我创建了一个使用SIMD进行64位* 64位到128位的功能.目前我已经使用SSE2(acutally SSE4.1)实现了它.这意味着它可以同时运行两个64b * 64b到128b的产品.同样的想法可以扩展到AVX2或AVX512,同时提供四个或八个64b * 64到128b的产品.
我的算法基于 http://www.hackersdelight.org/hdcodetxt/muldws.c.txt
我的算法基于 http://www.hackersdelight.org/hdcodetxt/muldws.c.txt
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？
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);
}
}
解决方法
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