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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.

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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.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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