sin cos

#!/usr/bin/env ruby
def sincos(x, n)
  if x < 0
    s, c = sincos(-x, n)
    return [-s + 0, c]
  end
  x -= 2 * Math::PI while x >= 2 * Math::PI
  case x
  when 0 .. Math::PI / 4
    return sincos_sub(x, n)
  when Math::PI / 4 .. Math::PI / 2
    s, c = sincos_sub(Math::PI / 2 - x, n)
    return [c, s]
  when Math::PI / 2 .. Math::PI
    s, c = sincos(Math::PI - x, n)
    return [s, -c]
  when Math::PI .. 2 * Math::PI
    s, c = sincos(2 * Math::PI - x, n)
    return [-s, c]
  end
end

def sincos_sub(x, n)
  sign = 1; pow = 1.0; fact = 1; sin = 0.0; cos = 0.0
  n.times do |i|
    cos += sign * pow / fact
    pow *= x
    fact *= 2 * i + 1
    sin += sign * pow / fact
    pow *= x
    fact *= 2 * i + 2
    sign = -sign
  end
  [sin, cos]
end

def main
  puts '#deg: sin(err) cos(err)'
  0.step(by: 5, to: 360) do |i|
    x = i * Math::PI / 180.0
    s, c = sincos(x, 1000)
    next if s.nan? or c.nan?
    ds = (s - Math.sin(x)).abs
    dc = (c - Math.cos(x)).abs
    puts "#{i}: #{s}(#{ds}) #{c}(#{dc})"
  end
end

main