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FloatLib.Numerics.IEEEStatus

Shared IEEE exception indicators #

Binary and decimal operations signal the same five exceptions. Their numerical conditions, including tininess detection, belong to each format. The flag record and sticky accumulation do not depend on radix, precision, storage, or rounding direction.

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structure FloatLib.Numerics.IEEEStatus :
Type

The five default exception indicators of IEEE 754-2019 §7.

  • invalid : Bool

    An operand or operation was invalid.

  • divideByZero : Bool

    An exact infinite result was obtained from finite operands.

  • overflow : Bool

    The precision-rounded result exceeded the finite exponent range.

  • underflow : Bool

    A tiny result was inexact.

  • inexact : Bool

    The delivered result differs from the exact result.

Instances For
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    def FloatLib.Numerics.instReprIEEEStatus.repr :
    IEEEStatus → Nat → Std.Format
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      @[instance_reducible]
      instance FloatLib.Numerics.instReprIEEEStatus :
      Repr IEEEStatus
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      def FloatLib.Numerics.instDecidableEqIEEEStatus.decEq (x✝ x✝¹ : IEEEStatus) :
      Decidable (x✝ = x✝¹)
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        @[instance_reducible]
        instance FloatLib.Numerics.instDecidableEqIEEEStatus :
        DecidableEq IEEEStatus
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        @[instance_reducible]
        instance FloatLib.Numerics.instInhabitedIEEEStatus :
        Inhabited IEEEStatus
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        inductive FloatLib.Numerics.IEEEException :
        Type

        The five IEEE floating-point exceptions, individually addressable as flags.

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          @[instance_reducible]
          instance FloatLib.Numerics.instDecidableEqIEEEException :
          DecidableEq IEEEException
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          def FloatLib.Numerics.instReprIEEEException.repr :
          IEEEException → Nat → Std.Format
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            @[instance_reducible]
            instance FloatLib.Numerics.instReprIEEEException :
            Repr IEEEException
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            def FloatLib.Numerics.IEEEStatus.clear :
            IEEEStatus

            No exception was raised.

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              def FloatLib.Numerics.IEEEStatus.union (earlier raised : IEEEStatus) :
              IEEEStatus

              Accumulate exceptions, preserving every flag raised by either computation.

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                def FloatLib.Numerics.IEEEStatus.isSet (flags : IEEEStatus) :
                IEEEException → Bool

                Read one exception flag.

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                  def FloatLib.Numerics.IEEEStatus.ofPredicate (selected : IEEEException → Bool) :
                  IEEEStatus

                  Construct a flag group by specifying its members.

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                    def FloatLib.Numerics.IEEEStatus.singleton (exception : IEEEException) :
                    IEEEStatus

                    A group containing exactly one exception.

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                      def FloatLib.Numerics.IEEEStatus.allFlags :
                      IEEEStatus

                      The group of all five exceptions.

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                        def FloatLib.Numerics.IEEEStatus.raiseFlags (flags group : IEEEStatus) :
                        IEEEStatus

                        Set each flag in a group, preserving all other flags.

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                          def FloatLib.Numerics.IEEEStatus.lowerFlags (flags group : IEEEStatus) :
                          IEEEStatus

                          Clear each flag in a group, preserving all other flags.

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                            def FloatLib.Numerics.IEEEStatus.testFlags (flags group : IEEEStatus) :
                            Bool

                            Whether at least one selected flag is raised.

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                              def FloatLib.Numerics.IEEEStatus.saveAllFlags (flags : IEEEStatus) :
                              IEEEStatus

                              Save all flags as an immutable value.

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                                def FloatLib.Numerics.IEEEStatus.testSavedFlags (saved group : IEEEStatus) :
                                Bool

                                Test a saved snapshot without changing the current environment.

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                                  def FloatLib.Numerics.IEEEStatus.restoreFlags (flags saved group : IEEEStatus) :
                                  IEEEStatus

                                  Restore the selected flags from a saved value, preserving flags outside the group.

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