AVXmat4inv实现比SSE慢

我在SSE2和AVX中实现了4x4矩阵逆.两者都比普通实现更快.但是如果启用AVX(-mavx),则SSE2实现比手动AVX实现运行得更快.似乎编译器使我的SSE2实现与AVX更友好:(

在我的AVX实现中,乘法次数减少,添加次数减少......所以我希望AVX可以比SSE更快.也许有些像说明资讯_mm256_permute2f128_ps,_mm256_permutevar_ps/_mm256_permute_ps使得AVX慢？我不是要将SSE/XMM寄存器加载到AVX/YMM寄存器.

如何使我的AVX实现比SSE更快？

我的CPU:Intel(R)Core(TM)i7-3615QM CPU @ 2.30GHz(Ivy Bridge)

Plain with -O3      : 0.045853 secs
SSE2  with -O3      : 0.026021 secs
SSE2  with -O3 -mavx: 0.024336 secs
AVX1  with -O3 -mavx: 0.031798 secs

Updated (See bottom of question) all have -O3 -mavx flags:
AVX1 (reduced div)  : 0.027666 secs
AVX1 (using rcp_ps) : 0.023205 secs
SSE2 (using rcp_ps) : 0.021969 secs

初始矩阵:

Matrix (float4x4):
    |0.0714    -0.6589  0.7488  2.0000|
    |0.9446     0.2857  0.1613  4.0000|
    |-0.3202    0.6958  0.6429  6.0000|
    |0.0000     0.0000  0.0000  1.0000|

测试代码:

start = clock();

for (int i = 0; i <1000000; i++) {
  glm_mat4_inv_sse2(m, m);

  // glm_mat4_inv_avx(m, m);
  // glm_mat4_inv(m, m)
}

end   = clock();
total = (float)(end - start) / CLOCKS_PER_SEC;
printf("%f secs\n\n", total);

实现:

图书馆:http://github.com/recp/cglm

SSE Impl:https://gist.github.com/recp/690025c955c2e69a91e3a60a13768dee

AVX Impl:https://gist.github.com/recp/8ccc5ad0d19f5516de55f9bf7b5045b2

SSE2实现输出(使用godbolt;选项-O3):

glm_mat4_inv_sse2:
        movaps  xmm8, XMMWORD PTR [rdi+32]
        movaps  xmm2, XMMWORD PTR [rdi+16]
        movaps  xmm5, XMMWORD PTR [rdi+48]
        movaps  xmm6, XMMWORD PTR [rdi]
        movaps  xmm4, xmm8
        movaps  xmm13, xmm8
        movaps  xmm11, xmm8
        shufps  xmm11, xmm2, 170
        shufps  xmm4, xmm5, 238
        movaps  xmm3, xmm11
        movaps  xmm1, xmm8
        pshufd  xmm12, xmm4, 127
        shufps  xmm13, xmm2, 255
        movaps  xmm0, xmm13
        movaps  xmm9, xmm8
        pshufd  xmm4, xmm4, 42
        shufps  xmm9, xmm2, 85
        shufps  xmm1, xmm5, 153
        movaps  xmm7, xmm9
        mulps   xmm0, xmm4
        pshufd  xmm10, xmm1, 42
        movaps  xmm1, xmm11
        shufps  xmm5, xmm8, 0
        mulps   xmm3, xmm12
        pshufd  xmm5, xmm5, 128
        mulps   xmm7, xmm12
        mulps   xmm1, xmm10
        subps   xmm3, xmm0
        movaps  xmm0, xmm13
        mulps   xmm0, xmm10
        mulps   xmm13, xmm5
        subps   xmm7, xmm0
        movaps  xmm0, xmm9
        mulps   xmm0, xmm4
        subps   xmm0, xmm1
        movaps  xmm1, xmm8
        movaps  xmm8, xmm11
        shufps  xmm1, xmm2, 0
        mulps   xmm8, xmm5
        movaps  xmm11, xmm7
        mulps   xmm4, xmm1
        mulps   xmm5, xmm9
        movaps  xmm9, xmm2
        mulps   xmm12, xmm1
        shufps  xmm9, xmm6, 85
        pshufd  xmm9, xmm9, 168
        mulps   xmm1, xmm10
        movaps  xmm10, xmm2
        shufps  xmm10, xmm6, 0
        pshufd  xmm10, xmm10, 168
        subps   xmm4, xmm8
        mulps   xmm7, xmm10
        movaps  xmm8, xmm2
        shufps  xmm2, xmm6, 255
        shufps  xmm8, xmm6, 170
        pshufd  xmm8, xmm8, 168
        pshufd  xmm2, xmm2, 168
        mulps   xmm11, xmm8
        subps   xmm12, xmm13
        movaps  xmm13, XMMWORD PTR .LC0[rip]
        subps   xmm1, xmm5
        movaps  xmm5, xmm3
        mulps   xmm5, xmm9
        mulps   xmm3, xmm10
        subps   xmm5, xmm11
        movaps  xmm11, xmm0
        mulps   xmm11, xmm2
        mulps   xmm0, xmm10
        addps   xmm5, xmm11
        movaps  xmm11, xmm12
        mulps   xmm11, xmm8
        mulps   xmm12, xmm9
        xorps   xmm5, xmm13
        subps   xmm3, xmm11
        movaps  xmm11, xmm4
        mulps   xmm4, xmm9
        subps   xmm7, xmm12
        mulps   xmm11, xmm2
        mulps   xmm2, xmm1
        mulps   xmm1, xmm8
        subps   xmm0, xmm4
        addps   xmm3, xmm11
        movaps  xmm11, XMMWORD PTR .LC1[rip]
        addps   xmm2, xmm7
        addps   xmm0, xmm1
        movaps  xmm1, xmm5
        xorps   xmm3, xmm11
        xorps   xmm2, xmm13
        shufps  xmm1, xmm3, 0
        xorps   xmm0, xmm11
        movaps  xmm4, xmm2
        shufps  xmm4, xmm0, 0
        shufps  xmm1, xmm4, 136
        mulps   xmm1, xmm6
        pshufd  xmm4, xmm1, 27
        addps   xmm1, xmm4
        pshufd  xmm4, xmm1, 65
        addps   xmm1, xmm4
        movaps  xmm4, XMMWORD PTR .LC2[rip]
        divps   xmm4, xmm1
        mulps   xmm5, xmm4
        mulps   xmm3, xmm4
        mulps   xmm2, xmm4
        mulps   xmm0, xmm4
        movaps  XMMWORD PTR [rsi], xmm5
        movaps  XMMWORD PTR [rsi+16], xmm3
        movaps  XMMWORD PTR [rsi+32], xmm2
        movaps  XMMWORD PTR [rsi+48], xmm0
        ret
.LC0:
        .long   0
        .long   2147483648
        .long   0
        .long   2147483648
.LC1:
        .long   2147483648
        .long   0
        .long   2147483648
        .long   0
.LC2:
        .long   1065353216
        .long   1065353216
        .long   1065353216
        .long   1065353216

SSE2实现(启用AVX)输出(使用godbolt;选项-O3 -mavx):

glm_mat4_inv_sse2:
        vmovaps xmm9, XMMWORD PTR [rdi+32]
        vmovaps xmm6, XMMWORD PTR [rdi+48]
        vmovaps xmm2, XMMWORD PTR [rdi+16]
        vmovaps xmm7, XMMWORD PTR [rdi]
        vshufps xmm5, xmm9, xmm6, 238
        vpshufd xmm13, xmm5, 127
        vpshufd xmm5, xmm5, 42
        vshufps xmm1, xmm9, xmm6, 153
        vshufps xmm11, xmm9, xmm2, 170
        vshufps xmm12, xmm9, xmm2, 255
        vmulps  xmm3, xmm11, xmm13
        vpshufd xmm1, xmm1, 42
        vmulps  xmm0, xmm12, xmm5
        vshufps xmm10, xmm9, xmm2, 85
        vshufps xmm6, xmm6, xmm9, 0
        vpshufd xmm6, xmm6, 128
        vmulps  xmm8, xmm10, xmm13
        vmulps  xmm4, xmm10, xmm5
        vsubps  xmm3, xmm3, xmm0
        vmulps  xmm0, xmm12, xmm1
        vsubps  xmm8, xmm8, xmm0
        vmulps  xmm0, xmm11, xmm1
        vsubps  xmm4, xmm4, xmm0
        vshufps xmm0, xmm9, xmm2, 0
        vmulps  xmm9, xmm12, xmm6
        vmulps  xmm13, xmm0, xmm13
        vmulps  xmm5, xmm0, xmm5
        vmulps  xmm0, xmm0, xmm1
        vsubps  xmm12, xmm13, xmm9
        vmulps  xmm9, xmm11, xmm6
        vmovaps xmm13, XMMWORD PTR .LC0[rip]
        vmulps  xmm6, xmm10, xmm6
        vshufps xmm10, xmm2, xmm7, 85
        vpshufd xmm10, xmm10, 168
        vsubps  xmm5, xmm5, xmm9
        vshufps xmm9, xmm2, xmm7, 170
        vpshufd xmm9, xmm9, 168
        vsubps  xmm1, xmm0, xmm6
        vmulps  xmm11, xmm8, xmm9
        vshufps xmm0, xmm2, xmm7, 0
        vshufps xmm2, xmm2, xmm7, 255
        vmulps  xmm6, xmm3, xmm10
        vpshufd xmm2, xmm2, 168
        vpshufd xmm0, xmm0, 168
        vmulps  xmm3, xmm3, xmm0
        vmulps  xmm8, xmm8, xmm0
        vmulps  xmm0, xmm4, xmm0
        vsubps  xmm6, xmm6, xmm11
        vmulps  xmm11, xmm4, xmm2
        vaddps  xmm6, xmm6, xmm11
        vmulps  xmm11, xmm12, xmm9
        vmulps  xmm12, xmm12, xmm10
        vxorps  xmm6, xmm6, xmm13
        vsubps  xmm3, xmm3, xmm11
        vmulps  xmm11, xmm5, xmm2
        vmulps  xmm5, xmm5, xmm10
        vsubps  xmm8, xmm8, xmm12
        vmulps  xmm2, xmm1, xmm2
        vmulps  xmm1, xmm1, xmm9
        vaddps  xmm3, xmm3, xmm11
        vmovaps xmm11, XMMWORD PTR .LC1[rip]
        vsubps  xmm0, xmm0, xmm5
        vaddps  xmm2, xmm8, xmm2
        vxorps  xmm3, xmm3, xmm11
        vaddps  xmm0, xmm0, xmm1
        vshufps xmm1, xmm6, xmm3, 0
        vxorps  xmm2, xmm2, xmm13
        vxorps  xmm0, xmm0, xmm11
        vshufps xmm4, xmm2, xmm0, 0
        vshufps xmm1, xmm1, xmm4, 136
        vmulps  xmm1, xmm1, xmm7
        vpshufd xmm4, xmm1, 27
        vaddps  xmm1, xmm1, xmm4
        vpshufd xmm4, xmm1, 65
        vaddps  xmm1, xmm1, xmm4
        vmovaps xmm4, XMMWORD PTR .LC2[rip]
        vdivps  xmm1, xmm4, xmm1
        vmulps  xmm6, xmm6, xmm1
        vmulps  xmm3, xmm3, xmm1
        vmulps  xmm2, xmm2, xmm1
        vmulps  xmm1, xmm0, xmm1
        vmovaps XMMWORD PTR [rsi], xmm6
        vmovaps XMMWORD PTR [rsi+16], xmm3
        vmovaps XMMWORD PTR [rsi+32], xmm2
        vmovaps XMMWORD PTR [rsi+48], xmm1
        ret
.LC0:
        .long   0
        .long   2147483648
        .long   0
        .long   2147483648
.LC1:
        .long   2147483648
        .long   0
        .long   2147483648
        .long   0
.LC2:
        .long   1065353216
        .long   1065353216
        .long   1065353216
        .long   1065353216

AVX实现输出(使用godbolt;选项-O3 -mavx):

glm_mat4_inv_avx:
        vmovaps ymm3, YMMWORD PTR [rdi]
        vmovaps ymm1, YMMWORD PTR [rdi+32]
        vmovdqa ymm2, YMMWORD PTR .LC1[rip]
        vmovdqa ymm0, YMMWORD PTR .LC0[rip]
        vperm2f128      ymm6, ymm3, ymm3, 3
        vperm2f128      ymm5, ymm1, ymm1, 0
        vperm2f128      ymm1, ymm1, ymm1, 17
        vmovdqa ymm10, YMMWORD PTR .LC4[rip]
        vpermilps       ymm9, ymm5, ymm0
        vpermilps       ymm7, ymm1, ymm2
        vperm2f128      ymm8, ymm6, ymm6, 0
        vpermilps       ymm1, ymm1, ymm0
        vpermilps       ymm5, ymm5, ymm2
        vpermilps       ymm0, ymm8, ymm0
        vmulps  ymm4, ymm7, ymm9
        vpermilps       ymm8, ymm8, ymm2
        vpermilps       ymm11, ymm6, 1
        vmulps  ymm2, ymm5, ymm1
        vmulps  ymm7, ymm0, ymm7
        vmulps  ymm1, ymm8, ymm1
        vmulps  ymm0, ymm0, ymm5
        vmulps  ymm5, ymm8, ymm9
        vmovdqa ymm9, YMMWORD PTR .LC3[rip]
        vmovdqa ymm8, YMMWORD PTR .LC2[rip]
        vsubps  ymm4, ymm4, ymm2
        vsubps  ymm7, ymm7, ymm1
        vperm2f128      ymm2, ymm4, ymm4, 0
        vperm2f128      ymm4, ymm4, ymm4, 17
        vshufps ymm1, ymm2, ymm4, 77
        vpermilps       ymm1, ymm1, ymm9
        vsubps  ymm5, ymm0, ymm5
        vpermilps       ymm0, ymm2, ymm8
        vmulps  ymm0, ymm0, ymm11
        vperm2f128      ymm1, ymm1, ymm2, 0
        vshufps ymm2, ymm2, ymm4, 74
        vpermilps       ymm4, ymm6, 90
        vmulps  ymm1, ymm1, ymm4
        vpermilps       ymm2, ymm2, ymm10
        vpermilps       ymm6, ymm6, 191
        vmovaps ymm11, YMMWORD PTR .LC5[rip]
        vperm2f128      ymm2, ymm2, ymm2, 0
        vperm2f128      ymm4, ymm3, ymm3, 0
        vpermilps       ymm12, ymm4, YMMWORD PTR .LC7[rip]
        vmulps  ymm2, ymm2, ymm6
        vinsertf128     ymm6, ymm7, xmm5, 1
        vperm2f128      ymm5, ymm7, ymm5, 49
        vshufps ymm7, ymm6, ymm5, 77
        vpermilps       ymm9, ymm7, ymm9
        vsubps  ymm0, ymm0, ymm1
        vpermilps       ymm1, ymm4, YMMWORD PTR .LC6[rip]
        vpermilps       ymm4, ymm4, YMMWORD PTR .LC8[rip]
        vaddps  ymm2, ymm0, ymm2
        vpermilps       ymm0, ymm6, ymm8
        vshufps ymm6, ymm6, ymm5, 74
        vpermilps       ymm6, ymm6, ymm10
        vmulps  ymm1, ymm1, ymm0
        vmulps  ymm0, ymm12, ymm9
        vmulps  ymm6, ymm4, ymm6
        vxorps  ymm2, ymm2, ymm11
        vdpps   ymm3, ymm3, ymm2, 255
        vsubps  ymm0, ymm1, ymm0
        vdivps  ymm2, ymm2, ymm3
        vaddps  ymm0, ymm0, ymm6
        vxorps  ymm0, ymm0, ymm11
        vdivps  ymm0, ymm0, ymm3
        vperm2f128      ymm5, ymm2, ymm2, 3
        vshufps ymm1, ymm2, ymm5, 68
        vshufps ymm2, ymm2, ymm5, 238
        vperm2f128      ymm4, ymm0, ymm0, 3
        vshufps ymm6, ymm0, ymm4, 68
        vshufps ymm0, ymm0, ymm4, 238
        vshufps ymm3, ymm1, ymm6, 136
        vshufps ymm1, ymm1, ymm6, 221
        vinsertf128     ymm1, ymm3, xmm1, 1
        vshufps ymm3, ymm2, ymm0, 136
        vshufps ymm0, ymm2, ymm0, 221
        vinsertf128     ymm0, ymm3, xmm0, 1
        vmovaps YMMWORD PTR [rsi], ymm1
        vmovaps YMMWORD PTR [rsi+32], ymm0
        vzeroupper
        ret
.LC0:
        .long   2
        .long   1
        .long   1
        .long   0
        .long   0
        .long   0
        .long   0
        .long   0
.LC1:
        .long   3
        .long   3
        .long   2
        .long   3
        .long   2
        .long   1
        .long   1
        .long   1
.LC2:
        .long   0
        .long   0
        .long   1
        .long   2
        .long   0
        .long   0
        .long   1
        .long   2
.LC3:
        .long   0
        .long   1
        .long   1
        .long   2
        .long   0
        .long   1
        .long   1
        .long   2
.LC4:
        .long   0
        .long   2
        .long   3
        .long   3
        .long   0
        .long   2
        .long   3
        .long   3
.LC5:
        .long   0
        .long   2147483648
        .long   0
        .long   2147483648
        .long   2147483648
        .long   0
        .long   2147483648
        .long   0
.LC6:
        .long   1
        .long   0
        .long   0
        .long   0
        .long   1
        .long   0
        .long   0
        .long   0
.LC7:
        .long   2
        .long   2
        .long   1
        .long   1
        .long   2
        .long   2
        .long   1
        .long   1
.LC8:
        .long   3
        .long   3
        .long   3
        .long   2
        .long   3
        .long   3
        .long   3
        .long   2

编辑:

我在macOS上使用Xcode(版本10.0(10A255))(在MacBook Pro(2012年中期),Retina,15')上使用-O3优化选项构建和运行测试.它用clang编译测试代码.我在godbolt中使用GCC 8.2来查看asm(对不起),但是程序集输出看起来很相似.

我通过启用cglm选项启用了shuffd:CGLM_USE_INT_DOMAIN.我忘了在查看asm时禁用它.

#ifdef CGLM_USE_INT_DOMAIN
#  define glmm_shuff1(xmm, z, y, x, w)                                        \
     _mm_castsi128_ps(_mm_shuffle_epi32(_mm_castps_si128(xmm),                \
                                        _MM_SHUFFLE(z, y, x, w)))
#else
#  define glmm_shuff1(xmm, z, y, x, w)                                        \
     _mm_shuffle_ps(xmm, xmm, _MM_SHUFFLE(z, y, x, w))
#endif

整个测试代码(标题除外):

#include 

#include 
#include 

int
main(int argc, const char * argv[]) {
  CGLM_ALIGN(32) mat4 m = GLM_MAT4_IDENTITY_INIT;

  double start, end, total;

  /* generate invertible matrix */
  glm_translate(m, (vec3){1,2,3});
  glm_rotate(m, M_PI_2, (vec3){1,2,3});
  glm_translate(m, (vec3){1,2,3});

  glm_mat4_print(m, stderr);

  start = clock();

  for (int i = 0; i <1000000; i++) {
    glm_mat4_inv_sse2(m, m);

    // glm_mat4_inv_avx(m, m);
    // glm_mat4_inv(m, m);
  }

  end   = clock();
  total = (float)(end - start) / CLOCKS_PER_SEC;

  printf("%f secs\n\n", total);

  glm_mat4_print(m, stderr);
}

编辑2:

我通过使用乘法减少了一个除法(1 set_ps + 1 div_ps + 2 mul_ps似乎优于2 div_ps):

旧版:

r1 = _mm256_div_ps(r1, y4);
r2 = _mm256_div_ps(r2, y4);

新版本(SSE2版本使用了这样的部门):

y5 = _mm256_div_ps(_mm256_set1_ps(1.0f), y4);
r1 = _mm256_mul_ps(r1, y5);
r2 = _mm256_mul_ps(r2, y5);

新版本(快速版):

y5 = _mm256_rcp_ps(y4);
r1 = _mm256_mul_ps(r1, y5);
r2 = _mm256_mul_ps(r2, y5);

现在它比以前更好,但仍然不比常春藤桥CPU上的SSE快.我更新了测试结果.

您的CPU是Intel IvyBridge.

Sandybridge/IvyBridge具有每时钟1个mul并在不同端口上增加吞吐量,因此它们不会相互竞争.

但是,对于256位shuffle和所有FP shuffle(甚至128位shufps),每个时钟只有1个随机播放吞吐量. 但是,对于整数shuffle,它具有每时钟2个吞吐量,并且我注意到您的编译器pshufd用作FP指令之间的复制和混洗. 在为SSE2编译时,这是一个可靠的胜利,特别是在VEX编码不可用的情况下(因此它movaps通过替换movaps xmm0, xmm1/ shufps xmm0, xmm0, 65或其他来节省一个.)即使AVX可用,你的编译器也会这样做,所以它可以使用vshufps xmm0, xmm1,xmm1, 65,但它要么巧妙地选择vpshufd微架构的原因,或者它很幸运,或者它的启发式/指令成本模型的设计考虑到了这一点.(我怀疑它是铿锵的,但你没有在问题中说出来或显示你编译的C源代码).

在Haswell及更高版本(支持AVX2,因此支持每个整数shuffle的256位版本)中,所有shuffle只能在端口5上运行.但在仅支持AVX1的IvB中,它只有FP shuffle,最高可达256位.整数shuffle总是只有128位,并且可以在端口1或端口5上运行,因为这两个端口上都有128位的shuffle执行单元.(https://agner.org/optimize/)

我没有详细查看asm,因为它很长,但是如果使用更宽的向量来节省添加/倍数会花费更多的时间,那就会更慢.

除了因为你所有的shuffle都变成了FP shuffle所以它们只能在端口5上运行,而不是利用端口1.我怀疑它有很多改组,它是一个瓶颈,而不是端口0(FP乘法)或端口1(FP add) .

BTW,Haswell和后来有两个FMA单元,每个单元在p0和p1上,因此乘法吞吐量是其两倍.Skylake以及后来在这些FMA单元上运行FP add,因此它们每个时钟吞吐量都有2个.(如果您可以有效地使用实际的FMA指令,您可以完成两倍的工作.)

此外,您的基准测试是测试延迟,而不是吞吐量,因为m输入和输出也是如此. 但是,可能有足够的指令级并行性来解决混乱吞吐量的瓶颈问题.

在IvB上,车道交叉改组vperm2f128并且vinsertf128具有2个周期延迟,而对于仅具有单周期延迟的车道内改组(包括所有128位改组).英特尔的指南声称有一个不同的数字,IIRC,但是2个周期是Agner Fog在依赖链中实际发现的实际测量结果.(这可能是1个周期+某种旁路延迟).在Haswell和之后,交叉点改组是3个周期的延迟. 为什么英特尔公布的一些Haswell AVX延迟比Sandy Bridge慢3倍？

还有关:AVX512中的128位跨通道操作能提供更好的性能吗？ 你有时可以通过在一个有用的点切成128位半部分的未对齐负载来减少混洗量,然后使用内部随机播放.这对于AVX1可能有用,因为它缺少vpermps粒度小于128位的其他通道混洗.