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+#--
+# benchmark.rb - a performance benchmarking library
+#
+# $Id: benchmark.rb 47526 2014-09-11 08:09:07Z normal $
+#
+# Created by Gotoken (gotoken@notwork.org).
+#
+# Documentation by Gotoken (original RD), Lyle Johnson (RDoc conversion), and
+# Gavin Sinclair (editing).
+#++
+#
+# == Overview
+#
+# The Benchmark module provides methods for benchmarking Ruby code, giving
+# detailed reports on the time taken for each task.
+#
+
+# The Benchmark module provides methods to measure and report the time
+# used to execute Ruby code.
+#
+# * Measure the time to construct the string given by the expression
+#   <code>"a"*1_000_000_000</code>:
+#
+#       require 'benchmark'
+#
+#       puts Benchmark.measure { "a"*1_000_000_000 }
+#
+#   On my machine (OSX 10.8.3 on i5 1.7 Ghz) this generates:
+#
+#       0.350000   0.400000   0.750000 (  0.835234)
+#
+#   This report shows the user CPU time, system CPU time, the sum of
+#   the user and system CPU times, and the elapsed real time. The unit
+#   of time is seconds.
+#
+# * Do some experiments sequentially using the #bm method:
+#
+#       require 'benchmark'
+#
+#       n = 5000000
+#       Benchmark.bm do |x|
+#         x.report { for i in 1..n; a = "1"; end }
+#         x.report { n.times do   ; a = "1"; end }
+#         x.report { 1.upto(n) do ; a = "1"; end }
+#       end
+#
+#   The result:
+#
+#              user     system      total        real
+#          1.010000   0.000000   1.010000 (  1.014479)
+#          1.000000   0.000000   1.000000 (  0.998261)
+#          0.980000   0.000000   0.980000 (  0.981335)
+#
+# * Continuing the previous example, put a label in each report:
+#
+#       require 'benchmark'
+#
+#       n = 5000000
+#       Benchmark.bm(7) do |x|
+#         x.report("for:")   { for i in 1..n; a = "1"; end }
+#         x.report("times:") { n.times do   ; a = "1"; end }
+#         x.report("upto:")  { 1.upto(n) do ; a = "1"; end }
+#       end
+#
+# 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)
+#
+# * The times for some benchmarks depend on the order in which items
+#   are run.  These differences are due to the cost of memory
+#   allocation and garbage collection. To avoid these discrepancies,
+#   the #bmbm method is provided.  For example, to compare ways to
+#   sort an array of floats:
+#
+#       require 'benchmark'
+#
+#       array = (1..1000000).map { rand }
+#
+#       Benchmark.bmbm do |x|
+#         x.report("sort!") { array.dup.sort! }
+#         x.report("sort")  { array.dup.sort  }
+#       end
+#
+#   The result:
+#
+#        Rehearsal -----------------------------------------
+#        sort!   1.490000   0.010000   1.500000 (  1.490520)
+#        sort    1.460000   0.000000   1.460000 (  1.463025)
+#        -------------------------------- total: 2.960000sec
+#
+#                    user     system      total        real
+#        sort!   1.460000   0.000000   1.460000 (  1.460465)
+#        sort    1.450000   0.010000   1.460000 (  1.448327)
+#
+# * Report statistics of sequential experiments with unique labels,
+#   using the #benchmark method:
+#
+#       require 'benchmark'
+#       include Benchmark         # we need the CAPTION and FORMAT constants
+#
+#       n = 5000000
+#       Benchmark.benchmark(CAPTION, 7, FORMAT, ">total:", ">avg:") do |x|
+#         tf = x.report("for:")   { for i in 1..n; a = "1"; end }
+#         tt = x.report("times:") { n.times do   ; a = "1"; end }
+#         tu = x.report("upto:")  { 1.upto(n) do ; a = "1"; end }
+#         [tf+tt+tu, (tf+tt+tu)/3]
+#       end
+#
+#   The result:
+#
+#                     user     system      total        real
+#        for:      0.950000   0.000000   0.950000 (  0.952039)
+#        times:    0.980000   0.000000   0.980000 (  0.984938)
+#        upto:     0.950000   0.000000   0.950000 (  0.946787)
+#        >total:   2.880000   0.000000   2.880000 (  2.883764)
+#        >avg:     0.960000   0.000000   0.960000 (  0.961255)
+
+module Benchmark
+
+  BENCHMARK_VERSION = "2002-04-25" # :nodoc:
+
+  # Invokes the block with a Benchmark::Report object, which
+  # may be used to collect and report on the results of individual
+  # benchmark tests. Reserves +label_width+ leading spaces for
+  # labels on each line. Prints +caption+ at the top of the
+  # report, and uses +format+ to format each line.
+  # Returns an array of Benchmark::Tms objects.
+  #
+  # If the block returns an array of
+  # Benchmark::Tms objects, these will be used to format
+  # additional lines of output. If +label+ parameters are
+  # given, these are used to label these extra lines.
+  #
+  # _Note_: Other methods provide a simpler interface to this one, and are
+  # suitable for nearly all benchmarking requirements.  See the examples in
+  # Benchmark, and the #bm and #bmbm methods.
+  #
+  # Example:
+  #
+  #     require 'benchmark'
+  #     include Benchmark          # we need the CAPTION and FORMAT constants
+  #
+  #     n = 5000000
+  #     Benchmark.benchmark(CAPTION, 7, FORMAT, ">total:", ">avg:") do |x|
+  #       tf = x.report("for:")   { for i in 1..n; a = "1"; end }
+  #       tt = x.report("times:") { n.times do   ; a = "1"; end }
+  #       tu = x.report("upto:")  { 1.upto(n) do ; a = "1"; end }
+  #       [tf+tt+tu, (tf+tt+tu)/3]
+  #     end
+  #
+  # Generates:
+  #
+  #                     user     system      total        real
+  #       for:      0.970000   0.000000   0.970000 (  0.970493)
+  #       times:    0.990000   0.000000   0.990000 (  0.989542)
+  #       upto:     0.970000   0.000000   0.970000 (  0.972854)
+  #       >total:   2.930000   0.000000   2.930000 (  2.932889)
+  #       >avg:     0.976667   0.000000   0.976667 (  0.977630)
+  #
+
+  def benchmark(caption = "", label_width = nil, format = nil, *labels) # :yield: report
+    sync = STDOUT.sync
+    STDOUT.sync = true
+    label_width ||= 0
+    label_width += 1
+    format ||= FORMAT
+    print ' '*label_width + caption unless caption.empty?
+    report = Report.new(label_width, format)
+    results = yield(report)
+    Array === results and results.grep(Tms).each {|t|
+      print((labels.shift || t.label || "").ljust(label_width), t.format(format))
+    }
+    report.list
+  ensure
+    STDOUT.sync = sync unless sync.nil?
+  end
+
+
+  # A simple interface to the #benchmark method, #bm generates sequential
+  # reports with labels.  The parameters have the same meaning as for
+  # #benchmark.
+  #
+  #     require 'benchmark'
+  #
+  #     n = 5000000
+  #     Benchmark.bm(7) do |x|
+  #       x.report("for:")   { for i in 1..n; a = "1"; end }
+  #       x.report("times:") { n.times do   ; a = "1"; end }
+  #       x.report("upto:")  { 1.upto(n) do ; a = "1"; end }
+  #     end
+  #
+  # Generates:
+  #
+  #                     user     system      total        real
+  #       for:      0.960000   0.000000   0.960000 (  0.957966)
+  #       times:    0.960000   0.000000   0.960000 (  0.960423)
+  #       upto:     0.950000   0.000000   0.950000 (  0.954864)
+  #
+
+  def bm(label_width = 0, *labels, &blk) # :yield: report
+    benchmark(CAPTION, label_width, FORMAT, *labels, &blk)
+  end
+
+
+  # Sometimes benchmark results are skewed because code executed
+  # earlier encounters different garbage collection overheads than
+  # that run later. #bmbm attempts to minimize this effect by running
+  # the tests twice, the first time as a rehearsal in order to get the
+  # runtime environment stable, the second time for
+  # real. GC.start is executed before the start of each of
+  # the real timings; the cost of this is not included in the
+  # timings. In reality, though, there's only so much that #bmbm can
+  # do, and the results are not guaranteed to be isolated from garbage
+  # collection and other effects.
+  #
+  # Because #bmbm takes two passes through the tests, it can
+  # calculate the required label width.
+  #
+  #       require 'benchmark'
+  #
+  #       array = (1..1000000).map { rand }
+  #
+  #       Benchmark.bmbm do |x|
+  #         x.report("sort!") { array.dup.sort! }
+  #         x.report("sort")  { array.dup.sort  }
+  #       end
+  #
+  # Generates:
+  #
+  #        Rehearsal -----------------------------------------
+  #        sort!   1.440000   0.010000   1.450000 (  1.446833)
+  #        sort    1.440000   0.000000   1.440000 (  1.448257)
+  #        -------------------------------- total: 2.890000sec
+  #
+  #                    user     system      total        real
+  #        sort!   1.460000   0.000000   1.460000 (  1.458065)
+  #        sort    1.450000   0.000000   1.450000 (  1.455963)
+  #
+  # #bmbm yields a Benchmark::Job object and returns an array of
+  # Benchmark::Tms objects.
+  #
+  def bmbm(width = 0) # :yield: job
+    job = Job.new(width)
+    yield(job)
+    width = job.width + 1
+    sync = STDOUT.sync
+    STDOUT.sync = true
+
+    # rehearsal
+    puts 'Rehearsal '.ljust(width+CAPTION.length,'-')
+    ets = job.list.inject(Tms.new) { |sum,(label,item)|
+      print label.ljust(width)
+      res = Benchmark.measure(&item)
+      print res.format
+      sum + res
+    }.format("total: %tsec")
+    print " #{ets}\n\n".rjust(width+CAPTION.length+2,'-')
+
+    # take
+    print ' '*width + CAPTION
+    job.list.map { |label,item|
+      GC.start
+      print label.ljust(width)
+      Benchmark.measure(label, &item).tap { |res| print res }
+    }
+  ensure
+    STDOUT.sync = sync unless sync.nil?
+  end
+
+  # :stopdoc:
+  case
+  when defined?(Process::CLOCK_MONOTONIC)
+    BENCHMARK_CLOCK = Process::CLOCK_MONOTONIC
+  else
+    BENCHMARK_CLOCK = Process::CLOCK_REALTIME
+  end
+  # :startdoc:
+
+  #
+  # Returns the time used to execute the given block as a
+  # Benchmark::Tms object.
+  #
+  def measure(label = "") # :yield:
+    t0, r0 = Process.times, Process.clock_gettime(BENCHMARK_CLOCK)
+    yield
+    t1, r1 = Process.times, Process.clock_gettime(BENCHMARK_CLOCK)
+    Benchmark::Tms.new(t1.utime  - t0.utime,
+                       t1.stime  - t0.stime,
+                       t1.cutime - t0.cutime,
+                       t1.cstime - t0.cstime,
+                       r1 - r0,
+                       label)
+  end
+
+  #
+  # Returns the elapsed real time used to execute the given block.
+  #
+  def realtime # :yield:
+    r0 = Process.clock_gettime(BENCHMARK_CLOCK)
+    yield
+    Process.clock_gettime(BENCHMARK_CLOCK) - r0
+  end
+
+  module_function :benchmark, :measure, :realtime, :bm, :bmbm
+
+  #
+  # A Job is a sequence of labelled blocks to be processed by the
+  # Benchmark.bmbm method.  It is of little direct interest to the user.
+  #
+  class Job # :nodoc:
+    #
+    # Returns an initialized Job instance.
+    # Usually, one doesn't call this method directly, as new
+    # Job objects are created by the #bmbm method.
+    # +width+ is a initial value for the label offset used in formatting;
+    # the #bmbm method passes its +width+ argument to this constructor.
+    #
+    def initialize(width)
+      @width = width
+      @list = []
+    end
+
+    #
+    # Registers the given label and block pair in the job list.
+    #
+    def item(label = "", &blk) # :yield:
+      raise ArgumentError, "no block" unless block_given?
+      label = label.to_s
+      w = label.length
+      @width = w if @width < w
+      @list << [label, blk]
+      self
+    end
+
+    alias report item
+
+    # An array of 2-element arrays, consisting of label and block pairs.
+    attr_reader :list
+
+    # Length of the widest label in the #list.
+    attr_reader :width
+  end
+
+  #
+  # This class is used by the Benchmark.benchmark and Benchmark.bm methods.
+  # It is of little direct interest to the user.
+  #
+  class Report # :nodoc:
+    #
+    # Returns an initialized Report instance.
+    # Usually, one doesn't call this method directly, as new
+    # Report objects are created by the #benchmark and #bm methods.
+    # +width+ and +format+ are the label offset and
+    # format string used by Tms#format.
+    #
+    def initialize(width = 0, format = nil)
+      @width, @format, @list = width, format, []
+    end
+
+    #
+    # Prints the +label+ and measured time for the block,
+    # formatted by +format+. See Tms#format for the
+    # formatting rules.
+    #
+    def item(label = "", *format, &blk) # :yield:
+      print label.to_s.ljust(@width)
+      @list << res = Benchmark.measure(label, &blk)
+      print res.format(@format, *format)
+      res
+    end
+
+    alias report item
+
+    # An array of Benchmark::Tms objects representing each item.
+    attr_reader :list
+  end
+
+
+
+  #
+  # A data object, representing the times associated with a benchmark
+  # measurement.
+  #
+  class Tms
+
+    # Default caption, see also Benchmark::CAPTION
+    CAPTION = "      user     system      total        real\n"
+
+    # Default format string, see also Benchmark::FORMAT
+    FORMAT = "%10.6u %10.6y %10.6t %10.6r\n"
+
+    # User CPU time
+    attr_reader :utime
+
+    # System CPU time
+    attr_reader :stime
+
+    # User CPU time of children
+    attr_reader :cutime
+
+    # System CPU time of children
+    attr_reader :cstime
+
+    # Elapsed real time
+    attr_reader :real
+
+    # Total time, that is +utime+ + +stime+ + +cutime+ + +cstime+
+    attr_reader :total
+
+    # Label
+    attr_reader :label
+
+    #
+    # Returns an initialized Tms object which has
+    # +utime+ as the user CPU time, +stime+ as the system CPU time,
+    # +cutime+ as the children's user CPU time, +cstime+ as the children's
+    # system CPU time, +real+ as the elapsed real time and +label+ as the label.
+    #
+    def initialize(utime = 0.0, stime = 0.0, cutime = 0.0, cstime = 0.0, real = 0.0, label = nil)
+      @utime, @stime, @cutime, @cstime, @real, @label = utime, stime, cutime, cstime, real, label.to_s
+      @total = @utime + @stime + @cutime + @cstime
+    end
+
+    #
+    # Returns a new Tms object whose times are the sum of the times for this
+    # Tms object, plus the time required to execute the code block (+blk+).
+    #
+    def add(&blk) # :yield:
+      self + Benchmark.measure(&blk)
+    end
+
+    #
+    # An in-place version of #add.
+    #
+    def add!(&blk)
+      t = Benchmark.measure(&blk)
+      @utime  = utime + t.utime
+      @stime  = stime + t.stime
+      @cutime = cutime + t.cutime
+      @cstime = cstime + t.cstime
+      @real   = real + t.real
+      self
+    end
+
+    #
+    # Returns a new Tms object obtained by memberwise summation
+    # of the individual times for this Tms object with those of the other
+    # Tms object.
+    # This method and #/() are useful for taking statistics.
+    #
+    def +(other); memberwise(:+, other) end
+
+    #
+    # Returns a new Tms object obtained by memberwise subtraction
+    # of the individual times for the other Tms object from those of this
+    # Tms object.
+    #
+    def -(other); memberwise(:-, other) end
+
+    #
+    # Returns a new Tms object obtained by memberwise multiplication
+    # of the individual times for this Tms object by _x_.
+    #
+    def *(x); memberwise(:*, x) end
+
+    #
+    # Returns a new Tms object obtained by memberwise division
+    # of the individual times for this Tms object by _x_.
+    # This method and #+() are useful for taking statistics.
+    #
+    def /(x); memberwise(:/, x) end
+
+    #
+    # Returns the contents of this Tms object as
+    # a formatted string, according to a format string
+    # like that passed to Kernel.format. In addition, #format
+    # accepts the following extensions:
+    #
+    # <tt>%u</tt>::     Replaced by the user CPU time, as reported by Tms#utime.
+    # <tt>%y</tt>::     Replaced by the system CPU time, as reported by #stime (Mnemonic: y of "s*y*stem")
+    # <tt>%U</tt>::     Replaced by the children's user CPU time, as reported by Tms#cutime
+    # <tt>%Y</tt>::     Replaced by the children's system CPU time, as reported by Tms#cstime
+    # <tt>%t</tt>::     Replaced by the total CPU time, as reported by Tms#total
+    # <tt>%r</tt>::     Replaced by the elapsed real time, as reported by Tms#real
+    # <tt>%n</tt>::     Replaced by the label string, as reported by Tms#label (Mnemonic: n of "*n*ame")
+    #
+    # If _format_ is not given, FORMAT is used as default value, detailing the
+    # user, system and real elapsed time.
+    #
+    def format(format = nil, *args)
+      str = (format || FORMAT).dup
+      str.gsub!(/(%[-+.\d]*)n/) { "#{$1}s" % label }
+      str.gsub!(/(%[-+.\d]*)u/) { "#{$1}f" % utime }
+      str.gsub!(/(%[-+.\d]*)y/) { "#{$1}f" % stime }
+      str.gsub!(/(%[-+.\d]*)U/) { "#{$1}f" % cutime }
+      str.gsub!(/(%[-+.\d]*)Y/) { "#{$1}f" % cstime }
+      str.gsub!(/(%[-+.\d]*)t/) { "#{$1}f" % total }
+      str.gsub!(/(%[-+.\d]*)r/) { "(#{$1}f)" % real }
+      format ? str % args : str
+    end
+
+    #
+    # Same as #format.
+    #
+    def to_s
+      format
+    end
+
+    #
+    # Returns a new 6-element array, consisting of the
+    # label, user CPU time, system CPU time, children's
+    # user CPU time, children's system CPU time and elapsed
+    # real time.
+    #
+    def to_a
+      [@label, @utime, @stime, @cutime, @cstime, @real]
+    end
+
+    protected
+
+    #
+    # Returns a new Tms object obtained by memberwise operation +op+
+    # of the individual times for this Tms object with those of the other
+    # Tms object.
+    #
+    # +op+ can be a mathematical operation such as <tt>+</tt>, <tt>-</tt>,
+    # <tt>*</tt>, <tt>/</tt>
+    #
+    def memberwise(op, x)
+      case x
+      when Benchmark::Tms
+        Benchmark::Tms.new(utime.__send__(op, x.utime),
+                           stime.__send__(op, x.stime),
+                           cutime.__send__(op, x.cutime),
+                           cstime.__send__(op, x.cstime),
+                           real.__send__(op, x.real)
+                           )
+      else
+        Benchmark::Tms.new(utime.__send__(op, x),
+                           stime.__send__(op, x),
+                           cutime.__send__(op, x),
+                           cstime.__send__(op, x),
+                           real.__send__(op, x)
+                           )
+      end
+    end
+  end
+
+  # The default caption string (heading above the output times).
+  CAPTION = Benchmark::Tms::CAPTION
+
+  # The default format string used to display times.  See also Benchmark::Tms#format.
+  FORMAT = Benchmark::Tms::FORMAT
+end