考虑这段代码。我不熟悉 INTEL 版本,但这比 DirectX 中的 XMMatrixMultiply 更快。这不是关于每条指令完成多少数学运算,而是关于减少指令数(只要您使用快速指令,这个实现就是这样做的)。
// 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
struct MATRIX {
union {
float f[4][4];
__m128 m[4];
__m256 n[2];
};
}; MATRIX myMultiply(MATRIX M1, MATRIX M2) {
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;
}