Results for: "match"

Raised when attempting to convert special float values (in particular Infinity or NaN) to numerical classes which don’t support them.

Float::INFINITY.to_r   #=> FloatDomainError: Infinity

Provides mathematical functions.

Example:

require "bigdecimal/math"

include BigMath

a = BigDecimal((PI(100)/2).to_s)
puts sin(a,100) # => 0.99999999999999999999......e0

The Benchmark module provides methods to measure and report the time used to execute Ruby code.

The result:

              user     system      total        real
for:      1.010000   0.000000   1.010000 (  1.015688)
times:    1.000000   0.000000   1.000000 (  1.003611)
upto:     1.030000   0.000000   1.030000 (  1.028098)

mkmf.rb is used by Ruby C extensions to generate a Makefile which will correctly compile and link the C extension to Ruby and a third-party library.

Module Math provides methods for basic trigonometric, logarithmic, and transcendental functions, and for extracting roots.

You can write its constants and method calls thus:

Math::PI      # => 3.141592653589793
Math::E       # => 2.718281828459045
Math.sin(0.0) # => 0.0
Math.cos(0.0) # => 1.0

If you include module Math, you can write simpler forms:

include Math
PI       # => 3.141592653589793
E        # => 2.718281828459045
sin(0.0) # => 0.0
cos(0.0) # => 1.0

For simplicity, the examples here assume:

include Math
INFINITY = Float::INFINITY

The domains and ranges for the methods are denoted by open or closed intervals, using, respectively, parentheses or square brackets:

Many values returned by Math methods are numerical approximations. This is because many such values are, in mathematics, of infinite precision, while in numerical computation the precision is finite.

Thus, in mathematics, cos(π/2) is exactly zero, but in our computation cos(PI/2) is a number very close to zero:

cos(PI/2) # => 6.123031769111886e-17

For very large and very small returned values, we have added formatted numbers for clarity:

tan(PI/2)  # => 1.633123935319537e+16   # 16331239353195370.0
tan(PI)    # => -1.2246467991473532e-16 # -0.0000000000000001

See class Float for the constants that affect Ruby’s floating-point arithmetic.

What’s Here

Trigonometric Functions

Inverse Trigonometric Functions

Hyperbolic Trigonometric Functions

Inverse Hyperbolic Trigonometric Functions

Exponentiation and Logarithmic Functions

Fraction and Exponent Functions

Root Functions

Error Functions

Gamma Functions

Hypotenuse Function

Represents a regular expression literal that contains interpolation that is being used in the predicate of a conditional to implicitly match against the last line read by an IO object.

if /foo #{bar} baz/ then end
   ^^^^^^^^^^^^^^^^

Generated when trying to lookup a gem to indicate that the gem was found, but that it isn’t usable on the current platform.

fetch and install read these and report them to the user to aid in figuring out why a gem couldn’t be installed.

Represents the use of a case statement for pattern matching.

case true
in false
end
^^^^^^^^^

Raised when a gem dependencies file specifies a ruby version that does not match the current version.

Response class for Non-Authoritative Information responses (status code 203).

The Non-Authoritative Information response indicates that the server is a transforming proxy (such as a Web accelerator) that received a 200 OK response from its origin, and is returning a modified version of the origin’s response.

References:

The dispatcher class fires events for nodes that are found while walking an AST to all registered listeners. It’s useful for performing different types of analysis on the AST while only having to walk the tree once.

To use the dispatcher, you would first instantiate it and register listeners for the events you’re interested in:

class OctalListener
  def on_integer_node_enter(node)
    if node.octal? && !node.slice.start_with?("0o")
      warn("Octal integers should be written with the 0o prefix")
    end
  end
end

dispatcher = Dispatcher.new
dispatcher.register(listener, :on_integer_node_enter)

Then, you can walk any number of trees and dispatch events to the listeners:

result = Prism.parse("001 + 002 + 003")
dispatcher.dispatch(result.value)

Optionally, you can also use ‘#dispatch_once` to dispatch enter and leave events for a single node without recursing further down the tree. This can be useful in circumstances where you want to reuse the listeners you already have registers but want to stop walking the tree at a certain point.

integer = result.value.statements.body.first.receiver.receiver
dispatcher.dispatch_once(integer)

A Float object represents a sometimes-inexact real number using the native architecture’s double-precision floating point representation.

Floating point has a different arithmetic and is an inexact number. So you should know its esoteric system. See following:

You can create a Float object explicitly with:

You can convert certain objects to Floats with:

What’s Here

First, what’s elsewhere. Class Float:

Here, class Float provides methods for:

Querying

Comparing

Converting

Continuation objects are generated by Kernel#callcc, after having +require+d continuation. They hold a return address and execution context, allowing a nonlocal return to the end of the callcc block from anywhere within a program. Continuations are somewhat analogous to a structured version of C’s setjmp/longjmp (although they contain more state, so you might consider them closer to threads).

For instance:

require "continuation"
arr = [ "Freddie", "Herbie", "Ron", "Max", "Ringo" ]
callcc{|cc| $cc = cc}
puts(message = arr.shift)
$cc.call unless message =~ /Max/

produces:

Freddie
Herbie
Ron
Max

Also you can call callcc in other methods:

require "continuation"

def g
  arr = [ "Freddie", "Herbie", "Ron", "Max", "Ringo" ]
  cc = callcc { |cc| cc }
  puts arr.shift
  return cc, arr.size
end

def f
  c, size = g
  c.call(c) if size > 1
end

f

This (somewhat contrived) example allows the inner loop to abandon processing early:

require "continuation"
callcc {|cont|
  for i in 0..4
    print "#{i}: "
    for j in i*5...(i+1)*5
      cont.call() if j == 17
      printf "%3d", j
    end
  end
}
puts

produces:

0:   0  1  2  3  4
1:   5  6  7  8  9
2:  10 11 12 13 14
3:  15 16

A class which allows both internal and external iteration.

An Enumerator can be created by the following methods.

Most methods have two forms: a block form where the contents are evaluated for each item in the enumeration, and a non-block form which returns a new Enumerator wrapping the iteration.

enumerator = %w(one two three).each
puts enumerator.class # => Enumerator

enumerator.each_with_object("foo") do |item, obj|
  puts "#{obj}: #{item}"
end

# foo: one
# foo: two
# foo: three

enum_with_obj = enumerator.each_with_object("foo")
puts enum_with_obj.class # => Enumerator

enum_with_obj.each do |item, obj|
  puts "#{obj}: #{item}"
end

# foo: one
# foo: two
# foo: three

This allows you to chain Enumerators together. For example, you can map a list’s elements to strings containing the index and the element as a string via:

puts %w[foo bar baz].map.with_index { |w, i| "#{i}:#{w}" }
# => ["0:foo", "1:bar", "2:baz"]

External Iteration

An Enumerator can also be used as an external iterator. For example, Enumerator#next returns the next value of the iterator or raises StopIteration if the Enumerator is at the end.

e = [1,2,3].each   # returns an enumerator object.
puts e.next   # => 1
puts e.next   # => 2
puts e.next   # => 3
puts e.next   # raises StopIteration

next, next_values, peek, and peek_values are the only methods which use external iteration (and Array#zip(Enumerable-not-Array) which uses next internally).

These methods do not affect other internal enumeration methods, unless the underlying iteration method itself has side-effect, e.g. IO#each_line.

FrozenError will be raised if these methods are called against a frozen enumerator. Since rewind and feed also change state for external iteration, these methods may raise FrozenError too.

External iteration differs significantly from internal iteration due to using a Fiber:

Concretely:

Thread.current[:fiber_local] = 1
Fiber[:storage_var] = 1
e = Enumerator.new do |y|
  p Thread.current[:fiber_local] # for external iteration: nil, for internal iteration: 1
  p Fiber[:storage_var] # => 1, inherited
  Fiber[:storage_var] += 1
  y << 42
end

p e.next # => 42
p Fiber[:storage_var] # => 1 (it ran in a different Fiber)

e.each { p _1 }
p Fiber[:storage_var] # => 2 (it ran in the same Fiber/"stack" as the current Fiber)

Convert External Iteration to Internal Iteration

You can use an external iterator to implement an internal iterator as follows:

def ext_each(e)
  while true
    begin
      vs = e.next_values
    rescue StopIteration
      return $!.result
    end
    y = yield(*vs)
    e.feed y
  end
end

o = Object.new

def o.each
  puts yield
  puts yield(1)
  puts yield(1, 2)
  3
end

# use o.each as an internal iterator directly.
puts o.each {|*x| puts x; [:b, *x] }
# => [], [:b], [1], [:b, 1], [1, 2], [:b, 1, 2], 3

# convert o.each to an external iterator for
# implementing an internal iterator.
puts ext_each(o.to_enum) {|*x| puts x; [:b, *x] }
# => [], [:b], [1], [:b, 1], [1, 2], [:b, 1, 2], 3

Raised to stop the iteration, in particular by Enumerator#next. It is rescued by Kernel#loop.

loop do
  puts "Hello"
  raise StopIteration
  puts "World"
end
puts "Done!"

produces:

Hello
Done!

fatal is an Exception that is raised when Ruby has encountered a fatal error and must exit.

BigDecimal provides arbitrary-precision floating point decimal arithmetic.

Introduction

Ruby provides built-in support for arbitrary precision integer arithmetic.

For example:

42**13  #=>   1265437718438866624512

BigDecimal provides similar support for very large or very accurate floating point numbers.

Decimal arithmetic is also useful for general calculation, because it provides the correct answers people expect–whereas normal binary floating point arithmetic often introduces subtle errors because of the conversion between base 10 and base 2.

For example, try:

sum = 0
10_000.times do
  sum = sum + 0.0001
end
print sum #=> 0.9999999999999062

and contrast with the output from:

require 'bigdecimal'

sum = BigDecimal("0")
10_000.times do
  sum = sum + BigDecimal("0.0001")
end
print sum #=> 0.1E1

Similarly:

(BigDecimal("1.2") - BigDecimal("1.0")) == BigDecimal("0.2") #=> true

(1.2 - 1.0) == 0.2 #=> false

A Note About Precision

For a calculation using a BigDecimal and another value, the precision of the result depends on the type of value:

Special features of accurate decimal arithmetic

Because BigDecimal is more accurate than normal binary floating point arithmetic, it requires some special values.

Infinity

BigDecimal sometimes needs to return infinity, for example if you divide a value by zero.

BigDecimal("1.0") / BigDecimal("0.0")  #=> Infinity
BigDecimal("-1.0") / BigDecimal("0.0")  #=> -Infinity

You can represent infinite numbers to BigDecimal using the strings 'Infinity', '+Infinity' and '-Infinity' (case-sensitive)

Not a Number

When a computation results in an undefined value, the special value NaN (for ‘not a number’) is returned.

Example:

BigDecimal("0.0") / BigDecimal("0.0") #=> NaN

You can also create undefined values.

NaN is never considered to be the same as any other value, even NaN itself:

n = BigDecimal('NaN')
n == 0.0 #=> false
n == n #=> false

Positive and negative zero

If a computation results in a value which is too small to be represented as a BigDecimal within the currently specified limits of precision, zero must be returned.

If the value which is too small to be represented is negative, a BigDecimal value of negative zero is returned.

BigDecimal("1.0") / BigDecimal("-Infinity") #=> -0.0

If the value is positive, a value of positive zero is returned.

BigDecimal("1.0") / BigDecimal("Infinity") #=> 0.0

(See BigDecimal.mode for how to specify limits of precision.)

Note that -0.0 and 0.0 are considered to be the same for the purposes of comparison.

Note also that in mathematics, there is no particular concept of negative or positive zero; true mathematical zero has no sign.

bigdecimal/util

When you require bigdecimal/util, the to_d method will be available on BigDecimal and the native Integer, Float, Rational, and String classes:

require 'bigdecimal/util'

42.to_d         # => 0.42e2
0.5.to_d        # => 0.5e0
(2/3r).to_d(3)  # => 0.667e0
"0.5".to_d      # => 0.5e0

Methods for Working with JSON

These methods are provided by the JSON gem. To make these methods available:

require 'json/add/bigdecimal'

Copyright © 2002 by Shigeo Kobayashi <shigeo@tinyforest.gr.jp>.

BigDecimal is released under the Ruby and 2-clause BSD licenses. See LICENSE.txt for details.

Maintained by mrkn <mrkn@mrkn.jp> and ruby-core members.

Documented by zzak <zachary@zacharyscott.net>, mathew <meta@pobox.com>, and many other contributors.

A rational number can be represented as a pair of integer numbers: a/b (b>0), where a is the numerator and b is the denominator. Integer a equals rational a/1 mathematically.

You can create a Rational object explicitly with:

You can convert certain objects to Rationals with:

Examples

Rational(1)      #=> (1/1)
Rational(2, 3)   #=> (2/3)
Rational(4, -6)  #=> (-2/3) # Reduced.
3.to_r           #=> (3/1)
2/3r             #=> (2/3)

You can also create rational objects from floating-point numbers or strings.

Rational(0.3)    #=> (5404319552844595/18014398509481984)
Rational('0.3')  #=> (3/10)
Rational('2/3')  #=> (2/3)

0.3.to_r         #=> (5404319552844595/18014398509481984)
'0.3'.to_r       #=> (3/10)
'2/3'.to_r       #=> (2/3)
0.3.rationalize  #=> (3/10)

A rational object is an exact number, which helps you to write programs without any rounding errors.

10.times.inject(0) {|t| t + 0.1 }              #=> 0.9999999999999999
10.times.inject(0) {|t| t + Rational('0.1') }  #=> (1/1)

However, when an expression includes an inexact component (numerical value or operation), it will produce an inexact result.

Rational(10) / 3   #=> (10/3)
Rational(10) / 3.0 #=> 3.3333333333333335

Rational(-8) ** Rational(1, 3)
                   #=> (1.0000000000000002+1.7320508075688772i)

Class Date provides methods for storing and manipulating calendar dates.

Consider using class Time instead of class Date if:

A Date object, once created, is immutable, and cannot be modified.

Creating a Date

You can create a date for the current date, using Date.today:

Date.today # => #<Date: 1999-12-31>

You can create a specific date from various combinations of arguments:

See also the specialized methods in “Specialized Format Strings” in Formats for Dates and Times

Argument limit

Certain singleton methods in Date that parse string arguments also take optional keyword argument limit, which can limit the length of the string argument.

When limit is:

DateTime

A subclass of Date that easily handles date, hour, minute, second, and offset.

DateTime class is considered deprecated. Use Time class.

DateTime does not consider any leap seconds, does not track any summer time rules.

A DateTime object is created with DateTime::new, DateTime::jd, DateTime::ordinal, DateTime::commercial, DateTime::parse, DateTime::strptime, DateTime::now, Time#to_datetime, etc.

require 'date'

DateTime.new(2001,2,3,4,5,6)
                    #=> #<DateTime: 2001-02-03T04:05:06+00:00 ...>

The last element of day, hour, minute, or second can be a fractional number. The fractional number’s precision is assumed at most nanosecond.

DateTime.new(2001,2,3.5)
                    #=> #<DateTime: 2001-02-03T12:00:00+00:00 ...>

An optional argument, the offset, indicates the difference between the local time and UTC. For example, Rational(3,24) represents ahead of 3 hours of UTC, Rational(-5,24) represents behind of 5 hours of UTC. The offset should be -1 to +1, and its precision is assumed at most second. The default value is zero (equals to UTC).

DateTime.new(2001,2,3,4,5,6,Rational(3,24))
                    #=> #<DateTime: 2001-02-03T04:05:06+03:00 ...>

The offset also accepts string form:

DateTime.new(2001,2,3,4,5,6,'+03:00')
                    #=> #<DateTime: 2001-02-03T04:05:06+03:00 ...>

An optional argument, the day of calendar reform (start), denotes a Julian day number, which should be 2298874 to 2426355 or negative/positive infinity. The default value is Date::ITALY (2299161=1582-10-15).

A DateTime object has various methods. See each reference.

d = DateTime.parse('3rd Feb 2001 04:05:06+03:30')
                    #=> #<DateTime: 2001-02-03T04:05:06+03:30 ...>
d.hour              #=> 4
d.min               #=> 5
d.sec               #=> 6
d.offset            #=> (7/48)
d.zone              #=> "+03:30"
d += Rational('1.5')
                    #=> #<DateTime: 2001-02-04%16:05:06+03:30 ...>
d = d.new_offset('+09:00')
                    #=> #<DateTime: 2001-02-04%21:35:06+09:00 ...>
d.strftime('%I:%M:%S %p')
                    #=> "09:35:06 PM"
d > DateTime.new(1999)
                    #=> true

When should you use DateTime and when should you use Time?

It’s a common misconception that William Shakespeare and Miguel de Cervantes died on the same day in history - so much so that UNESCO named April 23 as World Book Day because of this fact. However, because England hadn’t yet adopted the Gregorian Calendar Reform (and wouldn’t until 1752) their deaths are actually 10 days apart. Since Ruby’s Time class implements a proleptic Gregorian calendar and has no concept of calendar reform there’s no way to express this with Time objects. This is where DateTime steps in:

shakespeare = DateTime.iso8601('1616-04-23', Date::ENGLAND)
 #=> Tue, 23 Apr 1616 00:00:00 +0000
cervantes = DateTime.iso8601('1616-04-23', Date::ITALY)
 #=> Sat, 23 Apr 1616 00:00:00 +0000

Already you can see something is weird - the days of the week are different. Taking this further:

cervantes == shakespeare
 #=> false
(shakespeare - cervantes).to_i
 #=> 10

This shows that in fact they died 10 days apart (in reality 11 days since Cervantes died a day earlier but was buried on the 23rd). We can see the actual date of Shakespeare’s death by using the gregorian method to convert it:

shakespeare.gregorian
 #=> Tue, 03 May 1616 00:00:00 +0000

So there’s an argument that all the celebrations that take place on the 23rd April in Stratford-upon-Avon are actually the wrong date since England is now using the Gregorian calendar. You can see why when we transition across the reform date boundary:

# start off with the anniversary of Shakespeare's birth in 1751
shakespeare = DateTime.iso8601('1751-04-23', Date::ENGLAND)
 #=> Tue, 23 Apr 1751 00:00:00 +0000

# add 366 days since 1752 is a leap year and April 23 is after February 29
shakespeare + 366
 #=> Thu, 23 Apr 1752 00:00:00 +0000

# add another 365 days to take us to the anniversary in 1753
shakespeare + 366 + 365
 #=> Fri, 04 May 1753 00:00:00 +0000

As you can see, if we’re accurately tracking the number of solar years since Shakespeare’s birthday then the correct anniversary date would be the 4th May and not the 23rd April.

So when should you use DateTime in Ruby and when should you use Time? Almost certainly you’ll want to use Time since your app is probably dealing with current dates and times. However, if you need to deal with dates and times in a historical context you’ll want to use DateTime to avoid making the same mistakes as UNESCO. If you also have to deal with timezones then best of luck - just bear in mind that you’ll probably be dealing with local solar times, since it wasn’t until the 19th century that the introduction of the railways necessitated the need for Standard Time and eventually timezones.

Pathname represents the name of a file or directory on the filesystem, but not the file itself.

The pathname depends on the Operating System: Unix, Windows, etc. This library works with pathnames of local OS, however non-Unix pathnames are supported experimentally.

A Pathname can be relative or absolute. It’s not until you try to reference the file that it even matters whether the file exists or not.

Pathname is immutable. It has no method for destructive update.

The goal of this class is to manipulate file path information in a neater way than standard Ruby provides. The examples below demonstrate the difference.

All functionality from File, FileTest, and some from Dir and FileUtils is included, in an unsurprising way. It is essentially a facade for all of these, and more.

Examples

Example 1: Using Pathname

require 'pathname'
pn = Pathname.new("/usr/bin/ruby")
size = pn.size              # 27662
isdir = pn.directory?       # false
dir  = pn.dirname           # Pathname:/usr/bin
base = pn.basename          # Pathname:ruby
dir, base = pn.split        # [Pathname:/usr/bin, Pathname:ruby]
data = pn.read
pn.open { |f| _ }
pn.each_line { |line| _ }

Example 2: Using standard Ruby

pn = "/usr/bin/ruby"
size = File.size(pn)        # 27662
isdir = File.directory?(pn) # false
dir  = File.dirname(pn)     # "/usr/bin"
base = File.basename(pn)    # "ruby"
dir, base = File.split(pn)  # ["/usr/bin", "ruby"]
data = File.read(pn)
File.open(pn) { |f| _ }
File.foreach(pn) { |line| _ }

Example 3: Special features

p1 = Pathname.new("/usr/lib")   # Pathname:/usr/lib
p2 = p1 + "ruby/1.8"            # Pathname:/usr/lib/ruby/1.8
p3 = p1.parent                  # Pathname:/usr
p4 = p2.relative_path_from(p3)  # Pathname:lib/ruby/1.8
pwd = Pathname.pwd              # Pathname:/home/gavin
pwd.absolute?                   # true
p5 = Pathname.new "."           # Pathname:.
p5 = p5 + "music/../articles"   # Pathname:music/../articles
p5.cleanpath                    # Pathname:articles
p5.realpath                     # Pathname:/home/gavin/articles
p5.children                     # [Pathname:/home/gavin/articles/linux, ...]

Breakdown of functionality

Core methods

These methods are effectively manipulating a String, because that’s all a path is. None of these access the file system except for mountpoint?, children, each_child, realdirpath and realpath.

File status predicate methods

These methods are a facade for FileTest:

File property and manipulation methods

These methods are a facade for File:

Directory methods

These methods are a facade for Dir:

IO

These methods are a facade for IO:

Utilities

These methods are a mixture of Find, FileUtils, and others:

Method documentation

As the above section shows, most of the methods in Pathname are facades. The documentation for these methods generally just says, for instance, “See FileTest.writable?”, as you should be familiar with the original method anyway, and its documentation (e.g. through ri) will contain more information. In some cases, a brief description will follow.

TCPServer represents a TCP/IP server socket.

A simple TCP server may look like:

require 'socket'

server = TCPServer.new 2000 # Server bind to port 2000
loop do
  client = server.accept    # Wait for a client to connect
  client.puts "Hello !"
  client.puts "Time is #{Time.now}"
  client.close
end

A more usable server (serving multiple clients):

require 'socket'

server = TCPServer.new 2000
loop do
  Thread.start(server.accept) do |client|
    client.puts "Hello !"
    client.puts "Time is #{Time.now}"
    client.close
  end
end

TCPSocket represents a TCP/IP client socket.

A simple client may look like:

require 'socket'

s = TCPSocket.new 'localhost', 2000

while line = s.gets # Read lines from socket
  puts line         # and print them
end

s.close             # close socket when done

This library provides three different ways to delegate method calls to an object. The easiest to use is SimpleDelegator. Pass an object to the constructor and all methods supported by the object will be delegated. This object can be changed later.

Going a step further, the top level DelegateClass method allows you to easily setup delegation through class inheritance. This is considerably more flexible and thus probably the most common use for this library.

Finally, if you need full control over the delegation scheme, you can inherit from the abstract class Delegator and customize as needed. (If you find yourself needing this control, have a look at Forwardable which is also in the standard library. It may suit your needs better.)

SimpleDelegator’s implementation serves as a nice example of the use of Delegator:

require 'delegate'

class SimpleDelegator < Delegator
  def __getobj__
    @delegate_sd_obj # return object we are delegating to, required
  end

  def __setobj__(obj)
    @delegate_sd_obj = obj # change delegation object,
                           # a feature we're providing
  end
end

Notes

Be advised, RDoc will not detect delegated methods.

A concrete implementation of Delegator, this class provides the means to delegate all supported method calls to the object passed into the constructor and even to change the object being delegated to at a later time with __setobj__.

class User
  def born_on
    Date.new(1989, 9, 10)
  end
end

require 'delegate'

class UserDecorator < SimpleDelegator
  def birth_year
    born_on.year
  end
end

decorated_user = UserDecorator.new(User.new)
decorated_user.birth_year  #=> 1989
decorated_user.__getobj__  #=> #<User: ...>

A SimpleDelegator instance can take advantage of the fact that SimpleDelegator is a subclass of Delegator to call super to have methods called on the object being delegated to.

class SuperArray < SimpleDelegator
  def [](*args)
    super + 1
  end
end

SuperArray.new([1])[0]  #=> 2

Here’s a simple example that takes advantage of the fact that SimpleDelegator’s delegation object can be changed at any time.

class Stats
  def initialize
    @source = SimpleDelegator.new([])
  end

  def stats(records)
    @source.__setobj__(records)

    "Elements:  #{@source.size}\n" +
    " Non-Nil:  #{@source.compact.size}\n" +
    "  Unique:  #{@source.uniq.size}\n"
  end
end

s = Stats.new
puts s.stats(%w{James Edward Gray II})
puts
puts s.stats([1, 2, 3, nil, 4, 5, 1, 2])

Prints:

Elements:  4
 Non-Nil:  4
  Unique:  4

Elements:  8
 Non-Nil:  7
  Unique:  6
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