module BigMath

def E(prec)
  raise ArgumentError, "Zero or negative precision for E" if prec <= 0
  BigMath.exp(1, prec)
end

def PI(prec)
  raise ArgumentError, "Zero or negative precision for PI" if prec <= 0
  n      = prec + BigDecimal.double_fig
  zero   = BigDecimal("0")
  one    = BigDecimal("1")
  two    = BigDecimal("2")
  m25    = BigDecimal("-0.04")
  m57121 = BigDecimal("-57121")
  pi     = zero
  d = one
  k = one
  t = BigDecimal("-80")
  while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t   = t*m25
    d   = t.div(k,m)
    k   = k+two
    pi  = pi + d
  end
  d = one
  k = one
  t = BigDecimal("956")
  while d.nonzero? && ((m = n - (pi.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t   = t.div(m57121,n)
    d   = t.div(k,m)
    pi  = pi + d
    k   = k+two
  end
  pi
end

def atan(x, prec)
  raise ArgumentError, "Zero or negative precision for atan" if prec <= 0
  return BigDecimal("NaN") if x.nan?
  pi = PI(prec)
  x = -x if neg = x < 0
  return pi.div(neg ? -2 : 2, prec) if x.infinite?
  return pi / (neg ? -4 : 4) if x.round(prec) == 1
  x = BigDecimal("1").div(x, prec) if inv = x > 1
  x = (-1 + sqrt(1 + x**2, prec))/x if dbl = x > 0.5
  n    = prec + BigDecimal.double_fig
  y = x
  d = y
  t = x
  r = BigDecimal("3")
  x2 = x.mult(x,n)
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    t = -t.mult(x2,n)
    d = t.div(r,m)
    y += d
    r += 2
  end
  y *= 2 if dbl
  y = pi / 2 - y if inv
  y = -y if neg
  y
end

def cos(x, prec)
  raise ArgumentError, "Zero or negative precision for cos" if prec <= 0
  return BigDecimal("NaN") if x.infinite? || x.nan?
  n    = prec + BigDecimal.double_fig
  one  = BigDecimal("1")
  two  = BigDecimal("2")
  x = -x if x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x %= twopi
    else
      x -= twopi while x > twopi
    end
  end
  x1 = one
  x2 = x.mult(x,n)
  sign = 1
  y = one
  d = y
  i = BigDecimal("0")
  z = one
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    sign = -sign
    x1  = x2.mult(x1,n)
    i  += two
    z  *= (i-one) * i
    d   = sign * x1.div(z,m)
    y  += d
  end
  y
end

def sin(x, prec)
  raise ArgumentError, "Zero or negative precision for sin" if prec <= 0
  return BigDecimal("NaN") if x.infinite? || x.nan?
  n    = prec + BigDecimal.double_fig
  one  = BigDecimal("1")
  two  = BigDecimal("2")
  x = -x if neg = x < 0
  if x > (twopi = two * BigMath.PI(prec))
    if x > 30
      x %= twopi
    else
      x -= twopi while x > twopi
    end
  end
  x1   = x
  x2   = x.mult(x,n)
  sign = 1
  y    = x
  d    = y
  i    = one
  z    = one
  while d.nonzero? && ((m = n - (y.exponent - d.exponent).abs) > 0)
    m = BigDecimal.double_fig if m < BigDecimal.double_fig
    sign = -sign
    x1  = x2.mult(x1,n)
    i  += two
    z  *= (i-one) * i
    d   = sign * x1.div(z,m)
    y  += d
  end
  neg ? -y : y
end

def sqrt(x, prec)
  x.sqrt(prec)
end