C 有效地转置大（密集）二元矩阵
有一个二进制矩阵（一个由0和1组成的矩阵），我想转置它。矩阵的每一行是一个由32位整数组成的一维数组，整个矩阵是一个由行组成的一维数组 下面是一个C 有效地转置大（密集）二元矩阵,c,matrix,cuda,linear-algebra,transpose,C,Matrix,Cuda,Linear Algebra,Transpose,有一个二进制矩阵（一个由0和1组成的矩阵），我想转置它。矩阵的每一行是一个由32位整数组成的一维数组，整个矩阵是一个由行组成的一维数组 下面是一个128 x 128二进制矩阵的示例，由128行128/3232位整数组成。（实际上，矩阵是一个nxn矩阵，因为N有成千上万个。） //gcc示例0.c-std=c99&&./a.out #包括 #包括 #包括 类型定义uint32\u t uint32； #定义N（32*4）//假设它可以被32整除。该矩阵是一个nxn矩阵 #每行定义整数（N/32）
128 x 128128128/32nxnN//gcc示例0.c-std=c99&&./a.out
#包括
#包括
#包括
类型定义uint32\u t uint32；
#定义N（32*4）//假设它可以被32整除。该矩阵是一个nxn矩阵
#每行定义整数（N/32）
int main（int argc，字符**argv）{
uint32**矩阵=malloc（N*sizeof（uint32*）；
对于（int i=0；i，这里有一种可能的方法，使用@tera建议的\u ballot（）
以合并的方式，将数据按分片加载到共享内存中
在加载过程中，在共享内存中进行初始转置，将列排列成行，以便于\u ballot（）
操作
执行投票，从列数据（已存储在行中）中构建“最终”行数据
把数据写出来
步骤1-3在GPU上应该是相当有效的，至少是我所知道的。步骤4受到以下事实的阻碍：位块的逐位转置不会产生一组内存中相邻的32位量。因此，在一般情况下，全局存储上的内存访问模式是分散的
输出索引操作是最繁琐的可视化/排列操作
下面是一个包含4个测试用例的完整示例。对于这些测试用例，我还编写了一个朴素的CPU函数来执行“黄金”测试，借用了下面的问题
$ cat t435.cu
#include <stdio.h>
#include <stdlib.h>
#define IDX(d,x,y,ld) d[y*ld+x]
#define cudaCheckErrors(msg) \
do { \
cudaError_t __err = cudaGetLastError(); \
if (__err != cudaSuccess) { \
fprintf(stderr, "Fatal error: %s (%s at %s:%d)\n", \
msg, cudaGetErrorString(__err), \
__FILE__, __LINE__); \
fprintf(stderr, "*** FAILED - ABORTING\n"); \
exit(1); \
} \
} while (0)
#include <time.h>
#include <sys/time.h>
#define USECPSEC 1000000ULL
unsigned long dtime_usec(unsigned long start){
timeval tv;
gettimeofday(&tv, 0);
return ((tv.tv_sec*USECPSEC)+tv.tv_usec)-start;
}
__global__ void bt(const unsigned * __restrict__ in, unsigned * __restrict__ out, const unsigned idim){
// assumes "square" binary matrix transpose
// assumes kernel is launched with 1024 threads per block, 2D, 32x32
// assumes input matrix dimension idim is evenly divisible by 32 bits
// assumes idim is specified in bits
__shared__ unsigned smem[32][33];
int idx = threadIdx.x+blockDim.x*blockIdx.x;
int idy = threadIdx.y+blockDim.y*blockIdx.y;
smem[threadIdx.x][threadIdx.y] = ((idx < idim/32)&&(idy < idim))?IDX(in,idx,idy,idim/32):0;
__syncthreads();
unsigned myval = smem[threadIdx.y][31-threadIdx.x];
__syncthreads();
smem[ 0][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<31)&myval));
smem[ 1][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<30)&myval));
smem[ 2][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<29)&myval));
smem[ 3][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<28)&myval));
smem[ 4][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<27)&myval));
smem[ 5][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<26)&myval));
smem[ 6][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<25)&myval));
smem[ 7][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<24)&myval));
smem[ 8][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<23)&myval));
smem[ 9][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<22)&myval));
smem[10][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<21)&myval));
smem[11][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<20)&myval));
smem[12][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<19)&myval));
smem[13][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<18)&myval));
smem[14][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<17)&myval));
smem[15][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<16)&myval));
smem[16][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<15)&myval));
smem[17][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<14)&myval));
smem[18][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<13)&myval));
smem[19][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<12)&myval));
smem[20][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<11)&myval));
smem[21][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<10)&myval));
smem[22][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 9)&myval));
smem[23][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 8)&myval));
smem[24][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 7)&myval));
smem[25][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 6)&myval));
smem[26][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 5)&myval));
smem[27][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 4)&myval));
smem[28][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 3)&myval));
smem[29][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 2)&myval));
smem[30][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 1)&myval));
smem[31][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 0)&myval));
__syncthreads();
int indx = (idx*idim)+(gridDim.y*threadIdx.y)+blockIdx.y;
if ((idx < (idim/32))&&(idy < idim)) out[indx] = smem[threadIdx.y][threadIdx.x];
}
void naive_cpu_bt(const unsigned *in, unsigned *out, const unsigned idim){
memset(out, 0, idim*(idim/32)*sizeof(unsigned));
for (int i = 0; i < (idim/32); i++)
for (int j = 0; j < idim; j++){
for (int bit = 0; bit < 32; bit++){
if ((in[(j*(idim/32)) + i]>>bit)&1) out[(((i*32)+(31-bit))*(idim/32))+(j/32)] |= 1<<(31 - (j%32));
}
}
}
int main(){
unsigned *h_idata, *h_odata, *d_idata, *d_odata, *c_odata;
unsigned idim;
// test case 1, 32x32, upper triangular
idim = 32;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
unsigned data = 0x0FFFFFFFFU;
for (int i = 0; i < 32; i++){
h_idata[i] = data;
data>>=1;}
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,1),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) {printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 32; i++) printf("0x%8x\n", h_odata[i]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 2, 64x64, opposite diagonal
idim = 64;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
data = 0x01;
for (int i = 0; i < 32; i++){
h_idata[2*i] = 0; h_idata[(2*i)+1] = data;
h_idata[64+(2*i)] = data; h_idata[65+(2*i)] = 0xFFFFFFFFU;
data<<=1; data++;}
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,2),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 64; i++) printf("0x%8x 0x%8x\n", h_odata[i*2], h_odata[(i*2)+1]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 3, 96x96, ones in alternating columns
idim = 96;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
data = 0x55555555U;
for (int i = 0; i < idim*(idim/32); i++)
h_idata[i] = data;
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,3),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 96; i++) printf("0x%8x 0x%8x 0x%8x\n", h_odata[i*3], h_odata[(i*3)+1], h_odata[(i*3)+2]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 4, 8kx8k random
idim = 8192;
int xblocks = (idim/1024)+((idim%1024)?1:0);
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
for (int i = 0; i < idim*(idim/32); i++)
h_idata[i] = rand();
unsigned long gt = dtime_usec(0);
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
unsigned long gkt = dtime_usec(0);
bt<<<dim3(xblocks,(idim/32)),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaDeviceSynchronize();
gkt = dtime_usec(gkt);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
gt = dtime_usec(gt);
unsigned long ct = dtime_usec(0);
naive_cpu_bt(h_idata, c_odata, idim);
ct = dtime_usec(ct);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
printf("gputime: %fms, kerneltime: %fms, cputime: %fms\n", (gt*1000)/(float)USECPSEC, (gkt*1000)/(float)USECPSEC, (ct*1000)/(float)USECPSEC);
printf("kernel bandwidth = %fMB/s\n", (idim*(idim/32)*4*2)/(float)gkt);
printf("Success!\n");
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
return 0;
}
$ nvcc -arch=sm_61 -o t435 t435.cu
$ ./t435
0x80000000
0xc0000000
0xe0000000
0xf0000000
0xf8000000
0xfc000000
0xfe000000
0xff000000
0xff800000
0xffc00000
0xffe00000
0xfff00000
0xfff80000
0xfffc0000
0xfffe0000
0xffff0000
0xffff8000
0xffffc000
0xffffe000
0xfffff000
0xfffff800
0xfffffc00
0xfffffe00
0xffffff00
0xffffff80
0xffffffc0
0xffffffe0
0xfffffff0
0xfffffff8
0xfffffffc
0xfffffffe
0xffffffff
0x 0 0x 1
0x 0 0x 3
0x 0 0x 7
0x 0 0x f
0x 0 0x 1f
0x 0 0x 3f
0x 0 0x 7f
0x 0 0x ff
0x 0 0x 1ff
0x 0 0x 3ff
0x 0 0x 7ff
0x 0 0x fff
0x 0 0x 1fff
0x 0 0x 3fff
0x 0 0x 7fff
0x 0 0x ffff
0x 0 0x 1ffff
0x 0 0x 3ffff
0x 0 0x 7ffff
0x 0 0x fffff
0x 0 0x 1fffff
0x 0 0x 3fffff
0x 0 0x 7fffff
0x 0 0x ffffff
0x 0 0x 1ffffff
0x 0 0x 3ffffff
0x 0 0x 7ffffff
0x 0 0x fffffff
0x 0 0x1fffffff
0x 0 0x3fffffff
0x 0 0x7fffffff
0x 0 0xffffffff
0x 1 0xffffffff
0x 3 0xffffffff
0x 7 0xffffffff
0x f 0xffffffff
0x 1f 0xffffffff
0x 3f 0xffffffff
0x 7f 0xffffffff
0x ff 0xffffffff
0x 1ff 0xffffffff
0x 3ff 0xffffffff
0x 7ff 0xffffffff
0x fff 0xffffffff
0x 1fff 0xffffffff
0x 3fff 0xffffffff
0x 7fff 0xffffffff
0x ffff 0xffffffff
0x 1ffff 0xffffffff
0x 3ffff 0xffffffff
0x 7ffff 0xffffffff
0x fffff 0xffffffff
0x 1fffff 0xffffffff
0x 3fffff 0xffffffff
0x 7fffff 0xffffffff
0x ffffff 0xffffffff
0x 1ffffff 0xffffffff
0x 3ffffff 0xffffffff
0x 7ffffff 0xffffffff
0x fffffff 0xffffffff
0x1fffffff 0xffffffff
0x3fffffff 0xffffffff
0x7fffffff 0xffffffff
0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
gputime: 5.530000ms, kerneltime: 0.301000ms, cputime: 659.205994ms
kernel bandwidth = 55738.257812MB/s
Success!
$
$cat t435.cu
#包括
#包括
#定义IDX（d，x，y，ld）d[y*ld+x]
#定义cudaCheckErrors（msg）\
做{\
cudaError\u t\u err=cudaGetLastError（）\
如果（_err！=cudaSuccess）{\
fprintf（标准，“致命错误：%s（%s位于%s:%d）\n”\
msg，cudaGetErrorString（_err）\
__文件（行）\
fprintf（stderr，“***失败-中止\n”）\
出口（1）\
} \
}而（0）
#包括
#包括
#定义USECPSEC 10000000ull
无符号长dtime\u usec（无符号长启动）{
蒂梅瓦尔电视；
gettimeofday（&tv，0）；
返回（（tv.tv_sec*USECPSEC）+tv.tv_usec）-开始；
}
__全局无效bt（常量无符号*\uuuu限制\uuuuu输入，无符号*\uu限制\uuuu输出，常量无符号idim）{
//假设“平方”二进制矩阵转置
//假设内核启动时每个块有1024个线程，2D，32x32
//假设输入矩阵维数idim可被32位整除
//假设idim是以位为单位指定的
__共享的_uuu未签名的smem[32][33]；
int idx=threadIdx.x+blockDim.x*blockIdx.x；
int-idy=threadIdx.y+blockDim.y*blockIdx.y；
smem[threadIdx.x][threadIdx.y]=（（idx\uuuuu ballot（）
）
以合并的方式，将数据按分片加载到共享内存中
在加载过程中，在共享内存中进行初始转置，将列排列成行，以便于\u ballot（）
操作
执行投票，从列数据（已存储在行中）中构建“最终”行数据
把数据写出来
步骤1-3在GPU上应该是相当有效的，至少是我所知道的。步骤4受到以下事实的阻碍：位块的逐位转置不会产生一组内存中相邻的32位量。因此，在一般情况下，全局存储上的内存访问模式是分散的
输出索引操作是最繁琐的可视化/排列操作
下面是一个包含4个测试用例的完整示例。对于这些测试用例，我还编写了一个朴素的CPU函数来执行“黄金”测试，借用了下面的问题
$ cat t435.cu
#include <stdio.h>
#include <stdlib.h>
#define IDX(d,x,y,ld) d[y*ld+x]
#define cudaCheckErrors(msg) \
do { \
cudaError_t __err = cudaGetLastError(); \
if (__err != cudaSuccess) { \
fprintf(stderr, "Fatal error: %s (%s at %s:%d)\n", \
msg, cudaGetErrorString(__err), \
__FILE__, __LINE__); \
fprintf(stderr, "*** FAILED - ABORTING\n"); \
exit(1); \
} \
} while (0)
#include <time.h>
#include <sys/time.h>
#define USECPSEC 1000000ULL
unsigned long dtime_usec(unsigned long start){
timeval tv;
gettimeofday(&tv, 0);
return ((tv.tv_sec*USECPSEC)+tv.tv_usec)-start;
}
__global__ void bt(const unsigned * __restrict__ in, unsigned * __restrict__ out, const unsigned idim){
// assumes "square" binary matrix transpose
// assumes kernel is launched with 1024 threads per block, 2D, 32x32
// assumes input matrix dimension idim is evenly divisible by 32 bits
// assumes idim is specified in bits
__shared__ unsigned smem[32][33];
int idx = threadIdx.x+blockDim.x*blockIdx.x;
int idy = threadIdx.y+blockDim.y*blockIdx.y;
smem[threadIdx.x][threadIdx.y] = ((idx < idim/32)&&(idy < idim))?IDX(in,idx,idy,idim/32):0;
__syncthreads();
unsigned myval = smem[threadIdx.y][31-threadIdx.x];
__syncthreads();
smem[ 0][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<31)&myval));
smem[ 1][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<30)&myval));
smem[ 2][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<29)&myval));
smem[ 3][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<28)&myval));
smem[ 4][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<27)&myval));
smem[ 5][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<26)&myval));
smem[ 6][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<25)&myval));
smem[ 7][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<24)&myval));
smem[ 8][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<23)&myval));
smem[ 9][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<22)&myval));
smem[10][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<21)&myval));
smem[11][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<20)&myval));
smem[12][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<19)&myval));
smem[13][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<18)&myval));
smem[14][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<17)&myval));
smem[15][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<16)&myval));
smem[16][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<15)&myval));
smem[17][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<14)&myval));
smem[18][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<13)&myval));
smem[19][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<12)&myval));
smem[20][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<11)&myval));
smem[21][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<<10)&myval));
smem[22][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 9)&myval));
smem[23][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 8)&myval));
smem[24][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 7)&myval));
smem[25][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 6)&myval));
smem[26][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 5)&myval));
smem[27][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 4)&myval));
smem[28][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 3)&myval));
smem[29][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 2)&myval));
smem[30][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 1)&myval));
smem[31][threadIdx.y] = __ballot_sync(0xFFFFFFFFU, ((1U<< 0)&myval));
__syncthreads();
int indx = (idx*idim)+(gridDim.y*threadIdx.y)+blockIdx.y;
if ((idx < (idim/32))&&(idy < idim)) out[indx] = smem[threadIdx.y][threadIdx.x];
}
void naive_cpu_bt(const unsigned *in, unsigned *out, const unsigned idim){
memset(out, 0, idim*(idim/32)*sizeof(unsigned));
for (int i = 0; i < (idim/32); i++)
for (int j = 0; j < idim; j++){
for (int bit = 0; bit < 32; bit++){
if ((in[(j*(idim/32)) + i]>>bit)&1) out[(((i*32)+(31-bit))*(idim/32))+(j/32)] |= 1<<(31 - (j%32));
}
}
}
int main(){
unsigned *h_idata, *h_odata, *d_idata, *d_odata, *c_odata;
unsigned idim;
// test case 1, 32x32, upper triangular
idim = 32;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
unsigned data = 0x0FFFFFFFFU;
for (int i = 0; i < 32; i++){
h_idata[i] = data;
data>>=1;}
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,1),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) {printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 32; i++) printf("0x%8x\n", h_odata[i]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 2, 64x64, opposite diagonal
idim = 64;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
data = 0x01;
for (int i = 0; i < 32; i++){
h_idata[2*i] = 0; h_idata[(2*i)+1] = data;
h_idata[64+(2*i)] = data; h_idata[65+(2*i)] = 0xFFFFFFFFU;
data<<=1; data++;}
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,2),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 64; i++) printf("0x%8x 0x%8x\n", h_odata[i*2], h_odata[(i*2)+1]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 3, 96x96, ones in alternating columns
idim = 96;
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
data = 0x55555555U;
for (int i = 0; i < idim*(idim/32); i++)
h_idata[i] = data;
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
bt<<<dim3(1,3),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
naive_cpu_bt(h_idata, c_odata, idim);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
for (int i = 0; i < 96; i++) printf("0x%8x 0x%8x 0x%8x\n", h_odata[i*3], h_odata[(i*3)+1], h_odata[(i*3)+2]);
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
// test case 4, 8kx8k random
idim = 8192;
int xblocks = (idim/1024)+((idim%1024)?1:0);
h_idata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
h_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
c_odata = (unsigned *)malloc(idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_idata, idim*(idim/32)*sizeof(unsigned));
cudaMalloc(&d_odata, idim*(idim/32)*sizeof(unsigned));
for (int i = 0; i < idim*(idim/32); i++)
h_idata[i] = rand();
unsigned long gt = dtime_usec(0);
cudaMemcpy(d_idata, h_idata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyHostToDevice);
unsigned long gkt = dtime_usec(0);
bt<<<dim3(xblocks,(idim/32)),dim3(32,32)>>>(d_idata, d_odata, idim);
cudaDeviceSynchronize();
gkt = dtime_usec(gkt);
cudaMemcpy(h_odata, d_odata, idim*(idim/32)*sizeof(unsigned), cudaMemcpyDeviceToHost);
gt = dtime_usec(gt);
unsigned long ct = dtime_usec(0);
naive_cpu_bt(h_idata, c_odata, idim);
ct = dtime_usec(ct);
for (int i = 0; i < (idim/32)*idim; i++) if (c_odata[i] != h_odata[i]) { printf("mismatch at %u, was: %u, should be: %u\n", i, h_odata[i], c_odata[i]); return -1;}
printf("gputime: %fms, kerneltime: %fms, cputime: %fms\n", (gt*1000)/(float)USECPSEC, (gkt*1000)/(float)USECPSEC, (ct*1000)/(float)USECPSEC);
printf("kernel bandwidth = %fMB/s\n", (idim*(idim/32)*4*2)/(float)gkt);
printf("Success!\n");
free(h_idata);
free(h_odata);
free(c_odata);
cudaFree(d_idata);
cudaFree(d_odata);
return 0;
}
$ nvcc -arch=sm_61 -o t435 t435.cu
$ ./t435
0x80000000
0xc0000000
0xe0000000
0xf0000000
0xf8000000
0xfc000000
0xfe000000
0xff000000
0xff800000
0xffc00000
0xffe00000
0xfff00000
0xfff80000
0xfffc0000
0xfffe0000
0xffff0000
0xffff8000
0xffffc000
0xffffe000
0xfffff000
0xfffff800
0xfffffc00
0xfffffe00
0xffffff00
0xffffff80
0xffffffc0
0xffffffe0
0xfffffff0
0xfffffff8
0xfffffffc
0xfffffffe
0xffffffff
0x 0 0x 1
0x 0 0x 3
0x 0 0x 7
0x 0 0x f
0x 0 0x 1f
0x 0 0x 3f
0x 0 0x 7f
0x 0 0x ff
0x 0 0x 1ff
0x 0 0x 3ff
0x 0 0x 7ff
0x 0 0x fff
0x 0 0x 1fff
0x 0 0x 3fff
0x 0 0x 7fff
0x 0 0x ffff
0x 0 0x 1ffff
0x 0 0x 3ffff
0x 0 0x 7ffff
0x 0 0x fffff
0x 0 0x 1fffff
0x 0 0x 3fffff
0x 0 0x 7fffff
0x 0 0x ffffff
0x 0 0x 1ffffff
0x 0 0x 3ffffff
0x 0 0x 7ffffff
0x 0 0x fffffff
0x 0 0x1fffffff
0x 0 0x3fffffff
0x 0 0x7fffffff
0x 0 0xffffffff
0x 1 0xffffffff
0x 3 0xffffffff
0x 7 0xffffffff
0x f 0xffffffff
0x 1f 0xffffffff
0x 3f 0xffffffff
0x 7f 0xffffffff
0x ff 0xffffffff
0x 1ff 0xffffffff
0x 3ff 0xffffffff
0x 7ff 0xffffffff
0x fff 0xffffffff
0x 1fff 0xffffffff
0x 3fff 0xffffffff
0x 7fff 0xffffffff
0x ffff 0xffffffff
0x 1ffff 0xffffffff
0x 3ffff 0xffffffff
0x 7ffff 0xffffffff
0x fffff 0xffffffff
0x 1fffff 0xffffffff
0x 3fffff 0xffffffff
0x 7fffff 0xffffffff
0x ffffff 0xffffffff
0x 1ffffff 0xffffffff
0x 3ffffff 0xffffffff
0x 7ffffff 0xffffffff
0x fffffff 0xffffffff
0x1fffffff 0xffffffff
0x3fffffff 0xffffffff
0x7fffffff 0xffffffff
0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
0x 0 0x 0 0x 0
0xffffffff 0xffffffff 0xffffffff
gputime: 5.530000ms, kerneltime: 0.301000ms, cputime: 659.205994ms
kernel bandwidth = 55738.257812MB/s
Success!
$
$cat t435.cu
#包括
#包括
#定义IDX（d，x，y，ld）d[y*ld+x]
#定义cudaCheckErrors（msg）\
做{\
cudaError\u t\u err=cudaGetLastError（）\
如果（_err！=cudaSuccess）{\
fprintf（标准，“致命错误：%s（%s位于%s:%d）\n”\
msg，cudaGetErrorString（_err）\
__文件（行）\
fprintf（stderr，“***失败-中止\n”）\
出口（1）\
} \
}而（0）
#包括
#包括
#定义USECPSEC 10000000ull
无符号长dtime\u usec（无符号长启动）{
蒂梅瓦尔电视；
gettimeofday（&tv，0）；
返回（（tv.tv_sec*USECPSEC）+tv.tv_usec）-开始；
}
__全局无效bt（常量无符号*\uuuu限制\uuuuu输入，无符号*\uu限制\uuuu输出，常量无符号idim）{
//假设“平方”二进制矩阵转置
//假设内核启动时每个块有1024个线程，2D，32x32
//假设输入矩阵维数idim可被32位整除
//假设idim是以位为单位指定的
__共享的_uuu未签名的smem[32][33]；
int idx=threadIdx.x+blockDim.x*blockIdx.x；
int-idy=threadIdx.y+blockDim.y*blockIdx.y；
smem[threadIdx.x][threadIdx.y]=（（idxN*M
矩阵，最好假设N！=M
，并在它们不同的地方使用示例-它们更容易理解。您的示例是N*N
，但这是针对正方形矩阵还是矩形矩阵？您展示的代码没有转置任何东西.不确定你是把它作为转置的例子还是矩阵设置的例子。好