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- /*
- * big.js v5.2.2
- * A small, fast, easy-to-use library for arbitrary-precision decimal arithmetic.
- * Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
- * https://github.com/MikeMcl/big.js/LICENCE
- */
- /************************************** EDITABLE DEFAULTS *****************************************/
- // The default values below must be integers within the stated ranges.
- /*
- * The maximum number of decimal places (DP) of the results of operations involving division:
- * div and sqrt, and pow with negative exponents.
- */
- var DP = 20, // 0 to MAX_DP
- /*
- * The rounding mode (RM) used when rounding to the above decimal places.
- *
- * 0 Towards zero (i.e. truncate, no rounding). (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;
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