Code examples about "prior knowledge"

test-01.rb

#!/bin/ruby

require 'benchmark'

def sin radians
    h = Hash.new(Math.sin(radians))
    h[0.0] = 0
    h[90.0] = 1
    h[180.0] = 0
    h[270.0] = -1
    degrees = (radians / Math::PI * 180) % 360 # think in degrees for ease
    h[degrees]
end

def sin2 x
  rad = (x / Math::PI * 180) % 360 # think in degrees for ease
  case rad
  when 0; 0
  when 90; 1
  when 180; 0
  when 270; -1
  else Math.sin(x)
  end
end

REPEAT = 1_000_000

Benchmark.bmbm 20 do |x|
  x.report "Math.sin(0)" do
    REPEAT.times { Math.sin(0) }
  end

  x.report "Math.sin(0.0)" do
    REPEAT.times { Math.sin(0.0) }
  end

  x.report "sin(0)" do
    REPEAT.times { sin(0) }
  end

  x.report "sin(0.0)" do
    REPEAT.times { sin(0.0) }
  end

  x.report "sin2(0)" do
    REPEAT.times { sin2(0) }
  end

  x.report "sin2(0.0)" do
    REPEAT.times { sin2(0.0) }
  end

end

test-02.rb

require 'benchmark'

def fib1(n)
 case n
 when 0 then 0
 when 1 then 1
 else fib1(n-1) + fib1(n-2)
 end
end

def fib2(n)
 case n
 when 0 then 0
 when 1 then 1
 else 
   f0 = 0
   f1 = 1

   for i in 2..n
     f0, f1 = f1, f0 + f1
   end

   f1
 end
end

fib3 = Hash.new do |h, n|
  last = nil

  for i in 2..n
    h[i] = last = h[i - 1] + h[i - 2]
  end  

  last
end.update(0 => 0, 1 => 1)

fib4 = Hash.new do |h, n|
  last = nil

  (h.m + 1).upto n do |i|
    h[i] = last = h[i - 1] + h[i - 2]
  end  

  h.m = n # we know n > h.m
  last
end.update(0 => 0, 1 => 1)

class <<fib4
  attr_accessor :m
end

fib4.instance_variable_set '@m', 1

10.times do |n|
  f1 = fib1 n
  f2 = fib2 n
  f3 = fib3[n]
  f4 = fib4[n]

  printf "%10d %10d %10d %10d\n", f1, f2, f3, f4 unless f1 == f2 && f2 == f3 && f2 == f4
end

REPEAT = 100_000

Benchmark.bm 20 do |x|
  x.report "fib1" do
    REPEAT.times { fib1 10 }
  end

  x.report "fib2" do
    REPEAT.times { fib2 10 }
  end

  x.report "fib3" do
    REPEAT.times { fib3[10] }
  end

  x.report "fib4" do
    REPEAT.times { fib4[10] }
  end
end