该算法进行一次无符号乘法,一次有符号乘法和两次有符号*无符号乘法.使用_mm_mul_epi32和_mm_mul_epu32可以轻松完成签名的* signed和unsigned * unsigned操作.但混合签名和未签名的产品给我带来了麻烦.
例如,考虑一下.

int32_t x = 0x80000000;
uint32_t y = 0x7fffffff;
int64_t z = (int64_t)x*y;

双字产品应为0xc000000080000000.但是如果你假设编译器知道如何处理混合类型,你怎么能得到这个？这就是我提出的：

int64_t sign = x<0; sign*=-1;        //get the sign and make it all ones
uint32_t t = abs(x);                 //if x<0 take two's complement again
uint64_t prod = (uint64_t)t*y;       //unsigned product
int64_t z = (prod ^ sign) - sign;    //take two's complement based on the sign

使用SSE可以这样做

__m128i xh;    //(xl2,xh2,xl1,xh1) high is signed,low unsigned
__m128i yl;    //(yh2,yl2,yh2,yl2)
__m128i xs     = _mm_cmpgt_epi32(_mm_setzero_si128(),xh); // get sign
        xs     = _mm_shuffle_epi32(xs,0xA0);              // extend sign
__m128i t      = _mm_sign_epi32(xh,xh);                    // abs(xh)
__m128i prod   = _mm_mul_epu32(t,yl);                     // unsigned (xh2*yl2,xh1*yl1)
__m128i inv    = _mm_xor_si128(prod,xs);                   // invert bits if negative
__m128i z      = _mm_sub_epi64(inv,xs);                    // add 1 if negative

这给出了正确的结果.但是我必须做两次(平时一次)它现在是我功能的重要部分.使用SSE4.2,AVX2(四个128位产品),甚至AVX512(八个128位产品)是否有更有效的方法？

也许有比SIMD更有效的方法吗？获得高位字是很多计算方法.

编辑：基于@ElderBug的评论,看起来这样做的方法不是使用SIMD而是使用mul指令.对于它的价值,万一有人想要看到它有多复杂,这里是完整的工作功能(我只是让它工作,所以我没有优化它,但我不认为这是值得的).

void muldws1_sse(__m128i x,__m128i y,__m128i *lo,__m128i *hi) {
    __m128i lomask = _mm_set1_epi64x(0xffffffff);

    __m128i xh     = _mm_shuffle_epi32(x,0xB1);    // x0l,x0h,x1l,x1h
    __m128i yh     = _mm_shuffle_epi32(y,0xB1);    // y0l,y0h,y1l,y1h

    __m128i xs     = _mm_cmpgt_epi32(_mm_setzero_si128(),xh);
    __m128i ys     = _mm_cmpgt_epi32(_mm_setzero_si128(),yh);
            xs     = _mm_shuffle_epi32(xs,0xA0);
            ys     = _mm_shuffle_epi32(ys,0xA0);

    __m128i w0     = _mm_mul_epu32(x,y);          // x0l*y0l,y0l*y0h
    __m128i w3     = _mm_mul_epi32(xh,yh);         // x0h*y0h,x1h*y1h
            xh     = _mm_sign_epi32(xh,xh);
            yh     = _mm_sign_epi32(yh,yh);

    __m128i w1     = _mm_mul_epu32(x,yh);         // x0l*y0h,x1l*y1h
    __m128i w2     = _mm_mul_epu32(xh,y);          // x0h*y0l,x1h*y0l

    __m128i yinv   = _mm_xor_si128(w1,ys);          // invert bits if negative
            w1     = _mm_sub_epi64(yinv,ys);         // add 1
    __m128i xinv   = _mm_xor_si128(w2,xs);          // invert bits if negative
            w2     = _mm_sub_epi64(xinv,xs);         // add 1

    __m128i w0l    = _mm_and_si128(w0,lomask);
    __m128i w0h    = _mm_srli_epi64(w0,32);

    __m128i s1     = _mm_add_epi64(w1,w0h);         // xl*yh + w0h;
    __m128i s1l    = _mm_and_si128(s1,lomask);      // lo(wl*yh + w0h);
    __m128i s1h    = _mm_srai_epi64(s1,32);

    __m128i s2     = _mm_add_epi64(w2,s1l);         //xh*yl + s1l
    __m128i s2l    = _mm_slli_epi64(s2,32);
    __m128i s2h    = _mm_srai_epi64(s2,32);           //arithmetic shift right

    __m128i hi1    = _mm_add_epi64(w3,s1h);
            hi1    = _mm_add_epi64(hi1,s2h);

    __m128i lo1    = _mm_add_epi64(w0l,s2l);
    *hi = hi1;
    *lo = lo1;
}

它变得更糟.在AVX512之前没有_mm_srai_epi64内在/指令所以我必须自己制作.

static inline __m128i _mm_srai_epi64(__m128i a,int b) {
    __m128i sra = _mm_srai_epi32(a,32);
    __m128i srl = _mm_srli_epi64(a,32);
    __m128i mask = _mm_set_epi32(-1,-1,0);
    __m128i out = _mm_blendv_epi8(srl,sra,mask);
}

我上面的_mm_srai_epi64的实现是不完整的.我想我正在使用Agner Fog的Vector Class Library.如果你查看文件vectori128.h,你会发现

static inline Vec2q operator >> (Vec2q const & a,int32_t b) {
    // instruction does not exist. Split into 32-bit shifts
    if (b <= 32) {
        __m128i bb   = _mm_cvtsi32_si128(b);               // b
        __m128i sra  = _mm_sra_epi32(a,bb);                // a >> b signed dwords
        __m128i srl  = _mm_srl_epi64(a,bb);                // a >> b unsigned qwords
        __m128i mask = _mm_setr_epi32(0,-1);          // mask for signed high part
        return  selectb(mask,srl);
    }
    else {  // b > 32
        __m128i bm32 = _mm_cvtsi32_si128(b-32);            // b - 32
        __m128i sign = _mm_srai_epi32(a,31);               // sign of a
        __m128i sra2 = _mm_sra_epi32(a,bm32);              // a >> (b-32) signed dwords
        __m128i sra3 = _mm_srli_epi64(sra2,32);            // a >> (b-32) >> 32 (second shift unsigned qword)
        __m128i mask = _mm_setr_epi32(0,-1);          // mask for high part containing only sign
        return  selectb(mask,sign,sra3);
    }
}