Algorithm.Gutenberg.Fibonaccis

Provides the first 1001 Fibonacci numbers, retrieved from the Gutenberg Project, along with functions to retrieve and query these numbers.

Examples:

>>> fibsLen
1001

>>> fibsUpTo 35
[1, 1, 2, 3, 5, 8, 13, 21, 34]

>>> isFib 21
True

>>> isFib 23
False

>>> firstFib
1

>>> nthFib 6
8

>>> nthFib lastFib
70330367711422815821835254877183549770181269836358732742604905087154537118196933579742249494562611733487750449241765991088186363265450223647106012053374121273867339111198139373125598767690091902245245323403501

Changes in 1.1.0:

• Added function firstFib
• Fixed documentation formatting
• Created Git repository at https://github.com/justinhanekom/gutenberg-fibonaccis

Changes in 1.0.5:

• Updated and expanded documentation using Haddock markup

Documentation

fibsLen :: Int

The fibsLen function returns the number of Fibonacci numbers in the first1001Fibs list.

As this list is based on the list of the first 1001 Fibonacci numbers as retrieved from the Gutenberg Project at http://www.ibiblio.org/pub/docs/books/gutenberg/etext01/fbncc10.txt it will be equal to 1001.

If a subsequent version of this module uses a new, expanded list from the Gutenberg Project then this number will change accordingly.

fibsUpTo

Arguments

:: Integer

The maximum Fibonacci number to return

-> [Integer]

Returns all Fibonaccis below the threshold

The fibsUpTo function returns the list of Fibonacci numbers that are less than or equal to the given number.

An error is thrown if the number given is less than the minimum Fibonacci number represented by this module (i.e. firstFib) or greater than the maximum Fibonacci number represented by this module (i.e. lastFib).

first1001Fibs :: [Integer]

first1001Fibs is a list of the first 1001 Fibonacci numbers.

This list was retrieved from the Gutenberg Project at http://www.ibiblio.org/pub/docs/books/gutenberg/etext01/fbncc10.txt

The first Fibonacci number in the list is 1.

The last Fibonacci number in the list is 70,330,367,711,422,815,821,835,254,877,183,549,770,181,269,836,358,732,742,604,905,087,154,537,118,196,933,579,742,249,494,562,611,733,487,750,449,241,765,991,088,186,363,265,450,223,647,106,012,053,374,121,273,867,339,111,198,139,373,125,598,767,690,091,902,245,245,323,403,501.

firstFib

Arguments

:: Integer

Returns the first Fibonacci number

The firstFib function returns the first Fibonacci number in the first1001Fibs list.

The first Fibonacci number in this list is 1.

isFib

Arguments

:: Integer

The number to test

-> Bool

Returns whether or not the number is a Fibonacci

The isFib function returns whether or not the given number is a Fibonacci number.

An error is thrown if the number given is less than the minumum Fibonacci number represented by this module (i.e. firstFib) or greater than the maximum Fibonacci number represented by this module (i.e. lastFib).

lastFib :: Integer

The lastFib function returns the last Fibonacci number in the list of Fibonacci numbers, first1001Fibs.

The last Fibonacci number in the list is 70,330,367,711,422,815,821,835,254,877,183,549,770,181,269,836,358,732,742,604,905,087,154,537,118,196,933,579,742,249,494,562,611,733,487,750,449,241,765,991,088,186,363,265,450,223,647,106,012,053,374,121,273,867,339,111,198,139,373,125,598,767,690,091,902,245,245,323,403,501.

nthFib

Arguments

:: Int

The index of the Fibonacci number

-> Integer

Returns the requested Fibonacci number

The nthFib function returns the nth Fibonacci number.

An error is thrown if the index number given is less than one (1), the index of the first Fibonacci, or greater than the number of Fibonacci numbers in the first1001Fibs list, i.e., fibsLen.