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Compaq ECQD2KCTE manual Division by Zero, Overflow, Underflow, Inexact

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Table B–3shows the IEEE standard charts. In the charts, the second column is the result when the user signal handler is disabled; the third column is the result when that handler is enabled. The OS completion handler supplies the IEEE default that is specified in the second column. The contents of the Alpha registers contain sufficient information for an enabled user handler to compute the value in the third column.

Table B–3: IEEE Standard Charts

	Exception		User Signal Handler	User Signal Handler
	Exception		Disabled (IEEE Default)	Enabled (Optional)
			Disabled (IEEE Default)	Enabled (Optional)

	Invalid Operation

	(1)	Input signaling NaN	Quiet NaN
	(2)	Mag. subtract Inf.	Quiet NaN
	(3)	0 * Inf.	Quiet NaN
	(4)	0/0 or Inf/Inf	Quiet NaN
	(5) x REM 0 or Inf REM y		Quiet NaN
	(6)	SQRT(negative non-zero)	Quiet NaN
	(7)	Cvt to int(ovfl)	Low-order bits
	(8)	Cvt to int(Inf, NaN)	0
	(9)	Compare unordered	Quiet NaN

	Division by Zero

	x/0, x finite <>0		+/–Inf

	Overflow

	Round nearest		+/–Inf.	Res /2**192 or 1536
	Round to zero		+/–MAX	Res/2**192 or 1536
	Round to –Inf		+MAX/–Inf	Res/2**192 or 1536
	Round to +Inf		+Inf/–MAX	Res/2**192 or 1536

	Underflow

	Underflow		0/denorm	Res2*192 or 1536

	Inexact

	Inexact		Rounded	Res

B–12Alpha Architecture Handbook

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Compaq ECQD2KCTE manual Division by Zero, Overflow, Underflow, Inexact

Contents

Alpha Architecture Handbook October Table of Contents Instruction Formats Page 10.19 Integer Register to Floating-Point Register Move System Architecture and Programming Implications Digital Unix Ieee Floating-Point Conformance Index Figures Tables Xiii Xiv Preface Page Alpha Is a True 64-Bit Architecture ChapterAlpha Approach to Risc Architecture Alpha Is Designed for Very High-Speed ImplementationsAlpha Instructions Include Hints for Achieving Higher Speed Alpha Approach to Byte ManipulationAlpha Approach to Multiprocessor Shared Memory PALcode Alpha’s Very Flexible Privileged Software LibraryData Format Overview Alpha and Programming LanguagesPALcode Instructions Instruction Format OverviewInstruction Overview Integer Operate Instructions Branch InstructionsLoad/Store Instructions Floating-Point Operate Instructions Instruction Set CharacteristicsTerminology and Conventions Unpredictable and Undefined NumberingSecurity Holes Unaligned Ranges and ExtentsAligned and Unaligned Should Be Zero SBZ Must Be Zero MBZRead As Zero RAZ Ignore IGNPage Byte AddressingData Types WordLongword QuadwordVAX Floating-Point Formats FfloatingFfloating Load Exponent Mapping Mapf GfloatingGfloating Register Format DfloatingIeee Floating-Point Formats SFloating Sfloating Load Exponent Mapping Maps Memory RegisterTfloating 13 Tfloating Datum14 Tfloating Register Format XFloating15 Xfloating Datum XFloating Big-Endian FormatsLongword Integer Format in Floating-Point Unit 17 Xfloating Big-Endian DatumQuadword Integer Format in Floating-Point Unit Data Types with No Hardware SupportBig-Endian Addressing Support 23 Little-Endian Byte Addressing14Alpha Architecture Handbook Integer Registers Alpha RegistersProgram Counter Implementation noteFloating-Point Registers Lock RegistersOptional Registers NotationProcessor Cycle Counter PCC Register Memory Prefetch RegistersOperand Value Notation Meaning Operand NotationOperand Notation Meaning Expression Operand Notation MeaningInstruction Operand Notation Operand Access Type NotationOperand Access Type Notation Meaning Operand Name NotationOperand Data Type Notation Meaning OperatorsOperand Data Type Notation Operators MeaningBit concatenation Loadlocked CaseDIV Priorityencode NotPhysicaladdress LTUSoftware Note Instruction FormatsNotation Conventions XORMemory Instruction Format Memory Format Instructions with a Function CodeMemory Format Jump Instructions Branch Instruction FormatOperate Instruction Format Floating-Point Operate Instruction Format Floating-Point Operate Instruction FormatFloating-Point/Integer Register Moves PALcode Instruction FormatFloating-Point Convert Instructions PALcode Instruction Format Page Instruction Set Overview Instruction Type SectionSubsetting Rules Floating-Point SubsetsOpcode Qualifiers Meaning Software Emulation RulesOpcode Qualifiers Memory Integer Load/Store Instructions Memory Integer Load/Store Instructions Mnemonic OperationLoad Address Load Memory Data into Integer Register LDLImplementation Notes Load Unaligned Memory Data into Integer Register Load Memory Data into Integer Register Locked 10Alpha Architecture Handbook Implementation Notes Store Integer Register Data into Memory Conditional Stqc BEQ Hardware/Software Implementation Note Store Integer Register Data into Memory 16Alpha Architecture Handbook Store Unaligned Integer Register Data into Memory Control Instructions Control Instructions Summary Mnemonic OperationJMP BNEBSR JSRConditional Branch Unconditional Branch Jumps Encoding Meaning Integer Arithmetic Instructions Summary Mnemonic Operation Integer Arithmetic InstructionsCount instruction CIX extension implementation note Longword Add AddlS8ADDL Scaled Longword AddS4ADDL Quadword Add AddqS8ADDQ Scaled Quadword AddS4ADDQ Integer Signed Compare Integer Unsigned Compare Count Leading Zero Count Population Count Trailing Zero Longword Multiply MullQuadword Multiply MulqUnsigned Quadword Multiply High Longword Subtract SublS8SUBL Scaled Longword SubtractS4SUBL Quadword Subtract SubqS8SUBQ Scaled Quadword SubtractS4SUBQ Logical and Shift Instructions Logical and Shift Instructions Summary Mnemonic OperationLogical Functions Conditional Move Integer Is exactly equivalent to Shift Logical Shift Arithmetic Byte Manipulation Instructions Instruction Meaning Described in SectionInsqh InswhInslh MskblCompare Byte BEQ LoopTo compare two character strings for greater/equal/less Extract Byte Ldqu Optimized examples Big-endian examples Byte Insert 56Alpha Architecture Handbook Byte Mask Insqh Inswh Sign Extend Zero Bytes Single-Precision Operations Subsets and FaultsFloating-Point Instructions Definitions Alpha finite numberInfinity DenormalDirty zero Non-finite numberSign Exponent Fraction Vax EncodingsTrue zero Meaning FiniteIeee Rounding Modes Rounding ModesVAX Rounding Modes Computational Models VAX Rounding Mode Instruction NotationIeee Rounding Mode Instruction Notation VAX-Format Arithmetic with Precise ExceptionsIEEE-Compliant Arithmetic Without Inexact Exception High-Performance VAX-Format ArithmeticIEEE-Compliant Arithmetic VAX Trapping Modes Trapping ModesHigh-Performance IEEE-Format Arithmetic When /U or /V mode is specified VAX Trapping Modes Summary Trap Mode Notation Meaning Ieee Trapping ModesSummary of Ieee Trapping Modes Trap Mode Notation Meaning SUIArithmetic Trap Completion SVITrap Shadow Length Rules Page Invalid Operation INV Arithmetic Trap Division by Zero DZE Arithmetic Trap Overflow OVF Arithmetic TrapInexact Result INE Arithmetic Trap Ieee Floating-Point Trap Disable BitsUnderflow UNF Arithmetic Trap Integer Overflow IOV Arithmetic TrapFloating-Point Control Register Fpcr Ieee Denormal Control BitsIeee Rounding Mode Selected Floating-Point Control Register Fpcr FormatPage Accessing the Fpcr Software Notes Default Values of the FpcrSaving and Restoring the Fpcr Floating-Point Instruction Function Field Format Floating-Point Instruction Function FieldContents Meaning for Opcodes 1616 SQRTS/SQRTT FNCITOFS/ITOFT Unpredictable Ieee Standard Conversion of NaN and Infinity ValuesPropagating NaN Values Copying NaN ValuesGenerating NaN Values Memory Format Floating-Point Instructions Load Ffloating Load Gfloating Load Sfloating Load Tfloating Store Ffloating Store Gfloating Store Sfloating Store Tfloating Branch Format Floating-Point Instructions FBxx Fa.rq,disp.al Branch format Page Floating-Point Operate Format Instructions Adds AddfAddg IeeeMuls MulfMulg MultCopy Sign Convert Integer to Integer Floating-Point Conditional Move Fcmovne F3,F2,F1 Move from/to Floating-Point Control Register VAX Floating Add Ieee Floating Add Cmpgle VAX Floating CompareCmpgeq CmpgltCmptle Ieee Floating CompareCmpteq CmptltConvert VAX Floating to Integer Convert Integer to VAX Floating Convert VAX Floating to VAX Floating Convert Ieee Floating to Integer Convert Integer to Ieee Floating Convert Ieee SFloating to Ieee TFloating Convert Ieee TFloating to Ieee SFloating VAX Floating Divide Ieee Floating Divide Floating-Point Register to Integer Register Move Integer Register to Floating-Point Register Move Itofs is exactly equivalent to the sequence VAX Floating Multiply Ieee Floating Multiply VAX Floating Square Root Ieee Floating Square Root VAX Floating Subtract Ieee Floating Subtract Miscellaneous Instructions 17 Miscellaneous Instructions Summary Mnemonic OperationArchitecture Mask 134Alpha Architecture Handbook Call Privileged Architecture Library Evict Data Cache Block Implementation Note Exception Barrier Prefetch Data 140Alpha Architecture Handbook Implementation Version Memory Barrier Read Processor Cycle Counter Trap Barrier Write Hint Implementation Note Write Memory Barrier Processor Processor j VAX Compatibility Instructions 18 VAX Compatibility Instructions Summary Mnemonic OperationVAX Compatibility Instructions Multimedia Graphics and Video Support Mnemonic OperationByte and Word Minimum and Maximum Instruction mnemonics Pixel Error Pack Bytes Unpack Bytes Introduction Physical Address Space CharacteristicsCoherency of Memory Access Granularity of Memory Access Software/Hardware NoteWidth of Memory Access Memory-Like and Non-Memory-Like BehaviorHardware/Software Coordination Note Translation Buffers and Virtual CachesCaches and Write Buffers Page Atomic Change of a Single Datum Atomic Update of a Single DatumData Sharing Atomic Update of Data Structures STQ8Alpha Architecture Handbook Ordering Considerations for Shared Data Structures Read/Write Ordering Alpha Shared Memory ModelImplementation Note Definition of Before and After Architectural Definition of Processor Issue SequenceDefinition of Processor Issue Constraints Processor Issue Constraints 1st↓ 2nd → PiIn=4y,b PiRny,b PiWny,b PiMB PiIMBDefinition of Storage Definition of Location Access ConstraintsDefinition of Visibility Definition of Dependence Constraint Definition of Load-Locked and Store-Conditional Litmus Test 1 Impossible Sequence Litmus TestsTimeliness PiPjLitmus Test 2 Impossible Sequence Litmus Test 3 Impossible SequenceLitmus Test 6 Sequence Okay Litmus Test 4 Sequence OkayLitmus Test 5 Sequence Okay Litmus Test 7 Impossible Sequence Litmus Test 8 Impossible SequenceLitmus Test 11 Impossible Sequence Litmus Test 9 Impossible SequenceLitmus Test 10 Sequence Okay Single Processor Data Stream Implied BarriersImplications for Software Single Processor Instruction StreamSee Footnote 1 on Multiprocessor Context Switch First Processor Second ProcessorPage Multiprocessor Send/Receive Interrupt Implications for Memory Mapped I/O Multiple Processors Writing to a Single I/O Device Implications for Hardware Arithmetic Traps DictablePALcode PALcode Instructions and FunctionsPALcode Environment Special Functions Required for PALcodePALcode Replacement PALcode Effects on System CodeRequired PALcode Instructions PALcode Instructions that Require Recognition Mnemonic NameHalt Required PALcode Instructions Mnemonic Type OperationDraina IMBDrain Aborts Callpal DrainaHalt Callpal HaltInstruction Memory Barrier Callpal IMBConsole Subsystem Overview Page Input/Output Overview Page OpenVMS Alpha Unprivileged OpenVMS Alpha PALcodeChms ChmeChmk ChmuInsqhiq InsqhilInsqhilr InsqhiqrInsqtiqr InsqtilrInsqtiq InsquelREI RdpsReadunq RemqhilRemqtilr RemqhiqrRemqtil RemqtiqRscc RemquelRemqueq SwastenLdqp Privileged OpenVMS Alpha PalcodeCflush MfprWtint StqpSwpctx Page Unprivileged Digital Unix PALcode Mnemonic Operation and DescriptionPrivileged Digital Unix PALcode 10-3 10-4Alpha Architecture Handbook Unprivileged Windows NT Alpha PALcode Unprivileged Windows NT Alpha PALcode Instruction SummaryPrivileged Windows NT Alpha PALcode 11-3 11-4Alpha Architecture Handbook 11-5 Page Appendix a Hardware-Software CompactBranch Prediction and Minimizing Branch-Taken Factor Instruction-Stream ConsiderationsInstruction Alignment Figure A-1 Branch-Format BSR and BR Opcodes Instruction Scheduling Factor Data-Stream ConsiderationsImproving I-Stream Density Factor Data Alignment FactorShared Data in Multiple Processors Factor Avoiding Cache/TB Conflicts Factor Figure A-3 Bad Allocation in Cache Sequential Read/Write Factor Prefetching FactorAligned Byte/Word Within Register Memory Accesses Code SequencesDivision 4.1 NOP Byte SwapStylized Code Forms Clear a Register Load Literal4.6 not Register-to-Register MoveNegate BooleansExceptions and Trap Barriers Pseudo-Operations Stylized Code FormsSoftware Considerations A-15 Timing Considerations Atomic Sequences Appendix B Alpha Choices for Ieee Options2Alpha Architecture Handbook Alpha Support for OS Completion Handlers Ieee Floating-Point Control FPC Quadword Figure B-1 Ieee Floating-Point Control FPC QuadwordPage Mapping to Ieee Standard Figure B-2 Ieee Trap Handling Behavior Completion Signal Alpha Instructions Code Handler Table B-2 Ieee Floating-Point Trap Handling User Hardware1MULx Output Exceptions CVTff Output Exceptions Cmptlt Cmptle Input ExceptionsSQRTx Output Exceptions Underflow Division by ZeroOverflow InexactAppendix C Common Architecture Instruction SummaryADDQ/V Table C-2 Common Architecture InstructionsADDL/V 15.0AF Convert Gfloating to quadword MULL/V MULQ/VSUBL/V SUBQ/VIeee Floating-Point Instructions Table C-3 Ieee Floating-Point Instruction Function CodesVAX Floating-Point Instructions Programming NoteIndependent Floating-Point Instructions Opcode SummaryTable C-7 Key to Opcode Summary Symbol Meaning Table C-6 Opcode SummaryCommon Architecture Opcodes in Numerical Order Table C-8 Common Architecture Opcodes in Numerical OrderInstruction Summary C-11 Addt Instruction Summary C-13 OpenVMS Alpha PALcode Instruction Summary Mfprfen MfprasnMfpresp MfpriplMnemonic Opcode Description Digital Unix PALcode Instruction SummaryTable C-12 Digital Unix Privileged PALcode Instructions Windows NT Alpha Instruction Summary Table C-14 Windows NT Alpha Privileged PALcode instructionsWindows NT PALcode Opcodes in Numerical OrderTable C-15 PALcode Opcodes in Numerical Order OpenVMS AlphaWtint 00.003F 00.0063 Table C-16 Required PALcode Opcodes Mnemonic Type Required PALcode OpcodesOpcodes Reserved to PALcode Table C-17 Opcodes Reserved for PALcode MnemonicTable C-18 Opcodes Reserved for Compaq Mnemonic Opcodes Reserved to CompaqUnused Function Code Behavior OPC01 OPC02 OPC03 OPC04 OPC05 OPC06 OPC07Ascii Character Set Table C-19 Ascii Character Set Hex CodeTable D-1 Processor Type Assignments Major Type Minor Type Appendix DProcessor Type Assignments EV3PALcode Variation Assignments Table D-4 Implver Value Assignments Meaning Architecture Mask and Implementation ValuesTable D-3 Amask Bit Assignments Bit Meaning Digital UnixPage Appendix E WaiversDECchip 21264 LDxL/STxC with WH64 Violation Implementation-Specific Functionality DECchip 21064/21066/21068 Performance MonitoringFor the OpenVMS Alpha Operating System Disable performance monitoring Functions and Arguments for the DECchip 21064/21066/21068= PCMUX0 Select desired events muxctlSelect performance monitoring options = PCMUX1Value Description PC0 PC1DECchip 21164/21164PC Performance Monitoring Performance Monitor Interrupt MechanismInput Contents Register Bits Meaning Windows NT Alpha Functions and ArgumentPCSEL0 CTR0CTR1 PCSEL1 OpenVMS Alpha and Digital Unix Functions and ArgumentsModeselect PCSEL2Disable performance monitoring do not reset counters Select desired events MuxselectSelect interrupt frequencies Read the countersOperate on counter MBZ PCSEL1 MBZ PCSEL0MBZ S U P Counters Operate Under These Modes When Bits SetBits Meaning 6310 Table E-13 21164/21164PC Counter 1 PCSEL1 Event Selection Table E-14 21164/21164PC Counter 2 PCSEL2 Event Selection Table E-16 21164 CBOX2 Event Selection Table E-15 21164 CBOX1 Event SelectionValue Meaning Table E-17 21164PC PM0MUX Event Selection Table E-18 21164PC PM1MUX Event Selection3 21264 Performance Monitoring IERCMPCEN0 SEXTPCTR0CTL47PCTR0 PCTR1SL1 Bit value MeaningSelect logging options Enable and write selected counters R17/a1 Bits Meaning Table E-26 21264 Enable and Write Counters for OpenVMS Alpha Page Index Index-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Index-12 Index-13