##
# Math Test

##
# Performs fuzzy check for equality on methods returning floats
# on the basis of the Math::TOLERANCE constant.
def check_float(a, b)
  tolerance = Math::TOLERANCE
  a = a.to_f
  b = b.to_f
  if a.finite? and b.finite?
    (a-b).abs < tolerance
  else
    true
  end
end

assert('Math.sin 0') do
  check_float(Math.sin(0), 0)
end

assert('Math.sin PI/2') do
  check_float(Math.sin(Math::PI / 2), 1)
end

assert('Math.cos 0') do
  check_float(Math.cos(0), 1)
end

assert('Math.cos PI/2') do
  check_float(Math.cos(Math::PI / 2), 0)
end

assert('Math.tan 0') do
  check_float(Math.tan(0), 0)
end

assert('Math.tan PI/4') do
  check_float(Math.tan(Math::PI / 4), 1)
end

assert('Fundamental trig identities') do
  result = true
  N = 13
  N.times do |i|
    a  = Math::PI / N * i
    ca = Math::PI / 2 - a
    s  = Math.sin(a)
    c  = Math.cos(a)
    t  = Math.tan(a)
    result &= check_float(s, Math.cos(ca))
    result &= check_float(t, 1 / Math.tan(ca))
    result &= check_float(s ** 2 + c ** 2, 1)
    result &= check_float(t ** 2 + 1, (1/c) ** 2)
    result &= check_float((1/t) ** 2 + 1, (1/s) ** 2)
  end
  result
end

assert('Math.erf 0') do
  check_float(Math.erf(0), 0)
end

assert('Math.exp 0') do
  check_float(Math.exp(0), 1.0)
end

assert('Math.exp 1') do
  check_float(Math.exp(1), 2.718281828459045)
end

assert('Math.exp 1.5') do
  check_float(Math.exp(1.5), 4.4816890703380645)
end

assert('Math.log 1') do
  check_float(Math.log(1), 0)
end

assert('Math.log E') do
  check_float(Math.log(Math::E), 1.0)
end

assert('Math.log E**3') do
  check_float(Math.log(Math::E**3), 3.0)
end

assert('Math.log2 1') do
  check_float(Math.log2(1), 0.0)
end

assert('Math.log2 2') do
  check_float(Math.log2(2), 1.0)
end

assert('Math.log10 1') do
  check_float(Math.log10(1), 0.0)
end

assert('Math.log10 10') do
  check_float(Math.log10(10), 1.0)
end

assert('Math.log10 10**100') do
  check_float(Math.log10(10**100), 100.0)
end

assert('Math.sqrt') do
  num = [0.0, 1.0, 2.0, 3.0, 4.0]
  sqr = [0, 1, 4, 9, 16]
  result = true
  sqr.each_with_index do |v,i|
    result &= check_float(Math.sqrt(v), num[i])
  end
  result
end

assert('Math.cbrt') do
  num = [-2.0, -1.0, 0.0, 1.0, 2.0]
  cub = [-8, -1, 0, 1, 8]
  result = true
  cub.each_with_index do |v,i|
    result &= check_float(Math.cbrt(v), num[i])
  end
  result
end

assert('Math.hypot') do
  check_float(Math.hypot(3, 4), 5.0)
end

assert('Math.frexp 1234') do
  n = 1234
  fraction, exponent = Math.frexp(n)
  check_float(Math.ldexp(fraction, exponent), n)
end

assert('Math.erf 1') do
  check_float(Math.erf(1), 0.842700792949715)
end

assert('Math.erfc 1') do
  check_float(Math.erfc(1), 0.157299207050285)
end

assert('Math.erf -1') do
  check_float(Math.erf(-1), -0.8427007929497148)
end

assert('Math.erfc -1') do
  check_float(Math.erfc(-1), 1.8427007929497148)
end