Advanced Computer Architecture CSE 8383ContentsFloating Point MultiplicationLinear Pipeline for floating-point multiplicationLinear Pipeline for floating-point AdditionCombined Adder and MultiplierReservation Table for MultiplyReservation Table for AdditionNonlinear Pipeline DesignNonlinear Pipeline Design contMul – Mul Collision (launch after 1 cycle)Mul –Mul Collision (lunch after 2 cycles)Mul – Mul Collision (launch after 3 cycles)Collision Vector for Multiply after MultiplyExampleReservation Tables for X & YForbidden LatenciesX after XSlide 19Collision VectorY after YSlide 22Exercise – Find the collision vectorState Diagram for XCyclesComputer Science and EngineeringCopyright by Hesham El-RewiniAdvanced Computer Advanced Computer ArchitectureArchitectureCSE 8383CSE 8383January 31 2006January 31 2006Session 5Session 5Computer Science and EngineeringCopyright by Hesham El-RewiniContentsArithmetic OperationsDesign of Multifunction PipelinesComputer Science and EngineeringCopyright by Hesham El-RewiniFloating Point MultiplicationInputs (Mantissa1, Exponenet1), (Mantissa2, Exponent2)Add the two exponents  Exponent-outMultiple the 2 mantissasNormalize mantissa and adjust exponentRound the product mantissa to a single length mantissa. You may adjust the exponentComputer Science and EngineeringCopyright by Hesham El-RewiniLinear Pipeline for floating-point multiplicationAdd ExponentsMultiply MantissaNormalizeRound Partial ProductsAccumulatorAdd ExponentsNormalizeRoundRenormalizeComputer Science and EngineeringCopyright by Hesham El-RewiniLinear Pipeline for floating-point Addition Partial ShiftAddMantissaSubtract ExponentsFind Leading 1RoundRenormalize Partial ShiftComputer Science and EngineeringCopyright by Hesham El-RewiniCombined Adder and Multiplier Partial ShiftAddMantissaExponentsSubtract / ADDFind Leading 1RoundRenormalize Partial Shift Partial ProductsCABE DFGHComputer Science and EngineeringCopyright by Hesham El-RewiniReservation Table for Multiply1 2 3 4 5 6 7A XB X XC X XD X XE XFGHComputer Science and EngineeringCopyright by Hesham El-RewiniReservation Table for Addition1 2 3 4 5 6 7 8 9A YBC YD YE YF Y YG YH Y YComputer Science and EngineeringCopyright by Hesham El-RewiniNonlinear Pipeline DesignLatencyThe number of clock cycles between two initiations of a pipelineCollisionResource ConflictForbidden LatenciesLatencies that cause collisionsComputer Science and EngineeringCopyright by Hesham El-RewiniNonlinear Pipeline Design contLatency SequenceA sequence of permissible latencies between successive task initiationsLatency CycleA sequence that repeats the same subsequenceCollision vectorC = (Cm, Cm-1, …, C2, C1), m <= n-1n = number of column in reservation tableCi = 1 if latency i causes collision, 0 otherwiseComputer Science and EngineeringCopyright by Hesham El-RewiniMul – Mul Collision (launch after 1 cycle)1 2 3 4 5 6 7A X ZB X X Z ZC X X Z ZD X Z XE X ZFGHComputer Science and EngineeringCopyright by Hesham El-RewiniMul –Mul Collision (lunch after 2 cycles)1 2 3 4 5 6 7A X ZB X X Z ZC X X Z ZD X X ZE XFGHComputer Science and EngineeringCopyright by Hesham El-RewiniMul – Mul Collision (launch after 3 cycles)1 2 3 4 5 6 7A X ZB X X Z ZC X X Z ZD X XE XFGHComputer Science and EngineeringCopyright by Hesham El-RewiniCollision Vector for Multiply after MultiplyForbidden Latencies: 1, 2Collision vector0 0 0 0 1 1  11Maximum forbidden latency = 2  m = 2Computer Science and EngineeringCopyright by Hesham El-RewiniExampleS1S2S3YXComputer Science and EngineeringCopyright by Hesham El-RewiniReservation Tables for X & YX X XX XX X XY YYY Y YS1S2S3S1S2S3Computer Science and EngineeringCopyright by Hesham El-RewiniForbidden LatenciesX after XX after YY after XY after YComputer Science and EngineeringCopyright by Hesham El-RewiniX after XX1 X2 X1 X2 X1X1 X2 X1 X2X1 X2 X1 X2 X1S1S2S3X1 X2 X1 X1X1 X1 X2X1 X1 X1 X2S1S2S352Computer Science and EngineeringCopyright by Hesham El-RewiniX after XX1 X2 X1 X1X1 X1 X2 X2X1 X1 X2 X1S1S2S3S1S2S347X1 X1 X2 X1X1 X1X1 X1 X1Computer Science and EngineeringCopyright by Hesham El-RewiniCollision VectorForbidden Latencies: 2, 4, 5, 7Collision Vector = 1 0 1 1 0 1 0Computer Science and EngineeringCopyright by Hesham El-RewiniY after YY Y YY YY Y Y Y YS1S2S3S1S2S3Y Y YYY Y Y YComputer Science and EngineeringCopyright by Hesham El-RewiniCollision VectorForbidden Latencies: 2, 4Collision Vector = 1 0 1 0Computer Science and EngineeringCopyright by Hesham El-RewiniExercise – Find the collision vector1 2 3 4 5 6 7A X X XB X XC X XD XComputer Science and EngineeringCopyright by Hesham El-RewiniState Diagram for X1 0 1 1 0 1 01 1 1 1 1 1 11 0 1 1 0 1 1368+68+8+3*1*Computer Science and EngineeringCopyright by Hesham El-RewiniCyclesSimple cycles  each state appears only once (3), (6), (8), (1, 8), (3, 8), and (6,8)Greedy Cycles  simple cycles whose edges are all made with minimum latencies from their respective starting states (1,8), (3)  one of them is