Casio FX-115MS bug

[Albert Chan]

Solving cubic with hyperbolic sine formula, discovered Casio FX-115MS asinh bug
(asinh bug also hit my Casio FX-3650P ...)

Solve X³ + 11 X - 1000100 = 0 for X, using formula X = -2 √(r) sinh(1/3 * asinh(s/r^1.5))

asinh(s/r^1.5)) = asinh(-500050/(11/3)^1.5) = asinh(-71220.70789) = -11.86817286 ???

Even my pocket Casio FX-260Solar get this right, asinh(-71220.70789) = -11.86668608

My guess the problem is the Quadratic Solver subtraction cancellation.

Solving sinh(x) = (exp(x) - 1/exp(x))/2 = -71220.70789, solver gives exp(x) = 7.01e-6
x = ln(7.01e-6) = -11.86817286 (same as the produced bug)

As a temporary fix, force asinh to use big root:

asinh(x) = ln(√(x²+1) + x) = - ln(√(x²+1) - x) = - asinh(-x)

asinh(x) = sign(x) * asinh(|x|)

asinh(-71220.70789) = -1 * asinh(+71220.70789) = -11.86668608