雙曲線函數

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-----------------------------------------------------------------------
-- Pure Lua implementation for the hyperbolic trigonometric functions
-- Freely adapted from P.J.Plauger, "The Standard C Library"
-- author: Roberto Ierusalimschy
-----------------------------------------------------------------------

local M = {}

local exp = math.exp

function M.cosh (x)
  if x == 0.0 then return 1.0 end
  if x < 0.0 then x = -x end
  x = exp(x)
  x = x / 2.0 + 0.5 / x
  return x
end


function M.sinh (x)
  if x == 0 then return 0.0 end
  local neg = false
  if x < 0 then x = -x; neg = true end
  if x < 1.0 then
    local y = x * x
    x = x + x * y *
        (((-0.78966127417357099479e0  * y +
           -0.16375798202630751372e3) * y +
           -0.11563521196851768270e5) * y +
           -0.35181283430177117881e6) /
        ((( 0.10000000000000000000e1  * y +
           -0.27773523119650701667e3) * y +
            0.36162723109421836460e5) * y +
           -0.21108770058106271242e7)
  else
    x =  exp(x)
    x = x / 2.0 - 0.5 / x
  end
  if neg then x = -x end
  return x
end


function M.tanh (x)
  if x == 0 then return 0.0 end
  local neg = false
  if x < 0 then x = -x; neg = true end
  if x < 0.54930614433405 then
    local y = x * x
    x = x + x * y *
        ((-0.96437492777225469787e0  * y +
          -0.99225929672236083313e2) * y +
          -0.16134119023996228053e4) /
        (((0.10000000000000000000e1  * y +
           0.11274474380534949335e3) * y +
           0.22337720718962312926e4) * y +
           0.48402357071988688686e4)
  else
    x = exp(x)
    x = 1.0 - 2.0 / (x * x + 1.0)
  end
  if neg then x = -x end
  return x
end

return M