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							924 lines
						
					
					
						
							20 KiB
						
					
					
				
			
		
		
	
	
							924 lines
						
					
					
						
							20 KiB
						
					
					
				/* | 
						|
 *  big.js v5.2.2 | 
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 *  A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic. | 
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 *  Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com> | 
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 *  https://github.com/MikeMcl/big.js/LICENCE | 
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 */ | 
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 | 
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 | 
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/************************************** EDITABLE DEFAULTS *****************************************/ | 
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 | 
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 | 
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  // The default values below must be integers within the stated ranges. | 
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 | 
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  /* | 
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   * The maximum number of decimal places (DP) of the results of operations involving division: | 
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   * div and sqrt, and pow with negative exponents. | 
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   */ | 
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var DP = 20,          // 0 to MAX_DP | 
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 | 
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  /* | 
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   * The rounding mode (RM) used when rounding to the above decimal places. | 
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   * | 
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   *  0  Towards zero (i.e. truncate, no rounding).       (ROUND_DOWN) | 
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   *  1  To nearest neighbour. If equidistant, round up.  (ROUND_HALF_UP) | 
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   *  2  To nearest neighbour. If equidistant, to even.   (ROUND_HALF_EVEN) | 
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   *  3  Away from zero.                                  (ROUND_UP) | 
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   */ | 
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  RM = 1,             // 0, 1, 2 or 3 | 
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 | 
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  // The maximum value of DP and Big.DP. | 
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  MAX_DP = 1E6,       // 0 to 1000000 | 
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 | 
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  // The maximum magnitude of the exponent argument to the pow method. | 
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  MAX_POWER = 1E6,    // 1 to 1000000 | 
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 | 
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  /* | 
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   * The negative exponent (NE) at and beneath which toString returns exponential notation. | 
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   * (JavaScript numbers: -7) | 
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   * -1000000 is the minimum recommended exponent value of a Big. | 
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   */ | 
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  NE = -7,            // 0 to -1000000 | 
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 | 
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  /* | 
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   * The positive exponent (PE) at and above which toString returns exponential notation. | 
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   * (JavaScript numbers: 21) | 
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   * 1000000 is the maximum recommended exponent value of a Big. | 
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   * (This limit is not enforced or checked.) | 
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   */ | 
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  PE = 21,            // 0 to 1000000 | 
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 | 
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 | 
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/**************************************************************************************************/ | 
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 | 
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 | 
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  // Error messages. | 
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  NAME = '[big.js] ', | 
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  INVALID = NAME + 'Invalid ', | 
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  INVALID_DP = INVALID + 'decimal places', | 
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  INVALID_RM = INVALID + 'rounding mode', | 
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  DIV_BY_ZERO = NAME + 'Division by zero', | 
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 | 
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  // The shared prototype object. | 
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  P = {}, | 
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  UNDEFINED = void 0, | 
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  NUMERIC = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i; | 
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 | 
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 | 
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/* | 
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 * Create and return a Big constructor. | 
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 * | 
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 */ | 
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function _Big_() { | 
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 | 
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  /* | 
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   * The Big constructor and exported function. | 
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   * Create and return a new instance of a Big number object. | 
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   * | 
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   * n {number|string|Big} A numeric value. | 
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   */ | 
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  function Big(n) { | 
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    var x = this; | 
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 | 
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    // Enable constructor usage without new. | 
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    if (!(x instanceof Big)) return n === UNDEFINED ? _Big_() : new Big(n); | 
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 | 
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    // Duplicate. | 
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    if (n instanceof Big) { | 
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      x.s = n.s; | 
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      x.e = n.e; | 
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      x.c = n.c.slice(); | 
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    } else { | 
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      parse(x, n); | 
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    } | 
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 | 
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    /* | 
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     * Retain a reference to this Big constructor, and shadow Big.prototype.constructor which | 
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     * points to Object. | 
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     */ | 
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    x.constructor = Big; | 
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  } | 
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 | 
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  Big.prototype = P; | 
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  Big.DP = DP; | 
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  Big.RM = RM; | 
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  Big.NE = NE; | 
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  Big.PE = PE; | 
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  Big.version = '5.2.2'; | 
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 | 
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  return Big; | 
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} | 
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 | 
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 | 
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/* | 
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 * Parse the number or string value passed to a Big constructor. | 
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 * | 
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 * x {Big} A Big number instance. | 
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 * n {number|string} A numeric value. | 
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 */ | 
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function parse(x, n) { | 
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  var e, i, nl; | 
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 | 
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  // Minus zero? | 
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  if (n === 0 && 1 / n < 0) n = '-0'; | 
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  else if (!NUMERIC.test(n += '')) throw Error(INVALID + 'number'); | 
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 | 
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  // Determine sign. | 
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  x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1; | 
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 | 
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  // Decimal point? | 
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  if ((e = n.indexOf('.')) > -1) n = n.replace('.', ''); | 
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 | 
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  // Exponential form? | 
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  if ((i = n.search(/e/i)) > 0) { | 
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 | 
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    // Determine exponent. | 
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    if (e < 0) e = i; | 
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    e += +n.slice(i + 1); | 
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    n = n.substring(0, i); | 
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  } else if (e < 0) { | 
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 | 
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    // Integer. | 
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    e = n.length; | 
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  } | 
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 | 
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  nl = n.length; | 
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 | 
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  // Determine leading zeros. | 
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  for (i = 0; i < nl && n.charAt(i) == '0';) ++i; | 
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 | 
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  if (i == nl) { | 
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 | 
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    // Zero. | 
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    x.c = [x.e = 0]; | 
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  } else { | 
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 | 
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    // Determine trailing zeros. | 
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    for (; nl > 0 && n.charAt(--nl) == '0';); | 
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    x.e = e - i - 1; | 
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    x.c = []; | 
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 | 
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    // Convert string to array of digits without leading/trailing zeros. | 
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    for (e = 0; i <= nl;) x.c[e++] = +n.charAt(i++); | 
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  } | 
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 | 
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  return x; | 
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} | 
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 | 
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 | 
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/* | 
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 * Round Big x to a maximum of dp decimal places using rounding mode rm. | 
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 * Called by stringify, P.div, P.round and P.sqrt. | 
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 * | 
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 * x {Big} The Big to round. | 
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 * dp {number} Integer, 0 to MAX_DP inclusive. | 
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 * rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP) | 
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 * [more] {boolean} Whether the result of division was truncated. | 
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 */ | 
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function round(x, dp, rm, more) { | 
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  var xc = x.c, | 
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    i = x.e + dp + 1; | 
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 | 
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  if (i < xc.length) { | 
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    if (rm === 1) { | 
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 | 
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      // xc[i] is the digit after the digit that may be rounded up. | 
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      more = xc[i] >= 5; | 
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    } else if (rm === 2) { | 
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      more = xc[i] > 5 || xc[i] == 5 && | 
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        (more || i < 0 || xc[i + 1] !== UNDEFINED || xc[i - 1] & 1); | 
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    } else if (rm === 3) { | 
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      more = more || !!xc[0]; | 
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    } else { | 
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      more = false; | 
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      if (rm !== 0) throw Error(INVALID_RM); | 
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    } | 
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 | 
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    if (i < 1) { | 
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      xc.length = 1; | 
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 | 
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      if (more) { | 
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 | 
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        // 1, 0.1, 0.01, 0.001, 0.0001 etc. | 
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        x.e = -dp; | 
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        xc[0] = 1; | 
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      } else { | 
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 | 
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        // Zero. | 
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        xc[0] = x.e = 0; | 
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      } | 
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    } else { | 
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 | 
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      // Remove any digits after the required decimal places. | 
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      xc.length = i--; | 
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 | 
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      // Round up? | 
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      if (more) { | 
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 | 
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        // Rounding up may mean the previous digit has to be rounded up. | 
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        for (; ++xc[i] > 9;) { | 
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          xc[i] = 0; | 
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          if (!i--) { | 
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            ++x.e; | 
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            xc.unshift(1); | 
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          } | 
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        } | 
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      } | 
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 | 
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      // Remove trailing zeros. | 
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      for (i = xc.length; !xc[--i];) xc.pop(); | 
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    } | 
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  } else if (rm < 0 || rm > 3 || rm !== ~~rm) { | 
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    throw Error(INVALID_RM); | 
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  } | 
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 | 
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  return x; | 
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} | 
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 | 
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 | 
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/* | 
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 * Return a string representing the value of Big x in normal or exponential notation. | 
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 * Handles P.toExponential, P.toFixed, P.toJSON, P.toPrecision, P.toString and P.valueOf. | 
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 * | 
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 * x {Big} | 
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 * id? {number} Caller id. | 
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 *         1 toExponential | 
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 *         2 toFixed | 
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 *         3 toPrecision | 
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 *         4 valueOf | 
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 * n? {number|undefined} Caller's argument. | 
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 * k? {number|undefined} | 
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 */ | 
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function stringify(x, id, n, k) { | 
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  var e, s, | 
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    Big = x.constructor, | 
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    z = !x.c[0]; | 
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 | 
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  if (n !== UNDEFINED) { | 
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    if (n !== ~~n || n < (id == 3) || n > MAX_DP) { | 
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      throw Error(id == 3 ? INVALID + 'precision' : INVALID_DP); | 
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    } | 
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 | 
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    x = new Big(x); | 
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 | 
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    // The index of the digit that may be rounded up. | 
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    n = k - x.e; | 
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 | 
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    // Round? | 
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    if (x.c.length > ++k) round(x, n, Big.RM); | 
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 | 
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    // toFixed: recalculate k as x.e may have changed if value rounded up. | 
						|
    if (id == 2) k = x.e + n + 1; | 
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 | 
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    // Append zeros? | 
						|
    for (; x.c.length < k;) x.c.push(0); | 
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  } | 
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 | 
						|
  e = x.e; | 
						|
  s = x.c.join(''); | 
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  n = s.length; | 
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 | 
						|
  // Exponential notation? | 
						|
  if (id != 2 && (id == 1 || id == 3 && k <= e || e <= Big.NE || e >= Big.PE)) { | 
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    s = s.charAt(0) + (n > 1 ? '.' + s.slice(1) : '') + (e < 0 ? 'e' : 'e+') + e; | 
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 | 
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  // Normal notation. | 
						|
  } else if (e < 0) { | 
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    for (; ++e;) s = '0' + s; | 
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    s = '0.' + s; | 
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  } else if (e > 0) { | 
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    if (++e > n) for (e -= n; e--;) s += '0'; | 
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    else if (e < n) s = s.slice(0, e) + '.' + s.slice(e); | 
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  } else if (n > 1) { | 
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    s = s.charAt(0) + '.' + s.slice(1); | 
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  } | 
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 | 
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  return x.s < 0 && (!z || id == 4) ? '-' + s : s; | 
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} | 
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 | 
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 | 
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// Prototype/instance methods | 
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 | 
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 | 
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/* | 
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 * Return a new Big whose value is the absolute value of this Big. | 
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 */ | 
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P.abs = function () { | 
						|
  var x = new this.constructor(this); | 
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  x.s = 1; | 
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  return x; | 
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}; | 
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 | 
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 | 
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/* | 
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 * Return 1 if the value of this Big is greater than the value of Big y, | 
						|
 *       -1 if the value of this Big is less than the value of Big y, or | 
						|
 *        0 if they have the same value. | 
						|
*/ | 
						|
P.cmp = function (y) { | 
						|
  var isneg, | 
						|
    x = this, | 
						|
    xc = x.c, | 
						|
    yc = (y = new x.constructor(y)).c, | 
						|
    i = x.s, | 
						|
    j = y.s, | 
						|
    k = x.e, | 
						|
    l = y.e; | 
						|
 | 
						|
  // Either zero? | 
						|
  if (!xc[0] || !yc[0]) return !xc[0] ? !yc[0] ? 0 : -j : i; | 
						|
 | 
						|
  // Signs differ? | 
						|
  if (i != j) return i; | 
						|
 | 
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  isneg = i < 0; | 
						|
 | 
						|
  // Compare exponents. | 
						|
  if (k != l) return k > l ^ isneg ? 1 : -1; | 
						|
 | 
						|
  j = (k = xc.length) < (l = yc.length) ? k : l; | 
						|
 | 
						|
  // Compare digit by digit. | 
						|
  for (i = -1; ++i < j;) { | 
						|
    if (xc[i] != yc[i]) return xc[i] > yc[i] ^ isneg ? 1 : -1; | 
						|
  } | 
						|
 | 
						|
  // Compare lengths. | 
						|
  return k == l ? 0 : k > l ^ isneg ? 1 : -1; | 
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}; | 
						|
 | 
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 | 
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/* | 
						|
 * Return a new Big whose value is the value of this Big divided by the value of Big y, rounded, | 
						|
 * if necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM. | 
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 */ | 
						|
P.div = function (y) { | 
						|
  var x = this, | 
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    Big = x.constructor, | 
						|
    a = x.c,                  // dividend | 
						|
    b = (y = new Big(y)).c,   // divisor | 
						|
    k = x.s == y.s ? 1 : -1, | 
						|
    dp = Big.DP; | 
						|
 | 
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  if (dp !== ~~dp || dp < 0 || dp > MAX_DP) throw Error(INVALID_DP); | 
						|
 | 
						|
  // Divisor is zero? | 
						|
  if (!b[0]) throw Error(DIV_BY_ZERO); | 
						|
 | 
						|
  // Dividend is 0? Return +-0. | 
						|
  if (!a[0]) return new Big(k * 0); | 
						|
 | 
						|
  var bl, bt, n, cmp, ri, | 
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    bz = b.slice(), | 
						|
    ai = bl = b.length, | 
						|
    al = a.length, | 
						|
    r = a.slice(0, bl),   // remainder | 
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    rl = r.length, | 
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    q = y,                // quotient | 
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    qc = q.c = [], | 
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    qi = 0, | 
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    d = dp + (q.e = x.e - y.e) + 1;    // number of digits of the result | 
						|
 | 
						|
  q.s = k; | 
						|
  k = d < 0 ? 0 : d; | 
						|
 | 
						|
  // Create version of divisor with leading zero. | 
						|
  bz.unshift(0); | 
						|
 | 
						|
  // Add zeros to make remainder as long as divisor. | 
						|
  for (; rl++ < bl;) r.push(0); | 
						|
 | 
						|
  do { | 
						|
 | 
						|
    // n is how many times the divisor goes into current remainder. | 
						|
    for (n = 0; n < 10; n++) { | 
						|
 | 
						|
      // Compare divisor and remainder. | 
						|
      if (bl != (rl = r.length)) { | 
						|
        cmp = bl > rl ? 1 : -1; | 
						|
      } else { | 
						|
        for (ri = -1, cmp = 0; ++ri < bl;) { | 
						|
          if (b[ri] != r[ri]) { | 
						|
            cmp = b[ri] > r[ri] ? 1 : -1; | 
						|
            break; | 
						|
          } | 
						|
        } | 
						|
      } | 
						|
 | 
						|
      // If divisor < remainder, subtract divisor from remainder. | 
						|
      if (cmp < 0) { | 
						|
 | 
						|
        // Remainder can't be more than 1 digit longer than divisor. | 
						|
        // Equalise lengths using divisor with extra leading zero? | 
						|
        for (bt = rl == bl ? b : bz; rl;) { | 
						|
          if (r[--rl] < bt[rl]) { | 
						|
            ri = rl; | 
						|
            for (; ri && !r[--ri];) r[ri] = 9; | 
						|
            --r[ri]; | 
						|
            r[rl] += 10; | 
						|
          } | 
						|
          r[rl] -= bt[rl]; | 
						|
        } | 
						|
 | 
						|
        for (; !r[0];) r.shift(); | 
						|
      } else { | 
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        break; | 
						|
      } | 
						|
    } | 
						|
 | 
						|
    // Add the digit n to the result array. | 
						|
    qc[qi++] = cmp ? n : ++n; | 
						|
 | 
						|
    // Update the remainder. | 
						|
    if (r[0] && cmp) r[rl] = a[ai] || 0; | 
						|
    else r = [a[ai]]; | 
						|
 | 
						|
  } while ((ai++ < al || r[0] !== UNDEFINED) && k--); | 
						|
 | 
						|
  // 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. | 
						|
    qc.shift(); | 
						|
    q.e--; | 
						|
  } | 
						|
 | 
						|
  // Round? | 
						|
  if (qi > d) round(q, dp, Big.RM, r[0] !== UNDEFINED); | 
						|
 | 
						|
  return q; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return true if the value of this Big is equal to the value of Big y, otherwise return false. | 
						|
 */ | 
						|
P.eq = function (y) { | 
						|
  return !this.cmp(y); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return true if the value of this Big is greater than the value of Big y, otherwise return | 
						|
 * false. | 
						|
 */ | 
						|
P.gt = function (y) { | 
						|
  return this.cmp(y) > 0; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return true if the value of this Big is greater than or equal to the value of Big y, otherwise | 
						|
 * return false. | 
						|
 */ | 
						|
P.gte = function (y) { | 
						|
  return this.cmp(y) > -1; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return true if the value of this Big is less than the value of Big y, otherwise return false. | 
						|
 */ | 
						|
P.lt = function (y) { | 
						|
  return this.cmp(y) < 0; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return true if the value of this Big is less than or equal to the value of Big y, otherwise | 
						|
 * return false. | 
						|
 */ | 
						|
P.lte = function (y) { | 
						|
  return this.cmp(y) < 1; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the value of this Big minus the value of Big y. | 
						|
 */ | 
						|
P.minus = P.sub = function (y) { | 
						|
  var i, j, t, xlty, | 
						|
    x = this, | 
						|
    Big = x.constructor, | 
						|
    a = x.s, | 
						|
    b = (y = new Big(y)).s; | 
						|
 | 
						|
  // Signs differ? | 
						|
  if (a != b) { | 
						|
    y.s = -b; | 
						|
    return x.plus(y); | 
						|
  } | 
						|
 | 
						|
  var xc = x.c.slice(), | 
						|
    xe = x.e, | 
						|
    yc = y.c, | 
						|
    ye = y.e; | 
						|
 | 
						|
  // Either zero? | 
						|
  if (!xc[0] || !yc[0]) { | 
						|
 | 
						|
    // y is non-zero? x is non-zero? Or both are zero. | 
						|
    return yc[0] ? (y.s = -b, y) : new Big(xc[0] ? x : 0); | 
						|
  } | 
						|
 | 
						|
  // Determine which is the bigger number. Prepend zeros to equalise exponents. | 
						|
  if (a = xe - ye) { | 
						|
 | 
						|
    if (xlty = a < 0) { | 
						|
      a = -a; | 
						|
      t = xc; | 
						|
    } else { | 
						|
      ye = xe; | 
						|
      t = yc; | 
						|
    } | 
						|
 | 
						|
    t.reverse(); | 
						|
    for (b = a; b--;) t.push(0); | 
						|
    t.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) { | 
						|
    t = xc; | 
						|
    xc = yc; | 
						|
    yc = t; | 
						|
    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 = yc.length) - (i = xc.length)) > 0) for (; b--;) xc[i++] = 0; | 
						|
 | 
						|
  // Subtract yc from xc. | 
						|
  for (b = i; j > a;) { | 
						|
    if (xc[--j] < yc[j]) { | 
						|
      for (i = j; i && !xc[--i];) xc[i] = 9; | 
						|
      --xc[i]; | 
						|
      xc[j] += 10; | 
						|
    } | 
						|
 | 
						|
    xc[j] -= yc[j]; | 
						|
  } | 
						|
 | 
						|
  // Remove trailing zeros. | 
						|
  for (; xc[--b] === 0;) xc.pop(); | 
						|
 | 
						|
  // Remove leading zeros and adjust exponent accordingly. | 
						|
  for (; xc[0] === 0;) { | 
						|
    xc.shift(); | 
						|
    --ye; | 
						|
  } | 
						|
 | 
						|
  if (!xc[0]) { | 
						|
 | 
						|
    // n - n = +0 | 
						|
    y.s = 1; | 
						|
 | 
						|
    // Result must be zero. | 
						|
    xc = [ye = 0]; | 
						|
  } | 
						|
 | 
						|
  y.c = xc; | 
						|
  y.e = ye; | 
						|
 | 
						|
  return y; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the value of this Big modulo the value of Big y. | 
						|
 */ | 
						|
P.mod = function (y) { | 
						|
  var ygtx, | 
						|
    x = this, | 
						|
    Big = x.constructor, | 
						|
    a = x.s, | 
						|
    b = (y = new Big(y)).s; | 
						|
 | 
						|
  if (!y.c[0]) throw Error(DIV_BY_ZERO); | 
						|
 | 
						|
  x.s = y.s = 1; | 
						|
  ygtx = y.cmp(x) == 1; | 
						|
  x.s = a; | 
						|
  y.s = b; | 
						|
 | 
						|
  if (ygtx) return new Big(x); | 
						|
 | 
						|
  a = Big.DP; | 
						|
  b = Big.RM; | 
						|
  Big.DP = Big.RM = 0; | 
						|
  x = x.div(y); | 
						|
  Big.DP = a; | 
						|
  Big.RM = b; | 
						|
 | 
						|
  return this.minus(x.times(y)); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the value of this Big plus the value of Big y. | 
						|
 */ | 
						|
P.plus = P.add = function (y) { | 
						|
  var t, | 
						|
    x = this, | 
						|
    Big = x.constructor, | 
						|
    a = x.s, | 
						|
    b = (y = new Big(y)).s; | 
						|
 | 
						|
  // Signs differ? | 
						|
  if (a != b) { | 
						|
    y.s = -b; | 
						|
    return x.minus(y); | 
						|
  } | 
						|
 | 
						|
  var xe = x.e, | 
						|
    xc = x.c, | 
						|
    ye = y.e, | 
						|
    yc = y.c; | 
						|
 | 
						|
  // Either zero? y is non-zero? x is non-zero? Or both are zero. | 
						|
  if (!xc[0] || !yc[0]) return yc[0] ? y : new Big(xc[0] ? x : a * 0); | 
						|
 | 
						|
  xc = xc.slice(); | 
						|
 | 
						|
  // Prepend zeros to equalise exponents. | 
						|
  // Note: reverse faster than unshifts. | 
						|
  if (a = xe - ye) { | 
						|
    if (a > 0) { | 
						|
      ye = xe; | 
						|
      t = yc; | 
						|
    } else { | 
						|
      a = -a; | 
						|
      t = xc; | 
						|
    } | 
						|
 | 
						|
    t.reverse(); | 
						|
    for (; a--;) t.push(0); | 
						|
    t.reverse(); | 
						|
  } | 
						|
 | 
						|
  // Point xc to the longer array. | 
						|
  if (xc.length - yc.length < 0) { | 
						|
    t = yc; | 
						|
    yc = xc; | 
						|
    xc = t; | 
						|
  } | 
						|
 | 
						|
  a = yc.length; | 
						|
 | 
						|
  // Only start adding at yc.length - 1 as the further digits of xc can be left as they are. | 
						|
  for (b = 0; a; xc[a] %= 10) b = (xc[--a] = xc[a] + yc[a] + b) / 10 | 0; | 
						|
 | 
						|
  // No need to check for zero, as +x + +y != 0 && -x + -y != 0 | 
						|
 | 
						|
  if (b) { | 
						|
    xc.unshift(b); | 
						|
    ++ye; | 
						|
  } | 
						|
 | 
						|
  // Remove trailing zeros. | 
						|
  for (a = xc.length; xc[--a] === 0;) xc.pop(); | 
						|
 | 
						|
  y.c = xc; | 
						|
  y.e = ye; | 
						|
 | 
						|
  return y; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a Big whose value is the value of this Big raised to the power n. | 
						|
 * If n is negative, round to a maximum of Big.DP decimal places using rounding | 
						|
 * mode Big.RM. | 
						|
 * | 
						|
 * n {number} Integer, -MAX_POWER to MAX_POWER inclusive. | 
						|
 */ | 
						|
P.pow = function (n) { | 
						|
  var x = this, | 
						|
    one = new x.constructor(1), | 
						|
    y = one, | 
						|
    isneg = n < 0; | 
						|
 | 
						|
  if (n !== ~~n || n < -MAX_POWER || n > MAX_POWER) throw Error(INVALID + 'exponent'); | 
						|
  if (isneg) n = -n; | 
						|
 | 
						|
  for (;;) { | 
						|
    if (n & 1) y = y.times(x); | 
						|
    n >>= 1; | 
						|
    if (!n) break; | 
						|
    x = x.times(x); | 
						|
  } | 
						|
 | 
						|
  return isneg ? one.div(y) : y; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the value of this Big rounded using rounding mode rm | 
						|
 * to a maximum of dp decimal places, or, if dp is negative, to an integer which is a | 
						|
 * multiple of 10**-dp. | 
						|
 * If dp is not specified, round to 0 decimal places. | 
						|
 * If rm is not specified, use Big.RM. | 
						|
 * | 
						|
 * dp? {number} Integer, -MAX_DP to MAX_DP inclusive. | 
						|
 * rm? 0, 1, 2 or 3 (ROUND_DOWN, ROUND_HALF_UP, ROUND_HALF_EVEN, ROUND_UP) | 
						|
 */ | 
						|
P.round = function (dp, rm) { | 
						|
  var Big = this.constructor; | 
						|
  if (dp === UNDEFINED) dp = 0; | 
						|
  else if (dp !== ~~dp || dp < -MAX_DP || dp > MAX_DP) throw Error(INVALID_DP); | 
						|
  return round(new Big(this), dp, rm === UNDEFINED ? Big.RM : rm); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the square root of the value of this Big, rounded, if | 
						|
 * necessary, to a maximum of Big.DP decimal places using rounding mode Big.RM. | 
						|
 */ | 
						|
P.sqrt = function () { | 
						|
  var r, c, t, | 
						|
    x = this, | 
						|
    Big = x.constructor, | 
						|
    s = x.s, | 
						|
    e = x.e, | 
						|
    half = new Big(0.5); | 
						|
 | 
						|
  // Zero? | 
						|
  if (!x.c[0]) return new Big(x); | 
						|
 | 
						|
  // Negative? | 
						|
  if (s < 0) throw Error(NAME + 'No square root'); | 
						|
 | 
						|
  // Estimate. | 
						|
  s = Math.sqrt(x + ''); | 
						|
 | 
						|
  // Math.sqrt underflow/overflow? | 
						|
  // Re-estimate: pass x coefficient to Math.sqrt as integer, then adjust the result exponent. | 
						|
  if (s === 0 || s === 1 / 0) { | 
						|
    c = x.c.join(''); | 
						|
    if (!(c.length + e & 1)) c += '0'; | 
						|
    s = Math.sqrt(c); | 
						|
    e = ((e + 1) / 2 | 0) - (e < 0 || e & 1); | 
						|
    r = new Big((s == 1 / 0 ? '1e' : (s = s.toExponential()).slice(0, s.indexOf('e') + 1)) + e); | 
						|
  } else { | 
						|
    r = new Big(s); | 
						|
  } | 
						|
 | 
						|
  e = r.e + (Big.DP += 4); | 
						|
 | 
						|
  // Newton-Raphson iteration. | 
						|
  do { | 
						|
    t = r; | 
						|
    r = half.times(t.plus(x.div(t))); | 
						|
  } while (t.c.slice(0, e).join('') !== r.c.slice(0, e).join('')); | 
						|
 | 
						|
  return round(r, Big.DP -= 4, Big.RM); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a new Big whose value is the value of this Big times the value of Big y. | 
						|
 */ | 
						|
P.times = P.mul = function (y) { | 
						|
  var c, | 
						|
    x = this, | 
						|
    Big = x.constructor, | 
						|
    xc = x.c, | 
						|
    yc = (y = new Big(y)).c, | 
						|
    a = xc.length, | 
						|
    b = yc.length, | 
						|
    i = x.e, | 
						|
    j = y.e; | 
						|
 | 
						|
  // Determine sign of result. | 
						|
  y.s = x.s == y.s ? 1 : -1; | 
						|
 | 
						|
  // Return signed 0 if either 0. | 
						|
  if (!xc[0] || !yc[0]) return new Big(y.s * 0); | 
						|
 | 
						|
  // Initialise exponent of result as x.e + y.e. | 
						|
  y.e = i + j; | 
						|
 | 
						|
  // If array xc has fewer digits than yc, swap xc and yc, and lengths. | 
						|
  if (a < b) { | 
						|
    c = xc; | 
						|
    xc = yc; | 
						|
    yc = c; | 
						|
    j = a; | 
						|
    a = b; | 
						|
    b = j; | 
						|
  } | 
						|
 | 
						|
  // Initialise coefficient array of result with zeros. | 
						|
  for (c = new Array(j = a + b); j--;) c[j] = 0; | 
						|
 | 
						|
  // Multiply. | 
						|
 | 
						|
  // i is initially xc.length. | 
						|
  for (i = b; i--;) { | 
						|
    b = 0; | 
						|
 | 
						|
    // a is yc.length. | 
						|
    for (j = a + i; j > i;) { | 
						|
 | 
						|
      // Current sum of products at this digit position, plus carry. | 
						|
      b = c[j] + yc[i] * xc[j - i - 1] + b; | 
						|
      c[j--] = b % 10; | 
						|
 | 
						|
      // carry | 
						|
      b = b / 10 | 0; | 
						|
    } | 
						|
 | 
						|
    c[j] = (c[j] + b) % 10; | 
						|
  } | 
						|
 | 
						|
  // Increment result exponent if there is a final carry, otherwise remove leading zero. | 
						|
  if (b) ++y.e; | 
						|
  else c.shift(); | 
						|
 | 
						|
  // Remove trailing zeros. | 
						|
  for (i = c.length; !c[--i];) c.pop(); | 
						|
  y.c = c; | 
						|
 | 
						|
  return y; | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a string representing the value of this Big in exponential notation to dp fixed decimal | 
						|
 * places and rounded using Big.RM. | 
						|
 * | 
						|
 * dp? {number} Integer, 0 to MAX_DP inclusive. | 
						|
 */ | 
						|
P.toExponential = function (dp) { | 
						|
  return stringify(this, 1, dp, dp); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a string representing the value of this Big in normal notation to dp fixed decimal | 
						|
 * places and rounded using Big.RM. | 
						|
 * | 
						|
 * dp? {number} Integer, 0 to MAX_DP inclusive. | 
						|
 * | 
						|
 * (-0).toFixed(0) is '0', but (-0.1).toFixed(0) is '-0'. | 
						|
 * (-0).toFixed(1) is '0.0', but (-0.01).toFixed(1) is '-0.0'. | 
						|
 */ | 
						|
P.toFixed = function (dp) { | 
						|
  return stringify(this, 2, dp, this.e + dp); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a string representing the value of this Big rounded to sd significant digits using | 
						|
 * Big.RM. Use exponential notation if sd is less than the number of digits necessary to represent | 
						|
 * the integer part of the value in normal notation. | 
						|
 * | 
						|
 * sd {number} Integer, 1 to MAX_DP inclusive. | 
						|
 */ | 
						|
P.toPrecision = function (sd) { | 
						|
  return stringify(this, 3, sd, sd - 1); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a string representing the value of this Big. | 
						|
 * Return exponential notation if this Big has a positive exponent equal to or greater than | 
						|
 * Big.PE, or a negative exponent equal to or less than Big.NE. | 
						|
 * Omit the sign for negative zero. | 
						|
 */ | 
						|
P.toString = function () { | 
						|
  return stringify(this); | 
						|
}; | 
						|
 | 
						|
 | 
						|
/* | 
						|
 * Return a string representing the value of this Big. | 
						|
 * Return exponential notation if this Big has a positive exponent equal to or greater than | 
						|
 * Big.PE, or a negative exponent equal to or less than Big.NE. | 
						|
 * Include the sign for negative zero. | 
						|
 */ | 
						|
P.valueOf = P.toJSON = function () { | 
						|
  return stringify(this, 4); | 
						|
}; | 
						|
 | 
						|
 | 
						|
// Export | 
						|
 | 
						|
 | 
						|
export var Big = _Big_(); | 
						|
 | 
						|
export default Big;
 | 
						|
 |