Tuesday, December 13, 2011

Half a million Monte Carlo simulations per second in Microsoft Excel 2010

Half a million Monte Carlo simulations per second! Release the power of your GPU from MS Excel 2010. Implementing user defined functions using CUDA ot OpenCL opens a whole new dimension in supercomputing in Microsoft Office.




The algorithm is composed of three parts:
1. Generate random numbers for n series
2. Compute the performance for each of these series using
3. Distribute performances into the resulting set.

Step 1: This is done using the curand nVidia librairy.
Step 2: This is performed by the performanceStorageKernel function described bellow. 
Step 3: The trick here is to use an atomic operation (atomicAdd) to generate the resulting Gauss-like curve. Note that atomic operations are only availble on architectures equals or higher to sm_13. This is performed by the frequenciesKernel function.


Cuda Kernel

#include <curand.h>
#include <cuda.h>
#include <math.h>
#include <windows.h>

cudaDeviceProp _dDeviceProp;

// Device buffers
float* _dObjects;
float* _dSeries;
float* _dPerformances;
int*   _dFrequencies;

// Variables
int _dNbObjects;
int _dNbFrequencies;
int _dNbSeries;

/**
* @brief Initializes the testcase by
* - Allocating the GPU memory
* - Copying the buffer from RAM to GPU memory.
* This function is executed on the Host
* @ param hBuffer Pointer to array of floats in host memory
* @ param N Number of objects in the array (an Objects consists of 6 floats)
*/
extern "C"
void initialize_device( int NbSeries, int NbObjects, int NbFrequencies )
{
  // Testcase initialization
  _dNbObjects = NbObjects;
  _dNbFrequencies = NbFrequencies;
  _dNbSeries = NbSeries;

  // Device allocation
  cudaMalloc( (void**)&_dObjects, NbSeries*NbObjects*sizeof(float) );
  cudaMalloc( (void**)&_dSeries, NbSeries*sizeof(float) );
  cudaMalloc( (void**)&_dFrequencies, NbFrequencies*sizeof(int) );
  cudaMalloc( (void**)&_dPerformances, NbObjects*sizeof(float) );
}

/**
* @brief
*/
__global__ void performanceStorageKernel( float* series, float* objects, int nbObjects, float* performances )
{
  // Compute the index
  unsigned int x = blockIdx.x*blockDim.x+threadIdx.x;
  unsigned int y = blockIdx.y*blockDim.y+threadIdx.y;
  unsigned int index = (y*blockDim.x) + x;

  int objectsIndex = index*nbObjects;
  // Compute performance
  __shared__ float localPerformance[2];
  localPerformance[0] = 1.0; // current performance
  localPerformance[1] = 0.0; // previous performance
  for( int i(0); i<nbObjects; ++i ) {
    localPerformance[1] = localPerformance[0];
    localPerformance[0] = (1.0+objects[objectsIndex+i])*localPerformance[1];
   
   if( index == 0 ) performances[i] = localPerformance[0];
  }
  // Store performance
  series[index] = localPerformance[0] - 1.0;
}

/**
* @brief Kernel function to be executed on the GPU
* @param ptr Pointer to an array of floats stored in GPU memory
*/
__global__ void frequenciesKernel( float* series, float range, int* frequencies, int nbFrequencies )
{
  // Compute the index
  unsigned int x = blockIdx.x*blockDim.x+threadIdx.x;
  unsigned int y = blockIdx.y*blockDim.y+threadIdx.y;
  unsigned int index = (y*blockDim.x) + x;

  float v = series[index]-(-range/2);
  int position = (v/(range/nbFrequencies));
  atomicAdd(&frequencies[position],1);
}

/**
* @brief Run the kernel on the GPU.
* This function is executed on the Host.
*/
extern "C"
void run_kernel( float range, float mu, float sigma, int random, int nbThreadsPerBlock )
{
  // Create pseudo-random number generator
  curandGenerator_t gen;
  curandCreateGenerator(&gen, CURAND_RNG_PSEUDO_DEFAULT);
  curandSetPseudoRandomGeneratorSeed(gen, random);
  curandGenerateNormal(gen, _dObjects, _dNbSeries*_dNbObjects, mu, sigma );
  curandDestroyGenerator(gen);

  dim3 block(8, 8, 1);
  int gridDim = (int)sqrt(float(_dNbSeries));
  dim3 gridPerformances( gridDim/block.x, gridDim/block.y, 1);
  performanceStorageKernel<<<gridPerformances,block>>>(_dSeries, _dObjects, _dNbObjects, _dPerformances );

  // Reset memory
  cudaMemset( _dFrequencies, 0, _dNbFrequencies*sizeof(int) );

  // compute Frequencies
  gridDim = (int)sqrt(float(_dNbSeries));
  dim3 gridFrequencies( gridDim/block.x, gridDim/block.y, 1);
  frequenciesKernel<<<gridFrequencies,block>>>( _dSeries, range, _dFrequencies, _dNbFrequencies );
}

/*
* This function is executed on the Host.
* @brief Copy the data back to the Host and releases the buffer on
* GPU device.
* This function is executed on the Host
* @ param hBuffer Pointer to array of floats in host memory
* @ param N Number of objects in the array (an Objects consists of 6 floats)
*/
extern "C"
void device_to_host( int* hOutFrequencies, float* hOutPerformances, float* hOutSeries )
{
  cudaMemcpy( hOutFrequencies, _dFrequencies, _dNbFrequencies*sizeof(int),     cudaMemcpyDeviceToHost);
  cudaMemcpy( hOutPerformances, _dPerformances, _dNbObjects*sizeof(float), cudaMemcpyDeviceToHost);
}

/*
* This function is executed on the Host.
* @brief Releases the buffer on GPU device.
* This function is executed on the Host
*/
extern "C"
void destroy_device()
{
  cudaFree( _dObjects );
  cudaFree( _dFrequencies );
  cudaFree( _dSeries );
  cudaFree( _dPerformances );
}