP_POS = dp;

  return str;
};


/*
 * Return a string array representing the value of this BigNumber as a
 * simple fraction with an integer numerator and an integer denominator.
 * The denominator will be a positive non-zero value less than or equal to
 * the specified maximum denominator. If a maximum denominator is not
 * specified, the denominator will be the lowest value necessary to
 * represent the number exactly.
 *
 * [maxD] {number|string|BigNumber} Integer >= 1 and < Infinity.
 */
P['toFraction'] = P['toFr'] = function(maxD) {
  var q, frac, n0, d0, d2, n, e,
    n1 = d0 = new BigNumber(ONE),
    d1 = n0 = new BigNumber('0'),
    x = this,
    xc = x['c'],
    exp = MAX_EXP,
    dp = DECIMAL_PLACES,
    rm = ROUNDING_MODE,
    d = new BigNumber(ONE);

  // NaN, Infinity.
  if (!xc) {
    return x['toS']();
  }

  e = d['e'] = xc.length - x['e'] - 1;

  // If max denominator is undefined or null...
  if (maxD == null ||

    // or NaN...
    (!(id = 12, n = new BigNumber(maxD))['s'] ||

      // or less than 1, or Infinity...
      (outOfRange = n['cmp'](n1) < 0 || !n['c']) ||

      // or not an integer...
      (ERRORS && n['e'] < n['c'].length - 1)) &&

    // 'toFr() max denominator not an integer: {maxD}'
    // 'toFr() max denominator out of range: {maxD}'
    !ifExceptionsThrow(maxD, 'max denominator', 'toFr') ||

    // or greater than the maxD needed to specify the value exactly...
    (maxD = n)['cmp'](d) > 0) {

    // d is e.g. 10, 100, 1000, 10000... , n1 is 1.
    maxD = e > 0 ? d : n1;
  }

  MAX_EXP = 1 / 0;
  n = new BigNumber(xc.join(''));

  for (DECIMAL_PLACES = 0, ROUNDING_MODE = 1;;) {
    q = n['div'](d);
    d2 = d0['plus'](q['times'](d1));

    if (d2['cmp'](maxD) == 1) {
      break;
    }

    d0 = d1, d1 = d2;

    n1 = n0['plus'](q['times'](d2 = n1));
    n0 = d2;

    d = n['minus'](q['times'](d2 = d));
    n = d2;
  }

  d2 = maxD['minus'](d0)['div'](d1);
  n0 = n0['plus'](d2['times'](n1));
  d0 = d0['plus'](d2['times'](d1));

  n0['s'] = n1['s'] = x['s'];

  DECIMAL_PLACES = e * 2;
  ROUNDING_MODE = rm;

  // Determine which fraction is closer to x, n0 / d0 or n1 / d1?
  frac = n1['div'](d1)['minus'](x)['abs']()['cmp'](
    n0['div'](d0)['minus'](x)['abs']()) < 1 ? [n1['toS'](), d1['toS']()] : [n0['toS'](), d0['toS']()];

  return MAX_EXP = exp, DECIMAL_PLACES = dp, frac;
};


/*
 * Return a string representing the value of this BigNumber to sd significant
 * digits and rounded using ROUNDING_MODE if necessary.
 * If sd is less than the number of digits necessary to represent the integer
 * part of the value in normal notation, then use exponential notation.
 *
 * sd {number} Integer, 1 to MAX inclusive.
 */
P['toPrecision'] = P['toP'] = function(sd) {

  /*
   * ERRORS true: Throw if sd not undefined, null or an integer in range.
   * ERRORS false: Ignore sd if not a number or not in range.
   * Truncate non-integers.
   */
  return sd == null || (((outOfRange = sd < 1 || sd > MAX) ||
      parse(sd) != sd) &&

    // 'toP() precision not an integer: {sd}'
    // 'toP() precision out of range: {sd}'
    !ifExceptionsThrow(sd, 'precision', 'toP')) ? this['toS']() : format(this, --sd | 0, 2);
};


/*
 * Return a string representing the value of this BigNumber in base b, or
 * base 10 if b is omitted. If a base is specified, including base 10,
 * round according to DECIMAL_PLACES and ROUNDING_MODE.
 * If a base is not specified, and this BigNumber has a positive exponent
 * that is equal to or greater than TO_EXP_POS, or a negative exponent equal
 * to or less than TO_EXP_NEG, return exponential notation.
 *
 * [b] {number} Integer, 2 to 64 inclusive.
 */
P['toString'] = P['toS'] = function(b) {
  var u, str, strL,
    x = this,
    xe = x['e'];

  // Infinity or NaN?
  if (xe === null) {
    str = x['s'] ? 'Infinity' : 'NaN';

    // Exponential format?
  } else if (b === u && (xe <= TO_EXP_NEG || xe >= TO_EXP_POS)) {
    return format(x, x['c'].length - 1, 1);
  } else {
    str = x['c'].join('');

    // Negative exponent?
    if (xe < 0) {

      // Prepend zeros.
      for (; ++xe; str = '0' + str) {}
      str = '0.' + str;

      // Positive exponent?
    } else if (strL = str.length, xe > 0) {

      if (++xe > strL) {

        // Append zeros.
        for (xe -= strL; xe--; str += '0') {}
      } else if (xe < strL) {
        str = str.slice(0, xe) + '.' + str.slice(xe);
      }

      // Exponent zero.
    } else {
      if (u = str.charAt(0), strL > 1) {
        str = u + '.' + str.slice(1);

        // Avoid '-0'
      } else if (u == '0') {
        return u;
      }
    }

    if (b != null) {

      if (!(outOfRange = !(b >= 2 && b < 65)) &&
        (b == (b | 0) || !ERRORS)) {
        str = convert(str, b | 0, 10, x['s']);

        // Avoid '-0'
        if (str == '0') {
          return str;
        }
      } else {

        // 'toS() base not an integer: {b}'
        // 'toS() base out of range: {b}'
        ifExceptionsThrow(b, 'base', 'toS');
      }
    }

  }

  return x['s'] < 0 ? '-' + str : str;
};

P['toNumber'] = function() {
  return parseInt(this['toString'](), 10);
};


/*
 * Return as toString, but do not accept a base argument.
 */
P['valueOf'] = function() {
  return this['toS']();
};


// Add aliases for BigDecimal methods.
//P['add'] = P['plus'];
//P['subtract'] = P['minus'];
//P['multiply'] = P['times'];
//P['divide'] = P['div'];
//P['remainder'] = P['mod'];
//P['compareTo'] = P['cmp'];
//P['negate'] = P['neg'];


// EXPORT
BigNumber.config({
  EXPONENTIAL_AT: 9999999,
  DECIMAL_PLACES: 0,
  ROUNDING_MODE: 1
});
module.exports = BigNumber;