class Minitest::Benchmark

def self.bench_exp min, max, base = 10
  min = (Math.log10(min) / Math.log10(base)).to_i
  max = (Math.log10(max) / Math.log10(base)).to_i
  (min..max).map { |m| base ** m }.to_a
end

def self.bench_linear min, max, step = 10
  (min..max).step(step).to_a
rescue LocalJumpError # 1.8.6
  r = []; (min..max).step(step) { |n| r << n }; r
end

def self.bench_range
  bench_exp 1, 10_000
end

def self.io # :nodoc:
  @io
end

def self.run reporter, options = {} # :nodoc:
  @io = reporter.io
  super
end

def self.runnable_methods # :nodoc:
  methods_matching(/^bench_/)
end

def assert_performance validation, &work
  range = self.class.bench_range
  io.print "#{self.name}"
  times = []
  range.each do |x|
    GC.start
    t0 = Minitest.clock_time
    instance_exec(x, &work)
    t = Minitest.clock_time - t0
    io.print "\t%9.6f" % t
    times << t
  end
  io.puts
  validation[range, times]
end

def assert_performance_constant threshold = 0.99, &work
  validation = proc do |range, times|
    a, b, rr = fit_linear range, times
    assert_in_delta 0, b, 1 - threshold
    [a, b, rr]
  end
  assert_performance validation, &work
end

def assert_performance_exponential threshold = 0.99, &work
  assert_performance validation_for_fit(:exponential, threshold), &work
end

def assert_performance_linear threshold = 0.99, &work
  assert_performance validation_for_fit(:linear, threshold), &work
end

def assert_performance_logarithmic threshold = 0.99, &work
  assert_performance validation_for_fit(:logarithmic, threshold), &work
end

def assert_performance_power threshold = 0.99, &work
  assert_performance validation_for_fit(:power, threshold), &work
end

def fit_error xys
  y_bar  = sigma(xys) { |_, y| y } / xys.size.to_f
  ss_tot = sigma(xys) { |_, y| (y    - y_bar) ** 2 }
  ss_err = sigma(xys) { |x, y| (yield(x) - y) ** 2 }
  1 - (ss_err / ss_tot)
end

def fit_exponential xs, ys
  n     = xs.size
  xys   = xs.zip(ys)
  sxlny = sigma(xys) { |x, y| x * Math.log(y) }
  slny  = sigma(xys) { |_, y| Math.log(y)     }
  sx2   = sigma(xys) { |x, _| x * x           }
  sx    = sigma xs
  c = n * sx2 - sx ** 2
  a = (slny * sx2 - sx * sxlny) / c
  b = ( n * sxlny - sx * slny ) / c
  return Math.exp(a), b, fit_error(xys) { |x| Math.exp(a + b * x) }
end

def fit_linear xs, ys
  n   = xs.size
  xys = xs.zip(ys)
  sx  = sigma xs
  sy  = sigma ys
  sx2 = sigma(xs)  { |x|   x ** 2 }
  sxy = sigma(xys) { |x, y| x * y  }
  c = n * sx2 - sx**2
  a = (sy * sx2 - sx * sxy) / c
  b = ( n * sxy - sx * sy ) / c
  return a, b, fit_error(xys) { |x| a + b * x }
end

def fit_logarithmic xs, ys
  n     = xs.size
  xys   = xs.zip(ys)
  slnx2 = sigma(xys) { |x, _| Math.log(x) ** 2 }
  slnx  = sigma(xys) { |x, _| Math.log(x)      }
  sylnx = sigma(xys) { |x, y| y * Math.log(x)  }
  sy    = sigma(xys) { |_, y| y                }
  c = n * slnx2 - slnx ** 2
  b = ( n * sylnx - sy * slnx ) / c
  a = (sy - b * slnx) / n
  return a, b, fit_error(xys) { |x| a + b * Math.log(x) }
end

def fit_power xs, ys
  n       = xs.size
  xys     = xs.zip(ys)
  slnxlny = sigma(xys) { |x, y| Math.log(x) * Math.log(y) }
  slnx    = sigma(xs)  { |x   | Math.log(x)               }
  slny    = sigma(ys)  { |   y| Math.log(y)               }
  slnx2   = sigma(xs)  { |x   | Math.log(x) ** 2          }
  b = (n * slnxlny - slnx * slny) / (n * slnx2 - slnx ** 2)
  a = (slny - b * slnx) / n
  return Math.exp(a), b, fit_error(xys) { |x| (Math.exp(a) * (x ** b)) }
end

def io # :nodoc:
  self.class.io
end

def sigma enum, &block
  enum = enum.map(&block) if block
  enum.inject { |sum, n| sum + n }
end

def validation_for_fit msg, threshold
  proc do |range, times|
    a, b, rr = send "fit_#{msg}", range, times
    assert_operator rr, :>=, threshold
    [a, b, rr]
  end
end