學校課程/平行程式

批改娘 10097. Advanced Matrix Calculator (OpenCL)

contents

  1. 1. 題目描述
    1. 1.1. sequence.c
  2. 2. 輸入格式
  3. 3. 輸出格式
  4. 4. 範例輸入 1
  5. 5. 範例輸出 1
  6. 6. 編譯參數
  7. 7. Solution
    1. 7.1. main.c
    2. 7.2. matrix-lib.cl

題目描述

小明的數學作業要計算方陣，現在請你幫幫他！

題目給定數個 $N \times N$ 的矩陣和 $Q$ 小題，每一小題只由加法和乘法構成。

sequence.c

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#include <stdio.h>
#include <stdint.h>
// #define DEBUG
#define UINT uint32_t
#define MAXN 1024
void multiply(int N, UINT A[][MAXN], UINT B[][MAXN], UINT C[][MAXN]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            UINT sum = 0;    // overflow, let it go.
            for (int k = 0; k < N; k++)
                sum += A[i][k] * B[k][j];
            C[i][j] = sum;
        }
    }
}
void add(int N, UINT A[][MAXN], UINT B[][MAXN], UINT C[][MAXN]) {
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++)
        	C[i][j] = A[i][j] + B[i][j];
    }
}
void rand_gen(UINT c, int N, UINT A[][MAXN]) {
    UINT x = 2, n = N*N;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++) {
            x = (x * x + c + i + j)%n;
            A[i][j] = x;
        }
    }
}
void print_matrix(int N, UINT A[][MAXN]) {
    for (int i = 0; i < N; i++) {
        fprintf(stderr, "[");
        for (int j = 0; j < N; j++)
            fprintf(stderr, " %u", A[i][j]);
        fprintf(stderr, " ]\n");
    }
}
UINT signature(int N, UINT A[][MAXN]) {
    UINT h = 0;
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++)
            h = (h + A[i][j]) * 2654435761LU;
    }
    return h;
}
UINT IN[6][MAXN][MAXN], TMP[6][MAXN][MAXN];
int main() {
    int N, S[6];
    scanf("%d", &N);
    for (int i = 0; i < 6; i++) {
        scanf("%d", &S[i]);
        rand_gen(S[i], N, IN[i]);
    }
    // AB
    multiply(N, IN[0], IN[1], TMP[0]);
    // CD
    multiply(N, IN[2], IN[3], TMP[1]);
    // AB+CD
    add(N, TMP[0], TMP[1], TMP[2]);
    printf("%u\n", signature(N, TMP[2]));
    
    // ABE
    multiply(N, TMP[0], IN[4], TMP[3]);
    // CDF
    multiply(N, TMP[1], IN[5], TMP[4]);
    // ABE+CDF
    add(N, TMP[3], TMP[4], TMP[5]);
    printf("%u\n", signature(N, TMP[5]));
    return 0;
}

輸入格式

測資只有一組，第一行會有兩個整數 $M,N$，表示題目給定 $M$ 個 $N \times N$ 矩陣，第二行上會有 $N$ 個整數 $S_i$ 個第 $i$ 個矩陣生成種子。最後會有一行一個整數 $Q$，表示接下來有 $Q$ 行詢問，每一行上會有一個字串 $E$ 表示接下來要處理的矩陣表達式，$E$ 只包含 A-Z 以及 +。

  • $1 \le M \le 26$
  • $1 \le N \le 1024$
  • $0 \le S_i \le 2^{31}$
  • $1 \le Q \le 100$
  • $|E| \le 26$

輸出格式

對於每一組測資輸出一行。

範例輸入 1

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6 2
0 1 2 3 4 5
2
AB+CD
ABE+CDF

範例輸出 1

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2
2385860290
1374821695

編譯參數

1
2
$ gcc -std=c99 -O2 main.c -lm -lOpenCL -fopenmp
$ ./main

Solution

這一題是 10095. Matrix Calculator (OpenCL) 的強化版，針對計算量在多個 GPU 裝置上分配工作。由於每一個表達式的計算量多寡不定，為了批次解決一坨工作，讓三個 GPU 的執行時間最大值最小化，貪心分配表達式，將計算量由大排到小後，依序取出，挑選目前 workload 最小的 GPU 分配到這之上，但 GPU 計算能力不同 (例如頻率或傳輸效率 … 等)，需要多乘上一個常數比較。

main.c

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#include <stdio.h>
#include <assert.h>
#include <inttypes.h>
#include <string.h>
#include <signal.h>
#include <unistd.h>
#include <CL/cl.h>
#include <omp.h>
#define MAXGPU 3
#define MAXN 1024
#define MAXM 26
#define MAXMID 32
uint32_t	hostMtx[MAXM][MAXN*MAXN];
int N, M, Q;
char expr[1024];
char clSrcFormat[32767] = ""; 
char clSrc[32767] = "";
// -- start working with OpenCL
const int clNeedDevCnt = 3;
cl_context				clCtx[MAXGPU];
cl_program				clPrg[MAXGPU];
cl_kernel				clKrnAdd[MAXGPU], clKrnMul[MAXGPU];
cl_command_queue		clQue[MAXGPU];
cl_mem					clMemIn[MAXGPU][MAXM], clMemMid[MAXGPU][MAXMID];
typedef struct Node {
    struct Node *l, *r;
    int opcode;
    uint32_t *hostV;
    cl_mem	clV;
    cl_event event, *waitEvents;
    int waitEventsN;
    int pid, mid;
    long long h;
} Node;
#define CheckFailAndExit(status) \
    if (status != CL_SUCCESS) { \
        fprintf(stderr, "Error %d: Line %u in file %s\n\n", status, __LINE__, __FILE__), \
        destroyGPU(clCtx, clPrg, clKrnAdd, clKrnMul, clQue, clMemIn); \
    }
#define clFuncArgs cl_context clCtx[], cl_program clPrg[], cl_kernel clKrnAdd[], \
    cl_kernel clKrnMul[], cl_command_queue clQue[], cl_mem clMemIn[][MAXM]
#define clCallFunc clCtx, clPrg, clKrnAdd, clKrnMul, clQue, clMemIn
#define clCallFuncOuter clCtx, clPrg, clKrnAdd, clKrnMul, clQue, clMemIn
void assignGPU(Node *u, int gpuIdx) {
    if (u == NULL)	return ;
    if (u->l == NULL) {
        u->hostV = hostMtx[u->mid];
        u->clV = clMemIn[gpuIdx][u->mid];
        return ;
    }
    assignGPU(u->l, gpuIdx);
    assignGPU(u->r, gpuIdx);
}
Node* parseExpr(int l, int r, char expr[], int procId, clFuncArgs) {
    cl_int clStat;
    Node *u = (Node *) calloc(1, sizeof(Node));
    u->pid = procId;
    if (l == r) {
        int idx = expr[l] - 'A';
        u->hostV = hostMtx[idx];
        u->mid = idx;
        u->h = 0;
        return u;
    }
    int cnt = 0;
    for (int i = l; i <= r; i++) {
        if (expr[i] == '(') {
            cnt++;
        } else if (expr[i] == ')') {
            cnt--;
        } else if (expr[i] == '+' && cnt == 0) {
            u->l = parseExpr(l, i-1, expr, procId, clCallFunc);
            u->r = parseExpr(i+1, r, expr, procId, clCallFunc);
            u->opcode = '+';
            u->h = u->l->h + u->r->h + N;
            return u;
        }
    }
    for (int i = l; i <= r; i++) {
        if (expr[i] == '(') {
            if (cnt == 0 && i != l) {
                u->l = parseExpr(l, i-1, expr, procId, clCallFunc);
                u->r = parseExpr(i, r, expr, procId, clCallFunc);
                u->opcode = '*';
                u->h = u->l->h + u->r->h + N*N;
                return u;
            }
            cnt++;
        } else if (expr[i] == ')') {
            cnt--;
        } else if (expr[i] >= 'A' && expr[i] <= 'Z' && cnt == 0 && i != l) {
            u->l = parseExpr(l, i-1, expr, procId, clCallFunc);
            u->r = parseExpr(i, r, expr, procId, clCallFunc);
            u->opcode = '*';
            u->h = u->l->h + u->r->h + N*N;
            return u;
        }
    }
    free(u);
    return parseExpr(l+1, r-1, expr, procId, clCallFunc);
}
uint32_t writeMatrixOut(int N, uint32_t *A) {
    uint32_t h = 0;
    for (int i = 0; i < N; i++)
        for (int j = 0; j < N; j++)
            h = (h + A[i*N + j]) * 2654435761LU;
    return h;
}
void destroyGPU(clFuncArgs) {
    fprintf(stderr, "Starting Cleanup ...\n\n");
    for (int i = 0; i < clNeedDevCnt; i++) {
        for (int j = 0; j < M; j++) { 
            if (clMemIn[i][j])
                clReleaseMemObject(clMemIn[i][j]);
        }
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        for (int j = 0; j < MAXMID; j++) {
            if (clMemMid[i][j])
                clReleaseMemObject(clMemMid[i][j]);
        }
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        if (clKrnAdd[i])	clReleaseKernel(clKrnAdd[i]);
        if (clKrnMul[i])	clReleaseKernel(clKrnMul[i]);
        if (clPrg[i])		clReleaseProgram(clPrg[i]);
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        if (clQue[i])	
            clReleaseCommandQueue(clQue[i]);
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        if (clCtx[i])	
            clReleaseContext(clCtx[i]);
    }
    exit(0);
}
int initAllGPU(char fileName[], clFuncArgs) {
    // -- generate kernel code
    FILE *codefin = fopen(fileName, "r");
    assert(codefin != NULL);
    assert(fread(clSrcFormat, 1, 32767, codefin) < 32767);
    sprintf(clSrc, clSrcFormat, N);
    size_t clSrcLen = strlen(clSrc);
    fclose(codefin);
    cl_int					clStat;
    cl_uint					clPlatN, clGPUN, clDevN;
    cl_platform_id			clPlatID;
    cl_device_id			clGPUID[MAXGPU];
    const char				*clSrcPtr = clSrc;
    // -- basic OpenCL setup
    clGetPlatformIDs(1, &clPlatID, &clPlatN);
    clGetDeviceIDs(clPlatID, CL_DEVICE_TYPE_GPU, MAXGPU, clGPUID, &clDevN);
    assert(clDevN >= clNeedDevCnt);
    for (int i = 0; i < clNeedDevCnt; i++) {
        clCtx[i] = clCreateContext(NULL, 1, clGPUID+i, NULL, NULL, &clStat);
        CheckFailAndExit(clStat);
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        clQue[i] = clCreateCommandQueue(clCtx[i], clGPUID[i], 
                /*CL_QUEUE_OUT_OF_ORDER_EXEC_MODE_ENABLE*/ 0, &clStat);
        CheckFailAndExit(clStat);
    }
    for (int i = 0; i < clNeedDevCnt; i++) {
        clPrg[i] = clCreateProgramWithSource(clCtx[i], 1, &clSrcPtr, &clSrcLen, &clStat);
        CheckFailAndExit(clStat);
        clStat = clBuildProgram(clPrg[i], 1, clGPUID+i, NULL, NULL, NULL);
        if (clStat != CL_SUCCESS) {
            fprintf(stderr, "Error: Line %u in file %s\n\n", __LINE__, __FILE__);
            size_t log_size;
            clGetProgramBuildInfo(*clPrg, clGPUID[0],
                    CL_PROGRAM_BUILD_LOG, 0, NULL, &log_size);
            char *program_log = (char *) calloc(log_size+1, sizeof(char));
            clGetProgramBuildInfo(*clPrg, clGPUID[0],
                    CL_PROGRAM_BUILD_LOG, log_size+1, program_log, NULL);
            printf("%s", program_log);
            free(program_log);
            CheckFailAndExit(CL_BUILD_PROGRAM_FAILURE);
        }
        clKrnAdd[i] = clCreateKernel(clPrg[i], "matrixAdd", &clStat);
        CheckFailAndExit(clStat);
        clKrnMul[i] = clCreateKernel(clPrg[i], "matrixMul", &clStat);
        CheckFailAndExit(clStat);
    }
    // -- create all buffers
    cl_mem_flags clInBuffFlag = CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR;
    for (int d = 0; d < clNeedDevCnt; d++) {
        for (int i = 0; i < M; i++) {
            clMemIn[d][i] = clCreateBuffer(clCtx[d], clInBuffFlag, sizeof(uint32_t)*N*N,
                    hostMtx[i], &clStat);
            CheckFailAndExit(clStat);
        }
    }
    for (int d = 0; d < clNeedDevCnt; d++) {
        for (int i = 0; i < MAXMID; i++) {
            clMemMid[d][i] = clCreateBuffer(clCtx[d], CL_MEM_READ_WRITE, 
                    sizeof(uint32_t)*N*N, NULL, &clStat);
            CheckFailAndExit(clStat);
        }
    }
    return 1;
}
void GPUmultiply(int N, Node *U, Node *L, Node *R, int devIdx, clFuncArgs) {
    cl_int clStat;
    size_t globalOffset[] = {0};
    size_t globalSize[] = {N*N};
    size_t localSize[] = {0};
    for (int i = 1; i <= 1024; i++) {
        if (N*N%i == 0)
            localSize[0] = i;
    }
    // -- set argument to kernel
    clStat = clSetKernelArg(clKrnMul[devIdx], 0, sizeof(cl_mem), &(L->clV));
    CheckFailAndExit(clStat);
    clStat = clSetKernelArg(clKrnMul[devIdx], 1, sizeof(cl_mem), &(R->clV));
    CheckFailAndExit(clStat);
    clStat = clSetKernelArg(clKrnMul[devIdx], 2, sizeof(cl_mem), &(U->clV));
    CheckFailAndExit(clStat);
    // -- find wait events
    int waitN = 0, waitCnt = 0;
    if (L->event)	waitCnt++;
    if (R->event)	waitCnt++;
    cl_event *events = (cl_event*) malloc(sizeof(cl_event) * waitCnt);
    if (L->event)	events[waitN++] = L->event;
    if (R->event)	events[waitN++]	= R->event;
    U->waitEvents = events, U->waitEventsN = waitCnt;
    // -- execute
    clStat = clEnqueueNDRangeKernel(clQue[devIdx], clKrnMul[devIdx], 1, globalOffset,
            globalSize, localSize, U->waitEventsN, U->waitEvents, &(U->event) );
    CheckFailAndExit(clStat);
}
void GPUadd(int N, Node *U, Node *L, Node *R, int devIdx, clFuncArgs) {
    cl_int clStat;
    size_t globalOffset[] = {0};
    size_t globalSize[] = {N*N};
    size_t localSize[] = {0};
    for (int i = 1; i <= 1024; i++) {
        if (N*N%i == 0)
            localSize[0] = i;
    }
    // -- set argument to kernel	
    clStat = clSetKernelArg(clKrnAdd[devIdx], 0, sizeof(cl_mem), &(L->clV));
    CheckFailAndExit(clStat);
    clStat = clSetKernelArg(clKrnAdd[devIdx], 1, sizeof(cl_mem), &(R->clV));
    CheckFailAndExit(clStat);
    clStat = clSetKernelArg(clKrnAdd[devIdx], 2, sizeof(cl_mem), &(U->clV));
    CheckFailAndExit(clStat);
    // -- find wait events
    int waitN = 0, waitCnt = 0;
    if (L->event)	waitCnt++;
    if (R->event)	waitCnt++;
    cl_event *events = (cl_event*) malloc(sizeof(cl_event) * waitCnt);
    if (L->event)	events[waitN++] = L->event;
    if (R->event)	events[waitN++]	= R->event;
    U->waitEvents = events, U->waitEventsN = waitCnt;
    // -- execute
    clStat = clEnqueueNDRangeKernel(clQue[devIdx], clKrnAdd[devIdx], 1, globalOffset,
            globalSize, localSize, U->waitEventsN, U->waitEvents, &(U->event) );
    CheckFailAndExit(clStat);
}
int executeGPU(Node *workQue[][128], int workQueSz[], uint32_t resultBuff[], clFuncArgs) {
    cl_int clStat;
    Node* nodes[MAXGPU][128];
    int offset[MAXGPU] = {};
#pragma omp parallel for
    for (int p = 0; p < clNeedDevCnt; p++) {
        for (int q = 0; q < workQueSz[p]; q++) {
            // -- flatten binary tree
            offset[p] = 0;
            nodes[p][offset[p]++] = workQue[p][q];
            for (int i = 0; i < offset[p]; i++) {
                Node *u = nodes[p][i];
                if (u->l != NULL)
                    nodes[p][offset[p]++] = u->l;
                if (u->r != NULL)
                    nodes[p][offset[p]++] = u->r;
            }
            // -- execute in order
            int reuseId = 0;
            for (int i = offset[p]-1; i >= 0; i--) {
                Node *u = nodes[p][i];
                if (u->l == NULL)	// is leaf
                    continue;
                u->clV = clMemMid[p][reuseId++];
                if (u->opcode == '*')
                    GPUmultiply(N, u, u->l, u->r, p, clCallFunc);	
                else
                    GPUadd(N, u, u->l, u->r, p, clCallFunc);
            }
            clFlush(clQue[p]);
            clFinish(clQue[p]);
            nodes[p][0]->hostV = (uint32_t *) malloc(sizeof(uint32_t)*N*N);
            int waitN = nodes[p][0]->event != NULL;
            clStat = clEnqueueReadBuffer(clQue[p], nodes[p][0]->clV, CL_TRUE, 0, 
                    sizeof(uint32_t)*N*N, nodes[p][0]->hostV, waitN, 
                    waitN ? &(nodes[p][0]->event): NULL, NULL);
            uint32_t ret = writeMatrixOut(N, nodes[p][0]->hostV);
            resultBuff[nodes[p][0]->pid] = ret;
            // -- free inner node buffer
            for (int i = 0; i < offset[p]; i++) {
                Node *u = nodes[p][i];
                if (u->l != NULL && u->hostV)
                    free(u->hostV);
                if (u->l != NULL && u->event)
                    clReleaseEvent(u->event);
                if (u->l != NULL && u->waitEvents)
                    free(u->waitEvents);
                free(u);
            }
        }
    }
    return 1;
}
int readIn() {
    if (scanf("%s", expr) != 1)
        return 0;
    return 1;
}
int balance_cmp(const void *a, const void *b) {
    Node *x = *(Node **) a;
    Node *y = *(Node **) b;
    if (x->h == y->h)	return 0;
    if (x->h < y->h)	return 1;
    return -1;
}
void onStart(clFuncArgs) {
    int S[64];
    assert(scanf("%d %d", &M, &N) == 2);
    for (int i = 0; i < M; i++)
        assert(scanf("%d", &S[i]) == 1);
#pragma omp parallel for
    for (int p = 0; p < M; p++) {
        uint32_t x = 2, n = N*N;
        uint32_t c = S[p];
        for (int i = 0; i < N; i++) {
            for (int j = 0; j < N; j++) {
                x = (x * x + c + i + j)%n;
                hostMtx[p][i*N+j] = x;
            }
        }
    }
    initAllGPU("matrix-lib.cl", clCallFunc);
    Node *procBuff[128];
    if (scanf("%d", &Q) != 1)
        return ;
    for (int i = 0; i < Q; i++) {
        readIn();
        int expr_len = strlen(expr);
        procBuff[i] = parseExpr(0, expr_len-1, expr, i, clCallFunc);
    }
    /*	
		for (int i = 0; i < Q; i++)
		executeCPU(procBuff[i]);
		return ; 
	 */	
    qsort(procBuff, Q, sizeof(Node*), balance_cmp);
    float gpuSpeed[16] = {1.f, 1.8f, 3.2f};
    long long workload[16] = {};
    int workQueSz[MAXGPU] = {};
    uint32_t resultBuff[128] = {};
    Node *workQue[MAXGPU][128];
    for (int i = 0; i < Q; i++) {
        int mn = 0;
        for (int j = 0; j < clNeedDevCnt; j++) {
            if (workload[j]*gpuSpeed[j] < workload[mn]*gpuSpeed[mn])
                mn = j;
        }
        assignGPU(procBuff[i], mn);
        workload[mn] += procBuff[i]->h;
        workQue[mn][workQueSz[mn]++] = procBuff[i];
    }
    executeGPU(workQue, workQueSz, resultBuff, clCallFunc);
    for (int i = 0; i < Q; i++)
        printf("%u\n", resultBuff[i]);
    destroyGPU(clCallFunc);
}
void sigHandler(int signo) {
    printf("God Bless Me\n");
    destroyGPU(clCallFuncOuter);
    exit(0);
}
int main(int argc, char *argv[]) {
    const char sigErr[] = "I can't catch signal.\n";
    if (signal(SIGTRAP, sigHandler) == SIG_ERR)
        fprintf(stderr, sigErr);
    if (signal(SIGSEGV, sigHandler) == SIG_ERR)
        fprintf(stderr, sigErr);
    if (signal(SIGILL, sigHandler) == SIG_ERR)
        fprintf(stderr, sigErr);
    if (signal(SIGFPE, sigHandler) == SIG_ERR)
        fprintf(stderr, sigErr);
    if (signal(SIGKILL, sigHandler) == SIG_ERR)     
        fprintf(stderr, sigErr);
    if (signal(SIGINT, sigHandler) == SIG_ERR)     
        fprintf(stderr, sigErr);
    onStart(clCallFuncOuter);
    return 0;
}

matrix-lib.cl

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#define N %d
#define CTYPE unsigned int
#define UNLOOP 8
__kernel void matrixAdd(__global CTYPE *in1,
        __global CTYPE *in2,
        __global CTYPE *out) {
    int x = get_global_id(0);
    out[x] = in1[x] + in2[x];
}
__kernel void matrixMul(__global CTYPE *in1,
        __global CTYPE *in2,
        __global CTYPE *out) {
    int r = get_global_id(0);
    int x = r / N, y = r % N;
    unsigned int sum = 0;
    for (int i = 0; i < N; i++)
        sum += in1[x*N+i] * in2[i*N+y];
    out[x*N+y] = sum;
}