Hyperbolic Functions

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As Lua 5.3 will deprecate the trigonometric hyperbolic functions in the standard math library, these pure Lua implementations can be useful. Preliminary tests show them to produce results that differ at most by one bit when compared to the libC implementations.

-----------------------------------------------------------------------
-- 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


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Last edited August 4, 2014 8:06 pm GMT (diff)