added coercion util functions

6 files changed, 4584 insertions, 25 deletions

diff --git a/packages/instant/src/index.umd.ts b/packages/instant/src/index.umd.ts
index 0c2ce5ec1..45913aa47 100644
--- a/packages/instant/src/index.umd.ts
+++ b/packages/instant/src/index.umd.ts
@@ -18,8 +18,8 @@ import { Network, OrderSource } from './types';
 import { analytics } from './util/analytics';
 import { assert } from './util/assert';
 import { providerFactory } from './util/provider_factory';
+import { signedOrderCoercionUtil } from './util/signed_order_coercion';
 import { util } from './util/util';
-import { coerceSignedOrderBigNumberOfString } from './util/signed_order_coercion'
 
 const isInstantRendered = (): boolean => !!document.getElementById(INJECTED_DIV_ID);
 
@@ -94,13 +94,12 @@ export interface ZeroExInstantConfig extends ZeroExInstantOverlayProps {
 }
 
 export const render = (config: ZeroExInstantConfig, selector: string = DEFAULT_ZERO_EX_CONTAINER_SELECTOR) => {
-    validateInstantRenderConfig(config, selector);
-
-    // TODO(David Sun) test functionality of order bignumber version coercion
     if (!_.isString(config.orderSource)) {
-        config.orderSource = config.orderSource.map(coerceSignedOrderBigNumberOfString);
+        config.orderSource = config.orderSource.map(signedOrderCoercionUtil.bigNumberCoercion);
     }
 
+    validateInstantRenderConfig(config, selector);
+
     if (config.shouldDisablePushToHistory) {
         if (!isInstantRendered()) {
             renderInstant(config, selector);
diff --git a/packages/instant/src/util/maybe_big_number.ts b/packages/instant/src/util/maybe_big_number.ts
index f48473389..7e206a125 100644
--- a/packages/instant/src/util/maybe_big_number.ts
+++ b/packages/instant/src/util/maybe_big_number.ts
@@ -16,6 +16,17 @@ export const maybeBigNumberUtil = {
 
         return validBigNumber.isNaN() ? undefined : validBigNumber;
     },
+    // converts a BigNumber or String to the BigNumber used by 0x libraries
+    bigNumberOrStringToMaybeBigNumber: (value: any): Maybe<BigNumber> => {
+        if (_.isString(value)) {
+            return maybeBigNumberUtil.stringToMaybeBigNumber(value);
+        }
+        // checks for pre v8 bignumber with member variable
+        if (BigNumber.isBigNumber(value) || value.isBigNumber) {
+            return new BigNumber(value.toString());
+        }
+        return undefined;
+    },
     areMaybeBigNumbersEqual: (val1: Maybe<BigNumber>, val2: Maybe<BigNumber>): boolean => {
         if (!_.isUndefined(val1) && !_.isUndefined(val2)) {
             return val1.isEqualTo(val2);
diff --git a/packages/instant/src/util/signed_order_coercion.ts b/packages/instant/src/util/signed_order_coercion.ts
index 649596a3d..4209e05e1 100644
--- a/packages/instant/src/util/signed_order_coercion.ts
+++ b/packages/instant/src/util/signed_order_coercion.ts
@@ -1,25 +1,26 @@
-import { BigNumber } from '@0x/asset-buyer';
 import { SignedOrder } from '@0x/types';
+import { BigNumber } from '@0x/utils';
+import * as _ from 'lodash';
 
-export const coerceBigNumberOrString = (value: any): BigNumber => {
-    if (typeof value === 'string') {
-        return new BigNumber(value);
-    }
-    if (BigNumber.isBigNumber(value)) {
-        return new BigNumber(value.toString());
-    }
-    return value;
+import { maybeBigNumberUtil } from './maybe_big_number';
+
+const coerceBigNumberOrString = (value: any): BigNumber => {
+    const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(value);
+    return !!bn ? bn : value;
 };
 
-// function implies that the signed order already has been invalidated
-export const coerceSignedOrderBigNumberOfString = (order: SignedOrder): SignedOrder => {
-    return {
-        ...order,
-        makerFee: coerceBigNumberOrString(order.makerFee),
-        takerFee: coerceBigNumberOrString(order.takerFee),
-        makerAssetAmount: coerceBigNumberOrString(order.makerAssetAmount),
-        takerAssetAmount: coerceBigNumberOrString(order.takerAssetAmount),
-        salt: coerceBigNumberOrString(order.salt),
-        expirationTimeSeconds: coerceBigNumberOrString(order.expirationTimeSeconds),
-    };
+// function implies that the signed order already has been validated
+export const signedOrderCoercionUtil = {
+    // coerces order big number values to the BigNumber version utilized by 0x
+    bigNumberCoercion: (order: SignedOrder): SignedOrder => {
+        return {
+            ...order,
+            makerFee: coerceBigNumberOrString(order.makerFee),
+            takerFee: coerceBigNumberOrString(order.takerFee),
+            makerAssetAmount: coerceBigNumberOrString(order.makerAssetAmount),
+            takerAssetAmount: coerceBigNumberOrString(order.takerAssetAmount),
+            salt: coerceBigNumberOrString(order.salt),
+            expirationTimeSeconds: coerceBigNumberOrString(order.expirationTimeSeconds),
+        };
+    },
 };
diff --git a/packages/instant/test/util/dependencies/prevbignumber.d.ts b/packages/instant/test/util/dependencies/prevbignumber.d.ts
new file mode 100644
index 000000000..9b802ec3e
--- /dev/null
+++ b/packages/instant/test/util/dependencies/prevbignumber.d.ts
@@ -0,0 +1,1772 @@
+// Type definitions for bignumber.js >=6.0.0
+// Project: https://github.com/MikeMcl/bignumber.js
+// Definitions by: Michael Mclaughlin <https://github.com/MikeMcl>
+// Definitions: https://github.com/MikeMcl/bignumber.js
+
+// Documentation: http://mikemcl.github.io/bignumber.js/
+//
+// Exports (available globally or when using import):
+//
+//   class     BigNumber (default export)
+//   type      BigNumber.Constructor
+//   type      BigNumber.Instance
+//   type      BigNumber.ModuloMode
+//   type      BigNumber.RoundingMOde
+//   type      BigNumber.Value
+//   interface BigNumber.Config
+//   interface BigNumber.Format
+//
+// Example (alternative syntax commented-out):
+//
+//   import {BigNumber} from "bignumber.js"
+//   //import BigNumber from "bignumber.js"
+//
+//   let rm: BigNumber.RoundingMode = BigNumber.ROUND_UP;
+//   let f: BigNumber.Format = { decimalSeparator: ',' };
+//   let c: BigNumber.Config = { DECIMAL_PLACES: 4, ROUNDING_MODE: rm, FORMAT: f };
+//   BigNumber.config(c);
+//
+//   let v: BigNumber.Value = '12345.6789';
+//   let b: BigNumber = new BigNumber(v);
+//   //let b: BigNumber.Instance = new BigNumber(v);
+//
+// The use of compiler option `--strictNullChecks` is recommended.
+
+
+type BigNumberConstructor = typeof BigNumber;
+type BigNumberInstance = BigNumber;
+type BigNumberModuloMode = BigNumberRoundingMode | 9;
+type BigNumberRoundingMode = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
+type BigNumberValue = string | number | BigNumber;
+
+/**
+ * See `BigNumber.config` and `BigNumber.clone`.
+ */
+interface BigNumberConfig {
+
+  /**
+   * An integer, 0 to 1e+9. Default value: 20.
+   *
+   * The maximum number of decimal places of the result of operations involving division, i.e.
+   * division, square root and base conversion operations, and exponentiation when the exponent is
+   * negative.
+   *
+   * ```ts
+   * BigNumber.config({ DECIMAL_PLACES: 5 })
+   * BigNumber.set({ DECIMAL_PLACES: 5 })
+   * ```
+   */
+  DECIMAL_PLACES?: number;
+
+  /**
+   * An integer, 0 to 8. Default value: `BigNumber.ROUND_HALF_UP` (4).
+   *
+   * The rounding mode used in operations that involve division (see `DECIMAL_PLACES`) and the
+   * default rounding mode of the `decimalPlaces`, `precision`, `toExponential`, `toFixed`,
+   * `toFormat` and `toPrecision` methods.
+   *
+   * The modes are available as enumerated properties of the BigNumber constructor.
+   *
+   * ```ts
+   * BigNumber.config({ ROUNDING_MODE: 0 })
+   * BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP })
+   * ```
+   */
+  ROUNDING_MODE?: BigNumberRoundingMode;
+
+  /**
+   * An integer, 0 to 1e+9, or an array, [-1e+9 to 0, 0 to 1e+9].
+   * Default value: `[-7, 20]`.
+   *
+   * The exponent value(s) at which `toString` returns exponential notation.
+   *
+   * If a single number is assigned, the value is the exponent magnitude.
+   *
+   * If an array of two numbers is assigned then the first number is the negative exponent value at
+   * and beneath which exponential notation is used, and the second number is the positive exponent
+   * value at and above which exponential notation is used.
+   *
+   * For example, to emulate JavaScript numbers in terms of the exponent values at which they begin
+   * to use exponential notation, use `[-7, 20]`.
+   *
+   * ```ts
+   * BigNumber.config({ EXPONENTIAL_AT: 2 })
+   * new BigNumber(12.3)         // '12.3'        e is only 1
+   * new BigNumber(123)          // '1.23e+2'
+   * new BigNumber(0.123)        // '0.123'       e is only -1
+   * new BigNumber(0.0123)       // '1.23e-2'
+   *
+   * BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
+   * new BigNumber(123456789)    // '123456789'   e is only 8
+   * new BigNumber(0.000000123)  // '1.23e-7'
+   *
+   * // Almost never return exponential notation:
+   * BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
+   *
+   * // Always return exponential notation:
+   * BigNumber.config({ EXPONENTIAL_AT: 0 })
+   * ```
+   *
+   * Regardless of the value of `EXPONENTIAL_AT`, the `toFixed` method will always return a value in
+   * normal notation and the `toExponential` method will always return a value in exponential form.
+   * Calling `toString` with a base argument, e.g. `toString(10)`, will also always return normal
+   * notation.
+   */
+  EXPONENTIAL_AT?: number|[number, number];
+
+  /**
+   * An integer, magnitude 1 to 1e+9, or an array, [-1e+9 to -1, 1 to 1e+9].
+   * Default value: `[-1e+9, 1e+9]`.
+   *
+   * The exponent value(s) beyond which overflow to Infinity and underflow to zero occurs.
+   *
+   * If a single number is assigned, it is the maximum exponent magnitude: values wth a positive
+   * exponent of greater magnitude become Infinity and those with a negative exponent of greater
+   * magnitude become zero.
+   *
+   * If an array of two numbers is assigned then the first number is the negative exponent limit and
+   * the second number is the positive exponent limit.
+   *
+   * For example, to emulate JavaScript numbers in terms of the exponent values at which they
+   * become zero and Infinity, use [-324, 308].
+   *
+   * ```ts
+   * BigNumber.config({ RANGE: 500 })
+   * BigNumber.config().RANGE     // [ -500, 500 ]
+   * new BigNumber('9.999e499')   // '9.999e+499'
+   * new BigNumber('1e500')       // 'Infinity'
+   * new BigNumber('1e-499')      // '1e-499'
+   * new BigNumber('1e-500')      // '0'
+   *
+   * BigNumber.config({ RANGE: [-3, 4] })
+   * new BigNumber(99999)         // '99999'      e is only 4
+   * new BigNumber(100000)        // 'Infinity'   e is 5
+   * new BigNumber(0.001)         // '0.01'       e is only -3
+   * new BigNumber(0.0001)        // '0'          e is -4
+   * ```
+   * The largest possible magnitude of a finite BigNumber is 9.999...e+1000000000.
+   * The smallest possible magnitude of a non-zero BigNumber is 1e-1000000000.
+   */
+  RANGE?: number|[number, number];
+
+  /**
+   * A boolean: `true` or `false`. Default value: `false`.
+   *
+   * The value that determines whether cryptographically-secure pseudo-random number generation is
+   * used. If `CRYPTO` is set to true then the random method will generate random digits using
+   * `crypto.getRandomValues` in browsers that support it, or `crypto.randomBytes` if using a
+   * version of Node.js that supports it.
+   *
+   * If neither function is supported by the host environment then attempting to set `CRYPTO` to
+   * `true` will fail and an exception will be thrown.
+   *
+   * If `CRYPTO` is `false` then the source of randomness used will be `Math.random` (which is
+   * assumed to generate at least 30 bits of randomness).
+   *
+   * See `BigNumber.random`.
+   *
+   * ```ts
+   * BigNumber.config({ CRYPTO: true })
+   * BigNumber.config().CRYPTO       // true
+   * BigNumber.random()              // 0.54340758610486147524
+   * ```
+   */
+  CRYPTO?: boolean;
+
+  /**
+   * An integer, 0 to 9. Default value: `BigNumber.ROUND_DOWN` (1).
+   *
+   * The modulo mode used when calculating the modulus: `a mod n`.
+   * The quotient, `q = a / n`, is calculated according to the `ROUNDING_MODE` that corresponds to
+   * the chosen `MODULO_MODE`.
+   * The remainder, `r`, is calculated as: `r = a - n * q`.
+   *
+   * The modes that are most commonly used for the modulus/remainder operation are shown in the
+   * following table. Although the other rounding modes can be used, they may not give useful
+   * results.
+   *
+   * Property           | Value | Description
+   * :------------------|:------|:------------------------------------------------------------------
+   *  `ROUND_UP`        |   0   | The remainder is positive if the dividend is negative.
+   *  `ROUND_DOWN`      |   1   | The remainder has the same sign as the dividend.
+   *                    |       | Uses 'truncating division' and matches JavaScript's `%` operator .
+   *  `ROUND_FLOOR`     |   3   | The remainder has the same sign as the divisor.
+   *                    |       | This matches Python's `%` operator.
+   *  `ROUND_HALF_EVEN` |   6   | The IEEE 754 remainder function.
+   *  `EUCLID`          |   9   | The remainder is always positive.
+   *                    |       | Euclidian division: `q = sign(n) * floor(a / abs(n))`
+   *
+   * The rounding/modulo modes are available as enumerated properties of the BigNumber constructor.
+   *
+   * See `modulo`.
+   *
+   * ```ts
+   * BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
+   * BigNumber.set({ MODULO_MODE: 9 })          // equivalent
+   * ```
+   */
+  MODULO_MODE?: BigNumberModuloMode;
+
+  /**
+   * An integer, 0 to 1e+9. Default value: 0.
+   *
+   * The maximum precision, i.e. number of significant digits, of the result of the power operation
+   * - unless a modulus is specified.
+   *
+   * If set to 0, the number of significant digits will not be limited.
+   *
+   * See `exponentiatedBy`.
+   *
+   * ```ts
+   * BigNumber.config({ POW_PRECISION: 100 })
+   * ```
+   */
+  POW_PRECISION?: number;
+
+  /**
+   * An object including any number of the properties shown below.
+   *
+   * The object configures the format of the string returned by the `toFormat` method.
+   * The example below shows the properties of the object that are recognised, and
+   * their default values.
+   *
+   * Unlike the other configuration properties, the values of the properties of the `FORMAT` object
+   * will not be checked for validity - the existing object will simply be replaced by the object
+   * that is passed in.
+   *
+   * See `toFormat`.
+   *
+   * ```ts
+   * BigNumber.config({
+   *   FORMAT: {
+   *     // the decimal separator
+   *     decimalSeparator: '.',
+   *     // the grouping separator of the integer part
+   *     groupSeparator: ',',
+   *     // the primary grouping size of the integer part
+   *     groupSize: 3,
+   *     // the secondary grouping size of the integer part
+   *     secondaryGroupSize: 0,
+   *     // the grouping separator of the fraction part
+   *     fractionGroupSeparator: ' ',
+   *     // the grouping size of the fraction part
+   *     fractionGroupSize: 0
+   *   }
+   * })
+   * ```
+   */
+  FORMAT?: BigNumberFormat;
+
+  /**
+   * A string representing the alphabet used for base conversion.
+   * Default value: `'0123456789abcdefghijklmnopqrstuvwxyz'`.
+   *
+   * The length of the alphabet corresponds to the maximum value of the base argument that can be
+   * passed to the BigNumber constructor or `toString`. There is no maximum length, but it must be
+   * at least 2 characters long, and it must not contain a repeated character, or `'.'` - the
+   * decimal separator for all values whatever their base.
+   *
+   * ```ts
+   * // duodecimal (base 12)
+   * BigNumber.config({ ALPHABET: '0123456789TE' })
+   * x = new BigNumber('T', 12)
+   * x.toString()                // '10'
+   * x.toString(12)              // 'T'
+   * ```
+   */
+  ALPHABET?: string;
+}
+
+
+/**
+ * See `FORMAT` and `toFormat`.
+ */
+interface BigNumberFormat {
+
+  /**
+   * The decimal separator.
+   */
+  decimalSeparator?: string;
+
+  /**
+   * The grouping separator of the integer part.
+   */
+  groupSeparator?: string;
+
+  /**
+   * The primary grouping size of the integer part.
+   */
+  groupSize?: number;
+
+  /**
+   * The secondary grouping size of the integer part.
+   */
+  secondaryGroupSize?: number;
+
+  /**
+   * The grouping separator of the fraction part.
+   */
+  fractionGroupSeparator?: string;
+
+  /**
+   * The grouping size of the fraction part.
+   */
+  fractionGroupSize?: number;
+}
+
+
+export declare class BigNumber {
+
+  /**
+   * Used internally by the `BigNumber.isBigNumber` method.
+   */
+  private readonly _isBigNumber: true;
+
+  /**
+   * The coefficient of the value of this BigNumber, an array of base 1e14 integer numbers.
+   */
+  readonly c: number[];
+
+  /**
+   * The exponent of the value of this BigNumber, an integer number, -1000000000 to 1000000000.
+   */
+  readonly e: number;
+
+  /**
+   * The sign of the value of this BigNumber, -1 or 1.
+   */
+  readonly s: number;
+
+  /**
+   * Returns a new instance of BigNumber with value `n`.
+   *
+   * Legitimate values for `n` include ±0, ±`Infinity` and `NaN`.
+   *
+   * Values of type number with more than 15 significant digits are considered invalid as calling
+   * `toString` or `valueOf` on such numbers may not result in the intended value.
+   *
+   * ```ts
+   * console.log( 823456789123456.3 );    // 823456789123456.2
+   * ```
+   *
+   * There is no limit to the number of digits of a value of type string (other than that of
+   * JavaScript's maximum array size). Decimal string values may be in exponential, as well as
+   * normal (fixed-point) notation. Non-decimal values must be in normal notation.
+   *
+   * String values in hexadecimal literal form, e.g. '0xff', are valid, as are string values with
+   * the octal and binary prefixs '0o' and '0b'. String values in octal literal form without the
+   * prefix will be interpreted as decimals, e.g. '011' is interpreted as 11, not 9.
+   *
+   * Values in any base may have fraction digits.
+   *
+   * If a base is specified, `n` is rounded according to the current `DECIMAL_PLACES` and
+   * `ROUNDING_MODE` settings. If base is omitted, or is `null` or `undefined`, base 10 is assumed.
+   *
+   * Throws an invalid `value` or `base`.
+   *
+   * ```ts
+   * x = new BigNumber(9)                       // '9'
+   * y = new BigNumber(x)                       // '9'
+   *
+   * // 'new' is optional
+   * BigNumber(435.345)                         // '435.345'
+   *
+   * new BigNumber('5032485723458348569331745.33434346346912144534543')
+   * new BigNumber('4.321e+4')                  // '43210'
+   * new BigNumber('-735.0918e-430')            // '-7.350918e-428'
+   * new BigNumber(Infinity)                    // 'Infinity'
+   * new BigNumber(NaN)                         // 'NaN'
+   * new BigNumber('.5')                        // '0.5'
+   * new BigNumber('+2')                        // '2'
+   * new BigNumber(-10110100.1, 2)              // '-180.5'
+   * new BigNumber(-0b10110100.1)               // '-180.5'
+   * new BigNumber('123412421.234324', 5)       // '607236.557696'
+   * new BigNumber('ff.8', 16)                  // '255.5'
+   * new BigNumber('0xff.8')                    // '255.5'
+   *
+   * // The following throws 'Not a base 2 number'.
+   * new BigNumber(9, 2)
+   *
+   * // The following throws 'Number primitive has more than 15 significant digits'.
+   * new BigNumber(96517860459076817.4395)
+   *
+   * // The following throws 'Not a number'.
+   * new BigNumber('blurgh')
+   *
+   * // A value is only rounded by the constructor if a base is specified.
+   * BigNumber.config({ DECIMAL_PLACES: 5 })
+   * new BigNumber(1.23456789)                  // '1.23456789'
+   * new BigNumber(1.23456789, 10)              // '1.23457'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param base The base of n, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
+   */
+  constructor(n: BigNumberValue, base?: number);
+
+  /**
+   * Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
+   * BigNumber.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber(-0.8)
+   * x.absoluteValue()           // '0.8'
+   * ```
+   */
+  absoluteValue(): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
+   * BigNumber.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber(-0.8)
+   * x.abs()           // '0.8'
+   * ```
+   */
+  abs(): BigNumber;
+
+  /**
+   *  Returns |                                                               |
+   * :-------:|:--------------------------------------------------------------|
+   *     1    | If the value of this BigNumber is greater than the value of `n`
+   *    -1    | If the value of this BigNumber is less than the value of `n`
+   *     0    | If this BigNumber and `n` have the same value
+   *  `null`  | If the value of either this BigNumber or `n` is `NaN`
+   *
+   * ```ts
+   *
+   * x = new BigNumber(Infinity)
+   * y = new BigNumber(5)
+   * x.comparedTo(y)                 // 1
+   * x.comparedTo(x.minus(1))        // 0
+   * y.comparedTo(NaN)               // null
+   * y.comparedTo('110', 2)          // -1
+   * ```
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  comparedTo(n: BigNumberValue, base?: number): number;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
+   * `roundingMode` to a maximum of `decimalPlaces` decimal places.
+   *
+   * If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
+   * decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
+   * ±`Infinity` or `NaN`.
+   *
+   * If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `decimalPlaces` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(1234.56)
+   * x.decimalPlaces()                      // 2
+   * x.decimalPlaces(1)                     // '1234.6'
+   * x.decimalPlaces(2)                     // '1234.56'
+   * x.decimalPlaces(10)                    // '1234.56'
+   * x.decimalPlaces(0, 1)                  // '1234'
+   * x.decimalPlaces(0, 6)                  // '1235'
+   * x.decimalPlaces(1, 1)                  // '1234.5'
+   * x.decimalPlaces(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'
+   * x                                      // '1234.56'
+   * y = new BigNumber('9.9e-101')
+   * y.decimalPlaces()                      // 102
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  decimalPlaces(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
+   * `roundingMode` to a maximum of `decimalPlaces` decimal places.
+   *
+   * If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
+   * decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
+   * ±`Infinity` or `NaN`.
+   *
+   * If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `decimalPlaces` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(1234.56)
+   * x.dp()                                 // 2
+   * x.dp(1)                                // '1234.6'
+   * x.dp(2)                                // '1234.56'
+   * x.dp(10)                               // '1234.56'
+   * x.dp(0, 1)                             // '1234'
+   * x.dp(0, 6)                             // '1235'
+   * x.dp(1, 1)                             // '1234.5'
+   * x.dp(1, BigNumber.ROUND_HALF_EVEN)     // '1234.6'
+   * x                                      // '1234.56'
+   * y = new BigNumber('9.9e-101')
+   * y.dp()                                 // 102
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  dp(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
+   * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+   *
+   * ```ts
+   * x = new BigNumber(355)
+   * y = new BigNumber(113)
+   * x.dividedBy(y)                  // '3.14159292035398230088'
+   * x.dividedBy(5)                  // '71'
+   * x.dividedBy(47, 16)             // '5'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  dividedBy(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
+   * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+   *
+   * ```ts
+   * x = new BigNumber(355)
+   * y = new BigNumber(113)
+   * x.div(y)                    // '3.14159292035398230088'
+   * x.div(5)                    // '71'
+   * x.div(47, 16)               // '5'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  div(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+   * `n`.
+   *
+   * ```ts
+   * x = new BigNumber(5)
+   * y = new BigNumber(3)
+   * x.dividedToIntegerBy(y)              // '1'
+   * x.dividedToIntegerBy(0.7)            // '7'
+   * x.dividedToIntegerBy('0.f', 16)      // '5'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  dividedToIntegerBy(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+   * `n`.
+   *
+   * ```ts
+   * x = new BigNumber(5)
+   * y = new BigNumber(3)
+   * x.idiv(y)                       // '1'
+   * x.idiv(0.7)                     // '7'
+   * x.idiv('0.f', 16)               // '5'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  idiv(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
+   * raised to the power `n`, and optionally modulo a modulus `m`.
+   *
+   * If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
+   * `ROUNDING_MODE` settings.
+   *
+   * As the number of digits of the result of the power operation can grow so large so quickly,
+   * e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
+   * limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
+   *
+   * By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
+   * digits will be calculated, and that the method's performance will decrease dramatically for
+   * larger exponents.
+   *
+   * If `m` is specified and the value of `m`, `n` and this BigNumber are positive integers, then a
+   * fast modular exponentiation algorithm is used, otherwise if any of the values is not a positive
+   * integer the operation will simply be performed as `x.exponentiatedBy(n).modulo(m)` with a
+   * `POW_PRECISION` of 0.
+   *
+   * Throws if `n` is not a primitive number, or is not an integer, or is out of range.
+   *
+   * ```ts
+   * Math.pow(0.7, 2)                    // 0.48999999999999994
+   * x = new BigNumber(0.7)
+   * x.exponentiatedBy(2)                // '0.49'
+   * BigNumber(3).exponentiatedBy(-2)    // '0.11111111111111111111'
+   * ```
+   *
+   * @param n The exponent, an integer, -9007199254740991 to 9007199254740991.
+   * @param [m] The modulus, a positive integer.
+   */
+  exponentiatedBy(n: number, m?: BigNumberValue): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
+   * raised to the power `n`, and optionally modulo a modulus `m`.
+   *
+   * If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
+   * `ROUNDING_MODE` settings.
+   *
+   * As the number of digits of the result of the power operation can grow so large so quickly,
+   * e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
+   * limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
+   *
+   * By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
+   * digits will be calculated, and that the method's performance will decrease dramatically for
+   * larger exponents.
+   *
+   * If `m` is specified and the value of `m`, `n` and this BigNumber are positive integers, then a
+   * fast modular exponentiation algorithm is used, otherwise if any of the values is not a positive
+   * integer the operation will simply be performed as `x.exponentiatedBy(n).modulo(m)` with a
+   * `POW_PRECISION` of 0.
+   *
+   * Throws if `n` is not a primitive number or an integer, or is out of range.
+   *
+   * ```ts
+   * Math.pow(0.7, 2)          // 0.48999999999999994
+   * x = new BigNumber(0.7)
+   * x.pow(2)                  // '0.49'
+   * BigNumber(3).pow(-2)      // '0.11111111111111111111'
+   * ```
+   *
+   * @param n The exponent, an integer, -9007199254740991 to 9007199254740991.
+   * @param [m] The modulus, a positive integer.
+   */
+  pow(n: number, m?: BigNumberValue): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
+   * rounding mode `rm`.
+   *
+   * If `rm` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `rm` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(123.456)
+   * x.integerValue()                        // '123'
+   * x.integerValue(BigNumber.ROUND_CEIL)    // '124'
+   * y = new BigNumber(-12.7)
+   * y.integerValue()                        // '-13'
+   * x.integerValue(BigNumber.ROUND_DOWN)    // '-12'
+   * ```
+   *
+   * @param {BigNumberRoundingMode} [rm] The roundng mode, an integer, 0 to 8.
+   */
+  integerValue(rm?: BigNumberRoundingMode): BigNumber;
+
+  /**
+   * Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
+   * `false`.
+   *
+   * As with JavaScript, `NaN` does not equal `NaN`.
+   *
+   * ```ts
+   * 0 === 1e-324                           // true
+   * x = new BigNumber(0)
+   * x.isEqualTo('1e-324')                  // false
+   * BigNumber(-0).isEqualTo(x)             // true  ( -0 === 0 )
+   * BigNumber(255).isEqualTo('ff', 16)     // true
+   *
+   * y = new BigNumber(NaN)
+   * y.isEqualTo(NaN)                // false
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  isEqualTo(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
+   * `false`.
+   *
+   * As with JavaScript, `NaN` does not equal `NaN`.
+   *
+   * ```ts
+   * 0 === 1e-324                    // true
+   * x = new BigNumber(0)
+   * x.eq('1e-324')                  // false
+   * BigNumber(-0).eq(x)             // true  ( -0 === 0 )
+   * BigNumber(255).eq('ff', 16)     // true
+   *
+   * y = new BigNumber(NaN)
+   * y.eq(NaN)                       // false
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  eq(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is a finite number, otherwise returns `false`.
+   *
+   * The only possible non-finite values of a BigNumber are `NaN`, `Infinity` and `-Infinity`.
+   *
+   * ```ts
+   * x = new BigNumber(1)
+   * x.isFinite()                    // true
+   * y = new BigNumber(Infinity)
+   * y.isFinite()                    // false
+   * ```
+   */
+  isFinite(): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
+   * returns `false`.
+   *
+   * ```ts
+   * 0.1 > (0.3 - 0.2)                             // true
+   * x = new BigNumber(0.1)
+   * x.isGreaterThan(BigNumber(0.3).minus(0.2))    // false
+   * BigNumber(0).isGreaterThan(x)                 // false
+   * BigNumber(11, 3).isGreaterThan(11.1, 2)       // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  isGreaterThan(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
+   * returns `false`.
+   *
+   * ```ts
+   * 0.1 > (0.3 - 0                     // true
+   * x = new BigNumber(0.1)
+   * x.gt(BigNumber(0.3).minus(0.2))    // false
+   * BigNumber(0).gt(x)                 // false
+   * BigNumber(11, 3).gt(11.1, 2)       // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  gt(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
+   * otherwise returns `false`.
+   *
+   * ```ts
+   * (0.3 - 0.2) >= 0.1                                  // false
+   * x = new BigNumber(0.3).minus(0.2)
+   * x.isGreaterThanOrEqualTo(0.1)                       // true
+   * BigNumber(1).isGreaterThanOrEqualTo(x)              // true
+   * BigNumber(10, 18).isGreaterThanOrEqualTo('i', 36)   // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  isGreaterThanOrEqualTo(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
+   * otherwise returns `false`.
+   *
+   * ```ts
+   * (0.3 - 0.2) >= 0.1                    // false
+   * x = new BigNumber(0.3).minus(0.2)
+   * x.gte(0.1)                            // true
+   * BigNumber(1).gte(x)                   // true
+   * BigNumber(10, 18).gte('i', 36)        // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  gte(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is an integer, otherwise returns `false`.
+   *
+   * ```ts
+   * x = new BigNumber(1)
+   * x.isInteger()                   // true
+   * y = new BigNumber(123.456)
+   * y.isInteger()                   // false
+   * ```
+   */
+  isInteger(): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
+   * `false`.
+   *
+   * ```ts
+   * (0.3 - 0.2) < 0.1                       // true
+   * x = new BigNumber(0.3).minus(0.2)
+   * x.isLessThan(0.1)                       // false
+   * BigNumber(0).isLessThan(x)              // true
+   * BigNumber(11.1, 2).isLessThan(11, 3)    // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  isLessThan(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
+   * `false`.
+   *
+   * ```ts
+   * (0.3 - 0.2) < 0.1                       // true
+   * x = new BigNumber(0.3).minus(0.2)
+   * x.lt(0.1)                               // false
+   * BigNumber(0).lt(x)                      // true
+   * BigNumber(11.1, 2).lt(11, 3)            // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  lt(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
+   * otherwise returns `false`.
+   *
+   * ```ts
+   * 0.1 <= (0.3 - 0.2)                                 // false
+   * x = new BigNumber(0.1)
+   * x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2))   // true
+   * BigNumber(-1).isLessThanOrEqualTo(x)               // true
+   * BigNumber(10, 18).isLessThanOrEqualTo('i', 36)     // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  isLessThanOrEqualTo(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
+   * otherwise returns `false`.
+   *
+   * ```ts
+   * 0.1 <= (0.3 - 0.2)                  // false
+   * x = new BigNumber(0.1)
+   * x.lte(BigNumber(0.3).minus(0.2))    // true
+   * BigNumber(-1).lte(x)                // true
+   * BigNumber(10, 18).lte('i', 36)      // true
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  lte(n: BigNumberValue, base?: number): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is `NaN`, otherwise returns `false`.
+   *
+   * ```ts
+   * x = new BigNumber(NaN)
+   * x.isNaN()                       // true
+   * y = new BigNumber('Infinity')
+   * y.isNaN()                       // false
+   * ```
+   */
+  isNaN(): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is negative, otherwise returns `false`.
+   *
+   * ```ts
+   * x = new BigNumber(-0)
+   * x.isNegative()                  // true
+   * y = new BigNumber(2)
+   * y.isNegative()                  // false
+   * ```
+   */
+  isNegative(): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is positive, otherwise returns `false`.
+   *
+   * ```ts
+   * x = new BigNumber(-0)
+   * x.isPositive()                  // false
+   * y = new BigNumber(2)
+   * y.isPositive()                  // true
+   * ```
+   */
+  isPositive(): boolean;
+
+  /**
+   * Returns `true` if the value of this BigNumber is zero or minus zero, otherwise returns `false`.
+   *
+   * ```ts
+   * x = new BigNumber(-0)
+   * x.isZero()                 // true
+   * ```
+   */
+  isZero(): boolean;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber minus `n`.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * 0.3 - 0.1                       // 0.19999999999999998
+   * x = new BigNumber(0.3)
+   * x.minus(0.1)                    // '0.2'
+   * x.minus(0.6, 20)                // '0'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  minus(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
+   * remainder of dividing this BigNumber by `n`.
+   *
+   * The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
+   * setting of this BigNumber constructor. If it is 1 (default value), the result will have the
+   * same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
+   * limits of double precision) and BigDecimal's `remainder` method.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * See `MODULO_MODE` for a description of the other modulo modes.
+   *
+   * ```ts
+   * 1 % 0.9                         // 0.09999999999999998
+   * x = new BigNumber(1)
+   * x.modulo(0.9)                   // '0.1'
+   * y = new BigNumber(33)
+   * y.modulo('a', 33)               // '3'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  modulo(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
+   * remainder of dividing this BigNumber by `n`.
+   *
+   * The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
+   * setting of this BigNumber constructor. If it is 1 (default value), the result will have the
+   * same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
+   * limits of double precision) and BigDecimal's `remainder` method.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * See `MODULO_MODE` for a description of the other modulo modes.
+   *
+   * ```ts
+   * 1 % 0.9                      // 0.09999999999999998
+   * x = new BigNumber(1)
+   * x.mod(0.9)                   // '0.1'
+   * y = new BigNumber(33)
+   * y.mod('a', 33)               // '3'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  mod(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * 0.6 * 3                                // 1.7999999999999998
+   * x = new BigNumber(0.6)
+   * y = x.multipliedBy(3)                  // '1.8'
+   * BigNumber('7e+500').multipliedBy(y)    // '1.26e+501'
+   * x.multipliedBy('-a', 16)               // '-6'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  multipliedBy(n: BigNumberValue, base?: number) : BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * 0.6 * 3                         // 1.7999999999999998
+   * x = new BigNumber(0.6)
+   * y = x.times(3)                  // '1.8'
+   * BigNumber('7e+500').times(y)    // '1.26e+501'
+   * x.times('-a', 16)               // '-6'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  times(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by -1.
+   *
+   * ```ts
+   * x = new BigNumber(1.8)
+   * x.negated()                     // '-1.8'
+   * y = new BigNumber(-1.3)
+   * y.negated()                     // '1.3'
+   * ```
+   */
+  negated(): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber plus `n`.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * 0.1 + 0.2                       // 0.30000000000000004
+   * x = new BigNumber(0.1)
+   * y = x.plus(0.2)                 // '0.3'
+   * BigNumber(0.7).plus(x).plus(y)  // '1'
+   * x.plus('0.1', 8)                // '0.225'
+   * ```
+   *
+   * @param n A numeric value.
+   * @param [base] The base of n.
+   */
+  plus(n: BigNumberValue, base?: number): BigNumber;
+
+  /**
+   * Returns the number of significant digits of the value of this BigNumber, or `null` if the value
+   * of this BigNumber is ±`Infinity` or `NaN`.
+   *
+   * If `includeZeros` is true then any trailing zeros of the integer part of the value of this
+   * BigNumber are counted as significant digits, otherwise they are not.
+   *
+   * Throws if `includeZeros` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(9876.54321)
+   * x.precision()                         // 9
+   * y = new BigNumber(987000)
+   * y.precision(false)                    // 3
+   * y.precision(true)                     // 6
+   * ```
+   *
+   * @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
+   */
+  precision(includeZeros?: boolean): number;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
+   * `significantDigits` significant digits using rounding mode `roundingMode`.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
+   *
+   * Throws if `significantDigits` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(9876.54321)
+   * x.precision(6)                         // '9876.54'
+   * x.precision(6, BigNumber.ROUND_UP)     // '9876.55'
+   * x.precision(2)                         // '9900'
+   * x.precision(2, 1)                      // '9800'
+   * x                                      // '9876.54321'
+   * ```
+   *
+   * @param significantDigits Significant digits, integer, 1 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  precision(significantDigits: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+  /**
+   * Returns the number of significant digits of the value of this BigNumber,
+   * or `null` if the value of this BigNumber is ±`Infinity` or `NaN`.
+   *
+   * If `includeZeros` is true then any trailing zeros of the integer part of
+   * the value of this BigNumber are counted as significant digits, otherwise
+   * they are not.
+   *
+   * Throws if `includeZeros` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(9876.54321)
+   * x.sd()                         // 9
+   * y = new BigNumber(987000)
+   * y.sd(false)                    // 3
+   * y.sd(true)                     // 6
+   * ```
+   *
+   * @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
+   */
+  sd(includeZeros?: boolean): number;
+
+  /*
+   * Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
+   * `significantDigits` significant digits using rounding mode `roundingMode`.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
+   *
+   * Throws if `significantDigits` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(9876.54321)
+   * x.sd(6)                           // '9876.54'
+   * x.sd(6, BigNumber.ROUND_UP)       // '9876.55'
+   * x.sd(2)                           // '9900'
+   * x.sd(2, 1)                        // '9800'
+   * x                                 // '9876.54321'
+   * ```
+   *
+   * @param significantDigits Significant digits, integer, 1 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  sd(significantDigits: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the value of this BigNumber shifted by `n` places.
+   *
+   * The shift is of the decimal point, i.e. of powers of ten, and is to the left if `n` is negative
+   * or to the right if `n` is positive.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * Throws if `n` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(1.23)
+   * x.shiftedBy(3)                      // '1230'
+   * x.shiftedBy(-3)                     // '0.00123'
+   * ```
+   *
+   * @param n The shift value, integer, -9007199254740991 to 9007199254740991.
+   */
+  shiftedBy(n: number): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
+   * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+   *
+   * The return value will be correctly rounded, i.e. rounded as if the result was first calculated
+   * to an infinite number of correct digits before rounding.
+   *
+   * ```ts
+   * x = new BigNumber(16)
+   * x.squareRoot()                  // '4'
+   * y = new BigNumber(3)
+   * y.squareRoot()                  // '1.73205080756887729353'
+   * ```
+   */
+  squareRoot(): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
+   * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+   *
+   * The return value will be correctly rounded, i.e. rounded as if the result was first calculated
+   * to an infinite number of correct digits before rounding.
+   *
+   * ```ts
+   * x = new BigNumber(16)
+   * x.sqrt()                  // '4'
+   * y = new BigNumber(3)
+   * y.sqrt()                  // '1.73205080756887729353'
+   * ```
+   */
+  sqrt(): BigNumber;
+
+  /**
+   * Returns a string representing the value of this BigNumber in exponential notation rounded using
+   * rounding mode `roundingMode` to `decimalPlaces` decimal places, i.e with one digit before the
+   * decimal point and `decimalPlaces` digits after it.
+   *
+   * If the value of this BigNumber in exponential notation has fewer than `decimalPlaces` fraction
+   * digits, the return value will be appended with zeros accordingly.
+   *
+   * If `decimalPlaces` is omitted, or is `null` or `undefined`, the number of digits after the
+   * decimal point defaults to the minimum number of digits necessary to represent the value
+   * exactly.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `decimalPlaces` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = 45.6
+   * y = new BigNumber(x)
+   * x.toExponential()               // '4.56e+1'
+   * y.toExponential()               // '4.56e+1'
+   * x.toExponential(0)              // '5e+1'
+   * y.toExponential(0)              // '5e+1'
+   * x.toExponential(1)              // '4.6e+1'
+   * y.toExponential(1)              // '4.6e+1'
+   * y.toExponential(1, 1)           // '4.5e+1'  (ROUND_DOWN)
+   * x.toExponential(3)              // '4.560e+1'
+   * y.toExponential(3)              // '4.560e+1'
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  toExponential(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+  /**
+   * Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+   * rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`.
+   *
+   * If the value of this BigNumber in normal notation has fewer than `decimalPlaces` fraction
+   * digits, the return value will be appended with zeros accordingly.
+   *
+   * Unlike `Number.prototype.toFixed`, which returns exponential notation if a number is greater or
+   * equal to 10**21, this method will always return normal notation.
+   *
+   * If `decimalPlaces` is omitted or is `null` or `undefined`, the return value will be unrounded
+   * and in normal notation. This is also unlike `Number.prototype.toFixed`, which returns the value
+   * to zero decimal places. It is useful when normal notation is required and the current
+   * `EXPONENTIAL_AT` setting causes `toString` to return exponential notation.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `decimalPlaces` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = 3.456
+   * y = new BigNumber(x)
+   * x.toFixed()                     // '3'
+   * y.toFixed()                     // '3.456'
+   * y.toFixed(0)                    // '3'
+   * x.toFixed(2)                    // '3.46'
+   * y.toFixed(2)                    // '3.46'
+   * y.toFixed(2, 1)                 // '3.45'  (ROUND_DOWN)
+   * x.toFixed(5)                    // '3.45600'
+   * y.toFixed(5)                    // '3.45600'
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  toFixed(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+  /**
+   * Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+   * rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`, and formatted
+   * according to the properties of the `FORMAT` object.
+   *
+   * The properties of the `FORMAT` object are shown in the examples below.
+   *
+   * If `decimalPlaces` is omitted or is `null` or `undefined`, then the return value is not
+   * rounded to a fixed number of decimal places.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `decimalPlaces` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * format = {
+   *     decimalSeparator: '.',
+   *     groupSeparator: ',',
+   *     groupSize: 3,
+   *     secondaryGroupSize: 0,
+   *     fractionGroupSeparator: ' ',
+   *     fractionGroupSize: 0
+   * }
+   * BigNumber.config({ FORMAT: format })
+   *
+   * x = new BigNumber('123456789.123456789')
+   * x.toFormat()                    // '123,456,789.123456789'
+   * x.toFormat(1)                   // '123,456,789.1'
+   *
+   * format.groupSeparator = ' '
+   * format.fractionGroupSize = 5
+   * x.toFormat()                    // '123 456 789.12345 6789'
+   *
+   * BigNumber.config({
+   *     FORMAT: {
+   *         decimalSeparator: ',',
+   *         groupSeparator: '.',
+   *         groupSize: 3,
+   *         secondaryGroupSize: 2
+   *     }
+   * })
+   *
+   * x.toFormat(6)                   // '12.34.56.789,123'
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer, 0 to 8.
+   */
+  toFormat(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+  /**
+   * Returns 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 `max_denominator`.
+   *
+   * If a maximum denominator, `max_denominator`, is not specified, or is `null` or `undefined`, the
+   * denominator will be the lowest value necessary to represent the number exactly.
+   *
+   * Throws if `max_denominator` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(1.75)
+   * x.toFraction()                  // '7, 4'
+   *
+   * pi = new BigNumber('3.14159265358')
+   * pi.toFraction()                 // '157079632679,50000000000'
+   * pi.toFraction(100000)           // '312689, 99532'
+   * pi.toFraction(10000)            // '355, 113'
+   * pi.toFraction(100)              // '311, 99'
+   * pi.toFraction(10)               // '22, 7'
+   * pi.toFraction(1)                // '3, 1'
+   * ```
+   *
+   * @param [max_denominator] The maximum denominator, integer, >= 1 and < Infinity.
+   */
+  toFraction(max_denominator?: BigNumberValue): BigNumber[];
+
+  /**
+   * As `valueOf`.
+   */
+  toJSON(): string;
+
+  /**
+   * Returns the value of this BigNumber as a JavaScript primitive number.
+   *
+   * Using the unary plus operator gives the same result.
+   *
+   * ```ts
+   * x = new BigNumber(456.789)
+   * x.toNumber()                    // 456.789
+   * +x                              // 456.789
+   *
+   * y = new BigNumber('45987349857634085409857349856430985')
+   * y.toNumber()                    // 4.598734985763409e+34
+   *
+   * z = new BigNumber(-0)
+   * 1 / z.toNumber()                // -Infinity
+   * 1 / +z                          // -Infinity
+   * ```
+   */
+  toNumber(): number;
+
+  /**
+   * Returns a string representing the value of this BigNumber rounded to `significantDigits`
+   * significant digits using rounding mode `roundingMode`.
+   *
+   * If `significantDigits` is less than the number of digits necessary to represent the integer
+   * part of the value in normal (fixed-point) notation, then exponential notation is used.
+   *
+   * If `significantDigits` is omitted, or is `null` or `undefined`, then the return value is the
+   * same as `n.toString()`.
+   *
+   * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+   *
+   * Throws if `significantDigits` or `roundingMode` is invalid.
+   *
+   * ```ts
+   * x = 45.6
+   * y = new BigNumber(x)
+   * x.toPrecision()                 // '45.6'
+   * y.toPrecision()                 // '45.6'
+   * x.toPrecision(1)                // '5e+1'
+   * y.toPrecision(1)                // '5e+1'
+   * y.toPrecision(2, 0)             // '4.6e+1'  (ROUND_UP)
+   * y.toPrecision(2, 1)             // '4.5e+1'  (ROUND_DOWN)
+   * x.toPrecision(5)                // '45.600'
+   * y.toPrecision(5)                // '45.600'
+   * ```
+   *
+   * @param [significantDigits] Significant digits, integer, 1 to 1e+9.
+   * @param [roundingMode] Rounding mode, integer 0 to 8.
+   */
+  toPrecision(significantDigits?: number, roundingMode?: BigNumberRoundingMode): string;
+
+  /**
+   * Returns a string representing the value of this BigNumber in base `base`, or base 10 if `base`
+   * is omitted or is `null` or `undefined`.
+   *
+   * For bases above 10, and using the default base conversion alphabet (see `ALPHABET`), values
+   * from 10 to 35 are represented by a-z (the same as `Number.prototype.toString`).
+   *
+   * If a base is specified the value is rounded according to the current `DECIMAL_PLACES` and
+   * `ROUNDING_MODE` settings, otherwise it is not.
+   *
+   * If a base is not specified, and this BigNumber has a positive exponent that is equal to or
+   * greater than the positive component of the current `EXPONENTIAL_AT` setting, or a negative
+   * exponent equal to or less than the negative component of the setting, then exponential notation
+   * is returned.
+   *
+   * If `base` is `null` or `undefined` it is ignored.
+   *
+   * Throws if `base` is invalid.
+   *
+   * ```ts
+   * x = new BigNumber(750000)
+   * x.toString()                    // '750000'
+   * BigNumber.config({ EXPONENTIAL_AT: 5 })
+   * x.toString()                    // '7.5e+5'
+   *
+   * y = new BigNumber(362.875)
+   * y.toString(2)                   // '101101010.111'
+   * y.toString(9)                   // '442.77777777777777777778'
+   * y.toString(32)                  // 'ba.s'
+   *
+   * BigNumber.config({ DECIMAL_PLACES: 4 });
+   * z = new BigNumber('1.23456789')
+   * z.toString()                    // '1.23456789'
+   * z.toString(10)                  // '1.2346'
+   * ```
+   *
+   * @param [base] The base, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
+   */
+  toString(base?: number): string;
+
+  /**
+   * As `toString`, but does not accept a base argument and includes the minus sign for negative
+   * zero.
+   *
+   * ``ts
+   * x = new BigNumber('-0')
+   * x.toString()                    // '0'
+   * x.valueOf()                     // '-0'
+   * y = new BigNumber('1.777e+457')
+   * y.valueOf()                     // '1.777e+457'
+   * ```
+   */
+  valueOf(): string;
+
+  /**
+   * Returns a new independent BigNumber constructor with configuration as described by `object`, or
+   * with the default configuration if object is `null` or `undefined`.
+   *
+   * Throws if `object` is not an object.
+   *
+   * ```ts
+   * BigNumber.config({ DECIMAL_PLACES: 5 })
+   * BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
+   *
+   * x = new BigNumber(1)
+   * y = new BN(1)
+   *
+   * x.div(3)                        // 0.33333
+   * y.div(3)                        // 0.333333333
+   *
+   * // BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
+   * BN = BigNumber.clone()
+   * BN.config({ DECIMAL_PLACES: 9 })
+   * ```
+   *
+   * @param [object] The configuration object.
+   */
+  static clone(object?: BigNumberConfig): BigNumberConstructor;
+
+  /**
+   * Configures the settings that apply to this BigNumber constructor.
+   *
+   * The configuration object, `object`, contains any number of the properties shown in the example
+   * below.
+   *
+   * Returns an object with the above properties and their current values.
+   *
+   * Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
+   * properties.
+   *
+   * ```ts
+   * BigNumber.config({
+   *     DECIMAL_PLACES: 40,
+   *     ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
+   *     EXPONENTIAL_AT: [-10, 20],
+   *     RANGE: [-500, 500],
+   *     CRYPTO: true,
+   *     MODULO_MODE: BigNumber.ROUND_FLOOR,
+   *     POW_PRECISION: 80,
+   *     FORMAT: {
+   *         groupSize: 3,
+   *         groupSeparator: ' ',
+   *         decimalSeparator: ','
+   *     },
+   *     ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+   * });
+   *
+   * BigNumber.config().DECIMAL_PLACES        // 40
+   * ```
+   *
+   * @param object The configuration object.
+   */
+  static config(object: BigNumberConfig): BigNumberConfig;
+
+  /**
+   * Returns `true` if `value` is a BigNumber instance, otherwise returns `false`.
+   *
+   * ```ts
+   * x = 42
+   * y = new BigNumber(x)
+   *
+   * BigNumber.isBigNumber(x)             // false
+   * y instanceof BigNumber               // true
+   * BigNumber.isBigNumber(y)             // true
+   *
+   * BN = BigNumber.clone();
+   * z = new BN(x)
+   * z instanceof BigNumber               // false
+   * BigNumber.isBigNumber(z)             // true
+   * ```
+   *
+   * @param value The value to test.
+   */
+  static isBigNumber(value: any): boolean;
+
+  /**
+   *
+   * Returns a BigNumber whose value is the maximum of the arguments.
+   *
+   * Accepts either an argument list or an array of values.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber('3257869345.0378653')
+   * BigNumber.maximum(4e9, x, '123456789.9')      // '4000000000'
+   *
+   * arr = [12, '13', new BigNumber(14)]
+   * BigNumber.maximum(arr)                        // '14'
+   * ```
+   *
+   * @param n A numeric value.
+   */
+  static maximum(...n: BigNumberValue[]): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the maximum of the arguments.
+   *
+   * Accepts either an argument list or an array of values.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber('3257869345.0378653')
+   * BigNumber.max(4e9, x, '123456789.9')      // '4000000000'
+   *
+   * arr = [12, '13', new BigNumber(14)]
+   * BigNumber.max(arr)                        // '14'
+   * ```
+   *
+   * @param n A numeric value.
+   */
+  static max(...n: BigNumberValue[]): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the minimum of the arguments.
+   *
+   * Accepts either an argument list or an array of values.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber('3257869345.0378653')
+   * BigNumber.minimum(4e9, x, '123456789.9')          // '123456789.9'
+   *
+   * arr = [2, new BigNumber(-14), '-15.9999', -12]
+   * BigNumber.minimum(arr)                            // '-15.9999'
+   * ```
+   *
+   * @param n A numeric value.
+   */
+  static minimum(...n: BigNumberValue[]): BigNumber;
+
+  /**
+   * Returns a BigNumber whose value is the minimum of the arguments.
+   *
+   * Accepts either an argument list or an array of values.
+   *
+   * The return value is always exact and unrounded.
+   *
+   * ```ts
+   * x = new BigNumber('3257869345.0378653')
+   * BigNumber.min(4e9, x, '123456789.9')             // '123456789.9'
+   *
+   * arr = [2, new BigNumber(-14), '-15.9999', -12]
+   * BigNumber.min(arr)                               // '-15.9999'
+   * ```
+   *
+   * @param n A numeric value.
+   */
+  static min(...n: BigNumberValue[]): BigNumber;
+
+  /**
+   * Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and less than 1.
+   *
+   * The return value will have `decimalPlaces` decimal places, or less if trailing zeros are
+   * produced. If `decimalPlaces` is omitted, the current `DECIMAL_PLACES` setting will be used.
+   *
+   * Depending on the value of this BigNumber constructor's `CRYPTO` setting and the support for the
+   * `crypto` object in the host environment, the random digits of the return value are generated by
+   * either `Math.random` (fastest), `crypto.getRandomValues` (Web Cryptography API in recent
+   * browsers) or `crypto.randomBytes` (Node.js).
+   *
+   * If `CRYPTO` is true, i.e. one of the `crypto` methods is to be used, the value of a returned
+   * BigNumber should be cryptographically secure and statistically indistinguishable from a random
+   * value.
+   *
+   * Throws if `decimalPlaces` is invalid.
+   *
+   * ```ts
+   * BigNumber.config({ DECIMAL_PLACES: 10 })
+   * BigNumber.random()              // '0.4117936847'
+   * BigNumber.random(20)            // '0.78193327636914089009'
+   * ```
+   *
+   * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+   */
+  static random(decimalPlaces?: number): BigNumber;
+
+  /**
+   * Configures the settings that apply to this BigNumber constructor.
+   *
+   * The configuration object, `object`, contains any number of the properties shown in the example
+   * below.
+   *
+   * Returns an object with the above properties and their current values.
+   *
+   * Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
+   * properties.
+   *
+   * ```ts
+   * BigNumber.set({
+   *     DECIMAL_PLACES: 40,
+   *     ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
+   *     EXPONENTIAL_AT: [-10, 20],
+   *     RANGE: [-500, 500],
+   *     CRYPTO: true,
+   *     MODULO_MODE: BigNumber.ROUND_FLOOR,
+   *     POW_PRECISION: 80,
+   *     FORMAT: {
+   *         groupSize: 3,
+   *         groupSeparator: ' ',
+   *         decimalSeparator: ','
+   *     },
+   *     ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+   * });
+   *
+   * BigNumber.set().DECIMAL_PLACES        // 40
+   * ```
+   *
+   * @param object The configuration object.
+   */
+  static set(object: BigNumberConfig): BigNumberConfig;
+
+  /**
+   * Helps ES6 import.
+   */
+  private static readonly default?: BigNumberConstructor;
+
+  /**
+   * Helps ES6 import.
+   */
+  private static readonly BigNumber?: BigNumberConstructor;
+
+  /**
+   * Rounds away from zero.
+   */
+  static readonly ROUND_UP: 0;
+
+  /**
+   * Rounds towards zero.
+   */
+  static readonly ROUND_DOWN: 1;
+
+  /**
+   * Rounds towards Infinity.
+   */
+  static readonly ROUND_CEIL: 2;
+
+  /**
+   * Rounds towards -Infinity.
+   */
+  static readonly ROUND_FLOOR: 3;
+
+  /**
+   * Rounds towards nearest neighbour. If equidistant, rounds away from zero .
+   */
+  static readonly ROUND_HALF_UP: 4;
+
+  /**
+   * Rounds towards nearest neighbour. If equidistant, rounds towards zero.
+   */
+  static readonly ROUND_HALF_DOWN: 5;
+
+  /**
+   * Rounds towards nearest neighbour. If equidistant, rounds towards even neighbour.
+   */
+  static readonly ROUND_HALF_EVEN: 6;
+
+  /**
+   * Rounds towards nearest neighbour. If equidistant, rounds towards Infinity.
+   */
+  static readonly ROUND_HALF_CEIL: 7;
+
+  /**
+   * Rounds towards nearest neighbour. If equidistant, rounds towards -Infinity.
+   */
+  static readonly ROUND_HALF_FLOOR: 8;
+
+  /**
+   * See `MODULO_MODE`.
+   */
+  static readonly EUCLID: 9;
+}
+
+
+export default BigNumber;
+
+export namespace BigNumber {
+  export type Config = BigNumberConfig;
+  export type Constructor = BigNumberConstructor;
+  export type Format = BigNumberFormat;
+  export type Instance = BigNumberInstance;
+  export type ModuloMode = BigNumberModuloMode;
+  export type RoundingMode = BigNumberRoundingMode;
+  export type Value = BigNumberValue;
+}
+
+/**
+ * Browsers.
+ */
+declare global {
+  const BigNumber: BigNumberConstructor;
+  type BigNumber = BigNumberInstance;
+
+  namespace BigNumber {
+    type Config = BigNumberConfig;
+    type Constructor = BigNumberConstructor;
+    type Format = BigNumberFormat;
+    type Instance = BigNumberInstance;
+    type ModuloMode = BigNumberModuloMode;
+    type RoundingMode = BigNumberRoundingMode;
+    type Value = BigNumberValue;
+  }
+}
\ No newline at end of file
diff --git a/packages/instant/test/util/dependencies/prevbignumber.js b/packages/instant/test/util/dependencies/prevbignumber.js
new file mode 100644
index 000000000..e2d3f2146
--- /dev/null
+++ b/packages/instant/test/util/dependencies/prevbignumber.js
@@ -0,0 +1,2705 @@
+/*
+ *      bignumber.js v6.0.0
+ *      A JavaScript library for arbitrary-precision arithmetic.
+ *      https://github.com/MikeMcl/bignumber.js
+ *      Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
+ *      MIT Licensed.
+ *
+ *      BigNumber.prototype methods     |  BigNumber methods
+ *                                      |
+ *      absoluteValue            abs    |  clone
+ *      comparedTo                      |  config               set
+ *      decimalPlaces            dp     |      DECIMAL_PLACES
+ *      dividedBy                div    |      ROUNDING_MODE
+ *      dividedToIntegerBy       idiv   |      EXPONENTIAL_AT
+ *      exponentiatedBy          pow    |      RANGE
+ *      integerValue                    |      CRYPTO
+ *      isEqualTo                eq     |      MODULO_MODE
+ *      isFinite                        |      POW_PRECISION
+ *      isGreaterThan            gt     |      FORMAT
+ *      isGreaterThanOrEqualTo   gte    |      ALPHABET
+ *      isInteger                       |  isBigNumber
+ *      isLessThan               lt     |  maximum              max
+ *      isLessThanOrEqualTo      lte    |  minimum              min
+ *      isNaN                           |  random
+ *      isNegative                      |
+ *      isPositive                      |
+ *      isZero                          |
+ *      minus                           |
+ *      modulo                   mod    |
+ *      multipliedBy             times  |
+ *      negated                         |
+ *      plus                            |
+ *      precision                sd     |
+ *      shiftedBy                       |
+ *      squareRoot               sqrt   |
+ *      toExponential                   |
+ *      toFixed                         |
+ *      toFormat                        |
+ *      toFraction                      |
+ *      toJSON                          |
+ *      toNumber                        |
+ *      toPrecision                     |
+ *      toString                        |
+ *      valueOf                         |
+ *
+ */
+
+
+var BigNumber,
+    isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
+
+    mathceil = Math.ceil,
+    mathfloor = Math.floor,
+
+    bignumberError = '[BigNumber Error] ',
+    tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
+
+    BASE = 1e14,
+    LOG_BASE = 14,
+    MAX_SAFE_INTEGER = 0x1fffffffffffff,         // 2^53 - 1
+    // MAX_INT32 = 0x7fffffff,                   // 2^31 - 1
+    POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
+    SQRT_BASE = 1e7,
+
+    // EDITABLE
+    // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
+    // the arguments to toExponential, toFixed, toFormat, and toPrecision.
+    MAX = 1E9;                                   // 0 to MAX_INT32
+
+
+/*
+ * Create and return a BigNumber constructor.
+ */
+function clone(configObject) {
+    var div, convertBase, parseNumeric,
+        P = BigNumber.prototype,
+        ONE = new BigNumber(1),
+
+
+        //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
+
+
+        // The default values below must be integers within the inclusive ranges stated.
+        // The values can also be changed at run-time using BigNumber.set.
+
+        // 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
+        // toExponential, toFixed, toFormat and toPrecision, 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 = -1e7,                          // -1 to -MAX
+
+        // The maximum exponent value, above which overflow to Infinity occurs.
+        // Number type:  308  (1.7976931348623157e+308)
+        // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
+        MAX_EXP = 1e7,                           // 1 to MAX
+
+        // Whether to use cryptographically-secure random number generation, if available.
+        CRYPTO = false,                          // true or false
+
+        // The modulo mode used when calculating the modulus: a mod n.
+        // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
+        // The remainder (r) is calculated as: r = a - n * q.
+        //
+        // UP        0 The remainder is positive if the dividend is negative, else is negative.
+        // DOWN      1 The remainder has the same sign as the dividend.
+        //             This modulo mode is commonly known as 'truncated division' and is
+        //             equivalent to (a % n) in JavaScript.
+        // FLOOR     3 The remainder has the same sign as the divisor (Python %).
+        // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
+        // EUCLID    9 Euclidian division. q = sign(n) * floor(a / abs(n)).
+        //             The remainder is always positive.
+        //
+        // The truncated division, floored division, Euclidian division and IEEE 754 remainder
+        // modes are commonly used for the modulus operation.
+        // Although the other rounding modes can also be used, they may not give useful results.
+        MODULO_MODE = 1,                         // 0 to 9
+
+        // The maximum number of significant digits of the result of the exponentiatedBy operation.
+        // If POW_PRECISION is 0, there will be unlimited significant digits.
+        POW_PRECISION = 0,                    // 0 to MAX
+
+        // The format specification used by the BigNumber.prototype.toFormat method.
+        FORMAT = {
+            decimalSeparator: '.',
+            groupSeparator: ',',
+            groupSize: 3,
+            secondaryGroupSize: 0,
+            fractionGroupSeparator: '\xA0',      // non-breaking space
+            fractionGroupSize: 0
+        },
+
+        // The alphabet used for base conversion.
+        // It must be at least 2 characters long, with no '.' or repeated character.
+        // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+        ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+
+
+    //------------------------------------------------------------------------------------------
+
+
+    // CONSTRUCTOR
+
+
+    /*
+     * The BigNumber constructor and 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 ALPHABET.length inclusive.
+     */
+    function BigNumber( n, b ) {
+        var alphabet, c, e, i, isNum, len, str,
+            x = this;
+
+        // Enable constructor usage without new.
+        if ( !( x instanceof BigNumber ) ) {
+
+            // Don't throw on constructor call without new (#81).
+            // '[BigNumber Error] Constructor call without new: {n}'
+            //throw Error( bignumberError + ' Constructor call without new: ' + n );
+            return new BigNumber( n, b );
+        }
+
+        if ( b == null ) {
+
+            // Duplicate.
+            if ( n instanceof BigNumber ) {
+                x.s = n.s;
+                x.e = n.e;
+                x.c = ( n = n.c ) ? n.slice() : n;
+                return;
+            }
+
+            isNum = typeof n == 'number';
+
+            if ( isNum && n * 0 == 0 ) {
+
+                // Use `1 / n` to handle minus zero also.
+                x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;
+
+                // Faster path for integers.
+                if ( n === ~~n ) {
+                    for ( e = 0, i = n; i >= 10; i /= 10, e++ );
+                    x.e = e;
+                    x.c = [n];
+                    return;
+                }
+
+                str = n + '';
+            } else {
+                if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, isNum );
+                x.s = str.charCodeAt(0) == 45 ? ( str = str.slice(1), -1 ) : 1;
+            }
+
+        } else {
+
+            // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+            intCheck( b, 2, ALPHABET.length, 'Base' );
+            str = n + '';
+
+            // Allow exponential notation to be used with base 10 argument, while
+            // also rounding to DECIMAL_PLACES as with other bases.
+            if ( b == 10 ) {
+                x = new BigNumber( n instanceof BigNumber ? n : str );
+                return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
+            }
+
+            isNum = typeof n == 'number';
+
+            if (isNum) {
+
+                // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+                if ( n * 0 != 0 ) return parseNumeric( x, str, isNum, b );
+
+                x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;
+
+                // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+                if ( str.replace( /^0\.0*|\./, '' ).length > 15 ) {
+                    throw Error
+                      ( tooManyDigits + n );
+                }
+
+                // Prevent later check for length on converted number.
+                isNum = false;
+            } else {
+                x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
+
+                // Allow e.g. hexadecimal 'FF' as well as 'ff'.
+                if ( b > 10 && b < 37 ) str = str.toLowerCase();
+            }
+
+            alphabet = ALPHABET.slice( 0, b );
+            e = i = 0;
+
+            // Check that str is a valid base b number.
+            // Don't use RegExp so alphabet can contain special characters.
+            for ( len = str.length; i < len; i++ ) {
+                if ( alphabet.indexOf( c = str.charAt(i) ) < 0 ) {
+                    if ( c == '.' ) {
+
+                        // If '.' is not the first character and it has not be found before.
+                        if ( i > e ) {
+                            e = len;
+                            continue;
+                        }
+                    }
+
+                    return parseNumeric( x, n + '', isNum, b );
+                }
+            }
+
+            str = convertBase( str, b, 10, x.s );
+        }
+
+        // Decimal point?
+        if ( ( e = str.indexOf('.') ) > -1 ) str = str.replace( '.', '' );
+
+        // Exponential form?
+        if ( ( i = str.search( /e/i ) ) > 0 ) {
+
+            // Determine exponent.
+            if ( e < 0 ) e = i;
+            e += +str.slice( i + 1 );
+            str = str.substring( 0, i );
+        } else if ( e < 0 ) {
+
+            // Integer.
+            e = str.length;
+        }
+
+        // Determine leading zeros.
+        for ( i = 0; str.charCodeAt(i) === 48; i++ );
+
+        // Determine trailing zeros.
+        for ( len = str.length; str.charCodeAt(--len) === 48; );
+        str = str.slice( i, len + 1 );
+
+        if (str) {
+            len = str.length;
+
+            // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+            if ( isNum && len > 15 && ( n > MAX_SAFE_INTEGER || n !== mathfloor(n) ) ) {
+                throw Error
+                  ( tooManyDigits + ( x.s * n ) );
+            }
+
+            e = e - i - 1;
+
+             // Overflow?
+            if ( e > MAX_EXP ) {
+
+                // Infinity.
+                x.c = x.e = null;
+
+            // Underflow?
+            } else if ( e < MIN_EXP ) {
+
+                // Zero.
+                x.c = [ x.e = 0 ];
+            } else {
+                x.e = e;
+                x.c = [];
+
+                // Transform base
+
+                // e is the base 10 exponent.
+                // i is where to slice str to get the first element of the coefficient array.
+                i = ( e + 1 ) % LOG_BASE;
+                if ( e < 0 ) i += LOG_BASE;
+
+                if ( i < len ) {
+                    if (i) x.c.push( +str.slice( 0, i ) );
+
+                    for ( len -= LOG_BASE; i < len; ) {
+                        x.c.push( +str.slice( i, i += LOG_BASE ) );
+                    }
+
+                    str = str.slice(i);
+                    i = LOG_BASE - str.length;
+                } else {
+                    i -= len;
+                }
+
+                for ( ; i--; str += '0' );
+                x.c.push( +str );
+            }
+        } else {
+
+            // Zero.
+            x.c = [ x.e = 0 ];
+        }
+    }
+
+
+    // CONSTRUCTOR PROPERTIES
+
+
+    BigNumber.clone = clone;
+
+    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;
+    BigNumber.EUCLID = 9;
+
+
+    /*
+     * Configure infrequently-changing library-wide settings.
+     *
+     * Accept an object with the following optional properties (if the value of a property is
+     * a number, it must be an integer within the inclusive range stated):
+     *
+     *   DECIMAL_PLACES   {number}           0 to MAX
+     *   ROUNDING_MODE    {number}           0 to 8
+     *   EXPONENTIAL_AT   {number|number[]}  -MAX to MAX  or  [-MAX to 0, 0 to MAX]
+     *   RANGE            {number|number[]}  -MAX to MAX (not zero)  or  [-MAX to -1, 1 to MAX]
+     *   CRYPTO           {boolean}          true or false
+     *   MODULO_MODE      {number}           0 to 9
+     *   POW_PRECISION       {number}           0 to MAX
+     *   ALPHABET         {string}           A string of two or more unique characters, and not
+     *                                       containing '.'. The empty string, null or undefined
+     *                                       resets the alphabet to its default value.
+     *   FORMAT           {object}           An object with some of the following properties:
+     *      decimalSeparator       {string}
+     *      groupSeparator         {string}
+     *      groupSize              {number}
+     *      secondaryGroupSize     {number}
+     *      fractionGroupSeparator {string}
+     *      fractionGroupSize      {number}
+     *
+     * (The values assigned to the above FORMAT object properties are not checked for validity.)
+     *
+     * E.g.
+     * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+     *
+     * Ignore properties/parameters set to null or undefined, except for ALPHABET.
+     *
+     * Return an object with the properties current values.
+     */
+    BigNumber.config = BigNumber.set = function (obj) {
+        var p, v;
+
+        if ( obj != null ) {
+
+            if ( typeof obj == 'object' ) {
+
+                // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+                // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
+                if ( obj.hasOwnProperty( p = 'DECIMAL_PLACES' ) ) {
+                    v = obj[p];
+                    intCheck( v, 0, MAX, p );
+                    DECIMAL_PLACES = v;
+                }
+
+                // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+                // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
+                if ( obj.hasOwnProperty( p = 'ROUNDING_MODE' ) ) {
+                    v = obj[p];
+                    intCheck( v, 0, 8, p );
+                    ROUNDING_MODE = v;
+                }
+
+                // EXPONENTIAL_AT {number|number[]}
+                // Integer, -MAX to MAX inclusive or
+                // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+                // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
+                if ( obj.hasOwnProperty( p = 'EXPONENTIAL_AT' ) ) {
+                    v = obj[p];
+                    if ( isArray(v) ) {
+                        intCheck( v[0], -MAX, 0, p );
+                        intCheck( v[1], 0, MAX, p );
+                        TO_EXP_NEG = v[0];
+                        TO_EXP_POS = v[1];
+                    } else {
+                        intCheck( v, -MAX, MAX, p );
+                        TO_EXP_NEG = -( TO_EXP_POS = v < 0 ? -v : v );
+                    }
+                }
+
+                // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+                // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+                // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
+                if ( obj.hasOwnProperty( p = 'RANGE' ) ) {
+                    v = obj[p];
+                    if ( isArray(v) ) {
+                        intCheck( v[0], -MAX, -1, p );
+                        intCheck( v[1], 1, MAX, p );
+                        MIN_EXP = v[0];
+                        MAX_EXP = v[1];
+                    } else {
+                        intCheck( v, -MAX, MAX, p );
+                        if (v) {
+                            MIN_EXP = -( MAX_EXP = v < 0 ? -v : v );
+                        } else {
+                            throw Error
+                              ( bignumberError + p + ' cannot be zero: ' + v );
+                        }
+                    }
+                }
+
+                // CRYPTO {boolean} true or false.
+                // '[BigNumber Error] CRYPTO not true or false: {v}'
+                // '[BigNumber Error] crypto unavailable'
+                if ( obj.hasOwnProperty( p = 'CRYPTO' ) ) {
+                    v = obj[p];
+                    if ( v === !!v ) {
+                        if (v) {
+                            if ( typeof crypto != 'undefined' && crypto &&
+                              (crypto.getRandomValues || crypto.randomBytes) ) {
+                                CRYPTO = v;
+                            } else {
+                                CRYPTO = !v;
+                                throw Error
+                                  ( bignumberError + 'crypto unavailable' );
+                            }
+                        } else {
+                            CRYPTO = v;
+                        }
+                    } else {
+                        throw Error
+                          ( bignumberError + p + ' not true or false: ' + v );
+                    }
+                }
+
+                // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+                // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
+                if ( obj.hasOwnProperty( p = 'MODULO_MODE' ) ) {
+                    v = obj[p];
+                    intCheck( v, 0, 9, p );
+                    MODULO_MODE = v;
+                }
+
+                // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+                // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
+                if ( obj.hasOwnProperty( p = 'POW_PRECISION' ) ) {
+                    v = obj[p];
+                    intCheck( v, 0, MAX, p );
+                    POW_PRECISION = v;
+                }
+
+                // FORMAT {object}
+                // '[BigNumber Error] FORMAT not an object: {v}'
+                if ( obj.hasOwnProperty( p = 'FORMAT' ) ) {
+                    v = obj[p];
+                    if ( typeof v == 'object' ) FORMAT = v;
+                    else throw Error
+                      ( bignumberError + p + ' not an object: ' + v );
+                }
+
+                // ALPHABET {string}
+                // '[BigNumber Error] ALPHABET invalid: {v}'
+                if ( obj.hasOwnProperty( p = 'ALPHABET' ) ) {
+                    v = obj[p];
+
+                    // Disallow if only one character, or contains '.' or a repeated character.
+                    if ( typeof v == 'string' && !/^.$|\.|(.).*\1/.test(v) ) {
+                        ALPHABET = v;
+                    } else {
+                        throw Error
+                          ( bignumberError + p + ' invalid: ' + v );
+                    }
+                }
+
+            } else {
+
+                // '[BigNumber Error] Object expected: {v}'
+                throw Error
+                  ( bignumberError + 'Object expected: ' + obj );
+            }
+        }
+
+        return {
+            DECIMAL_PLACES: DECIMAL_PLACES,
+            ROUNDING_MODE: ROUNDING_MODE,
+            EXPONENTIAL_AT: [ TO_EXP_NEG, TO_EXP_POS ],
+            RANGE: [ MIN_EXP, MAX_EXP ],
+            CRYPTO: CRYPTO,
+            MODULO_MODE: MODULO_MODE,
+            POW_PRECISION: POW_PRECISION,
+            FORMAT: FORMAT,
+            ALPHABET: ALPHABET
+        };
+    };
+
+
+    /*
+     * Return true if v is a BigNumber instance, otherwise return false.
+     *
+     * v {any}
+     */
+    BigNumber.isBigNumber = function (v) {
+        return v instanceof BigNumber || v && v._isBigNumber === true || false;
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the maximum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.maximum = BigNumber.max = function () {
+        return maxOrMin( arguments, P.lt );
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the minimum of the arguments.
+     *
+     * arguments {number|string|BigNumber}
+     */
+    BigNumber.minimum = BigNumber.min = function () {
+        return maxOrMin( arguments, P.gt );
+    };
+
+
+    /*
+     * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+     * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+     * zeros are produced).
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
+     * '[BigNumber Error] crypto unavailable'
+     */
+    BigNumber.random = (function () {
+        var pow2_53 = 0x20000000000000;
+
+        // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+        // Check if Math.random() produces more than 32 bits of randomness.
+        // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+        // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+        var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+          ? function () { return mathfloor( Math.random() * pow2_53 ); }
+          : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+              (Math.random() * 0x800000 | 0); };
+
+        return function (dp) {
+            var a, b, e, k, v,
+                i = 0,
+                c = [],
+                rand = new BigNumber(ONE);
+
+            if ( dp == null ) dp = DECIMAL_PLACES;
+            else intCheck( dp, 0, MAX );
+
+            k = mathceil( dp / LOG_BASE );
+
+            if (CRYPTO) {
+
+                // Browsers supporting crypto.getRandomValues.
+                if (crypto.getRandomValues) {
+
+                    a = crypto.getRandomValues( new Uint32Array( k *= 2 ) );
+
+                    for ( ; i < k; ) {
+
+                        // 53 bits:
+                        // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+                        // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+                        // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+                        //                                     11111 11111111 11111111
+                        // 0x20000 is 2^21.
+                        v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+
+                        // Rejection sampling:
+                        // 0 <= v < 9007199254740992
+                        // Probability that v >= 9e15, is
+                        // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+                        if ( v >= 9e15 ) {
+                            b = crypto.getRandomValues( new Uint32Array(2) );
+                            a[i] = b[0];
+                            a[i + 1] = b[1];
+                        } else {
+
+                            // 0 <= v <= 8999999999999999
+                            // 0 <= (v % 1e14) <= 99999999999999
+                            c.push( v % 1e14 );
+                            i += 2;
+                        }
+                    }
+                    i = k / 2;
+
+                // Node.js supporting crypto.randomBytes.
+                } else if (crypto.randomBytes) {
+
+                    // buffer
+                    a = crypto.randomBytes( k *= 7 );
+
+                    for ( ; i < k; ) {
+
+                        // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+                        // 0x100000000 is 2^32, 0x1000000 is 2^24
+                        // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+                        // 0 <= v < 9007199254740992
+                        v = ( ( a[i] & 31 ) * 0x1000000000000 ) + ( a[i + 1] * 0x10000000000 ) +
+                              ( a[i + 2] * 0x100000000 ) + ( a[i + 3] * 0x1000000 ) +
+                              ( a[i + 4] << 16 ) + ( a[i + 5] << 8 ) + a[i + 6];
+
+                        if ( v >= 9e15 ) {
+                            crypto.randomBytes(7).copy( a, i );
+                        } else {
+
+                            // 0 <= (v % 1e14) <= 99999999999999
+                            c.push( v % 1e14 );
+                            i += 7;
+                        }
+                    }
+                    i = k / 7;
+                } else {
+                    CRYPTO = false;
+                    throw Error
+                      ( bignumberError + 'crypto unavailable' );
+                }
+            }
+
+            // Use Math.random.
+            if (!CRYPTO) {
+
+                for ( ; i < k; ) {
+                    v = random53bitInt();
+                    if ( v < 9e15 ) c[i++] = v % 1e14;
+                }
+            }
+
+            k = c[--i];
+            dp %= LOG_BASE;
+
+            // Convert trailing digits to zeros according to dp.
+            if ( k && dp ) {
+                v = POWS_TEN[LOG_BASE - dp];
+                c[i] = mathfloor( k / v ) * v;
+            }
+
+            // Remove trailing elements which are zero.
+            for ( ; c[i] === 0; c.pop(), i-- );
+
+            // Zero?
+            if ( i < 0 ) {
+                c = [ e = 0 ];
+            } else {
+
+                // Remove leading elements which are zero and adjust exponent accordingly.
+                for ( e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+
+                // Count the digits of the first element of c to determine leading zeros, and...
+                for ( i = 1, v = c[0]; v >= 10; v /= 10, i++);
+
+                // adjust the exponent accordingly.
+                if ( i < LOG_BASE ) e -= LOG_BASE - i;
+            }
+
+            rand.e = e;
+            rand.c = c;
+            return rand;
+        };
+    })();
+
+
+    // PRIVATE FUNCTIONS
+
+
+    // Called by BigNumber and BigNumber.prototype.toString.
+    convertBase = ( function () {
+        var decimal = '0123456789';
+
+        /*
+         * Convert string of baseIn to an array of numbers of baseOut.
+         * Eg. toBaseOut('255', 10, 16) returns [15, 15].
+         * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
+         */
+        function toBaseOut( str, baseIn, baseOut, alphabet ) {
+            var j,
+                arr = [0],
+                arrL,
+                i = 0,
+                len = str.length;
+
+            for ( ; i < len; ) {
+                for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );
+
+                arr[0] += alphabet.indexOf( str.charAt( i++ ) );
+
+                for ( 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 a numeric string of baseIn to a numeric string of baseOut.
+        // If the caller is toString, we are converting from base 10 to baseOut.
+        // If the caller is BigNumber, we are converting from baseIn to base 10.
+        return function ( str, baseIn, baseOut, sign, callerIsToString ) {
+            var alphabet, d, e, k, r, x, xc, y,
+                i = str.indexOf( '.' ),
+                dp = DECIMAL_PLACES,
+                rm = ROUNDING_MODE;
+
+            // Non-integer.
+            if ( i >= 0 ) {
+                k = POW_PRECISION;
+
+                // Unlimited precision.
+                POW_PRECISION = 0;
+                str = str.replace( '.', '' );
+                y = new BigNumber(baseIn);
+                x = y.pow( str.length - i );
+                POW_PRECISION = k;
+
+                // Convert str as if an integer, then restore the fraction part by dividing the
+                // result by its base raised to a power.
+
+                y.c = toBaseOut( toFixedPoint( coeffToString( x.c ), x.e, '0' ),
+                  10, baseOut, decimal );
+                y.e = y.c.length;
+            }
+
+            // Convert the number as integer.
+
+            xc = toBaseOut( str, baseIn, baseOut, callerIsToString
+              ? ( alphabet = ALPHABET, decimal )
+              : ( alphabet = decimal, ALPHABET ) );
+
+
+            // xc now represents str as an integer and converted to baseOut. e is the exponent.
+            e = k = xc.length;
+
+            // Remove trailing zeros.
+            for ( ; xc[--k] == 0; xc.pop() );
+
+            // Zero?
+            if ( !xc[0] ) return alphabet.charAt(0);
+
+            // Does str represent an integer? If so, no need for the division.
+            if ( i < 0 ) {
+                --e;
+            } else {
+                x.c = xc;
+                x.e = e;
+
+                // The sign is needed for correct rounding.
+                x.s = sign;
+                x = div( x, y, dp, rm, baseOut );
+                xc = x.c;
+                r = x.r;
+                e = x.e;
+            }
+
+            // xc now represents str converted to baseOut.
+
+            // THe index of the rounding digit.
+            d = e + dp + 1;
+
+            // The rounding digit: the digit to the right of the digit that may be rounded up.
+            i = xc[d];
+
+            // Look at the rounding digits and mode to determine whether to round up.
+
+            k = baseOut / 2;
+            r = r || d < 0 || xc[d + 1] != null;
+
+            r = rm < 4 ? ( i != null || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+                       : i > k || i == k &&( rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+                         rm == ( x.s < 0 ? 8 : 7 ) );
+
+            // If the index of the rounding digit is not greater than zero, or xc represents
+            // zero, then the result of the base conversion is zero or, if rounding up, a value
+            // such as 0.00001.
+            if ( d < 1 || !xc[0] ) {
+
+                // 1^-dp or 0
+                str = r ? toFixedPoint( alphabet.charAt(1), -dp, alphabet.charAt(0) )
+                        : alphabet.charAt(0);
+            } else {
+
+                // Truncate xc to the required number of decimal places.
+                xc.length = d;
+
+                // Round up?
+                if (r) {
+
+                    // Rounding up may mean the previous digit has to be rounded up and so on.
+                    for ( --baseOut; ++xc[--d] > baseOut; ) {
+                        xc[d] = 0;
+
+                        if ( !d ) {
+                            ++e;
+                            xc = [1].concat(xc);
+                        }
+                    }
+                }
+
+                // Determine trailing zeros.
+                for ( k = xc.length; !xc[--k]; );
+
+                // E.g. [4, 11, 15] becomes 4bf.
+                for ( i = 0, str = ''; i <= k; str += alphabet.charAt( xc[i++] ) );
+
+                // Add leading zeros, decimal point and trailing zeros as required.
+                str = toFixedPoint( str, e, alphabet.charAt(0) );
+            }
+
+            // The caller will add the sign.
+            return str;
+        };
+    })();
+
+
+    // Perform division in the specified base. Called by div and convertBase.
+    div = (function () {
+
+        // Assume non-zero x and k.
+        function multiply( x, k, base ) {
+            var m, temp, xlo, xhi,
+                carry = 0,
+                i = x.length,
+                klo = k % SQRT_BASE,
+                khi = k / SQRT_BASE | 0;
+
+            for ( x = x.slice(); i--; ) {
+                xlo = x[i] % SQRT_BASE;
+                xhi = x[i] / SQRT_BASE | 0;
+                m = khi * xlo + xhi * klo;
+                temp = klo * xlo + ( ( m % SQRT_BASE ) * SQRT_BASE ) + carry;
+                carry = ( temp / base | 0 ) + ( m / SQRT_BASE | 0 ) + khi * xhi;
+                x[i] = temp % base;
+            }
+
+            if (carry) x = [carry].concat(x);
+
+            return x;
+        }
+
+        function compare( a, b, aL, bL ) {
+            var i, cmp;
+
+            if ( aL != bL ) {
+                cmp = aL > bL ? 1 : -1;
+            } else {
+
+                for ( i = cmp = 0; i < aL; i++ ) {
+
+                    if ( a[i] != b[i] ) {
+                        cmp = a[i] > b[i] ? 1 : -1;
+                        break;
+                    }
+                }
+            }
+            return cmp;
+        }
+
+        function subtract( a, b, aL, base ) {
+            var i = 0;
+
+            // Subtract b from a.
+            for ( ; aL--; ) {
+                a[aL] -= i;
+                i = a[aL] < b[aL] ? 1 : 0;
+                a[aL] = i * base + a[aL] - b[aL];
+            }
+
+            // Remove leading zeros.
+            for ( ; !a[0] && a.length > 1; a.splice(0, 1) );
+        }
+
+        // x: dividend, y: divisor.
+        return function ( x, y, dp, rm, base ) {
+            var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+                yL, yz,
+                s = x.s == y.s ? 1 : -1,
+                xc = x.c,
+                yc = y.c;
+
+            // Either NaN, Infinity or 0?
+            if ( !xc || !xc[0] || !yc || !yc[0] ) {
+
+                return new BigNumber(
+
+                  // Return NaN if either NaN, or both Infinity or 0.
+                  !x.s || !y.s || ( xc ? yc && xc[0] == yc[0] : !yc ) ? NaN :
+
+                    // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+                    xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+                );
+            }
+
+            q = new BigNumber(s);
+            qc = q.c = [];
+            e = x.e - y.e;
+            s = dp + e + 1;
+
+            if ( !base ) {
+                base = BASE;
+                e = bitFloor( x.e / LOG_BASE ) - bitFloor( y.e / LOG_BASE );
+                s = s / LOG_BASE | 0;
+            }
+
+            // Result exponent may be one less then the current value of e.
+            // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+            for ( i = 0; yc[i] == ( xc[i] || 0 ); i++ );
+
+            if ( yc[i] > ( xc[i] || 0 ) ) e--;
+
+            if ( s < 0 ) {
+                qc.push(1);
+                more = true;
+            } else {
+                xL = xc.length;
+                yL = yc.length;
+                i = 0;
+                s += 2;
+
+                // Normalise xc and yc so highest order digit of yc is >= base / 2.
+
+                n = mathfloor( base / ( yc[0] + 1 ) );
+
+                // Not necessary, but to handle odd bases where yc[0] == ( base / 2 ) - 1.
+                // if ( n > 1 || n++ == 1 && yc[0] < base / 2 ) {
+                if ( n > 1 ) {
+                    yc = multiply( yc, n, base );
+                    xc = multiply( xc, n, base );
+                    yL = yc.length;
+                    xL = xc.length;
+                }
+
+                xi = yL;
+                rem = xc.slice( 0, yL );
+                remL = rem.length;
+
+                // Add zeros to make remainder as long as divisor.
+                for ( ; remL < yL; rem[remL++] = 0 );
+                yz = yc.slice();
+                yz = [0].concat(yz);
+                yc0 = yc[0];
+                if ( yc[1] >= base / 2 ) yc0++;
+                // Not necessary, but to prevent trial digit n > base, when using base 3.
+                // else if ( base == 3 && yc0 == 1 ) yc0 = 1 + 1e-15;
+
+                do {
+                    n = 0;
+
+                    // Compare divisor and remainder.
+                    cmp = compare( yc, rem, yL, remL );
+
+                    // If divisor < remainder.
+                    if ( cmp < 0 ) {
+
+                        // Calculate trial digit, n.
+
+                        rem0 = rem[0];
+                        if ( yL != remL ) rem0 = rem0 * base + ( rem[1] || 0 );
+
+                        // n is how many times the divisor goes into the current remainder.
+                        n = mathfloor( rem0 / yc0 );
+
+                        //  Algorithm:
+                        //  1. product = divisor * trial digit (n)
+                        //  2. if product > remainder: product -= divisor, n--
+                        //  3. remainder -= product
+                        //  4. if product was < remainder at 2:
+                        //    5. compare new remainder and divisor
+                        //    6. If remainder > divisor: remainder -= divisor, n++
+
+                        if ( n > 1 ) {
+
+                            // n may be > base only when base is 3.
+                            if (n >= base) n = base - 1;
+
+                            // product = divisor * trial digit.
+                            prod = multiply( yc, n, base );
+                            prodL = prod.length;
+                            remL = rem.length;
+
+                            // Compare product and remainder.
+                            // If product > remainder.
+                            // Trial digit n too high.
+                            // n is 1 too high about 5% of the time, and is not known to have
+                            // ever been more than 1 too high.
+                            while ( compare( prod, rem, prodL, remL ) == 1 ) {
+                                n--;
+
+                                // Subtract divisor from product.
+                                subtract( prod, yL < prodL ? yz : yc, prodL, base );
+                                prodL = prod.length;
+                                cmp = 1;
+                            }
+                        } else {
+
+                            // n is 0 or 1, cmp is -1.
+                            // If n is 0, there is no need to compare yc and rem again below,
+                            // so change cmp to 1 to avoid it.
+                            // If n is 1, leave cmp as -1, so yc and rem are compared again.
+                            if ( n == 0 ) {
+
+                                // divisor < remainder, so n must be at least 1.
+                                cmp = n = 1;
+                            }
+
+                            // product = divisor
+                            prod = yc.slice();
+                            prodL = prod.length;
+                        }
+
+                        if ( prodL < remL ) prod = [0].concat(prod);
+
+                        // Subtract product from remainder.
+                        subtract( rem, prod, remL, base );
+                        remL = rem.length;
+
+                         // If product was < remainder.
+                        if ( cmp == -1 ) {
+
+                            // Compare divisor and new remainder.
+                            // If divisor < new remainder, subtract divisor from remainder.
+                            // Trial digit n too low.
+                            // n is 1 too low about 5% of the time, and very rarely 2 too low.
+                            while ( compare( yc, rem, yL, remL ) < 1 ) {
+                                n++;
+
+                                // Subtract divisor from remainder.
+                                subtract( rem, yL < remL ? yz : yc, remL, base );
+                                remL = rem.length;
+                            }
+                        }
+                    } else if ( cmp === 0 ) {
+                        n++;
+                        rem = [0];
+                    } // else cmp === 1 and n will be 0
+
+                    // Add the next digit, n, to the result array.
+                    qc[i++] = n;
+
+                    // Update the remainder.
+                    if ( rem[0] ) {
+                        rem[remL++] = xc[xi] || 0;
+                    } else {
+                        rem = [ xc[xi] ];
+                        remL = 1;
+                    }
+                } while ( ( xi++ < xL || rem[0] != null ) && s-- );
+
+                more = rem[0] != null;
+
+                // Leading zero?
+                if ( !qc[0] ) qc.splice(0, 1);
+            }
+
+            if ( base == BASE ) {
+
+                // To calculate q.e, first get the number of digits of qc[0].
+                for ( i = 1, s = qc[0]; s >= 10; s /= 10, i++ );
+
+                round( q, dp + ( q.e = i + e * LOG_BASE - 1 ) + 1, rm, more );
+
+            // Caller is convertBase.
+            } else {
+                q.e = e;
+                q.r = +more;
+            }
+
+            return q;
+        };
+    })();
+
+
+    /*
+     * Return a string representing the value of BigNumber n in fixed-point or exponential
+     * notation rounded to the specified decimal places or significant digits.
+     *
+     * n: a BigNumber.
+     * i: the index of the last digit required (i.e. the digit that may be rounded up).
+     * rm: the rounding mode.
+     * id: 1 (toExponential) or 2 (toPrecision).
+     */
+    function format( n, i, rm, id ) {
+        var c0, e, ne, len, str;
+
+        if ( rm == null ) rm = ROUNDING_MODE;
+        else intCheck( rm, 0, 8 );
+
+        if ( !n.c ) return n.toString();
+
+        c0 = n.c[0];
+        ne = n.e;
+
+        if ( i == null ) {
+            str = coeffToString( n.c );
+            str = id == 1 || id == 2 && ne <= TO_EXP_NEG
+              ? toExponential( str, ne )
+              : toFixedPoint( str, ne, '0' );
+        } else {
+            n = round( new BigNumber(n), i, rm );
+
+            // n.e may have changed if the value was rounded up.
+            e = n.e;
+
+            str = coeffToString( n.c );
+            len = str.length;
+
+            // 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 fixed-point notation.
+
+            // Exponential notation.
+            if ( id == 1 || id == 2 && ( i <= e || e <= TO_EXP_NEG ) ) {
+
+                // Append zeros?
+                for ( ; len < i; str += '0', len++ );
+                str = toExponential( str, e );
+
+            // Fixed-point notation.
+            } else {
+                i -= ne;
+                str = toFixedPoint( str, e, '0' );
+
+                // Append zeros?
+                if ( e + 1 > len ) {
+                    if ( --i > 0 ) for ( str += '.'; i--; str += '0' );
+                } else {
+                    i += e - len;
+                    if ( i > 0 ) {
+                        if ( e + 1 == len ) str += '.';
+                        for ( ; i--; str += '0' );
+                    }
+                }
+            }
+        }
+
+        return n.s < 0 && c0 ? '-' + str : str;
+    }
+
+
+    // Handle BigNumber.max and BigNumber.min.
+    function maxOrMin( args, method ) {
+        var m, n,
+            i = 0;
+
+        if ( isArray( args[0] ) ) args = args[0];
+        m = new BigNumber( args[0] );
+
+        for ( ; ++i < args.length; ) {
+            n = new BigNumber( args[i] );
+
+            // If any number is NaN, return NaN.
+            if ( !n.s ) {
+                m = n;
+                break;
+            } else if ( method.call( m, n ) ) {
+                m = n;
+            }
+        }
+
+        return m;
+    }
+
+
+    /*
+     * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+     * Called by minus, plus and times.
+     */
+    function normalise( n, c, e ) {
+        var i = 1,
+            j = c.length;
+
+         // Remove trailing zeros.
+        for ( ; !c[--j]; c.pop() );
+
+        // Calculate the base 10 exponent. First get the number of digits of c[0].
+        for ( j = c[0]; j >= 10; j /= 10, i++ );
+
+        // Overflow?
+        if ( ( e = i + e * LOG_BASE - 1 ) > MAX_EXP ) {
+
+            // Infinity.
+            n.c = n.e = null;
+
+        // Underflow?
+        } else if ( e < MIN_EXP ) {
+
+            // Zero.
+            n.c = [ n.e = 0 ];
+        } else {
+            n.e = e;
+            n.c = c;
+        }
+
+        return n;
+    }
+
+
+    // Handle values that fail the validity test in BigNumber.
+    parseNumeric = (function () {
+        var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+            dotAfter = /^([^.]+)\.$/,
+            dotBefore = /^\.([^.]+)$/,
+            isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+            whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+
+        return function ( x, str, isNum, b ) {
+            var base,
+                s = isNum ? str : str.replace( whitespaceOrPlus, '' );
+
+            // No exception on ±Infinity or NaN.
+            if ( isInfinityOrNaN.test(s) ) {
+                x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+                x.c = x.e = null;
+            } else {
+                if ( !isNum ) {
+
+                    // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+                    s = s.replace( basePrefix, function ( m, p1, p2 ) {
+                        base = ( p2 = p2.toLowerCase() ) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+                        return !b || b == base ? p1 : m;
+                    });
+
+                    if (b) {
+                        base = b;
+
+                        // E.g. '1.' to '1', '.1' to '0.1'
+                        s = s.replace( dotAfter, '$1' ).replace( dotBefore, '0.$1' );
+                    }
+
+                    if ( str != s ) return new BigNumber( s, base );
+                }
+
+                // '[BigNumber Error] Not a number: {n}'
+                // '[BigNumber Error] Not a base {b} number: {n}'
+                throw Error
+                  ( bignumberError + 'Not a' + ( b ? ' base ' + b : '' ) + ' number: ' + str );
+            }
+        }
+    })();
+
+
+    /*
+     * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+     * If r is truthy, it is known that there are more digits after the rounding digit.
+     */
+    function round( x, sd, rm, r ) {
+        var d, i, j, k, n, ni, rd,
+            xc = x.c,
+            pows10 = POWS_TEN;
+
+        // if x is not Infinity or NaN...
+        if (xc) {
+
+            // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+            // n is a base 1e14 number, the value of the element of array x.c containing rd.
+            // ni is the index of n within x.c.
+            // d is the number of digits of n.
+            // i is the index of rd within n including leading zeros.
+            // j is the actual index of rd within n (if < 0, rd is a leading zero).
+            out: {
+
+                // Get the number of digits of the first element of xc.
+                for ( d = 1, k = xc[0]; k >= 10; k /= 10, d++ );
+                i = sd - d;
+
+                // If the rounding digit is in the first element of xc...
+                if ( i < 0 ) {
+                    i += LOG_BASE;
+                    j = sd;
+                    n = xc[ ni = 0 ];
+
+                    // Get the rounding digit at index j of n.
+                    rd = n / pows10[ d - j - 1 ] % 10 | 0;
+                } else {
+                    ni = mathceil( ( i + 1 ) / LOG_BASE );
+
+                    if ( ni >= xc.length ) {
+
+                        if (r) {
+
+                            // Needed by sqrt.
+                            for ( ; xc.length <= ni; xc.push(0) );
+                            n = rd = 0;
+                            d = 1;
+                            i %= LOG_BASE;
+                            j = i - LOG_BASE + 1;
+                        } else {
+                            break out;
+                        }
+                    } else {
+                        n = k = xc[ni];
+
+                        // Get the number of digits of n.
+                        for ( d = 1; k >= 10; k /= 10, d++ );
+
+                        // Get the index of rd within n.
+                        i %= LOG_BASE;
+
+                        // Get the index of rd within n, adjusted for leading zeros.
+                        // The number of leading zeros of n is given by LOG_BASE - d.
+                        j = i - LOG_BASE + d;
+
+                        // Get the rounding digit at index j of n.
+                        rd = j < 0 ? 0 : n / pows10[ d - j - 1 ] % 10 | 0;
+                    }
+                }
+
+                r = r || sd < 0 ||
+
+                // Are there any non-zero digits after the rounding digit?
+                // The expression  n % pows10[ d - j - 1 ]  returns all digits of n to the right
+                // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+                  xc[ni + 1] != null || ( j < 0 ? n : n % pows10[ d - j - 1 ] );
+
+                r = rm < 4
+                  ? ( rd || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+                  : rd > 5 || rd == 5 && ( rm == 4 || r || rm == 6 &&
+
+                    // Check whether the digit to the left of the rounding digit is odd.
+                    ( ( i > 0 ? j > 0 ? n / pows10[ d - j ] : 0 : xc[ni - 1] ) % 10 ) & 1 ||
+                      rm == ( x.s < 0 ? 8 : 7 ) );
+
+                if ( sd < 1 || !xc[0] ) {
+                    xc.length = 0;
+
+                    if (r) {
+
+                        // Convert sd to decimal places.
+                        sd -= x.e + 1;
+
+                        // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+                        xc[0] = pows10[ ( LOG_BASE - sd % LOG_BASE ) % LOG_BASE ];
+                        x.e = -sd || 0;
+                    } else {
+
+                        // Zero.
+                        xc[0] = x.e = 0;
+                    }
+
+                    return x;
+                }
+
+                // Remove excess digits.
+                if ( i == 0 ) {
+                    xc.length = ni;
+                    k = 1;
+                    ni--;
+                } else {
+                    xc.length = ni + 1;
+                    k = pows10[ LOG_BASE - i ];
+
+                    // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+                    // j > 0 means i > number of leading zeros of n.
+                    xc[ni] = j > 0 ? mathfloor( n / pows10[ d - j ] % pows10[j] ) * k : 0;
+                }
+
+                // Round up?
+                if (r) {
+
+                    for ( ; ; ) {
+
+                        // If the digit to be rounded up is in the first element of xc...
+                        if ( ni == 0 ) {
+
+                            // i will be the length of xc[0] before k is added.
+                            for ( i = 1, j = xc[0]; j >= 10; j /= 10, i++ );
+                            j = xc[0] += k;
+                            for ( k = 1; j >= 10; j /= 10, k++ );
+
+                            // if i != k the length has increased.
+                            if ( i != k ) {
+                                x.e++;
+                                if ( xc[0] == BASE ) xc[0] = 1;
+                            }
+
+                            break;
+                        } else {
+                            xc[ni] += k;
+                            if ( xc[ni] != BASE ) break;
+                            xc[ni--] = 0;
+                            k = 1;
+                        }
+                    }
+                }
+
+                // Remove trailing zeros.
+                for ( i = xc.length; xc[--i] === 0; xc.pop() );
+            }
+
+            // Overflow? Infinity.
+            if ( x.e > MAX_EXP ) {
+                x.c = x.e = null;
+
+            // Underflow? Zero.
+            } else if ( x.e < MIN_EXP ) {
+                x.c = [ x.e = 0 ];
+            }
+        }
+
+        return x;
+    }
+
+
+    // PROTOTYPE/INSTANCE METHODS
+
+
+    /*
+     * Return a new BigNumber whose value is the absolute value of this BigNumber.
+     */
+    P.absoluteValue = P.abs = function () {
+        var x = new BigNumber(this);
+        if ( x.s < 0 ) x.s = 1;
+        return x;
+    };
+
+
+    /*
+     * 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 = function ( y, b ) {
+        return compare( this, new BigNumber( y, b ) );
+    };
+
+
+    /*
+     * If dp is undefined or null or true or false, return the number of decimal places of the
+     * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     *
+     * Otherwise, if dp is a number, 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
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.decimalPlaces = P.dp = function ( dp, rm ) {
+        var c, n, v,
+            x = this;
+
+        if ( dp != null ) {
+            intCheck( dp, 0, MAX );
+            if ( rm == null ) rm = ROUNDING_MODE;
+            else intCheck( rm, 0, 8 );
+
+            return round( new BigNumber(x), dp + x.e + 1, rm );
+        }
+
+        if ( !( c = x.c ) ) return null;
+        n = ( ( v = c.length - 1 ) - bitFloor( this.e / LOG_BASE ) ) * LOG_BASE;
+
+        // Subtract the number of trailing zeros of the last number.
+        if ( v = c[v] ) for ( ; v % 10 == 0; v /= 10, n-- );
+        if ( n < 0 ) n = 0;
+
+        return n;
+    };
+
+
+    /*
+     *  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 ) {
+        return div( this, new BigNumber( y, b ), DECIMAL_PLACES, ROUNDING_MODE );
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the integer part of dividing the value of this
+     * BigNumber by the value of BigNumber(y, b).
+     */
+    P.dividedToIntegerBy = P.idiv = function ( y, b ) {
+        return div( this, new BigNumber( y, b ), 0, 1 );
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isEqualTo = P.eq = function ( y, b ) {
+        return compare( this, new BigNumber( y, b ) ) === 0;
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
+     * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
+     */
+    P.integerValue = function (rm) {
+        var n = new BigNumber(this);
+        if ( rm == null ) rm = ROUNDING_MODE;
+        else intCheck( rm, 0, 8 );
+        return round( n, n.e + 1, rm );
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isGreaterThan = P.gt = function ( y, b ) {
+        return compare( this, new BigNumber( y, b ) ) > 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is greater than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isGreaterThanOrEqualTo = P.gte = function ( y, b ) {
+        return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;
+
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is a finite number, otherwise return false.
+     */
+    P.isFinite = function () {
+        return !!this.c;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is an integer, otherwise return false.
+     */
+    P.isInteger = function () {
+        return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is NaN, otherwise return false.
+     */
+    P.isNaN = function () {
+        return !this.s;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is negative, otherwise return false.
+     */
+    P.isNegative = function () {
+        return this.s < 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is positive, otherwise return false.
+     */
+    P.isPositive = function () {
+        return this.s > 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
+     */
+    P.isZero = function () {
+        return !!this.c && this.c[0] == 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+     * otherwise return false.
+     */
+    P.isLessThan = P.lt = function ( y, b ) {
+        return compare( this, new BigNumber( y, b ) ) < 0;
+    };
+
+
+    /*
+     * Return true if the value of this BigNumber is less than or equal to the value of
+     * BigNumber(y, b), otherwise return false.
+     */
+    P.isLessThanOrEqualTo = P.lte = function ( y, b ) {
+        return ( b = compare( this, new BigNumber( y, 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 = function ( y, b ) {
+        var i, j, t, xLTy,
+            x = this,
+            a = x.s;
+
+        y = new BigNumber( y, b );
+        b = y.s;
+
+        // Either NaN?
+        if ( !a || !b ) return new BigNumber(NaN);
+
+        // Signs differ?
+        if ( a != b ) {
+            y.s = -b;
+            return x.plus(y);
+        }
+
+        var xe = x.e / LOG_BASE,
+            ye = y.e / LOG_BASE,
+            xc = x.c,
+            yc = y.c;
+
+        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] ) {
+
+                // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+                return yc[0] ? ( y.s = -b, y ) : new BigNumber( xc[0] ? x :
+
+                  // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+                  ROUNDING_MODE == 3 ? -0 : 0 );
+            }
+        }
+
+        xe = bitFloor(xe);
+        ye = bitFloor(ye);
+        xc = xc.slice();
+
+        // Determine which is the bigger number.
+        if ( a = xe - ye ) {
+
+            if ( xLTy = a < 0 ) {
+                a = -a;
+                t = xc;
+            } else {
+                ye = xe;
+                t = yc;
+            }
+
+            t.reverse();
+
+            // Prepend zeros to equalise exponents.
+            for ( b = a; b--; t.push(0) );
+            t.reverse();
+        } else {
+
+            // Exponents equal. Check digit by digit.
+            j = ( xLTy = ( a = xc.length ) < ( b = yc.length ) ) ? a : b;
+
+            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;
+
+        b = ( j = yc.length ) - ( i = xc.length );
+
+        // Append zeros to xc if shorter.
+        // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+        if ( b > 0 ) for ( ; b--; xc[i++] = 0 );
+        b = BASE - 1;
+
+        // Subtract yc from xc.
+        for ( ; j > a; ) {
+
+            if ( xc[--j] < yc[j] ) {
+                for ( i = j; i && !xc[--i]; xc[i] = b );
+                --xc[i];
+                xc[j] += BASE;
+            }
+
+            xc[j] -= yc[j];
+        }
+
+        // Remove leading zeros and adjust exponent accordingly.
+        for ( ; xc[0] == 0; xc.splice(0, 1), --ye );
+
+        // Zero?
+        if ( !xc[0] ) {
+
+            // Following IEEE 754 (2008) 6.3,
+            // n - n = +0  but  n - n = -0  when rounding towards -Infinity.
+            y.s = ROUNDING_MODE == 3 ? -1 : 1;
+            y.c = [ y.e = 0 ];
+            return y;
+        }
+
+        // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+        // for finite x and y.
+        return normalise( y, xc, ye );
+    };
+
+
+    /*
+     *   n % 0 =  N
+     *   n % N =  N
+     *   n % I =  n
+     *   0 % n =  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 =  N
+     *   I % 0 =  N
+     *   I % N =  N
+     *   I % I =  N
+     *
+     * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
+     * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+     */
+    P.modulo = P.mod = function ( y, b ) {
+        var q, s,
+            x = this;
+
+        y = new BigNumber( y, b );
+
+        // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+        if ( !x.c || !y.s || y.c && !y.c[0] ) {
+            return new BigNumber(NaN);
+
+        // Return x if y is Infinity or x is zero.
+        } else if ( !y.c || x.c && !x.c[0] ) {
+            return new BigNumber(x);
+        }
+
+        if ( MODULO_MODE == 9 ) {
+
+            // Euclidian division: q = sign(y) * floor(x / abs(y))
+            // r = x - qy    where  0 <= r < abs(y)
+            s = y.s;
+            y.s = 1;
+            q = div( x, y, 0, 3 );
+            y.s = s;
+            q.s *= s;
+        } else {
+            q = div( x, y, 0, MODULO_MODE );
+        }
+
+        return x.minus( q.times(y) );
+    };
+
+
+    /*
+     *  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 multiplied by the value
+     * of BigNumber(y, b).
+     */
+    P.multipliedBy = P.times = function ( y, b ) {
+        var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+            base, sqrtBase,
+            x = this,
+            xc = x.c,
+            yc = ( y = new BigNumber( y, b ) ).c;
+
+        // Either NaN, ±Infinity or ±0?
+        if ( !xc || !yc || !xc[0] || !yc[0] ) {
+
+            // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+            if ( !x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc ) {
+                y.c = y.e = y.s = null;
+            } else {
+                y.s *= x.s;
+
+                // Return ±Infinity if either is ±Infinity.
+                if ( !xc || !yc ) {
+                    y.c = y.e = null;
+
+                // Return ±0 if either is ±0.
+                } else {
+                    y.c = [0];
+                    y.e = 0;
+                }
+            }
+
+            return y;
+        }
+
+        e = bitFloor( x.e / LOG_BASE ) + bitFloor( y.e / LOG_BASE );
+        y.s *= x.s;
+        xcL = xc.length;
+        ycL = yc.length;
+
+        // Ensure xc points to longer array and xcL to its length.
+        if ( xcL < ycL ) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+
+        // Initialise the result array with zeros.
+        for ( i = xcL + ycL, zc = []; i--; zc.push(0) );
+
+        base = BASE;
+        sqrtBase = SQRT_BASE;
+
+        for ( i = ycL; --i >= 0; ) {
+            c = 0;
+            ylo = yc[i] % sqrtBase;
+            yhi = yc[i] / sqrtBase | 0;
+
+            for ( k = xcL, j = i + k; j > i; ) {
+                xlo = xc[--k] % sqrtBase;
+                xhi = xc[k] / sqrtBase | 0;
+                m = yhi * xlo + xhi * ylo;
+                xlo = ylo * xlo + ( ( m % sqrtBase ) * sqrtBase ) + zc[j] + c;
+                c = ( xlo / base | 0 ) + ( m / sqrtBase | 0 ) + yhi * xhi;
+                zc[j--] = xlo % base;
+            }
+
+            zc[j] = c;
+        }
+
+        if (c) {
+            ++e;
+        } else {
+            zc.splice(0, 1);
+        }
+
+        return normalise( y, zc, e );
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber negated,
+     * i.e. multiplied by -1.
+     */
+    P.negated = function () {
+        var x = new BigNumber(this);
+        x.s = -x.s || null;
+        return 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 = function ( y, b ) {
+        var t,
+            x = this,
+            a = x.s;
+
+        y = new BigNumber( y, b );
+        b = y.s;
+
+        // Either NaN?
+        if ( !a || !b ) return new BigNumber(NaN);
+
+        // Signs differ?
+         if ( a != b ) {
+            y.s = -b;
+            return x.minus(y);
+        }
+
+        var xe = x.e / LOG_BASE,
+            ye = y.e / LOG_BASE,
+            xc = x.c,
+            yc = y.c;
+
+        if ( !xe || !ye ) {
+
+            // Return ±Infinity if either ±Infinity.
+            if ( !xc || !yc ) return new BigNumber( a / 0 );
+
+            // Either zero?
+            // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+            if ( !xc[0] || !yc[0] ) return yc[0] ? y : new BigNumber( xc[0] ? x : a * 0 );
+        }
+
+        xe = bitFloor(xe);
+        ye = bitFloor(ye);
+        xc = xc.slice();
+
+        // Prepend zeros to equalise exponents. Faster to use reverse then do 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();
+        }
+
+        a = xc.length;
+        b = yc.length;
+
+        // Point xc to the longer array, and b to the shorter length.
+        if ( a - b < 0 ) t = yc, yc = xc, xc = t, b = a;
+
+        // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+        for ( a = 0; b; ) {
+            a = ( xc[--b] = xc[b] + yc[b] + a ) / BASE | 0;
+            xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+        }
+
+        if (a) {
+            xc = [a].concat(xc);
+            ++ye;
+        }
+
+        // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+        // ye = MAX_EXP + 1 possible
+        return normalise( y, xc, ye );
+    };
+
+
+    /*
+     * If sd is undefined or null or true or false, return the number of significant digits of
+     * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+     * If sd is true include integer-part trailing zeros in the count.
+     *
+     * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
+     * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
+     * ROUNDING_MODE if rm is omitted.
+     *
+     * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
+     *                     boolean: whether to count integer-part trailing zeros: true or false.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.precision = P.sd = function ( sd, rm ) {
+        var c, n, v,
+            x = this;
+
+        if ( sd != null && sd !== !!sd ) {
+            intCheck( sd, 1, MAX );
+            if ( rm == null ) rm = ROUNDING_MODE;
+            else intCheck( rm, 0, 8 );
+
+            return round( new BigNumber(x), sd, rm );
+        }
+
+        if ( !( c = x.c ) ) return null;
+        v = c.length - 1;
+        n = v * LOG_BASE + 1;
+
+        if ( v = c[v] ) {
+
+            // Subtract the number of trailing zeros of the last element.
+            for ( ; v % 10 == 0; v /= 10, n-- );
+
+            // Add the number of digits of the first element.
+            for ( v = c[0]; v >= 10; v /= 10, n++ );
+        }
+
+        if ( sd && x.e + 1 > n ) n = x.e + 1;
+
+        return n;
+    };
+
+
+    /*
+     * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+     * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+     *
+     * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
+     */
+    P.shiftedBy = function (k) {
+        intCheck( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
+        return this.times( '1e' + k );
+    };
+
+
+    /*
+     *  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 m, n, r, rep, t,
+            x = this,
+            c = x.c,
+            s = x.s,
+            e = x.e,
+            dp = DECIMAL_PLACES + 4,
+            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 );
+
+        // 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 = coeffToString(c);
+            if ( ( n.length + e ) % 2 == 0 ) n += '0';
+            s = Math.sqrt(n);
+            e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );
+
+            if ( s == 1 / 0 ) {
+                n = '1e' + e;
+            } else {
+                n = s.toExponential();
+                n = n.slice( 0, n.indexOf('e') + 1 ) + e;
+            }
+
+            r = new BigNumber(n);
+        } else {
+            r = new BigNumber( s + '' );
+        }
+
+        // Check for zero.
+        // r could be zero if MIN_EXP is changed after the this value was created.
+        // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+        // coeffToString to throw.
+        if ( r.c[0] ) {
+            e = r.e;
+            s = e + dp;
+            if ( s < 3 ) s = 0;
+
+            // Newton-Raphson iteration.
+            for ( ; ; ) {
+                t = r;
+                r = half.times( t.plus( div( x, t, dp, 1 ) ) );
+
+                if ( coeffToString( t.c   ).slice( 0, s ) === ( n =
+                     coeffToString( r.c ) ).slice( 0, s ) ) {
+
+                    // The exponent of r may here be one less than the final result exponent,
+                    // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+                    // are indexed correctly.
+                    if ( r.e < e ) --s;
+                    n = n.slice( s - 3, s + 1 );
+
+                    // 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 ( n == '9999' || !rep && n == '4999' ) {
+
+                        // On the first iteration only, check to see if rounding up gives the
+                        // exact result as the nines may infinitely repeat.
+                        if ( !rep ) {
+                            round( t, t.e + DECIMAL_PLACES + 2, 0 );
+
+                            if ( t.times(t).eq(x) ) {
+                                r = t;
+                                break;
+                            }
+                        }
+
+                        dp += 4;
+                        s += 4;
+                        rep = 1;
+                    } else {
+
+                        // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
+                        // result. If not, then there are further digits and m will be truthy.
+                        if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {
+
+                            // Truncate to the first rounding digit.
+                            round( r, r.e + DECIMAL_PLACES + 2, 1 );
+                            m = !r.times(r).eq(x);
+                        }
+
+                        break;
+                    }
+                }
+            }
+        }
+
+        return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in exponential notation and
+     * rounded using ROUNDING_MODE to dp fixed decimal places.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toExponential = function ( dp, rm ) {
+        if ( dp != null ) {
+            intCheck( dp, 0, MAX );
+            dp++;
+        }
+        return format( this, dp, rm, 1 );
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounding
+     * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+     *
+     * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+     * but e.g. (-0.00001).toFixed(0) is '-0'.
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toFixed = function ( dp, rm ) {
+        if ( dp != null ) {
+            intCheck( dp, 0, MAX );
+            dp = dp + this.e + 1;
+        }
+        return format( this, dp, rm );
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber in fixed-point notation rounded
+     * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+     * of the FORMAT object (see BigNumber.set).
+     *
+     * FORMAT = {
+     *      decimalSeparator : '.',
+     *      groupSeparator : ',',
+     *      groupSize : 3,
+     *      secondaryGroupSize : 0,
+     *      fractionGroupSeparator : '\xA0',    // non-breaking space
+     *      fractionGroupSize : 0
+     * };
+     *
+     * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+     */
+    P.toFormat = function ( dp, rm ) {
+        var str = this.toFixed( dp, rm );
+
+        if ( this.c ) {
+            var i,
+                arr = str.split('.'),
+                g1 = +FORMAT.groupSize,
+                g2 = +FORMAT.secondaryGroupSize,
+                groupSeparator = FORMAT.groupSeparator,
+                intPart = arr[0],
+                fractionPart = arr[1],
+                isNeg = this.s < 0,
+                intDigits = isNeg ? intPart.slice(1) : intPart,
+                len = intDigits.length;
+
+            if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+
+            if ( g1 > 0 && len > 0 ) {
+                i = len % g1 || g1;
+                intPart = intDigits.substr( 0, i );
+
+                for ( ; i < len; i += g1 ) {
+                    intPart += groupSeparator + intDigits.substr( i, g1 );
+                }
+
+                if ( g2 > 0 ) intPart += groupSeparator + intDigits.slice(i);
+                if (isNeg) intPart = '-' + intPart;
+            }
+
+            str = fractionPart
+              ? intPart + FORMAT.decimalSeparator + ( ( g2 = +FORMAT.fractionGroupSize )
+                ? fractionPart.replace( new RegExp( '\\d{' + g2 + '}\\B', 'g' ),
+                  '$&' + FORMAT.fractionGroupSeparator )
+                : fractionPart )
+              : intPart;
+        }
+
+        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.
+     *
+     * [md] {number|string|BigNumber} Integer >= 1 and < Infinity. The maximum denominator.
+     *
+     * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
+     */
+    P.toFraction = function (md) {
+        var arr, d, d0, d1, d2, e, exp, n, n0, n1, q, s,
+            x = this,
+            xc = x.c;
+
+        if ( md != null ) {
+            n = new BigNumber(md);
+
+            if ( !n.isInteger() || n.lt(ONE) ) {
+                throw Error
+                  ( bignumberError + 'Argument ' +
+                    ( n.isInteger() ? 'out of range: ' : 'not an integer: ' ) + md );
+            }
+        }
+
+        if ( !xc ) return x.toString();
+
+        d = new BigNumber(ONE);
+        n1 = d0 = new BigNumber(ONE);
+        d1 = n0 = new BigNumber(ONE);
+        s = coeffToString(xc);
+
+        // Determine initial denominator.
+        // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+        e = d.e = s.length - x.e - 1;
+        d.c[0] = POWS_TEN[ ( exp = e % LOG_BASE ) < 0 ? LOG_BASE + exp : exp ];
+        md = !md || n.comparedTo(d) > 0 ? ( e > 0 ? d : n1 ) : n;
+
+        exp = MAX_EXP;
+        MAX_EXP = 1 / 0;
+        n = new BigNumber(s);
+
+        // n0 = d1 = 0
+        n0.c[0] = 0;
+
+        for ( ; ; )  {
+            q = div( n, d, 0, 1 );
+            d2 = d0.plus( q.times(d1) );
+            if ( d2.comparedTo(md) == 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 = div( md.minus(d0), d1, 0, 1 );
+        n0 = n0.plus( d2.times(n1) );
+        d0 = d0.plus( d2.times(d1) );
+        n0.s = n1.s = x.s;
+        e *= 2;
+
+        // Determine which fraction is closer to x, n0/d0 or n1/d1
+        arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().comparedTo(
+              div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
+                ? [ n1.toString(), d1.toString() ]
+                : [ n0.toString(), d0.toString() ];
+
+        MAX_EXP = exp;
+        return arr;
+    };
+
+
+    /*
+     * Return the value of this BigNumber converted to a number primitive.
+     */
+    P.toNumber = function () {
+        return +this;
+    };
+
+
+    /*
+     * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
+     *
+     * If m is present, return the result modulo m.
+     * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+     * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
+     *
+     * The modular power operation works efficiently when x, n, and m are positive integers,
+     * otherwise it is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
+     *
+     * n {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+     * [m] {number|string|BigNumber} The modulus.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {n}'
+     *
+     * Performs 54 loop iterations for n of 9007199254740991.
+     */
+    P.exponentiatedBy = P.pow = function ( n, m ) {
+        var i, k, y, z,
+            x = this;
+
+        intCheck( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
+        if ( m != null ) m = new BigNumber(m);
+
+        if (m) {
+            if ( n > 1 && x.gt(ONE) && x.isInteger() && m.gt(ONE) && m.isInteger() ) {
+                x = x.mod(m);
+            } else {
+                z = m;
+
+                // Nullify m so only a single mod operation is performed at the end.
+                m = null;
+            }
+        } else if (POW_PRECISION) {
+
+            // Truncating each coefficient array to a length of k after each multiplication
+            // equates to truncating significant digits to POW_PRECISION + [28, 41],
+            // i.e. there will be a minimum of 28 guard digits retained.
+            //k = mathceil( POW_PRECISION / LOG_BASE + 1.5 );   // gives [9, 21] guard digits.
+            k = mathceil( POW_PRECISION / LOG_BASE + 2 );
+        }
+
+        y = new BigNumber(ONE);
+
+        for ( i = mathfloor( n < 0 ? -n : n ); ; ) {
+            if ( i % 2 ) {
+                y = y.times(x);
+                if ( !y.c ) break;
+                if (k) {
+                    if ( y.c.length > k ) y.c.length = k;
+                } else if (m) {
+                    y = y.mod(m);
+                }
+            }
+
+            i = mathfloor( i / 2 );
+            if ( !i ) break;
+            x = x.times(x);
+            if (k) {
+                if ( x.c && x.c.length > k ) x.c.length = k;
+            } else if (m) {
+                x = x.mod(m);
+            }
+        }
+
+        if (m) return y;
+        if ( n < 0 ) y = ONE.div(y);
+
+        return z ? y.mod(z) : k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
+    };
+
+
+    /*
+     * Return a string representing the value of this BigNumber rounded to sd significant digits
+     * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+     * necessary to represent the integer part of the value in fixed-point notation, then use
+     * exponential notation.
+     *
+     * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+     * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+     *
+     * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+     */
+    P.toPrecision = function ( sd, rm ) {
+        if ( sd != null ) intCheck( sd, 1, MAX );
+        return format( this, sd, rm, 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 ALPHABET.length inclusive.
+     *
+     * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+     */
+    P.toString = function (b) {
+        var str,
+            n = this,
+            s = n.s,
+            e = n.e;
+
+        // Infinity or NaN?
+        if ( e === null ) {
+
+            if (s) {
+                str = 'Infinity';
+                if ( s < 0 ) str = '-' + str;
+            } else {
+                str = 'NaN';
+            }
+        } else {
+            str = coeffToString( n.c );
+
+            if ( b == null ) {
+                str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+                  ? toExponential( str, e )
+                  : toFixedPoint( str, e, '0' );
+            } else {
+                intCheck( b, 2, ALPHABET.length, 'Base' );
+                str = convertBase( toFixedPoint( str, e, '0' ), 10, b, s, true );
+            }
+
+            if ( s < 0 && n.c[0] ) str = '-' + str;
+        }
+
+        return str;
+    };
+
+
+    /*
+     * Return as toString, but do not accept a base argument, and include the minus sign for
+     * negative zero.
+     */
+    P.valueOf = P.toJSON = function () {
+        var str,
+            n = this,
+            e = n.e;
+
+        if ( e === null ) return n.toString();
+
+        str = coeffToString( n.c );
+
+        str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+            ? toExponential( str, e )
+            : toFixedPoint( str, e, '0' );
+
+        return n.s < 0 ? '-' + str : str;
+    };
+
+
+    P._isBigNumber = true;
+
+    if ( configObject != null ) BigNumber.set(configObject);
+
+    return BigNumber;
+}
+
+
+// PRIVATE HELPER FUNCTIONS
+
+
+function bitFloor(n) {
+    var i = n | 0;
+    return n > 0 || n === i ? i : i - 1;
+}
+
+
+// Return a coefficient array as a string of base 10 digits.
+function coeffToString(a) {
+    var s, z,
+        i = 1,
+        j = a.length,
+        r = a[0] + '';
+
+    for ( ; i < j; ) {
+        s = a[i++] + '';
+        z = LOG_BASE - s.length;
+        for ( ; z--; s = '0' + s );
+        r += s;
+    }
+
+    // Determine trailing zeros.
+    for ( j = r.length; r.charCodeAt(--j) === 48; );
+    return r.slice( 0, j + 1 || 1 );
+}
+
+
+// Compare the value of BigNumbers x and y.
+function compare( x, y ) {
+    var a, b,
+        xc = x.c,
+        yc = y.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;
+
+    a = i < 0;
+    b = k == l;
+
+    // Either Infinity?
+    if ( !xc || !yc ) return b ? 0 : !xc ^ a ? 1 : -1;
+
+    // Compare exponents.
+    if ( !b ) return k > l ^ a ? 1 : -1;
+
+    j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
+
+    // Compare digit by digit.
+    for ( i = 0; i < j; i++ ) if ( xc[i] != yc[i] ) return xc[i] > yc[i] ^ a ? 1 : -1;
+
+    // Compare lengths.
+    return k == l ? 0 : k > l ^ a ? 1 : -1;
+}
+
+
+/*
+ * Check that n is a primitive number, an integer, and in range, otherwise throw.
+ */
+function intCheck( n, min, max, name ) {
+    if ( n < min || n > max || n !== ( n < 0 ? mathceil(n) : mathfloor(n) ) ) {
+        throw Error
+          ( bignumberError + ( name || 'Argument' ) + ( typeof n == 'number'
+              ? n < min || n > max ? ' out of range: ' : ' not an integer: '
+              : ' not a primitive number: ' ) + n );
+    }
+}
+
+
+function isArray(obj) {
+    return Object.prototype.toString.call(obj) == '[object Array]';
+}
+
+
+function toExponential( str, e ) {
+    return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
+      ( e < 0 ? 'e' : 'e+' ) + e;
+}
+
+
+function toFixedPoint( str, e, z ) {
+    var len, zs;
+
+    // Negative exponent?
+    if ( e < 0 ) {
+
+        // Prepend zeros.
+        for ( zs = z + '.'; ++e; zs += z );
+        str = zs + str;
+
+    // Positive exponent
+    } else {
+        len = str.length;
+
+        // Append zeros.
+        if ( ++e > len ) {
+            for ( zs = z, e -= len; --e; zs += z );
+            str += zs;
+        } else if ( e < len ) {
+            str = str.slice( 0, e ) + '.' + str.slice(e);
+        }
+    }
+
+    return str;
+}
+
+
+// EXPORT
+
+
+BigNumber = clone();
+BigNumber['default'] = BigNumber.BigNumber = BigNumber;
+
+export default BigNumber;
\ No newline at end of file
diff --git a/packages/instant/test/util/maybe_big_number.test.ts b/packages/instant/test/util/maybe_big_number.test.ts
new file mode 100644
index 000000000..f32e33eb1
--- /dev/null
+++ b/packages/instant/test/util/maybe_big_number.test.ts
@@ -0,0 +1,71 @@
+import { BigNumber } from '@0x/utils';
+
+import { maybeBigNumberUtil } from '../../src/util/maybe_big_number';
+
+// import PrevBigNumber from './dependencies/prevbignumber';
+
+const BIG_NUMBER_1 = new BigNumber('10.1');
+const BIG_NUMBER_2 = new BigNumber('10.1');
+const BIG_NUMBER_3 = new BigNumber('11.1');
+// const PREVBIG_NUMBER_1 = new PrevBigNumber('11.1');
+
+describe('maybeBigNumberUtil', () => {
+    describe('stringToMaybeBigNumber', () => {
+        it('should return undefined if stringValue is NaN', () => {
+            expect(maybeBigNumberUtil.stringToMaybeBigNumber('NaN')).toEqual(undefined);
+        });
+        it('should return bignumber constructed with stringValue', () => {
+            const bn = maybeBigNumberUtil.stringToMaybeBigNumber('10.1');
+            if (!!bn) {
+                expect(bn.toString()).toEqual('10.1');
+            }
+        });
+        it('should return undefined if stringValue is not valid (i.e not numeric)', () => {
+            expect(maybeBigNumberUtil.stringToMaybeBigNumber('test')).toEqual(undefined);
+        });
+    });
+
+    describe('areMaybeBigNumbersEqual', () => {
+        it('should return true if val1 and val2 are equivalent BigNumber values', () => {
+            expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, BIG_NUMBER_2)).toEqual(true);
+        });
+        it('should return true if val1 and val2 are both undefined', () => {
+            expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(undefined, undefined)).toEqual(true);
+        });
+        it('should return false if either one val1 or val2 is undefined', () => {
+            expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, undefined)).toEqual(false);
+        });
+        it('should return false if val1 and val2 are equivalent values BigNumber', () => {
+            expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, BIG_NUMBER_3)).toEqual(false);
+        });
+    });
+
+    // describe('bigNumberOrStringToMaybeBigNumber', () => {
+    //     it('should return BigNumber (>=v8.0.0) constructed with value if type is string', () => {
+    //         const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('10.1');
+    //         if (!!bn) {
+    //             expect(bn.toString()).toEqual('10.1');
+    //         }
+    //     });
+    //     it('should return undefined if value is NaN', () => {
+    //         expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('NaN')).toEqual(undefined);
+    //     });
+    //     it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+    //         expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('test')).toEqual(undefined);
+    //     });
+    //     it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+    //         expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('test')).toEqual(undefined);
+    //     });
+    //     it('should return BigNumber (>=v8.0.0) when passed a value as BigNumber (<v8.0.0)', () => {
+    //         const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(PREVBIG_NUMBER_1);
+    //         expect(BigNumber.isBigNumber(bn)).toEqual(true);
+    //     });
+    //     it('should return BigNumber (>=v8.0.0) when passed a value as BigNumber (>=v8.0.0)', () => {
+    //         const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(BIG_NUMBER_1);
+    //         expect(BigNumber.isBigNumber(bn)).toEqual(true);
+    //     });
+    //     it('should return undefined if value is not BigNumber or string', () => {
+    //         expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(true)).toEqual(undefined);
+    //     });
+    // });
+});