arm*_*ndo 3 fortran simd openmp
我正在学习如何在 OpenMP/Fortran 中使用 SIMD 指令。我写了简单的代码：
program loop
implicit none
integer :: i,j
real*8 :: x
x = 0.0
do i=1,10000
do j=1,10000000
x = x + 1.0/(1.0*i)
enddo
enddo
print*, x
end program loop
当我编译这段代码并运行它时，我得到：
ifort -O3 -vec-report3 -xhost loop_simd.f90
loop_simd.f90(10): (col. 12) remark: LOOP WAS VECTORIZED
loop_simd.f90(9): (col. 7) remark: loop was not vectorized: not inner loop
time ./a.out
97876060.8355515
real 0m8.940s
user 0m8.937s
sys 0m0.005s
我做了编译器关于“非内循环”的建议，并添加了一个 SIMD collapse(2) 指令：
program loop
implicit none
integer :: i,j
real*8 :: x
x = 0.0
!$omp simd collapse(2) reduction(+:x)
do i=1,10000
do j=1,10000000
x = x + 1.0/(1.0*i)
enddo
enddo
print*, x
end program loop
然后我再次编译并运行代码，得到以下输出：
ifort -O3 -vec-report3 -openmp -xhost loop_simd.f90
loop_simd.f90(8): (col. 7) remark: OpenMP SIMD LOOP WAS VECTORIZED
time ./a.out
97876054.9903757
real 0m26.535s
user 0m26.540s
sys 0m0.003s
我不知道为什么 SIMD 会导致性能下降？什么时候 SIMD 会比标准 Fortran 代码更好？
.section .text
.LNDBG_TX:
# mark_description "Intel(R) Fortran Intel(R) 64 Compiler XE for applications running on Intel(R) 64, Version 14.0.2.144 Build 2";
# mark_description "0140120";
# mark_description "-O3 -vec-report3 -openmp -xhost -S";
.file "loop_simd.f90"
.text
..TXTST0:
L__routine_start_MAIN___0:
# -- Begin MAIN__
# mark_begin;
.align 16,0x90
.globl MAIN__
MAIN__:
..B1.1: # Preds ..B1.0
..___tag_value_MAIN__.1: #1.9
..LN0:
.file 1 "loop_simd.f90"
.loc 1 1 is_stmt 1
pushq %rbp #1.9
..___tag_value_MAIN__.3: #
..LN1:
movq %rsp, %rbp #1.9
..___tag_value_MAIN__.4: #
..LN2:
andq $-128, %rsp #1.9
..LN3:
subq $128, %rsp #1.9
..LN4:
movq $0x0000117fe, %rsi #1.9
..LN5:
movl $3, %edi #1.9
..LN6:
call __intel_new_feature_proc_init #1.9
..LN7:
# LOE rbx r12 r13 r14 r15
..B1.12: # Preds ..B1.1
..LN8:
vstmxcsr (%rsp) #1.9
..LN9:
movl $.2.3_2_kmpc_loc_struct_pack.1, %edi #1.9
..LN10:
xorl %esi, %esi #1.9
..LN11:
orl $32832, (%rsp) #1.9
..LN12:
xorl %eax, %eax #1.9
..LN13:
vldmxcsr (%rsp) #1.9
..___tag_value_MAIN__.6: #1.9
..LN14:
call __kmpc_begin #1.9
..___tag_value_MAIN__.7: #
..LN15:
# LOE rbx r12 r13 r14 r15
..B1.2: # Preds ..B1.12
..LN16:
movl $__NLITPACK_0.0.1, %edi #1.9
..LN17:
call for_set_reentrancy #1.9
..LN18:
# LOE rbx r12 r13 r14 r15
..B1.3: # Preds ..B1.2
..LN19:
.loc 1 8 is_stmt 1
movl $4, %eax #8.7
..LN20:
.loc 1 6 is_stmt 1
vxorpd %ymm2, %ymm2, %ymm2 #6.7
..LN21:
.loc 1 8 is_stmt 1
vmovd %eax, %xmm0 #8.7
..LN22:
xorl %eax, %eax #8.7
..LN23:
vpshufd $0, %xmm0, %xmm1 #8.7
..LN24:
vmovdqu .L_2il0floatpacket.19(%rip), %xmm0 #8.7
..LN25:
# LOE rbx r12 r13 r14 r15 eax xmm0 xmm1 ymm2
..B1.4: # Preds ..B1.6 ..B1.3
..LN26:
.loc 1 11 is_stmt 1
vcvtdq2ps %xmm0, %xmm3 #11.34
..LN27:
vrcpps %xmm3, %xmm5 #11.28
..LN28:
vmulps %xmm3, %xmm5, %xmm4 #11.28
..LN29:
vaddps %xmm5, %xmm5, %xmm6 #11.28
..LN30:
vmulps %xmm5, %xmm4, %xmm7 #11.28
..LN31:
.loc 1 10 is_stmt 1
xorl %edx, %edx #10.12
..LN32:
.loc 1 11 is_stmt 1
vsubps %xmm7, %xmm6, %xmm8 #11.28
..LN33:
vcvtps2pd %xmm8, %ymm3 #11.28
..LN34:
# LOE rbx r12 r13 r14 r15 eax edx xmm0 xmm1 ymm2 ymm3
..B1.5: # Preds ..B1.5 ..B1.4
..LN35:
.loc 1 10 is_stmt 1
incl %edx #10.12
..LN36:
.loc 1 11 is_stmt 1
vaddpd %ymm3, %ymm2, %ymm2 #11.17
..LN37:
.loc 1 10 is_stmt 1
cmpl $10000000, %edx #10.12
..LN38:
jb ..B1.5 # Prob 99% #10.12
..LN39:
# LOE rbx r12 r13 r14 r15 eax edx xmm0 xmm1 ymm2 ymm3
..B1.6: # Preds ..B1.5
..LN40:
.loc 1 8 is_stmt 1
addl $4, %eax #8.7
..LN41:
.loc 1 10 is_stmt 1
vpaddd %xmm1, %xmm0, %xmm0 #10.12
..LN42:
.loc 1 8 is_stmt 1
cmpl $10000, %eax #8.7
..LN43:
jb ..B1.4 # Prob 66% #8.7
..LN44:
# LOE rbx r12 r13 r14 r15 eax xmm0 xmm1 ymm2
..B1.7: # Preds ..B1.6
..LN45:
.loc 1 6 is_stmt 1
..LN46:
.loc 1 15 is_stmt 1
lea (%rsp), %rdi #15.7
..LN47:
.loc 1 6 is_stmt 1
vextractf128 $1, %ymm2, %xmm0 #6.7
..LN48:
.loc 1 15 is_stmt 1
movl $-1, %esi #15.7
..LN49:
.loc 1 6 is_stmt 1
vaddpd %xmm0, %xmm2, %xmm1 #6.7
..LN50:
vunpckhpd %xmm1, %xmm1, %xmm3 #6.7
..LN51:
.loc 1 15 is_stmt 1
lea 64(%rsp), %r8 #15.7
..LN52:
movq $0x1208384ff00, %rdx #15.7
..LN53:
movl $__STRLITPACK_0.0.1, %ecx #15.7
..LN54:
xorl %eax, %eax #15.7
..LN55:
.loc 1 6 is_stmt 1
vaddsd %xmm3, %xmm1, %xmm4 #6.7
..LN56:
.loc 1 15 is_stmt 1
vmovsd %xmm4, 64(%rsp) #15.7
..LN57:
movq $0, (%rsp) #15.7
..LN58:
vzeroupper #15.7
..LN59:
call for_write_seq_lis #15.7
..LN60:
# LOE rbx r12 r13 r14 r15
..B1.8: # Preds ..B1.7
..LN61:
.loc 1 18 is_stmt 1
movl $.2.3_2_kmpc_loc_struct_pack.12, %edi #18.1
..LN62:
xorl %eax, %eax #18.1
..___tag_value_MAIN__.8: #18.1
..LN63:
call __kmpc_end #18.1
..___tag_value_MAIN__.9: #
..LN64:
# LOE rbx r12 r13 r14 r15
..B1.9: # Preds ..B1.8
..LN65:
movl $1, %eax #18.1
..LN66:
movq %rbp, %rsp #18.1
..LN67:
popq %rbp #18.1
..___tag_value_MAIN__.10: #
..LN68:
ret #18.1
.align 16,0x90
..___tag_value_MAIN__.12: #
..LN69:
# LOE
..LN70:
# mark_end;
.type MAIN__,@function
.size MAIN__,.-MAIN__
..LNMAIN__.71:
.LNMAIN__:
.data
.align 4
.align 4
.2.3_2_kmpc_loc_struct_pack.1:
.long 0
.long 2
.long 0
.long 0
.quad .2.3_2__kmpc_loc_pack.0
.align 4
.2.3_2__kmpc_loc_pack.0:
.byte 59
.byte 117
.byte 110
.byte 107
.byte 110
.byte 111
.byte 119
.byte 110
.byte 59
.byte 77
.byte 65
.byte 73
.byte 78
.byte 95
.byte 95
.byte 59
.byte 49
.byte 59
.byte 49
.byte 59
.byte 59
.space 3, 0x00 # pad
.align 4
.2.3_2_kmpc_loc_struct_pack.12:
.long 0
.long 2
.long 0
.long 0
.quad .2.3_2__kmpc_loc_pack.11
.align 4
.2.3_2__kmpc_loc_pack.11:
.byte 59
.byte 117
.byte 110
.byte 107
.byte 110
.byte 111
.byte 119
.byte 110
.byte 59
.byte 77
.byte 65
.byte 73
.byte 78
.byte 95
.byte 95
.byte 59
.byte 49
.byte 56
.byte 59
.byte 49
.byte 56
.byte 59
.byte 59
.section .rodata, "a"
.align 16
.align 8
__NLITPACK_0.0.1:
.long 0x00000002,0x00000000
.align 4
__STRLITPACK_0.0.1:
.byte 48
.byte 1
.byte 1
.byte 0
.byte 0
.data
# -- End MAIN__
.section .rodata, "a"
.space 3, 0x00 # pad
.align 16
.L_2il0floatpacket.19:
.long 0x00000001,0x00000002,0x00000003,0x00000004
.type .L_2il0floatpacket.19,@object
.size .L_2il0floatpacket.19,16
.align 16
.L_2il0floatpacket.20:
.long 0x3f800000,0x3f800000,0x3f800000,0x3f800000
.type .L_2il0floatpacket.20,@object
.size .L_2il0floatpacket.20,16
.data
.section .note.GNU-stack, ""
# End
非 openmp 代码的 ASM 输出
.section .text
.LNDBG_TX:
# mark_description "Intel(R) Fortran Intel(R) 64 Compiler XE for applications running on Intel(R) 64, Version 14.0.2.144 Build 2";
# mark_description "0140120";
# mark_description "-O3 -vec-report3 -xhost -S";
.file "loop_simd.f90"
.text
..TXTST0:
L__routine_start_MAIN___0:
# -- Begin MAIN__
# mark_begin;
.align 16,0x90
.globl MAIN__
MAIN__:
..B1.1: # Preds ..B1.0
..___tag_value_MAIN__.1: #1.9
..LN0:
.file 1 "loop_simd.f90"
.loc 1 1 is_stmt 1
pushq %rbp #1.9
..___tag_value_MAIN__.3: #
..LN1:
movq %rsp, %rbp #1.9
..___tag_value_MAIN__.4: #
..LN2:
andq $-128, %rsp #1.9
..LN3:
subq $128, %rsp #1.9
..LN4:
movq $0x0000117fe, %rsi #1.9
..LN5:
movl $3, %edi #1.9
..LN6:
call __intel_new_feature_proc_init #1.9
..LN7:
# LOE rbx r12 r13 r14 r15
..B1.10: # Preds ..B1.1
..LN8:
vstmxcsr (%rsp) #1.9
..LN9:
movl $__NLITPACK_0.0.1, %edi #1.9
..LN10:
orl $32832, (%rsp) #1.9
..LN11:
vldmxcsr (%rsp) #1.9
..LN12:
call for_set_reentrancy #1.9
..LN13:
# LOE rbx r12 r13 r14 r15
..B1.2: # Preds ..B1.10
..LN14:
.loc 1 6 is_stmt 1
..LN15:
.loc 1 11 is_stmt 1
vmovss .L_2il0floatpacket.0(%rip), %xmm6 #11.28
..LN16:
.loc 1 9 is_stmt 1
xorl %eax, %eax #9.7
..LN17:
.loc 1 6 is_stmt 1
vxorpd %ymm8, %ymm8, %ymm8 #6.7
..LN18:
vmovapd %ymm8, %ymm7 #6.7
..LN19:
vmovapd %ymm8, %ymm0 #6.7
..LN20:
vmovapd %ymm8, %ymm1 #6.7
..LN21:
vmovapd %ymm8, %ymm2 #6.7
..LN22:
vmovapd %ymm8, %ymm3 #6.7
..LN23:
vmovapd %ymm8, %ymm4 #6.7
..LN24:
vmovapd %ymm8, %ymm5 #6.7
..LN25:
# LOE rbx r12 r13 r14 r15 eax xmm6 ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm7 ymm8
..B1.3: # Preds ..B1.5 ..B1.2
..LN26:
incl %eax #
..LN27:
.loc 1 11 is_stmt 1
vxorps %xmm9, %xmm9, %xmm9 #11.28
..LN28:
vcvtsi2ss %eax, %xmm9, %xmm9 #11.28
..LN29:
vdivss %xmm9, %xmm6, %xmm10 #11.28
..LN30:
vcvtss2sd %xmm10, %xmm10, %xmm10 #11.28
..LN31:
vmovddup %xmm10, %xmm11 #11.28
..LN32:
.loc 1 10 is_stmt 1
xorl %edx, %edx #10.12
..LN33:
.loc 1 11 is_stmt 1
vinsertf128 $1, %xmm11, %ymm11, %ymm9 #11.28
..LN34:
# LOE rbx r12 r13 r14 r15 eax edx xmm6 ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm7 ymm8 ymm9
..B1.4: # Preds ..B1.4 ..B1.3
..LN35:
.loc 1 10 is_stmt 1
addl $32, %edx #10.12
..LN36:
.loc 1 11 is_stmt 1
vaddpd %ymm9, %ymm8, %ymm8 #11.17
..LN37:
vaddpd %ymm7, %ymm9, %ymm7 #11.17
..LN38:
vaddpd %ymm0, %ymm9, %ymm0 #11.17
..LN39:
vaddpd %ymm1, %ymm9, %ymm1 #11.17
..LN40:
vaddpd %ymm2, %ymm9, %ymm2 #11.17
..LN41:
vaddpd %ymm3, %ymm9, %ymm3 #11.17
..LN42:
vaddpd %ymm4, %ymm9, %ymm4 #11.17
..LN43:
vaddpd %ymm5, %ymm9, %ymm5 #11.17
..LN44:
.loc 1 10 is_stmt 1
cmpl $10000000, %edx #10.12
..LN45:
jb ..B1.4 # Prob 99% #10.12
..LN46:
# LOE rbx r12 r13 r14 r15 eax edx xmm6 ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm7 ymm8 ymm9
..B1.5: # Preds ..B1.4
..LN47:
.loc 1 9 is_stmt 1
cmpl $10000, %eax #9.7
..LN48:
jb ..B1.3 # Prob 66% #9.7
..LN49:
# LOE rbx r12 r13 r14 r15 eax xmm6 ymm0 ymm1 ymm2 ymm3 ymm4 ymm5 ymm7 ymm8
..B1.6: # Preds ..B1.5
..LN50:
.loc 1 6 is_stmt 1
vaddpd %ymm7, %ymm8, %ymm6 #6.7
..LN51:
.loc 1 15 is_stmt 1
lea (%rsp), %rdi #15.7
..LN52:
.loc 1 6 is_stmt 1
vaddpd %ymm1, %ymm0, %ymm0 #6.7
..LN53:
vaddpd %ymm3, %ymm2, %ymm1 #6.7
..LN54:
vaddpd %ymm5, %ymm4, %ymm2 #6.7
..LN55:
vaddpd %ymm0, %ymm6, %ymm3 #6.7
..LN56:
vaddpd %ymm2, %ymm1, %ymm4 #6.7
..LN57:
vaddpd %ymm4, %ymm3, %ymm5 #6.7
..LN58:
.loc 1 15 is_stmt 1
movl $-1, %esi #15.7
..LN59:
movq $0x1208384ff00, %rdx #15.7
..LN60:
movl $__STRLITPACK_0.0.1, %ecx #15.7
..LN61:
xorl %eax, %eax #15.7
..LN62:
lea 64(%rsp), %r8 #15.7
..LN63:
movq $0, (%rsp) #15.7
..LN64:
.loc 1 6 is_stmt 1
vextractf128 $1, %ymm5, %xmm7 #6.7
..LN65:
vaddpd %xmm7, %xmm5, %xmm8 #6.7
..LN66:
vunpckhpd %xmm8, %xmm8, %xmm9 #6.7
..LN67:
vaddsd %xmm9, %xmm8, %xmm10 #6.7
..LN68:
.loc 1 15 is_stmt 1
vmovsd %xmm10, 64(%rsp) #15.7
..LN69:
vzeroupper #15.7
..LN70:
call for_write_seq_lis #15.7
..LN71:
# LOE rbx r12 r13 r14 r15
..B1.7: # Preds ..B1.6
..LN72:
.loc 1 18 is_stmt 1
movl $1, %eax #18.1
..LN73:
movq %rbp, %rsp #18.1
..LN74:
popq %rbp #18.1
..___tag_value_MAIN__.6: #
..LN75:
ret #18.1
.align 16,0x90
..___tag_value_MAIN__.8: #
..LN76:
# LOE
..LN77:
# mark_end;
.type MAIN__,@function
.size MAIN__,.-MAIN__
..LNMAIN__.78:
.LNMAIN__:
.section .rodata, "a"
.align 8
.align 8
__NLITPACK_0.0.1:
.long 0x00000000,0x00000000
.align 4
__STRLITPACK_0.0.1:
.byte 48
.byte 1
.byte 1
.byte 0
.byte 0
.data
# -- End MAIN__
.section .rodata, "a"
.space 3, 0x00 # pad
.align 4
.L_2il0floatpacket.0:
.long 0x3f800000
.type .L_2il0floatpacket.0,@object
.size .L_2il0floatpacket.0,4
.data
.section .note.GNU-stack, ""
# End
使用 OpenMP，Ifort 使用 SIMD 来矢量化外循环（over i），所以基本上所有的时间都花在了做
## set up ymm3 with 4 copies of 1.0/(1.0*i),
# and j = %edx = 0
..B1.5: do {
incl %edx # j++
vaddpd %ymm3, %ymm2, %ymm2 # ymm3 + ymm2 => ymm2
cmpl $10000000, %edx } while(j<10000000);
jb ..B1.5 # Prob 99%
10M 的迭代vaddpd将完全支配循环外的所有成本，所以重要的是这个内循环执行 10k / 4 次。（注意add $4, %eax/ cmp $10000, %eax/ jb，与内循环之前的分支目标回）。
由于它仅使用单个累加器，因此吞吐量受到循环携带依赖性（3 个周期）的限制。
它仍然在做全部的工作，而不是优化掉任何循环。
它像 with 一样自动矢量化#pragma openmp，但使用多个累加器来增加并行度。多个添加指令可以同时进行，而不是每个都依赖于前一个。
内循环的设置非常相似，然后内循环是：
## set up ymm3 with 4 copies of 1.0/(1.0*i),
..B1.4:
addl $32, %edx #10.12
vaddpd %ymm9, %ymm8, %ymm8 # ymm8 + ymm9 => ymm8
vaddpd %ymm7, %ymm9, %ymm7 # ymm7 + ymm9 => ymm7
vaddpd %ymm0, %ymm9, %ymm0 # ymm0 + ymm9 => ymm0
vaddpd %ymm1, %ymm9, %ymm1 # ...
vaddpd %ymm2, %ymm9, %ymm2
vaddpd %ymm3, %ymm9, %ymm3
vaddpd %ymm4, %ymm9, %ymm4
vaddpd %ymm5, %ymm9, %ymm5
cmpl $10000000, %edx
jb ..B1.4 # Prob 99%
# then combine the 8 vector accumulators down to one, and horizontal sum that.
8 个累加器可以同时保持 8vaddpd秒的飞行时间，但在 Intel SnB/IvB 上延迟仅为 3 个周期（请参阅Agner Fog 的 insn 表）。你没有说你使用的是什么微架构，但我可以从-xhost使用 AVX1 而不是 AVX2的事实推断 Sandybridge/Ivybridge 。（用vmovddup/广播vinsertf128，而不是 AVX2 vbroadcastsd %xmm9, %ymm9）
这完美地解释了 3 倍速比： 26.535 / 8.940 = 2.97 ~= 3。（vaddpd在 Skylake 之前的 Intel CPU 上每个时钟的吞吐量为 1，延迟 = 3。此版本受吞吐量而非延迟的限制，因为指令级并行性增加）。
使用这么多累加器展开将有助于 Skylake，其中 FP add 有 4 个周期延迟和两个每个周期吞吐量。（SKL 从端口 1 删除了低延迟专用向量 FP 添加单元，并在端口 0 和 1 上的改进的 4c 延迟 FMA 单元中运行它。）
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