For the transcendental functions it is difficult (if not mathematically impossible--the subject of ongoing research) to guarantee correctly rounded results algorithmically:
- Trigonometric functions: ArcCos, ArcSin, ArcTan, Cos, Sin, and Tan
- Hyperbolic functions: ArcCosh, ArcSinh, ArcTanh, Cosh, Sinh, and Tanh
- Exponential and logarithm functions: Annuity, Compound, Exp, Exp2, ExpMinus1, Log, Log10, Log1Plus, Log2, Power, and Hypotenuse (which is not transcendental, but is implemented with multiple roundings)
- Special functions: Erf, Erfc, Gamma, and LogGamma
For these functions, the computational model is merely an ideal. According to a trade-off between speed and accuracy, overall accuracy varies from platform to platform and from function to function within a platform. Some platforms ignore the rounding mode when computing transcendental functions; they compute with rounding to nearest.
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