updated order coercion utils architecture and testing

8 files changed, 180 insertions, 4544 deletions

diff --git a/packages/instant/src/index.umd.ts b/packages/instant/src/index.umd.ts
index 45913aa47..7b2b45a71 100644
--- a/packages/instant/src/index.umd.ts
+++ b/packages/instant/src/index.umd.ts
@@ -17,8 +17,8 @@ import { ZeroExInstantOverlay, ZeroExInstantOverlayProps } from './index';
 import { Network, OrderSource } from './types';
 import { analytics } from './util/analytics';
 import { assert } from './util/assert';
+import { orderCoercionUtil } from './util/order_coercion';
 import { providerFactory } from './util/provider_factory';
-import { signedOrderCoercionUtil } from './util/signed_order_coercion';
 import { util } from './util/util';
 
 const isInstantRendered = (): boolean => !!document.getElementById(INJECTED_DIV_ID);
@@ -94,8 +94,8 @@ export interface ZeroExInstantConfig extends ZeroExInstantOverlayProps {
 }
 
 export const render = (config: ZeroExInstantConfig, selector: string = DEFAULT_ZERO_EX_CONTAINER_SELECTOR) => {
-    if (!_.isString(config.orderSource)) {
-        config.orderSource = config.orderSource.map(signedOrderCoercionUtil.bigNumberCoercion);
+    if (_.isArray(config.orderSource)) {
+        config.orderSource = orderCoercionUtil.coerceOrderArrayFieldsToBigNumber(config.orderSource);
     }
 
     validateInstantRenderConfig(config, selector);
diff --git a/packages/instant/src/util/maybe_big_number.ts b/packages/instant/src/util/maybe_big_number.ts
index 7e206a125..95fbd8695 100644
--- a/packages/instant/src/util/maybe_big_number.ts
+++ b/packages/instant/src/util/maybe_big_number.ts
@@ -16,8 +16,14 @@ export const maybeBigNumberUtil = {
 
         return validBigNumber.isNaN() ? undefined : validBigNumber;
     },
+    areMaybeBigNumbersEqual: (val1: Maybe<BigNumber>, val2: Maybe<BigNumber>): boolean => {
+        if (!_.isUndefined(val1) && !_.isUndefined(val2)) {
+            return val1.isEqualTo(val2);
+        }
+        return _.isUndefined(val1) && _.isUndefined(val2);
+    },
     // converts a BigNumber or String to the BigNumber used by 0x libraries
-    bigNumberOrStringToMaybeBigNumber: (value: any): Maybe<BigNumber> => {
+    toMaybeBigNumber: (value: any): Maybe<BigNumber> => {
         if (_.isString(value)) {
             return maybeBigNumberUtil.stringToMaybeBigNumber(value);
         }
@@ -27,10 +33,4 @@ export const maybeBigNumberUtil = {
         }
         return undefined;
     },
-    areMaybeBigNumbersEqual: (val1: Maybe<BigNumber>, val2: Maybe<BigNumber>): boolean => {
-        if (!_.isUndefined(val1) && !_.isUndefined(val2)) {
-            return val1.isEqualTo(val2);
-        }
-        return _.isUndefined(val1) && _.isUndefined(val2);
-    },
 };
diff --git a/packages/instant/src/util/order_coercion.ts b/packages/instant/src/util/order_coercion.ts
new file mode 100644
index 000000000..a1b468baf
--- /dev/null
+++ b/packages/instant/src/util/order_coercion.ts
@@ -0,0 +1,42 @@
+import { BigNumber } from '@0x/utils';
+import * as _ from 'lodash';
+
+import { maybeBigNumberUtil } from './maybe_big_number';
+
+const coerceBigNumberOrString = (value: any): BigNumber => {
+    const bn = maybeBigNumberUtil.toMaybeBigNumber(value);
+    return !!bn ? bn : value;
+};
+
+// function implies that the signed order already has been validated
+export const orderCoercionUtil = {
+    // coerces order big number values to the BigNumber version utilized by 0x
+    coerceFieldsToBigNumbers(obj: any, fields: string[]): any {
+        const result = _.assign({}, obj);
+        _.each(fields, field => {
+            _.update(result, field, (value: string) => {
+                if (_.isUndefined(value)) {
+                    throw new Error(`Could not find field '${field}' while converting fields to BigNumber.`);
+                }
+                return coerceBigNumberOrString(value);
+            });
+        });
+        return result;
+    },
+
+    coerceOrderFieldsToBigNumber: (order: any): any => {
+        return orderCoercionUtil.coerceFieldsToBigNumbers(order, [
+            'makerFee',
+            'takerFee',
+            'makerAssetAmount',
+            'takerAssetAmount',
+            'salt',
+            'expirationTimeSeconds',
+        ]);
+    },
+    coerceOrderArrayFieldsToBigNumber: (orders: any[]): any[] => {
+        return _.map(orders, (value: any) => {
+            return orderCoercionUtil.coerceOrderFieldsToBigNumber(value);
+        });
+    },
+};
diff --git a/packages/instant/src/util/signed_order_coercion.ts b/packages/instant/src/util/signed_order_coercion.ts
deleted file mode 100644
index 4209e05e1..000000000
--- a/packages/instant/src/util/signed_order_coercion.ts
+++ /dev/null
@@ -1,26 +0,0 @@
-import { SignedOrder } from '@0x/types';
-import { BigNumber } from '@0x/utils';
-import * as _ from 'lodash';
-
-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 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
deleted file mode 100644
index 9b802ec3e..000000000
--- a/packages/instant/test/util/dependencies/prevbignumber.d.ts
+++ /dev/null
@@ -1,1772 +0,0 @@
-// 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
deleted file mode 100644
index e2d3f2146..000000000
--- a/packages/instant/test/util/dependencies/prevbignumber.js
+++ /dev/null
@@ -1,2705 +0,0 @@
-/*
- *      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
index f32e33eb1..508e8aaf0 100644
--- a/packages/instant/test/util/maybe_big_number.test.ts
+++ b/packages/instant/test/util/maybe_big_number.test.ts
@@ -2,12 +2,9 @@ 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', () => {
@@ -40,32 +37,29 @@ describe('maybeBigNumberUtil', () => {
         });
     });
 
-    // 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);
-    //     });
-    // });
+    // this doesn't test coercing a pre v8.0.0 version of big number to desired version
+    describe('toMaybeBigNumber', () => {
+        it('should return BigNumber (>=v8.0.0) constructed with value if type is string', () => {
+            const bn = maybeBigNumberUtil.toMaybeBigNumber('10.1');
+            if (!!bn) {
+                expect(bn.toString()).toEqual('10.1');
+            }
+        });
+        it('should return undefined if value is NaN', () => {
+            expect(maybeBigNumberUtil.toMaybeBigNumber('NaN')).toEqual(undefined);
+        });
+        it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+            expect(maybeBigNumberUtil.toMaybeBigNumber('test')).toEqual(undefined);
+        });
+        it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+            expect(maybeBigNumberUtil.toMaybeBigNumber('test')).toEqual(undefined);
+        });
+        it('should return BigNumber (>=v8.0.0) when passed a value as BigNumber (>=v8.0.0)', () => {
+            const bn = maybeBigNumberUtil.toMaybeBigNumber(BIG_NUMBER_1);
+            expect(BigNumber.isBigNumber(bn)).toEqual(true);
+        });
+        it('should return undefined if value is not BigNumber or string', () => {
+            expect(maybeBigNumberUtil.toMaybeBigNumber(true)).toEqual(undefined);
+        });
+    });
 });
diff --git a/packages/instant/test/util/order_coercion.test.ts b/packages/instant/test/util/order_coercion.test.ts
new file mode 100644
index 000000000..f7a958c9d
--- /dev/null
+++ b/packages/instant/test/util/order_coercion.test.ts
@@ -0,0 +1,103 @@
+import { BigNumber } from '@0x/utils';
+
+import { orderCoercionUtil } from '../../src/util/order_coercion';
+
+const ORDER = {
+    senderAddress: '0x0000000000000000000000000000000000000000',
+    makerAddress: '0x34a745008a643eebc58920eaa29fb1165b4a288e',
+    takerAddress: '0x0000000000000000000000000000000000000000',
+    makerFee: new BigNumber('0'),
+    takerFee: new BigNumber('0'),
+    makerAssetAmount: new BigNumber('200000000000000000000'),
+    takerAssetAmount: new BigNumber('10000000000000000000'),
+    makerAssetData: '0xf47261b00000000000000000000000008cb3971b8eb709c14616bd556ff6683019e90d9c',
+    takerAssetData: '0xf47261b0000000000000000000000000d0a1e359811322d97991e03f863a0c30c2cf029c',
+    expirationTimeSeconds: new BigNumber('1601535600'),
+    feeRecipientAddress: '0x0000000000000000000000000000000000000000',
+    salt: new BigNumber('3101985707338942582579795423923841749956600670712030922928319824580764688653'),
+    signature:
+        '0x1bd4d5686fea801fe33c68c4944356085e7e6cb553eb7073160abd815609f714e85fb47f44b7ffd0a2a1321ac40d72d55163869d0a50fdb5a402132150fe33a08403',
+    exchangeAddress: '0x35dd2932454449b14cee11a94d3674a936d5d7b2',
+};
+
+const STRING_ORDER = {
+    senderAddress: '0x0000000000000000000000000000000000000000',
+    makerAddress: '0x34a745008a643eebc58920eaa29fb1165b4a288e',
+    takerAddress: '0x0000000000000000000000000000000000000000',
+    makerFee: '0',
+    takerFee: '0',
+    makerAssetAmount: '300000000000000000000',
+    takerAssetAmount: '31000000000000000000',
+    makerAssetData: '0xf47261b00000000000000000000000002002d3812f58e35f0ea1ffbf80a75a38c32175fa',
+    takerAssetData: '0xf47261b0000000000000000000000000d0a1e359811322d97991e03f863a0c30c2cf029c',
+    expirationTimeSeconds: '2524636800',
+    feeRecipientAddress: '0x0000000000000000000000000000000000000000',
+    salt: '64592004666704945574675477805199411288137454783320798602050822322450089238268',
+    signature:
+        '0x1c13cacddca8d7d8248e91f412377e68f8f1f9891a59a6c1b2eea9f7b33558c30c4fb86a448e08ab7def40a28fb3a3062dcb33bb3c45302447fce5c4288b7c7f5b03',
+    exchangeAddress: '0x35dd2932454449b14cee11a94d3674a936d5d7b2',
+};
+
+const ORDERS = [ORDER, STRING_ORDER];
+
+describe('orderCoercionUtil', () => {
+    describe('coerceFieldsToBigNumbers', () => {
+        it('should coerce all fields specified to a big number', () => {
+            const coercedOrder = orderCoercionUtil.coerceFieldsToBigNumbers(STRING_ORDER, ['makerFee', 'takerFee']);
+            expect(coercedOrder.makerFee.toString()).toEqual('0');
+            expect(coercedOrder.takerFee.toString()).toEqual('0');
+        });
+        it("should throw if a field can't be found", () => {
+            expect(() => {
+                orderCoercionUtil.coerceFieldsToBigNumbers(ORDER, ['salty']);
+            }).toThrow("Could not find field 'salty' while converting fields to BigNumber.");
+        });
+        it('should not change value if not numeric string or big number', () => {
+            const obj = { number: 'number' };
+            const coercedObj = orderCoercionUtil.coerceFieldsToBigNumbers(obj, ['number']);
+            expect(coercedObj).toEqual({
+                number: 'number',
+            });
+        });
+    });
+    // Note: this doesn't test coercing pre v8.0.0 BigNumber versions to specified one used by 0x
+    describe('coerceOrderFieldsToBigNumber', () => {
+        it('should convert string values in order to big number', () => {
+            const coercedOrder = orderCoercionUtil.coerceOrderFieldsToBigNumber(STRING_ORDER);
+            expect(coercedOrder.makerFee.toString()).toEqual(STRING_ORDER.makerFee);
+            expect(coercedOrder.takerFee.toString()).toEqual(STRING_ORDER.takerFee);
+            expect(coercedOrder.takerAssetAmount.toString()).toEqual(STRING_ORDER.takerAssetAmount);
+            expect(coercedOrder.makerAssetAmount.toString()).toEqual(STRING_ORDER.makerAssetAmount);
+            expect(coercedOrder.salt.toString()).toEqual(STRING_ORDER.salt);
+            expect(coercedOrder.expirationTimeSeconds.toString()).toEqual(STRING_ORDER.expirationTimeSeconds);
+        });
+        it('should convert big number values in order to big number', () => {
+            const coercedOrder = orderCoercionUtil.coerceOrderFieldsToBigNumber(ORDER);
+            expect(coercedOrder.makerFee).toEqual(ORDER.makerFee);
+            expect(coercedOrder.takerFee).toEqual(ORDER.takerFee);
+            expect(coercedOrder.takerAssetAmount).toEqual(ORDER.takerAssetAmount);
+            expect(coercedOrder.makerAssetAmount).toEqual(ORDER.makerAssetAmount);
+            expect(coercedOrder.salt).toEqual(ORDER.salt);
+            expect(coercedOrder.expirationTimeSeconds).toEqual(ORDER.expirationTimeSeconds);
+        });
+    });
+    // Note: this doesn't test coercing pre v8.0.0 BigNumber versions to specified one used by 0x
+    describe('coerceOrderArrayFieldsToBigNumber', () => {
+        it('should convert string values and big numbers in orders to big number', () => {
+            const coercedOrders = orderCoercionUtil.coerceOrderArrayFieldsToBigNumber(ORDERS);
+            expect(coercedOrders[0].makerFee).toEqual(ORDER.makerFee);
+            expect(coercedOrders[0].takerFee).toEqual(ORDER.takerFee);
+            expect(coercedOrders[0].takerAssetAmount).toEqual(ORDER.takerAssetAmount);
+            expect(coercedOrders[0].makerAssetAmount).toEqual(ORDER.makerAssetAmount);
+            expect(coercedOrders[0].salt).toEqual(ORDER.salt);
+            expect(coercedOrders[0].expirationTimeSeconds).toEqual(ORDER.expirationTimeSeconds);
+
+            expect(coercedOrders[1].makerFee.toString()).toEqual(STRING_ORDER.makerFee);
+            expect(coercedOrders[1].takerFee.toString()).toEqual(STRING_ORDER.takerFee);
+            expect(coercedOrders[1].takerAssetAmount.toString()).toEqual(STRING_ORDER.takerAssetAmount);
+            expect(coercedOrders[1].makerAssetAmount.toString()).toEqual(STRING_ORDER.makerAssetAmount);
+            expect(coercedOrders[1].salt.toString()).toEqual(STRING_ORDER.salt);
+            expect(coercedOrders[1].expirationTimeSeconds.toString()).toEqual(STRING_ORDER.expirationTimeSeconds);
+        });
+    });
+});