xma*_*s79 11 c optimization sse simd matrix
我发现这个职位,说明如何进行转一个8x8矩阵的字节24点的操作,和几个卷轴后有代码实现转置.但是,这种方法没有利用我们可以阻止 8x8转置为4个4x4转置的事实,并且每个转换只能在一个shuffle指令中完成(这篇文章是参考文献).所以我推出了这个解决方案:
__m128i transpose4x4mask = _mm_set_epi8(15, 11, 7, 3, 14, 10, 6, 2, 13, 9, 5, 1, 12, 8, 4, 0);
__m128i shuffle8x8Mask = _mm_setr_epi8(0, 1, 2, 3, 8, 9, 10, 11, 4, 5, 6, 7, 12, 13, 14, 15);
void TransposeBlock8x8(uint8_t *src, uint8_t *dst, int srcStride, int dstStride) {
__m128i load0 = _mm_set_epi64x(*(uint64_t*)(src + 1 * srcStride), *(uint64_t*)(src + 0 * srcStride));
__m128i load1 = _mm_set_epi64x(*(uint64_t*)(src + 3 * srcStride), *(uint64_t*)(src + 2 * srcStride));
__m128i load2 = _mm_set_epi64x(*(uint64_t*)(src + 5 * srcStride), *(uint64_t*)(src + 4 * srcStride));
__m128i load3 = _mm_set_epi64x(*(uint64_t*)(src + 7 * srcStride), *(uint64_t*)(src + 6 * srcStride));
__m128i shuffle0 = _mm_shuffle_epi8(load0, shuffle8x8Mask);
__m128i shuffle1 = _mm_shuffle_epi8(load1, shuffle8x8Mask);
__m128i shuffle2 = _mm_shuffle_epi8(load2, shuffle8x8Mask);
__m128i shuffle3 = _mm_shuffle_epi8(load3, shuffle8x8Mask);
__m128i block0 = _mm_unpacklo_epi64(shuffle0, shuffle1);
__m128i block1 = _mm_unpackhi_epi64(shuffle0, shuffle1);
__m128i block2 = _mm_unpacklo_epi64(shuffle2, shuffle3);
__m128i block3 = _mm_unpackhi_epi64(shuffle2, shuffle3);
__m128i transposed0 = _mm_shuffle_epi8(block0, transpose4x4mask);
__m128i transposed1 = _mm_shuffle_epi8(block1, transpose4x4mask);
__m128i transposed2 = _mm_shuffle_epi8(block2, transpose4x4mask);
__m128i transposed3 = _mm_shuffle_epi8(block3, transpose4x4mask);
__m128i store0 = _mm_unpacklo_epi32(transposed0, transposed2);
__m128i store1 = _mm_unpackhi_epi32(transposed0, transposed2);
__m128i store2 = _mm_unpacklo_epi32(transposed1, transposed3);
__m128i store3 = _mm_unpackhi_epi32(transposed1, transposed3);
*((uint64_t*)(dst + 0 * dstStride)) = _mm_extract_epi64(store0, 0);
*((uint64_t*)(dst + 1 * dstStride)) = _mm_extract_epi64(store0, 1);
*((uint64_t*)(dst + 2 * dstStride)) = _mm_extract_epi64(store1, 0);
*((uint64_t*)(dst + 3 * dstStride)) = _mm_extract_epi64(store1, 1);
*((uint64_t*)(dst + 4 * dstStride)) = _mm_extract_epi64(store2, 0);
*((uint64_t*)(dst + 5 * dstStride)) = _mm_extract_epi64(store2, 1);
*((uint64_t*)(dst + 6 * dstStride)) = _mm_extract_epi64(store3, 0);
*((uint64_t*)(dst + 7 * dstStride)) = _mm_extract_epi64(store3, 1);
}
不包括加载/存储操作,此过程仅包含16条指令而不是24条指令.
我错过了什么？
除了读取pinsrq和写入内存的加载、存储和 -s 之外，步幅可能不等于 8 字节，您只需 12 条指令即可完成转置（此代码可以轻松地与 Z boson 的测试代码结合使用） ）：
void tran8x8b_SSE_v2(char *A, char *B) {
__m128i pshufbcnst = _mm_set_epi8(15,11,7,3, 14,10,6,2, 13,9,5,1, 12,8,4,0);
__m128i B0, B1, B2, B3, T0, T1, T2, T3;
B0 = _mm_loadu_si128((__m128i*)&A[ 0]);
B1 = _mm_loadu_si128((__m128i*)&A[16]);
B2 = _mm_loadu_si128((__m128i*)&A[32]);
B3 = _mm_loadu_si128((__m128i*)&A[48]);
T0 = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(B0),_mm_castsi128_ps(B1),0b10001000));
T1 = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(B2),_mm_castsi128_ps(B3),0b10001000));
T2 = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(B0),_mm_castsi128_ps(B1),0b11011101));
T3 = _mm_castps_si128(_mm_shuffle_ps(_mm_castsi128_ps(B2),_mm_castsi128_ps(B3),0b11011101));
B0 = _mm_shuffle_epi8(T0,pshufbcnst);
B1 = _mm_shuffle_epi8(T1,pshufbcnst);
B2 = _mm_shuffle_epi8(T2,pshufbcnst);
B3 = _mm_shuffle_epi8(T3,pshufbcnst);
T0 = _mm_unpacklo_epi32(B0,B1);
T1 = _mm_unpackhi_epi32(B0,B1);
T2 = _mm_unpacklo_epi32(B2,B3);
T3 = _mm_unpackhi_epi32(B2,B3);
_mm_storeu_si128((__m128i*)&B[ 0], T0);
_mm_storeu_si128((__m128i*)&B[16], T1);
_mm_storeu_si128((__m128i*)&B[32], T2);
_mm_storeu_si128((__m128i*)&B[48], T3);
}
这里我们使用32位浮点shuffle，它比epi32shuffle更加灵活。强制转换不会生成额外的指令（使用 gcc 5.4 生成的代码）：
tran8x8b_SSE_v2:
.LFB4885:
.cfi_startproc
vmovdqu 48(%rdi), %xmm5
vmovdqu 32(%rdi), %xmm2
vmovdqu 16(%rdi), %xmm0
vmovdqu (%rdi), %xmm1
vshufps $136, %xmm5, %xmm2, %xmm4
vshufps $221, %xmm5, %xmm2, %xmm2
vmovdqa .LC6(%rip), %xmm5
vshufps $136, %xmm0, %xmm1, %xmm3
vshufps $221, %xmm0, %xmm1, %xmm1
vpshufb %xmm5, %xmm3, %xmm3
vpshufb %xmm5, %xmm1, %xmm0
vpshufb %xmm5, %xmm4, %xmm4
vpshufb %xmm5, %xmm2, %xmm1
vpunpckldq %xmm4, %xmm3, %xmm5
vpunpckldq %xmm1, %xmm0, %xmm2
vpunpckhdq %xmm4, %xmm3, %xmm3
vpunpckhdq %xmm1, %xmm0, %xmm0
vmovups %xmm5, (%rsi)
vmovups %xmm3, 16(%rsi)
vmovups %xmm2, 32(%rsi)
vmovups %xmm0, 48(%rsi)
ret
.cfi_endproc
在某些（但不是全部）较旧的 cpu 上，在整数和浮点单元之间移动数据时可能会有较小的旁路延迟（0 到 2 个周期之间）。这会增加函数的延迟，但不一定会影响代码的吞吐量。
1e9 换位的简单延迟测试：
for (int i=0;i<500000000;i++){
tran8x8b_SSE(A,C);
tran8x8b_SSE(C,A);
}
print8x8b(A);
对于 tran8x8b_SSE，这大约需要 5.5 秒（19.7e9 周期）；对于 tran8x8b_SSE_v2（Intel core i5-6500），大约需要 4.5 秒（16.0e9 周期）。请注意，尽管函数内联在 for 循环中，但编译器并未消除加载和存储。
更新：AVX2-128 / SSE 4.1 混合解决方案。
“洗牌”（解包、洗牌）由端口 5 处理，在现代 cpu 上每个 cpu 周期有 1 条指令。有时用两种混合代替一种“洗牌”是值得的。在 Skylake 上，32 位混合指令可以在端口 0、1 或 5 上运行。
不幸的是，_mm_blend_epi32只有AVX2-128。一个有效的 SSE 4.1 替代方案是_mm_blend_ps与一些强制类型转换（通常是免费的）相结合。12 次“洗牌”被 8 次洗牌与 8 种混合组合所取代。
现在，简单的延迟测试运行时间约为 3.6 秒（13e9 个 cpu 周期），比tran8x8b_SSE_v2.
代码：
/* AVX2-128 version, sse 4.1 version see ----------------> SSE 4.1 version of tran8x8b_AVX2_128() */
void tran8x8b_AVX2_128(char *A, char *B) { /* void tran8x8b_SSE4_1(char *A, char *B) { */
__m128i pshufbcnst_0 = _mm_set_epi8(15, 7,11, 3,
13, 5, 9, 1, 14, 6,10, 2, 12, 4, 8, 0); /* __m128i pshufbcnst_0 = _mm_set_epi8(15, 7,11, 3, 13, 5, 9, 1, 14, 6,10, 2, 12, 4, 8, 0); */
__m128i pshufbcnst_1 = _mm_set_epi8(13, 5, 9, 1,
15, 7,11, 3, 12, 4, 8, 0, 14, 6,10, 2); /* __m128i pshufbcnst_1 = _mm_set_epi8(13, 5, 9, 1, 15, 7,11, 3, 12, 4, 8, 0, 14, 6,10, 2); */
__m128i pshufbcnst_2 = _mm_set_epi8(11, 3,15, 7,
9, 1,13, 5, 10, 2,14, 6, 8, 0,12, 4); /* __m128i pshufbcnst_2 = _mm_set_epi8(11, 3,15, 7, 9, 1,13, 5, 10, 2,14, 6, 8, 0,12, 4); */
__m128i pshufbcnst_3 = _mm_set_epi8( 9, 1,13, 5,
11, 3,15, 7, 8, 0,12, 4, 10, 2,14, 6); /* __m128i pshufbcnst_3 = _mm_set_epi8( 9, 1,13, 5, 11, 3,15, 7, 8, 0,12, 4, 10, 2,14, 6); */
__m128i B0, B1, B2, B3, T0, T1, T2, T3; /* __m128 B0, B1, B2, B3, T0, T1, T2, T3; */
/* */
B0 = _mm_loadu_si128((__m128i*)&A[ 0]); /* B0 = _mm_loadu_ps((float*)&A[ 0]); */
B1 = _mm_loadu_si128((__m128i*)&A[16]); /* B1 = _mm_loadu_ps((float*)&A[16]); */
B2 = _mm_loadu_si128((__m128i*)&A[32]); /* B2 = _mm_loadu_ps((float*)&A[32]); */
B3 = _mm_loadu_si128((__m128i*)&A[48]); /* B3 = _mm_loadu_ps((float*)&A[48]); */
/* */
B1 = _mm_shuffle_epi32(B1,0b10110001); /* B1 = _mm_shuffle_ps(B1,B1,0b10110001); */
B3 = _mm_shuffle_epi32(B3,0b10110001); /* B3 = _mm_shuffle_ps(B3,B3,0b10110001); */
T0 = _mm_blend_epi32(B0,B1,0b1010); /* T0 = _mm_blend_ps(B0,B1,0b1010); */
T1 = _mm_blend_epi32(B2,B3,0b1010); /* T1 = _mm_blend_ps(B2,B3,0b1010); */
T2 = _mm_blend_epi32(B0,B1,0b0101); /* T2 = _mm_blend_ps(B0,B1,0b0101); */
T3 = _mm_blend_epi32(B2,B3,0b0101); /* T3 = _mm_blend_ps(B2,B3,0b0101); */
/* */
B0 = _mm_shuffle_epi8(T0,pshufbcnst_0); /* B0 = _mm_castsi128_ps(_mm_shuffle_epi8(_mm_castps_si128(T0),pshufbcnst_0)); */
B1 = _mm_shuffle_epi8(T1,pshufbcnst_1); /* B1 = _mm_castsi128_ps(_mm_shuffle_epi8(_mm_castps_si128(T1),pshufbcnst_1)); */
B2 = _mm_shuffle_epi8(T2,pshufbcnst_2); /* B2 = _mm_castsi128_ps(_mm_shuffle_epi8(_mm_castps_si128(T2),pshufbcnst_2)); */
B3 = _mm_shuffle_epi8(T3,pshufbcnst_3); /* B3 = _mm_castsi128_ps(_mm_shuffle_epi8(_mm_castps_si128(T3),pshufbcnst_3)); */
/* */
T0 = _mm_blend_epi32(B0,B1,0b1010); /* T0 = _mm_blend_ps(B0,B1,0b1010); */
T1 = _mm_blend_epi32(B0,B1,0b0101); /* T1 = _mm_blend_ps(B0,B1,0b0101); */
T2 = _mm_blend_epi32(B2,B3,0b1010); /* T2 = _mm_blend_ps(B2,B3,0b1010); */
T3 = _mm_blend_epi32(B2,B3,0b0101); /* T3 = _mm_blend_ps(B2,B3,0b0101); */
T1 = _mm_shuffle_epi32(T1,0b10110001); /* T1 = _mm_shuffle_ps(T1,T1,0b10110001); */
T3 = _mm_shuffle_epi32(T3,0b10110001); /* T3 = _mm_shuffle_ps(T3,T3,0b10110001); */
/* */
_mm_storeu_si128((__m128i*)&B[ 0], T0); /* _mm_storeu_ps((float*)&B[ 0], T0); */
_mm_storeu_si128((__m128i*)&B[16], T1); /* _mm_storeu_ps((float*)&B[16], T1); */
_mm_storeu_si128((__m128i*)&B[32], T2); /* _mm_storeu_ps((float*)&B[32], T2); */
_mm_storeu_si128((__m128i*)&B[48], T3); /* _mm_storeu_ps((float*)&B[48], T3); */
} /* } */
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