做多轴机械臂的运动控制，免不了要对4x4的坐标变换矩阵进行乘法，C语言中可以用二维数组或者一维数组来实现矩阵，下面来比较一下二维数组和一维数组的性能差异。
        开发环境：Visual Studio 2022，分别在Debug和Release模式下测试函数Multi4x4和Multi16，Release模式下开了最大优化(优选速度)(/O2)，代码速度优先(/Ot)，每种情况重复测3次。(注：最后算出的sum值是2488321446960073699907076096.00)

#include<stdio.h>
#include<stdint.h>
#include<time.h>void Multi4x4(float A[4][4], float B[4][4], float C[4][4]) {C[0][0] = A[0][0] * B[0][0] + A[0][1] * B[1][0] + A[0][2] * B[2][0] + A[0][3] * B[3][0];C[0][1] = A[0][0] * B[0][1] + A[0][1] * B[1][1] + A[0][2] * B[2][1] + A[0][3] * B[3][1];C[0][2] = A[0][0] * B[0][2] + A[0][1] * B[1][2] + A[0][2] * B[2][2] + A[0][3] * B[3][2];C[0][3] = A[0][0] * B[0][3] + A[0][1] * B[1][3] + A[0][2] * B[2][3] + A[0][3] * B[3][3];C[1][0] = A[1][0] * B[0][0] + A[1][1] * B[1][0] + A[1][2] * B[2][0] + A[1][3] * B[3][0];C[1][1] = A[1][0] * B[0][1] + A[1][1] * B[1][1] + A[1][2] * B[2][1] + A[1][3] * B[3][1];C[1][2] = A[1][0] * B[0][2] + A[1][1] * B[1][2] + A[1][2] * B[2][2] + A[1][3] * B[3][2];C[1][3] = A[1][0] * B[0][3] + A[1][1] * B[1][3] + A[1][2] * B[2][3] + A[1][3] * B[3][3];C[2][0] = A[2][0] * B[0][0] + A[2][1] * B[1][0] + A[2][2] * B[2][0] + A[2][3] * B[3][0];C[2][1] = A[2][0] * B[0][1] + A[2][1] * B[1][1] + A[2][2] * B[2][1] + A[2][3] * B[3][1];C[2][2] = A[2][0] * B[0][2] + A[2][1] * B[1][2] + A[2][2] * B[2][2] + A[2][3] * B[3][2];C[2][3] = A[2][0] * B[0][3] + A[2][1] * B[1][3] + A[2][2] * B[2][3] + A[2][3] * B[3][3];C[3][0] = A[3][0] * B[0][0] + A[3][1] * B[1][0] + A[3][2] * B[2][0] + A[3][3] * B[3][0];C[3][1] = A[3][0] * B[0][1] + A[3][1] * B[1][1] + A[3][2] * B[2][1] + A[3][3] * B[3][1];C[3][2] = A[3][0] * B[0][2] + A[3][1] * B[1][2] + A[3][2] * B[2][2] + A[3][3] * B[3][2];C[3][3] = A[3][0] * B[0][3] + A[3][1] * B[1][3] + A[3][2] * B[2][3] + A[3][3] * B[3][3];
}void Multi16(float A[16], float B[16], float C[16]) {C[0] = A[0] * B[0] + A[1] * B[4] + A[2] * B[8] + A[3] * B[12];C[1] = A[0] * B[1] + A[1] * B[5] + A[2] * B[9] + A[3] * B[13];C[2] = A[0] * B[2] + A[1] * B[6] + A[2] * B[10] + A[3] * B[14];C[3] = A[0] * B[3] + A[1] * B[7] + A[2] * B[11] + A[3] * B[15];C[4] = A[4] * B[0] + A[5] * B[4] + A[6] * B[8] + A[7] * B[12];C[5] = A[4] * B[1] + A[5] * B[5] + A[6] * B[9] + A[7] * B[13];C[6] = A[4] * B[2] + A[5] * B[6] + A[6] * B[10] + A[7] * B[14];C[7] = A[4] * B[3] + A[5] * B[7] + A[6] * B[11] + A[7] * B[15];C[8] = A[8] * B[0] + A[9] * B[4] + A[10] * B[8] + A[11] * B[12];C[9] = A[8] * B[1] + A[9] * B[5] + A[10] * B[9] + A[11] * B[13];C[10] = A[8] * B[2] + A[9] * B[6] + A[10] * B[10] + A[11] * B[14];C[11] = A[8] * B[3] + A[9] * B[7] + A[10] * B[11] + A[11] * B[15];C[12] = A[12] * B[0] + A[13] * B[4] + A[14] * B[8] + A[15] * B[12];C[13] = A[12] * B[1] + A[13] * B[5] + A[14] * B[9] + A[15] * B[13];C[14] = A[12] * B[2] + A[13] * B[6] + A[14] * B[10] + A[15] * B[14];C[15] = A[12] * B[3] + A[13] * B[7] + A[14] * B[11] + A[15] * B[15];
}int main() {clock_t start;double sum = 0.0;start = clock();//float a[4][4], b[4][4], c[4][4], d[4][4];//for (long i = 0; i < 6e7; i++) {//	for (uint8_t j = 0; j < 16; j++) {//		*(a[0] + j) = i * 0.03 + j * 0.02f;//		*(b[0] + j) = i * 0.02 + j * 0.03f;//	}//	Multi4x4(a, b, c);//	Multi4x4(b, c, d);//	sum += d[0][0] + d[1][1] + d[2][2] + d[3][3];//}float a[16], b[16], c[16], d[16];for (long i = 0; i < 6e7; i++) {for (uint8_t j = 0; j < 16; j++) {*(a + j) = i * 0.03 + j * 0.02f;*(b + j) = i * 0.02 + j * 0.03f;}Multi16(a, b, c);Multi16(b, c, d);sum += d[0] + d[5] + d[10] + d[15];}printf("sum=%f, time = %f s\n", sum, (double)(clock() - start) / CLOCKS_PER_SEC);
}

耗时对比：

                            Multi4x4        Multi16

           Debug        16.7s            12.1s

        Release          2.7s              2.7s

---

Debug模式下，Multi4x4中C[0][0]=A[0][0]*B[0][0]+A[0][1]*B[1][0]+A[0][2]*B[2][0]+A[0][3]*B[3][0]对应的汇编指令：

mov         eax,10h
imul        rax,rax,0
mov         rcx,qword ptr [A]
add         rcx,rax
mov         rax,rcx
mov         ecx,4
imul        rcx,rcx,0
mov         edx,10h
imul        rdx,rdx,0
mov         r8,qword ptr [B]
add         r8,rdx
mov         rdx,r8
mov         r8d,4
imul        r8,r8,0
movss       xmm0,dword ptr [rax+rcx]
mulss       xmm0,dword ptr [rdx+r8]
mov         eax,10h
imul        rax,rax,0
mov         rcx,qword ptr [A]
add         rcx,rax
mov         rax,rcx
mov         ecx,4
imul        rcx,rcx,1
mov         edx,10h
imul        rdx,rdx,1
mov         r8,qword ptr [B]
add         r8,rdx
mov         rdx,r8
mov         r8d,4
imul        r8,r8,0
movss       xmm1,dword ptr [rax+rcx]
mulss       xmm1,dword ptr [rdx+r8]
addss       xmm0,xmm1
mov         eax,10h
imul        rax,rax,0
mov         rcx,qword ptr [A]
add         rcx,rax
mov         rax,rcx
mov         ecx,4
imul        rcx,rcx,2
mov         edx,10h
imul        rdx,rdx,2
mov         r8,qword ptr [B]
add         r8,rdx
mov         rdx,r8
mov         r8d,4
imul        r8,r8,0
movss       xmm1,dword ptr [rax+rcx]
mulss       xmm1,dword ptr [rdx+r8]
addss       xmm0,xmm1
mov         eax,10h
imul        rax,rax,0
mov         rcx,qword ptr [A]
add         rcx,rax
mov         rax,rcx
mov         ecx,4
imul        rcx,rcx,3
mov         edx,10h
imul        rdx,rdx,3
mov         r8,qword ptr [B]
add         r8,rdx
mov         rdx,r8
mov         r8d,4
imul        r8,r8,0
movss       xmm1,dword ptr [rax+rcx]
mulss       xmm1,dword ptr [rdx+r8]
addss       xmm0,xmm1
mov         eax,10h
imul        rax,rax,0
mov         rcx,qword ptr [C]
add         rcx,rax
mov         rax,rcx
mov         ecx,4
imul        rcx,rcx,0
movss       dword ptr [rax+rcx],xmm0

Debug模式下，Multi16中C[0]=A[0]*B[0]+A[1]*B[4]+A[2]*B[8]+A[3]*B[12]对应的汇编指令：

mov         eax,4
imul        rax,rax,0
mov         ecx,4
imul        rcx,rcx,0
mov         rdx,qword ptr [A]
mov         r8,qword ptr [B]
movss       xmm0,dword ptr [rdx+rax]
mulss       xmm0,dword ptr [r8+rcx]
mov         eax,4
imul        rax,rax,1
mov         ecx,4
imul        rcx,rcx,4
mov         rdx,qword ptr [A]
mov         r8,qword ptr [B]
movss       xmm1,dword ptr [rdx+rax]
mulss       xmm1,dword ptr [r8+rcx]
addss       xmm0,xmm1
mov         eax,4
imul        rax,rax,2
mov         ecx,4
imul        rcx,rcx,8
mov         rdx,qword ptr [A]
mov         r8,qword ptr [B]
movss       xmm1,dword ptr [rdx+rax]
mulss       xmm1,dword ptr [r8+rcx]
addss       xmm0,xmm1
mov         eax,4
imul        rax,rax,3
mov         ecx,4
imul        rcx,rcx,0Ch
mov         rdx,qword ptr [A]
mov         r8,qword ptr [B]
movss       xmm1,dword ptr [rdx+rax]
mulss       xmm1,dword ptr [r8+rcx]
addss       xmm0,xmm1
mov         eax,4
imul        rax,rax,0
mov         rcx,qword ptr [C]
movss       dword ptr [rcx+rax],xmm0

 Release模式下，Multi4x4和Multi16的汇编指令一样：

movss       xmm5,dword ptr [rcx+4]
movss       xmm4,dword ptr [rcx+8]
movss       xmm3,dword ptr [rcx]
movaps      xmm1,xmm4
mulss       xmm1,dword ptr [rdx+20h]
movss       xmm2,dword ptr [rdx]
movss       xmm0,dword ptr [rdx+10h]
mulss       xmm2,xmm3
mulss       xmm0,xmm5
movaps      xmmword ptr [rax-18h],xmm6
movss       xmm6,dword ptr [rcx+0Ch]
addss       xmm2,xmm0
movaps      xmmword ptr [rax-28h],xmm7

        结论：在Debug模式下，一维数组的汇编指令(39行)比二维数组(75行)几乎少一半，速度更快。因为访问二维数组的元素需要先找到其所在的行，再找到其所在的列，相当于进行了两次数组访问。在Release模式下，两者的汇编指令一样，都用了SSE指令集进行优化加速，速度一样。但SSE指令是intel和AMD等电脑CPU才有的(Arm的Neon类似于SSE)，单片机可没法用。因此，如果想在单片机上获得极致的速度，那还是使用一维数组吧。

        按照D-H表示法建立的4x4矩阵，第4行始终为[0, 0, 0, 1]，做乘法以后也不会改变，因此，专门做此类4x4矩阵乘法的函数可以进一步优化，即只取前12个元素参与运算。

void Multi16(float A[12], float B[12], float C[12]) {C[0] = A[0] * B[0] + A[1] * B[4] + A[2] * B[8] ;C[1] = A[0] * B[1] + A[1] * B[5] + A[2] * B[9] ;C[2] = A[0] * B[2] + A[1] * B[6] + A[2] * B[10] ;C[3] = A[0] * B[3] + A[1] * B[7] + A[2] * B[11] + A[3] ;C[4] = A[4] * B[0] + A[5] * B[4] + A[6] * B[8] ;C[5] = A[4] * B[1] + A[5] * B[5] + A[6] * B[9] ;C[6] = A[4] * B[2] + A[5] * B[6] + A[6] * B[10] ;C[7] = A[4] * B[3] + A[5] * B[7] + A[6] * B[11] + A[7] ;C[8] = A[8] * B[0] + A[9] * B[4] + A[10] * B[8] ;C[9] = A[8] * B[1] + A[9] * B[5] + A[10] * B[9] ;C[10] = A[8] * B[2] + A[9] * B[6] + A[10] * B[10] ;C[11] = A[8] * B[3] + A[9] * B[7] + A[10] * B[11] + A[11] ;
}