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authorDavid Sun <dvsuner@protonmail.com>2019-02-06 05:46:51 +0800
committerDavid Sun <dvsuner@protonmail.com>2019-02-06 05:46:51 +0800
commitd95af455f1102dc7aa833ebb7b84498cce564df3 (patch)
treed59490202c60a9ce25e9be2498548f714b6e2156
parent59f48d6d5702210acea868c3ac2ede6315f0c8ec (diff)
downloaddexon-0x-contracts-d95af455f1102dc7aa833ebb7b84498cce564df3.tar.gz
dexon-0x-contracts-d95af455f1102dc7aa833ebb7b84498cce564df3.tar.zst
dexon-0x-contracts-d95af455f1102dc7aa833ebb7b84498cce564df3.zip
added coercion util functions
Diffstat
-rw-r--r--packages/instant/src/index.umd.ts9
-rw-r--r--packages/instant/src/util/maybe_big_number.ts11
-rw-r--r--packages/instant/src/util/signed_order_coercion.ts41
-rw-r--r--packages/instant/test/util/dependencies/prevbignumber.d.ts1772
-rw-r--r--packages/instant/test/util/dependencies/prevbignumber.js2705
-rw-r--r--packages/instant/test/util/maybe_big_number.test.ts71
6 files changed, 4584 insertions, 25 deletions
diff --git a/packages/instant/src/index.umd.ts b/packages/instant/src/index.umd.ts
index 0c2ce5ec1..45913aa47 100644
--- a/packages/instant/src/index.umd.ts
+++ b/packages/instant/src/index.umd.ts
@@ -18,8 +18,8 @@ import { Network, OrderSource } from './types';
import { analytics } from './util/analytics';
import { assert } from './util/assert';
import { providerFactory } from './util/provider_factory';
+import { signedOrderCoercionUtil } from './util/signed_order_coercion';
import { util } from './util/util';
-import { coerceSignedOrderBigNumberOfString } from './util/signed_order_coercion'
const isInstantRendered = (): boolean => !!document.getElementById(INJECTED_DIV_ID);
@@ -94,13 +94,12 @@ export interface ZeroExInstantConfig extends ZeroExInstantOverlayProps {
}
export const render = (config: ZeroExInstantConfig, selector: string = DEFAULT_ZERO_EX_CONTAINER_SELECTOR) => {
- validateInstantRenderConfig(config, selector);
-
- // TODO(David Sun) test functionality of order bignumber version coercion
if (!_.isString(config.orderSource)) {
- config.orderSource = config.orderSource.map(coerceSignedOrderBigNumberOfString);
+ config.orderSource = config.orderSource.map(signedOrderCoercionUtil.bigNumberCoercion);
}
+ validateInstantRenderConfig(config, selector);
+
if (config.shouldDisablePushToHistory) {
if (!isInstantRendered()) {
renderInstant(config, selector);
diff --git a/packages/instant/src/util/maybe_big_number.ts b/packages/instant/src/util/maybe_big_number.ts
index f48473389..7e206a125 100644
--- a/packages/instant/src/util/maybe_big_number.ts
+++ b/packages/instant/src/util/maybe_big_number.ts
@@ -16,6 +16,17 @@ export const maybeBigNumberUtil = {
return validBigNumber.isNaN() ? undefined : validBigNumber;
},
+ // converts a BigNumber or String to the BigNumber used by 0x libraries
+ bigNumberOrStringToMaybeBigNumber: (value: any): Maybe<BigNumber> => {
+ if (_.isString(value)) {
+ return maybeBigNumberUtil.stringToMaybeBigNumber(value);
+ }
+ // checks for pre v8 bignumber with member variable
+ if (BigNumber.isBigNumber(value) || value.isBigNumber) {
+ return new BigNumber(value.toString());
+ }
+ return undefined;
+ },
areMaybeBigNumbersEqual: (val1: Maybe<BigNumber>, val2: Maybe<BigNumber>): boolean => {
if (!_.isUndefined(val1) && !_.isUndefined(val2)) {
return val1.isEqualTo(val2);
diff --git a/packages/instant/src/util/signed_order_coercion.ts b/packages/instant/src/util/signed_order_coercion.ts
index 649596a3d..4209e05e1 100644
--- a/packages/instant/src/util/signed_order_coercion.ts
+++ b/packages/instant/src/util/signed_order_coercion.ts
@@ -1,25 +1,26 @@
-import { BigNumber } from '@0x/asset-buyer';
import { SignedOrder } from '@0x/types';
+import { BigNumber } from '@0x/utils';
+import * as _ from 'lodash';
-export const coerceBigNumberOrString = (value: any): BigNumber => {
- if (typeof value === 'string') {
- return new BigNumber(value);
- }
- if (BigNumber.isBigNumber(value)) {
- return new BigNumber(value.toString());
- }
- return value;
+import { maybeBigNumberUtil } from './maybe_big_number';
+
+const coerceBigNumberOrString = (value: any): BigNumber => {
+ const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(value);
+ return !!bn ? bn : value;
};
-// function implies that the signed order already has been invalidated
-export const coerceSignedOrderBigNumberOfString = (order: SignedOrder): SignedOrder => {
- return {
- ...order,
- makerFee: coerceBigNumberOrString(order.makerFee),
- takerFee: coerceBigNumberOrString(order.takerFee),
- makerAssetAmount: coerceBigNumberOrString(order.makerAssetAmount),
- takerAssetAmount: coerceBigNumberOrString(order.takerAssetAmount),
- salt: coerceBigNumberOrString(order.salt),
- expirationTimeSeconds: coerceBigNumberOrString(order.expirationTimeSeconds),
- };
+// function implies that the signed order already has been validated
+export const signedOrderCoercionUtil = {
+ // coerces order big number values to the BigNumber version utilized by 0x
+ bigNumberCoercion: (order: SignedOrder): SignedOrder => {
+ return {
+ ...order,
+ makerFee: coerceBigNumberOrString(order.makerFee),
+ takerFee: coerceBigNumberOrString(order.takerFee),
+ makerAssetAmount: coerceBigNumberOrString(order.makerAssetAmount),
+ takerAssetAmount: coerceBigNumberOrString(order.takerAssetAmount),
+ salt: coerceBigNumberOrString(order.salt),
+ expirationTimeSeconds: coerceBigNumberOrString(order.expirationTimeSeconds),
+ };
+ },
};
diff --git a/packages/instant/test/util/dependencies/prevbignumber.d.ts b/packages/instant/test/util/dependencies/prevbignumber.d.ts
new file mode 100644
index 000000000..9b802ec3e
--- /dev/null
+++ b/packages/instant/test/util/dependencies/prevbignumber.d.ts
@@ -0,0 +1,1772 @@
+// Type definitions for bignumber.js >=6.0.0
+// Project: https://github.com/MikeMcl/bignumber.js
+// Definitions by: Michael Mclaughlin <https://github.com/MikeMcl>
+// Definitions: https://github.com/MikeMcl/bignumber.js
+
+// Documentation: http://mikemcl.github.io/bignumber.js/
+//
+// Exports (available globally or when using import):
+//
+// class BigNumber (default export)
+// type BigNumber.Constructor
+// type BigNumber.Instance
+// type BigNumber.ModuloMode
+// type BigNumber.RoundingMOde
+// type BigNumber.Value
+// interface BigNumber.Config
+// interface BigNumber.Format
+//
+// Example (alternative syntax commented-out):
+//
+// import {BigNumber} from "bignumber.js"
+// //import BigNumber from "bignumber.js"
+//
+// let rm: BigNumber.RoundingMode = BigNumber.ROUND_UP;
+// let f: BigNumber.Format = { decimalSeparator: ',' };
+// let c: BigNumber.Config = { DECIMAL_PLACES: 4, ROUNDING_MODE: rm, FORMAT: f };
+// BigNumber.config(c);
+//
+// let v: BigNumber.Value = '12345.6789';
+// let b: BigNumber = new BigNumber(v);
+// //let b: BigNumber.Instance = new BigNumber(v);
+//
+// The use of compiler option `--strictNullChecks` is recommended.
+
+
+type BigNumberConstructor = typeof BigNumber;
+type BigNumberInstance = BigNumber;
+type BigNumberModuloMode = BigNumberRoundingMode | 9;
+type BigNumberRoundingMode = 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8;
+type BigNumberValue = string | number | BigNumber;
+
+/**
+ * See `BigNumber.config` and `BigNumber.clone`.
+ */
+interface BigNumberConfig {
+
+ /**
+ * An integer, 0 to 1e+9. Default value: 20.
+ *
+ * The maximum number of decimal places of the result of operations involving division, i.e.
+ * division, square root and base conversion operations, and exponentiation when the exponent is
+ * negative.
+ *
+ * ```ts
+ * BigNumber.config({ DECIMAL_PLACES: 5 })
+ * BigNumber.set({ DECIMAL_PLACES: 5 })
+ * ```
+ */
+ DECIMAL_PLACES?: number;
+
+ /**
+ * An integer, 0 to 8. Default value: `BigNumber.ROUND_HALF_UP` (4).
+ *
+ * The rounding mode used in operations that involve division (see `DECIMAL_PLACES`) and the
+ * default rounding mode of the `decimalPlaces`, `precision`, `toExponential`, `toFixed`,
+ * `toFormat` and `toPrecision` methods.
+ *
+ * The modes are available as enumerated properties of the BigNumber constructor.
+ *
+ * ```ts
+ * BigNumber.config({ ROUNDING_MODE: 0 })
+ * BigNumber.set({ ROUNDING_MODE: BigNumber.ROUND_UP })
+ * ```
+ */
+ ROUNDING_MODE?: BigNumberRoundingMode;
+
+ /**
+ * An integer, 0 to 1e+9, or an array, [-1e+9 to 0, 0 to 1e+9].
+ * Default value: `[-7, 20]`.
+ *
+ * The exponent value(s) at which `toString` returns exponential notation.
+ *
+ * If a single number is assigned, the value is the exponent magnitude.
+ *
+ * If an array of two numbers is assigned then the first number is the negative exponent value at
+ * and beneath which exponential notation is used, and the second number is the positive exponent
+ * value at and above which exponential notation is used.
+ *
+ * For example, to emulate JavaScript numbers in terms of the exponent values at which they begin
+ * to use exponential notation, use `[-7, 20]`.
+ *
+ * ```ts
+ * BigNumber.config({ EXPONENTIAL_AT: 2 })
+ * new BigNumber(12.3) // '12.3' e is only 1
+ * new BigNumber(123) // '1.23e+2'
+ * new BigNumber(0.123) // '0.123' e is only -1
+ * new BigNumber(0.0123) // '1.23e-2'
+ *
+ * BigNumber.config({ EXPONENTIAL_AT: [-7, 20] })
+ * new BigNumber(123456789) // '123456789' e is only 8
+ * new BigNumber(0.000000123) // '1.23e-7'
+ *
+ * // Almost never return exponential notation:
+ * BigNumber.config({ EXPONENTIAL_AT: 1e+9 })
+ *
+ * // Always return exponential notation:
+ * BigNumber.config({ EXPONENTIAL_AT: 0 })
+ * ```
+ *
+ * Regardless of the value of `EXPONENTIAL_AT`, the `toFixed` method will always return a value in
+ * normal notation and the `toExponential` method will always return a value in exponential form.
+ * Calling `toString` with a base argument, e.g. `toString(10)`, will also always return normal
+ * notation.
+ */
+ EXPONENTIAL_AT?: number|[number, number];
+
+ /**
+ * An integer, magnitude 1 to 1e+9, or an array, [-1e+9 to -1, 1 to 1e+9].
+ * Default value: `[-1e+9, 1e+9]`.
+ *
+ * The exponent value(s) beyond which overflow to Infinity and underflow to zero occurs.
+ *
+ * If a single number is assigned, it is the maximum exponent magnitude: values wth a positive
+ * exponent of greater magnitude become Infinity and those with a negative exponent of greater
+ * magnitude become zero.
+ *
+ * If an array of two numbers is assigned then the first number is the negative exponent limit and
+ * the second number is the positive exponent limit.
+ *
+ * For example, to emulate JavaScript numbers in terms of the exponent values at which they
+ * become zero and Infinity, use [-324, 308].
+ *
+ * ```ts
+ * BigNumber.config({ RANGE: 500 })
+ * BigNumber.config().RANGE // [ -500, 500 ]
+ * new BigNumber('9.999e499') // '9.999e+499'
+ * new BigNumber('1e500') // 'Infinity'
+ * new BigNumber('1e-499') // '1e-499'
+ * new BigNumber('1e-500') // '0'
+ *
+ * BigNumber.config({ RANGE: [-3, 4] })
+ * new BigNumber(99999) // '99999' e is only 4
+ * new BigNumber(100000) // 'Infinity' e is 5
+ * new BigNumber(0.001) // '0.01' e is only -3
+ * new BigNumber(0.0001) // '0' e is -4
+ * ```
+ * The largest possible magnitude of a finite BigNumber is 9.999...e+1000000000.
+ * The smallest possible magnitude of a non-zero BigNumber is 1e-1000000000.
+ */
+ RANGE?: number|[number, number];
+
+ /**
+ * A boolean: `true` or `false`. Default value: `false`.
+ *
+ * The value that determines whether cryptographically-secure pseudo-random number generation is
+ * used. If `CRYPTO` is set to true then the random method will generate random digits using
+ * `crypto.getRandomValues` in browsers that support it, or `crypto.randomBytes` if using a
+ * version of Node.js that supports it.
+ *
+ * If neither function is supported by the host environment then attempting to set `CRYPTO` to
+ * `true` will fail and an exception will be thrown.
+ *
+ * If `CRYPTO` is `false` then the source of randomness used will be `Math.random` (which is
+ * assumed to generate at least 30 bits of randomness).
+ *
+ * See `BigNumber.random`.
+ *
+ * ```ts
+ * BigNumber.config({ CRYPTO: true })
+ * BigNumber.config().CRYPTO // true
+ * BigNumber.random() // 0.54340758610486147524
+ * ```
+ */
+ CRYPTO?: boolean;
+
+ /**
+ * An integer, 0 to 9. Default value: `BigNumber.ROUND_DOWN` (1).
+ *
+ * The modulo mode used when calculating the modulus: `a mod n`.
+ * The quotient, `q = a / n`, is calculated according to the `ROUNDING_MODE` that corresponds to
+ * the chosen `MODULO_MODE`.
+ * The remainder, `r`, is calculated as: `r = a - n * q`.
+ *
+ * The modes that are most commonly used for the modulus/remainder operation are shown in the
+ * following table. Although the other rounding modes can be used, they may not give useful
+ * results.
+ *
+ * Property | Value | Description
+ * :------------------|:------|:------------------------------------------------------------------
+ * `ROUND_UP` | 0 | The remainder is positive if the dividend is negative.
+ * `ROUND_DOWN` | 1 | The remainder has the same sign as the dividend.
+ * | | Uses 'truncating division' and matches JavaScript's `%` operator .
+ * `ROUND_FLOOR` | 3 | The remainder has the same sign as the divisor.
+ * | | This matches Python's `%` operator.
+ * `ROUND_HALF_EVEN` | 6 | The IEEE 754 remainder function.
+ * `EUCLID` | 9 | The remainder is always positive.
+ * | | Euclidian division: `q = sign(n) * floor(a / abs(n))`
+ *
+ * The rounding/modulo modes are available as enumerated properties of the BigNumber constructor.
+ *
+ * See `modulo`.
+ *
+ * ```ts
+ * BigNumber.config({ MODULO_MODE: BigNumber.EUCLID })
+ * BigNumber.set({ MODULO_MODE: 9 }) // equivalent
+ * ```
+ */
+ MODULO_MODE?: BigNumberModuloMode;
+
+ /**
+ * An integer, 0 to 1e+9. Default value: 0.
+ *
+ * The maximum precision, i.e. number of significant digits, of the result of the power operation
+ * - unless a modulus is specified.
+ *
+ * If set to 0, the number of significant digits will not be limited.
+ *
+ * See `exponentiatedBy`.
+ *
+ * ```ts
+ * BigNumber.config({ POW_PRECISION: 100 })
+ * ```
+ */
+ POW_PRECISION?: number;
+
+ /**
+ * An object including any number of the properties shown below.
+ *
+ * The object configures the format of the string returned by the `toFormat` method.
+ * The example below shows the properties of the object that are recognised, and
+ * their default values.
+ *
+ * Unlike the other configuration properties, the values of the properties of the `FORMAT` object
+ * will not be checked for validity - the existing object will simply be replaced by the object
+ * that is passed in.
+ *
+ * See `toFormat`.
+ *
+ * ```ts
+ * BigNumber.config({
+ * FORMAT: {
+ * // the decimal separator
+ * decimalSeparator: '.',
+ * // the grouping separator of the integer part
+ * groupSeparator: ',',
+ * // the primary grouping size of the integer part
+ * groupSize: 3,
+ * // the secondary grouping size of the integer part
+ * secondaryGroupSize: 0,
+ * // the grouping separator of the fraction part
+ * fractionGroupSeparator: ' ',
+ * // the grouping size of the fraction part
+ * fractionGroupSize: 0
+ * }
+ * })
+ * ```
+ */
+ FORMAT?: BigNumberFormat;
+
+ /**
+ * A string representing the alphabet used for base conversion.
+ * Default value: `'0123456789abcdefghijklmnopqrstuvwxyz'`.
+ *
+ * The length of the alphabet corresponds to the maximum value of the base argument that can be
+ * passed to the BigNumber constructor or `toString`. There is no maximum length, but it must be
+ * at least 2 characters long, and it must not contain a repeated character, or `'.'` - the
+ * decimal separator for all values whatever their base.
+ *
+ * ```ts
+ * // duodecimal (base 12)
+ * BigNumber.config({ ALPHABET: '0123456789TE' })
+ * x = new BigNumber('T', 12)
+ * x.toString() // '10'
+ * x.toString(12) // 'T'
+ * ```
+ */
+ ALPHABET?: string;
+}
+
+
+/**
+ * See `FORMAT` and `toFormat`.
+ */
+interface BigNumberFormat {
+
+ /**
+ * The decimal separator.
+ */
+ decimalSeparator?: string;
+
+ /**
+ * The grouping separator of the integer part.
+ */
+ groupSeparator?: string;
+
+ /**
+ * The primary grouping size of the integer part.
+ */
+ groupSize?: number;
+
+ /**
+ * The secondary grouping size of the integer part.
+ */
+ secondaryGroupSize?: number;
+
+ /**
+ * The grouping separator of the fraction part.
+ */
+ fractionGroupSeparator?: string;
+
+ /**
+ * The grouping size of the fraction part.
+ */
+ fractionGroupSize?: number;
+}
+
+
+export declare class BigNumber {
+
+ /**
+ * Used internally by the `BigNumber.isBigNumber` method.
+ */
+ private readonly _isBigNumber: true;
+
+ /**
+ * The coefficient of the value of this BigNumber, an array of base 1e14 integer numbers.
+ */
+ readonly c: number[];
+
+ /**
+ * The exponent of the value of this BigNumber, an integer number, -1000000000 to 1000000000.
+ */
+ readonly e: number;
+
+ /**
+ * The sign of the value of this BigNumber, -1 or 1.
+ */
+ readonly s: number;
+
+ /**
+ * Returns a new instance of BigNumber with value `n`.
+ *
+ * Legitimate values for `n` include ±0, ±`Infinity` and `NaN`.
+ *
+ * Values of type number with more than 15 significant digits are considered invalid as calling
+ * `toString` or `valueOf` on such numbers may not result in the intended value.
+ *
+ * ```ts
+ * console.log( 823456789123456.3 ); // 823456789123456.2
+ * ```
+ *
+ * There is no limit to the number of digits of a value of type string (other than that of
+ * JavaScript's maximum array size). Decimal string values may be in exponential, as well as
+ * normal (fixed-point) notation. Non-decimal values must be in normal notation.
+ *
+ * String values in hexadecimal literal form, e.g. '0xff', are valid, as are string values with
+ * the octal and binary prefixs '0o' and '0b'. String values in octal literal form without the
+ * prefix will be interpreted as decimals, e.g. '011' is interpreted as 11, not 9.
+ *
+ * Values in any base may have fraction digits.
+ *
+ * If a base is specified, `n` is rounded according to the current `DECIMAL_PLACES` and
+ * `ROUNDING_MODE` settings. If base is omitted, or is `null` or `undefined`, base 10 is assumed.
+ *
+ * Throws an invalid `value` or `base`.
+ *
+ * ```ts
+ * x = new BigNumber(9) // '9'
+ * y = new BigNumber(x) // '9'
+ *
+ * // 'new' is optional
+ * BigNumber(435.345) // '435.345'
+ *
+ * new BigNumber('5032485723458348569331745.33434346346912144534543')
+ * new BigNumber('4.321e+4') // '43210'
+ * new BigNumber('-735.0918e-430') // '-7.350918e-428'
+ * new BigNumber(Infinity) // 'Infinity'
+ * new BigNumber(NaN) // 'NaN'
+ * new BigNumber('.5') // '0.5'
+ * new BigNumber('+2') // '2'
+ * new BigNumber(-10110100.1, 2) // '-180.5'
+ * new BigNumber(-0b10110100.1) // '-180.5'
+ * new BigNumber('123412421.234324', 5) // '607236.557696'
+ * new BigNumber('ff.8', 16) // '255.5'
+ * new BigNumber('0xff.8') // '255.5'
+ *
+ * // The following throws 'Not a base 2 number'.
+ * new BigNumber(9, 2)
+ *
+ * // The following throws 'Number primitive has more than 15 significant digits'.
+ * new BigNumber(96517860459076817.4395)
+ *
+ * // The following throws 'Not a number'.
+ * new BigNumber('blurgh')
+ *
+ * // A value is only rounded by the constructor if a base is specified.
+ * BigNumber.config({ DECIMAL_PLACES: 5 })
+ * new BigNumber(1.23456789) // '1.23456789'
+ * new BigNumber(1.23456789, 10) // '1.23457'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param base The base of n, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
+ */
+ constructor(n: BigNumberValue, base?: number);
+
+ /**
+ * Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
+ * BigNumber.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber(-0.8)
+ * x.absoluteValue() // '0.8'
+ * ```
+ */
+ absoluteValue(): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the absolute value, i.e. the magnitude, of the value of this
+ * BigNumber.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber(-0.8)
+ * x.abs() // '0.8'
+ * ```
+ */
+ abs(): BigNumber;
+
+ /**
+ * Returns | |
+ * :-------:|:--------------------------------------------------------------|
+ * 1 | If the value of this BigNumber is greater than the value of `n`
+ * -1 | If the value of this BigNumber is less than the value of `n`
+ * 0 | If this BigNumber and `n` have the same value
+ * `null` | If the value of either this BigNumber or `n` is `NaN`
+ *
+ * ```ts
+ *
+ * x = new BigNumber(Infinity)
+ * y = new BigNumber(5)
+ * x.comparedTo(y) // 1
+ * x.comparedTo(x.minus(1)) // 0
+ * y.comparedTo(NaN) // null
+ * y.comparedTo('110', 2) // -1
+ * ```
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ comparedTo(n: BigNumberValue, base?: number): number;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
+ * `roundingMode` to a maximum of `decimalPlaces` decimal places.
+ *
+ * If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
+ * decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
+ * ±`Infinity` or `NaN`.
+ *
+ * If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `decimalPlaces` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(1234.56)
+ * x.decimalPlaces() // 2
+ * x.decimalPlaces(1) // '1234.6'
+ * x.decimalPlaces(2) // '1234.56'
+ * x.decimalPlaces(10) // '1234.56'
+ * x.decimalPlaces(0, 1) // '1234'
+ * x.decimalPlaces(0, 6) // '1235'
+ * x.decimalPlaces(1, 1) // '1234.5'
+ * x.decimalPlaces(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
+ * x // '1234.56'
+ * y = new BigNumber('9.9e-101')
+ * y.decimalPlaces() // 102
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ decimalPlaces(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber rounded by rounding mode
+ * `roundingMode` to a maximum of `decimalPlaces` decimal places.
+ *
+ * If `decimalPlaces` is omitted, or is `null` or `undefined`, the return value is the number of
+ * decimal places of the value of this BigNumber, or `null` if the value of this BigNumber is
+ * ±`Infinity` or `NaN`.
+ *
+ * If `roundingMode` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `decimalPlaces` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(1234.56)
+ * x.dp() // 2
+ * x.dp(1) // '1234.6'
+ * x.dp(2) // '1234.56'
+ * x.dp(10) // '1234.56'
+ * x.dp(0, 1) // '1234'
+ * x.dp(0, 6) // '1235'
+ * x.dp(1, 1) // '1234.5'
+ * x.dp(1, BigNumber.ROUND_HALF_EVEN) // '1234.6'
+ * x // '1234.56'
+ * y = new BigNumber('9.9e-101')
+ * y.dp() // 102
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ dp(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
+ * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+ *
+ * ```ts
+ * x = new BigNumber(355)
+ * y = new BigNumber(113)
+ * x.dividedBy(y) // '3.14159292035398230088'
+ * x.dividedBy(5) // '71'
+ * x.dividedBy(47, 16) // '5'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ dividedBy(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber divided by `n`, rounded
+ * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+ *
+ * ```ts
+ * x = new BigNumber(355)
+ * y = new BigNumber(113)
+ * x.div(y) // '3.14159292035398230088'
+ * x.div(5) // '71'
+ * x.div(47, 16) // '5'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ div(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+ * `n`.
+ *
+ * ```ts
+ * x = new BigNumber(5)
+ * y = new BigNumber(3)
+ * x.dividedToIntegerBy(y) // '1'
+ * x.dividedToIntegerBy(0.7) // '7'
+ * x.dividedToIntegerBy('0.f', 16) // '5'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ dividedToIntegerBy(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the integer part of dividing the value of this BigNumber by
+ * `n`.
+ *
+ * ```ts
+ * x = new BigNumber(5)
+ * y = new BigNumber(3)
+ * x.idiv(y) // '1'
+ * x.idiv(0.7) // '7'
+ * x.idiv('0.f', 16) // '5'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ idiv(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
+ * raised to the power `n`, and optionally modulo a modulus `m`.
+ *
+ * If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
+ * `ROUNDING_MODE` settings.
+ *
+ * As the number of digits of the result of the power operation can grow so large so quickly,
+ * e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
+ * limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
+ *
+ * By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
+ * digits will be calculated, and that the method's performance will decrease dramatically for
+ * larger exponents.
+ *
+ * If `m` is specified and the value of `m`, `n` and this BigNumber are positive integers, then a
+ * fast modular exponentiation algorithm is used, otherwise if any of the values is not a positive
+ * integer the operation will simply be performed as `x.exponentiatedBy(n).modulo(m)` with a
+ * `POW_PRECISION` of 0.
+ *
+ * Throws if `n` is not a primitive number, or is not an integer, or is out of range.
+ *
+ * ```ts
+ * Math.pow(0.7, 2) // 0.48999999999999994
+ * x = new BigNumber(0.7)
+ * x.exponentiatedBy(2) // '0.49'
+ * BigNumber(3).exponentiatedBy(-2) // '0.11111111111111111111'
+ * ```
+ *
+ * @param n The exponent, an integer, -9007199254740991 to 9007199254740991.
+ * @param [m] The modulus, a positive integer.
+ */
+ exponentiatedBy(n: number, m?: BigNumberValue): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber exponentiated by `n`, i.e.
+ * raised to the power `n`, and optionally modulo a modulus `m`.
+ *
+ * If `n` is negative the result is rounded according to the current `DECIMAL_PLACES` and
+ * `ROUNDING_MODE` settings.
+ *
+ * As the number of digits of the result of the power operation can grow so large so quickly,
+ * e.g. 123.456**10000 has over 50000 digits, the number of significant digits calculated is
+ * limited to the value of the `POW_PRECISION` setting (unless a modulus `m` is specified).
+ *
+ * By default `POW_PRECISION` is set to 0. This means that an unlimited number of significant
+ * digits will be calculated, and that the method's performance will decrease dramatically for
+ * larger exponents.
+ *
+ * If `m` is specified and the value of `m`, `n` and this BigNumber are positive integers, then a
+ * fast modular exponentiation algorithm is used, otherwise if any of the values is not a positive
+ * integer the operation will simply be performed as `x.exponentiatedBy(n).modulo(m)` with a
+ * `POW_PRECISION` of 0.
+ *
+ * Throws if `n` is not a primitive number or an integer, or is out of range.
+ *
+ * ```ts
+ * Math.pow(0.7, 2) // 0.48999999999999994
+ * x = new BigNumber(0.7)
+ * x.pow(2) // '0.49'
+ * BigNumber(3).pow(-2) // '0.11111111111111111111'
+ * ```
+ *
+ * @param n The exponent, an integer, -9007199254740991 to 9007199254740991.
+ * @param [m] The modulus, a positive integer.
+ */
+ pow(n: number, m?: BigNumberValue): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber rounded to an integer using
+ * rounding mode `rm`.
+ *
+ * If `rm` is omitted, or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `rm` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(123.456)
+ * x.integerValue() // '123'
+ * x.integerValue(BigNumber.ROUND_CEIL) // '124'
+ * y = new BigNumber(-12.7)
+ * y.integerValue() // '-13'
+ * x.integerValue(BigNumber.ROUND_DOWN) // '-12'
+ * ```
+ *
+ * @param {BigNumberRoundingMode} [rm] The roundng mode, an integer, 0 to 8.
+ */
+ integerValue(rm?: BigNumberRoundingMode): BigNumber;
+
+ /**
+ * Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
+ * `false`.
+ *
+ * As with JavaScript, `NaN` does not equal `NaN`.
+ *
+ * ```ts
+ * 0 === 1e-324 // true
+ * x = new BigNumber(0)
+ * x.isEqualTo('1e-324') // false
+ * BigNumber(-0).isEqualTo(x) // true ( -0 === 0 )
+ * BigNumber(255).isEqualTo('ff', 16) // true
+ *
+ * y = new BigNumber(NaN)
+ * y.isEqualTo(NaN) // false
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ isEqualTo(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is equal to the value of `n`, otherwise returns
+ * `false`.
+ *
+ * As with JavaScript, `NaN` does not equal `NaN`.
+ *
+ * ```ts
+ * 0 === 1e-324 // true
+ * x = new BigNumber(0)
+ * x.eq('1e-324') // false
+ * BigNumber(-0).eq(x) // true ( -0 === 0 )
+ * BigNumber(255).eq('ff', 16) // true
+ *
+ * y = new BigNumber(NaN)
+ * y.eq(NaN) // false
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ eq(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is a finite number, otherwise returns `false`.
+ *
+ * The only possible non-finite values of a BigNumber are `NaN`, `Infinity` and `-Infinity`.
+ *
+ * ```ts
+ * x = new BigNumber(1)
+ * x.isFinite() // true
+ * y = new BigNumber(Infinity)
+ * y.isFinite() // false
+ * ```
+ */
+ isFinite(): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
+ * returns `false`.
+ *
+ * ```ts
+ * 0.1 > (0.3 - 0.2) // true
+ * x = new BigNumber(0.1)
+ * x.isGreaterThan(BigNumber(0.3).minus(0.2)) // false
+ * BigNumber(0).isGreaterThan(x) // false
+ * BigNumber(11, 3).isGreaterThan(11.1, 2) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ isGreaterThan(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is greater than the value of `n`, otherwise
+ * returns `false`.
+ *
+ * ```ts
+ * 0.1 > (0.3 - 0 // true
+ * x = new BigNumber(0.1)
+ * x.gt(BigNumber(0.3).minus(0.2)) // false
+ * BigNumber(0).gt(x) // false
+ * BigNumber(11, 3).gt(11.1, 2) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ gt(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
+ * otherwise returns `false`.
+ *
+ * ```ts
+ * (0.3 - 0.2) >= 0.1 // false
+ * x = new BigNumber(0.3).minus(0.2)
+ * x.isGreaterThanOrEqualTo(0.1) // true
+ * BigNumber(1).isGreaterThanOrEqualTo(x) // true
+ * BigNumber(10, 18).isGreaterThanOrEqualTo('i', 36) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ isGreaterThanOrEqualTo(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is greater than or equal to the value of `n`,
+ * otherwise returns `false`.
+ *
+ * ```ts
+ * (0.3 - 0.2) >= 0.1 // false
+ * x = new BigNumber(0.3).minus(0.2)
+ * x.gte(0.1) // true
+ * BigNumber(1).gte(x) // true
+ * BigNumber(10, 18).gte('i', 36) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ gte(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is an integer, otherwise returns `false`.
+ *
+ * ```ts
+ * x = new BigNumber(1)
+ * x.isInteger() // true
+ * y = new BigNumber(123.456)
+ * y.isInteger() // false
+ * ```
+ */
+ isInteger(): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
+ * `false`.
+ *
+ * ```ts
+ * (0.3 - 0.2) < 0.1 // true
+ * x = new BigNumber(0.3).minus(0.2)
+ * x.isLessThan(0.1) // false
+ * BigNumber(0).isLessThan(x) // true
+ * BigNumber(11.1, 2).isLessThan(11, 3) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ isLessThan(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is less than the value of `n`, otherwise returns
+ * `false`.
+ *
+ * ```ts
+ * (0.3 - 0.2) < 0.1 // true
+ * x = new BigNumber(0.3).minus(0.2)
+ * x.lt(0.1) // false
+ * BigNumber(0).lt(x) // true
+ * BigNumber(11.1, 2).lt(11, 3) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ lt(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
+ * otherwise returns `false`.
+ *
+ * ```ts
+ * 0.1 <= (0.3 - 0.2) // false
+ * x = new BigNumber(0.1)
+ * x.isLessThanOrEqualTo(BigNumber(0.3).minus(0.2)) // true
+ * BigNumber(-1).isLessThanOrEqualTo(x) // true
+ * BigNumber(10, 18).isLessThanOrEqualTo('i', 36) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ isLessThanOrEqualTo(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is less than or equal to the value of `n`,
+ * otherwise returns `false`.
+ *
+ * ```ts
+ * 0.1 <= (0.3 - 0.2) // false
+ * x = new BigNumber(0.1)
+ * x.lte(BigNumber(0.3).minus(0.2)) // true
+ * BigNumber(-1).lte(x) // true
+ * BigNumber(10, 18).lte('i', 36) // true
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ lte(n: BigNumberValue, base?: number): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is `NaN`, otherwise returns `false`.
+ *
+ * ```ts
+ * x = new BigNumber(NaN)
+ * x.isNaN() // true
+ * y = new BigNumber('Infinity')
+ * y.isNaN() // false
+ * ```
+ */
+ isNaN(): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is negative, otherwise returns `false`.
+ *
+ * ```ts
+ * x = new BigNumber(-0)
+ * x.isNegative() // true
+ * y = new BigNumber(2)
+ * y.isNegative() // false
+ * ```
+ */
+ isNegative(): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is positive, otherwise returns `false`.
+ *
+ * ```ts
+ * x = new BigNumber(-0)
+ * x.isPositive() // false
+ * y = new BigNumber(2)
+ * y.isPositive() // true
+ * ```
+ */
+ isPositive(): boolean;
+
+ /**
+ * Returns `true` if the value of this BigNumber is zero or minus zero, otherwise returns `false`.
+ *
+ * ```ts
+ * x = new BigNumber(-0)
+ * x.isZero() // true
+ * ```
+ */
+ isZero(): boolean;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber minus `n`.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * 0.3 - 0.1 // 0.19999999999999998
+ * x = new BigNumber(0.3)
+ * x.minus(0.1) // '0.2'
+ * x.minus(0.6, 20) // '0'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ minus(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
+ * remainder of dividing this BigNumber by `n`.
+ *
+ * The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
+ * setting of this BigNumber constructor. If it is 1 (default value), the result will have the
+ * same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
+ * limits of double precision) and BigDecimal's `remainder` method.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * See `MODULO_MODE` for a description of the other modulo modes.
+ *
+ * ```ts
+ * 1 % 0.9 // 0.09999999999999998
+ * x = new BigNumber(1)
+ * x.modulo(0.9) // '0.1'
+ * y = new BigNumber(33)
+ * y.modulo('a', 33) // '3'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ modulo(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber modulo `n`, i.e. the integer
+ * remainder of dividing this BigNumber by `n`.
+ *
+ * The value returned, and in particular its sign, is dependent on the value of the `MODULO_MODE`
+ * setting of this BigNumber constructor. If it is 1 (default value), the result will have the
+ * same sign as this BigNumber, and it will match that of Javascript's `%` operator (within the
+ * limits of double precision) and BigDecimal's `remainder` method.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * See `MODULO_MODE` for a description of the other modulo modes.
+ *
+ * ```ts
+ * 1 % 0.9 // 0.09999999999999998
+ * x = new BigNumber(1)
+ * x.mod(0.9) // '0.1'
+ * y = new BigNumber(33)
+ * y.mod('a', 33) // '3'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ mod(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * 0.6 * 3 // 1.7999999999999998
+ * x = new BigNumber(0.6)
+ * y = x.multipliedBy(3) // '1.8'
+ * BigNumber('7e+500').multipliedBy(y) // '1.26e+501'
+ * x.multipliedBy('-a', 16) // '-6'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ multipliedBy(n: BigNumberValue, base?: number) : BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber multiplied by `n`.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * 0.6 * 3 // 1.7999999999999998
+ * x = new BigNumber(0.6)
+ * y = x.times(3) // '1.8'
+ * BigNumber('7e+500').times(y) // '1.26e+501'
+ * x.times('-a', 16) // '-6'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ times(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber negated, i.e. multiplied by -1.
+ *
+ * ```ts
+ * x = new BigNumber(1.8)
+ * x.negated() // '-1.8'
+ * y = new BigNumber(-1.3)
+ * y.negated() // '1.3'
+ * ```
+ */
+ negated(): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber plus `n`.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * 0.1 + 0.2 // 0.30000000000000004
+ * x = new BigNumber(0.1)
+ * y = x.plus(0.2) // '0.3'
+ * BigNumber(0.7).plus(x).plus(y) // '1'
+ * x.plus('0.1', 8) // '0.225'
+ * ```
+ *
+ * @param n A numeric value.
+ * @param [base] The base of n.
+ */
+ plus(n: BigNumberValue, base?: number): BigNumber;
+
+ /**
+ * Returns the number of significant digits of the value of this BigNumber, or `null` if the value
+ * of this BigNumber is ±`Infinity` or `NaN`.
+ *
+ * If `includeZeros` is true then any trailing zeros of the integer part of the value of this
+ * BigNumber are counted as significant digits, otherwise they are not.
+ *
+ * Throws if `includeZeros` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(9876.54321)
+ * x.precision() // 9
+ * y = new BigNumber(987000)
+ * y.precision(false) // 3
+ * y.precision(true) // 6
+ * ```
+ *
+ * @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
+ */
+ precision(includeZeros?: boolean): number;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
+ * `significantDigits` significant digits using rounding mode `roundingMode`.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
+ *
+ * Throws if `significantDigits` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(9876.54321)
+ * x.precision(6) // '9876.54'
+ * x.precision(6, BigNumber.ROUND_UP) // '9876.55'
+ * x.precision(2) // '9900'
+ * x.precision(2, 1) // '9800'
+ * x // '9876.54321'
+ * ```
+ *
+ * @param significantDigits Significant digits, integer, 1 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ precision(significantDigits: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+ /**
+ * Returns the number of significant digits of the value of this BigNumber,
+ * or `null` if the value of this BigNumber is ±`Infinity` or `NaN`.
+ *
+ * If `includeZeros` is true then any trailing zeros of the integer part of
+ * the value of this BigNumber are counted as significant digits, otherwise
+ * they are not.
+ *
+ * Throws if `includeZeros` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(9876.54321)
+ * x.sd() // 9
+ * y = new BigNumber(987000)
+ * y.sd(false) // 3
+ * y.sd(true) // 6
+ * ```
+ *
+ * @param [includeZeros] Whether to include integer trailing zeros in the significant digit count.
+ */
+ sd(includeZeros?: boolean): number;
+
+ /*
+ * Returns a BigNumber whose value is the value of this BigNumber rounded to a precision of
+ * `significantDigits` significant digits using rounding mode `roundingMode`.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` will be used.
+ *
+ * Throws if `significantDigits` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(9876.54321)
+ * x.sd(6) // '9876.54'
+ * x.sd(6, BigNumber.ROUND_UP) // '9876.55'
+ * x.sd(2) // '9900'
+ * x.sd(2, 1) // '9800'
+ * x // '9876.54321'
+ * ```
+ *
+ * @param significantDigits Significant digits, integer, 1 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ sd(significantDigits: number, roundingMode?: BigNumberRoundingMode): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the value of this BigNumber shifted by `n` places.
+ *
+ * The shift is of the decimal point, i.e. of powers of ten, and is to the left if `n` is negative
+ * or to the right if `n` is positive.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * Throws if `n` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(1.23)
+ * x.shiftedBy(3) // '1230'
+ * x.shiftedBy(-3) // '0.00123'
+ * ```
+ *
+ * @param n The shift value, integer, -9007199254740991 to 9007199254740991.
+ */
+ shiftedBy(n: number): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
+ * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+ *
+ * The return value will be correctly rounded, i.e. rounded as if the result was first calculated
+ * to an infinite number of correct digits before rounding.
+ *
+ * ```ts
+ * x = new BigNumber(16)
+ * x.squareRoot() // '4'
+ * y = new BigNumber(3)
+ * y.squareRoot() // '1.73205080756887729353'
+ * ```
+ */
+ squareRoot(): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the square root of the value of this BigNumber, rounded
+ * according to the current `DECIMAL_PLACES` and `ROUNDING_MODE` settings.
+ *
+ * The return value will be correctly rounded, i.e. rounded as if the result was first calculated
+ * to an infinite number of correct digits before rounding.
+ *
+ * ```ts
+ * x = new BigNumber(16)
+ * x.sqrt() // '4'
+ * y = new BigNumber(3)
+ * y.sqrt() // '1.73205080756887729353'
+ * ```
+ */
+ sqrt(): BigNumber;
+
+ /**
+ * Returns a string representing the value of this BigNumber in exponential notation rounded using
+ * rounding mode `roundingMode` to `decimalPlaces` decimal places, i.e with one digit before the
+ * decimal point and `decimalPlaces` digits after it.
+ *
+ * If the value of this BigNumber in exponential notation has fewer than `decimalPlaces` fraction
+ * digits, the return value will be appended with zeros accordingly.
+ *
+ * If `decimalPlaces` is omitted, or is `null` or `undefined`, the number of digits after the
+ * decimal point defaults to the minimum number of digits necessary to represent the value
+ * exactly.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `decimalPlaces` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = 45.6
+ * y = new BigNumber(x)
+ * x.toExponential() // '4.56e+1'
+ * y.toExponential() // '4.56e+1'
+ * x.toExponential(0) // '5e+1'
+ * y.toExponential(0) // '5e+1'
+ * x.toExponential(1) // '4.6e+1'
+ * y.toExponential(1) // '4.6e+1'
+ * y.toExponential(1, 1) // '4.5e+1' (ROUND_DOWN)
+ * x.toExponential(3) // '4.560e+1'
+ * y.toExponential(3) // '4.560e+1'
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ toExponential(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+ /**
+ * Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ * rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`.
+ *
+ * If the value of this BigNumber in normal notation has fewer than `decimalPlaces` fraction
+ * digits, the return value will be appended with zeros accordingly.
+ *
+ * Unlike `Number.prototype.toFixed`, which returns exponential notation if a number is greater or
+ * equal to 10**21, this method will always return normal notation.
+ *
+ * If `decimalPlaces` is omitted or is `null` or `undefined`, the return value will be unrounded
+ * and in normal notation. This is also unlike `Number.prototype.toFixed`, which returns the value
+ * to zero decimal places. It is useful when normal notation is required and the current
+ * `EXPONENTIAL_AT` setting causes `toString` to return exponential notation.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `decimalPlaces` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = 3.456
+ * y = new BigNumber(x)
+ * x.toFixed() // '3'
+ * y.toFixed() // '3.456'
+ * y.toFixed(0) // '3'
+ * x.toFixed(2) // '3.46'
+ * y.toFixed(2) // '3.46'
+ * y.toFixed(2, 1) // '3.45' (ROUND_DOWN)
+ * x.toFixed(5) // '3.45600'
+ * y.toFixed(5) // '3.45600'
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ toFixed(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+ /**
+ * Returns a string representing the value of this BigNumber in normal (fixed-point) notation
+ * rounded to `decimalPlaces` decimal places using rounding mode `roundingMode`, and formatted
+ * according to the properties of the `FORMAT` object.
+ *
+ * The properties of the `FORMAT` object are shown in the examples below.
+ *
+ * If `decimalPlaces` is omitted or is `null` or `undefined`, then the return value is not
+ * rounded to a fixed number of decimal places.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `decimalPlaces` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * format = {
+ * decimalSeparator: '.',
+ * groupSeparator: ',',
+ * groupSize: 3,
+ * secondaryGroupSize: 0,
+ * fractionGroupSeparator: ' ',
+ * fractionGroupSize: 0
+ * }
+ * BigNumber.config({ FORMAT: format })
+ *
+ * x = new BigNumber('123456789.123456789')
+ * x.toFormat() // '123,456,789.123456789'
+ * x.toFormat(1) // '123,456,789.1'
+ *
+ * format.groupSeparator = ' '
+ * format.fractionGroupSize = 5
+ * x.toFormat() // '123 456 789.12345 6789'
+ *
+ * BigNumber.config({
+ * FORMAT: {
+ * decimalSeparator: ',',
+ * groupSeparator: '.',
+ * groupSize: 3,
+ * secondaryGroupSize: 2
+ * }
+ * })
+ *
+ * x.toFormat(6) // '12.34.56.789,123'
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer, 0 to 8.
+ */
+ toFormat(decimalPlaces?: number, roundingMode?: BigNumberRoundingMode): string;
+
+ /**
+ * Returns a string array representing the value of this BigNumber as a simple fraction with an
+ * integer numerator and an integer denominator. The denominator will be a positive non-zero value
+ * less than or equal to `max_denominator`.
+ *
+ * If a maximum denominator, `max_denominator`, is not specified, or is `null` or `undefined`, the
+ * denominator will be the lowest value necessary to represent the number exactly.
+ *
+ * Throws if `max_denominator` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(1.75)
+ * x.toFraction() // '7, 4'
+ *
+ * pi = new BigNumber('3.14159265358')
+ * pi.toFraction() // '157079632679,50000000000'
+ * pi.toFraction(100000) // '312689, 99532'
+ * pi.toFraction(10000) // '355, 113'
+ * pi.toFraction(100) // '311, 99'
+ * pi.toFraction(10) // '22, 7'
+ * pi.toFraction(1) // '3, 1'
+ * ```
+ *
+ * @param [max_denominator] The maximum denominator, integer, >= 1 and < Infinity.
+ */
+ toFraction(max_denominator?: BigNumberValue): BigNumber[];
+
+ /**
+ * As `valueOf`.
+ */
+ toJSON(): string;
+
+ /**
+ * Returns the value of this BigNumber as a JavaScript primitive number.
+ *
+ * Using the unary plus operator gives the same result.
+ *
+ * ```ts
+ * x = new BigNumber(456.789)
+ * x.toNumber() // 456.789
+ * +x // 456.789
+ *
+ * y = new BigNumber('45987349857634085409857349856430985')
+ * y.toNumber() // 4.598734985763409e+34
+ *
+ * z = new BigNumber(-0)
+ * 1 / z.toNumber() // -Infinity
+ * 1 / +z // -Infinity
+ * ```
+ */
+ toNumber(): number;
+
+ /**
+ * Returns a string representing the value of this BigNumber rounded to `significantDigits`
+ * significant digits using rounding mode `roundingMode`.
+ *
+ * If `significantDigits` is less than the number of digits necessary to represent the integer
+ * part of the value in normal (fixed-point) notation, then exponential notation is used.
+ *
+ * If `significantDigits` is omitted, or is `null` or `undefined`, then the return value is the
+ * same as `n.toString()`.
+ *
+ * If `roundingMode` is omitted or is `null` or `undefined`, `ROUNDING_MODE` is used.
+ *
+ * Throws if `significantDigits` or `roundingMode` is invalid.
+ *
+ * ```ts
+ * x = 45.6
+ * y = new BigNumber(x)
+ * x.toPrecision() // '45.6'
+ * y.toPrecision() // '45.6'
+ * x.toPrecision(1) // '5e+1'
+ * y.toPrecision(1) // '5e+1'
+ * y.toPrecision(2, 0) // '4.6e+1' (ROUND_UP)
+ * y.toPrecision(2, 1) // '4.5e+1' (ROUND_DOWN)
+ * x.toPrecision(5) // '45.600'
+ * y.toPrecision(5) // '45.600'
+ * ```
+ *
+ * @param [significantDigits] Significant digits, integer, 1 to 1e+9.
+ * @param [roundingMode] Rounding mode, integer 0 to 8.
+ */
+ toPrecision(significantDigits?: number, roundingMode?: BigNumberRoundingMode): string;
+
+ /**
+ * Returns a string representing the value of this BigNumber in base `base`, or base 10 if `base`
+ * is omitted or is `null` or `undefined`.
+ *
+ * For bases above 10, and using the default base conversion alphabet (see `ALPHABET`), values
+ * from 10 to 35 are represented by a-z (the same as `Number.prototype.toString`).
+ *
+ * If a base is specified the value is rounded according to the current `DECIMAL_PLACES` and
+ * `ROUNDING_MODE` settings, otherwise it is not.
+ *
+ * If a base is not specified, and this BigNumber has a positive exponent that is equal to or
+ * greater than the positive component of the current `EXPONENTIAL_AT` setting, or a negative
+ * exponent equal to or less than the negative component of the setting, then exponential notation
+ * is returned.
+ *
+ * If `base` is `null` or `undefined` it is ignored.
+ *
+ * Throws if `base` is invalid.
+ *
+ * ```ts
+ * x = new BigNumber(750000)
+ * x.toString() // '750000'
+ * BigNumber.config({ EXPONENTIAL_AT: 5 })
+ * x.toString() // '7.5e+5'
+ *
+ * y = new BigNumber(362.875)
+ * y.toString(2) // '101101010.111'
+ * y.toString(9) // '442.77777777777777777778'
+ * y.toString(32) // 'ba.s'
+ *
+ * BigNumber.config({ DECIMAL_PLACES: 4 });
+ * z = new BigNumber('1.23456789')
+ * z.toString() // '1.23456789'
+ * z.toString(10) // '1.2346'
+ * ```
+ *
+ * @param [base] The base, integer, 2 to 36 (or `ALPHABET.length`, see `ALPHABET`).
+ */
+ toString(base?: number): string;
+
+ /**
+ * As `toString`, but does not accept a base argument and includes the minus sign for negative
+ * zero.
+ *
+ * ``ts
+ * x = new BigNumber('-0')
+ * x.toString() // '0'
+ * x.valueOf() // '-0'
+ * y = new BigNumber('1.777e+457')
+ * y.valueOf() // '1.777e+457'
+ * ```
+ */
+ valueOf(): string;
+
+ /**
+ * Returns a new independent BigNumber constructor with configuration as described by `object`, or
+ * with the default configuration if object is `null` or `undefined`.
+ *
+ * Throws if `object` is not an object.
+ *
+ * ```ts
+ * BigNumber.config({ DECIMAL_PLACES: 5 })
+ * BN = BigNumber.clone({ DECIMAL_PLACES: 9 })
+ *
+ * x = new BigNumber(1)
+ * y = new BN(1)
+ *
+ * x.div(3) // 0.33333
+ * y.div(3) // 0.333333333
+ *
+ * // BN = BigNumber.clone({ DECIMAL_PLACES: 9 }) is equivalent to:
+ * BN = BigNumber.clone()
+ * BN.config({ DECIMAL_PLACES: 9 })
+ * ```
+ *
+ * @param [object] The configuration object.
+ */
+ static clone(object?: BigNumberConfig): BigNumberConstructor;
+
+ /**
+ * Configures the settings that apply to this BigNumber constructor.
+ *
+ * The configuration object, `object`, contains any number of the properties shown in the example
+ * below.
+ *
+ * Returns an object with the above properties and their current values.
+ *
+ * Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
+ * properties.
+ *
+ * ```ts
+ * BigNumber.config({
+ * DECIMAL_PLACES: 40,
+ * ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
+ * EXPONENTIAL_AT: [-10, 20],
+ * RANGE: [-500, 500],
+ * CRYPTO: true,
+ * MODULO_MODE: BigNumber.ROUND_FLOOR,
+ * POW_PRECISION: 80,
+ * FORMAT: {
+ * groupSize: 3,
+ * groupSeparator: ' ',
+ * decimalSeparator: ','
+ * },
+ * ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+ * });
+ *
+ * BigNumber.config().DECIMAL_PLACES // 40
+ * ```
+ *
+ * @param object The configuration object.
+ */
+ static config(object: BigNumberConfig): BigNumberConfig;
+
+ /**
+ * Returns `true` if `value` is a BigNumber instance, otherwise returns `false`.
+ *
+ * ```ts
+ * x = 42
+ * y = new BigNumber(x)
+ *
+ * BigNumber.isBigNumber(x) // false
+ * y instanceof BigNumber // true
+ * BigNumber.isBigNumber(y) // true
+ *
+ * BN = BigNumber.clone();
+ * z = new BN(x)
+ * z instanceof BigNumber // false
+ * BigNumber.isBigNumber(z) // true
+ * ```
+ *
+ * @param value The value to test.
+ */
+ static isBigNumber(value: any): boolean;
+
+ /**
+ *
+ * Returns a BigNumber whose value is the maximum of the arguments.
+ *
+ * Accepts either an argument list or an array of values.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber('3257869345.0378653')
+ * BigNumber.maximum(4e9, x, '123456789.9') // '4000000000'
+ *
+ * arr = [12, '13', new BigNumber(14)]
+ * BigNumber.maximum(arr) // '14'
+ * ```
+ *
+ * @param n A numeric value.
+ */
+ static maximum(...n: BigNumberValue[]): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the maximum of the arguments.
+ *
+ * Accepts either an argument list or an array of values.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber('3257869345.0378653')
+ * BigNumber.max(4e9, x, '123456789.9') // '4000000000'
+ *
+ * arr = [12, '13', new BigNumber(14)]
+ * BigNumber.max(arr) // '14'
+ * ```
+ *
+ * @param n A numeric value.
+ */
+ static max(...n: BigNumberValue[]): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the minimum of the arguments.
+ *
+ * Accepts either an argument list or an array of values.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber('3257869345.0378653')
+ * BigNumber.minimum(4e9, x, '123456789.9') // '123456789.9'
+ *
+ * arr = [2, new BigNumber(-14), '-15.9999', -12]
+ * BigNumber.minimum(arr) // '-15.9999'
+ * ```
+ *
+ * @param n A numeric value.
+ */
+ static minimum(...n: BigNumberValue[]): BigNumber;
+
+ /**
+ * Returns a BigNumber whose value is the minimum of the arguments.
+ *
+ * Accepts either an argument list or an array of values.
+ *
+ * The return value is always exact and unrounded.
+ *
+ * ```ts
+ * x = new BigNumber('3257869345.0378653')
+ * BigNumber.min(4e9, x, '123456789.9') // '123456789.9'
+ *
+ * arr = [2, new BigNumber(-14), '-15.9999', -12]
+ * BigNumber.min(arr) // '-15.9999'
+ * ```
+ *
+ * @param n A numeric value.
+ */
+ static min(...n: BigNumberValue[]): BigNumber;
+
+ /**
+ * Returns a new BigNumber with a pseudo-random value equal to or greater than 0 and less than 1.
+ *
+ * The return value will have `decimalPlaces` decimal places, or less if trailing zeros are
+ * produced. If `decimalPlaces` is omitted, the current `DECIMAL_PLACES` setting will be used.
+ *
+ * Depending on the value of this BigNumber constructor's `CRYPTO` setting and the support for the
+ * `crypto` object in the host environment, the random digits of the return value are generated by
+ * either `Math.random` (fastest), `crypto.getRandomValues` (Web Cryptography API in recent
+ * browsers) or `crypto.randomBytes` (Node.js).
+ *
+ * If `CRYPTO` is true, i.e. one of the `crypto` methods is to be used, the value of a returned
+ * BigNumber should be cryptographically secure and statistically indistinguishable from a random
+ * value.
+ *
+ * Throws if `decimalPlaces` is invalid.
+ *
+ * ```ts
+ * BigNumber.config({ DECIMAL_PLACES: 10 })
+ * BigNumber.random() // '0.4117936847'
+ * BigNumber.random(20) // '0.78193327636914089009'
+ * ```
+ *
+ * @param [decimalPlaces] Decimal places, integer, 0 to 1e+9.
+ */
+ static random(decimalPlaces?: number): BigNumber;
+
+ /**
+ * Configures the settings that apply to this BigNumber constructor.
+ *
+ * The configuration object, `object`, contains any number of the properties shown in the example
+ * below.
+ *
+ * Returns an object with the above properties and their current values.
+ *
+ * Throws if `object` is not an object, or if an invalid value is assigned to one or more of the
+ * properties.
+ *
+ * ```ts
+ * BigNumber.set({
+ * DECIMAL_PLACES: 40,
+ * ROUNDING_MODE: BigNumber.ROUND_HALF_CEIL,
+ * EXPONENTIAL_AT: [-10, 20],
+ * RANGE: [-500, 500],
+ * CRYPTO: true,
+ * MODULO_MODE: BigNumber.ROUND_FLOOR,
+ * POW_PRECISION: 80,
+ * FORMAT: {
+ * groupSize: 3,
+ * groupSeparator: ' ',
+ * decimalSeparator: ','
+ * },
+ * ALPHABET: '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+ * });
+ *
+ * BigNumber.set().DECIMAL_PLACES // 40
+ * ```
+ *
+ * @param object The configuration object.
+ */
+ static set(object: BigNumberConfig): BigNumberConfig;
+
+ /**
+ * Helps ES6 import.
+ */
+ private static readonly default?: BigNumberConstructor;
+
+ /**
+ * Helps ES6 import.
+ */
+ private static readonly BigNumber?: BigNumberConstructor;
+
+ /**
+ * Rounds away from zero.
+ */
+ static readonly ROUND_UP: 0;
+
+ /**
+ * Rounds towards zero.
+ */
+ static readonly ROUND_DOWN: 1;
+
+ /**
+ * Rounds towards Infinity.
+ */
+ static readonly ROUND_CEIL: 2;
+
+ /**
+ * Rounds towards -Infinity.
+ */
+ static readonly ROUND_FLOOR: 3;
+
+ /**
+ * Rounds towards nearest neighbour. If equidistant, rounds away from zero .
+ */
+ static readonly ROUND_HALF_UP: 4;
+
+ /**
+ * Rounds towards nearest neighbour. If equidistant, rounds towards zero.
+ */
+ static readonly ROUND_HALF_DOWN: 5;
+
+ /**
+ * Rounds towards nearest neighbour. If equidistant, rounds towards even neighbour.
+ */
+ static readonly ROUND_HALF_EVEN: 6;
+
+ /**
+ * Rounds towards nearest neighbour. If equidistant, rounds towards Infinity.
+ */
+ static readonly ROUND_HALF_CEIL: 7;
+
+ /**
+ * Rounds towards nearest neighbour. If equidistant, rounds towards -Infinity.
+ */
+ static readonly ROUND_HALF_FLOOR: 8;
+
+ /**
+ * See `MODULO_MODE`.
+ */
+ static readonly EUCLID: 9;
+}
+
+
+export default BigNumber;
+
+export namespace BigNumber {
+ export type Config = BigNumberConfig;
+ export type Constructor = BigNumberConstructor;
+ export type Format = BigNumberFormat;
+ export type Instance = BigNumberInstance;
+ export type ModuloMode = BigNumberModuloMode;
+ export type RoundingMode = BigNumberRoundingMode;
+ export type Value = BigNumberValue;
+}
+
+/**
+ * Browsers.
+ */
+declare global {
+ const BigNumber: BigNumberConstructor;
+ type BigNumber = BigNumberInstance;
+
+ namespace BigNumber {
+ type Config = BigNumberConfig;
+ type Constructor = BigNumberConstructor;
+ type Format = BigNumberFormat;
+ type Instance = BigNumberInstance;
+ type ModuloMode = BigNumberModuloMode;
+ type RoundingMode = BigNumberRoundingMode;
+ type Value = BigNumberValue;
+ }
+} \ No newline at end of file
diff --git a/packages/instant/test/util/dependencies/prevbignumber.js b/packages/instant/test/util/dependencies/prevbignumber.js
new file mode 100644
index 000000000..e2d3f2146
--- /dev/null
+++ b/packages/instant/test/util/dependencies/prevbignumber.js
@@ -0,0 +1,2705 @@
+/*
+ * bignumber.js v6.0.0
+ * A JavaScript library for arbitrary-precision arithmetic.
+ * https://github.com/MikeMcl/bignumber.js
+ * Copyright (c) 2018 Michael Mclaughlin <M8ch88l@gmail.com>
+ * MIT Licensed.
+ *
+ * BigNumber.prototype methods | BigNumber methods
+ * |
+ * absoluteValue abs | clone
+ * comparedTo | config set
+ * decimalPlaces dp | DECIMAL_PLACES
+ * dividedBy div | ROUNDING_MODE
+ * dividedToIntegerBy idiv | EXPONENTIAL_AT
+ * exponentiatedBy pow | RANGE
+ * integerValue | CRYPTO
+ * isEqualTo eq | MODULO_MODE
+ * isFinite | POW_PRECISION
+ * isGreaterThan gt | FORMAT
+ * isGreaterThanOrEqualTo gte | ALPHABET
+ * isInteger | isBigNumber
+ * isLessThan lt | maximum max
+ * isLessThanOrEqualTo lte | minimum min
+ * isNaN | random
+ * isNegative |
+ * isPositive |
+ * isZero |
+ * minus |
+ * modulo mod |
+ * multipliedBy times |
+ * negated |
+ * plus |
+ * precision sd |
+ * shiftedBy |
+ * squareRoot sqrt |
+ * toExponential |
+ * toFixed |
+ * toFormat |
+ * toFraction |
+ * toJSON |
+ * toNumber |
+ * toPrecision |
+ * toString |
+ * valueOf |
+ *
+ */
+
+
+var BigNumber,
+ isNumeric = /^-?(?:\d+(?:\.\d*)?|\.\d+)(?:e[+-]?\d+)?$/i,
+
+ mathceil = Math.ceil,
+ mathfloor = Math.floor,
+
+ bignumberError = '[BigNumber Error] ',
+ tooManyDigits = bignumberError + 'Number primitive has more than 15 significant digits: ',
+
+ BASE = 1e14,
+ LOG_BASE = 14,
+ MAX_SAFE_INTEGER = 0x1fffffffffffff, // 2^53 - 1
+ // MAX_INT32 = 0x7fffffff, // 2^31 - 1
+ POWS_TEN = [1, 10, 100, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13],
+ SQRT_BASE = 1e7,
+
+ // EDITABLE
+ // The limit on the value of DECIMAL_PLACES, TO_EXP_NEG, TO_EXP_POS, MIN_EXP, MAX_EXP, and
+ // the arguments to toExponential, toFixed, toFormat, and toPrecision.
+ MAX = 1E9; // 0 to MAX_INT32
+
+
+/*
+ * Create and return a BigNumber constructor.
+ */
+function clone(configObject) {
+ var div, convertBase, parseNumeric,
+ P = BigNumber.prototype,
+ ONE = new BigNumber(1),
+
+
+ //----------------------------- EDITABLE CONFIG DEFAULTS -------------------------------
+
+
+ // The default values below must be integers within the inclusive ranges stated.
+ // The values can also be changed at run-time using BigNumber.set.
+
+ // The maximum number of decimal places for operations involving division.
+ DECIMAL_PLACES = 20, // 0 to MAX
+
+ // The rounding mode used when rounding to the above decimal places, and when using
+ // toExponential, toFixed, toFormat and toPrecision, and round (default value).
+ // UP 0 Away from zero.
+ // DOWN 1 Towards zero.
+ // CEIL 2 Towards +Infinity.
+ // FLOOR 3 Towards -Infinity.
+ // HALF_UP 4 Towards nearest neighbour. If equidistant, up.
+ // HALF_DOWN 5 Towards nearest neighbour. If equidistant, down.
+ // HALF_EVEN 6 Towards nearest neighbour. If equidistant, towards even neighbour.
+ // HALF_CEIL 7 Towards nearest neighbour. If equidistant, towards +Infinity.
+ // HALF_FLOOR 8 Towards nearest neighbour. If equidistant, towards -Infinity.
+ ROUNDING_MODE = 4, // 0 to 8
+
+ // EXPONENTIAL_AT : [TO_EXP_NEG , TO_EXP_POS]
+
+ // The exponent value at and beneath which toString returns exponential notation.
+ // Number type: -7
+ TO_EXP_NEG = -7, // 0 to -MAX
+
+ // The exponent value at and above which toString returns exponential notation.
+ // Number type: 21
+ TO_EXP_POS = 21, // 0 to MAX
+
+ // RANGE : [MIN_EXP, MAX_EXP]
+
+ // The minimum exponent value, beneath which underflow to zero occurs.
+ // Number type: -324 (5e-324)
+ MIN_EXP = -1e7, // -1 to -MAX
+
+ // The maximum exponent value, above which overflow to Infinity occurs.
+ // Number type: 308 (1.7976931348623157e+308)
+ // For MAX_EXP > 1e7, e.g. new BigNumber('1e100000000').plus(1) may be slow.
+ MAX_EXP = 1e7, // 1 to MAX
+
+ // Whether to use cryptographically-secure random number generation, if available.
+ CRYPTO = false, // true or false
+
+ // The modulo mode used when calculating the modulus: a mod n.
+ // The quotient (q = a / n) is calculated according to the corresponding rounding mode.
+ // The remainder (r) is calculated as: r = a - n * q.
+ //
+ // UP 0 The remainder is positive if the dividend is negative, else is negative.
+ // DOWN 1 The remainder has the same sign as the dividend.
+ // This modulo mode is commonly known as 'truncated division' and is
+ // equivalent to (a % n) in JavaScript.
+ // FLOOR 3 The remainder has the same sign as the divisor (Python %).
+ // HALF_EVEN 6 This modulo mode implements the IEEE 754 remainder function.
+ // EUCLID 9 Euclidian division. q = sign(n) * floor(a / abs(n)).
+ // The remainder is always positive.
+ //
+ // The truncated division, floored division, Euclidian division and IEEE 754 remainder
+ // modes are commonly used for the modulus operation.
+ // Although the other rounding modes can also be used, they may not give useful results.
+ MODULO_MODE = 1, // 0 to 9
+
+ // The maximum number of significant digits of the result of the exponentiatedBy operation.
+ // If POW_PRECISION is 0, there will be unlimited significant digits.
+ POW_PRECISION = 0, // 0 to MAX
+
+ // The format specification used by the BigNumber.prototype.toFormat method.
+ FORMAT = {
+ decimalSeparator: '.',
+ groupSeparator: ',',
+ groupSize: 3,
+ secondaryGroupSize: 0,
+ fractionGroupSeparator: '\xA0', // non-breaking space
+ fractionGroupSize: 0
+ },
+
+ // The alphabet used for base conversion.
+ // It must be at least 2 characters long, with no '.' or repeated character.
+ // '0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ$_'
+ ALPHABET = '0123456789abcdefghijklmnopqrstuvwxyz';
+
+
+ //------------------------------------------------------------------------------------------
+
+
+ // CONSTRUCTOR
+
+
+ /*
+ * The BigNumber constructor and exported function.
+ * Create and return a new instance of a BigNumber object.
+ *
+ * n {number|string|BigNumber} A numeric value.
+ * [b] {number} The base of n. Integer, 2 to ALPHABET.length inclusive.
+ */
+ function BigNumber( n, b ) {
+ var alphabet, c, e, i, isNum, len, str,
+ x = this;
+
+ // Enable constructor usage without new.
+ if ( !( x instanceof BigNumber ) ) {
+
+ // Don't throw on constructor call without new (#81).
+ // '[BigNumber Error] Constructor call without new: {n}'
+ //throw Error( bignumberError + ' Constructor call without new: ' + n );
+ return new BigNumber( n, b );
+ }
+
+ if ( b == null ) {
+
+ // Duplicate.
+ if ( n instanceof BigNumber ) {
+ x.s = n.s;
+ x.e = n.e;
+ x.c = ( n = n.c ) ? n.slice() : n;
+ return;
+ }
+
+ isNum = typeof n == 'number';
+
+ if ( isNum && n * 0 == 0 ) {
+
+ // Use `1 / n` to handle minus zero also.
+ x.s = 1 / n < 0 ? ( n = -n, -1 ) : 1;
+
+ // Faster path for integers.
+ if ( n === ~~n ) {
+ for ( e = 0, i = n; i >= 10; i /= 10, e++ );
+ x.e = e;
+ x.c = [n];
+ return;
+ }
+
+ str = n + '';
+ } else {
+ if ( !isNumeric.test( str = n + '' ) ) return parseNumeric( x, str, isNum );
+ x.s = str.charCodeAt(0) == 45 ? ( str = str.slice(1), -1 ) : 1;
+ }
+
+ } else {
+
+ // '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+ intCheck( b, 2, ALPHABET.length, 'Base' );
+ str = n + '';
+
+ // Allow exponential notation to be used with base 10 argument, while
+ // also rounding to DECIMAL_PLACES as with other bases.
+ if ( b == 10 ) {
+ x = new BigNumber( n instanceof BigNumber ? n : str );
+ return round( x, DECIMAL_PLACES + x.e + 1, ROUNDING_MODE );
+ }
+
+ isNum = typeof n == 'number';
+
+ if (isNum) {
+
+ // Avoid potential interpretation of Infinity and NaN as base 44+ values.
+ if ( n * 0 != 0 ) return parseNumeric( x, str, isNum, b );
+
+ x.s = 1 / n < 0 ? ( str = str.slice(1), -1 ) : 1;
+
+ // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+ if ( str.replace( /^0\.0*|\./, '' ).length > 15 ) {
+ throw Error
+ ( tooManyDigits + n );
+ }
+
+ // Prevent later check for length on converted number.
+ isNum = false;
+ } else {
+ x.s = str.charCodeAt(0) === 45 ? ( str = str.slice(1), -1 ) : 1;
+
+ // Allow e.g. hexadecimal 'FF' as well as 'ff'.
+ if ( b > 10 && b < 37 ) str = str.toLowerCase();
+ }
+
+ alphabet = ALPHABET.slice( 0, b );
+ e = i = 0;
+
+ // Check that str is a valid base b number.
+ // Don't use RegExp so alphabet can contain special characters.
+ for ( len = str.length; i < len; i++ ) {
+ if ( alphabet.indexOf( c = str.charAt(i) ) < 0 ) {
+ if ( c == '.' ) {
+
+ // If '.' is not the first character and it has not be found before.
+ if ( i > e ) {
+ e = len;
+ continue;
+ }
+ }
+
+ return parseNumeric( x, n + '', isNum, b );
+ }
+ }
+
+ str = convertBase( str, b, 10, x.s );
+ }
+
+ // Decimal point?
+ if ( ( e = str.indexOf('.') ) > -1 ) str = str.replace( '.', '' );
+
+ // Exponential form?
+ if ( ( i = str.search( /e/i ) ) > 0 ) {
+
+ // Determine exponent.
+ if ( e < 0 ) e = i;
+ e += +str.slice( i + 1 );
+ str = str.substring( 0, i );
+ } else if ( e < 0 ) {
+
+ // Integer.
+ e = str.length;
+ }
+
+ // Determine leading zeros.
+ for ( i = 0; str.charCodeAt(i) === 48; i++ );
+
+ // Determine trailing zeros.
+ for ( len = str.length; str.charCodeAt(--len) === 48; );
+ str = str.slice( i, len + 1 );
+
+ if (str) {
+ len = str.length;
+
+ // '[BigNumber Error] Number primitive has more than 15 significant digits: {n}'
+ if ( isNum && len > 15 && ( n > MAX_SAFE_INTEGER || n !== mathfloor(n) ) ) {
+ throw Error
+ ( tooManyDigits + ( x.s * n ) );
+ }
+
+ e = e - i - 1;
+
+ // Overflow?
+ if ( e > MAX_EXP ) {
+
+ // Infinity.
+ x.c = x.e = null;
+
+ // Underflow?
+ } else if ( e < MIN_EXP ) {
+
+ // Zero.
+ x.c = [ x.e = 0 ];
+ } else {
+ x.e = e;
+ x.c = [];
+
+ // Transform base
+
+ // e is the base 10 exponent.
+ // i is where to slice str to get the first element of the coefficient array.
+ i = ( e + 1 ) % LOG_BASE;
+ if ( e < 0 ) i += LOG_BASE;
+
+ if ( i < len ) {
+ if (i) x.c.push( +str.slice( 0, i ) );
+
+ for ( len -= LOG_BASE; i < len; ) {
+ x.c.push( +str.slice( i, i += LOG_BASE ) );
+ }
+
+ str = str.slice(i);
+ i = LOG_BASE - str.length;
+ } else {
+ i -= len;
+ }
+
+ for ( ; i--; str += '0' );
+ x.c.push( +str );
+ }
+ } else {
+
+ // Zero.
+ x.c = [ x.e = 0 ];
+ }
+ }
+
+
+ // CONSTRUCTOR PROPERTIES
+
+
+ BigNumber.clone = clone;
+
+ BigNumber.ROUND_UP = 0;
+ BigNumber.ROUND_DOWN = 1;
+ BigNumber.ROUND_CEIL = 2;
+ BigNumber.ROUND_FLOOR = 3;
+ BigNumber.ROUND_HALF_UP = 4;
+ BigNumber.ROUND_HALF_DOWN = 5;
+ BigNumber.ROUND_HALF_EVEN = 6;
+ BigNumber.ROUND_HALF_CEIL = 7;
+ BigNumber.ROUND_HALF_FLOOR = 8;
+ BigNumber.EUCLID = 9;
+
+
+ /*
+ * Configure infrequently-changing library-wide settings.
+ *
+ * Accept an object with the following optional properties (if the value of a property is
+ * a number, it must be an integer within the inclusive range stated):
+ *
+ * DECIMAL_PLACES {number} 0 to MAX
+ * ROUNDING_MODE {number} 0 to 8
+ * EXPONENTIAL_AT {number|number[]} -MAX to MAX or [-MAX to 0, 0 to MAX]
+ * RANGE {number|number[]} -MAX to MAX (not zero) or [-MAX to -1, 1 to MAX]
+ * CRYPTO {boolean} true or false
+ * MODULO_MODE {number} 0 to 9
+ * POW_PRECISION {number} 0 to MAX
+ * ALPHABET {string} A string of two or more unique characters, and not
+ * containing '.'. The empty string, null or undefined
+ * resets the alphabet to its default value.
+ * FORMAT {object} An object with some of the following properties:
+ * decimalSeparator {string}
+ * groupSeparator {string}
+ * groupSize {number}
+ * secondaryGroupSize {number}
+ * fractionGroupSeparator {string}
+ * fractionGroupSize {number}
+ *
+ * (The values assigned to the above FORMAT object properties are not checked for validity.)
+ *
+ * E.g.
+ * BigNumber.config({ DECIMAL_PLACES : 20, ROUNDING_MODE : 4 })
+ *
+ * Ignore properties/parameters set to null or undefined, except for ALPHABET.
+ *
+ * Return an object with the properties current values.
+ */
+ BigNumber.config = BigNumber.set = function (obj) {
+ var p, v;
+
+ if ( obj != null ) {
+
+ if ( typeof obj == 'object' ) {
+
+ // DECIMAL_PLACES {number} Integer, 0 to MAX inclusive.
+ // '[BigNumber Error] DECIMAL_PLACES {not a primitive number|not an integer|out of range}: {v}'
+ if ( obj.hasOwnProperty( p = 'DECIMAL_PLACES' ) ) {
+ v = obj[p];
+ intCheck( v, 0, MAX, p );
+ DECIMAL_PLACES = v;
+ }
+
+ // ROUNDING_MODE {number} Integer, 0 to 8 inclusive.
+ // '[BigNumber Error] ROUNDING_MODE {not a primitive number|not an integer|out of range}: {v}'
+ if ( obj.hasOwnProperty( p = 'ROUNDING_MODE' ) ) {
+ v = obj[p];
+ intCheck( v, 0, 8, p );
+ ROUNDING_MODE = v;
+ }
+
+ // EXPONENTIAL_AT {number|number[]}
+ // Integer, -MAX to MAX inclusive or
+ // [integer -MAX to 0 inclusive, 0 to MAX inclusive].
+ // '[BigNumber Error] EXPONENTIAL_AT {not a primitive number|not an integer|out of range}: {v}'
+ if ( obj.hasOwnProperty( p = 'EXPONENTIAL_AT' ) ) {
+ v = obj[p];
+ if ( isArray(v) ) {
+ intCheck( v[0], -MAX, 0, p );
+ intCheck( v[1], 0, MAX, p );
+ TO_EXP_NEG = v[0];
+ TO_EXP_POS = v[1];
+ } else {
+ intCheck( v, -MAX, MAX, p );
+ TO_EXP_NEG = -( TO_EXP_POS = v < 0 ? -v : v );
+ }
+ }
+
+ // RANGE {number|number[]} Non-zero integer, -MAX to MAX inclusive or
+ // [integer -MAX to -1 inclusive, integer 1 to MAX inclusive].
+ // '[BigNumber Error] RANGE {not a primitive number|not an integer|out of range|cannot be zero}: {v}'
+ if ( obj.hasOwnProperty( p = 'RANGE' ) ) {
+ v = obj[p];
+ if ( isArray(v) ) {
+ intCheck( v[0], -MAX, -1, p );
+ intCheck( v[1], 1, MAX, p );
+ MIN_EXP = v[0];
+ MAX_EXP = v[1];
+ } else {
+ intCheck( v, -MAX, MAX, p );
+ if (v) {
+ MIN_EXP = -( MAX_EXP = v < 0 ? -v : v );
+ } else {
+ throw Error
+ ( bignumberError + p + ' cannot be zero: ' + v );
+ }
+ }
+ }
+
+ // CRYPTO {boolean} true or false.
+ // '[BigNumber Error] CRYPTO not true or false: {v}'
+ // '[BigNumber Error] crypto unavailable'
+ if ( obj.hasOwnProperty( p = 'CRYPTO' ) ) {
+ v = obj[p];
+ if ( v === !!v ) {
+ if (v) {
+ if ( typeof crypto != 'undefined' && crypto &&
+ (crypto.getRandomValues || crypto.randomBytes) ) {
+ CRYPTO = v;
+ } else {
+ CRYPTO = !v;
+ throw Error
+ ( bignumberError + 'crypto unavailable' );
+ }
+ } else {
+ CRYPTO = v;
+ }
+ } else {
+ throw Error
+ ( bignumberError + p + ' not true or false: ' + v );
+ }
+ }
+
+ // MODULO_MODE {number} Integer, 0 to 9 inclusive.
+ // '[BigNumber Error] MODULO_MODE {not a primitive number|not an integer|out of range}: {v}'
+ if ( obj.hasOwnProperty( p = 'MODULO_MODE' ) ) {
+ v = obj[p];
+ intCheck( v, 0, 9, p );
+ MODULO_MODE = v;
+ }
+
+ // POW_PRECISION {number} Integer, 0 to MAX inclusive.
+ // '[BigNumber Error] POW_PRECISION {not a primitive number|not an integer|out of range}: {v}'
+ if ( obj.hasOwnProperty( p = 'POW_PRECISION' ) ) {
+ v = obj[p];
+ intCheck( v, 0, MAX, p );
+ POW_PRECISION = v;
+ }
+
+ // FORMAT {object}
+ // '[BigNumber Error] FORMAT not an object: {v}'
+ if ( obj.hasOwnProperty( p = 'FORMAT' ) ) {
+ v = obj[p];
+ if ( typeof v == 'object' ) FORMAT = v;
+ else throw Error
+ ( bignumberError + p + ' not an object: ' + v );
+ }
+
+ // ALPHABET {string}
+ // '[BigNumber Error] ALPHABET invalid: {v}'
+ if ( obj.hasOwnProperty( p = 'ALPHABET' ) ) {
+ v = obj[p];
+
+ // Disallow if only one character, or contains '.' or a repeated character.
+ if ( typeof v == 'string' && !/^.$|\.|(.).*\1/.test(v) ) {
+ ALPHABET = v;
+ } else {
+ throw Error
+ ( bignumberError + p + ' invalid: ' + v );
+ }
+ }
+
+ } else {
+
+ // '[BigNumber Error] Object expected: {v}'
+ throw Error
+ ( bignumberError + 'Object expected: ' + obj );
+ }
+ }
+
+ return {
+ DECIMAL_PLACES: DECIMAL_PLACES,
+ ROUNDING_MODE: ROUNDING_MODE,
+ EXPONENTIAL_AT: [ TO_EXP_NEG, TO_EXP_POS ],
+ RANGE: [ MIN_EXP, MAX_EXP ],
+ CRYPTO: CRYPTO,
+ MODULO_MODE: MODULO_MODE,
+ POW_PRECISION: POW_PRECISION,
+ FORMAT: FORMAT,
+ ALPHABET: ALPHABET
+ };
+ };
+
+
+ /*
+ * Return true if v is a BigNumber instance, otherwise return false.
+ *
+ * v {any}
+ */
+ BigNumber.isBigNumber = function (v) {
+ return v instanceof BigNumber || v && v._isBigNumber === true || false;
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the maximum of the arguments.
+ *
+ * arguments {number|string|BigNumber}
+ */
+ BigNumber.maximum = BigNumber.max = function () {
+ return maxOrMin( arguments, P.lt );
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the minimum of the arguments.
+ *
+ * arguments {number|string|BigNumber}
+ */
+ BigNumber.minimum = BigNumber.min = function () {
+ return maxOrMin( arguments, P.gt );
+ };
+
+
+ /*
+ * Return a new BigNumber with a random value equal to or greater than 0 and less than 1,
+ * and with dp, or DECIMAL_PLACES if dp is omitted, decimal places (or less if trailing
+ * zeros are produced).
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp}'
+ * '[BigNumber Error] crypto unavailable'
+ */
+ BigNumber.random = (function () {
+ var pow2_53 = 0x20000000000000;
+
+ // Return a 53 bit integer n, where 0 <= n < 9007199254740992.
+ // Check if Math.random() produces more than 32 bits of randomness.
+ // If it does, assume at least 53 bits are produced, otherwise assume at least 30 bits.
+ // 0x40000000 is 2^30, 0x800000 is 2^23, 0x1fffff is 2^21 - 1.
+ var random53bitInt = (Math.random() * pow2_53) & 0x1fffff
+ ? function () { return mathfloor( Math.random() * pow2_53 ); }
+ : function () { return ((Math.random() * 0x40000000 | 0) * 0x800000) +
+ (Math.random() * 0x800000 | 0); };
+
+ return function (dp) {
+ var a, b, e, k, v,
+ i = 0,
+ c = [],
+ rand = new BigNumber(ONE);
+
+ if ( dp == null ) dp = DECIMAL_PLACES;
+ else intCheck( dp, 0, MAX );
+
+ k = mathceil( dp / LOG_BASE );
+
+ if (CRYPTO) {
+
+ // Browsers supporting crypto.getRandomValues.
+ if (crypto.getRandomValues) {
+
+ a = crypto.getRandomValues( new Uint32Array( k *= 2 ) );
+
+ for ( ; i < k; ) {
+
+ // 53 bits:
+ // ((Math.pow(2, 32) - 1) * Math.pow(2, 21)).toString(2)
+ // 11111 11111111 11111111 11111111 11100000 00000000 00000000
+ // ((Math.pow(2, 32) - 1) >>> 11).toString(2)
+ // 11111 11111111 11111111
+ // 0x20000 is 2^21.
+ v = a[i] * 0x20000 + (a[i + 1] >>> 11);
+
+ // Rejection sampling:
+ // 0 <= v < 9007199254740992
+ // Probability that v >= 9e15, is
+ // 7199254740992 / 9007199254740992 ~= 0.0008, i.e. 1 in 1251
+ if ( v >= 9e15 ) {
+ b = crypto.getRandomValues( new Uint32Array(2) );
+ a[i] = b[0];
+ a[i + 1] = b[1];
+ } else {
+
+ // 0 <= v <= 8999999999999999
+ // 0 <= (v % 1e14) <= 99999999999999
+ c.push( v % 1e14 );
+ i += 2;
+ }
+ }
+ i = k / 2;
+
+ // Node.js supporting crypto.randomBytes.
+ } else if (crypto.randomBytes) {
+
+ // buffer
+ a = crypto.randomBytes( k *= 7 );
+
+ for ( ; i < k; ) {
+
+ // 0x1000000000000 is 2^48, 0x10000000000 is 2^40
+ // 0x100000000 is 2^32, 0x1000000 is 2^24
+ // 11111 11111111 11111111 11111111 11111111 11111111 11111111
+ // 0 <= v < 9007199254740992
+ v = ( ( a[i] & 31 ) * 0x1000000000000 ) + ( a[i + 1] * 0x10000000000 ) +
+ ( a[i + 2] * 0x100000000 ) + ( a[i + 3] * 0x1000000 ) +
+ ( a[i + 4] << 16 ) + ( a[i + 5] << 8 ) + a[i + 6];
+
+ if ( v >= 9e15 ) {
+ crypto.randomBytes(7).copy( a, i );
+ } else {
+
+ // 0 <= (v % 1e14) <= 99999999999999
+ c.push( v % 1e14 );
+ i += 7;
+ }
+ }
+ i = k / 7;
+ } else {
+ CRYPTO = false;
+ throw Error
+ ( bignumberError + 'crypto unavailable' );
+ }
+ }
+
+ // Use Math.random.
+ if (!CRYPTO) {
+
+ for ( ; i < k; ) {
+ v = random53bitInt();
+ if ( v < 9e15 ) c[i++] = v % 1e14;
+ }
+ }
+
+ k = c[--i];
+ dp %= LOG_BASE;
+
+ // Convert trailing digits to zeros according to dp.
+ if ( k && dp ) {
+ v = POWS_TEN[LOG_BASE - dp];
+ c[i] = mathfloor( k / v ) * v;
+ }
+
+ // Remove trailing elements which are zero.
+ for ( ; c[i] === 0; c.pop(), i-- );
+
+ // Zero?
+ if ( i < 0 ) {
+ c = [ e = 0 ];
+ } else {
+
+ // Remove leading elements which are zero and adjust exponent accordingly.
+ for ( e = -1 ; c[0] === 0; c.splice(0, 1), e -= LOG_BASE);
+
+ // Count the digits of the first element of c to determine leading zeros, and...
+ for ( i = 1, v = c[0]; v >= 10; v /= 10, i++);
+
+ // adjust the exponent accordingly.
+ if ( i < LOG_BASE ) e -= LOG_BASE - i;
+ }
+
+ rand.e = e;
+ rand.c = c;
+ return rand;
+ };
+ })();
+
+
+ // PRIVATE FUNCTIONS
+
+
+ // Called by BigNumber and BigNumber.prototype.toString.
+ convertBase = ( function () {
+ var decimal = '0123456789';
+
+ /*
+ * Convert string of baseIn to an array of numbers of baseOut.
+ * Eg. toBaseOut('255', 10, 16) returns [15, 15].
+ * Eg. toBaseOut('ff', 16, 10) returns [2, 5, 5].
+ */
+ function toBaseOut( str, baseIn, baseOut, alphabet ) {
+ var j,
+ arr = [0],
+ arrL,
+ i = 0,
+ len = str.length;
+
+ for ( ; i < len; ) {
+ for ( arrL = arr.length; arrL--; arr[arrL] *= baseIn );
+
+ arr[0] += alphabet.indexOf( str.charAt( i++ ) );
+
+ for ( j = 0; j < arr.length; j++ ) {
+
+ if ( arr[j] > baseOut - 1 ) {
+ if ( arr[j + 1] == null ) arr[j + 1] = 0;
+ arr[j + 1] += arr[j] / baseOut | 0;
+ arr[j] %= baseOut;
+ }
+ }
+ }
+
+ return arr.reverse();
+ }
+
+ // Convert a numeric string of baseIn to a numeric string of baseOut.
+ // If the caller is toString, we are converting from base 10 to baseOut.
+ // If the caller is BigNumber, we are converting from baseIn to base 10.
+ return function ( str, baseIn, baseOut, sign, callerIsToString ) {
+ var alphabet, d, e, k, r, x, xc, y,
+ i = str.indexOf( '.' ),
+ dp = DECIMAL_PLACES,
+ rm = ROUNDING_MODE;
+
+ // Non-integer.
+ if ( i >= 0 ) {
+ k = POW_PRECISION;
+
+ // Unlimited precision.
+ POW_PRECISION = 0;
+ str = str.replace( '.', '' );
+ y = new BigNumber(baseIn);
+ x = y.pow( str.length - i );
+ POW_PRECISION = k;
+
+ // Convert str as if an integer, then restore the fraction part by dividing the
+ // result by its base raised to a power.
+
+ y.c = toBaseOut( toFixedPoint( coeffToString( x.c ), x.e, '0' ),
+ 10, baseOut, decimal );
+ y.e = y.c.length;
+ }
+
+ // Convert the number as integer.
+
+ xc = toBaseOut( str, baseIn, baseOut, callerIsToString
+ ? ( alphabet = ALPHABET, decimal )
+ : ( alphabet = decimal, ALPHABET ) );
+
+
+ // xc now represents str as an integer and converted to baseOut. e is the exponent.
+ e = k = xc.length;
+
+ // Remove trailing zeros.
+ for ( ; xc[--k] == 0; xc.pop() );
+
+ // Zero?
+ if ( !xc[0] ) return alphabet.charAt(0);
+
+ // Does str represent an integer? If so, no need for the division.
+ if ( i < 0 ) {
+ --e;
+ } else {
+ x.c = xc;
+ x.e = e;
+
+ // The sign is needed for correct rounding.
+ x.s = sign;
+ x = div( x, y, dp, rm, baseOut );
+ xc = x.c;
+ r = x.r;
+ e = x.e;
+ }
+
+ // xc now represents str converted to baseOut.
+
+ // THe index of the rounding digit.
+ d = e + dp + 1;
+
+ // The rounding digit: the digit to the right of the digit that may be rounded up.
+ i = xc[d];
+
+ // Look at the rounding digits and mode to determine whether to round up.
+
+ k = baseOut / 2;
+ r = r || d < 0 || xc[d + 1] != null;
+
+ r = rm < 4 ? ( i != null || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+ : i > k || i == k &&( rm == 4 || r || rm == 6 && xc[d - 1] & 1 ||
+ rm == ( x.s < 0 ? 8 : 7 ) );
+
+ // If the index of the rounding digit is not greater than zero, or xc represents
+ // zero, then the result of the base conversion is zero or, if rounding up, a value
+ // such as 0.00001.
+ if ( d < 1 || !xc[0] ) {
+
+ // 1^-dp or 0
+ str = r ? toFixedPoint( alphabet.charAt(1), -dp, alphabet.charAt(0) )
+ : alphabet.charAt(0);
+ } else {
+
+ // Truncate xc to the required number of decimal places.
+ xc.length = d;
+
+ // Round up?
+ if (r) {
+
+ // Rounding up may mean the previous digit has to be rounded up and so on.
+ for ( --baseOut; ++xc[--d] > baseOut; ) {
+ xc[d] = 0;
+
+ if ( !d ) {
+ ++e;
+ xc = [1].concat(xc);
+ }
+ }
+ }
+
+ // Determine trailing zeros.
+ for ( k = xc.length; !xc[--k]; );
+
+ // E.g. [4, 11, 15] becomes 4bf.
+ for ( i = 0, str = ''; i <= k; str += alphabet.charAt( xc[i++] ) );
+
+ // Add leading zeros, decimal point and trailing zeros as required.
+ str = toFixedPoint( str, e, alphabet.charAt(0) );
+ }
+
+ // The caller will add the sign.
+ return str;
+ };
+ })();
+
+
+ // Perform division in the specified base. Called by div and convertBase.
+ div = (function () {
+
+ // Assume non-zero x and k.
+ function multiply( x, k, base ) {
+ var m, temp, xlo, xhi,
+ carry = 0,
+ i = x.length,
+ klo = k % SQRT_BASE,
+ khi = k / SQRT_BASE | 0;
+
+ for ( x = x.slice(); i--; ) {
+ xlo = x[i] % SQRT_BASE;
+ xhi = x[i] / SQRT_BASE | 0;
+ m = khi * xlo + xhi * klo;
+ temp = klo * xlo + ( ( m % SQRT_BASE ) * SQRT_BASE ) + carry;
+ carry = ( temp / base | 0 ) + ( m / SQRT_BASE | 0 ) + khi * xhi;
+ x[i] = temp % base;
+ }
+
+ if (carry) x = [carry].concat(x);
+
+ return x;
+ }
+
+ function compare( a, b, aL, bL ) {
+ var i, cmp;
+
+ if ( aL != bL ) {
+ cmp = aL > bL ? 1 : -1;
+ } else {
+
+ for ( i = cmp = 0; i < aL; i++ ) {
+
+ if ( a[i] != b[i] ) {
+ cmp = a[i] > b[i] ? 1 : -1;
+ break;
+ }
+ }
+ }
+ return cmp;
+ }
+
+ function subtract( a, b, aL, base ) {
+ var i = 0;
+
+ // Subtract b from a.
+ for ( ; aL--; ) {
+ a[aL] -= i;
+ i = a[aL] < b[aL] ? 1 : 0;
+ a[aL] = i * base + a[aL] - b[aL];
+ }
+
+ // Remove leading zeros.
+ for ( ; !a[0] && a.length > 1; a.splice(0, 1) );
+ }
+
+ // x: dividend, y: divisor.
+ return function ( x, y, dp, rm, base ) {
+ var cmp, e, i, more, n, prod, prodL, q, qc, rem, remL, rem0, xi, xL, yc0,
+ yL, yz,
+ s = x.s == y.s ? 1 : -1,
+ xc = x.c,
+ yc = y.c;
+
+ // Either NaN, Infinity or 0?
+ if ( !xc || !xc[0] || !yc || !yc[0] ) {
+
+ return new BigNumber(
+
+ // Return NaN if either NaN, or both Infinity or 0.
+ !x.s || !y.s || ( xc ? yc && xc[0] == yc[0] : !yc ) ? NaN :
+
+ // Return ±0 if x is ±0 or y is ±Infinity, or return ±Infinity as y is ±0.
+ xc && xc[0] == 0 || !yc ? s * 0 : s / 0
+ );
+ }
+
+ q = new BigNumber(s);
+ qc = q.c = [];
+ e = x.e - y.e;
+ s = dp + e + 1;
+
+ if ( !base ) {
+ base = BASE;
+ e = bitFloor( x.e / LOG_BASE ) - bitFloor( y.e / LOG_BASE );
+ s = s / LOG_BASE | 0;
+ }
+
+ // Result exponent may be one less then the current value of e.
+ // The coefficients of the BigNumbers from convertBase may have trailing zeros.
+ for ( i = 0; yc[i] == ( xc[i] || 0 ); i++ );
+
+ if ( yc[i] > ( xc[i] || 0 ) ) e--;
+
+ if ( s < 0 ) {
+ qc.push(1);
+ more = true;
+ } else {
+ xL = xc.length;
+ yL = yc.length;
+ i = 0;
+ s += 2;
+
+ // Normalise xc and yc so highest order digit of yc is >= base / 2.
+
+ n = mathfloor( base / ( yc[0] + 1 ) );
+
+ // Not necessary, but to handle odd bases where yc[0] == ( base / 2 ) - 1.
+ // if ( n > 1 || n++ == 1 && yc[0] < base / 2 ) {
+ if ( n > 1 ) {
+ yc = multiply( yc, n, base );
+ xc = multiply( xc, n, base );
+ yL = yc.length;
+ xL = xc.length;
+ }
+
+ xi = yL;
+ rem = xc.slice( 0, yL );
+ remL = rem.length;
+
+ // Add zeros to make remainder as long as divisor.
+ for ( ; remL < yL; rem[remL++] = 0 );
+ yz = yc.slice();
+ yz = [0].concat(yz);
+ yc0 = yc[0];
+ if ( yc[1] >= base / 2 ) yc0++;
+ // Not necessary, but to prevent trial digit n > base, when using base 3.
+ // else if ( base == 3 && yc0 == 1 ) yc0 = 1 + 1e-15;
+
+ do {
+ n = 0;
+
+ // Compare divisor and remainder.
+ cmp = compare( yc, rem, yL, remL );
+
+ // If divisor < remainder.
+ if ( cmp < 0 ) {
+
+ // Calculate trial digit, n.
+
+ rem0 = rem[0];
+ if ( yL != remL ) rem0 = rem0 * base + ( rem[1] || 0 );
+
+ // n is how many times the divisor goes into the current remainder.
+ n = mathfloor( rem0 / yc0 );
+
+ // Algorithm:
+ // 1. product = divisor * trial digit (n)
+ // 2. if product > remainder: product -= divisor, n--
+ // 3. remainder -= product
+ // 4. if product was < remainder at 2:
+ // 5. compare new remainder and divisor
+ // 6. If remainder > divisor: remainder -= divisor, n++
+
+ if ( n > 1 ) {
+
+ // n may be > base only when base is 3.
+ if (n >= base) n = base - 1;
+
+ // product = divisor * trial digit.
+ prod = multiply( yc, n, base );
+ prodL = prod.length;
+ remL = rem.length;
+
+ // Compare product and remainder.
+ // If product > remainder.
+ // Trial digit n too high.
+ // n is 1 too high about 5% of the time, and is not known to have
+ // ever been more than 1 too high.
+ while ( compare( prod, rem, prodL, remL ) == 1 ) {
+ n--;
+
+ // Subtract divisor from product.
+ subtract( prod, yL < prodL ? yz : yc, prodL, base );
+ prodL = prod.length;
+ cmp = 1;
+ }
+ } else {
+
+ // n is 0 or 1, cmp is -1.
+ // If n is 0, there is no need to compare yc and rem again below,
+ // so change cmp to 1 to avoid it.
+ // If n is 1, leave cmp as -1, so yc and rem are compared again.
+ if ( n == 0 ) {
+
+ // divisor < remainder, so n must be at least 1.
+ cmp = n = 1;
+ }
+
+ // product = divisor
+ prod = yc.slice();
+ prodL = prod.length;
+ }
+
+ if ( prodL < remL ) prod = [0].concat(prod);
+
+ // Subtract product from remainder.
+ subtract( rem, prod, remL, base );
+ remL = rem.length;
+
+ // If product was < remainder.
+ if ( cmp == -1 ) {
+
+ // Compare divisor and new remainder.
+ // If divisor < new remainder, subtract divisor from remainder.
+ // Trial digit n too low.
+ // n is 1 too low about 5% of the time, and very rarely 2 too low.
+ while ( compare( yc, rem, yL, remL ) < 1 ) {
+ n++;
+
+ // Subtract divisor from remainder.
+ subtract( rem, yL < remL ? yz : yc, remL, base );
+ remL = rem.length;
+ }
+ }
+ } else if ( cmp === 0 ) {
+ n++;
+ rem = [0];
+ } // else cmp === 1 and n will be 0
+
+ // Add the next digit, n, to the result array.
+ qc[i++] = n;
+
+ // Update the remainder.
+ if ( rem[0] ) {
+ rem[remL++] = xc[xi] || 0;
+ } else {
+ rem = [ xc[xi] ];
+ remL = 1;
+ }
+ } while ( ( xi++ < xL || rem[0] != null ) && s-- );
+
+ more = rem[0] != null;
+
+ // Leading zero?
+ if ( !qc[0] ) qc.splice(0, 1);
+ }
+
+ if ( base == BASE ) {
+
+ // To calculate q.e, first get the number of digits of qc[0].
+ for ( i = 1, s = qc[0]; s >= 10; s /= 10, i++ );
+
+ round( q, dp + ( q.e = i + e * LOG_BASE - 1 ) + 1, rm, more );
+
+ // Caller is convertBase.
+ } else {
+ q.e = e;
+ q.r = +more;
+ }
+
+ return q;
+ };
+ })();
+
+
+ /*
+ * Return a string representing the value of BigNumber n in fixed-point or exponential
+ * notation rounded to the specified decimal places or significant digits.
+ *
+ * n: a BigNumber.
+ * i: the index of the last digit required (i.e. the digit that may be rounded up).
+ * rm: the rounding mode.
+ * id: 1 (toExponential) or 2 (toPrecision).
+ */
+ function format( n, i, rm, id ) {
+ var c0, e, ne, len, str;
+
+ if ( rm == null ) rm = ROUNDING_MODE;
+ else intCheck( rm, 0, 8 );
+
+ if ( !n.c ) return n.toString();
+
+ c0 = n.c[0];
+ ne = n.e;
+
+ if ( i == null ) {
+ str = coeffToString( n.c );
+ str = id == 1 || id == 2 && ne <= TO_EXP_NEG
+ ? toExponential( str, ne )
+ : toFixedPoint( str, ne, '0' );
+ } else {
+ n = round( new BigNumber(n), i, rm );
+
+ // n.e may have changed if the value was rounded up.
+ e = n.e;
+
+ str = coeffToString( n.c );
+ len = str.length;
+
+ // toPrecision returns exponential notation if the number of significant digits
+ // specified is less than the number of digits necessary to represent the integer
+ // part of the value in fixed-point notation.
+
+ // Exponential notation.
+ if ( id == 1 || id == 2 && ( i <= e || e <= TO_EXP_NEG ) ) {
+
+ // Append zeros?
+ for ( ; len < i; str += '0', len++ );
+ str = toExponential( str, e );
+
+ // Fixed-point notation.
+ } else {
+ i -= ne;
+ str = toFixedPoint( str, e, '0' );
+
+ // Append zeros?
+ if ( e + 1 > len ) {
+ if ( --i > 0 ) for ( str += '.'; i--; str += '0' );
+ } else {
+ i += e - len;
+ if ( i > 0 ) {
+ if ( e + 1 == len ) str += '.';
+ for ( ; i--; str += '0' );
+ }
+ }
+ }
+ }
+
+ return n.s < 0 && c0 ? '-' + str : str;
+ }
+
+
+ // Handle BigNumber.max and BigNumber.min.
+ function maxOrMin( args, method ) {
+ var m, n,
+ i = 0;
+
+ if ( isArray( args[0] ) ) args = args[0];
+ m = new BigNumber( args[0] );
+
+ for ( ; ++i < args.length; ) {
+ n = new BigNumber( args[i] );
+
+ // If any number is NaN, return NaN.
+ if ( !n.s ) {
+ m = n;
+ break;
+ } else if ( method.call( m, n ) ) {
+ m = n;
+ }
+ }
+
+ return m;
+ }
+
+
+ /*
+ * Strip trailing zeros, calculate base 10 exponent and check against MIN_EXP and MAX_EXP.
+ * Called by minus, plus and times.
+ */
+ function normalise( n, c, e ) {
+ var i = 1,
+ j = c.length;
+
+ // Remove trailing zeros.
+ for ( ; !c[--j]; c.pop() );
+
+ // Calculate the base 10 exponent. First get the number of digits of c[0].
+ for ( j = c[0]; j >= 10; j /= 10, i++ );
+
+ // Overflow?
+ if ( ( e = i + e * LOG_BASE - 1 ) > MAX_EXP ) {
+
+ // Infinity.
+ n.c = n.e = null;
+
+ // Underflow?
+ } else if ( e < MIN_EXP ) {
+
+ // Zero.
+ n.c = [ n.e = 0 ];
+ } else {
+ n.e = e;
+ n.c = c;
+ }
+
+ return n;
+ }
+
+
+ // Handle values that fail the validity test in BigNumber.
+ parseNumeric = (function () {
+ var basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i,
+ dotAfter = /^([^.]+)\.$/,
+ dotBefore = /^\.([^.]+)$/,
+ isInfinityOrNaN = /^-?(Infinity|NaN)$/,
+ whitespaceOrPlus = /^\s*\+(?=[\w.])|^\s+|\s+$/g;
+
+ return function ( x, str, isNum, b ) {
+ var base,
+ s = isNum ? str : str.replace( whitespaceOrPlus, '' );
+
+ // No exception on ±Infinity or NaN.
+ if ( isInfinityOrNaN.test(s) ) {
+ x.s = isNaN(s) ? null : s < 0 ? -1 : 1;
+ x.c = x.e = null;
+ } else {
+ if ( !isNum ) {
+
+ // basePrefix = /^(-?)0([xbo])(?=\w[\w.]*$)/i
+ s = s.replace( basePrefix, function ( m, p1, p2 ) {
+ base = ( p2 = p2.toLowerCase() ) == 'x' ? 16 : p2 == 'b' ? 2 : 8;
+ return !b || b == base ? p1 : m;
+ });
+
+ if (b) {
+ base = b;
+
+ // E.g. '1.' to '1', '.1' to '0.1'
+ s = s.replace( dotAfter, '$1' ).replace( dotBefore, '0.$1' );
+ }
+
+ if ( str != s ) return new BigNumber( s, base );
+ }
+
+ // '[BigNumber Error] Not a number: {n}'
+ // '[BigNumber Error] Not a base {b} number: {n}'
+ throw Error
+ ( bignumberError + 'Not a' + ( b ? ' base ' + b : '' ) + ' number: ' + str );
+ }
+ }
+ })();
+
+
+ /*
+ * Round x to sd significant digits using rounding mode rm. Check for over/under-flow.
+ * If r is truthy, it is known that there are more digits after the rounding digit.
+ */
+ function round( x, sd, rm, r ) {
+ var d, i, j, k, n, ni, rd,
+ xc = x.c,
+ pows10 = POWS_TEN;
+
+ // if x is not Infinity or NaN...
+ if (xc) {
+
+ // rd is the rounding digit, i.e. the digit after the digit that may be rounded up.
+ // n is a base 1e14 number, the value of the element of array x.c containing rd.
+ // ni is the index of n within x.c.
+ // d is the number of digits of n.
+ // i is the index of rd within n including leading zeros.
+ // j is the actual index of rd within n (if < 0, rd is a leading zero).
+ out: {
+
+ // Get the number of digits of the first element of xc.
+ for ( d = 1, k = xc[0]; k >= 10; k /= 10, d++ );
+ i = sd - d;
+
+ // If the rounding digit is in the first element of xc...
+ if ( i < 0 ) {
+ i += LOG_BASE;
+ j = sd;
+ n = xc[ ni = 0 ];
+
+ // Get the rounding digit at index j of n.
+ rd = n / pows10[ d - j - 1 ] % 10 | 0;
+ } else {
+ ni = mathceil( ( i + 1 ) / LOG_BASE );
+
+ if ( ni >= xc.length ) {
+
+ if (r) {
+
+ // Needed by sqrt.
+ for ( ; xc.length <= ni; xc.push(0) );
+ n = rd = 0;
+ d = 1;
+ i %= LOG_BASE;
+ j = i - LOG_BASE + 1;
+ } else {
+ break out;
+ }
+ } else {
+ n = k = xc[ni];
+
+ // Get the number of digits of n.
+ for ( d = 1; k >= 10; k /= 10, d++ );
+
+ // Get the index of rd within n.
+ i %= LOG_BASE;
+
+ // Get the index of rd within n, adjusted for leading zeros.
+ // The number of leading zeros of n is given by LOG_BASE - d.
+ j = i - LOG_BASE + d;
+
+ // Get the rounding digit at index j of n.
+ rd = j < 0 ? 0 : n / pows10[ d - j - 1 ] % 10 | 0;
+ }
+ }
+
+ r = r || sd < 0 ||
+
+ // Are there any non-zero digits after the rounding digit?
+ // The expression n % pows10[ d - j - 1 ] returns all digits of n to the right
+ // of the digit at j, e.g. if n is 908714 and j is 2, the expression gives 714.
+ xc[ni + 1] != null || ( j < 0 ? n : n % pows10[ d - j - 1 ] );
+
+ r = rm < 4
+ ? ( rd || r ) && ( rm == 0 || rm == ( x.s < 0 ? 3 : 2 ) )
+ : rd > 5 || rd == 5 && ( rm == 4 || r || rm == 6 &&
+
+ // Check whether the digit to the left of the rounding digit is odd.
+ ( ( i > 0 ? j > 0 ? n / pows10[ d - j ] : 0 : xc[ni - 1] ) % 10 ) & 1 ||
+ rm == ( x.s < 0 ? 8 : 7 ) );
+
+ if ( sd < 1 || !xc[0] ) {
+ xc.length = 0;
+
+ if (r) {
+
+ // Convert sd to decimal places.
+ sd -= x.e + 1;
+
+ // 1, 0.1, 0.01, 0.001, 0.0001 etc.
+ xc[0] = pows10[ ( LOG_BASE - sd % LOG_BASE ) % LOG_BASE ];
+ x.e = -sd || 0;
+ } else {
+
+ // Zero.
+ xc[0] = x.e = 0;
+ }
+
+ return x;
+ }
+
+ // Remove excess digits.
+ if ( i == 0 ) {
+ xc.length = ni;
+ k = 1;
+ ni--;
+ } else {
+ xc.length = ni + 1;
+ k = pows10[ LOG_BASE - i ];
+
+ // E.g. 56700 becomes 56000 if 7 is the rounding digit.
+ // j > 0 means i > number of leading zeros of n.
+ xc[ni] = j > 0 ? mathfloor( n / pows10[ d - j ] % pows10[j] ) * k : 0;
+ }
+
+ // Round up?
+ if (r) {
+
+ for ( ; ; ) {
+
+ // If the digit to be rounded up is in the first element of xc...
+ if ( ni == 0 ) {
+
+ // i will be the length of xc[0] before k is added.
+ for ( i = 1, j = xc[0]; j >= 10; j /= 10, i++ );
+ j = xc[0] += k;
+ for ( k = 1; j >= 10; j /= 10, k++ );
+
+ // if i != k the length has increased.
+ if ( i != k ) {
+ x.e++;
+ if ( xc[0] == BASE ) xc[0] = 1;
+ }
+
+ break;
+ } else {
+ xc[ni] += k;
+ if ( xc[ni] != BASE ) break;
+ xc[ni--] = 0;
+ k = 1;
+ }
+ }
+ }
+
+ // Remove trailing zeros.
+ for ( i = xc.length; xc[--i] === 0; xc.pop() );
+ }
+
+ // Overflow? Infinity.
+ if ( x.e > MAX_EXP ) {
+ x.c = x.e = null;
+
+ // Underflow? Zero.
+ } else if ( x.e < MIN_EXP ) {
+ x.c = [ x.e = 0 ];
+ }
+ }
+
+ return x;
+ }
+
+
+ // PROTOTYPE/INSTANCE METHODS
+
+
+ /*
+ * Return a new BigNumber whose value is the absolute value of this BigNumber.
+ */
+ P.absoluteValue = P.abs = function () {
+ var x = new BigNumber(this);
+ if ( x.s < 0 ) x.s = 1;
+ return x;
+ };
+
+
+ /*
+ * Return
+ * 1 if the value of this BigNumber is greater than the value of BigNumber(y, b),
+ * -1 if the value of this BigNumber is less than the value of BigNumber(y, b),
+ * 0 if they have the same value,
+ * or null if the value of either is NaN.
+ */
+ P.comparedTo = function ( y, b ) {
+ return compare( this, new BigNumber( y, b ) );
+ };
+
+
+ /*
+ * If dp is undefined or null or true or false, return the number of decimal places of the
+ * value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+ *
+ * Otherwise, if dp is a number, return a new BigNumber whose value is the value of this
+ * BigNumber rounded to a maximum of dp decimal places using rounding mode rm, or
+ * ROUNDING_MODE if rm is omitted.
+ *
+ * [dp] {number} Decimal places: integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.decimalPlaces = P.dp = function ( dp, rm ) {
+ var c, n, v,
+ x = this;
+
+ if ( dp != null ) {
+ intCheck( dp, 0, MAX );
+ if ( rm == null ) rm = ROUNDING_MODE;
+ else intCheck( rm, 0, 8 );
+
+ return round( new BigNumber(x), dp + x.e + 1, rm );
+ }
+
+ if ( !( c = x.c ) ) return null;
+ n = ( ( v = c.length - 1 ) - bitFloor( this.e / LOG_BASE ) ) * LOG_BASE;
+
+ // Subtract the number of trailing zeros of the last number.
+ if ( v = c[v] ) for ( ; v % 10 == 0; v /= 10, n-- );
+ if ( n < 0 ) n = 0;
+
+ return n;
+ };
+
+
+ /*
+ * n / 0 = I
+ * n / N = N
+ * n / I = 0
+ * 0 / n = 0
+ * 0 / 0 = N
+ * 0 / N = N
+ * 0 / I = 0
+ * N / n = N
+ * N / 0 = N
+ * N / N = N
+ * N / I = N
+ * I / n = I
+ * I / 0 = I
+ * I / N = N
+ * I / I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber divided by the value of
+ * BigNumber(y, b), rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+ */
+ P.dividedBy = P.div = function ( y, b ) {
+ return div( this, new BigNumber( y, b ), DECIMAL_PLACES, ROUNDING_MODE );
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the integer part of dividing the value of this
+ * BigNumber by the value of BigNumber(y, b).
+ */
+ P.dividedToIntegerBy = P.idiv = function ( y, b ) {
+ return div( this, new BigNumber( y, b ), 0, 1 );
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is equal to the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isEqualTo = P.eq = function ( y, b ) {
+ return compare( this, new BigNumber( y, b ) ) === 0;
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber rounded to an integer
+ * using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+ *
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {rm}'
+ */
+ P.integerValue = function (rm) {
+ var n = new BigNumber(this);
+ if ( rm == null ) rm = ROUNDING_MODE;
+ else intCheck( rm, 0, 8 );
+ return round( n, n.e + 1, rm );
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is greater than the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isGreaterThan = P.gt = function ( y, b ) {
+ return compare( this, new BigNumber( y, b ) ) > 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is greater than or equal to the value of
+ * BigNumber(y, b), otherwise return false.
+ */
+ P.isGreaterThanOrEqualTo = P.gte = function ( y, b ) {
+ return ( b = compare( this, new BigNumber( y, b ) ) ) === 1 || b === 0;
+
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is a finite number, otherwise return false.
+ */
+ P.isFinite = function () {
+ return !!this.c;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is an integer, otherwise return false.
+ */
+ P.isInteger = function () {
+ return !!this.c && bitFloor( this.e / LOG_BASE ) > this.c.length - 2;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is NaN, otherwise return false.
+ */
+ P.isNaN = function () {
+ return !this.s;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is negative, otherwise return false.
+ */
+ P.isNegative = function () {
+ return this.s < 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is positive, otherwise return false.
+ */
+ P.isPositive = function () {
+ return this.s > 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is 0 or -0, otherwise return false.
+ */
+ P.isZero = function () {
+ return !!this.c && this.c[0] == 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is less than the value of BigNumber(y, b),
+ * otherwise return false.
+ */
+ P.isLessThan = P.lt = function ( y, b ) {
+ return compare( this, new BigNumber( y, b ) ) < 0;
+ };
+
+
+ /*
+ * Return true if the value of this BigNumber is less than or equal to the value of
+ * BigNumber(y, b), otherwise return false.
+ */
+ P.isLessThanOrEqualTo = P.lte = function ( y, b ) {
+ return ( b = compare( this, new BigNumber( y, b ) ) ) === -1 || b === 0;
+ };
+
+
+ /*
+ * n - 0 = n
+ * n - N = N
+ * n - I = -I
+ * 0 - n = -n
+ * 0 - 0 = 0
+ * 0 - N = N
+ * 0 - I = -I
+ * N - n = N
+ * N - 0 = N
+ * N - N = N
+ * N - I = N
+ * I - n = I
+ * I - 0 = I
+ * I - N = N
+ * I - I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber minus the value of
+ * BigNumber(y, b).
+ */
+ P.minus = function ( y, b ) {
+ var i, j, t, xLTy,
+ x = this,
+ a = x.s;
+
+ y = new BigNumber( y, b );
+ b = y.s;
+
+ // Either NaN?
+ if ( !a || !b ) return new BigNumber(NaN);
+
+ // Signs differ?
+ if ( a != b ) {
+ y.s = -b;
+ return x.plus(y);
+ }
+
+ var xe = x.e / LOG_BASE,
+ ye = y.e / LOG_BASE,
+ xc = x.c,
+ yc = y.c;
+
+ if ( !xe || !ye ) {
+
+ // Either Infinity?
+ if ( !xc || !yc ) return xc ? ( y.s = -b, y ) : new BigNumber( yc ? x : NaN );
+
+ // Either zero?
+ if ( !xc[0] || !yc[0] ) {
+
+ // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+ return yc[0] ? ( y.s = -b, y ) : new BigNumber( xc[0] ? x :
+
+ // IEEE 754 (2008) 6.3: n - n = -0 when rounding to -Infinity
+ ROUNDING_MODE == 3 ? -0 : 0 );
+ }
+ }
+
+ xe = bitFloor(xe);
+ ye = bitFloor(ye);
+ xc = xc.slice();
+
+ // Determine which is the bigger number.
+ if ( a = xe - ye ) {
+
+ if ( xLTy = a < 0 ) {
+ a = -a;
+ t = xc;
+ } else {
+ ye = xe;
+ t = yc;
+ }
+
+ t.reverse();
+
+ // Prepend zeros to equalise exponents.
+ for ( b = a; b--; t.push(0) );
+ t.reverse();
+ } else {
+
+ // Exponents equal. Check digit by digit.
+ j = ( xLTy = ( a = xc.length ) < ( b = yc.length ) ) ? a : b;
+
+ for ( a = b = 0; b < j; b++ ) {
+
+ if ( xc[b] != yc[b] ) {
+ xLTy = xc[b] < yc[b];
+ break;
+ }
+ }
+ }
+
+ // x < y? Point xc to the array of the bigger number.
+ if (xLTy) t = xc, xc = yc, yc = t, y.s = -y.s;
+
+ b = ( j = yc.length ) - ( i = xc.length );
+
+ // Append zeros to xc if shorter.
+ // No need to add zeros to yc if shorter as subtract only needs to start at yc.length.
+ if ( b > 0 ) for ( ; b--; xc[i++] = 0 );
+ b = BASE - 1;
+
+ // Subtract yc from xc.
+ for ( ; j > a; ) {
+
+ if ( xc[--j] < yc[j] ) {
+ for ( i = j; i && !xc[--i]; xc[i] = b );
+ --xc[i];
+ xc[j] += BASE;
+ }
+
+ xc[j] -= yc[j];
+ }
+
+ // Remove leading zeros and adjust exponent accordingly.
+ for ( ; xc[0] == 0; xc.splice(0, 1), --ye );
+
+ // Zero?
+ if ( !xc[0] ) {
+
+ // Following IEEE 754 (2008) 6.3,
+ // n - n = +0 but n - n = -0 when rounding towards -Infinity.
+ y.s = ROUNDING_MODE == 3 ? -1 : 1;
+ y.c = [ y.e = 0 ];
+ return y;
+ }
+
+ // No need to check for Infinity as +x - +y != Infinity && -x - -y != Infinity
+ // for finite x and y.
+ return normalise( y, xc, ye );
+ };
+
+
+ /*
+ * n % 0 = N
+ * n % N = N
+ * n % I = n
+ * 0 % n = 0
+ * -0 % n = -0
+ * 0 % 0 = N
+ * 0 % N = N
+ * 0 % I = 0
+ * N % n = N
+ * N % 0 = N
+ * N % N = N
+ * N % I = N
+ * I % n = N
+ * I % 0 = N
+ * I % N = N
+ * I % I = N
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber modulo the value of
+ * BigNumber(y, b). The result depends on the value of MODULO_MODE.
+ */
+ P.modulo = P.mod = function ( y, b ) {
+ var q, s,
+ x = this;
+
+ y = new BigNumber( y, b );
+
+ // Return NaN if x is Infinity or NaN, or y is NaN or zero.
+ if ( !x.c || !y.s || y.c && !y.c[0] ) {
+ return new BigNumber(NaN);
+
+ // Return x if y is Infinity or x is zero.
+ } else if ( !y.c || x.c && !x.c[0] ) {
+ return new BigNumber(x);
+ }
+
+ if ( MODULO_MODE == 9 ) {
+
+ // Euclidian division: q = sign(y) * floor(x / abs(y))
+ // r = x - qy where 0 <= r < abs(y)
+ s = y.s;
+ y.s = 1;
+ q = div( x, y, 0, 3 );
+ y.s = s;
+ q.s *= s;
+ } else {
+ q = div( x, y, 0, MODULO_MODE );
+ }
+
+ return x.minus( q.times(y) );
+ };
+
+
+ /*
+ * n * 0 = 0
+ * n * N = N
+ * n * I = I
+ * 0 * n = 0
+ * 0 * 0 = 0
+ * 0 * N = N
+ * 0 * I = N
+ * N * n = N
+ * N * 0 = N
+ * N * N = N
+ * N * I = N
+ * I * n = I
+ * I * 0 = N
+ * I * N = N
+ * I * I = I
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber multiplied by the value
+ * of BigNumber(y, b).
+ */
+ P.multipliedBy = P.times = function ( y, b ) {
+ var c, e, i, j, k, m, xcL, xlo, xhi, ycL, ylo, yhi, zc,
+ base, sqrtBase,
+ x = this,
+ xc = x.c,
+ yc = ( y = new BigNumber( y, b ) ).c;
+
+ // Either NaN, ±Infinity or ±0?
+ if ( !xc || !yc || !xc[0] || !yc[0] ) {
+
+ // Return NaN if either is NaN, or one is 0 and the other is Infinity.
+ if ( !x.s || !y.s || xc && !xc[0] && !yc || yc && !yc[0] && !xc ) {
+ y.c = y.e = y.s = null;
+ } else {
+ y.s *= x.s;
+
+ // Return ±Infinity if either is ±Infinity.
+ if ( !xc || !yc ) {
+ y.c = y.e = null;
+
+ // Return ±0 if either is ±0.
+ } else {
+ y.c = [0];
+ y.e = 0;
+ }
+ }
+
+ return y;
+ }
+
+ e = bitFloor( x.e / LOG_BASE ) + bitFloor( y.e / LOG_BASE );
+ y.s *= x.s;
+ xcL = xc.length;
+ ycL = yc.length;
+
+ // Ensure xc points to longer array and xcL to its length.
+ if ( xcL < ycL ) zc = xc, xc = yc, yc = zc, i = xcL, xcL = ycL, ycL = i;
+
+ // Initialise the result array with zeros.
+ for ( i = xcL + ycL, zc = []; i--; zc.push(0) );
+
+ base = BASE;
+ sqrtBase = SQRT_BASE;
+
+ for ( i = ycL; --i >= 0; ) {
+ c = 0;
+ ylo = yc[i] % sqrtBase;
+ yhi = yc[i] / sqrtBase | 0;
+
+ for ( k = xcL, j = i + k; j > i; ) {
+ xlo = xc[--k] % sqrtBase;
+ xhi = xc[k] / sqrtBase | 0;
+ m = yhi * xlo + xhi * ylo;
+ xlo = ylo * xlo + ( ( m % sqrtBase ) * sqrtBase ) + zc[j] + c;
+ c = ( xlo / base | 0 ) + ( m / sqrtBase | 0 ) + yhi * xhi;
+ zc[j--] = xlo % base;
+ }
+
+ zc[j] = c;
+ }
+
+ if (c) {
+ ++e;
+ } else {
+ zc.splice(0, 1);
+ }
+
+ return normalise( y, zc, e );
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber negated,
+ * i.e. multiplied by -1.
+ */
+ P.negated = function () {
+ var x = new BigNumber(this);
+ x.s = -x.s || null;
+ return x;
+ };
+
+
+ /*
+ * n + 0 = n
+ * n + N = N
+ * n + I = I
+ * 0 + n = n
+ * 0 + 0 = 0
+ * 0 + N = N
+ * 0 + I = I
+ * N + n = N
+ * N + 0 = N
+ * N + N = N
+ * N + I = N
+ * I + n = I
+ * I + 0 = I
+ * I + N = N
+ * I + I = I
+ *
+ * Return a new BigNumber whose value is the value of this BigNumber plus the value of
+ * BigNumber(y, b).
+ */
+ P.plus = function ( y, b ) {
+ var t,
+ x = this,
+ a = x.s;
+
+ y = new BigNumber( y, b );
+ b = y.s;
+
+ // Either NaN?
+ if ( !a || !b ) return new BigNumber(NaN);
+
+ // Signs differ?
+ if ( a != b ) {
+ y.s = -b;
+ return x.minus(y);
+ }
+
+ var xe = x.e / LOG_BASE,
+ ye = y.e / LOG_BASE,
+ xc = x.c,
+ yc = y.c;
+
+ if ( !xe || !ye ) {
+
+ // Return ±Infinity if either ±Infinity.
+ if ( !xc || !yc ) return new BigNumber( a / 0 );
+
+ // Either zero?
+ // Return y if y is non-zero, x if x is non-zero, or zero if both are zero.
+ if ( !xc[0] || !yc[0] ) return yc[0] ? y : new BigNumber( xc[0] ? x : a * 0 );
+ }
+
+ xe = bitFloor(xe);
+ ye = bitFloor(ye);
+ xc = xc.slice();
+
+ // Prepend zeros to equalise exponents. Faster to use reverse then do unshifts.
+ if ( a = xe - ye ) {
+ if ( a > 0 ) {
+ ye = xe;
+ t = yc;
+ } else {
+ a = -a;
+ t = xc;
+ }
+
+ t.reverse();
+ for ( ; a--; t.push(0) );
+ t.reverse();
+ }
+
+ a = xc.length;
+ b = yc.length;
+
+ // Point xc to the longer array, and b to the shorter length.
+ if ( a - b < 0 ) t = yc, yc = xc, xc = t, b = a;
+
+ // Only start adding at yc.length - 1 as the further digits of xc can be ignored.
+ for ( a = 0; b; ) {
+ a = ( xc[--b] = xc[b] + yc[b] + a ) / BASE | 0;
+ xc[b] = BASE === xc[b] ? 0 : xc[b] % BASE;
+ }
+
+ if (a) {
+ xc = [a].concat(xc);
+ ++ye;
+ }
+
+ // No need to check for zero, as +x + +y != 0 && -x + -y != 0
+ // ye = MAX_EXP + 1 possible
+ return normalise( y, xc, ye );
+ };
+
+
+ /*
+ * If sd is undefined or null or true or false, return the number of significant digits of
+ * the value of this BigNumber, or null if the value of this BigNumber is ±Infinity or NaN.
+ * If sd is true include integer-part trailing zeros in the count.
+ *
+ * Otherwise, if sd is a number, return a new BigNumber whose value is the value of this
+ * BigNumber rounded to a maximum of sd significant digits using rounding mode rm, or
+ * ROUNDING_MODE if rm is omitted.
+ *
+ * sd {number|boolean} number: significant digits: integer, 1 to MAX inclusive.
+ * boolean: whether to count integer-part trailing zeros: true or false.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+ */
+ P.precision = P.sd = function ( sd, rm ) {
+ var c, n, v,
+ x = this;
+
+ if ( sd != null && sd !== !!sd ) {
+ intCheck( sd, 1, MAX );
+ if ( rm == null ) rm = ROUNDING_MODE;
+ else intCheck( rm, 0, 8 );
+
+ return round( new BigNumber(x), sd, rm );
+ }
+
+ if ( !( c = x.c ) ) return null;
+ v = c.length - 1;
+ n = v * LOG_BASE + 1;
+
+ if ( v = c[v] ) {
+
+ // Subtract the number of trailing zeros of the last element.
+ for ( ; v % 10 == 0; v /= 10, n-- );
+
+ // Add the number of digits of the first element.
+ for ( v = c[0]; v >= 10; v /= 10, n++ );
+ }
+
+ if ( sd && x.e + 1 > n ) n = x.e + 1;
+
+ return n;
+ };
+
+
+ /*
+ * Return a new BigNumber whose value is the value of this BigNumber shifted by k places
+ * (powers of 10). Shift to the right if n > 0, and to the left if n < 0.
+ *
+ * k {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {k}'
+ */
+ P.shiftedBy = function (k) {
+ intCheck( k, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
+ return this.times( '1e' + k );
+ };
+
+
+ /*
+ * sqrt(-n) = N
+ * sqrt( N) = N
+ * sqrt(-I) = N
+ * sqrt( I) = I
+ * sqrt( 0) = 0
+ * sqrt(-0) = -0
+ *
+ * Return a new BigNumber whose value is the square root of the value of this BigNumber,
+ * rounded according to DECIMAL_PLACES and ROUNDING_MODE.
+ */
+ P.squareRoot = P.sqrt = function () {
+ var m, n, r, rep, t,
+ x = this,
+ c = x.c,
+ s = x.s,
+ e = x.e,
+ dp = DECIMAL_PLACES + 4,
+ half = new BigNumber('0.5');
+
+ // Negative/NaN/Infinity/zero?
+ if ( s !== 1 || !c || !c[0] ) {
+ return new BigNumber( !s || s < 0 && ( !c || c[0] ) ? NaN : c ? x : 1 / 0 );
+ }
+
+ // Initial estimate.
+ s = Math.sqrt( +x );
+
+ // Math.sqrt underflow/overflow?
+ // Pass x to Math.sqrt as integer, then adjust the exponent of the result.
+ if ( s == 0 || s == 1 / 0 ) {
+ n = coeffToString(c);
+ if ( ( n.length + e ) % 2 == 0 ) n += '0';
+ s = Math.sqrt(n);
+ e = bitFloor( ( e + 1 ) / 2 ) - ( e < 0 || e % 2 );
+
+ if ( s == 1 / 0 ) {
+ n = '1e' + e;
+ } else {
+ n = s.toExponential();
+ n = n.slice( 0, n.indexOf('e') + 1 ) + e;
+ }
+
+ r = new BigNumber(n);
+ } else {
+ r = new BigNumber( s + '' );
+ }
+
+ // Check for zero.
+ // r could be zero if MIN_EXP is changed after the this value was created.
+ // This would cause a division by zero (x/t) and hence Infinity below, which would cause
+ // coeffToString to throw.
+ if ( r.c[0] ) {
+ e = r.e;
+ s = e + dp;
+ if ( s < 3 ) s = 0;
+
+ // Newton-Raphson iteration.
+ for ( ; ; ) {
+ t = r;
+ r = half.times( t.plus( div( x, t, dp, 1 ) ) );
+
+ if ( coeffToString( t.c ).slice( 0, s ) === ( n =
+ coeffToString( r.c ) ).slice( 0, s ) ) {
+
+ // The exponent of r may here be one less than the final result exponent,
+ // e.g 0.0009999 (e-4) --> 0.001 (e-3), so adjust s so the rounding digits
+ // are indexed correctly.
+ if ( r.e < e ) --s;
+ n = n.slice( s - 3, s + 1 );
+
+ // The 4th rounding digit may be in error by -1 so if the 4 rounding digits
+ // are 9999 or 4999 (i.e. approaching a rounding boundary) continue the
+ // iteration.
+ if ( n == '9999' || !rep && n == '4999' ) {
+
+ // On the first iteration only, check to see if rounding up gives the
+ // exact result as the nines may infinitely repeat.
+ if ( !rep ) {
+ round( t, t.e + DECIMAL_PLACES + 2, 0 );
+
+ if ( t.times(t).eq(x) ) {
+ r = t;
+ break;
+ }
+ }
+
+ dp += 4;
+ s += 4;
+ rep = 1;
+ } else {
+
+ // If rounding digits are null, 0{0,4} or 50{0,3}, check for exact
+ // result. If not, then there are further digits and m will be truthy.
+ if ( !+n || !+n.slice(1) && n.charAt(0) == '5' ) {
+
+ // Truncate to the first rounding digit.
+ round( r, r.e + DECIMAL_PLACES + 2, 1 );
+ m = !r.times(r).eq(x);
+ }
+
+ break;
+ }
+ }
+ }
+ }
+
+ return round( r, r.e + DECIMAL_PLACES + 1, ROUNDING_MODE, m );
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in exponential notation and
+ * rounded using ROUNDING_MODE to dp fixed decimal places.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.toExponential = function ( dp, rm ) {
+ if ( dp != null ) {
+ intCheck( dp, 0, MAX );
+ dp++;
+ }
+ return format( this, dp, rm, 1 );
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in fixed-point notation rounding
+ * to dp fixed decimal places using rounding mode rm, or ROUNDING_MODE if rm is omitted.
+ *
+ * Note: as with JavaScript's number type, (-0).toFixed(0) is '0',
+ * but e.g. (-0.00001).toFixed(0) is '-0'.
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.toFixed = function ( dp, rm ) {
+ if ( dp != null ) {
+ intCheck( dp, 0, MAX );
+ dp = dp + this.e + 1;
+ }
+ return format( this, dp, rm );
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in fixed-point notation rounded
+ * using rm or ROUNDING_MODE to dp decimal places, and formatted according to the properties
+ * of the FORMAT object (see BigNumber.set).
+ *
+ * FORMAT = {
+ * decimalSeparator : '.',
+ * groupSeparator : ',',
+ * groupSize : 3,
+ * secondaryGroupSize : 0,
+ * fractionGroupSeparator : '\xA0', // non-breaking space
+ * fractionGroupSize : 0
+ * };
+ *
+ * [dp] {number} Decimal places. Integer, 0 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {dp|rm}'
+ */
+ P.toFormat = function ( dp, rm ) {
+ var str = this.toFixed( dp, rm );
+
+ if ( this.c ) {
+ var i,
+ arr = str.split('.'),
+ g1 = +FORMAT.groupSize,
+ g2 = +FORMAT.secondaryGroupSize,
+ groupSeparator = FORMAT.groupSeparator,
+ intPart = arr[0],
+ fractionPart = arr[1],
+ isNeg = this.s < 0,
+ intDigits = isNeg ? intPart.slice(1) : intPart,
+ len = intDigits.length;
+
+ if (g2) i = g1, g1 = g2, g2 = i, len -= i;
+
+ if ( g1 > 0 && len > 0 ) {
+ i = len % g1 || g1;
+ intPart = intDigits.substr( 0, i );
+
+ for ( ; i < len; i += g1 ) {
+ intPart += groupSeparator + intDigits.substr( i, g1 );
+ }
+
+ if ( g2 > 0 ) intPart += groupSeparator + intDigits.slice(i);
+ if (isNeg) intPart = '-' + intPart;
+ }
+
+ str = fractionPart
+ ? intPart + FORMAT.decimalSeparator + ( ( g2 = +FORMAT.fractionGroupSize )
+ ? fractionPart.replace( new RegExp( '\\d{' + g2 + '}\\B', 'g' ),
+ '$&' + FORMAT.fractionGroupSeparator )
+ : fractionPart )
+ : intPart;
+ }
+
+ return str;
+ };
+
+
+ /*
+ * Return a string array representing the value of this BigNumber as a simple fraction with
+ * an integer numerator and an integer denominator. The denominator will be a positive
+ * non-zero value less than or equal to the specified maximum denominator. If a maximum
+ * denominator is not specified, the denominator will be the lowest value necessary to
+ * represent the number exactly.
+ *
+ * [md] {number|string|BigNumber} Integer >= 1 and < Infinity. The maximum denominator.
+ *
+ * '[BigNumber Error] Argument {not an integer|out of range} : {md}'
+ */
+ P.toFraction = function (md) {
+ var arr, d, d0, d1, d2, e, exp, n, n0, n1, q, s,
+ x = this,
+ xc = x.c;
+
+ if ( md != null ) {
+ n = new BigNumber(md);
+
+ if ( !n.isInteger() || n.lt(ONE) ) {
+ throw Error
+ ( bignumberError + 'Argument ' +
+ ( n.isInteger() ? 'out of range: ' : 'not an integer: ' ) + md );
+ }
+ }
+
+ if ( !xc ) return x.toString();
+
+ d = new BigNumber(ONE);
+ n1 = d0 = new BigNumber(ONE);
+ d1 = n0 = new BigNumber(ONE);
+ s = coeffToString(xc);
+
+ // Determine initial denominator.
+ // d is a power of 10 and the minimum max denominator that specifies the value exactly.
+ e = d.e = s.length - x.e - 1;
+ d.c[0] = POWS_TEN[ ( exp = e % LOG_BASE ) < 0 ? LOG_BASE + exp : exp ];
+ md = !md || n.comparedTo(d) > 0 ? ( e > 0 ? d : n1 ) : n;
+
+ exp = MAX_EXP;
+ MAX_EXP = 1 / 0;
+ n = new BigNumber(s);
+
+ // n0 = d1 = 0
+ n0.c[0] = 0;
+
+ for ( ; ; ) {
+ q = div( n, d, 0, 1 );
+ d2 = d0.plus( q.times(d1) );
+ if ( d2.comparedTo(md) == 1 ) break;
+ d0 = d1;
+ d1 = d2;
+ n1 = n0.plus( q.times( d2 = n1 ) );
+ n0 = d2;
+ d = n.minus( q.times( d2 = d ) );
+ n = d2;
+ }
+
+ d2 = div( md.minus(d0), d1, 0, 1 );
+ n0 = n0.plus( d2.times(n1) );
+ d0 = d0.plus( d2.times(d1) );
+ n0.s = n1.s = x.s;
+ e *= 2;
+
+ // Determine which fraction is closer to x, n0/d0 or n1/d1
+ arr = div( n1, d1, e, ROUNDING_MODE ).minus(x).abs().comparedTo(
+ div( n0, d0, e, ROUNDING_MODE ).minus(x).abs() ) < 1
+ ? [ n1.toString(), d1.toString() ]
+ : [ n0.toString(), d0.toString() ];
+
+ MAX_EXP = exp;
+ return arr;
+ };
+
+
+ /*
+ * Return the value of this BigNumber converted to a number primitive.
+ */
+ P.toNumber = function () {
+ return +this;
+ };
+
+
+ /*
+ * Return a BigNumber whose value is the value of this BigNumber exponentiated by n.
+ *
+ * If m is present, return the result modulo m.
+ * If n is negative round according to DECIMAL_PLACES and ROUNDING_MODE.
+ * If POW_PRECISION is non-zero and m is not present, round to POW_PRECISION using ROUNDING_MODE.
+ *
+ * The modular power operation works efficiently when x, n, and m are positive integers,
+ * otherwise it is equivalent to calculating x.exponentiatedBy(n).modulo(m) with a POW_PRECISION of 0.
+ *
+ * n {number} Integer, -MAX_SAFE_INTEGER to MAX_SAFE_INTEGER inclusive.
+ * [m] {number|string|BigNumber} The modulus.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {n}'
+ *
+ * Performs 54 loop iterations for n of 9007199254740991.
+ */
+ P.exponentiatedBy = P.pow = function ( n, m ) {
+ var i, k, y, z,
+ x = this;
+
+ intCheck( n, -MAX_SAFE_INTEGER, MAX_SAFE_INTEGER );
+ if ( m != null ) m = new BigNumber(m);
+
+ if (m) {
+ if ( n > 1 && x.gt(ONE) && x.isInteger() && m.gt(ONE) && m.isInteger() ) {
+ x = x.mod(m);
+ } else {
+ z = m;
+
+ // Nullify m so only a single mod operation is performed at the end.
+ m = null;
+ }
+ } else if (POW_PRECISION) {
+
+ // Truncating each coefficient array to a length of k after each multiplication
+ // equates to truncating significant digits to POW_PRECISION + [28, 41],
+ // i.e. there will be a minimum of 28 guard digits retained.
+ //k = mathceil( POW_PRECISION / LOG_BASE + 1.5 ); // gives [9, 21] guard digits.
+ k = mathceil( POW_PRECISION / LOG_BASE + 2 );
+ }
+
+ y = new BigNumber(ONE);
+
+ for ( i = mathfloor( n < 0 ? -n : n ); ; ) {
+ if ( i % 2 ) {
+ y = y.times(x);
+ if ( !y.c ) break;
+ if (k) {
+ if ( y.c.length > k ) y.c.length = k;
+ } else if (m) {
+ y = y.mod(m);
+ }
+ }
+
+ i = mathfloor( i / 2 );
+ if ( !i ) break;
+ x = x.times(x);
+ if (k) {
+ if ( x.c && x.c.length > k ) x.c.length = k;
+ } else if (m) {
+ x = x.mod(m);
+ }
+ }
+
+ if (m) return y;
+ if ( n < 0 ) y = ONE.div(y);
+
+ return z ? y.mod(z) : k ? round( y, POW_PRECISION, ROUNDING_MODE ) : y;
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber rounded to sd significant digits
+ * using rounding mode rm or ROUNDING_MODE. If sd is less than the number of digits
+ * necessary to represent the integer part of the value in fixed-point notation, then use
+ * exponential notation.
+ *
+ * [sd] {number} Significant digits. Integer, 1 to MAX inclusive.
+ * [rm] {number} Rounding mode. Integer, 0 to 8 inclusive.
+ *
+ * '[BigNumber Error] Argument {not a primitive number|not an integer|out of range}: {sd|rm}'
+ */
+ P.toPrecision = function ( sd, rm ) {
+ if ( sd != null ) intCheck( sd, 1, MAX );
+ return format( this, sd, rm, 2 );
+ };
+
+
+ /*
+ * Return a string representing the value of this BigNumber in base b, or base 10 if b is
+ * omitted. If a base is specified, including base 10, round according to DECIMAL_PLACES and
+ * ROUNDING_MODE. If a base is not specified, and this BigNumber has a positive exponent
+ * that is equal to or greater than TO_EXP_POS, or a negative exponent equal to or less than
+ * TO_EXP_NEG, return exponential notation.
+ *
+ * [b] {number} Integer, 2 to ALPHABET.length inclusive.
+ *
+ * '[BigNumber Error] Base {not a primitive number|not an integer|out of range}: {b}'
+ */
+ P.toString = function (b) {
+ var str,
+ n = this,
+ s = n.s,
+ e = n.e;
+
+ // Infinity or NaN?
+ if ( e === null ) {
+
+ if (s) {
+ str = 'Infinity';
+ if ( s < 0 ) str = '-' + str;
+ } else {
+ str = 'NaN';
+ }
+ } else {
+ str = coeffToString( n.c );
+
+ if ( b == null ) {
+ str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+ ? toExponential( str, e )
+ : toFixedPoint( str, e, '0' );
+ } else {
+ intCheck( b, 2, ALPHABET.length, 'Base' );
+ str = convertBase( toFixedPoint( str, e, '0' ), 10, b, s, true );
+ }
+
+ if ( s < 0 && n.c[0] ) str = '-' + str;
+ }
+
+ return str;
+ };
+
+
+ /*
+ * Return as toString, but do not accept a base argument, and include the minus sign for
+ * negative zero.
+ */
+ P.valueOf = P.toJSON = function () {
+ var str,
+ n = this,
+ e = n.e;
+
+ if ( e === null ) return n.toString();
+
+ str = coeffToString( n.c );
+
+ str = e <= TO_EXP_NEG || e >= TO_EXP_POS
+ ? toExponential( str, e )
+ : toFixedPoint( str, e, '0' );
+
+ return n.s < 0 ? '-' + str : str;
+ };
+
+
+ P._isBigNumber = true;
+
+ if ( configObject != null ) BigNumber.set(configObject);
+
+ return BigNumber;
+}
+
+
+// PRIVATE HELPER FUNCTIONS
+
+
+function bitFloor(n) {
+ var i = n | 0;
+ return n > 0 || n === i ? i : i - 1;
+}
+
+
+// Return a coefficient array as a string of base 10 digits.
+function coeffToString(a) {
+ var s, z,
+ i = 1,
+ j = a.length,
+ r = a[0] + '';
+
+ for ( ; i < j; ) {
+ s = a[i++] + '';
+ z = LOG_BASE - s.length;
+ for ( ; z--; s = '0' + s );
+ r += s;
+ }
+
+ // Determine trailing zeros.
+ for ( j = r.length; r.charCodeAt(--j) === 48; );
+ return r.slice( 0, j + 1 || 1 );
+}
+
+
+// Compare the value of BigNumbers x and y.
+function compare( x, y ) {
+ var a, b,
+ xc = x.c,
+ yc = y.c,
+ i = x.s,
+ j = y.s,
+ k = x.e,
+ l = y.e;
+
+ // Either NaN?
+ if ( !i || !j ) return null;
+
+ a = xc && !xc[0];
+ b = yc && !yc[0];
+
+ // Either zero?
+ if ( a || b ) return a ? b ? 0 : -j : i;
+
+ // Signs differ?
+ if ( i != j ) return i;
+
+ a = i < 0;
+ b = k == l;
+
+ // Either Infinity?
+ if ( !xc || !yc ) return b ? 0 : !xc ^ a ? 1 : -1;
+
+ // Compare exponents.
+ if ( !b ) return k > l ^ a ? 1 : -1;
+
+ j = ( k = xc.length ) < ( l = yc.length ) ? k : l;
+
+ // Compare digit by digit.
+ for ( i = 0; i < j; i++ ) if ( xc[i] != yc[i] ) return xc[i] > yc[i] ^ a ? 1 : -1;
+
+ // Compare lengths.
+ return k == l ? 0 : k > l ^ a ? 1 : -1;
+}
+
+
+/*
+ * Check that n is a primitive number, an integer, and in range, otherwise throw.
+ */
+function intCheck( n, min, max, name ) {
+ if ( n < min || n > max || n !== ( n < 0 ? mathceil(n) : mathfloor(n) ) ) {
+ throw Error
+ ( bignumberError + ( name || 'Argument' ) + ( typeof n == 'number'
+ ? n < min || n > max ? ' out of range: ' : ' not an integer: '
+ : ' not a primitive number: ' ) + n );
+ }
+}
+
+
+function isArray(obj) {
+ return Object.prototype.toString.call(obj) == '[object Array]';
+}
+
+
+function toExponential( str, e ) {
+ return ( str.length > 1 ? str.charAt(0) + '.' + str.slice(1) : str ) +
+ ( e < 0 ? 'e' : 'e+' ) + e;
+}
+
+
+function toFixedPoint( str, e, z ) {
+ var len, zs;
+
+ // Negative exponent?
+ if ( e < 0 ) {
+
+ // Prepend zeros.
+ for ( zs = z + '.'; ++e; zs += z );
+ str = zs + str;
+
+ // Positive exponent
+ } else {
+ len = str.length;
+
+ // Append zeros.
+ if ( ++e > len ) {
+ for ( zs = z, e -= len; --e; zs += z );
+ str += zs;
+ } else if ( e < len ) {
+ str = str.slice( 0, e ) + '.' + str.slice(e);
+ }
+ }
+
+ return str;
+}
+
+
+// EXPORT
+
+
+BigNumber = clone();
+BigNumber['default'] = BigNumber.BigNumber = BigNumber;
+
+export default BigNumber; \ No newline at end of file
diff --git a/packages/instant/test/util/maybe_big_number.test.ts b/packages/instant/test/util/maybe_big_number.test.ts
new file mode 100644
index 000000000..f32e33eb1
--- /dev/null
+++ b/packages/instant/test/util/maybe_big_number.test.ts
@@ -0,0 +1,71 @@
+import { BigNumber } from '@0x/utils';
+
+import { maybeBigNumberUtil } from '../../src/util/maybe_big_number';
+
+// import PrevBigNumber from './dependencies/prevbignumber';
+
+const BIG_NUMBER_1 = new BigNumber('10.1');
+const BIG_NUMBER_2 = new BigNumber('10.1');
+const BIG_NUMBER_3 = new BigNumber('11.1');
+// const PREVBIG_NUMBER_1 = new PrevBigNumber('11.1');
+
+describe('maybeBigNumberUtil', () => {
+ describe('stringToMaybeBigNumber', () => {
+ it('should return undefined if stringValue is NaN', () => {
+ expect(maybeBigNumberUtil.stringToMaybeBigNumber('NaN')).toEqual(undefined);
+ });
+ it('should return bignumber constructed with stringValue', () => {
+ const bn = maybeBigNumberUtil.stringToMaybeBigNumber('10.1');
+ if (!!bn) {
+ expect(bn.toString()).toEqual('10.1');
+ }
+ });
+ it('should return undefined if stringValue is not valid (i.e not numeric)', () => {
+ expect(maybeBigNumberUtil.stringToMaybeBigNumber('test')).toEqual(undefined);
+ });
+ });
+
+ describe('areMaybeBigNumbersEqual', () => {
+ it('should return true if val1 and val2 are equivalent BigNumber values', () => {
+ expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, BIG_NUMBER_2)).toEqual(true);
+ });
+ it('should return true if val1 and val2 are both undefined', () => {
+ expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(undefined, undefined)).toEqual(true);
+ });
+ it('should return false if either one val1 or val2 is undefined', () => {
+ expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, undefined)).toEqual(false);
+ });
+ it('should return false if val1 and val2 are equivalent values BigNumber', () => {
+ expect(maybeBigNumberUtil.areMaybeBigNumbersEqual(BIG_NUMBER_1, BIG_NUMBER_3)).toEqual(false);
+ });
+ });
+
+ // describe('bigNumberOrStringToMaybeBigNumber', () => {
+ // it('should return BigNumber (>=v8.0.0) constructed with value if type is string', () => {
+ // const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('10.1');
+ // if (!!bn) {
+ // expect(bn.toString()).toEqual('10.1');
+ // }
+ // });
+ // it('should return undefined if value is NaN', () => {
+ // expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('NaN')).toEqual(undefined);
+ // });
+ // it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+ // expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('test')).toEqual(undefined);
+ // });
+ // it('should return undefined if value as string is not valid (i.e not numeric)', () => {
+ // expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber('test')).toEqual(undefined);
+ // });
+ // it('should return BigNumber (>=v8.0.0) when passed a value as BigNumber (<v8.0.0)', () => {
+ // const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(PREVBIG_NUMBER_1);
+ // expect(BigNumber.isBigNumber(bn)).toEqual(true);
+ // });
+ // it('should return BigNumber (>=v8.0.0) when passed a value as BigNumber (>=v8.0.0)', () => {
+ // const bn = maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(BIG_NUMBER_1);
+ // expect(BigNumber.isBigNumber(bn)).toEqual(true);
+ // });
+ // it('should return undefined if value is not BigNumber or string', () => {
+ // expect(maybeBigNumberUtil.bigNumberOrStringToMaybeBigNumber(true)).toEqual(undefined);
+ // });
+ // });
+});
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