$6\mathrm{.}16\mathrm{.}4$: $[10].$

help$\_$outline

Consider the following piece of C code:

for $($j $=2$; j $<=1000$; j$++)$ D$[$j$]=$ D$[$j $1]+$ D$[$j $2]$;

The ARMv$8$ code corresponding to the above fragment is:

MOV X$10$ #$8000$ ADD X$2,$ X$0,$ X$10$ ADDI X$1,$ X$0,$ #$16$ LOOP: LDUR D$0,[$X$1,$ #$-16]$ LDUR D$2,[$X$1,$ #$-8]$ FADDD D$4,$ D$0,$ D$2$ STUR D$4,[$X$1,$ #$0]$ ADDI X$1,$ X$1,$ #$8$ CMP X$1,$ X$2$ B$.$LE LOOP

The latency of an instruction is the number of cycles that must come between that instruction and an instruction using the result. Assume floating point instructions have the following associated latencies $($in cycles$)$:

$($a$)$

How many cycles does it take to execute this code?

$($b$)$

When an instruction in a later iteration of a loop depends upon a data value produced in an earlier iteration of the same loop, we say that there is a loop$-$carried dependence between iterations of the loop. Identify the loop$-$carried dependences in the above code. Identify the dependent program variable and assembly$-$level registers. You can ignore the loop induction variable j$.$instruction.$)$

$($c$)$

Rewrite the code by using registers to carry the data between iterations of the loop $($as opposed to storing and re$-$loading the data from main memory$).$ Show where this code stalls and calculate the number of cycles required to execute.