除了@asm，我想我也会发布我的答案，所以这个 SO 问题可以是一种思想库。与@asm 类似，我检测并存储进位条件以及“结转”条件，即。当中间字结果全为 1 (0xF...FFF) 时，如果进位传播到该字中，它将“携带”到下一个字。
我的代码中没有使用任何 PTX 或 asm，因此我选择使用 64 位无符号整数而不是 32 位，以实现 2048x32 位的能力，使用 1024 个线程。
与@asm 的代码更大的区别在于我的并行进位传播方案。我构造了一个位压缩数组（“进位”），其中每个位表示从 1024 个线程中的每个线程的独立中间 64 位相加生成的进位条件。我还构造了一个位压缩数组（“carry_through”），其中每个位代表各个 64 位中间结果的进位条件。对于 1024 个线程，这相当于每个位压缩数组的 1024/64 = 16x64 位字的共享内存，因此共享内存的总使用量为 64+3 个 32 位数量。使用这些位压缩数组，我执行以下操作来生成组合的传播进位指示符：
carry = carry | (carry_through ^ ((carry & carry_through) + carry_through);
（注意进位左移一位：carry[i]表示a[i-1] + b[i-1]的结果产生了进位）解释如下：
- 进位和进位通的按位与生成候选，其中进位将与一个或多个进位条件序列交互
- 将第一步的结果添加到进位通过生成一个结果，该结果已更改位，这些位表示将受到进位传播到进位通过序列影响的所有字
- 对 carry_through 进行异或加上步骤 2 的结果显示受影响的结果，用 1 位表示
- 对第 3 步的结果和普通进位指示符进行按位或运算，得出一个组合进位条件，然后将其用于更新所有中间结果。
请注意，步骤 2 中的添加需要另一个多字添加（对于由超过 64 个字组成的大整数）。我相信这个算法是有效的，它已经通过了我提出的测试用例。
这是实现此功能的示例代码：
// parallel add of large integers
// requires CC 2.0 or higher
// compile with:
// nvcc -O3 -arch=sm_20 -o paradd2 paradd2.cu
#include <stdio.h>
#include <stdlib.h>
#define MAXSIZE 1024 // the number of 64 bit quantities that can be added
#define LLBITS 64 // the number of bits in a long long
#define BSIZE ((MAXSIZE + LLBITS -1)/LLBITS) // MAXSIZE when packed into bits
#define nTPB MAXSIZE
// define either GPU or GPUCOPY, not both -- for timing
#define GPU
//#define GPUCOPY
#define LOOPCNT 1000
#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)
// perform c = a + b, for unsigned integers of psize*64 bits.
// all work done in a single threadblock.
// multiple threadblocks are handling multiple separate addition problems
// least significant word is at a[0], etc.
__global__ void paradd(const unsigned size, const unsigned psize, unsigned long long *c, const unsigned long long *a, const unsigned long long *b){
__shared__ unsigned long long carry_through[BSIZE];
__shared__ unsigned long long carry[BSIZE+1];
__shared__ volatile unsigned mcarry;
__shared__ volatile unsigned mcarry_through;
unsigned idx = threadIdx.x + (psize * blockIdx.x);
if ((threadIdx.x < psize) && (idx < size)){
// handle 64 bit unsigned add first
unsigned long long cr1 = a[idx];
unsigned long long lc = cr1 + b[idx];
// handle carry
if (threadIdx.x < BSIZE){
carry[threadIdx.x] = 0;
carry_through[threadIdx.x] = 0;
}
if (threadIdx.x == 0){
mcarry = 0;
mcarry_through = 0;
}
__syncthreads();
if (lc < cr1){
if ((threadIdx.x%LLBITS) != (LLBITS-1))
atomicAdd(&(carry[threadIdx.x/LLBITS]), (2ull<<(threadIdx.x%LLBITS)));
else atomicAdd(&(carry[(threadIdx.x/LLBITS)+1]), 1);
}
// handle carry-through
if (lc == 0xFFFFFFFFFFFFFFFFull)
atomicAdd(&(carry_through[threadIdx.x/LLBITS]), (1ull<<(threadIdx.x%LLBITS)));
__syncthreads();
if (threadIdx.x < ((psize + LLBITS-1)/LLBITS)){
// only 1 warp executing within this if statement
unsigned long long cr3 = carry_through[threadIdx.x];
cr1 = carry[threadIdx.x] & cr3;
// start of sub-add
unsigned long long cr2 = cr3 + cr1;
if (cr2 < cr1) atomicAdd((unsigned *)&mcarry, (2u<<(threadIdx.x)));
if (cr2 == 0xFFFFFFFFFFFFFFFFull) atomicAdd((unsigned *)&mcarry_through, (1u<<threadIdx.x));
if (threadIdx.x == 0) {
unsigned cr4 = mcarry & mcarry_through;
cr4 += mcarry_through;
mcarry |= (mcarry_through ^ cr4);
}
if (mcarry & (1u<<threadIdx.x)) cr2++;
// end of sub-add
carry[threadIdx.x] |= (cr2 ^ cr3);
}
__syncthreads();
if (carry[threadIdx.x/LLBITS] & (1ull<<(threadIdx.x%LLBITS))) lc++;
c[idx] = lc;
}
}
int main() {
unsigned long long *h_a, *h_b, *h_c, *d_a, *d_b, *d_c, *c;
unsigned at_once = 256; // valid range = 1 .. 65535
unsigned prob_size = MAXSIZE ; // valid range = 1 .. MAXSIZE
unsigned dsize = at_once * prob_size;
cudaEvent_t t_start_gpu, t_start_cpu, t_end_gpu, t_end_cpu;
float et_gpu, et_cpu, tot_gpu, tot_cpu;
tot_gpu = 0;
tot_cpu = 0;
if (sizeof(unsigned long long) != (LLBITS/8)) {printf("Word Size Error\n"); return 1;}
if ((c = (unsigned long long *)malloc(dsize * sizeof(unsigned long long))) == 0) {printf("Malloc Fail\n"); return 1;}
cudaHostAlloc((void **)&h_a, dsize * sizeof(unsigned long long), cudaHostAllocDefault);
cudaCheckErrors("cudaHostAlloc1 fail");
cudaHostAlloc((void **)&h_b, dsize * sizeof(unsigned long long), cudaHostAllocDefault);
cudaCheckErrors("cudaHostAlloc2 fail");
cudaHostAlloc((void **)&h_c, dsize * sizeof(unsigned long long), cudaHostAllocDefault);
cudaCheckErrors("cudaHostAlloc3 fail");
cudaMalloc((void **)&d_a, dsize * sizeof(unsigned long long));
cudaCheckErrors("cudaMalloc1 fail");
cudaMalloc((void **)&d_b, dsize * sizeof(unsigned long long));
cudaCheckErrors("cudaMalloc2 fail");
cudaMalloc((void **)&d_c, dsize * sizeof(unsigned long long));
cudaCheckErrors("cudaMalloc3 fail");
cudaMemset(d_c, 0, dsize*sizeof(unsigned long long));
cudaEventCreate(&t_start_gpu);
cudaEventCreate(&t_end_gpu);
cudaEventCreate(&t_start_cpu);
cudaEventCreate(&t_end_cpu);
for (unsigned loops = 0; loops <LOOPCNT; loops++){
//create some test cases
if (loops == 0){
for (int j=0; j<at_once; j++)
for (int k=0; k<prob_size; k++){
int i= (j*prob_size) + k;
h_a[i] = 0xFFFFFFFFFFFFFFFFull;
h_b[i] = 0;
}
h_a[prob_size-1] = 0;
h_b[prob_size-1] = 1;
h_b[0] = 1;
}
else if (loops == 1){
for (int i=0; i<dsize; i++){
h_a[i] = 0xFFFFFFFFFFFFFFFFull;
h_b[i] = 0;
}
h_b[0] = 1;
}
else if (loops == 2){
for (int i=0; i<dsize; i++){
h_a[i] = 0xFFFFFFFFFFFFFFFEull;
h_b[i] = 2;
}
h_b[0] = 1;
}
else {
for (int i = 0; i<dsize; i++){
h_a[i] = (((unsigned long long)lrand48())<<33) + (unsigned long long)lrand48();
h_b[i] = (((unsigned long long)lrand48())<<33) + (unsigned long long)lrand48();
}
}
#ifdef GPUCOPY
cudaEventRecord(t_start_gpu, 0);
#endif
cudaMemcpy(d_a, h_a, dsize*sizeof(unsigned long long), cudaMemcpyHostToDevice);
cudaCheckErrors("cudaMemcpy1 fail");
cudaMemcpy(d_b, h_b, dsize*sizeof(unsigned long long), cudaMemcpyHostToDevice);
cudaCheckErrors("cudaMemcpy2 fail");
#ifdef GPU
cudaEventRecord(t_start_gpu, 0);
#endif
paradd<<<at_once, nTPB>>>(dsize, prob_size, d_c, d_a, d_b);
cudaCheckErrors("Kernel Fail");
#ifdef GPU
cudaEventRecord(t_end_gpu, 0);
#endif
cudaMemcpy(h_c, d_c, dsize*sizeof(unsigned long long), cudaMemcpyDeviceToHost);
cudaCheckErrors("cudaMemcpy3 fail");
#ifdef GPUCOPY
cudaEventRecord(t_end_gpu, 0);
#endif
cudaEventSynchronize(t_end_gpu);
cudaEventElapsedTime(&et_gpu, t_start_gpu, t_end_gpu);
tot_gpu += et_gpu;
cudaEventRecord(t_start_cpu, 0);
//also compute result on CPU for comparison
for (int j=0; j<at_once; j++) {
unsigned rc=0;
for (int n=0; n<prob_size; n++){
unsigned i = (j*prob_size) + n;
c[i] = h_a[i] + h_b[i];
if (c[i] < h_a[i]) {
c[i] += rc;
rc=1;}
else {
if ((c[i] += rc) != 0) rc=0;
}
if (c[i] != h_c[i]) {printf("Results mismatch at offset %d, GPU = 0x%lX, CPU = 0x%lX\n", i, h_c[i], c[i]); return 1;}
}
}
cudaEventRecord(t_end_cpu, 0);
cudaEventSynchronize(t_end_cpu);
cudaEventElapsedTime(&et_cpu, t_start_cpu, t_end_cpu);
tot_cpu += et_cpu;
if ((loops%(LOOPCNT/10)) == 0) printf("*\n");
}
printf("\nResults Match!\n");
printf("Average GPU time = %fms\n", (tot_gpu/LOOPCNT));
printf("Average CPU time = %fms\n", (tot_cpu/LOOPCNT));
return 0;
}