Hyperbolic Functions

wiki

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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

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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