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FloatLib.Floats.Formats.Posit.Hyperbolic.Runtime

Correctly rounded posit hyperbolic functions #

The operations compare their exact real result with rational posit rounding boundaries. There is no intermediate posit rounding. NaR propagates, and inputs outside an inverse function's real domain produce NaR.

Reference #

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def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.tanhRat (format : Format) (argument : ℚ) :
Model format

Round hyperbolic tangent of an exact rational argument.

Instances For
    source
    def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.artanhRat (format : Format) (argument : ℚ) :
    Model format

    Round inverse hyperbolic tangent, rejecting both endpoints and the exterior domain.

    Instances For
      source
      def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.sinhRat (format : Format) (argument : ℚ) :
      Model format

      Round hyperbolic sine of an exact rational argument.

      Instances For
        source
        def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.coshRat (format : Format) (argument : ℚ) :
        Model format

        Round hyperbolic cosine of an exact rational argument.

        Instances For
          source
          def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.arsinhRat (format : Format) (argument : ℚ) :
          Model format

          Round inverse hyperbolic sine of an exact rational argument.

          Instances For
            source
            def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.arcoshRat (format : Format) (argument : ℚ) :
            Model format

            Round inverse hyperbolic cosine on its real domain [1, ∞).

            Instances For
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              def FloatLib.Floats.Formats.Posit.Model.Hyperbolic.applyRat {format : Format} (operation : ℚ → Model format) (value : Model format) :
              Model format

              Apply a rational hyperbolic operation to a finite posit, propagating NaR.

              Instances For
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                def FloatLib.Floats.Formats.Posit.Model.tanH {format : Format} (value : Model format) :
                Model format

                Correctly rounded hyperbolic tangent; NaR propagates.

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                  def FloatLib.Floats.Formats.Posit.Model.arcTanH {format : Format} (value : Model format) :
                  Model format

                  Correctly rounded inverse hyperbolic tangent, with real domain -1 < x < 1.

                  Instances For
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                    def FloatLib.Floats.Formats.Posit.Model.sinH {format : Format} (value : Model format) :
                    Model format

                    Correctly rounded hyperbolic sine; NaR propagates.

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                      def FloatLib.Floats.Formats.Posit.Model.cosH {format : Format} (value : Model format) :
                      Model format

                      Correctly rounded hyperbolic cosine; NaR propagates.

                      Instances For
                        source
                        def FloatLib.Floats.Formats.Posit.Model.arcSinH {format : Format} (value : Model format) :
                        Model format

                        Correctly rounded inverse hyperbolic sine; NaR propagates.

                        Instances For
                          source
                          def FloatLib.Floats.Formats.Posit.Model.arcCosH {format : Format} (value : Model format) :
                          Model format

                          Correctly rounded inverse hyperbolic cosine; inputs below 1 produce NaR.

                          Instances For