Krz*_*icz 15 c optimization assembly sse matrix-multiplication
我正在寻找一种更快,更棘手的方法来将C中的两个4x4矩阵相乘.我目前的研究主要集中在具有SIMD扩展的x86-64汇编上.到目前为止,我已经创建了一个函数,比一个简单的C实现快6倍,这超出了我对性能改进的期望.不幸的是,只有在没有使用优化标志进行编译时(GCC 4.7),这种情况才会成立.随着-O2,C变得更快,我的努力变得毫无意义.
我知道现代编译器利用复杂的优化技术来实现几乎完美的代码,通常比巧妙的手工装配更快.但在少数性能关键的情况下,人类可能会尝试使用编译器争取时钟周期.特别是,当一些支持现代ISA的数学可以被探索时(就像我的情况一样).
我的函数如下(AT&T语法,GNU汇编程序):
.text
.globl matrixMultiplyASM
.type matrixMultiplyASM, @function
matrixMultiplyASM:
movaps (%rdi), %xmm0 # fetch the first matrix (use four registers)
movaps 16(%rdi), %xmm1
movaps 32(%rdi), %xmm2
movaps 48(%rdi), %xmm3
xorq %rcx, %rcx # reset (forward) loop iterator
.ROW:
movss (%rsi), %xmm4 # Compute four values (one row) in parallel:
shufps $0x0, %xmm4, %xmm4 # 4x 4FP mul's, 3x 4FP add's 6x mov's per row,
mulps %xmm0, %xmm4 # expressed in four sequences of 5 instructions,
movaps %xmm4, %xmm5 # executed 4 times for 1 matrix multiplication.
addq $0x4, %rsi
movss (%rsi), %xmm4 # movss + shufps comprise _mm_set1_ps intrinsic
shufps $0x0, %xmm4, %xmm4 #
mulps %xmm1, %xmm4
addps %xmm4, %xmm5
addq $0x4, %rsi # manual pointer arithmetic simplifies addressing
movss (%rsi), %xmm4
shufps $0x0, %xmm4, %xmm4
mulps %xmm2, %xmm4 # actual computation happens here
addps %xmm4, %xmm5 #
addq $0x4, %rsi
movss (%rsi), %xmm4 # one mulps operand fetched per sequence
shufps $0x0, %xmm4, %xmm4 # |
mulps %xmm3, %xmm4 # the other is already waiting in %xmm[0-3]
addps %xmm4, %xmm5
addq $0x4, %rsi # 5 preceding comments stride among the 4 blocks
movaps %xmm5, (%rdx,%rcx) # store the resulting row, actually, a column
addq $0x10, %rcx # (matrices are stored in column-major order)
cmpq $0x40, %rcx
jne .ROW
ret
.size matrixMultiplyASM, .-matrixMultiplyASM
它通过处理在128位SSE寄存器中打包的四个浮点数来计算每次迭代的结果矩阵的整列.通过一些数学运算(操作重新排序和聚合)和mullps/ addps4xfloat包的并行乘法/加法指令,可以实现完全矢量化.该代码重用意味着传递参数寄存器(%rdi,%rsi,%rdx:GNU/Linux的ABI),从(内)循环展开益处和保持一个矩阵完全在XMM寄存器,以减少存储器的读取.你可以看到,我已经研究过这个话题,并且花了很多时间来尽我所能地实现它.
征服我的代码的天真C计算如下所示:
void matrixMultiplyNormal(mat4_t *mat_a, mat4_t *mat_b, mat4_t *mat_r) {
for (unsigned int i = 0; i < 16; i += 4)
for (unsigned int j = 0; j < 4; ++j)
mat_r->m[i + j] = (mat_b->m[i + 0] * mat_a->m[j + 0])
+ (mat_b->m[i + 1] * mat_a->m[j + 4])
+ (mat_b->m[i + 2] * mat_a->m[j + 8])
+ (mat_b->m[i + 3] * mat_a->m[j + 12]);
}
我已经研究了上面C代码的优化汇编输出,它在XMM寄存器中存储浮点数时不涉及任何并行操作 - 只是标量计算,指针运算和条件跳转.编译器的代码似乎不那么刻意,但它仍然比我的矢量化版本稍微更有效,预计会快4倍.我确信一般的想法是正确的 - 程序员做同样的事情并获得有益的结果.但这里有什么问题？是否有任何我不知道的寄存器分配或指令调度问题？你知道任何x86-64组装工具或技巧来支持我对抗机器的战斗吗？
Z b*_*son 29
4x4矩阵乘法是64次乘法和48次加法.使用SSE,这可以减少到16次乘法和12次加法(和16次广播).以下代码将为您执行此操作.它只需要SSE(#include <xmmintrin.h>).该阵列A,B以及C需要进行16字节对齐.使用诸如hadd(SSE3)和dpps(SSE4.1)之类的水平指令效率较低(尤其是dpps).我不知道循环展开是否会有所帮助.
void M4x4_SSE(float *A, float *B, float *C) {
__m128 row1 = _mm_load_ps(&B[0]);
__m128 row2 = _mm_load_ps(&B[4]);
__m128 row3 = _mm_load_ps(&B[8]);
__m128 row4 = _mm_load_ps(&B[12]);
for(int i=0; i<4; i++) {
__m128 brod1 = _mm_set1_ps(A[4*i + 0]);
__m128 brod2 = _mm_set1_ps(A[4*i + 1]);
__m128 brod3 = _mm_set1_ps(A[4*i + 2]);
__m128 brod4 = _mm_set1_ps(A[4*i + 3]);
__m128 row = _mm_add_ps(
_mm_add_ps(
_mm_mul_ps(brod1, row1),
_mm_mul_ps(brod2, row2)),
_mm_add_ps(
_mm_mul_ps(brod3, row3),
_mm_mul_ps(brod4, row4)));
_mm_store_ps(&C[4*i], row);
}
}
Krz*_*icz 11
有一种方法可以加速代码并超越编译器.它不涉及任何复杂的流水线分析或深度代码微优化(这并不意味着它不能从这些中进一步受益).优化使用三个简单的技巧:
该功能现在是32字节对齐的(这显着提高了性能),
主循环反向,这减少了与零测试的比较(基于EFLAGS),
事实证明,指令级地址算法比"外部"指针计算更快(即使它在3/4情况下需要两倍的加法).它通过四条指令缩短了循环体,并减少了其执行路径中的数据依赖性.见相关问题.
此外,代码使用相对跳转语法来抑制符号重定义错误,这种错误发生在GCC尝试内联它时(在放入asm语句并编译后-O3).
.text
.align 32 # 1. function entry alignment
.globl matrixMultiplyASM # (for a faster call)
.type matrixMultiplyASM, @function
matrixMultiplyASM:
movaps (%rdi), %xmm0
movaps 16(%rdi), %xmm1
movaps 32(%rdi), %xmm2
movaps 48(%rdi), %xmm3
movq $48, %rcx # 2. loop reversal
1: # (for simpler exit condition)
movss (%rsi, %rcx), %xmm4 # 3. extended address operands
shufps $0, %xmm4, %xmm4 # (faster than pointer calculation)
mulps %xmm0, %xmm4
movaps %xmm4, %xmm5
movss 4(%rsi, %rcx), %xmm4
shufps $0, %xmm4, %xmm4
mulps %xmm1, %xmm4
addps %xmm4, %xmm5
movss 8(%rsi, %rcx), %xmm4
shufps $0, %xmm4, %xmm4
mulps %xmm2, %xmm4
addps %xmm4, %xmm5
movss 12(%rsi, %rcx), %xmm4
shufps $0, %xmm4, %xmm4
mulps %xmm3, %xmm4
addps %xmm4, %xmm5
movaps %xmm5, (%rdx, %rcx)
subq $16, %rcx # one 'sub' (vs 'add' & 'cmp')
jge 1b # SF=OF, idiom: jump if positive
ret
这是迄今为止我见过的最快的x86-64实现.我会很感激,投票并接受任何答案,为此目的提供更快的装配!
小智 5
Sandy Bridge上面扩展了指令集，支持8元素向量运算。考虑这个实现。
struct MATRIX {
union {
float f[4][4];
__m128 m[4];
__m256 n[2];
};
};
MATRIX myMultiply(MATRIX M1, MATRIX M2) {
// Perform a 4x4 matrix multiply by a 4x4 matrix
// Be sure to run in 64 bit mode and set right flags
// Properties, C/C++, Enable Enhanced Instruction, /arch:AVX
// Having MATRIX on a 32 byte bundry does help performance
MATRIX mResult;
__m256 a0, a1, b0, b1;
__m256 c0, c1, c2, c3, c4, c5, c6, c7;
__m256 t0, t1, u0, u1;
t0 = M1.n[0]; // t0 = a00, a01, a02, a03, a10, a11, a12, a13
t1 = M1.n[1]; // t1 = a20, a21, a22, a23, a30, a31, a32, a33
u0 = M2.n[0]; // u0 = b00, b01, b02, b03, b10, b11, b12, b13
u1 = M2.n[1]; // u1 = b20, b21, b22, b23, b30, b31, b32, b33
a0 = _mm256_shuffle_ps(t0, t0, _MM_SHUFFLE(0, 0, 0, 0)); // a0 = a00, a00, a00, a00, a10, a10, a10, a10
a1 = _mm256_shuffle_ps(t1, t1, _MM_SHUFFLE(0, 0, 0, 0)); // a1 = a20, a20, a20, a20, a30, a30, a30, a30
b0 = _mm256_permute2f128_ps(u0, u0, 0x00); // b0 = b00, b01, b02, b03, b00, b01, b02, b03
c0 = _mm256_mul_ps(a0, b0); // c0 = a00*b00 a00*b01 a00*b02 a00*b03 a10*b00 a10*b01 a10*b02 a10*b03
c1 = _mm256_mul_ps(a1, b0); // c1 = a20*b00 a20*b01 a20*b02 a20*b03 a30*b00 a30*b01 a30*b02 a30*b03
a0 = _mm256_shuffle_ps(t0, t0, _MM_SHUFFLE(1, 1, 1, 1)); // a0 = a01, a01, a01, a01, a11, a11, a11, a11
a1 = _mm256_shuffle_ps(t1, t1, _MM_SHUFFLE(1, 1, 1, 1)); // a1 = a21, a21, a21, a21, a31, a31, a31, a31
b0 = _mm256_permute2f128_ps(u0, u0, 0x11); // b0 = b10, b11, b12, b13, b10, b11, b12, b13
c2 = _mm256_mul_ps(a0, b0); // c2 = a01*b10 a01*b11 a01*b12 a01*b13 a11*b10 a11*b11 a11*b12 a11*b13
c3 = _mm256_mul_ps(a1, b0); // c3 = a21*b10 a21*b11 a21*b12 a21*b13 a31*b10 a31*b11 a31*b12 a31*b13
a0 = _mm256_shuffle_ps(t0, t0, _MM_SHUFFLE(2, 2, 2, 2)); // a0 = a02, a02, a02, a02, a12, a12, a12, a12
a1 = _mm256_shuffle_ps(t1, t1, _MM_SHUFFLE(2, 2, 2, 2)); // a1 = a22, a22, a22, a22, a32, a32, a32, a32
b1 = _mm256_permute2f128_ps(u1, u1, 0x00); // b0 = b20, b21, b22, b23, b20, b21, b22, b23
c4 = _mm256_mul_ps(a0, b1); // c4 = a02*b20 a02*b21 a02*b22 a02*b23 a12*b20 a12*b21 a12*b22 a12*b23
c5 = _mm256_mul_ps(a1, b1); // c5 = a22*b20 a22*b21 a22*b22 a22*b23 a32*b20 a32*b21 a32*b22 a32*b23
a0 = _mm256_shuffle_ps(t0, t0, _MM_SHUFFLE(3, 3, 3, 3)); // a0 = a03, a03, a03, a03, a13, a13, a13, a13
a1 = _mm256_shuffle_ps(t1, t1, _MM_SHUFFLE(3, 3, 3, 3)); // a1 = a23, a23, a23, a23, a33, a33, a33, a33
b1 = _mm256_permute2f128_ps(u1, u1, 0x11); // b0 = b30, b31, b32, b33, b30, b31, b32, b33
c6 = _mm256_mul_ps(a0, b1); // c6 = a03*b30 a03*b31 a03*b32 a03*b33 a13*b30 a13*b31 a13*b32 a13*b33
c7 = _mm256_mul_ps(a1, b1); // c7 = a23*b30 a23*b31 a23*b32 a23*b33 a33*b30 a33*b31 a33*b32 a33*b33
c0 = _mm256_add_ps(c0, c2); // c0 = c0 + c2 (two terms, first two rows)
c4 = _mm256_add_ps(c4, c6); // c4 = c4 + c6 (the other two terms, first two rows)
c1 = _mm256_add_ps(c1, c3); // c1 = c1 + c3 (two terms, second two rows)
c5 = _mm256_add_ps(c5, c7); // c5 = c5 + c7 (the other two terms, second two rose)
// Finally complete addition of all four terms and return the results
mResult.n[0] = _mm256_add_ps(c0, c4); // n0 = a00*b00+a01*b10+a02*b20+a03*b30 a00*b01+a01*b11+a02*b21+a03*b31 a00*b02+a01*b12+a02*b22+a03*b32 a00*b03+a01*b13+a02*b23+a03*b33
// a10*b00+a11*b10+a12*b20+a13*b30 a10*b01+a11*b11+a12*b21+a13*b31 a10*b02+a11*b12+a12*b22+a13*b32 a10*b03+a11*b13+a12*b23+a13*b33
mResult.n[1] = _mm256_add_ps(c1, c5); // n1 = a20*b00+a21*b10+a22*b20+a23*b30 a20*b01+a21*b11+a22*b21+a23*b31 a20*b02+a21*b12+a22*b22+a23*b32 a20*b03+a21*b13+a22*b23+a23*b33
// a30*b00+a31*b10+a32*b20+a33*b30 a30*b01+a31*b11+a32*b21+a33*b31 a30*b02+a31*b12+a32*b22+a33*b32 a30*b03+a31*b13+a32*b23+a33*b33
return mResult;
}