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5HFDOO6RIWZDUH3LSHOLQLQJ 5HFDOO6RIWZDUH3LSHOLQLQJ([DPSOH %HIRUH8QUROOHGWLPHV After: Software Pipelined ‡ 2EVHUYDWLRQLILWHUDWLRQVIURPORRSVDUHLQGHSHQGHQW  LD F0,0(R1) 1 SD 0(R1),F4 ; Stores M[i] WKHQFDQJHWPRUH,/3E\WDNLQJLQVWUXFWLRQVIURP  ADDD F4,F0,F2 2 ADDD F4,F0,F2 ; Adds to M[i-1] GLIIHUHQW LWHUDWLRQV  SD 0(R1),F4 3 LD F0,-16(R1); Loads M[i-2]  LD F6,-8(R1) 4 SUBI R1,R1,#8 ‡ 6RIWZDUHSLSHOLQLQJUHRUJDQL]HVORRSVVRWKDWHDFK  ADDD F8,F6,F2 5 BNEZ R1,LOOP LWHUDWLRQLVPDGHIURPLQVWUXFWLRQVFKRVHQIURP  SD -8(R1),F8 GLIIHUHQWLWHUDWLRQVRIWKHRULJLQDOORRS 7RPDVXOR LQ  LD F10,-16(R1) 6:  ADDD F12,F10,F2 SW Pipeline Iteration  SD -16(R1),F12 0 Iteration  1 Iteration SUBI R1,R1,#24 2 Iteration  BNEZ R1,LOOP Time 3 Iteration 4 Loop Unrolled • Symbolic Loop Unrolling

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'$;3< < D ;< 0HPRU\RSHUDWLRQV Assuming vectors X, Y LD F0,a ;load scalar a are length 64 LV V1,Rx ;load vector X ‡ /RDGVWRUHRSHUDWLRQVPRYHJURXSVRIGDWD Scalar vs. Vector MULTS V2,F0,V1 ;vector-scalar mult. EHWZHHQUHJLVWHUVDQGPHPRU\ LV V3,Ry ;load vector Y ‡ 7KUHHW\SHVRIDGGUHVVLQJ ADDV V4,V2,V3 ;add ² 8QLWVWULGH LD F0,a SV Ry,V4 ;store the result ª )DVWHVW ADDI R4,Rx,#512 ;last address to load 578 (2+9*64) vs. ² 1RQXQLW FRQVWDQW VWULGH loop: LD F2, 0(Rx) ;load X(i) 321 (1+5*64) ops (1.8X) ² ,QGH[HG JDWKHUVFDWWHU MULTD F2,F0,F2 ;a*X(i) 578 (2+9*64) vs. ª 9HFWRUHTXLYDOHQWRIUHJLVWHULQGLUHFW LD F4, 0(Ry) ;load Y(i) 6 instructions (96X) ª *RRGIRUVSDUVHDUUD\VRIGDWD ADDD F4,F2, F4 ;a*X(i) + Y(i) ª ,QFUHDVHVQXPEHURISURJUDPVWKDWYHFWRUL]H SD F4 ,0(Ry) ;store into Y(i) 64 operation vectors + ADDI Rx,Rx,#8 ;increment index to X no loop overhead ADDI Ry,Ry,#8 ;increment index to Y also 64X fewer pipeline SUB R20,R4,Rx ;compute bound hazards &6.XELDWRZLF] BNZ R20,loop ;check if done &6.XELDWRZLF]   /HF  32 /HF  ([DPSOH9HFWRU0DFKLQHV 9HFWRU/LQSDFN 3HUIRUPDQFH 0)/236

Machine Year Clock Regs Elements FUs LSUs Machine Year Clock 100x100 1kx1k Peak(Procs) Cray 1 1976 80 MHz 8 64 6 1 Cray 1 1976 80 MHz 12 110 160(1) Cray XMP 1983 120 MHz 8 64 8 2 L, 1 S Cray XMP 1983 120 MHz 121 218 940(4) Cray YMP 1988 166 MHz 8 64 8 2 L, 1 S Cray YMP 1988 166 MHz 150 307 2,667(8) Cray C-90 1991 240 MHz 8 128 8 4 Cray C-90 1991 240 MHz 387 902 15,238(16) Cray T-90 1996 455 MHz 8 128 8 4 Cray T-90 1996 455 MHz 705 1603 57,600(32) Conv. C-1 1984 10 MHz 8 128 4 1 Conv. C-1 1984 10 MHz 3 -- 20(1) Conv. C-4 1994 133 MHz 16 128 3 1 Conv. C-4 1994 135 MHz 160 2531 3240(4) Fuj. VP200 1982 133 MHz 8-256 32-1024 3 2 Fuj. VP200 1982 133 MHz 18 422 533(1) Fuj. VP300 1996 100 MHz 8-256 32-1024 3 2 NEC SX/2 1984 166 MHz 43 885 1300(1) NEC SX/2 1984 160 MHz 8+8K 256+var 16 8 NEC SX/3 1995 400 MHz 368 2757 25,600(4)

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