This repo contains the Kotlin class PhiNumber for computations in the field ℚ[√5], including conversion to and from base φ (i.e., the golden ratio). There are also functions for calculating powers of φ, calculating Fibonacci numbers, and reducing fractions.
Please feel free to create a new issue if you want more functionality!
Helper class representing a fraction of two BigIntegers.
typealias BigFraction = Pair<BigInteger, BigInteger>
Predefined values:
val FRACTION_ZERO = Pair(ZERO, ONE)
val FRACTION_ONE = Pair(ONE, ONE)
val FRACTION_INFINITY = Pair(ONE, ZERO)
val FRACTION_MU = Pair(ZERO, ZERO)
Constructs a PhiNumber of the form (aNumer + bNumer * φ) / denom. if root5 = true, constructs a PhiNumber of the form (aNumer + bNumer * √5) / denom.
<init>(aNumer: BigInteger, bNumer: BigInteger = ZERO, denom: BigInteger = ONE, root5: Boolean = false)
<init>(aNumer: Int, bNumer: Int = 0, denom: Int = 1, root5: Boolean = false)
Constructs a rational PhiNumber from the fraction a.
<init>(a: BigFraction)
Copies an existing PhiNumber.
<init>(p: PhiNumber)
Parses a string. The string can contain digits (including a to z for 10 to 35), the radix point ., a colon : to mark the start of the repeating part, a leading minus - or leading .. for complement notation, a fraction slash /, an underscore _ to separate a leading part from a fraction (e.g. 10_101/1001).
It can also contain a list of numbers with a semicolon ; separating the first two and commas , as further separators. In this case, the string is interpreted as a continued fraction or, if continuedOrEgyptian = IS_EGYPTIAN, as an Egyptian fraction.
If negative = true, the input is interpreted as being in base minus φ.
<init>(phinary: String, continuedOrEgyptian: Int = 0, negative: Boolean = false)
BigFractions that represent the PhiNumber as a + b * φ. They are given in reduced form with non-negative denominators.
BigFractions that represent the PhiNumber as r + s * √5. They are given in reduced form with non-negative denominators.
When constructing a PhiNumber by parsing a string, this property will contain information from the parser. It can be a combination of the following:
val IS_NUMBER = 0x0001
val IS_COMPLEMENT = 0x0002
val IS_FRACTION = 0x0004
val IS_MIXED = 0x0008
val IS_CONTINUED = 0x0010
val IS_EGYPTIAN = 0x0020
val IS_ANY_FRACTION = IS_FRACTION or IS_MIXED or IS_CONTINUED or IS_EGYPTIAN
val NONSTANDARD_DIGIT = 0x0100
val INVALID_CHAR = 0x0200
PhiNumber knows the usual operators + - * / with their variants += ++ etc., and < <= > >= == !=. All except == != can be used together with BigFractions and BigIntegers as well.
Returns the multiplicative inverse.
fun inv(): PhiNumber
Returns the absolute value.
fun abs(): PhiNumber
Returns a string representation in the form a + b * φ or r + s * √5 (depending on the value of root5) in the given base (or radix), which can be in the range 2..36. The coefficients are given as fractions.
fun toString(root5: Boolean = false, radix: Int = 10): String
Returns a string representation in base φ, optionally grouping digits by 4 and/or truncating the string after maxDigits digits after the radix point. If alt = true, returns an alternative representation (analogous to repeating 9's representations in decimal). If complement = true and the number is negative, returns the number in complement notation. Do not use the parameter negative
fun toBasePhi(groupDigits: Boolean = false, maxDigits: Int = Int.MAX_VALUE, alt: Boolean = false,
complement: Boolean = false, negative: Boolean = false): String
Return representations in base φ as a (proper or improper) fraction, as a mixed fraction, or as a continued fraction. The representations are chosen in a way not to include numbers with radix points. Again, do not use the parameter negative
fun toBasePhiFraction(groupDigits: Boolean = false, complement: Boolean = false, negative: Boolean = false): String
fun toBasePhiMixed(groupDigits: Boolean = false, complement: Boolean = false, negative: Boolean = false): String
fun toBasePhiContinued(groupDigits: Boolean = false, complement: Boolean = false, negative: Boolean = false): String
fun toFloat(): Float
fun toDouble(): Double
Reduces the internal representation. Only needed if you modify any of aNumer bNumer denom directly.
fun reduce()
val PHI_ZERO = PhiNumber(ZERO)
val PHI_ONE = PhiNumber(ONE)
val PHI = PhiNumber(ZERO, ONE)
val INV_PHI = PhiNumber(-ONE, ONE) /* PHI^-1 */
val PHI_INFINITY = PhiNumber(ONE, ZERO, ZERO)
fun String.toPhiNumber(continuedOrEgyptian: Int = 0, negative: Boolean = false): PhiNumber
fun Int.toPhiNumber(): PhiNumber
fun BigInteger.toPhiNumber(): PhiNumber
fun BigFraction.toPhiNumber(): PhiNumber
fun BigFraction.toBasePhi(): String
fun BigFraction.toFractionString(radix: Int = 10): BigFraction
Calculates the nth power of φ or of −φ.
fun phiPower(n: Int, negative: Boolean = false): PhiNumber
Calculates the nth Fibonacci number, where n can also be negative. Uses the function matrixFibonacci below.
fun fibonacci(n: Int): BigInteger
Calculates two consecutive Fibonacci numbers faster than calling fibonacci twice. Does not work for negative n. Uses the matrix multiplication algorithm from StackOverflow.
fun matrixFibonacci(n: Int): Pair<BigInteger, BigInteger>
Reduces a fraction and makes sure the denominator is non-negative.
fun reduceFraction(numer: BigInteger, denom: BigInteger): BigFraction