AMD 250 manual Fadd, 147

25112 Rev. 3.06 September 2005 Software Optimization Guide for AMD64 Processors

Without loop unrolling, this is the equivalent assembly-language code:

mov ecx, MAX_LENGTH mov eax, OFFSET a mov ebx, OFFSET b

add_loop:

fld	QWORD PTR [eax]
fadd	QWORD PTR [ebx]
fstp	QWORD PTR [eax]
add	eax, 8
add	ebx, 8
dec	ecx
jnz	add_loop

;Initialize counter.

;Load address of array a into EAX.

;Load address of array b into EBX.

;Push object pointed to by EAX onto the FP stack.

;Add object pointed to by EBX to ST(0).

;Copy ST(0) to object pointed to by EAX; pop ST(0).

;Point to next element of array a.

;Point to next element of array b.

;Decrement counter.

;If elements remain, then jump.

The rolled loop consists of seven instructions. AMD Athlon 64 and AMD Opteron processors can decode and retire as many as three instructions per cycle, so it cannot execute faster than three iterations in seven cycles (3/7 of a floating-point add per cycle). However, the pipelined floating-point adder allows one add every cycle.

3 instructions	x	iteration	1 FADD	=	3 FADDs	= 0.429 FADDs		cycle
cycle		7 instructionsxiteration			----------------------7 cycles		⁄
--------------------------------		--------------------------------	----------------------

After partial loop unrolling using an unroll factor of two, the new code creates a potential end case that must be handled outside the loop:

mov ecx, MAX_LENGTH mov eax, OFFSET a mov ebx, OFFSET b

shr ecx, 1 jnc add_loop

;Handle the end case. fld QWORD PTR [eax] fadd QWORD PTR [ebx] fstp QWORD PTR [eax] add eax, 8

add ebx, 8

add_loop:

fld	QWORD PTR [eax]
fadd	QWORD PTR [ebx]
fstp	QWORD PTR [eax]
fld	QWORD PTR [eax+8]
fadd	QWORD PTR [ebx+8]
fstp	QWORD PTR [eax+8]
add	eax, 16
add	ebx, 16
dec	ecx
jnz	add_loop

;Initialize counter.

;Load address of array a into EAX.

;Load address of array b into EBX.

;Divide counter by 2 (the unroll factor).

;If original counter was even, then jump.

;Push object pointed to by EAX onto the FP stack.

;Add object pointed to by EBX to ST(0).

;Copy ST(0) to object pointed to by EAX; pop ST(0).

;Point to next element of array a.

;Point to next element of array b.

;Push object pointed to by EAX onto the FP stack.

;Add object pointed to by EBX to ST(0).

;Copy ST(0) to object pointed to by EAX; pop ST(0).

;Repeat for next element.

;Point to next element of array a.

;Point to next element of array b.

;Decrement counter.

;If elements remain, then jump.

Chapter 7 Scheduling Optimizations 147