JSDoc: Class: rat

Constructor

new rat()

Source:

rat.js, line 70

Requires:

module:integer

Requires

module:integer

Members

(static, readonly) EPSILON

Machine Epsilon, floats within this distance of eachother are considered equal (to avoid rounding errors)

Properties:

Name	Type	Description
`EPSILON`

Source:

rat.js, line 84

(static, readonly) INFINITESIMAL :rat

Infinitesimal, the limit for approximations

Type:

Properties:

Name	Type	Description
`INFINITESIMAL`

Source:

rat.js, line 1119

(static, readonly) INFINITY :rat

Infinity, a non-Zero number divided by Zero

Type:

Properties:

Name	Type	Description
`INFINITY`

Source:

rat.js, line 1099

(static, readonly) INFINULL :rat

Infinull, Zero divided by Zero

Type:

Properties:

Name	Type	Description
`INFINULL`

Source:

rat.js, line 1109

(static, readonly) MAX_LOOPS

Exit (possibly infinite) loops after this many iterations

Properties:

Name	Type	Description
`MAX_LOOPS`

Source:

rat.js, line 93

(static, readonly) NEGONE :rat

Negative One, Zero minus One

Type:

Properties:

Name	Type	Description
`NEGONE`

Source:

rat.js, line 1089

(static, readonly) ONE :rat

One, the multiplicative identity

Type:

Properties:

Name	Type	Description
`ONE`

Source:

rat.js, line 1079

(static, readonly) PI :rat

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

Type:

Properties:

Name	Type	Description
`PI`

Source:

rat.js, line 1129

(static, readonly) ZERO :rat

Zero, the additive identity

Type:

Properties:

Name	Type	Description
`ZERO`

Source:

rat.js, line 1069

Methods

(static) abs(out, a) → {rat}

Absolute value of a rat

Parameters:

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

Source:

rat.js, line 168

Returns:

out

Type: rat

(static) add(out, a, b) → {rat}

Adds two rats

Parameters:

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

Source:

rat.js, line 202

Returns:

out

Type: rat

(static) approximates(a, b) → {Bool}

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

Parameters:

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

Source:

rat.js, line 314

Returns:

true when the difference between the two rats is less than rat.INFINITESIMAL

Type: Bool

(static) ceil(a) → {Integer}

Returns the closest integer approximation by rounding up

Parameters:

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

Source:

rat.js, line 654

Returns:

integer approximation of the number

Type: Integer

(static) clone(a) → {rat}

Creates a new rat initialized with values from an existing number

Parameters:

Name	Type	Description
`a`	rat	number to clone

Source:

rat.js, line 113

Returns:

a new rational number

Type: rat

(static) copy(out, a) → {rat}

Copy the values from one rat to another

Parameters:

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

Source:

rat.js, line 141

Returns:

out

Type: rat

(static) cos(out, a) → {rat}

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

Parameters:

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

Source:

rat.js, line 795

Returns:

out

Type: rat

(static) create() → {rat}

Creates a new, empty rat

Source:

rat.js, line 100

Returns:

a new rational number

Type: rat

(static) dec()

Alias for rat.toDecimal

Source:

rat.js, line 620

(static) div()

Alias for rat.divide

Source:

rat.js, line 292

(static) divide(out, a, b) → {rat}

Divides two rats

Parameters:

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

Source:

rat.js, line 282

Returns:

out

Type: rat

(static) dot(a, b) → {Integer}

Calculates the dot product of two rats

Parameters:

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

Source:

rat.js, line 592

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`	rat	number to dump

Source:

rat.js, line 1046

Returns:

string various conversions

Type: String

(static) equals(a, b) → {Bool}

Returns true when the first rat is equal to the second

Parameters:

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

Source:

rat.js, line 301

Returns:

true when the two rats are equal

Type: Bool

(static) floor(a) → {Integer}

Returns the closest integer approximation by rounding down

Parameters:

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

Source:

rat.js, line 644

Returns:

integer approximation of the number

Type: Integer

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

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

Parameters:

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

Source:

rat.js, line 1031

Returns:

out

Type: rat

(static) fromDecimal(a) → {rat}

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

Parameters:

Name	Type	Description
`a`	Number	decimal number

Source:

rat.js, line 714

Returns:

out

Type: rat

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

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

Parameters:

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

Source:

rat.js, line 725

Returns:

out

Type: rat

(static) fromInteger(signed) → {rat}

Returns a rat from an integer, creating a new rat

Parameters:

Name	Type	Description
`signed`	Integer	integer

Source:

rat.js, line 677

Returns:

out

Type: rat

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

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

Parameters:

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

Source:

rat.js, line 665

Returns:

out

Type: rat

(static) fromIntegerInverse(signed) → {rat}

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

Parameters:

Name	Type	Description
`signed`	Integer	integer

Source:

rat.js, line 704

Returns:

out

Type: rat

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

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

Parameters:

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

Source:

rat.js, line 688

Returns:

out

Type: rat

(static) fromRandom(out) → {rat}

Creates a new rat from two random integers

Parameters:

Name	Type	Description
`out`	rat	the receiving number

Source:

rat.js, line 765

Returns:

a random rational number

Type: rat

(static) fromValues(n, d) → {rat}

Creates a new rat initialized with the given values

Parameters:

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

Source:

rat.js, line 127

Returns:

a new rational number

Type: rat

(static) invert(out, a) → {rat}

Inverts a rat

Parameters:

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

Source:

rat.js, line 181

Returns:

out

Type: rat

(static) isGreaterThan(a, b) → {Bool}

Returns true when the first rat is larger than the second

Parameters:

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

Source:

rat.js, line 329

Returns:

true when the first operand is larger

Type: Bool

(static) isLessThan(a, b) → {Bool}

Returns true when the first rat is smaller than the second

Parameters:

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

Source:

rat.js, line 341

Returns:

true when the first operand is smaller

Type: Bool

(static) isNegative(a) → {Bool}

Returns true when the rat is negative

Parameters:

Name	Type	Description
`a`	rat	the number to check

Source:

rat.js, line 352

Returns:

true when the number is less than zero

Type: Bool

(static) max(out, a, b) → {rat}

Returns the maximum of two rats

Parameters:

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

Source:

rat.js, line 384

Returns:

out

Type: rat

(static) mediant(out, a, b) → {rat}

Mediant of two rats

Parameters:

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

Source:

rat.js, line 268

Returns:

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

Type: rat

(static) min(out, a, b) → {rat}

Returns the minimum of two rats

Parameters:

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

Source:

rat.js, line 364

Returns:

out

Type: rat

(static) mul()

Alias for rat.multiply

Source:

rat.js, line 258

(static) multiply(out, a, b) → {rat}

Multiplies two rats

Parameters:

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

Source:

rat.js, line 248

Returns:

out

Type: rat

(static) neg()

Alias for rat.opposite

Source:

rat.js, line 492

(static) negative()

Alias for rat.opposite

Source:

rat.js, line 486

(static) normalize(out, a) → {rat}

Normalize a rat

Parameters:

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

Source:

rat.js, line 432

Returns:

out

Type: rat

(static) nthRoot(out, a, n) → {rat}

Find a rat approximation which equals the input rat 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`	rat	the receiving number
`a`	rat	the number to find the root of
`n`	Integer

Source:

rat.js, line 549

Returns:

out

Type: rat

(static) opposite(out, a) → {rat}

Negates a rat

Parameters:

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

Source:

rat.js, line 476

Returns:

out

Type: rat

(static) pow()

Alias for rat.power

Source:

rat.js, line 526

(static) power(out, a, p) → {rat}

Raises a rat to an integer exponent

Parameters:

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

Source:

rat.js, line 502

Returns:

out

Type: rat

(static) reciprocal()

Alias for rat.invert

Source:

rat.js, line 192

(static) round()

Alias for rat.toInteger

Source:

rat.js, line 636

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

Multiplies a rat's denominator by an integer

Parameters:

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

Source:

rat.js, line 419

Returns:

out

Type: rat

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

Multiplies a rat's numerator by an integer

Parameters:

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

Source:

rat.js, line 404

Returns:

out

Type: rat

(static) set(out, n, d) → {rat}

Set the components of a rat to the given values

Parameters:

Name	Type	Description
`out`	rat	the receiving number
`n`	Number	Numerator
`d`	Number	Denominator

Source:

rat.js, line 155

Returns:

out

Type: rat

(static) sin(out, a) → {rat}

Parametric sine: 2a / (1 + a²)

Parameters:

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

Source:

rat.js, line 778

Returns:

out

Type: rat

(static) sqrt(out, a) → {rat}

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

Parameters:

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

Source:

rat.js, line 535

Returns:

out

Type: rat

(static) str(a) → {String}

Returns a string representation

Parameters:

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

Source:

rat.js, line 602

Returns:

string representation of the number

Type: String

(static) sub()

Alias for rat.subtract

Source:

rat.js, line 238

(static) subtract(out, a, b) → {rat}

Subtracts two rats

Parameters:

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

Source:

rat.js, line 222

Returns:

out

Type: rat

(static) tan(out, a) → {rat}

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

Parameters:

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

Source:

rat.js, line 813

Returns:

out

Type: rat

(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`	rat	number to represent as a Babylonian fraction

Source:

rat.js, line 864

Returns:

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

Type: String

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

Returns an array of integers representing the continued fraction

Parameters:

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

Source:

rat.js, line 966

Returns:

integers of the continued fraction

Type: Array

(static) toDecimal(a) → {Float}

Returns a decimal approximation

Parameters:

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

Source:

rat.js, line 612

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`	rat	number to represent as an Egyptian fraction

Source:

rat.js, line 832

Returns:

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

Type: String

(static) toInteger(a) → {Integer}

Returns the closest integer approximation

Parameters:

Name	Type	Description
`a`	rat	number to round to the nearest integer

Source:

rat.js, line 628

Returns:

integer approximation of the number

Type: Integer

(static) traceSternBrocot(a) → {String}

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

Parameters:

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

Source:

rat.js, line 896

Returns:

Stern Brocot path

Type: String