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(ROUND_DOWN) * 1 To nearest neighbour. If equidistant, round up. (ROUND_HALF_UP) * 2 To nearest neighbour. If equidistant, to even. (ROUND_HALF_EVEN) * 3 Away from zero. (ROUND_UP) */ RM = 1, // 0, 1, 2 or 3 // The maximum value of DP and Big.DP. MAX_DP = 1E6, // 0 to 1000000 // The maximum magnitude of the exponent argument to the pow method. MAX_POWER = 1E6, // 1 to 1000000 /* * The negative exponent (NE) at and beneath which toString returns exponential notation. * (JavaScript numbers: -7) * -1000000 is the minimum recommended exponent value of a Big. */ NE = -7, // 0 to -1000000 /* * The positive exponent (PE) at and above which toString returns exponential notation. * (JavaScript numbers: 21) * 1000000 is the maximum recommended exponent value of a Big. * (This limit is not enforced or checked.) */ PE = 21, // 0 to 1000000 /**************************************************************************************************/ // Error messages. NAME = '[big.js] ', INVALID = NAME + 'Invalid ', INVALID_DP = INVALID + 'decimal places', INVALID_RM = INVALID + 'rounding mode', DIV_BY_ZERO = NAME + 'Division by zero', // The shared prototype object. P = {}, UNDEFINED = void 0, NUMERIC = /^-?(\d+(\.\d*)?|\.\d+)(e[+-]?\d+)?$/i; /* * Create and return a Big constructor. * */ function _Big_() { /* * The Big constructor and exported function. * Create and return a new instance of a Big number object. * * n {number|string|Big} A numeric value. */ function Big(n) { var x = this; // Enable constructor usage without new. if (!(x instanceof Big)) return n === UNDEFINED ? _Big_() : new Big(n); // Duplicate. if (n instanceof Big) { x.s = n.s; x.e = n.e; x.c = n.c.slice(); } else { parse(x, n); } /* * Retain a reference to this Big constructor, and shadow Big.prototype.constructor which * points to Object. */ x.constructor = Big; } Big.prototype = P; Big.DP = DP; Big.RM = RM; Big.NE = NE; Big.PE = PE; Big.version = '5.2.2'; return Big; } /* * Parse the number or string value passed to a Big constructor. * * x {Big} A Big number instance. * n {number|string} A numeric value. */ function parse(x, n) { var e, i, nl; // Minus zero? if (n === 0 && 1 / n < 0) n = '-0'; else if (!NUMERIC.test(n += '')) throw Error(INVALID + 'number'); // Determine sign. x.s = n.charAt(0) == '-' ? (n = n.slice(1), -1) : 1; // 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; } nl = n.length; // Determine leading zeros. for (i = 0; i < nl && n.charAt(i) == '0';) ++i; if (i == nl) { // Zero. x.c = [x.e = 0]; } else { // Determine trailing zeros. for (; nl > 0 && n.charAt(--nl) == '0';); x.e = e - i - 1; x.c = []; // Convert string to array of digits without leading/trailing zeros. for (e = 0; i <= nl;) x.c[e++] = +n.charAt(i++); } return x; } /* * Round Big x to a maximum of dp decimal places using rounding mode rm. * Called by stringify, P.div, P.round and P.sqrt. * * x {Big} The Big to round. * dp {number} Integer, 0 to MAX_DP inclusive. * rm {number} 0, 1, 2 or 3 (DOWN, HALF_UP, HALF_EVEN, UP) * [more] {boolean} Whether the result of division was truncated. */ function round(x, dp, rm, more) { var xc = x.c, i = x.e + dp + 1; if (i < xc.length) { if (rm === 1) { // xc[i] is the digit after the digit that may be rounded up. more = xc[i] >= 5; } else if (rm === 2) { more = xc[i] > 5 || xc[i] == 5 && (more || i < 0 || xc[i + 1] !== UNDEFINED || xc[i - 1] & 1); } else if (rm === 3) { more = more || !!xc[0]; } else { more = false; if (rm !== 0) throw Error(INVALID_RM); } if (i < 1) { xc.length = 1; if (more) { // 1, 0.1, 0.01, 0.001, 0.0001 etc. x.e = -dp; xc[0] = 1; } else { // Zero. xc[0] = x.e = 0; } } else { // Remove any digits after the required decimal places. xc.length = i--; // Round up? if (more) { // Rounding up may mean the previous digit has to be rounded up. for (; ++xc[i] > 9;) { xc[i] = 0; if (!i--) { ++x.e; xc.unshift(1); } } } // Remove trailing zeros. for (i = xc.length; !xc[--i];) xc.pop(); } } else if (rm < 0 || rm > 3 || rm !== ~~rm) { throw Error(INVALID_RM); } return x; } /* * Return a string representing the value of Big x in normal or exponential notation. * Handles P.toExponential, P.toFixed, P.toJSON, P.toPrecision, P.toString and P.valueOf. * * x {Big} * id? {number} Caller id. * 1 toExponential * 2 toFixed * 3 toPrecision * 4 valueOf * n? {number|undefined} Caller's argument. * k? {number|undefined} */ function stringify(x, id, n, k) { var e, s, Big = x.constructor, z = !x.c[0]; if (n !== UNDEFINED) { if (n !== ~~n || n < (id == 3) || n > MAX_DP) { throw Error(id == 3 ? INVALID + 'precision' : INVALID_DP); } x = new Big(x); // The index of the digit that may be rounded up. n = k - x.e; // Round? if (x.c.length > ++k) round(x, n, Big.RM); // toFixed: recalculate k as x.e may have changed if value rounded up. if (id == 2) k = x.e + n + 1; // Append zeros? for (; x.c.length < k;) x.c.push(0); } e = x.e; s = x.c.join(''); n = s.length; // Exponential notation? if (id != 2 && (id == 1 || id == 3 && k <= e || e <= Big.NE || e >= Big.PE)) { s = s.charAt(0) + (n > 1 ? '.' + s.slice(1) : '') + (e < 0 ? 'e' : 'e+') + e; // Normal notation. } else if (e < 0) { for (; ++e;) s = '0' + s; s = '0.' + s; } else if (e > 0) { if (++e > n) for (e -= n; e--;) s += '0'; else if (e < n) s = s.slice(0, e) + '.' + s.slice(e); } else if (n > 1) { s = s.charAt(0) + '.' + s.slice(1); } return x.s < 0 && (!z || id == 4) ? '-' + s : s; } // Prototype/instance methods /* * Return a new Big whose value is the absolute value of this Big. */ P.abs = function () { var x = new this.constructor(this); x.s = 1; return x; }; /* * 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; 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; }; /* * 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. */ P.div = function (y) { var x = this, Big = x.constructor, a = x.c, // dividend b = (y = new Big(y)).c, // divisor k = x.s == y.s ? 1 : -1, dp = Big.DP; 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, bz = b.slice(), ai = bl = b.length, al = a.length, r = a.slice(0, bl), // remainder rl = r.length, q = y, // quotient qc = q.c = [], qi = 0, 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 { 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;