TorchLean API

Docs HomeInstallationGuideExamplesGraphsTools

FloatLib.Floats.Formats.BinaryInterchange.Operations.Compare.Predicates.Runtime

Quiet and signaling binary comparisons #

IEEE 754-2019 Tables 5.1–5.2 specify 22 comparison operations. Their truth values depend on exact numerical comparison, with NaNs unordered and signed zeros equal. Quiet operations raise invalid for signaling NaNs; signaling operations do so for any NaN. Neither family raises any of the other four exceptions.

source
@[reducible, inline]
abbrev FloatLib.Floats.Formats.BinaryInterchange.Model.Comparison.Predicate :
Type

Shared IEEE truth sets, independent of the operand format.

Instances For
    source
    @[reducible, inline]
    abbrev FloatLib.Floats.Formats.BinaryInterchange.Model.Comparison.Result :
    Type

    A Boolean comparison result paired with its exception indicators.

    Instances For
      source
      def FloatLib.Floats.Formats.BinaryInterchange.Model.Comparison.quiet {fmt : FloatFormat} (predicate : Predicate) (x y : Model fmt) :
      Result

      Evaluate a quiet predicate; only signaling NaNs raise invalid.

      Instances For
        source
        def FloatLib.Floats.Formats.BinaryInterchange.Model.Comparison.signaling {fmt : FloatFormat} (predicate : Predicate) (x y : Model fmt) :
        Result

        Evaluate a signaling predicate; either kind of NaN raises invalid.

        Instances For
          source
          def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietEqual {fmt : FloatFormat} (x y : Model fmt) :
          Comparison.Result

          Quiet equality, equating signed zeros.

          Instances For
            source
            def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietNotEqual {fmt : FloatFormat} (x y : Model fmt) :
            Comparison.Result

            Quiet inequality, including unordered operands.

            Instances For
              source
              def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietGreater {fmt : FloatFormat} (x y : Model fmt) :
              Comparison.Result

              Quiet greater-than comparison.

              Instances For
                source
                def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietGreaterEqual {fmt : FloatFormat} (x y : Model fmt) :
                Comparison.Result

                Quiet greater-than-or-equal comparison.

                Instances For
                  source
                  def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietLess {fmt : FloatFormat} (x y : Model fmt) :
                  Comparison.Result

                  Quiet less-than comparison.

                  Instances For
                    source
                    def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietLessEqual {fmt : FloatFormat} (x y : Model fmt) :
                    Comparison.Result

                    Quiet less-than-or-equal comparison.

                    Instances For
                      source
                      def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietUnordered {fmt : FloatFormat} (x y : Model fmt) :
                      Comparison.Result

                      Quiet test for unordered operands.

                      Instances For
                        source
                        def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietOrdered {fmt : FloatFormat} (x y : Model fmt) :
                        Comparison.Result

                        Quiet test for ordered operands.

                        Instances For
                          source
                          def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietLessUnordered {fmt : FloatFormat} (x y : Model fmt) :
                          Comparison.Result

                          Quiet less-than-or-unordered comparison.

                          Instances For
                            source
                            def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietNotGreater {fmt : FloatFormat} (x y : Model fmt) :
                            Comparison.Result

                            Quiet complement of greater-than.

                            Instances For
                              source
                              def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietNotLess {fmt : FloatFormat} (x y : Model fmt) :
                              Comparison.Result

                              Quiet complement of less-than.

                              Instances For
                                source
                                def FloatLib.Floats.Formats.BinaryInterchange.Model.compareQuietGreaterUnordered {fmt : FloatFormat} (x y : Model fmt) :
                                Comparison.Result

                                Quiet greater-than-or-unordered comparison.

                                Instances For
                                  source
                                  def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingEqual {fmt : FloatFormat} (x y : Model fmt) :
                                  Comparison.Result

                                  Signaling equality.

                                  Instances For
                                    source
                                    def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingNotEqual {fmt : FloatFormat} (x y : Model fmt) :
                                    Comparison.Result

                                    Signaling inequality, including unordered operands.

                                    Instances For
                                      source
                                      def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingGreater {fmt : FloatFormat} (x y : Model fmt) :
                                      Comparison.Result

                                      Signaling greater-than comparison.

                                      Instances For
                                        source
                                        def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingGreaterEqual {fmt : FloatFormat} (x y : Model fmt) :
                                        Comparison.Result

                                        Signaling greater-than-or-equal comparison.

                                        Instances For
                                          source
                                          def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingLess {fmt : FloatFormat} (x y : Model fmt) :
                                          Comparison.Result

                                          Signaling less-than comparison.

                                          Instances For
                                            source
                                            def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingLessEqual {fmt : FloatFormat} (x y : Model fmt) :
                                            Comparison.Result

                                            Signaling less-than-or-equal comparison.

                                            Instances For
                                              source
                                              def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingNotGreater {fmt : FloatFormat} (x y : Model fmt) :
                                              Comparison.Result

                                              Signaling complement of greater-than.

                                              Instances For
                                                source
                                                def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingNotLess {fmt : FloatFormat} (x y : Model fmt) :
                                                Comparison.Result

                                                Signaling complement of less-than.

                                                Instances For
                                                  source
                                                  def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingLessUnordered {fmt : FloatFormat} (x y : Model fmt) :
                                                  Comparison.Result

                                                  Signaling less-than-or-unordered comparison.

                                                  Instances For
                                                    source
                                                    def FloatLib.Floats.Formats.BinaryInterchange.Model.compareSignalingGreaterUnordered {fmt : FloatFormat} (x y : Model fmt) :
                                                    Comparison.Result

                                                    Signaling greater-than-or-unordered comparison.

                                                    Instances For