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.

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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

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Last edited August 4, 2014 3:06 pm GMT (diff)