JSDoc: Class: bigrat

Constructor

new bigrat()

Source:

bigrat.js, line 53

Requires:

module:bigint

Requires

module:bigint

Members

(static, readonly) EPSILON

Machine Epsilon, floats within this distance of each other are considered equal

Properties:

Name	Type	Description
`EPSILON`

Source:

bigrat.js, line 67

(static, readonly) INFINITESIMAL

Infinitesimal, the limit for approximations

Properties:

Name	Type	Description
`INFINITESIMAL`

Source:

bigrat.js, line 1194

(static, readonly) INFINITY

Infinity, a non-Zero number divided by Zero

Properties:

Name	Type	Description
`INFINITY`

Source:

bigrat.js, line 1174

(static, readonly) INFINULL

Infinull, Zero divided by Zero

Properties:

Name	Type	Description
`INFINULL`

Source:

bigrat.js, line 1184

(static, readonly) MAX_LOOPS

Exit (possibly infinite) loops after this many iterations

Properties:

Name	Type	Description
`MAX_LOOPS`

Source:

bigrat.js, line 76

(static, readonly) NEGONE

Negative One, Zero minus One

Properties:

Name	Type	Description
`NEGONE`

Source:

bigrat.js, line 1164

(static, readonly) ONE

One, the multiplicative identity

Properties:

Name	Type	Description
`ONE`

Source:

bigrat.js, line 1155

(static, readonly) PI

Pi, an approximation of the ratio between a circle's circumference and it's diameter

Properties:

Name	Type	Description
`PI`

Source:

bigrat.js, line 1204

(static, readonly) ZERO

Zero, the additive identity

Properties:

Name	Type	Description
`ZERO`

Source:

bigrat.js, line 1146

Methods

(static) abs(out, a) → {bigrat}

Absolute value of a bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number to take the absolute value of

Source:

bigrat.js, line 173

Returns:

out

Type: bigrat

(static) add(out, a, b) → {bigrat}

Adds two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 207

Returns:

out

Type: bigrat

(static) approximates(a, b) → {Bool}

Returns true when the first bigrat is approximately equal to the second

Parameters:

Name	Type	Description
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 319

Returns:

true when the difference between the two bigrats is less than bigrat.INFINITESIMAL

Type: Bool

(static) ceil(a) → {Integer}

Returns the closest integer approximation by rounding up

Parameters:

Name	Type	Description
`a`	bigrat	number to round up to the nearest integer

Source:

bigrat.js, line 658

Returns:

integer approximation of the number

Type: Integer

(static) clone(a) → {bigrat}

Creates a new bigrat initialized with values from an existing number

Parameters:

Name	Type	Description
`a`	bigrat	number to clone

Source:

bigrat.js, line 96

Returns:

a new bigrational number

Type: bigrat

(static) copy(out, a) → {bigrat}

Copy the values from one bigrat to another

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the source number

Source:

bigrat.js, line 124

Returns:

out

Type: bigrat

(static) cos(out, a) → {bigrat}

Parametric cosine: (1 - a²) / (1 + a²)

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number for which to calculate the parametric cosine

Source:

bigrat.js, line 844

Returns:

out

Type: bigrat

(static) create() → {bigrat}

Creates a new, empty bigrat

Source:

bigrat.js, line 83

Returns:

a new bigrational number

Type: bigrat

(static) dec()

Alias for bigrat.toDecimal

Source:

bigrat.js, line 614

(static) div()

Alias for bigrat.divide

Source:

bigrat.js, line 297

(static) divide(out, a, b) → {bigrat}

Divides two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 287

Returns:

out

Type: bigrat

(static) dot(a, b) → {Integer}

Calculates the dot product of two bigrats

Parameters:

Name	Type	Description
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 586

Returns:

dot product of a and b

Type: Integer

(static) dump(a) → {String}

Returns a string with the fraction in various formats

Parameters:

Name	Type	Description
`a`	bigrat	number to dump

Source:

bigrat.js, line 1124

Returns:

string various conversions

Type: String

(static) equals(a, b) → {Bool}

Returns true when the first bigrat is equal to the second

Parameters:

Name	Type	Description
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 306

Returns:

true when the two bigrats are equal

Type: Bool

(static) floor(a) → {Integer}

Returns the closest integer approximation by rounding down

Parameters:

Name	Type	Description
`a`	bigrat	number to round down to the nearest integer

Source:

bigrat.js, line 648

Returns:

integer approximation of the number

Type: Integer

(static) fromContinuedFraction(out, integers) → {bigrat}

Returns a bigrat from an array of integers representing a continued fraction

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`integers`	Array	of the continued fraction

Source:

bigrat.js, line 1091

Returns:

out

Type: bigrat

(static) fromDecimal(a) → {bigrat}

Returns a bigrat from a decimal number, creating a new bigrat

Parameters:

Name	Type	Description
`a`	Number	decimal number

Source:

bigrat.js, line 718

Returns:

out

Type: bigrat

(static) fromDecimal_copy(out, a) → {bigrat}

Returns a bigrat from a decimal number, copying to an existing bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	Number	decimal number

Source:

bigrat.js, line 729

Returns:

out

Type: bigrat

(static) fromFactorial(out, n) → {bigrat}

Return the factorial of n as a big rational number

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`n`	Integer

Source:

bigrat.js, line 1107

Returns:

factorial of n

Type: bigrat

(static) fromInteger(signed) → {bigrat}

Returns a bigrat from an integer, creating a new bigrat

Parameters:

Name	Type	Description
`signed`	Integer	integer

Source:

bigrat.js, line 681

Returns:

out

Type: bigrat

(static) fromInteger_copy(out, signed) → {bigrat}

Returns a bigrat from an integer, copying to an existing bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`signed`	Integer	integer

Source:

bigrat.js, line 669

Returns:

out

Type: bigrat

(static) fromIntegerInverse(signed) → {bigrat}

Returns a bigrat from the inverse of an integer, creating a new bigrat

Parameters:

Name	Type	Description
`signed`	Integer	integer

Source:

bigrat.js, line 708

Returns:

out

Type: bigrat

(static) fromIntegerInverse_copy(out, signed) → {bigrat}

Returns a bigrat from the inverse of an integer, copying to an existing bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`signed`	Integer	integer

Source:

bigrat.js, line 692

Returns:

out

Type: bigrat

(static) fromRandom(out) → {bigrat}

Creates a new bigrat from two random integers

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number

Source:

bigrat.js, line 814

Returns:

a random bigrational number

Type: bigrat

(static) fromRat(out, a) → {bigrat}

Returns a bigrat from a rat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	rat	number to convert

Source:

bigrat.js, line 162

Returns:

out

Type: bigrat

(static) fromValues(n, d) → {bigrat}

Creates a new bigrat initialized with the given values

Parameters:

Name	Type	Description
`n`	Number	Numerator
`d`	Number	Denominator

Source:

bigrat.js, line 110

Returns:

a new bigrational number

Type: bigrat

(static) invert(out, a) → {bigrat}

Inverts a bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number to invert

Source:

bigrat.js, line 186

Returns:

out

Type: bigrat

(static) isGreaterThan(a, b) → {Bool}

Returns true when the first bigrat is larger than the second

Parameters:

Name	Type	Description
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 334

Returns:

true when the first operand is larger

Type: Bool

(static) isLessThan(a, b) → {Bool}

Returns true when the first bigrat is smaller than the second

Parameters:

Name	Type	Description
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 346

Returns:

true when the first operand is smaller

Type: Bool

(static) isNegative(a) → {Bool}

Returns true when the bigrat is negative

Parameters:

Name	Type	Description
`a`	bigrat	the number to check

Source:

bigrat.js, line 357

Returns:

true when the number is less than zero

Type: Bool

(static) max(out, a, b) → {bigrat}

Returns the maximum of two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 389

Returns:

out

Type: bigrat

(static) mediant(out, a, b) → {bigrat}

Mediant of two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 273

Returns:

out the sum of the numerators divided by the sum of the denominators

Type: bigrat

(static) min(out, a, b) → {bigrat}

Returns the minimum of two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 369

Returns:

out

Type: bigrat

(static) mul()

Alias for bigrat.multiply

Source:

bigrat.js, line 263

(static) multiply(out, a, b) → {bigrat}

Multiplies two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 253

Returns:

out

Type: bigrat

(static) neg()

Alias for bigrat.opposite

Source:

bigrat.js, line 481

(static) negative()

Alias for bigrat.opposite

Source:

bigrat.js, line 475

(static) normalize(out, a) → {bigrat}

Normalize a bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number to normalize

Source:

bigrat.js, line 437

Returns:

out

Type: bigrat

(static) nthRoot(out, a, n) → {bigrat}

Find a bigrat approximation which equals the input bigrat when raised to the given integer exponent Newton's method converges alot faster... could that be used to find the pattern in the SB tree?

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the number to find the root of
`n`	Integer

Source:

bigrat.js, line 538

Returns:

out

Type: bigrat

(static) opposite(out, a) → {bigrat}

Negates a bigrat

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number to negate

Source:

bigrat.js, line 465

Returns:

out

Type: bigrat

(static) pow()

Alias for bigrat.power

Source:

bigrat.js, line 515

(static) power(out, a, p) → {bigrat}

Raises a bigrat to an integer exponent

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the number to exponentiate
`p`	Integer	power to raise the number by

Source:

bigrat.js, line 491

Returns:

out

Type: bigrat

(static) reciprocal()

Alias for bigrat.invert

Source:

bigrat.js, line 197

(static) round()

Alias for bigrat.toInteger

Source:

bigrat.js, line 630

(static) scalar_divide(out, a, b) → {bigrat}

Multiplies a bigrat's denominator by an integer

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the number to divide
`b`	Integer	amount to divide by

Source:

bigrat.js, line 424

Returns:

out

Type: bigrat

(static) scalar_multiply(out, a, b) → {bigrat}

Multiplies a bigrat's numerator by an integer

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the number to multiply
`b`	Integer	amount to multiply the number by

Source:

bigrat.js, line 409

Returns:

out

Type: bigrat

(static) set(out, n, d) → {bigrat}

Set the components of a bigrat to the given values

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`n`	BigInteger	Numerator
`d`	BigInteger	Denominator

Source:

bigrat.js, line 138

Returns:

out

Type: bigrat

(static) sin(out, a) → {bigrat}

Parametric sine: 2a / (1 + a²)

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number for which to calculate the parametric sine

Source:

bigrat.js, line 827

Returns:

out

Type: bigrat

(static) sqrt(out, a) → {bigrat}

Find a bigrational number which approximates the input number when multiplied by itself

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the number to find the root of

Source:

bigrat.js, line 524

Returns:

out

Type: bigrat

(static) str(a) → {String}

Returns a string representation

Parameters:

Name	Type	Description
`a`	bigrat	number to represent as a string

Source:

bigrat.js, line 596

Returns:

string representation of the number

Type: String

(static) sub()

Alias for bigrat.subtract

Source:

bigrat.js, line 243

(static) subtract(out, a, b) → {bigrat}

Subtracts two bigrats

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	the first operand
`b`	bigrat	the second operand

Source:

bigrat.js, line 227

Returns:

out

Type: bigrat

(static) tan(out, a) → {bigrat}

Parametric tangent: sin(a) / cos(a)

Parameters:

Name	Type	Description
`out`	bigrat	the receiving number
`a`	bigrat	number for which to calculate the parametric tangent

Source:

bigrat.js, line 862

Returns:

out

Type: bigrat

(static) toBabylonian(a) → {String}

Returns a Babylonian representation (base 60) The returned string can be evaluated in "calc - arbitrary precision calculator"

Parameters:

Name	Type	Description
`a`	bigrat	number to represent as a Babylonian fraction

Source:

bigrat.js, line 913

Returns:

string containing the decimal representations of the base 60 digits and their powers, in "calc" format

Type: String

(static) toBigInteger(a) → {BigInteger}

Returns a big integer approximation (truncated towards zero)

Parameters:

Name	Type	Description
`a`	bigrat	number to round

Source:

bigrat.js, line 638

Returns:

big integer approximation of the number

Type: BigInteger

(static) toContinuedFraction(a, maximum) → {Array}

Returns an array of integers representing the continued fraction

Parameters:

Name	Type	Description
`a`	bigrat	number to convert to a continued fraction
`maximum`	Integer	number of iterations

Source:

bigrat.js, line 1021

Returns:

integers of the continued fraction

Type: Array

(static) toDecimal(a) → {Float}

Returns a decimal approximation

Parameters:

Name	Type	Description
`a`	bigrat	number to approximate as a decimal

Source:

bigrat.js, line 606

Returns:

decimal approximation of the number

Type: Float

(static) toEgyptian(a) → {String}

Returns an Egyptian representation The returned string can be evaluated in "calc - arbitrary precision calculator"

Parameters:

Name	Type	Description
`a`	bigrat	number to represent as an Egyptian fraction

Source:

bigrat.js, line 881

Returns:

string representing the most simple sum of fractions having a numerator of one, in "calc" format

Type: String

(static) toInteger(a) → {Integer}

Returns a big integer approximation (truncated towards zero)

Parameters:

Name	Type	Description
`a`	bigrat	number to round

Source:

bigrat.js, line 622

Returns:

native integer approximation of the number

Type: Integer

(static) toRat(out, a) → {rat}

Returns a rat from a bigrat

Parameters:

Name	Type	Description
`out`	rat	the receiving number
`a`	bigrat	number to truncate

Source:

bigrat.js, line 151

Returns:

out

Type: rat

(static) traceSternBrocot(a) → {String}

Returns a string of L's and R's representing the Stern Brocot path

Parameters:

Name	Type	Description
`a`	bigrat	number to trace in the Stern Brocot tree

Source:

bigrat.js, line 945

Returns:

Stern Brocot path

Type: String