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FloatLib.Floats.Formats.Logarithmic.Configured.Runtime

Executable exact logarithmic operations #

Every value is zero or a signed integral power of the radix. Multiplication is the only arithmetic operation supplied; it is closed and exact because signs xor and exponents add. Addition and arbitrary real conversion would require rounding because integral powers of the radix are not closed under addition. Division by a nonzero value could subtract exponents exactly, but no division operation or zero-divisor policy is supplied.

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@[inline]
def FloatLib.Floats.ExecFloat.Logarithmic.ofCode {radix : Numerics.Radix} (code : Formats.Logarithmic.Code radix) :
Logarithmic radix

Wrap a complete logarithmic code without conversion.

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    @[inline]
    def FloatLib.Floats.ExecFloat.Logarithmic.toCode {radix : Numerics.Radix} (value : Logarithmic radix) :
    Formats.Logarithmic.Code radix

    Recover the complete logarithmic code without conversion.

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      @[inline]
      def FloatLib.Floats.ExecFloat.Logarithmic.zero {radix : Numerics.Radix} :
      Logarithmic radix

      Construct the unique zero code.

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        @[inline]
        def FloatLib.Floats.ExecFloat.Logarithmic.ofSignExponent {radix : Numerics.Radix} (negative : Bool) (exponent : ℤ) :
        Logarithmic radix

        Construct the exact value (-1)^negative * radix^exponent.

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          @[inline]
          noncomputable def FloatLib.Floats.ExecFloat.Logarithmic.toReal {radix : Numerics.Radix} (value : Logarithmic radix) :
          ℝ

          Decode a configured logarithmic value to its exact real meaning.

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            @[inline]
            def FloatLib.Floats.ExecFloat.Logarithmic.mul {radix : Numerics.Radix} (left right : Logarithmic radix) :
            Logarithmic radix

            Exact multiplication of configured logarithmic values.

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