# 1-15-Ruby.rb
#
# Ruby has a number of conventions that distinguish
# it from C and C++. For example, parentheses are
# often omitted when calling simple methods, and the
# value of the final expression in a method is
# automatically returned.

# my_sin(x)
#
# Approximate sin(x) using the Taylor series
#
#                 x^3   x^5   x^7
#     sin(x) = x - --- + --- - --- + ...
#                  3!    5!    7!
#
# Rather than calculating each power and factorial
# separately, calculate each term from the previous
# term:
#
#                    x^2
#     next = -term -----------
#                  n(n + 1)
#
# where n takes the values 2, 4, 6, ...
def my_sin(x)
  return Float::NAN unless x.finite?

  result = x
  term = x
  n = 2.0

  loop do
    term *= -(x/n)*(x/(n + 1.0))

    break if term.abs < 1e-16

    result += term
    n += 2.0
  end

  result
end

x = 3.2

puts "my_sin(x): #{my_sin(x)}"
puts "Math.sin(x): #{Math.sin(x)}"
puts "reference: #{-0.058374143427579909137}"

# Ruby provides named floating-point values for
# positive infinity and NaN.
puts "my_sin(Float::INFINITY): #{my_sin(Float::INFINITY)}"